I

DISSOCIATION OF CYANOGEN HALIDES

IN SHOCK WAVES

A Thesis presented by

PETER JOHN KAYES in partial fulfilment of the requirements

for the degree of

DOCTOR OF PHILOSOPHY

Department of Chemistry Cellge of Science .:.rd Techn.ology

j,..21y 1972 2

ABSTRACT

In this thesis, an investigation of the decomposition of cyanogen bromide and cyanogen chloride is reported. The light emitted from the

CN radical behind incident shocks is used to monitor the kinetics and mathematical modelling techniques are used to simulate the observed intensity profiles, so that the reaction mechanism can be elucidated and rate constants for the important elementary steps determined.

In Chapter I, the background theory to reaction rates and shock tube operation is described.

The experimental methods employed throughout this work are presented in Chapter II.

4n introduction to the theories of luminous systems and the use of intensity measurements in kinetic studies is given in Chapter III. The absolute calibration, using the light emitted from shock heated sulphur dioxide as an intermediate. standard, is also reported in this chapter.-

The numerical methods, used in the simulation of the experimental intensity profiles, are discussed in Chapter IV.

In Chapter V, a review of the kinetics and emission from CN containing systems is presented.

The experimental results for the decomposition of cyanogen bromide and cyanogen chloride are reported in terms of an apparent rate of reaction in Chanters VI and M. The simulation of the apnarent rate and the detailed intensity profiles, using the mathematical modelling techniques described in Chanter IV, are also discussed. In all four separate mechanisms for the decompositions are described: classical chain kinetics and more unconventional energy chain mechanisms involving vibrationally excited species are discussed.

In Chapter VIII a separate study of the ecuilibrium emission from shock heated sulphur dioxide/argon mixtures (some dosed with oxygen) 3 is presented and discussed in terms of the 0 + SO chemiluminescence. 4

ACKNOWLEDGEMMTS

It is my pleasure to thank Dr. Bryan P. Levitt for his guidance, supervision and unfailing encouragement during the course of this work. I am indebted to Professor R.M. Barrer, F.R.S. for providing the research facilities in the Department of Chemistry at Imperial College.

I thank the Science Research Council for my Research Studentship.

I particularly thank Mr. J. Bilton for conducting the mass spectroscopic analysis of the gas samples; Mr. H. Cobley (and the

Workshop staff), Mr. A. Madell (and the staff of the Glass-blowing section) and Mr. D. Alger (and the staff of the Instrument section) for their help in maintaining and improving the shock tube and associated equipment.

I thank the University of London Computing Centre for the use of the CDC 6600 computer and Imperial College Computing Centre for the use of their IBM 7090/4 and CDC 6400 computers. I also wish to thank the staff of the Program Advisory Service at Imperial College for their help and suggestions in developing the program PROFIL.

Finally, it is my privilege to thank my parents for their continued interest and support in the completion of this work. 5

PREFACE

The contents of this thesis are divided into three parts.

In part I, the general theory underlying the determination of reaction kinetics and the application of shock tube methods are outlined.

The experimental methods, which are common to the kinetic investigations reported later in the thesis, are also given.

In Part II, the experimental results and discussion of the kinetics of the thermal decomposition of the cyanogen halides, BrCN and C1CN , are presented.

A separate kinetic investigation of the equilibrium emission obtained behind incident shocks into sulphur dioxide/argon mixtures, is reported in Part III.

It is worthwhile commenting that the SO 2 work was conducted first and arose out of the absolute calibration procedure reported in Part I.

The study of the pyrolysis of cyanogen bromide followed this and represents the bulk of the work undertaken.

The final brief investigation of the pyrolysis of cyanogen chloride is closely related to the cyanogen bromide work, both in experimental technique and analysis. 6

CONTENTS

PART I THE INTRODUCTION ArD THE DESCRIPTION OF

THE SHOCK TUBE TECHNIQUES

PAGE

CHAPTER I

GAS PHASE KINETICS

1:1 Introduction 14 1:2 The Reaction Rate Constant 14

1:3 Theoretical Considerations 14 1:3:1 Dissociation and detailed rate theory 16

1:3:2 Concluding remarks 22

1:4 The Shock Tube Applied to the Investigation of Reaction Kinetics 23

1:5 Shock Wave Formation and Propagation 24

1:6 Shock Tube Coordinates and Nomenclature 15

1:7 Time Scales 26

1:8 Processes Occurring Behind Incident Shock Waves 28 1:9 Boundary Layer Formation 29

CHAPTER II

EXPERIMENTAL =HODS

2:1 Introduction 34

2:2 The Shock Tube 34

2:2:1 The driver section 34

2:2:2 The test section 36

2:2:3 The dump tank 37

2:2:4 The windows 38 7 PAGE 2:3 The Glass Vacuum Line 38 2:3:1 The gas handling limb 40 2:3:2 The pressure measuring limb 40

2:4. The Pumping System 41

2:5 Leak Detection 44

2:6 Diaphragms 45

2:7 Gas Preparation 46

2:8 Gas Purification 47

2:9 The Instrumentation 48 2:9:1 The optical system 50 2:9:2 The monochromators 50 2:9:3 The electronics 52 2:9:4. The timer photomultipliers 52

2:9:5 The pulse shaper 53 2:9:6 Signal matching 53 2:9:7 The quantitative photomultipliers 54 2:9:8 The oscilloscopes 55 2:9:9 The overall rise—time 55

CHAPTER III

EMISSION FROM SHOCK HEATED GASES

3:1 Introduction 56

3:2 Thermal ?mission 57

3:2:1 Quenching probabilities 58

3:3 Chemiluminescence 62

3:4. The Absolute Calibration Using the Thermal Emission from Shock 64 Heated Sulphur Dioxide as an Intermediate Standard

3:4:1 Procedure 67 8

PART II - THE THERMAL DECOMPOSITION OF THE

CYANOGEN HALIDES: BrCN AND C1CN

PAGE CHAPTF12 IV

COMPUTATIONAL TECHNIQUES

4:1 Introduction 72 4:1:1 Machine methods 74

4:2 The Program (FROFIL) Description 76 4:2:1 Input 77 4:2:2 Preliminary calculations 78 a) Shock front

b) Equilibrium

9) The rate constants

d) Experimental data

202:3 Integration 81 4:2:4 Integration control 83

4:2:5 Diagnostic information 84

4:3 Flow Corrections 86

4:4 The Analysis 87

4:4:1 The preliminary analysis - The apparent rate 87

constant (Ke) )+:4:2 Detailed fitting - The simulated profiles 91

CHAPTER V

CN Ca1TAINT7G SYSTEMS

5:1 The Kinetics of CKX Systems 94 9

PAGE 5:1:1 Previous investigations 94

5:1:2 Theoretical calculations 100

5:1:3 The thermochemistry of the CN radical 102

5:2 Emission from Systems Containing Carbon and Nitrogen 107

5:2:1 Previous investigations 107

5:2:2 Equilibrium populations of the electronic states of CN 110 5:2:3 The AV = Al band of the CN violet (B2E 7(22:) 112 emission

5:2:k Impurities 112

5:3 The Emissivity of the CN Molecule 114

5:3:1 Experimental 116

5:3:2 Results 116

CHAPTER VI

THE PYROLYSIS OF CYANOGEN BROMIDE

6:1 Introduction 120

6:2 Results 120

6:2:1 The emission profiles at A = 11 21.5nm 120

a) Lean mixtures b) Rich mixtures

6:2:2 The rate of rise of emission at 421.5 nm 125

a) Lean mixtures

b) Rich mixtures

c) Intermediate mixtures

d.) Time resolution

e) Optical thickness

6:2:3 The alnarent seconi order rate comtant (Ka) 137

6:2:4 Errors 142

6:3 Schere - A 'Simple' Dissociation lechanism 143 10

PAGE

6:3:1 Discussion — The computer predictions for scheme I 143

a) Rich mixtures

b) Lean mixtures

6:4 Scheme II — A Simple Chain Mechanism 147

a) Initial estimates for the rate constants

6:4:1 Discussion — The computer simulations for scheme II 156

a) Rich mixtures

b) Lean mixtures

6:1+:2 Conclusions from scheme II simulations — Comparison of 170

computer and experimental profiles

6:4:3 Possible modifications to scheme II 178

a) Possible effects due to contamination

6:5 Scheme III — An Energy Chain Branching Mechanism 180

a) General considerations

6:5:1 A + BC ---*— ABv° + C reactions 182

a) Energy chains — Previous investigations

b) Reactions involving vibrationally excited cyanogen

c) The degree cf vibrational excitation (a 0) for the vo reaction: BrCN + CN --4— C N + Br 2 2

6:5:2 The thermodynamics of C2'N 2 v, 193

6:5:3 Estimates for the rate constants 196

6:5:4. Discussion — The computer simulations for Scheme III 198

a) Lean mixtures

b) Rich mixtures

6:5:5 Conclusions from scheme III simulations 206

a) Lean mixtures — 3000 to 4300K

b) Lean mixtures — less than 3000K

c) Rich mixtures /, a) The significance of the best fit values of ' '12 and 1;13 11 PAGE

6:6 The Comparison of Results from Schemes II and III 218

6:6:1 The comparison with the predictions of Keck and Kalelkar 222

6:6:2 Uncertainties in the rate constants as determined from 223

the computer modelling

6:7 Scheme IV - The Solution by Iteration of the Average Energy of

223 Excitation (Ev) at the Moment of Dissociation a) Assumptions

b) The rate constants

c) The computation

6:7:1 Discussion - The computer predictions of from scheme IV 226

6:8 Concluding Remarks 230 6:9 Recommendations for Future Work 233.

CHAPTER VII

THE PYROLYSIS OF CYANMEN CHLORIDE

7:1 IntrodUction 232

7:2 Results 232

7:2:1 The emission profiles at X = 421 5 nm 232

7:2:2 The apparent rate constant (Ka) 232

7:3 Discussion and Comparison with the Computer Predictions 236

7:4 Conclusion 244

7:4:1 An energy chain mechanism 244

7:4.:2 Lean mixtures: 'Shuffle' mechanism 246

7:4:3 Rich mixtures and Lean mixtures at high temperatures 247

7:5 Recommendations for Future Work 248

PART. III - 7" 7.WILIBT,IUM 71:TSSTO7f FROM

SUT.PHUR TNCIDNT

SHO(a 12 PAGE

CHAPTER VIII

THE 0 — SO PECOMBINATION

8:1 Introduction 250

8:2 Experimental 253

8:3 The :emission Records at = 280 nm 253 8:l. The Method of Analysis 255

8:5 Results 258 8:6 Discussion 265

8:7 Conclusion 266

APPENDIX I 270

APPENDIX II 272

APPENDIX III 275

BIBLIOGRAPHY 278 13

PART I

THE INTRODUCTION AND THE DESCRIPTION

OF THE SHOCK TUBE TECHNIQUES

In this section of the thesis, a brief outline and appraisal of the theories which have been developed to explain reaction kinetics are given. The applicability of the shock tube to the study of pyrolysis is discussed and the description of the shock tube, optical systems and the electronics, which are required for the measurement of the intensity of light emitted behind luminous shocks, is presented.

Details of the gas preparation, purification and handling facilities are also reported. Finally, an introduction to the processes leading to emission'in shock waves is presented and the absolute calibration of the equipment reported. 14

CHAPTER I

GAS PHASE KINETICS

1:1 Introduction The intermole3ular forces involved in homogeneous gas phase encounters

between reacting molecules are far less complex than the interactions

observed at heterogeneous interfaces or even those involved in the liquid

phase. It has been found that real gases, far removed from their condensation points, are adequately described by the ideal gas laws and kinetic theory. It is not surprising, therefore, that theoretical

treatments of reacting systems have been most successful for those

occuring homogeneously in the gas phase. It is of particular interest to study the pyrolysis of gaseous

molecules, where energy transfer processes are important and where the kinetics may be complex due to reaction paths involving highly reactive

species such.as free radicals.

1:2 The Reaction Rate Constant

Detailed discussions of reaction kinetics and kinetic laws are given

in standard texts (e.g. refs. 1 — 4). The rate of reaction for the

elementary step

aA + bB + •"›.--Products

is given by

k [A] a [ ] b 4) dciV) = a a B

The constant of proportionality (k) is termed the rate constant.

1:3 Theoretical Considerations Experimentally determined rate constants for elementary reaction steps

are often expressed in terms of the empiric Arrhenius equation

15

k = A exp (- Ea/RT) EQ 1:1

where A is termed a frequency factor or pre-exponential and Ea is the

apparent activation energy required before reaction proceeds.

Early attempts to derive expressions of this form were based upon the

kinetic theory of gases, which assumes that molecules behave like hard spheres

(5). The frequency with which a particular molecule experiences collisions with other molecules is given by

Z o = ZT2

2 where TI L. 6 8k EQ 1:2 103

and L = Avagadrots Number

k = Boltzman's constant

Cr = the collision diameter

= the reduced mass of the colliding pair

T = the temperature of the heat bath molecules

In keeping with the units used throughout this thesis the collision

frequency is defined in 1, mole units.

If energy is transferred between molecules only upon 'collision' and

only translational degrees of freedom along the line of centres of the

colliding pair are considered, the rate of reaction is given by the

product of the number of collisions between reactant molecules per second

and the fraction of these collisions which are effective in producing

chemical change. If E o is the energy required before reaction can occur, then the chance that a molecule possesses energy greater than or

equal to Po is given by a power series(6)

f m exp (-E0/12T) if EIRT>> 1

where only the first term is significant. The ate constant is, therefore,

given by

16

k Z exp/RT) EQ. 1:3 SCT = o

The variable parameter P is introduced, so that experimentally

determined rate constants can be compared to the predictions of simple

collision theory (SCT) and is defined by

P = kexptikSCT

P is often termed the steric factor; historically values of P below

unity were associated with the probability that the molecule was correctly

orientated upon collision but it is now apparent that this alone is not

sufficient to account for the range of P factors which have been observed.

Furthermore, if the hard sphere model is correct, then the critical

energy Bo should be given by

E = E — fRT o a EQ. 1:4

because of the T term included in the collision frequency. In many

cases, however, this does not predict the correct activation energy when

compared to the spectroscopically determined dissociation energy or the

thermodynamically defined heat of reaction. Also, in many cases reaction

proceeds orders of magnitude faster than the prediction of simple collisiOn

theory (i.e. P factors>> unity).

1:1 Dissociation and detailed rate theories

A notable feature of many gas phase dissociations (excluding the

particular case of the diatomics) is the dependence of the order

of the reaction upon the total gas pressure. The dissociation is often

unimolecular at high pressures but bimolecular at low pressures; there

being a smooth transition at intermediate pressures. Lindemann (7) has

interpreted this phenomenum in terms of the collisional formation of an

energetically 'activated) species (A*) prior to the decomposition

A + A ---->-- A* + A R:1

A* + A A + A R:-1

A B + C R:2 17 Applying the stationary state hypothesis to FA*.] , limiting expressions for the rates at high and low pressures can be obtained. That is

(i) high pressure limit

1 k A] / at = 11; 2 [

(ii) low pressure limit

d [A] idt = k1 [A]2

This simply implies that at low pressures the rate of collisional activation/deactivation is rate determining.

Using simple collision theory for the rate constants, the agreement with experiment is not always very good. For example the unimolecular isomerisation of cyclopropane (25) proceeds approximately 5 x 1014- times faster than predicted. However, anomolies between experiment and simple collision theory are hardly surprising, because the latter takes no account of the role of degrees of freedom other than translation (e.g. rotation and vibration) in the detailed energy transfers which lead to the acquisition of energy by the molecule prior to chemical reaction.

Hinshelwood (8) has extended the classical approach to detailed rate theory based upon the Lindemann conception of the activating/ deactivating role of molecular collisions. It was proposed that those molecules possessing energy (Ei) greater than or equal to the critical energy (E0) are activated and that all such activated molecules dissociate at the same specific rate (ki). That is ki is independentofF.as long as E. ;= Eo . Molecules containing energy less than were termed 2 2 o uninteresting and assumed to have k. = 0. Although this approach yielded an expression of the correct form for the high pressure unimolecular regime, it failed to reproduce the experimentally observed drop in activation energy as the pressure is reduced. 18

Kassel(9) using a quantised oscillator model and Rice and Rampsberger(10), employing the concept of an energy continuum among an assembly of oscillators (any energy allowed in any oscillator) proposed more detailed mechanisms. The P.RK theory assumes that only those molecules where

E is concentrated in the bond to be broken (i.e. the weak bond) are o active and that alternative distributions are inactive. When the weak bond accumulates this critical energy it will break. The specific rates, ki now become a function of the detailed energy distribution in the molecule and the problem is one of calculating the rate at which the available energy concentrates in a particular bond. RRK theory regards the molecule•as a sot of nk weakly coupled oscillators such that the oscillator experiencing rupture has (nk —i) further oscillators coupled to it and these can act as an energy reservoir. The rate of reaction is proportional to the chance that the molecule, containing energy (E1) will have Eo of it localised in one oscillator and the constant of proportionality is the mean rate of internal energy transfer in the molecule.

Slater(11), however, has developed a more rigorous theory, which takes the detailed distribution of energy immediately after a collision to be the important step,thereforel implying that redistribution of internal energy is not important. In the Slater model, the energy is distributed upon collision between n3 normal modes of vibration and reaction occurs when these normal modes enter into a suitable phase relationship such that the amplitude of vibration of some critical coordinate becomes large enough for reaction to occur. At this amplitude, with the critical coordinate extended, the potential energy of the molecule is eouatable with the previously defined critical energy E0 . The configuration of the molecule at this point correlates with concepts of a transition state.

T If the dissociation process has a relaxation time of DISS and the mean relaxation time for the redistribution of internal energy 19 is INT then the differences between RRK and Slater are summarised by the inequalities

Slater T INT > > DISS EQ. 1:5

RRK T INT < < T DISS EQ. 1:6 It has been argued (12) from considerations of symmetry and the quantisation of energy levels that the redistribution of energy between a set of oscillators will conform to EQ. 1:5. However, as noted by

Benson (page 219; ref. 1) at energies close to the transition state, the symmetry rules may not apply rigorously and the effect of anharmonicity and rotational energy transfers could act as a buffer of unknown efficiency in permitting the redistribution.

Unfortunately, experimental data from the study of unimolecular reactions alone rarely distinguishes between the two approaches. Both methods yield a high pressure limit of the same form

i.e. 160 = V exp ( - EIRT ) EQ. 1:7 where V is the frequency factor. ExperimAntally determined values 12 of V typically fall in the range 10 to io14 see-1 ; of the order A of a mean molecular vibration ( z 1013 sec-1).

In the low pressure, second order regime the RRK theory simplifies to 4, // B Pic-1 ZT4 k 0 exp ( -EIRT ) EQ. 1:8 (n1)1 \\ RT,/ where E is equated with t1 dissociation energy of the bond to be o broken and (no l) is the number of other degrees of freedom besides translation along the line of centres which can contribute towards the energy required for reaction. Slater (ref. 11, pp. 145, 156) has shown that his theory yields an expression of the same form and gives the same results if his n s normal modes of vibration are related to Kassel's nk oscillators by

ns - 1 = 2(nk - 1) 20

An alternative theory of absolute reaction rates, based upon an

equilibrium distribution of energised molecules which must pass through

a transition state before decomposing, has been developed by Eyring (13) and others.

A A* > Products.

where A* is an interesting energised molecule and .&is the

activated complex. The detailed derivation has been discussed elsewhere (14) and yields a unimolecular rate constant of

kolo = kT Q exp -Ea/RT) EQ. 1:9

where E is the energy between the ground states of A and A ; ei< a is the partition function for the activated complex with the vibrational

coordinates corresponding to bond rupture factored out. ( Q does, however, include contributions from other vibrations and rotations); R is the transmission coefficient and kT/h is termed the universal

frequency.

The parameters for the activated complex are estimated from a

knowledge of the molecular parameters of the normal reactants. Equation EQ. 1:9 may be re-written

kOD = 14.4 exp ( A S /R) exp /RT) EQ.1:10

whereAe* and AB4are the entropy and enthalpy changes respectively in going to the transition state.

The essential correctness of EQ. 1:10 has been demonstrated by the observation of both large and small unimolecular frequency factors 13 compared to a mean molecular vibration of 10 sec-1 (i.e. 1016 to 21 18 -1 11 -1 10 sec and a few of approximately 10 sec ). These anomalies

have been reviewed (15) and are explained in terms of the entropy term

accompanying structural changes in going from energised molecules to

the activated complex. Changes in the numbers of vibrations or

rotations may lead to significant changes in entropy which, depending

upon the sign, will lead to larger or smaller values for the frequency

factor which incorporates the exp( A&A) term. For example, the

large frequency factor found for the well characterised unimolecular

dissociation of di-nitrogen tetroxide

N 0 2 4 2NO2 (ref. 16)

is thought to be due to the increase in entropy as the two degenerate

4. become free rotations in the transition state bending modes of N20 (pp. 21.6; ref. 1).

Marcus(17) has re-formulated RRX theory to incorporate such entropy

terms. Approximations to facilitate the computations of the rate

constant fall-off from unimolecular to bimolecular kinetics are included.

The resultant RRKM theory is one of the strong collision.approach,in

which it is assumed that all the bound quantum states of the reactants

are populated in a Boltzman distribution defined by the bulk gas

translational temperature. The rate of activation of energised

molecules to unbound states is assumed to be slow compared to the

relaxation of the population of all the bound states of the molecule

and the Boltzman distribution is maintained even though some molecules

dissociate. At high temperatures, the strong collision theory may not be

appropriate because the rate of dissociation of high energy but bound

states can become faster than the relaxation of the population of all

the bound states to the Boltzman distribution. The population of

these upper levels can, therefore, become depleted relative to the expected Boltzman distribution and hence limit the net rate of 22

dissociation. The effect is most marked for diatomic molecules,

because the rate of vibrational relaxation is slow compared to the

dissociative process (18,19). However, depletion of levels within

kT of the dissociation limit has been observed for other molecules

(e.g. nitrogen dioxide - ref. 20).

Departures from strong collision theory are usually manifest as

low apparent activation energies. For example the dissociation of

HBr yields an apparent activation energy some 3 - 6RT lower than

dissociation energy (70). The solution of the kinetics requires the

detailed computation of all the energy transfer processes for each

vibrational level of each vibrational mode. Such mathematical models

(e.g. Step-ladder climbing models) have been used with some success in

the theoretical investigation of the dissociation of diatomic molecules

(21) but in these cases only one vibrational degree of freedom is

involved. The problem becomes far too complicated if there are other

vibrational degrees of freedom present.

1:3:1 Concluding remarks

Gill and Laidler(22) have criticised Slater's rigid orthogonality

postulate for the vibrational modes, particularly for relatively small

molecules (e.g. H2O and N20 ). However, they have noted the

importance of orthogonality in the calculations for more complex molecules.

Spicer and Rabinovitch (23) have recently reviewed the evidence in favour

of the PRICM calculations for the dissociation rates of molecules contain-

ing more than two atcms.

Rabinovitch et al (24.) have conducted a series of experiments

designed to test the applicability of the inequalities EQ. 1:5 and EQ. 1:6

to large polyatomic molecules. Energetically activated species, -1 containing some 140-90 kcal mole in excess of the initial energy required for dissociation, were found to yield a distribution of products

which showed that the internal energy of the molecule is completely randomised prior to dissociation and. demonstrated the- tralidity of equation 23

EQ. 1:5. Furthermore, the investigations of the isomerisation of

cyclopropane and cyclopropane-d2 (25, 26) are of particular significance.

Slater has claimed (27) that the former is an excellent test and

vindication of his theory. Cyclopropane processes 7 degenerate modes

which yields ns=14 on Slater's theory, in excellent agreement with

experiment. Cyclopropane-d2 does not, however, possess this

degeneracy and the expected value of ns on Slater's theory is 17-18. This, however, contrasts markedly with the experimental observation (25) that n s is still only 14.. In view of these developments, Slater (28) has proposed that his original orthogonality postulate should be relaxed.

Benson (pp. 250-252 ref. 1) has discussed the relative merits of collision and transition state theories and concludes that, while in principle, the latter enables the calculation of frequency factors, in practice, uncertainties in the values chosen to describe the activated complex do not recommend its use exclusively over the collision theories.

In this work it is therefore assumed that an approximate value for the dissociation rate constant of triatomic molecules can be obtained, to within at least an order of magnitude, by comparison with the Tassel type equation Q. 1:8 and RRKM calculations. This is discussed in greater detail with particular reference to the cyanogen halides in

Chapter V.

The Shock Tube Auelied to the Investigation of Reaction Kinetics

High temperatures of the order of several thousand degrees Kelvin are obtainable in the shock tube within the time required for only a few molecular collisions. The processes which result in the generation of shock waves are briefly outlined in the following sections. Because of this rapid heating effect, the shock tube is especially suited to the study of very fast ( lsec time scales) elementary reactions and indeed most of the high temperature data for dissociation kinetics have been obtained using the shock tube. The rapid growth of shock tube studies 24 is shown in the important texts due to Bradley (29), Greene and Toenies (30),

Gaydon and Hurle (30a) and Oertel (31), supplemented by the reviews due

to Bauer (32) and Belford and Strehlow (33); detailed discussions of

basic and applied hydrodynamic theory are also included in these texts.

The instrumentation is largely dictated by considerations of the

region of the shock wave cycle (incident, reflected or quenched) to be

studied and the property to be investigated. The relative merits of

each region have been discussed elsewhere (33) and it is indicated that

incident shock waves are well suited to the study of pyrolysis,

particularly when a rate measurement is to be made.

The time resolved measurements reported in this thesis were obtained

using the incident shock wave region together with selective emission

spectroscopy at stations perpendicular to the motion of the shock wave.

1:5 Shock Wave Formation and Propagation

An elegant description has been given by Becker (3) for a gas

confined in a cylinder equipped with a moveable piston. If a small but

abrupt accelerating force is applied to the piston a corresponding small

poise will propagate through the gas ahead of the piston. This will

travel at the sound speed of the gas as a compression wave with a velocity

(a ) characterised by the temperature T n n of the gas; for this first wave n = 1 and

= /y 2 a R Tn EQ. 1:11 M

where a , is termed the sound speed of the gas

y is the ratio of the specific heats

R is the universal gas constant

and. M is the molecular weight of the gas.

The compression is rapid and may be regarded as adiabatic, so that

the passage of the first compression wave raises the temperature of the

gas to T2 . A subsequent small acceleration of the piston therefore 25 generates a further compression wavelet, which will travel at the velocity characterised by T2 (i.e. a2 from EQ. 1:11). Each successive compression wavelet increases the temperature of the gas so that

T T and from EQ. 1:11 a n n-1 n > a n-I4 implying that each wavelet tends to overtake its immediate predecessor. However, any wavelet succeeding in overtaking its predecessor enters gas at the lower temperature Tn..1 and therefore decelerates. In consequence, the succession of wavelets tend to coalesce and form an abrupt discontinuity in temperature, pressure and density.

This discontinuity, once formed, propagates at uniform velocity which is supersonic relative to the undisturbed gas at the original temperature Ti ahead of it but subsonic compared to the hot gas behind it. The shock formation, while adiabatic, is non reversible and therefore non-'isentropic.

1:6 Shock Tube Coordinates and Nomenclature

A simple shock tube is shown in figure 1:1(A). To obtain strong shocksl a driver gas of low molecular weight (e.g. hydrogen) and a large pressure ratio (134/P1) across the diaphragm, separating the high pressure section from the low pressure test section, are required. The idealised pressure variation along a simple shock tube after t seconds have elapsed is shown in figure 1:1(B). The shock history is plotted as an x-t diagram in figure 1:1(C). As the shock moves away from the diaphragm at supersonic speeds into the test gas a rarefaction fan moves into the high pressure driver gas at the sound speed of 'cold' hydrogen gas. Ideally, there is no gas flow across the contact surface and P2 = P3 ; however, for real gases there is some diffusive mixing.

The solution of the hydrodynamic equations is usually accomplished by transforming the spatial coordinates so that the test gas is regarded as flowing with the velocity U1 =-W1 into a stationary shock front, to emerge the other side at the lower velocity U2 = W1-172 .

r5 F I CU RE1:1

DIA PHPAGM

HIGH P4 LOW CA)

CONTACT E

1 I 1 SSUR 1 1 P (B) E 4 1 1 P3 1 2 I I I PR

SHOCK FRONT

DISTANCE

T, U 2 W W 1 2 Hi CD) 0 27

The nomenclature is shown in figure 1:1(D) where the symbols have the following meanings.

Subscripts 1.undisturbed test gas ahead of the shock wave.

2.shock heated and compressed gas.

3. driver gas after the passage of the rarefaction

fan.

4.. driver gas before the passage of the rarefaction

fan.

Symbols W velocity of the shock front

U velocity of the test gas using transformed

coordinates

P pressure

T temperature

density

H total gas enthalpy.

Conservation equations may be written in terms of the rate of passage of the gas through unit area of the shock front for a given pair of perpendicular planes in the shocked and unshocked gas such that

ul pi .U 2 P2 mass

2 2 rx U = U I-, momentum i p 2 2

2 H1 -lu 21 2-22 H2 energy

At the low pressures and high temperatures employed in the shock tube, ideal gas theory can be applied and the initial and post—shock gas conditions are simply given by

P1 = N 1RT1 N RT 2 2 P1 p2 where N is the mole number (i.e. the number of moles per gram of gas). 28 1:7 Time Scales

Due to the compression of the bulk gas by the passage of the shock wave, a stationary observer will see elements of gas which have been heated for successively longer periods of time than that simply indicated by the, laboratory time scale. Assuming ideal shock tube theory (i.e. ignoring the effects of flow non—uniformities due to viscous drag at the walls, etc.) the laboratory time scale (-blab) is related to the actual time scale for which the gas has been heated (tg) by the relationship

tg = tlab • ( P2/131) EQ. 1:12 where 1J2/f)1 is the density ratio between shocked and initial gas conditions.

However, deviations due to boundary layer formation can be severe and must be carefully considered, particularly in the reduction of kinetic measurements.

1:8 Processes Occurring Behind Incident shock 'laves

For monatomic gases only translational degrees of freedom are usually important; the processes of electronic excitation and ionisation requiring considerable amounts of energy. Incident shocks into such gases, therefore, resemble a step function in the thermodynamic properties of the gas, because the available kinetic energy is rapidly equilibrated among the translational degrees of freedom.

However, for gases containing two or more atoms, additional 'structure' may be observed due to the slower relaxation of energy between the additional degrees of freedom (i.e. rotational and vibrational). even slower relaxation due to chemical reaction is possible and will result in the observation of further structure at much later test times. The extent to which these processes will be separable (if at all) depends upon the rate of relaxation compared to the resolution of the equipment.

The reaction zones contributing to such possible structure are shown 29 schematically in figure 1:2. The effect upon temperature is the most

marked; indeed, the variation in pressure is very small and the shock

tube may be regarded as an adiabatic constant pressure reactor. It this

work, the relaxation of internal degrees of freedom is assumed to be

fast compared to the resolution of the equipment, unless specifically

stated to the contrary. The shock front ?froze& temperature was,

therefore, always calculated for complete vibrational relaxation but

before the onset of chemical reaction and is referred to throughout as

T2,0 . The method used to solve the shock wave equations for T2,0

has been described (35) and is accomplished with the aid of a computer

program ISimshkt using thermodynamic input data taken from standard

tables (36, 37), unless otherwise specified.

The calculation of full chemical relaxation has recently been

reviewed (38). In this work, equilibrium conditions were initially

calculated using the Hug machine code (39) based upon the method

due to Brinkley (40). The free energy solution yields a complete

description of the system at equilibrium behind incident shock waves,

including the concentrations of all product species. In addition, the

position cf chemical equilibrium could also be calculated using a free

energy minimisation method incorporated in the chemical reaction program,

PROFIL. The calculation of the detailed histories of any property behind

the incident shock wave is very difficult. Sophisticated computer

programs are required to integrate trial sets of differential equations

(representing the rates of individual elementary reaction steps) coupled

to the shock calculation. The method used in the program FROFIL is

discussed in Chapter IV.

1.0 Bound<_ry Lever Formation

For small diameter shock tubes, operated at low initial pressures,

it is known (41) that the observed test tines can be very much shorter

than those predicted by ideal theory (EQ. 1:12). To a smaller but nevertheless significant extent, deviations from the predicted pressure 33

TEMPERATU RE Full curve: net relaxation including chemistry. Dashed curve:relaxation but no chemical reaction.

Teq.

T eq.

TIME

DENSITY PRESSURE

B

TI ME TIME

F I GURE 1:2 .

THE VARIATION OF TY0ERATURE, PPESSURE OD DENSITY FOR AN Ti!NDOTITRMIC REACTION. 33. temperature and density histories of the shocked gas are also observed.

However, depending upon the nature of the measurements involved, ccrrections may be applied, using 'simplified' models based uncn the formation of a boundary layer of cold gas behind the shock front; the layer is adjacent to the shock tube walls.

The formation of a boundary layer, sometime after the rupture of the diaphragm, is shown schematically in figure 1:3(A) (see also ref. 42). lobs is the observed separation between the shock front and the contact surface. For luminous shocks, the measurement of lobs is relatively easy because the emission is quenched at the contact surface. The shock velocity is attenuated by the mass flow from the hot test gas into the cold boundary layer, while the particles further into the flow are accelerated because of the apparent reduction in the cross—sectional area of the shock tube following the growth of the boundary layer. As can be seen from the x—t diagram (figure 1:3(B)), the shock front decelerates and the contact surface accelerates. Eventually, a 'steady state' between the propagation of the shock front and the contact surface is achieved, so that the distance of separation becomes constant with time. This limiting separation (1m) is sometimes referred to as the Mirels' length, after the author who tabulated (Z3) the ratio (1/lm) as a function of the shocked gas pressure, temperature and density for shocks into argon, where 1 is the distance from the shock front at which a measurement is made.

Immediately behind the shock front, where 1 = o , ideal theory calculations using the instantaneous shock velocity are appropriate but further behind the shock front, as 1 increases, the pressure, density and temperature also increase. At values of f= 1/ 1m greater than 0**1 these thermodynamic parameters become nearly constant (43). However, from purely practical considerations, the shock front and the contact surface do not reach their limiting separation by the time measurements are made: thus lobs

BOUNDARY LAYER FORMATION

FIGURE 1:3 A

DRIVER -->- GAS

I CONTACT SHOCK SURFACE COLD FRONT BOUNDARY LAYER

D I STANCE 33 and Colgan (45) find that, if f = 1/lobs is used to define the region where f=*0.1 reasonable corrections can be applied, at least for the more drastic time compression effect. It should be noted that Colgan's results may be due, to some extent, to laminar — turbulent boundary layer transitions. Recently, Mirels(46) has re—stated the basis of his parameter and has emphasised that this does not conflict with the m empiric use of f = > 061 in the correction of experimental 1/lobs results.

The treatment of flow corrections to the time scale of an experiment, as required in kinetic studies, is discussed in detail in Chapter IV.

In Chapter V and VIII equilibrium measurements (CN emissivity and 0 + SO recombination respectively) are reported and the appropriate flow corrections on Mirels' theory (4.6 — and references to earlier work included) are discussed. 34

CHAPTER II

EXPERIMENTAL METHODS

2:1 Introduction

The shock tube was of conventional design; the three main sections

(driver, test section and dump tank) are shown in figure 2:1.

Measurements were made only behind the incident shock wave (reflected shocks were not used). The shocks were generated by the rupture of thin plastic diaphragms placed at D1 which separated the driver gas from the test gas.

To ensure that dangerously high static pressures could not build up in the test section and to prevent the formation of reflected shocks, the incident wave was dissipated into an evacuated dump tank of large capacity, following the rupture of a light gauge cellophane diaphragm placed at

D2 .

The shock tube and associated instrumentation, which was used for the bulk of this work, was constructed by Colgan (1i5) from the design developed by Sheen (35). Improvements have been made to the pumping system and ultimate vacuum capability in the test section. Modifications have also been made to the vacuum line and electronics. Improved methods have been used to align the shock tube windows and the optical geometry.

2:2 The Shock Tube

2:2:1 The driver section

The driver section is a 5' length of brass tubing, 2" in diameter, closed at one end and with a carefully machined face—plate mounted on the other. It is designed to withstand an internal pressure of at least 1000 p.s.i. The alignment of the test/driver sections is readily accomplished using dowel pins set into the driver section face-plate which mate into holes accurately reamed in a similar plate on the test section.

DUMP TANK TEST SECT! ON D RIVER >--

PUMP PUMP GLASS LINE & I PUMP I-12 1 NLET S2

S4 QUARTZ WINDOWS SI V1 D

6 S3

A

FIGURE 2:1

SCHEMATIC PLAN OF THE SHOCK TUBE -SIDE VIEW 36

'0' rings fitted into recesses in these plates provided an adequate and re-usable vacuum seal. The 101 ring on the test section is of larger diameter than that on the driver, enhancing the sealing properties and grip on the diaphragm.

The driver section is mounted on rollers, resting on a steel girder

(0 firmly clamped to the bench. Connections via flexible copper tubing (I) to a manifold system enable the driver section to be evacuated or filled with hydrogen and the plunger (P) to be operated.

The gas operated plunger can be used at any desired pressure of driver gas and is angled so that its blunt point will strike the centre of the diaphragms at D1 . This ensures reproduceable conditions for shock formation within the constraints outlined in section 2:6.

Cold hydrogen was always used as the driver gas and was delivered directly from a cylinder (British Oxygen Company) to the manifold, via suitable reduction valves, without further purification. The driver gas pressure was measured using Bundenberg (steel bourdon tube) gauges for the ranges 0-100, 0-400 and 0-1000 psi. Before firing a shock, the driver section was always evacuated and flushed with hydrogen to 20 psi.

2:2:2 The test section

The test channel is of square cross-section, internal width 11" . It was constructed from two 9' lengths of brass angle, ilf." in thickness and soldered together along their length. Metal reinforcing straps were placed at approximately 1 1 intervals. The square section is connected via the junction (J) to a short length of round section steel tubing of the same diameter as the driver section. The transition from round to square was machined so that sharp edges do not disturb the gas flow. Cam action Saunderts valves (S1 and S3) permitted access to the pumping system and the atmosphere. After firing a shock the waste gases were pumped from the shock tube via the dump tank and air was rapidly admitted via S3. This ensured that diaphragm fragments left 37

in the test section, are swept into the dump tank.

The first pair of observation windows (A) are sited approximately

51' (about 414. tube diameters) downstream of the diaphragm D1 . For the conditions of this work, it has been reported (4.7a) that the shock

front is well formed within only 10 tube diameters, even allowing for

the poor opening characteristics of plastic diaphragms. Two further

sets of windows are mounted at B and C as shown in figure 2:1.

The windows fit into accurately reamed holes, the centres of which are exactly 50 cm apart.

A re-usable vacuum seal junction at D2 , between the dump tank

and the test section, is similar to that previously described for the

driver) test section junction at D1 (cf. section 2:2:1). A light

plastic coated cellophane diaphragm was always used between the face

plates at D2 . The test section was rigidly clamped to the steel girders

(G) in order to damp the recoil upon firing a shock.

2:2:5 The dump tank

The dump tank is made from a 22" length of steel tubing 9" in

diameter with an end plate securely welded to one end. The end remote

from this end plate is fitted with a 6" length of steel tubing, 2" internal

diameter, which acts as a manifold for the evacuation or the admission

of air via the Saunders valves S4. and 52 . This also carries the

dump tank face plate for the junction at D2 .

The dump tank acted as a deposit for diaphragm fragments and as a

large column into which the shock wave could expand. However, as an

added safety precaution, a spring leaded valve (v1) , situated close to

the dump tank end plate is designed to operate at just over 1 atmosphere

positive internal pressure. 'alien operated, processed gases and hydrogen

are vented directly into an all copier exhaust system. As a matter of

shock tube cleanliness, gas flews were always in the direction driver to

dump tank. 38

2:2:4 The windows

Optically flat quartz discs (Thermal Syndicate Ltd, 1" diameter

4" thick) are used throughout. Details of the special brass mounts into which they are cemented have already been given (35, 45). The windows are of sufficient diameter to minimise the problems associated with viewing the approach of a luminous shock front, by reflections and refractions though the clear cement.

The window mounts are screwed into special carriers so that, when in position, the windows are flush with the inner walls of the shock tube.

The square carriers were clamped together in pairs across the tube at A,

B and C using bolts located at each corner. As recommended (45), a double

101 ring seal was always used between each window mount/carrier assembly and the polished surface of the shock tube.

A dummy carrier was used to position each window in turn, in the manner described by Sheen (35). The alignment in both the horizontal and vertical planes was checked optically by using a low power laser beam

( 0.5 Mw Optics Technology Inc. model 160®G HeATe fir). The laser beam was adjusted so that it passed through the centres of the windows at any given station and was incident normally to the axis of the shock tube. When correctly aligned the reflections from the front and rear surfaces of the windows gave coincident images. This procedure ensured that the windms were not tilted in the shock tube by uneven tensioning of the four clamping bolts. As a final check, the contours of the shock tube was visually inspected for protrusions by illuminating the shock tube interior with light from a low intensity source and searching for shadows.

The Glass Vacuum Line

This is shown schematically in figure 2:2 and consists of two rain limbs;

a) Gas handling (GHL)

b) Pressure measuring (PIO S (57. MANOMETER TORAGE BULBS B24.

ARGON

PY REX TAPS, B14.

-a- V2 LDC St SPIRAL n GAUGE DIFF. MANOMETER PI RANI McLEOD ED 330 PUMP 51_4 -1-,2 PUMP 53 FIGURE 2:2 S. T. THE GLASS LINE + AIR INLET 40

The connections to the shock tube and rotary pump are shown in detail in figure 2:3. A flexible vacuum tight connection was made to the shock tube test section, immediately downstream of the diaphragms at

D1 (figure 2:1), by using a glass/metal '0' ring seal and flexible ball and socket joints. The description of the connection to the pumping system is given in section 2:9. Apiezon 'L' grease was used throughout and there was no indication of attack by the gas samples which were used. However, mixtures of sulphur dioxide stored for long periods of time did eventually attack the grease. The results presented in this thesis were obtained from mixtures which had been stored for no longer than about two weeks.

2:3:1 The gas handling limb

Gas samples and test mixtures were prepared and stored in this limb of the vacuum line. Gases were dried over either Linde type tAt molecular sieves or phosphorous pentoxide; provision for drying using cold traps was also made. Before use, the molecular sieves were always re-activated by heating to approximately 150°C while pumping with the gas ballast on, followed by cooling to room temperature and evacuation using the mercury diffusion pump. Both drying agents were always stored under vacuum at room temperature.

Gas mixtures were prepared by admitting the pure dry gases in the ascending order of their final partial pressures in the desired mixture.

Jet/turbulent mixing was accomplished by the large pressure gradients maintained across the storage bulb taps when the argon diluent was finally added. Diffusive mixing was allowed for at least twenty-four hours before the gas mixtures were used.

A thin by-pass line from the gas handling limb to the shock tube test section was fitted with a silicon oil manometer and was used so that test gas could be conserved.

213;2 The pressqre meiasurin&limb The instrumentation included a glass spiral gauge (0 - 760 torn) , 41 a silicon oil manometer (0 — 35 torr) and a McLeod mercury gauge -1 -6 (10 to 10 torr) . The mirror of the spiral gauge was quartz coated to prevent loss of reflectivity due to attack by the corrosive gases studied. gm 1 The silicon oil (Hopkins and Williams type MS550; density 1-09Lcc )

Was used unbuffered. However, silicon oil absorbs water vapour and it was, therefore, thoroughly degassed before use; thereafter, it was always stored under vacuum. No indication of attack or dissolution of the test gases was ever apparent and indeed a sample of 5% cyanogen bromide in argon, kept over the silicon oil at a pressure of 20 torr for several hours, showed no deviation in pressure.

The silicon oil suffers from the disadvantage that it 'wets' the glass walls of the manometer and special techniques were employed for the admission of test gas to high pressures (e.g. 20 torr). Two silicon oil manometers were used to minimise the error introduced by this phenomenum.

Prior to the evacuation of the test section, one of the manometers was preset to the pressure desired for the next run, using the appropriate test gas. After evacuation of the test section, test gas was metered into the shock tube to within about 1 torr of the desired pressure, using the other manometer: the remainder was admitted using the pre—set manometer. In this way, the total travel of the silicon oil in the manometer used for the final pressure measurement never exceeded 1 cm and wetting of the walls was negligible.

The Pirani gauge was manufactured from a 100 watt tungsten filament (45) and formed one arm of a Wheatstone bridge circuit. The out—of—balance current was measured on a micrometer calibrated for the direct reading of pressure.

2:jL The Pumping System

The driver section and the dump tank were evacuated by a common

N.G.N. (PS912) rotary oil pump, with a nominal capacity of 360 litres 42 -2 per minute. A vacuum of approximately 10 torr was achieved in about ten minutes. All inlet connections were of large (1") diameter copper tubing: Instanter plumbing connections were found to be adequate for vacuum purposes. The ultimate working vacuum achieved for the driver section and dump tank was of the order of 1 micron.

The test section and vacuum line were evacuated using a Klemperer single stage mercury diffusion pump, backed by a second three stage diffusion pump, which was, in turn, backed by a rotary oil pump (cf. figure 2:1). The Klemperer was fitted with a wide inlet throat

(approximately 7 cm in diameter) and could be operated at throat -2 pressures as high as 10 torr; at these pressures, however, the pumping speed was slow. A large liquid nitrogen cold trap, situated between the throat of the Klemperer and the vacuum line, protected a) the glass line from contamination by mercury vapour, b) the mercury from attack by condensable corrosive gases and c) improved the,ultimate vacuum and pumping speed. A smaller cold trap protected the system from the tbackt diffusion of oil from the rotary pump.

For approximately one third of the work an N.G.N. (FSR12) pump, connected to the glass line via an automatic isolation valve, 1" diameter copper tubing and a semi..flexible length of reinforced plastic tubing, was used. The backing pressure of this rather elderly pump was not much better than 10 microns. In series with the mercury pump, an ultimate vacuum of better than 104 torr could only be achieved in the test section after approximately two hours.

The time required for the evacuation of the shock tube was dramatically reduced upon replacement of the N.G.N. pump with an

Edwards ED 330 single stage pump (nominal capacity of 330 litres/Minute).

Connection to the glass line was made using a stainless steel flexible bellows and standard Edwards couplings. Provision was also made for the easy attachment of the department's mass spectroscopic leak detector. The arrangement is shown schematically in figure 2:3. The large diameter 43 FIGURE 2:3 THE PUMPING SYSTEM & LEAK DETECTION

VVS

SLE PE RScli

DETECTOR "0 RINGS

ED 330 PUMP 44 diaphragm valve V2 (Edwards 1" diameter) does not restrict the gas flow. The IT° pieces for the leak detector couplings (L.D.C.) were standard 1" Yorkshire fittings with 2" side arms and all intermediate copper tubing was of 1" diameter.

The ED 330 pump was found to be especially suitable for shock tube work, where large quantities of gas must be pumped and absorbed from the walls before every run. The ED 330 has a rapid pumping rate and, unaided, reduced the pressure in the test section to below a micron within 15 - 20 minutes. At these pressures, the operation of the

Klemperer diffusion pump becomes efficient. It should be noted that at higher throat pressures the mercury becomes prematurely contaminated and tends to block the jets of the diffusion pump. This was a considerable cause of inconvenience when the old N.G.N. pump was in use.

The pumping time for those runs with the ED 330 combination was approximately 45 minutes, unless stated otherwise. Within this time an ultimate vacuum of 5 x 10-5 tort could be achieved. The glass vacuum line.could be evacuated to approximately 5 x 10-6 tort . Large diameter (25 mm) pyrex tubing and taps were used to connect the pumping system, the gas handling facilities and the shock tube test section. In order to further promote fast pumping speeds, the number of bends in the tubing was kept to a minimum.

The two separate pumping systems (i.e. the test section and the driver/dump tank pumps) shared a common all copper exhaust, which vented waste gases to the exterior of the building.

2:5 Leak Detection

Small leaks in the shock tube test section and the glass vacuum line were located using a mass spectroscopic leak detector (Universal

Twentieth Century). The procedure, although lengthy, was a vast

1mpro7ement unon the previous techniques of bubble formation and Pirani gauge response to organic volatile solvents. Using the detector, leaks could be pin-pointed rather than large areas found to be suspect. The 45 experimental arrangement is shown in figure 2:3.

All the vacuum connections were of the standard Edwards ,O, ring type. Flexible steel sheathed tubing linked the leak detector sampling valve (V3) with the shock tube via the T pieces (LDC). In operation, the valve V 2 was closed so that all the gases pumped from the apparatus always passed through the sampling valve. Adjustment of the latter enabled fine regulation of the pressure at the entrance to the mass spectrometer head. Typically, the pressures maintained in the mass -6 spectrometer head and the sampling valve were 10 and 10 torr respectively. The detector could be used with either hydrogen or helium, applied to the exterior of the apparatus with a sensitive

1mirco—puffer1.

The sensitivity of the detector is a complex function of the electronics, the flow rate through the sampling valve, the flow rate into the mass spectrometer head and the local concentration of the tracer gas in the vicinity of the leak. This flexibility ensures that a wide range of leak rates can be determined.

The ultimate vacuum in the test section could not be improved beyond 5 x 10-5 tors, the limiting factor being the outgassing rate of the diaphragms and small permanent gas leaks around the windows.

Sheen (35) has discussed the problems associated with the water content of the diaphragm material: it was noted that the apparent leak rate can be resolved into contributions from the permanent and condensable gases present, by making pressure measurements using the Pirani and McLeod gauges with and without liquid nitrogen cold traps. In this work, the permanent gas leak rate never exceeded 0.5 micron per minute. The shock tube was filled with test gas within one minute and the time lapse between disconnection of the pumps and firing a shock was always less than five minutes.

2:6 Diarh.aeems Single o r multiple diaphragms of melinex, available in 46

various nominal gauges, were always used at the driver/test section

junction D1 ( cf. figure 2:1). In order to minimise the degassing

of water vapour from the melinex into the test section, a guard

diaphragm of plastic coated cellophane (British Sidac type MXXT)

was always included. Similarly, a single diaphram of cellophane was

always used at the dump tank/test section function D2 . The cellophane diaphragms showed no indication of chemical attack by the corrosive

gases studied.

Ideal shock tube theory assumes that the diaphragm is removed

instantaneously. This is closely approximated when the diaphragm

shatters. Cellophane does shatter but melinex usually tears. However,

if the driver pressure, is close to or equal .to the spontaneous bursting

pressure tearing can be rapid and the diaph pture occurs in a manner

analogous to the bursting of a balloon by over—pressurisation. Levitt (47)

has observed that reproducible non—attenuating shocks can be obtained

using melinex, as long as the blunt plunger is operated for driver

pressures above 60% of the spontaneous bursting pressure. Unfortunately,

however, small fluctuations in the strength of any given gauge of

melinex were reflected in small variations in the spontaneous bursting

pressure. Nevertheless, shocks exhibiting attenuation or acceleration

due to poor diaphram rupture were easily recognizable by the disagreement between the shock transit time t for the metre AC and that calculated from the observed transit time (t 1) for the distance AB.

211__Gas Pre Fixation

It should be noted that, of the cyanogen halides, only the thermal decompositions of cyanogen bromide and cyanogen chloride were investigated in this work: the fluoride is a particularly corrosive gas and the iodide possesses a very low vapour pressure (4B), making them unsuitable for use in the present shock tube.

Only cyanogen chloride was not available coinnercielly: this was prepared by a standard method (49). Dry chlorine was slowly bubbled 47 through a fine suspension of sodium cyanide in dry carbon tetrachloride/ acetic acid. The simple exchange reaction

Na CN + Cl 2-->— Na + C 1CN is exothermic and was conducted at —10°C. Precautions were taken to exclude atmospheric water vapour in order to prevent the hydrolysis of the product to cyanic acid. The temperature was carefully controlled, because above 0°C the cyanogen chloride readily reacts with sodium cyanide to form the black polymer (CN)m — paracyanogen. Reaction was, therefore, taken to completion before the product was distilled from the solvent at approximately 50°C and in a stream of dry nitrogen.

Excess chlorine was removed from the crude product by refluxing using a Dufton column cooled to approximately -.30°C . The product was fractionally distilled into a special storage bottle made of annealed and toughened pyrex and capable of withstanding positive internal pressures. The bottle was fitted with a stainless steel needle valve.

Further purification was conducted by vacuum distillation. The cyanogen chloride was thoroughly degassed by alternate freezing (-196°C) pumping and melting and finally distilled between traps maintained at —196°C and —40°C . Approximately the first and last 5% of the distillate were discarded. The purified cyanogen chloride was kept under vacuum in the storage bottle at temperatures below _50oc

After some time a yellowish tinge appeared in the liquid phase, probably due to the formation of low molecular weight polymers of CN. This was easily removed by further vacuum distillation.

The pure cyanogen chloride formed white crystals,which melted to a colourless liquid,which in turn boiled at approximately 13°C to form a colourless gas,in good agreement with the literature (48, 49).

2:8 Gas Purification Argon (B.O.C.) was taken directly from a cylinder and dried by 48 passing it slowly over fresh phosphorus pentoxide; it was thoroughly degassed by alternate freezing, pumping and melting.

Crystalline cyanogen bromide (Cambrian Chemicals) was purified by vacuum sublimation to a cold trap maintained at -78°C . Because of the low vapour pressure and the large heat of sublimation of cyanogen bromide, water vapour was easily removed by alternate pumping and warming to room temperature without serious loss of the bromide.

Cyanogen chloride was always re-purified immediately before use, by degassing and vacuum distillation between cold traps maintained at o -196°C and -40 C.

The purities of the gases used were checked after completion of the above purification procedures using an ?S9 mass spectrometer. No impurity levels were detectable within the background of the instrument.

The check for water vapour was necessarily crude because precautions to avoid the preferential absorption of water on the walls of the glass containers were not undertaken. It is estimated, however, that the maximum contamination of the purified gases from any given contaminant is 0.03% (i.e. less than about 300 ppm cannot be detected on the }.S9).

2:9 The Instrumentation

A schematic plan of the optical/electronic system is given in figure 2:2.

The signals derived from the photomultiplier response to the unfiltered but collimated radiation from the shock front at A and were, after suitable amplication and pulse shaping, used to operate the 9start/stopl gates of a microsecond timer (Racal SA 535). The reciprocal of the transit time for the one metre distance A to was taken to be the instantaneous shock velocity et the central observation station B. A time delayed trigger, taken from the Istart' channel, was used to fire the single sweep of the oscilloscopes just before the shock front passed the slits mounted at B . Time resolved H T 1 POWER INC, SIGNAL H .T.2 INPUT ,11111111111111111W MATCH 0 RCA z PM.

I, 1 C B A SHOCK TUBE. U PM. " PULSE 0 PRE P 2 SHAPER" AMF? AMP z )---5 STA RT NO NMI OW STO P DELAYS MD ONO ONO OM =NM

FIGURE 2:4

THE ELECTRONICS. 50 measurements in two spectral regions of the emission from the shock heated gas could be simultaneously recorded using the two monochromator/ photomultiplier/oscillosccpe combinations.

2:9:1 The optical system

Using the shadows cast by an illuminated optical pin system, the optical benches were accurately aligned with marks scribed over the centres of A, B and C (i.e. 50 cm apart). The slits required for the time resolved measurements could be mounted to within . 0.5 mm employing this technique. The slit dimensions were: A and C

0.5 mm x 20 mm; and B 1 mm x 13 mm. Similarly, 0•5 mm wide slits were also mounted on the two RCA 931A photomultipliers used in the measurement of the shock transit time for the distance A to C .

2:9:2 The monochromators

Large aperture double grating monochromators (Optika CF4),suitable for use in the ultra-violet, visible and infra-red were positioned on opposite sides of the shock tube at station B The slit function appropriate to these monochromators is triangular and is discussed in appendix I of this thesis. The maximum slit width used was 3.6 mm corresponding to a triangular half-width of 7.5 nn .

The optical path for the ultra-violet/visible grating is shown in figure 2:5. The light entering the large aperture transverses the entire length of the instrument, is rendered parallel by a concave mirror and is projected onto a diffraction grating. The image of the slit mounted on the shock tube occupies an area approximately six times that of the grating but is only just of smaller width. The use of the monochromator, therefore, involves a geometrical loss factor ( G ) of 1 about /6 in the intensity of light emerging from the exit slit.

Sheen (page 46 of ref. 35) has emphasised the importance of correctly aligning the shock tube slits and the optical axis of the monochromators, 51

Fi GU RE 2:5

OPTICAL AXIS INSPECTION. HATCH

UV GRATING

SLITS PM

ENTRANCE A PERTURE OPTICAL AX I S

THE CF4 MONOCHROMATOR 52 if uniform illumination of the diffraction grating and maximum transmission are to be achieved. In order to facilitate this alignment, the low powered H laser ee was employed to mark the position of the optical axis. The end of each monochromator remote from the entrance slit is fitted with an inspection hatch, through which the mirror assembly can be removed. Targets drawn on melinex plastic were cellotaped a) in place of the mirror assembly and b) over the entrance aperture, so that the centres of the targets defined the optical/geometrical axis of each monochromator. The laser was positioned on the side of the shock tube remote from the intended placement of the first monochromator, using the optical bench previously positioned at B as a reference. The narrow beam of light was arranged to pass centrally and horizontally through the two slits mounted at B . It was a simple matter to adjust the monochromator so that the narrowleserbeam also passed through the centres of the targets on the semi-transparent Iscreensl and hence along the optical axis. The second monochromator was positioned in an analogous manner employing thelasarbeam but using the optical axis of the first monochromator as the reference.

Using a narrow band width, the wavelength scales of both instruments were checked in situ by-observing the radiation from the strong visible lines of the mercury spectrum.

2:9:3 The electronics

Detailed descriptions of the electronics have been given elsewhere

(35, 245) and consequently only the major features of interest are noted in this thesis.

2:9:4 The timer photomultinliers

RCA 931A photo-tubes, housed in light proof boxes, were used to derive signals for the measurement of the shock velocity. The negative

H.T. bias to the 9 x 47 kohm dynode chains of both photomultipliers Was supplied by a Power Designs Inc. stable power pack (0 - 2012 volts; 15mA; 53 maximum peak to peak ripple 1 mV; stability 0'005% per hour) via a potential divider and signal matching unit.

Light incident on the photo—cathode produces a low impedance signal across an anode load resistor of 4.7 kohm, stabilised by the cathode of one half of a double triode. The signal is amplified by a x25 pentode stage and is fed to the grid of one half of a double triode. A low impedance signal of approximately 0°5 volts appears at the cathode follower and is transmitted via coaxial cable to the input of the pulseshaper/amplifier network.

2:9:5 The pulse shaper,

The pulse shaper consists of two independent channels, the gain of one being adjustable so that the two channels can be matched. Input signals derived from the start/stop photomultipliers are amplified by a x25 pent/ode stage. A phase splitting triode stage produces equal negative and positive pulses which are applied to the grids of a double triode cathode follower with a common anode load. This yields 10 . 20 volt positive pulses irrespective of the original polarity, with a maximum rise time of 0.2 pec. suitable for operation of the chronometer gates. A trigger from the start channel is provided to operate the single sweep of an oscilloscope.

2:9:6 Signal hatching

The channels of the pulse shaper were matched by equalising the amplitude of the output signals obtained from a square wave input to each channel; the outputs were displayed on a dual trace oscilloscope.

The gain in the pentode stage of one channel was altered by using a potentiometer in series with its anode load.

Equal light intensities, falling on the two slit/photomultiplier combinations at A and C, did not necessarily give rise to equal signals for the same H.T. due to small differences in the slit 54

dimensions, valves, photo-cathode sensitivities, etc. Fortunately,

both RCA 931A photomultipliers possess the same qualitative dependence

of the cathode sensitivity to wavelength. Using chopped radiation from

a continuous source (i.e. a tungsten filament car head lamp bulb) the

signals from these timing photomultipliers were matched, simply by

adjusting the H.T. supplied to one of the photomultipliers using

a potential divider network.

2:9:7 The quantitative nhotomultipliers

Quantitative measurements were made at station B using an EMI 9558Q

(or the equivalent Centronic 42830 A) and an RCA 931A. The approximate

spectral ranges are:-

EMI/Centronic 200 to 800 nm

RCA 931A 320 to 750 nm both profiles peaking at approximately 400 nm.

The detailed description of the circuitry used to drive the

EMI/Centronic tubes has been given (35, 45). The negative HT to the

10 x 27 kohm dynode chain is supplied from a Power Designs Inc. stable

power pack. The photo-tube is electrostatically screened with metal foil. The potential drop across the anode load resistor of 10 kohm

produced when light is incident on the photo-cathode, is transferred unamplified (via a low impedance white cathode follower and coaxial cable) to the input of the oscilloscope. The output impedance of the white cathode follower is only 20 ohms ensuring that stray capacities to earth, introduced by the coaxial cable, do not attenuate the fast

pulses monitored by the photo-tubes.

The circuitry of the 931A photo-tube is similar, except that the dynode chain consists of 8 x 47 kohm resistors and has an anode load of 4.7 kohm . The resultant signals were also transmitted unamplified via a white cathode follower and coaxial cable. 55

2al1121111Maaa Tektronix oscilloscopes (Types 54.5B and 533) were used with a variety of plug—in units to display the photomultiplier responses at station B. The 545B 'scope was fitted with a built—in delay vstem, suitable for delaying the single sweep of the oscilloscope after the receipt of an external triggering pulse derived from the pulse shaper unit. The delay was set from an estimate of the shock transit time for the distance A to B so that the single sweep of the oscilloscope was 'fired' immediately before the shock front uncovered the slits at station B. The traces were photographed using Teleford type A and Coleman model 5 oscilloscope cameras. Either Polaroid Type 4.7 land roll film (A.S.A. 3000) or Kodak Ortho—Royal sheet film (A.S.A. 400) were used.

The cut film was developed in high contrast X—ray developer because of its relatively slow speed.

2.1.2191 Because of the distinctive shape of the emission profiles for shocks into cyanogen bromide/argon mixtures, discussion of the rise time of the equipment is deferred until the experimental records have been introduced. From the geometry, however, the expected rise time defined by the slits at B is expected to be approximately 1 Ilsec for the shock velocities used in this work. 56

CHAPTER III

EMISSION FROM SHOCK HEATED GASES

3:1 Introduction

Emission spectra in the visible and ultra—violet generally correspond to electronic transitions: that is an electronic change from one orbital to another of lower energy. The difference in the energy levels is equal to the energy of the photon emitted. The population of energy levels above the ground state may be accomplished by

(i) irradiation

(ii)thermal excitation

(iii)chemical reaction.

The emission from (i) is termed fluorescence if the spin is conserved between the relevant states and phosphorescence if not; from (ii) is called thermal emission and from (iii) chemiluminescence. The detailed mechanisms of many emitting systems and their quantitative treatment have been reviewed elsewhere (refs 50 — 53).

In the shock tube, where high temperatures are commonplace, the mean molecular velocities will be high and processes (ii) and (iii) above can become rapid. The light emitted behind incident shock waves can exhibit effects attributable to both thermal emission and chemiluminescence. However, where both occur, the relative contributions from each mechanism to the total intensity can often be resolved. The relaxation rate for chemical reaction is typically several orders of magnitude slower than the rates of collisional activation or quenching of the excited states which give rise to thermal emission and it is normally slow compared to the radiative lifetimes of the electronic 57 levels. Thus in the region immediately behind the shock front, where the degree of dissociation or chemical reaction is small the probability

of observing chemiluminescent recombination reactions is low. The light

emitted in this region is attributable solely to thermally induced

processes. At longer test times, however, the concentrations of reaction products may become sufficiently large so that chemiluminescence is the major source of emitted light.

:2 Thermal Emission.

The major processes which influence the observed intensity are a) the rate of collisonal population of excited levels, and b) the depletion of these levels by quenching, radiation and further chemical reaction. Careful consideration must be given to the relative importance

of each contribution to the over—all excitation kinetics, before meaning.. ful reduction of the experimental data can be achieved.

A simplified scheme for the formation and fate of electronically excited species may be written: (where represents an electronically excited species)

collisional excitation : A +M--->-- A* + M (R:1)

collisional quenching : A* +M----->--A+ M (R:-1)

radiative depletion A* A + h\/ (R:2)

dissociation A* + M > products + M (R:3)

chemical reaction/quenching + A products (R:4)

It should be noted, however, that, as written, step R:1 and R:-1 are simplifications of a detailed energy transfer mechanism involving steps such as

ABv +C > AB +C (R:5) where the superscript v denotes a vibrationally excited species. This is discussed in detail later in this section with particular reference 58 to the quenching steps R:-1 and R:-5

Levitt I 54) has explained the emission from NO M 2 behind incident shock waves in terms of steps R:1 to R:3 . The radiative

depletion was found to be slow relative to the collisional quenching.

In addition, however, the excited state of NO2 was found to dissociate. Similarly Levitt and Sheen (55, 56) have resolved the emission from

several excited states of sulphur dioxide in terms of the same steps.

Gaydon, Kimbell and Palmer (57) have suggested that chemical quenching

of the 3B1 state of sulphur dioxide is important in the decomposition kinetics

SO * + SO SO + SO 2 2 3 but this has been criticised (58).

The intensity of light (I) emitted from a luminous system is

proportional to the concentration of the excited state. Therefore from

step R:2

I = k2 [A*] EQ 3:1 where the constant of proportionality is the Einstein coefficient for spontaneous emission (Ann) for the electronic transition n4— m and is simply given by the reciprocal of the radiative lifetime (1 ) for the transition concerned. (i.e. T = 1/k2 ) Applying the stationary state hypothesis to the rate of formation of A* in steps R:1 to R:4 inclusive, gives

k1 + k + k [A] / [N] + k [1,1]) [A] = [A](k-1 3 2 EQ 3:2 Inspection of this equation shows that the population of A* and hence the intensity of light emitted can exhibit complex behaviour with respect to total pressure and concentration of the ground state molecule. If the concentration of the excited species is low (i.e. in mixtures 59 heavily diluted with inert gas) chemical reactions involving these species will be negligible compared to collisional excitation and

quenching. Indeed, steps R:3 and R:4 can often be discarded from the net excitation kinetics. Applying the stationary state hypothesis to steps R:1 , R:..1 and R:2 .

[A4] = ki [A] [Id I [M] + k2) EQ. 3:3

Combining equations EQ. 3:1 and EQ. 3:3 and re-writing the rate constants in terms of simple collision theory (section 1:2) so that -E k = P Z exp ( a/RT) and k..1 = P 4Z l 1 o o

I = Pi%[A] [M] exp (-Ea/RT) EQ. 3:4 ( Z [M] + 1/T ) P_1 o where E a is the apparent energy for excitation; P1 and P...1 are defined as the probabilities that an inert gas collision will result in excitation or quenching respectively. At sufficiently high pressure the inequality'

P-1 Z0 [14] I » 1 EQ. 3:5 will apply and the radiative depletion will be negligible compared to collisional quenching. The quantity 1%.1 Zo [M] I is the number of collisions an excited species will experience before it radiates and in the absence of Quenching. Equation EQ. 3:4 simplifies to

-E . exp( a/RT) EQ. 3:6

The problem can be recast in terms of chemical statistics. Assuming that radiative depletion only negligibly perturbs a thermodynamic equilibrium betneen A and A* , maintained by collisional activation and quenching, the intensity of emitted is given by: 60

I :z 2-, [A] exp (_Eo/RT) EQ. 3:7 where Q is the ratio of the partition functions for the two states and is nearly independent of temperature; E o is the energy of the lowest vibrational level of the upper state relative to that of the ground state.

If A is an atom, Q is simply the ratio of the electronic degeneracies

(g1A2) • If A is a molecule, however, the contribution to the total partition function due to vibrations and rotations for both electronic states must be considered. In general, however, the contributions are approximately the same and Q is still adequately described by (g1/g2) . Inspection of equations EQ. 3:6 and EQ. 3:7 shows that

Q = el/g2 = P1/P.4

22:1 Collisional uenchinp robabilities

Typically, radiative lifetimes of excited electronic states are of -7 the order of 10 seconds, whereas the gas kinetic collision frequency 10 1 (at one atmosphere pressure) is of the order of 10 sec . An excited molecule will therefore experience somewhere in the region of 103 collisions before radiation can occur and some of these may result in deactivation.

However, from energy transfer theory (19), the quenching probability

, introduced in the previous section) depends upon the.energy released to translation. For resonant energy exchange between two states

P energy is not released to translation and -1 is relatively large (of the order of 10-3 or more). If the energy released to translation is

P of the order of a vibrational quantum, the values of 1 are often several orders of magnitude lower than this. The energies involved, however, in electronic transitions are of the order of lev or more and the direct liberation of this amount of energy to translation is improbable (P.,1 becomes negligibly small).

Applying the principle of microscopic reversibility, collisional excitation and quenching involving atom's only is, therefore, negligibly 61 slow. However, increased complexity of either A or M can considerably enhance these probabilities.

(i) If the collision partner possesses more than one atom, vibrational- electronic interaction becomes important. Indeed, it has been found that the quenching probability for the reaction

2 lia( P) -IN (v=0)-*- Na(2 2 S) +N2(v=8) (R:6) is close to unity. Hurle (59) has shock heated nitrogen with added sodium in order to observe the excitation process. The sodium D line emission follows the increasing vibrational temperature of the relaxing nitrogen, rather than the decreasing translational temperature (cf. section 1:8; figure 1:2).

(ii) If the emitter is polyatomic and the collision partner is monatomic, intramolecular conversion of the electronic energy of the excited species (A*) to vibrational energy of the ground state (A) is possible. This can be efficient because of collision induced crossing from the lowest vibrational levels of A* to the upper levels of A either directly or via an intermediate state (cf. step R:5 section 3:2).

(iii) If the collision partner is also polyatomic, the quenching probabilities can tend further towards unity because of the increased complexity of the collision. This is, however, dependent.upon the detailed nature of A B M and the collision. For example, Wray (60) has shown that N atoms are approximately 100 times more efficient in exciting N2 than are N2 molecules. Wray has explained this in terms of the crossing of the potential surfaces of the N-N 2 complex enhancing the energy transfer. Laidler (61) has discussed excitation phenomena in terms of such collision complexes and inter systems crossing.

In experimental determinations of quenching probabilities the effects of the various components in the gas are usually resolved by using the Stern-Vogmerrelationship (62). For a given luminous system the effect of adding a foreign gas is observed. For instance in the 62 absence of chemical reaction, consider the following quenching steps:-

self-quenching : AB* + AB —4- AB + AB (R:7)

inert-gas quenching : AB* + D —+- AB + D (R:8)

The effect of adding the foreign gas D is found by solving the kinetics for a stationary state in [AB*] . That is

T = + [AB] + k T [D] 8

7 where k T [AB] and k8 T [D] are simply the number of collisions experienced by the excited species (before it radiates and in the absence of quenching) with the ground state molecule AB and the foreign gas

D It is the intensity of the emission in the absence of the foreign gas extrapolated to zero concentration of AB and I is the measured intensity for any given mixture composition; I is the radiative lifetime of AB* .

Quenching for triatomic molecules is efficient when it is spin allowed. Kaufman et al (59) have used the Stern-Vohlmer relationship to investigate the quenching of nitrogen dioxide luminescence and find that the probabilities for argon nitrogen and self-quenching are respectively 0.08, 0.10 and'0°24 . For those systems where the quenching probability is high, the rate of radiative depletion of excited states will be slow compared to the collisionsl processes and the intensity of light emitted is given by equations of the form of

EQ. 3:6 and 3:7.

3:3 Chemiluminescence

The rapid establishment of large concentrations of reaction products at shock tube temperatures can result in significant contributions from chemiluminescent recombination reactions to the total intensity of light emitted. The fate of the excited species in terms of radiation, quenching and chemical reaction is governed by the same principles as 63 outlined in the previous section for thermally excited species. Thrush

(52) and Garvin and Carrington (51) have reviewed the processes which lead to the formation of electronically excited species. The luminescence accompanying recombination reactions can result from two or three body mechanisms. If the emission is confined to transitions from vibrational levels close to the dissociation limit, the two body process is indicated: emission from lower levels is evidence of a three body mechanism.

Theoretical and experimental evidence has shown that the two body processes have a very low reaction probability. Thrush (52) has 6 estimated that a maximum of 1 in 10 two body collisions of 0 + NO results in radiative recombination to NO2 . Experimental investigations yield probabilities even smaller than this. Fair and Thrush (64) have 2 discussed the emission from the V =10 level of the B state of S2 , populated by the two body recombination of sulphur atoms and find the probability of reaction to be approximately 10-7 . The kinetics of the emission due to the three body recombination

(A+B+M) , where M is an inert collision partner can be summarised as follows:

Recombination: A+B+M --4— AB*+M (R:8)

Quenching: AB*+M --->— AB+M (R:9) Emission: AB* AB + hv (R:10) The recombination step R:8 is of course a simplication of the complex energy transfer processes, involving collision induced crossing of potential energy surfaces as indicated for thermal emission. Applying the stationary state hypothesis to the concentration of the excited species gives [AB] = k8 [B] [MP (k 10 + k9 EM] EQ. 3:8

The intensity of light emitted is simply given by I =[A134:1 1 0 EQ. 3:9

64 where k is the reciprocal of the radiative lifetime (T ) of the 10 electronic level populated by the energy made available upon recombina— tion.

The third body may be interpreted as a 'catalyst' in stabilising the incipient_ molecule in an excited electronic state and in vibrational levels sufficiently below the dissociation threshold so that re—dissociation of AB* is unlikely. This is in accord with the reverse process of dissociation, where energy is transferred to vibrational degrees of freedom in small steps and dissociation occurs from levels within kT of the dissociation threshold (54).

Inspection of equation EQ. 3:8 and 3:9 shows that at sufficiently high pressures, where the inequality

9 [] >> k 10 EQ. 3:10 is valid

k k I= 8 10 k [B] 9

=IoA [B] EQ. 3:11 where IoA is termed the radiative rate constant. From the form of this relationship, because ko is probably a simple collision number having no activation energy and k10 is a simple first order spontaneous decay constant, I —n oA is expected to exhibit a T dependence. This arises from the T2 term in the collision frequency for k and the 9 characteristic T—m dependence observed for termolecular recombination reactions (e.g. the recombination of halogenatoms — ref. 65).

2.:A The Absolute Calibration Usin Shook Hoatod Sulphur Dioxide as an

Intel-,aediate Standard

The original absolute calibration of the shock tube and associated ecuiTpment was conducted by Sheen (35) using known photon sources. The 65

calibration in the visible was achieved using the method devised by

Levitt (47) employing a tungsten filament lamp and was extended to the

ultra-violet using a hydrogen discharge lamp.

Using the calibration,Levitt and Sheen (55,56) have measured the

absolute emissivity of shock heated sulphur dioxide (dilute in argon)

as a function of wavelength. The apparent continuum, stretching from

250nm to 550 nm, was attributed to the overlap of fine structure due I to transitions from three excited states t 3B ; B 2 ; and possibly a IB S ). The absolute emissivity at 3333K and the apparent activation

energy required for emission were presented as a function of wavelength.

In this work the recalibration was achieved by using the emissivity of

sulphur dioxide as an intermediate standard. This method has been

successfully applied by Levitt and Parsons (66) in the study of the

absolute emissivity of the cyanogen radical: the emissivity of SO2

was also checked (67).

From Levitt and Sheen (55, 56), it is noted that the emission from

SO rose to at least 2 a of its peak value within the rise-time of the optical geometry. This was attributed to the rapid equilibration of

energy among the degrees of freedom available to SO2, resulting in

the generation of thermally excited species at the shock front. The

emission records characteristically showed a subsequent decay to a lower level, which, at long wavelengths, was associated with the dissociation of the ground state molecule and the accompanying fall

in temperature. It should be noted, however, that the intensity of light emitted at shorter wavelengths, in this region of the experimental

observation, were anomolously high compared to the intensity calculated for thermal emission from the undiseociated SO2'• this region, attributed to the 0+S0 chemiluminescent recombination, is re-investigated and discussed in Chapter VIII of this thesis.

Levitt and Sheengs intensity measurements at the shock front were found to be proportional, to the initial post-shock concentration of 66 sulphur dioxide, but independent of the total gas pressure, indicating that radiative depletion is negligible compared to collisional quenching.

Therefore, from EQ. 3:6 and 3:7 the observed intensity is given by

I = I0 FS021 ((f: ' 2 exp ("Ea/RT) EQ. 3:12 P where I is an instrumental constant for the gas being studied and o incorporates the necessary calibration factors, etc; [302] is the { concentration of the sulphur dioxide in the unshocked gas and P 2/P1) is the density ratio across the shock front. More precisely, from spectroscopic theory (69) it may be shown that the absolute emissivity (Ix) at a particular wavelength, X. , is related to the observed millivolt signal (Dx ) derived from the photo-multiplier by

X4 CIX

D x = j Ix t x d x Gx Sx V [SO,] (P2) P1

EQ. 3:13 where for the wavelength interval A to = d A observed by the photomultiplier:

(i) f I x tx d A is the transmission integral applicable to the triangular slit profile of the monoehromator

S A is the cathode sensitivity

,(iii) If is the effective volume of the emitting gas (i.e. the integral volume of ref. 35 - Appendix I).

(iv) Gx is the geometrical loss in using a monochromator,

Sulphur dioxide is particularly useful as an intermediate standard 67

because it emits over a large spectral range not possessing fine structure, the repl lucibility of the thermal emission at the shock front is good

and deviations from ideal flow are negligible at the shock front. Indeed,

the method provides a rapid and simple check upon changes in the

calibration which are deliberate, accidental or due to 'aging' of the

electronics.

3:4:1 Procedure

Levitt and Sheen (55) have reported detailed measurements of the

absolute emissivity of the frontal emission in S02/Ar shocks at

436 nm. The photomultiplier response, optical geometry, etc. were,

therefore, checked at this wavelength.

A few shocks were conducted for a 10% S0 2/Ar mixture at initial unshocked gas pressures of 5 and 10 mm , so that the shock front /frozen' temperatures clustered about 3335K. In all cases, the shocked gas conditions immediately behind the shock front were calculated

assuming that the internal degrees of freedom of S02 are completely

relaxed but that chemical reaction (i.e. dissociation) has not occurred:

these assumptions have been fully discussed elsewhere (35, 45).

The log 10 of the emissivity at the shock front is shown plotted

as a function of temperature in figure 3:1 ; it is a good test of equation

EQ. 3:12. The results, measured initially in arbitrary units, are shown

sealed, so that the value interpolated at exactly n33k is matched

to the absolute emissivity (Ix) determined by Levitt and Sheen (55).

These authors, have also reported the temperature dependence of the

emissivity and this is represented by the solid line. The results are

an excellent fit confirming the performance of the shock tube and allied

equipment.

It is the aim of this work to conduct measurements, monitoring part

of the Av = -1 sequence of the GN(B2P X22:-) violet bands

centred at 421•5 nm. In order to check the photo-cathode sensitivity, 68

CALIBRATION: TH! MISSIVITY OF SO AT 436nm. 2 IN ARBITRARY 'E'XPERIMENTAL UNITS FIGURE 3:1 LOG ID / [SO 10 r 2j

Solid Line: The absolute emissivity due to ref. 55, where dI/dA=1033'°exp(-73200/RT) -1 -1 -1 photons sec. 1. cm. , matched to the, present experimental results.

4 10 /T2,0

2.5 3.0 3.5 R.,o.o5; 1,1=5 mm. — s02/Ar

0 M=0.05;' =10 mm. - SO 2 /Ar 69 FIGURE 3:2

THE CALIBRATION ATA =421.5nm: THE PEAK

HEICHT I (lor units) AGAINST RECIPROCAL

TEMPERATURE

Slope of line is E/R2.303, where E is -1 taken to be 74 kcal mole from refs. 55,56

4 /T 2p 2-5 340 3.5 10 70 a few runs into 5% S02Ar mixtures at an initial pressure of 10 mm were conducted so that the shock front Ifrozent temperature again clustered about 3333k. The variation of the frontal intensity (in log units) with temperature is shown in figure 3:2. The value at 3333k can be matched to the reported value (55) of the absolute emissivity at this temperature and wavelength, using equation EQ.3:13. The application of this calibration procedure to check the absolute emissivity of the

CN radical is discussed in Chapter IV. 71

PART II

THE THERMAL DECOMPOSITION OF

THE GYANOGEN HALIDES : BrCN and C1CN

In this section of the thesis, the techniques specific to the

investigation of the pyrolysis of cyanogen bromide and cyanogen

chloride are described.

The solution of reaction mechanisms by computational methods

(i.e. mathematical modelling of the reaction system) is discussed and

the particular procedures adopted in this work are presented.

A review of the known reactions of the CN radical and the

application of emission measurements, pertinent to the determination

of reaction rates for the pyrolysis of Br CN and C1CN are given.

For convenience, the results for the apparent rates of decomposition

of these compounds are reported and discussed in separate Chapters.

Furthermore, the results of the computer simulations for various

reaction schemes are incorporated in these discussions and ordered

so as to emphasise the progression from the initially adopted rate

parameters and reaction mechanism to the final Most fit? mathematical

model. 72

CHAPTER IV

COMPUTATIONAL TECHNIQUES

4:1 Introduction

Studies of gas phase reactions, particularly at high temperatures, often yield complex rate laws due to the contributions to the observed kinetics from several elementary steps. This is particularly noticeable in combustion studies, where fuel and oxidant can rapidly produce significant concentrations of reactive intermediates. Semenov (71) has given a comprehensive survey of the tclassicalt methods (such as the application of the stationary state hypothesis) used to determine mechanisms and rate constants in such binary reactive mixtures. This approach is used in Chapter III to derive expressions for the excitation kinetics of luminous systems. Applied to more formal chemical reactions, an apparent rate law is derived for a particular reaction mechanism and compared to experiment; further mechanisms are postulated until the desired rate law is predicted. For complex systems such as chain reactions, this normally leads to the determination of values for the ratios of groups of rate constants or to the formulation of rate constant inequalities. In this manner, it is often possible to eliminate some of the proposed steps from the effective reaction mechanism for different limiting conditions.

At elevated temperatures, however, steady state conditions may not be achieved and Iclassicall methods are no longer applicable. In these circumstances, it is appropriate to simulate the observed changes accompanying reaction 'ey integration of sets of coupled differential equations, representing the rates of individual elementary reactions. 73

The equations are coupled because the rate of each step, and hence its contribution to the overall kinetics, is a function of the concentration of the reactants; these may participate in more than one elementary step.

It has even been emphasised (72) that integration techniques should often be applied to shock tube determinations of simple dissociation rate constants. The drop in temperature, changes in density, etc., accompanying an endothermic dissociation, in an adiabatic system, can be sufficient to give anomolous apparent rate constants and activation energies.

This is particularly so if the results are derived from emission records, for the extonential term in the expression derived for thermal excitation

(EQ. 3:6) introduces a strong temperature dependence in the observed emission intensity. Indeed, Fishburne and Slack (73) have been criticised for ignoring these effects in their determination of the dissociation rate constant for cyanogen.

The rate (Ri) of ith elementary step is simply defined by

= k. [Ala [B] b [N] n Ri EQ. 4.:1 where k. is the rate constant and a, b and n represent the number of

moles of a given reagent A, B or N which are consumed by the reaction.

Rate constants for each forward reaction step must be selected from the known literature or by careful estimation. For completeness, the rate

of the ith reverse step can be included in an analogous manner, where

k. is conveniently calculated from a knowledge of the equilibrium

constant using the familiar relationship (Keq(i))

Keq(i) = ki/k_i EQ. Z.:2

The integration of ERi can be accomplished by numerical methods in a step-,wise fashion. However, after each step in the integration the

temperature, pressare, and density must be adjusted to comply with the

physical constraints of the system (in this case, accompliAed by the solution of the shock hydrodynamic equwaons). 74

The integration predicts the variation of some observable, usually a species concentration, with time and this can be directly compared with the experimental record. The values for all the ki rate constants of the proposed reaction mechanism are adjusted until a match between the two is obtained. Alternatively some other experimentally derived property may be compared to the computer prediction of the same property, instead of the detailed matching of complete reaction profiles. For example, Bradley and Frend (74) have matched the apparent rate constant for the pyrolysis of ethane by adjusting both the reaction mechanism and the values of the rate constants. Dean and Kistiakowsky (75) have matched four properties, derived from their experimental records

(induction periodsl an apparent rate, peak height and the time to reach the peak), in their computer analysis of shocked CO or CH4/02/Ar rixtures.

Fortunately, the formidable task of computer fitting procedures is somewhat simplified, because the choice of possible rate constants is subject to the constraints a) that some of them are known from the literature and b) that the remainder must be reasonable compared to similar known processes.

4:1:1 Machine methods

The computation of reaction profiles by hand is impracticable, even for relatively simple systems (e.g. the dissociation/recombination of oxygen). Profiles can be constructed, however, using suitably programmed analogue or digital computers. The former have been discussed elsewhere (76, 77) and are not suitable for the simulation of the gas kinetics in shock tubes. In this work, the computation was conducted using a digital computer (CDC 6400/6600 and IBM 7090/94).

Numerical integrations have been conducted for a variety d' shock tube- experiments. The early work due to Duff (78), in which reaction profiles were qualitatively predicted by introducing approximations into the shock wave equations, clearly indicated the potential of the 75 simulation technique. Further calculations by Duff (79), for the

H2-02-Xe detonation, were based upon the assumption that the forward rate constant for the ith elementary step of a given mechanism may be written

n -E4 1 k.1. = A.1 T exp ( "VRT) EQ. 4.:3

(at least for gases in vibrational equilibrium) and that the reverse step was independent of temperature. Greene and Toenies (30) have reviewed the early progress achieved in such mathematical modelling of shock tube experiments.

Since Duff's early calculations, considerable improvements in computer speeds, memory sizes and programming methods have been achieved.

The procedures commonly adopted have been given (77, 80) and the codes for many (e.g. Runge-'Kutta) are readily available.

Snow (81, 82) has claimed that, by linking the integration with the tpartial steady state' postulate, a 30% reduction in computer time can The H + Br be achieved. 2 2 chain reaction and the pyrolysis of ethane were investigated and it was found that simple Runge-Kutta methods were not always suitable for free radical systems. Emmanuel (83) and

Kollrack (80 have noted, however, that indeterminate quantities can be introduced and retained in the rate equations by switching from the step by step integration to a partial steady state formulation.

Bauer et al (85) have investigated the complex decomposition of cyanogen chloride. The rate equations for six elementary steps were cast into master rate equations by defining the concentration of each component in the reacting system, including undissociated cyanogen chloride, in terms of the initial post-shook concentration of cyanogen chloride.

The integration was accomplished by a Runge-Kutta method. However, the coding for the integration is not general and, because new equations and code would have to be derived for different reaction schemes, it is not particularly suitable for the investigation of reaction mechanisms. 76

Levitt (86) has tried Runge—Kutta and other complex forms of integration and finds that they frequently fail either because the ratio

of the largest to the lowest rates is too high or because rapid consecutive

reactions maintain a low concentration of reactive intermediates. The

initial concentration of an intermediate, such as a free radical, is zero

but, immediately it is formed, it can participate in rapid removal

reactions which can effectively indicate a large negative net rate of

formation until the rates of other formation steps become fast. The

predicted concentration of the intermediate falls tout-of-'balances and

negative values can result, causing the integration to oscillate.

Bradley and Frend (74) have recently discussed the unstable "e

propagation of absolute errors occurring in step—by—step methods and

have outlined a variable order technique due to Gear (87). The

integration commences with a first order formulation which can be readily

increased, in unit steps, up to a fifth order method so that the error

propagation is stable with most values of the step length. Unfortunately,

however, the adoption of more complex integrations normally increases the

execution time of the computer program.

1~:2 Pr o,raF~20'IL) Description

The program (FROFIL), written in Fortran IV, is based upon the

original code developed by Levitt (86). FROFIL calculates the shocked

gas conditions immediately behind the shock front, finds the position

of chemical equilibrium for any given set of species behind the incident

shock wave and integrates any arbitrary set of reaction stop rate

equations (automatically including the reverse step). The integration

step length is determined as reaction proceeds and includes several

checking operations. The first order method used in the integration was

suitable for the present pyrolysis study, where the range of rate constants

is not likely to be greater than a factor of 10' The program executes in a field length of approximately 22K words 77

of central memory and under favourable conditions creates a complete

output file (including a punched record of the integration) within about

10 seconds of CDC 6400 computer time. The output is comprehensive and

self—explanatory, including full diagnostics for various integration

truncation mechanisms. The program automatically plots out the

concentration profile of the control species and the emission profile

of the species monitored in the experimental observations. A detailed

list of the content° of the output file is given in Appendix II.

The program is subdivided into several task oriented subroutines :

SHIN , EQB , GPIVOT , PRINT , START , PREP SHUG INTEG I

PLOT , ?TOT PNCH called via the main routine PROFIL. The

compactness of the program enables its execution under the special

operating facilities of 'INTERCOM' available on the CDC 6400 computer.

By suitable use of the CDC software (e.g. EDITOR) data files can be

constructed, programs attached and executed to generate output files

for immediate interrogation at a tele—typewriter terminal.

4:2:1 Input

Full details of the punched:card data input and a description of

the integration control parameters are available (88): only the essential

features are given here.

Up to 100 chemical species and 50 elementary reactions (i.e. 25

forward reaction steps and their reverses) can be handled. Thermodynamic

data for all the species to be consideredweretaken directly from the

Janaf tables (37) unless stated to the contrary (i.e. A HfoCN cf. Chanter V) and were cast in the form of a polynomial (89) according to

the definition given in the Hug (39) program for chemical equilibrium

in shock waves. To enable the calculation of the shook front conditions

before the initiation of chemical reaction, the initial unshocked gas

cc position, total gas pressure and. the shock velocity are sunplied. 78 For a given reaction scheme each elementary step is defined on a separate punched card together with the parameters defining the rate constant according to equation EQ. L.:2.

4.:2:2 Preliminary calculations

All the species included either for the equilibrium calculation or for the integration were assumed to obey the ideal gas laws. a) The shock front

The temperature T , pressure P and density of the 2o, 2o, test gas, after passage of the shock wave but before the onset of chemical reaction, are obtained by solving the hydrodynamic equations for the initial unshocked gas parameters and the shock velocity according to the method given by Sheen (Appendix ref. 35; cf. section 1:8).

The coding for the solution of the shock wave equations is embodied in the subroutine SHIN . b) Equilibrium

The gas composition and thermodynamic properties of the test gas at chemical equilibrium are calculated for any arbitrary set of species by a free energy minimisation method. An equilibrium program, developed for flames by White, Johnson and Dantzig (90) and modified by

Taylor (91), was matched into the shock wave solution as the subroutines

EQB and GPIVOT .

These subroutines simply calculate the mole fractions of the species at equilibrium for a given fixed temperature and pressure. The starting values for these quantities are supplied by the initial shock solution for T and P . The hydrodynamic equations for the set of mole 2io 209 fractions (xi) , calculated by. EQB and GPIVOT for this temperature and pressure are solved using SHIM yielding new trial values (T„ z,1 and p ) for the equilibrium conditions. Alternate solutions for 2 1 the tequilibriumt composition and the shock wave equations are repeated until the temperature for successive iterations is constant. 79

Unfortunately, these solutions can often diverge and the program

begins to oscillate. Details of these effects have been given in a

monograph on the computation of chemical equilibria by Van Zeggeren'and

Storey (38). Oscillations occur most frequently for systems where

the chemical reaction is strongly endothermic. Under these conditions

the equilibrium temperature (Te) is expected to be far below the

shock front temperature (T20) . However, the iteration begins with

a free energy minimisation using T 2,o and, therefore, predicts a much larger degree of dissociation than is expected for equilibrium at Te

The next shock solution for this degree of dissociation will yield a

trial value for the temperature T21, which will now be lower than

T ; a subsequent 'equilibrium/ calculation at this low temperature e will give a much smaller degree of dissociation than at the true

equilibrium. The next shock solution will give a new trial value

for the temperature T, 2, for this small degree of dissociation, close

to the shock front temperature T Successive iterations, therefore, 2 o give values which oscillate well above and below the anticipated

equilibrium temperature Te

Convergence is forced, however, by the simple device of taking

the arithmetic mean of the last two trial values of the temperature to

be the next trial value for the equilibrium calculation.

i.e. T2,n+1 - -1;- (T2,n T

where n is the number of iterations. It is apparent from the previous

considerations that

T T • T 21n -e ' 2,n-1 C Te

(or vice versa, depending upon whether n is odd or even) and that the-

mean is closer to T than either one of T e 2 n or lin In practice, the temperature was found to converos very rapidly. 80 c) The rate constants

Because the shock tube behaves like an adiabitic reactor, the absolute values of the rate constants for each elementary step change throughout the course of the reaction. To facilitate the computation, the rate constant as defined by equation EQ 4:3 is recast in terms of a polynomial for the temperature range T to T obtained from 2 o e the shock calculations. From the principal of microscopic reversability, the reverse rate constant was calculated from equation EQ 4:2 and cast in a similar polynomial form. d) Experimental data

Facilities were provided by which experimental data, taken directly from the photographic records, could be displayed on the same graphical output as the simulated profile. In this work, the property matched was always the thermal emission due to electronic transitions of the CN radical (discussed in detail in Chapter 'V). The computed intensity of the thermal emission (Ic) is simply defined by the analogue of equation EQ. 3:12 where I0 is arbitrarily set equal to unity.

Hence,

I = D / -E c N] exp k aAT) EQ. 4:4 where the apparent activation energy is supplied as input data.

However, from section 3:41 the absolute values of for the 10 experimental records is not unity and the experimental units (I my; i.e. my signal) are, therefore, converted into computer units using the experimentally determined calibration factor 10 .

i.e. I/ 1 = I _/I oxp) my o EQ. 4:5

(exp) and I - c are plotted against laboratory time uncorrected. for flow non-uniformities. The neglect of flow corrections is discussed in section 4:6 and the determination of E and 1 a o for the emission due to CN is reported in Chapter V. 83. 4:2:3 Integration

A simple marching method of integration was found to be adequate for most of the range of rate constants and mechanisms investigated.

The problems associated with Istiffnesst in the individual rate equations

(as outlined in section 4:10) are not severe probably because the rate of dissociation and other steps forming a particular radical intermediate becomes comparable (if not greater)with the rabeflow activation energy steps which remove the same radical: in consequence, the concentrations of radical intermediates are the more easily kept in balance. The major feature which determines the stability of the integration is the degree to which the ratio of radical removal to radical formation rates tend to infinity (i.e. as R r/Rf ) the integration becomes unstable.

For the investigations reported in this thesis it was found that the integration is stable if R r/Rf < approximately 103

The mathematical form of the 1st order integration for a simple differential rate equation

dc,/dt = C (t,c) written in terms of the concentration c of a given reagent involved in an elementary step, is given by

= C + At f(t Cn+1 n n,Cn) where n is the step number and At is the step length in time. The procedure used is simply to calculate the change in the mole number

(defined in section 1:8), due to reaction at a constant temperature and pressure for a time equal to the chosen step length. The temperature and pressure are subsequently adjusted to new values appropriate to the new mole numbers by solving the hydrodynamic equations using the subroutine

SHIM . This is justifiable only if the step length is small and the temperature and pressure can be regarded as single valued functions of the gas composition. 82

It is to be noted that the stability ratio Rr/Rf is sensitive to the initial value chosen for At and can be improved by reducing its magnitude. However, the optimum value of the step length usually varies as integration proceeds. A small value can be necessary for the accurate integration during the initial period, when the concentrations are changing rapidly, but this may not be suitable for the integration later in the reaction,when changes in the concentrations are relatively small and slow. Bauer et al (85), using Runge-Kutta methods, have found that the initial step length (111sec intervals) had to be increased by a factor of about 20 to enable the integration to proceed satisfactorily at longer test times. Some workers (87) have used iterative techniques to check the step length at each point in the integration. In this work, the step length is calculated at each point from the time scale of the individual reaction rates. The extra computation involved is balanced by the reduction in the total number of steps required for the complete integration.

TherateR. of the ith step 1 k i aA + bB + cC T-4- dD + eE + fF k-1 . is defined by

[D] [E] e [p] f Ri = [A]a [13 b c d

The characteristic time for the rate of change of say A due to this step is therefore

1/( din LA] /dt) = a [A] / Ri EQ. 4:6

The smallest step length is the most conservative to use and can be derived for the species with the lowest concentration, which changes in the fastest reaction step as defined by the manitude of Ri . In practice, however, longer steps are somewhat more suitable and the 2 optiuum2 value at any 83 particular point in the integration is derived from the longest characteristic time (cf. EQ. 4:6) for the fastest step. If a [A is the largest stoichiometry/concentration product for the step with the largest Ri, then the step length for the next step in the integration is taken to be

At = a [A] A Ri. INST) where INST is the step length control integer supplied as input data.

Species which appear as both reactant and product (i.e. third body collision partners or inert gases) are ignored and in practice a default value of INST = 500 is nearly always suitable.

4.:2:L. Integration control

The integration and print-out are controlled by the choice of a given species concentration (X) . Defining its initial concentration as Xn (i.e. at the shock front), the equilibrium concentration as z o X (taken from the free energy minimisation of EQB and GPIVOT) ., and e the instantaneous concentration as X , the fraction reacted in terms of this particular control species is given by

F = (X Xe) f(X2,0 ^ Xe) EQ. 4:7

The results for all the variables of the reacting system are printed out at values of F = 0.0 , 0'01 , 0'02 *** 0°1 , 0.15 0.20 ,

0°85 . At 855 of the reaction the integration is stopped.

During the course of the integration, several checking procedures

(e.g. non-monatomic variation of the control species) are conducted and, if satisfied, the integration is truncated before F = 855 . Furthermore, the concentration range is checked so that a satisfactory plot of the simulation is obtained. In those cases where the integration is truncated, the concentration range is redefined by adjusting Xe in equation EQ. 4:7 and the integration is repeated. A full diagnostic, including the description of the system at the point of truncation, is always printed. 84

1+.121.5 Diagnostic i 0/:21110.1.1. After completion of the initial simulation, further integrations to

20% of the defined reaction are performed,with selected parameters altered, in order to produce diagnostic information about the program stability and the sensitivity of the computed apparent rate (R ) to variations c of individual rate constants.

(i) The step length control integer, INST , is doubled (i.e. step length halved) to check the accuracy of the integration. For simulations

where the integration becomes unstable, the ratio of the original time for 20% reaction to that with the step length halved is several times larger than unity. Regions of instability could normally be avoided

by an appropriate choice for the control species and/or an increased

value of INST . Typically, however, the ratio of the times to 20%

reaction was always within 1% of unity and was normally less than 0.3% .

(ii)The integration is repeated to 20% of the defined reaction with the rate constant for each forward step (and hence its reverse)

doubled in turn: for i forward steps , i further integrations are

performed. The following ratios were found to be particularly useful in the elucidation of the effective reaction path for any given simulation. a) The ratio of the original time to 20% reaction to

that with ki doubled: this yields i (t1/t2) ratios.

The apparent rate of reaction to 20% (Re) is inversely proportional to the time taken and, therefore,

j2) ( ) R A R. 1 EQ. 4:8 e(l) t2:) i

However, (A Re)i is a function of the sensitivity of the apparent rate to adjustments of the ith rate constant

and may be defined by N. Rdi = A k; EQ. 4:9 85

where N. is the sensitivity factor. For the particular

casewherek.is doubled equations EQ. 4:8 and EQ. 4:9 combine to give

Ni = in (t02)/ In (2) EQ. 4:10

Thatis,N.=0ifRc isindependentofk.:and Ni 1 1 11 if R tends to c is sensitive to the value chosen for k. . 1 This sensitivity factor, for each elementary step, can

be used to investigate the degree to which a set of rate constants

has been uniquely determined. If Ni = 0 , then the

particularrateconstant(k.), corresponding to this

sensitivity factor,has not been determined. If several rate

constantshavevalueseN.which are greater than 0 the

error introduced in a particular rate constant (k1) due to an error in some other rate constant (k 2) can be estimated from EQ. 4:10 . That is, if k 2 is adjusted (by say a factor of two), the magnitude of the corresponding adjustment of ki , required so that the computed apparent rate of reaction to

20310 remains unchanged, is given by

N ln(Ak) = N 2 ln(Ak2 ) = 2 1n(2) EQ. 4:11 N1 N1

b) The ratio of the original rate of rise of intensity

to 20% reaction (i.e. Io ,„"tcAdp/_) to that with each rate constant doubled in turn. This set of ratios is the most

useful in quantitatively estimating the effect which a change

in any given rate constant will have on the emission profile.

(iii) In order to facilitate further analysis and progress in the quantitative fitting of exporimental an& simulated emission profiles, the value for all the variables, computed for 201c, reaction (e.g. 86

T2 1205 , , etc.) with each rate constant in turn doubled, are printed. This information is particularly relevant in -estimating

the effect of small changes in the rate constants upon the detailed fit

of the emission profiles.

/1.:3 The Effect of Boundary Layer Formation

It has been emphasised (33) that corrections due to boundary layer

formation should be included in the comparison of experimental and

simulated profiles, particularly at long test times. (cf. section 1:9).

For example, Modica (92) has found that, at test times greater than

1C0 pec laboratory time, these corrections can be significant.

Brabbs and Belles (93) have remarked that, although flow corrections

have frequently been applied to kinetic results, it is not always clear

from the data whether Mirelst theory (431 46) is a proper basis for

making the correction. They have investigated the kinetics of the

H -0 2 2 reaction in order to determine the effects of turbulent/laminar boundary layer formation. The transition from laminar to turbulent

flow can be a difficulty in the application of suitable flow corrections

(41). In general, however, whenlncluded, the correction to reaction

profiles is conducted by an iterative method based upon the apparent

reduction in the cross-sectional area of the shock tube presented to

the hot gas flow (cf. appendix ref. 92).

If experimental observations are restricted to test gas close to

the shock front, then deviations from the ideal shock equations are

small compared to other sources of error (33, 4.6 - discussion). At these early shocked gas times, corrections to the pressure,temperature

and density are negligible; the major deviation is likely to be due

to the extra time compression effect associated with the boundary layer

formation. Colgan (41) has used the method due to Hobson et al (44)

to obtain corrections for his measurements of the vibrational relaxation

of nitrogen at distances from the shock front before the Mirels7 limiting conditions (i.e. f> 0-1; section 1:9) have been reached. Hobson et al, 67

(44) have defined a correction factor C by

C (part) = tg where t gis the gas particle time for ideal inviscid flow and t( part) is the true gasparticle time; the factor C was presented graphically 1 as a function of /1m Colgan (41) has found, however, that for shocks where the limiting separation has not been achieved, it is more appropriate to substitute the observed separation for l (lobs) m in determining the correction factor C .

In order to estimate the magnitude of the correction applicable in this work, a few runs into a 55 BralAr mixture were conducted so that -1 the shock velocities clustered about 2.5 x 105 cm sec . Because flow corrections are most severe for shocks into test gas at low initial pressures (ID1) , the above runs were conducted for an initial unshocked gas pressure of 3 torr (the lowest used in this work). For a measurement made 10 pLsec laboratory time behind the shock front, the correction is only of the order of 10% . As the pressure is increased this will become smaller. Typically, less than 101,1sec of the cyanogen halide experimental records was over used in the analysis and flow corrections were, therefore, never incorporated in the matching of reaction profiles.

2+:4:1 The preliminary anal tsis — The apparent rate constant Y. 1

Before the detailed matching of the emission profiles is attempted, it is convenient to conduct a preliminary analysis based upon an apparent rate constant. This can be derived from experiment (Ka) and compared to the computer prediction (K0). Care must be taken, however, that K a and :0 are defined in exactly the same manner. This provides a rapid method by which the essential features of the emission profiles (e.g. time scales) can be matched to better than an order of magnitude.

The experillental apparent rate constant is given by a 1st or 2nd order expression for the apparent rate and is chosen so that the best scaling in total gas pressure and reactant concentration is achieved. The apparent rate 88 is defined by the variation of some species concentration with time.

It will be shown that, for the decomposition of the cyanogen halides,

CNX , dilute in argon and at low initial pressures, the apparent rate in terms of the CM formation is best described by a 2nd order expression

i.e• apparent rate rcA = K [CMi] [2412, dt g 210 o EQ. 4:12 where K = Ke or Ka ; the subscripts (2,o) refer to shocked gas conditions before the onset of chemical reaction; and denotes the total gas concentration. For thermal emission measurements, the rate of rise of intensity, as predicted by the computer simulation, is defined by differentiating equation EQ. 4:4..

N die/ dtg = expd (—Ea/hT210) EQ 4:13 g where it is assumed that close to the shock front, where the rate measurement is made, the temperature is constant and independent of time. Combining equations EQ. 4.:12 and 4:13.

Kc = ( die/ dtg) exp (Ea&22,0) / ( [1 ) 2,o 2,o EQ. 4":14'

From equation EQ 4:14, it is apparent that, if Y:a and Ke are to be directly comparable, the rate of rise of intensity and hence the rate of reaction must be measured in exactly the same way. An apparent rate can be defined from (i) the initial rate of rise at the shock front,

(ii) the maximum rate of rise or (iii) the average rate of rise over a fixed observation time or fraction reacted. Typically, however, exnerimental records obtained in the early stages of reaction exhibit either a concave or a convex curvature. For the former, the initial rise can be wholly obscured by subsequent events and for the latter, the initial rise may be dependent upon the time resolution and the signal to noise ratio: the maximum and average rates will be effected to a lesser degree. 89

In order to facilitate the comparison of Ka and Ke , the latter is computed internally from the integration results at each value of

the fraction reacted, F . However, in order to make due allowance for

the considerations outlined above, it is necessary to compute two types

of apparent rates of rise in the intensity.

(i) ( dI0/ dtg)1 is calculated from the slope between consecutive

print-out values of I and tg c determined by the quantity F (equation EQ. /07). Hence

(dIo/dtg)1 = (Ic(F) Ic(F.4))Atg(r) ) EQ. 4:15

From this a maximum apparent rate constant can be calculated by

substitution in equation EQ. 4:14. (ii) (di /at ) c g 2 is calculated from the time required to reach a given fraction reacted (i.e. a given intensity) from the shock front. For

an emission record rising from zero at the shock front this is simply

(dicidtd2 = IF/tp EQ. 4:16

From this an initial or an average apparent rate constant can be calculated

by substitution in equation EQ. 4:14. The physical significance of the

rates defined above is shown in figure 14.:1. In both cases, K is :c obtained as a function of the fraction reacted and hence laboratory time.

The individual kits of the reaction scheme are systematically and E . This adjusted to obtain the best match between Ka adjustment is facilitated by consideration of sensitivity factors outlined

in section 4:5 particularly the ratio of the rate of rise of intensity to

205 reaction with and without the rate constants doubled. For example

if K is say a factor of 2 lower than Ka and the ratio for a particular c k. is 1°5 then to achieve a factor of 2 increase in IC upon the next .c silnulation this particular rate constant is increased by 4/1°5 . This

procedure assumes that mall variations in the rate constants contribute 90

KVITIPU Y VALUE:; BY 1.0E-13 5b I • I I 53 I a I I 50 1 I I 46 I I 44 I I I I 41 I I 38 I I I 35 I I 33 I I I 29 1 I 26 24 I Efild 2 I 20 I I 18 I 2 I 16 I a 15 I 14 I 12 I 2 11 I 10 I 22 9I a 8I 71 6 SIMULATION BIG 1 5I 3I 2 I 1 I 0 1 1 I I 1 1 1 1 I 2 2 2 2 2 111 22 2333414 5556 66777888999 0 1 2 3 5 6 7 8 9 1 2 4 6 8 37D37C570370370370370470470470 4 7 7 0 0 4 4 7 1 7 4 4 7 ADD 0 TO VALUES OF X SHOWN. MULTIPLY X VALUES BY 1.0E -7 PLOT OF INTENSITY OF ON AGAINST LABORATORY TIME

Note:- This is a type-written copy of a computer line printer plot, generated by the subroutine 'PIOT'.

FIGURE 4:1 THE COTUUTED APPARENT RISE IN INTENSITY. 91 linearly to the apparent rate of reaction. Ka and Ke should be matched over the entire pressure, concentration and temperature range studied by one set of rate constants. A successful scheme, at this point, will predict the observed apparent activation energies and the absolute magnitudes of Ka for the range of shocked gas conditions studied. However, this of itself, is not sufficient to uniquely define the rate constants used in the reaction scheme, for although the apparent rates may agree the qualitative shapes and time scales of the simulated and experimental profiles may be quite. different. This is amplified for the particular case of matching the rich mixture cyanogen bromide profiles in Chapter VI.

4:4;2 Detailed fitting — The simulated profiles

The participation of individual steps in the overall reaction profile is readily identified by comparison of the relative rates of the elementary reactions and the species concentrations from the computer output. An example is shown in figure 4:2; the calculated values for the integration variables upon which the analysis is based and the reaction mechanism considered are shown in Append. III. In obtaining a detailed match between the experimental and computed profiles, it becomes necessary to adjust pairs of rate constants in the reaction scheme and the detailed knowledge of reaction rates, as the decomposition proceeds, is required.

The graphical outputs of the control species concentration and the intensity of light emitted are automatically plotted using the subroutine

PLOT (94). However, for fine adjustments of the rate constants, the automatic scaling and truncation incorporated in PLOT is not always suitable. Detailed comparisons of the emission profiles, due to various trial values of the rate constants for one experimental. record, should be plotted accurately using the same scale. Towards the latter stages of this work, a program (CALKIN) was developed which used the CALCOMP/

KINEMATIC facilities available on. the college's CDC 6400- machine.

92

MULTIPLY Y VALUES BY 1.0E -7 I 83 I I I 78 I 2 I 73 1 I 68 2 SIMULATION B5L 7 63 I 8 I 60 I 3.1 Region 53 I

48 / I 45 I a f 40

35 I Region... I 30 I a Region 25 / 2

20 I 2 • 18 I a I 15 I 2 i3 I 8 12 I 2 Scale Expansion: 10 I 8 I + + 7 I ga91egion -1 + + 5 I 2 3 I am 2 I2 + 0a 1 1 1 11 1 1 1 1 1 2 3111 2222 3 4 5 6 8 9 o 0 2 33 4 5 5 8 9 0 670257 2419' 6 6 8 8 2 2 2 9 1 36 8 3 8 70 2 4 6 ADD 0 TO VALUES OF X SHOWN. MULTIPLY X VALUES BY 1.0E-6 FOR a, AND BY 1.0E -7 FOR + PIO1 OP CONCENTRATION OF CN AGAINST GAS PARTICLE TIME Note: This is a type-written copy of a computer line printer plot9 generated by the subroutine 'PLOT'.

FIGURBAs,2 THE IDENTIFICATION OF REACTION ZONES 93

The values calculated for the reaction profile at each step in the integration were automatically written to a PUNCH file in a specially compressed BCD format. Suitable identifying codes were also transmitted.

The card punch output from PROM was read as input data to the program

CALKIN ; up to 10 simulations could be plotted, together with the experimental profile, on one graph. All the identification and scaling operations were conducted automatically. Because each simulation could take up to 5000 steps and in order to keep the central memory required by CALKIN to a minimum, provision was made for allocating input data, in excess of the available, core to mass storage. The coding was designed to keep the pen movements of the plotter to a minimum, thus improving the execution time. Each plot of each graph was fully and automatically labelled, identified and scaled. Unfortunately due to lack of time, not all the simulations could be processed in this manner; those that were are shown in Chapter VI. 94

CHAF1ER V

CM CONTAINING SYSTEMS

The The compounds CNX , where X a F, Cl, Br, I and CM , are classed as psuedo-halogens and are, within certain limitations, expected to exhibit similarities in chemicoophysical properties not only among themselves but also with the diatomic halogens. However; compared to the relatively simple kinetics for the decomposition of the homonuclear halogens, particularly at low temperatures where deviations from strong collision theory are less apparent, it is possible to propose many reaction steps for the decomposition of CNX . These steps can involve one or more of the decomposition products (e.g. halogen atom, cyanide radical, etc.)

5:1:1 Previous investigations

The decomposition of cyanogen has been investigated by several authors; in all cases contributions to the overall rate from reactions other than the bimolecular dissociation

C N 2 2 + M ---*- 2CN + M (R:1) were found to be important.

Tsang Bauer and Cowperthwaite (95) have studied the pyrolysis in the incident and reflected regions of the shock wave. The kinetics behind incident shocks, at temperatures below 2500K, were explained in terms of R:1 but at higher temperatures and particularly in the reflected region, it was concluded that reactions involving the formation and degradation of CnNn polymers are significant. Bauer and Watt (96) 95 have used the reflected shock technique to generate large concentrations of CN from cyanogen/argon mixtures. The rate of removal of CN in a subsequent expansion wave was measured and related to the generation and decomposition of CnNn polymers up to and including n = 6 .

Fishburne and Slack (73, 97) have extended the incident shock results for cyanogen dissociation to higher temperatures. In contrast to Bauer et al (95), however, they find that polymer formation is not important within the short residence times of the incident shock region and that rather C 2 formation, via a chain mechanism involving atomic carbon and nitrogen as chain carriers, is important.

i.e. CN + M C + N + M (R:2)

CN + C -4- C + N 2 (11:3) CN + N -4- N + C 2 (R:4)

The view that CN decomposes very rapidly via a chain mechanism involving C and N has also been proposed by Thrush et al (98, 99) to explain the intensity of emission observed in cyanogen discharge flow studies. However, in these studies, it was found that the bulk of the CN radicals formed in the discharge are removed by rapid reaction with undissociated cyanogen: the mechanism

CN + c N —±- C N + N (R:5) 2 2 3 2 was proposed.

Paul and Dalby (100) similarly report that removal via a CN + CNX step is probably rate determining in the flash photolysis of CNX (where

X also includes H ). Unfortunately, the reaction products were not identified and attempts to detect a transient C3N3 rani cal. in the flash photolysis of cyanocen proved unsuccessful. However, Paul and Dalby tentatively identify the white end product with low molecular weight polymers. Hognes and Tsai (10i) have suggested that the CN + CNX removal in the important initial step in the formation of paracyanogen, 96 in order to account for the high quantum yield (p = 3) for their photolysis of cyancgen.

Schofield Tsang and Bauer (85) have investigated the decomposition of cyanogen chloride, dilute in argon, using incident shocks at temperatures below about 2800K. The concentration of CN radicals in their ground state was monitored by selective absorption spectroscopy and was compared to calculations based upon a master rate equation

(cf. section 4:1:1) cast in terms of the following forward reaction steps.

CICN + M --÷— Cl + CN + N (R:6)

C1CN + CN-\—7 C2N2 + Cl (R:7)

C1CN + C1--->-- C12 + CN (R:8)

C 2N2 + N --4— 2CN + M (R:9)

Cl2 + M --4— 2C1 + N (R:10)

2C1CN --÷— Cl + C N (R:11) 2 2 2

For the dilute mixtures employed by Bauer et al (85),where the initial mole fraction of C1CN was only 0'005 for the bulk of the experiments, it was found that

(i) within even short time scales (less than 5 JJ.sec. laboratory time) reaction R:7 is the major route for the removal of CN

(ii)at longer test times, reactions R:8 and R:9 begin to make

significant contributions to the overall rate of formation of CN and (iii) reaction R:11 is always unimportant for dilute mixtures.

In contrast to the apparently complex decomposition of cyanogen chloride, Patterson and Greene (102) have proposed that cyanogen bromide decomposes via a much simpler mechanism. At shock front temperatures below 4000 K , an apparent rate constant, calculated from the rate of

rise of the intensity of the emission at 421.5nm due to the CN violet bands, was simply indentified with the bimolecular dissociation 97

BrCN M Br CN M (R:12)

Above 4000 K , however, it was found that appreciable concentrations of

C2 are formed within the rise-utinie of the CN emission. This was attributed to the reaction

2CN ---*- C 4. N (R:13) 2 2 but has been critised by Fishburne and Slack (73, 97, 103) who note that reaction R:13 is simply a specific case of their more generalised chain mechanism (reactions R:2 to R:4). Indeed, Patterson and Green (102) were required to include CN dissociation in order to account for the anomolous results obtained for their most dilute mixtures.

That the published kinetics for the decomposition of cyanogen chloride and cyanogen bromide are not identical is not, of itself, particularly surprising. Although the reactions of the CNX family are likely to be similar, the magnitudes of the rate constants for analogous elementary steps are probably markedly different (i.e. by orders of magnitude) because of the different heats of reaction for these steps. The H2 + X2 thermally initiated reaction, where X = Cl, Br and I (104) is a typical example of the variation in the apparent rate law for analogous systems.

In view of the apparent discrepancy between the C1CN and BrCN apparent kinetics of decomposition, it is convenient to summarise the regions investigated, not only in this work but also in the earlier studies, in the form of a gdomain? map. The region studied in this work was selected to overlap these other investigations both in the initial gas composition and temperature. This is shown in figures 5:1(A) and (B). The symbols plotted refer to:-

(i) Circles: the experimental limits published by Patterson and

Greene (102). A detailed account of the experimental conditions is not given but it appears that the richer mixtures were used predominantly FIGURE 5:1A

THE PRESSURE/CONCENTRATION DOMAIN MAP,

O PG. - ref.102 STB.- ref. 85 3 THIS WORK.

— 2.0

— 2.4 0.0 1 .5 LO G mm 1 1 0 .) FIGURE 5:1B 0 T K 2,0

PG r.71 THIS 4000 WORK

3000 T BC

PG ref. 102 TBC ref. 85

2000

THE TEMPERATURE DOMAIN 100

in the kinetic analysis.

(ii) Triangles: the individual shocks conducted by Schofield Tsang

and Bauer (85) where each point represents one run at one shock strength

and hence at one temperature. Due to the approximations involved in

the calculations (e.g. the neglect of temperature variation behind the

shock front) the kinetic analysis favours the experiments conducted on

the leanest mixtures.

(iii) Filled squares: the series of runs for a range of temperatures

at the specified initial gas composition, which were conducted in this work

(i.e. for the conditions denoted by each point an apparent activation

energy could be calculated).

The diluent gas for each of the above investigations was argon and the

shocked gas temperature at the front was always calculated assuming

complete vibrational relaxation but no chemical reaction.

:1:2 Theoretical calculations

Belford (33) has discussed the applicability of strong collision

theory to the dissociation of triatomic molecules and indicates that the

assumption is valid for the cyanogen halides. This has been confirmed

by the Monte Carlo calculations due to Bunker (105), who found that

cyanogen iodide behaves as a trandomt molecule. Furthermore, from

experiments where cyanogen bromide and cyanogen iodide were flashed

photolysed with 40 —' 90 kcal mole-1 in excess of the dissociation

threshold (106), the product CN is formed vibrationally cold,also

indicating that the internal energy is randomised before dissociation:

presumably, if internal energy randomisation were slow, at least some of

the excess energy of the flash would reside in the product CN as vibration.

Detailed calculations of dissociation rate constants, based upon a

simplified R1U model (cf. Chapter I) and using the statistical theory

due to Keck (107), have been conducted by Keck and Kalelkar (108). 101

Employing the familiar Lindemann model for activation/deactivation by molecular collisions, it was assumed that the spontaneous 1st order decay rate of A* is a function only of energy; conservation

of angular momentum was neglected. Bunker (105) has noted that in

general, this will lead to an over-estimate of the rate constant with respect to energy by about a factor of four for the triatomics.

Typically, however, the theory tends to underestimate the statistical

weight of any given energy by approximately a factor of two, in part

cancelling the angular momentum effects.

Comparing the experimentally determined rate constant to the

calculated value for 21 molecules of moderate complexity (i.e.

containing 3 to 6 atoms), the results are encouraging. In only one

case is the discrepancy between experiment and calculation outside the

expected limits: the exception was for cyanogen bromide. The

experimental results due to Patterson and Greene (102) for the dissociation

of BrCN are almost two orders of magnitude lower than the theoretically

predicted value at 3000K. This is particularly remarkable because

the agreement between theory and experiment for the analogous compounds

C1CN and C2N2 is good: viz. at the mean conditions of the experimen-

tal work (refs 85 and 95 respectively) k (calculated) is a factor of

3.2 larger than k (experiment) for C1CN and a factor of 2 for

C N 2 2 ' Keck and Kalelkar (108) have suggested that the experimental results

for BrCN are low because the assumption of thermal emission from CN

(i.e. thermodynamic equilibrium maintained between CN* and CN ) which

was invoked by Greene and Patterson (102) in the analysis of the emission

intensity records, is not applicable. It is worth noting that the

dissociation studies of C1CN and C2N2 were conducted in absorption,

where such difficulties will not be present, and the agreement in rate

constant is good. However, it will be shown in the following sections 102 that this simple explanation is not correct and that the discrepancy between predicted and experimental rate constants is probably due to misinterpretation of the reaction kinetics.

5:1:3 The thermochemistry of the CN radical

In the past the assignment of a heat of formation, AHED , of CN has been uncertain. This has, unfortunately, been reflected in the kinetic studies involving CN as a reactive intermediate. The values of AHfo(CN) obtained by a number of different workers using a variety of techniques are summarised in Table 5:1.

Bauer (95) has critically reviewed the values given in numbers

1 — 12 of this table, where the discussion is cast in terms of the enthalpy change accompanying the dissociation of cyanogen. Levitt and

Parsons (66) have discussed the values obtained in numbers 14 — 19 in terms of the dissociation energy of ground state CN . Both reviewers have favoured the lower values of (CN) and have supported their fo conclusions with further experimental studies. The very low value due to Kistiakowsky et al has been critised by Bauer on the grounds of insufficient spectroscopic resolution: re-analysis of the data by

Brewer (cited in ref. 85) has brought the value more into line with the 4 lower results of AHfo(CN) 100 kcal mole-l. Bauer has also given empirical arguments; based upon the thermochemical cycles of the isoelectronic C 2 II radical, which further support the low value. The

Jaraf Tables of Thermodynamic Data (37) and its more recent addendum (37a) favour the higher values of Knight and. Rink and White.

Boden and Thrush (99) have found that A Hfo = 100 i 3 kcal mole-1 is most suitable for the kinetic analysis of the reactions of the CN radical in discharge flow systems and also note that the similarity between the H2 + Br2 and the H2 + C2N2 reaction and a consideration of the relative energetics, effectively excludes the janaf value of —1 108•4 kcal mole . TABLE 5:1

THE HEAT OF FORMATION OF CN

No. AUTHOR METHOD Ali kcal mole I fo

1 Hognes and Tsai (101) Photo-polymerisation 100.4 nd 2 Kistiakowsky and Gershinowitz 2 Law (spectroscopic) 75•4 1 2

Robertson and Pease Kinetics of the C N + H 99.4 - 101.9 3 2 2 2 system

2 1,4hite 3rd Law (spectroscopic) 110.9 - 112.9 5 Clockler Born-Haber cycles for crystal energies 95.9 - 96.9 of NaCN and KCN

0e Long Thermochemical cycles with CH CN , 3 92.9 - 96.9 ICI and HCN

7 Stevenson Electron impact 90.4- ± 2.5 8 Brewer, Templeton and Jenkins Carbon furnace 94•4 i 6 9 MacDowell and Warren Electron impact 92.9

10 Knight and Rink (133) Shock tube X-ray densiometry 108.4 1 2

11 Herron and Dibeler Electron impact 88.9

12 Dibeler, Reese and Franklin Electron impact 88.9 TABLE 5:1 - contd

-1 No. AUTHOR METHOD kcal mole-1

13 Tsang, Bauer and Cowperthwaite (85) Kinetics of C2N2 dissociation 99.4 ± 4 sensitive to iterative technique for H (C N ) f 2 2

14. Berkowitz Graphite and carbon in a Knudsen I 109.2 cell

15 Fairbairn Shock tube study of N2 + CO2 97.7

16 Thomas and Menard Electric arc driven tube + a) 100 i 7 cylindrical model b) 118 ± 2.5 • a) broad band measurements b) narrow band measurements

17 Reis Gun tunnel 95.4

18 Whittling, Arnold and Lyle Shock tube 93.1 19 Dibeler and Liston Photo-ionisation (e.g. BrCN , HCN , 101 C N ) 2 2

20 Levitt and Parsons (66) Emissivity of CN in a shock tube pyrolysis of BrCN 102±9.5

21 Bowden and Thrush (98) 0 + C N discharge flow 2 2 100 ± 3

22 Setser and Stedman (109) Collisions of CN compounds with 103.5 metastable Argon (e.g. BrCN , HCN C ) ' 2 N2 • TABLE 5:1 — c onta

-1 No. AUTHOR METHOD kcal mole Allfo

Fishburne and. Slack (73, 97) Kinetics of C N dissociation in a 103.4. ± 2 23 2 2 shock tube

24 Davies and Okabe (110) Photo-ionisation of ICN 101 25 Berkowitz, Chupka and Walter (111) Photo-ionisation of HCN 105.5

rotes: Numbers i - 12 cited in reference 85 Numbers - 19 cited in reference 102 106

Gaydon has reviewed the thermochemistry of CN on three separate occasions and has supported (in chronological order) the values 108,

96'3 and 104.4 kcal mole-l. The latest edition (112) critically summarises the data available up to 1968. Gaydon notes that White assumed an oscillator strength of f = 0°1 in his analysis of the absorption due to CN . Re-analysing this data using f = 0.027 from

Bennet and Dalby's (113) measured radiative lifetime, establishes a -1 lower limit to White's study of 102 kcal mole . Gaydon also criticises the analysis of the dissociation of cyanogen due to Knight and Rink, remarking that A Hfo (CND 105'3 kcal mole-1 adequately fits -1 the data and that a value of 102 kcal mole cannot be discounted.

The use of a) photoionisation methods by Dibeler and Liston, b) photodissociation by Davis and Okabe (110) and c) metastable Ar(3P0) atoms with an excess energy of 270 kcal mole-1 by Setser and Stedman (113) have significantly added to the precision of the measurements of heats of dissociation because, while completely independent, these techniques share the common advantage of measuring threshold energies. From the observed threshold energy the heat of formation can be deduced. The agreement between the three methods strongly argues for a low value for

A If (CN) . fo It should be noted, however, that Berkowitz and Chuppka (111), using the photoionisation method to monitor the threshold appearance of 11.1. from HCN (in contrast to Dibeler and Listones observation of the higher energy CN+ fragment) determine a slightly larger value for the dissociation limit. This, however, could be an artefact of studying the polar HCN molecule, which also has a low moment of inertia, instead of larger non-polar molecules such as C2N2

In keeping with the concensus opinion favouring the low values, the -1 heat of formation of CN was taken to be 99 kcal mole , ihroughout the course of this work. It is to be noted that, while the RRKM calculations 107 of the dissociation rate constants for CNX were not particularly sensitive to values of Alifo (in fact Alifo = 99.4. kcal mole-1 was always used), the analysis,of shock tube data, collected from emission results, requires the determination of the absolute emissivity of CN , which is dependent upon the detailed thermochemistry (66). In their calculation of the dissociation rate constant for cyanogen bromide, Patterson and Greene (102) have used the high value of Alifo (CN) = 108'4 kcal mole-1 due to Knight and Rink and this is probably a contributing factor in the disagreement between experiment and Keck and Kalelkarts theoretical calculations.

512 Emission from Systems Containin Carbon and Nitro en

In view of the discussion given in section 5:1:2, it is appropriate at this point to review the sources of emission possible in CNX systems.

The principal emission from CN is due to electronic transitions from either the A211 (red) or the higher energy B2 E (violet) states of CN . The emission from CN exhibits the banded spectrum characteristic of diatomic molecules: this is due to vibrational/rotational fine structure. For systems in which CN emission is observed, emission from the C 2 Swan bands (green) due to the transition (3r1g- x3Fl u) is normally found as well.

:2:1 Previous investigations

Campbell and Thrush (115) have observed intense emission in the violet from N atom flames in carbon containing systems. The results indicated that the B2E state was populated in a non-thermal distribution 2 ri and emission from the A i was small. Young and Sharpless (116) have confirmed these findings, observing that the B2E state is strongly populated to the Vt = 5,9 levels with emission extending from levels as high as Vt = 15 . Brown and Broida (117) have titrated N atoms in halomethane systems and have observed similar non-thermal distributions in the blue. Similar experiments but for slightly different flame 108 compositions, have been conducted by Radford and Broida (118): the intense emission in the blue was not observed and, instead, orange flames due to transitions involving the A2 n state were produced. The A21-1 state was populated up to the V = 10 level while the emission in the violet came predominantly from the V = 0 level of the B2 L state.

These levels are known (119) to be rotationally perturbed and at low gas pressures yield extra lines (the CN ttailt bands) in the emission spectrum.

Early attempts to explain this complex behaviour in the kinetics of excitation were contradictory. Brown and Broida (117) suggested that the strong violet emission observed in their studies is due to the cherniluminescent reaction

N +. NCN N + CN* R. :1 4. 2

Thrush et al (98) have, however, conclusively identified the emission with a collisonal mechanism but where the collision partner is energetically excited. It was proposed that the energy rich collider is either the metastable A3X: u state of N2 or molecular nitrogen in its ground state but highly vibrationally excited: these species are formed by the recombination of N atoms in the discharge flow and, as discussed in section 3:2:1, the energy transfer via

N2 (A3/: u+) + CN ---4-- N2 ()CIE g+) CN* or V=n + V = 0 (X1E +) + CN N (X g ) + CIV4 ir2 2 will be efficient. Thrush and Setser (99) have also concluded that chemiluminescent reactions are unimportant in 0 + C2N2 discharge flow exeeriments.

The formation of the CN Itail' bands and the anomolous intensity distribution in N + BrCN and N + C1g7T flames has been investigated by 109

Bayes (120) and Broida and Golden (121). By 'smearing' out the rotational energy eigen values for the perturbed vibrational levels of the CN(B2Z) and the 0(A2(l) states (i.e. the V = 0 and

V = 10 levels respectively) some of the 00 transitions are preferentially enhanced relative to others. Broida and Golden interpreted this behaviour in terms of a simplified kinetic model, based upon the competition between the formation, radiation and collisional interchange of states. Above a pressure of 11 torr the collisional processes are more efficient than radiation and a quenching probability of unity was estimated for the rotationally perturbed lines of the B2E state (nitrogen as collision partner).

The spectra obtained from shock wave studies do not generally exhibit any of the above complexities. The formation of excited collision partners in sufficient concentrations to provide a major route to the excitation kinetics of emission, as in the N + C2N2 discharge flow studies, is unlikely. Furthermore, because shocked gas pressures are relatively high, collisional processes are very rapid. The wide slits and low resolution employed in shock tube studies also ensures that rotational anomolies in the emission will not be observed.

Greene (122) has monitored the emission from shock heated mixtures of the cyanogen halides dilute in argon. It was indicated that dissociation of the parent molecule to form ground state CN is followed 2 by rapid collisional excitation and quenching of both the B L.L. and

A2 Fl states. Using the reflected region to obtain highly luminous samples of hot gas, the banded structures of both the red and the violet systems were observed. The intensity of the red to violet emission decreased with increasing shock velocity/temperature; this would be anticipated for thermal emission in contrast to the characteristically weak temperature dependence of chemiluminescence. Accompanyingthe CN emission Greene also observed the green Swan bands due to C2 . Subsequent 110 experiments by Greene and Patterson (102), for shocks into cyanogen bromide/argon, apparently confirm these results for the temperature range 2500K to 7000K . Fairbairn (123) has shock heated mixtures

of carbon dioxide and nitrogen to 8000K . Even at these temperatures,

the drum camera spectrographs showed that the predominent source of radiation is the CN radical: the (2,0) , (3,0) and (410)

transitions of the red and the (0,2) , (0,1) and (0,0) transitions

of the violet were clearly visible. Besides the carbon line at 247.8nm

and some weak emission due to C 2 , no other carbon containing species was observed to emit. There was, however, a low intensity background

continuum, extending from the blue to beyond 250nm , which was identified

+ first negative and the with the N2 N2 second positive systems. Fairbairn (12)+) has also shock heated cyanogen bromide/argon mixtures to

very high temperatures and finds that, in terms of the total black body

radiation emitted at a given temperature, chemiluminescent contributions

to the total intensity can be excluded. Levitt and Parsons (66) at lower temperatures (about 4000K) have observed a strong temperature

dependence in the equilibrium emission due to CN from incident shocks

into BrCN/Ar mixtures, further indicating that chemiluminescence is

not important.

:2:2 F uilibrium no ulations of the electronic states of CN

It was noted in section 5:1:2 that Kock and Kalelkar OW have

criticised the assumption of an equilibrium population of the B2 E and

X2E states of CN , maintained by purely collisional processes. In

view of the extent of the literature, this objection does not seem to

be reasonable.

At low total gas pressures, collisional processes can become slow

and the radiative depletion of excited species becomes possible. However,

from equation EQ. 3:4, if radiative depletion is important the pressure

scaling will break down. The lowest pressure used by Patterson and 111

Greene (102) in their kinetic analysis was 1 torr (unshocked gas pressure) and yet scaling in total gas pressure is reported over a

10—fold range. Similarly, Levitt and Parsons (66) have observed a pressure scaling down to 3 torr (unshocked gas pressure) in their emissivity measurements.

In a preliminary investigation of the effect of diluent upon a) the excitation kinetics of the CN radical and b) the apparent rate of decomposition of BrCN , Levitt and Parsons (67) found that, with argon or nitrcgen as the diluent, both processes are independent of the nature of the collision partner. Monitoring the AV = —1 sequence of the violet bands, the intensity of light emitted followed the translational temperature of the shocked gas and not the vibrational relaxation of nitrogen. This contrasts with the sodium D line emission observed by Hurle (59) and is strongly reminiscent of the thermal emission from sulphur dioxide (125) and nitrogen dioxide (126) dilute in nitrogen. 1 Using the inequality P 1 >>. /(Z0[M]t ) , as derived in section

3:2 (equation P.Q. 3:/b) for the limiting condition before radiative depletion becomes important, Levitt and Parsons (67) have estimated that the quenching probability for the CN violet emission with argon is at least 0'3 : T is given by Bennet and Dalby (109) for the (0,0) transition. This is in agreement with the quenching probability with nitrogen of approximately unity, which was estimated by Broida and

Golden (115).

In this thesis, it is therefore assumed, both in the computational analysis (previously discussed in Chapter IV) and in the experimental analysis, that radiative depletion is slow and that the intensity of light emitted is proportional to the cencentratien of the ground state species. In order to analyse the kinetics of the pyrolysis of the cyanogen halides, the emissivity of the CN molecule, in the particular spectral region monitored, must therefore be determined. 112

5:2:3 The A V = —1 sequenceclttlat....CLELLz etbands_

In figure 5:2 the potential energy curves for the electronic states

of a molecule are shown schematically. r is the difference between Q e the abscissa values for the minima of the curves. Nicholl (125) has given a background to the theory of electronic transitions in diatomic

molecules and has discussed the correlation of the Condon loci on a

Deslandres diagram of the vibrational/electronic transitions, with the strength of a given sequence. For the r is small case (as in the A e violet system of CN ), the Condon locus lies along the first few diagonal

sequences, centred over the AV = 0 sequence; consequently the Ay = 0 is the mostjntense. In this work, part of the less intense Av = .1

sequence was monitored, in order to avoid the problems associated with

optical thickness noted by Fairbairn (123). The assumption that the

gas is optically thin was investigated experimentally and is reported in

Chapter VI.

5:2:4 Emission from impurities

At the elevated temperatures attainable in the shock tube, emission from impurities, which may be present in the gas phase or scrubbed from

the shock tube walls, can become troublesome. Emission from CN and

C radicals have been observed in ionisation studies of the rare gases. 2 This has been attributed to the pyrolysis of pump oil (page 219; ref. 30a)

or other organic contaminants. Charatis et al (114) have observed such

emission and Turner (128) has attributed the appearance of the green C 2 Swan bands to the recombination of gaseous atomic carbon.

In this study, much lower temperatures are employed and the background

emission from trace imnurities will be much smaller. This was checked

experimentally by firing shocks into pure argon so that the shock front

temperatures clustered about the mean temperature of the kinetic studies.

Using the photomultiplier/monochromator combination at normal sensitivity,

no emission at 421'5nm (CN; AV = —1) or 511•8nm (C2; Swan bands) 113

FIGURE 5:2

09 10 12 14 1.6 16, 2.0 r(C-N)(A) Potential energy curves for Cis REF 99 b

114 was observed. At maximum sensitivity, however, the timing photomultipliers, which monitor the total intensity radiated, detected very weak emission; just sufficient to operate the microsecond counter.

5: The Emissivity of the CN Molecule The banded structure observed in the spectra of diatomic molecules is comprised of vibrational/rotational fine structure. The transitions comprising the sequence V' Vtt = m , where m is constant, fall into a single band. The intensity of light (Im) radiated in this band can be calculated as a function of the radiative lifetime of the excited state and the vibrational and rotational populations to which suitable Frank-Condon factors must be applied. The rotational terms are included to account for the splitting due to the interaction of rotational and vibrational transitions. The detailed derivation of the expression for I m has been given elsewhere (131, 132) and was used in the intensity summation over all levels performed by Levitt and Parsons (66) in the calculation of the absolute emissivity of the CN molecule. The detailed summation for I m is tedious but, fortunately, Levitt and Parsons have cast the results for the AV = m = -1 sequence in terms of a polynomial in temperature valid for the temperature range 2000 to 10000K

Mogi Olm = -1.63787F1 -1229148 T + 0.32872E-422 - 0.8435E-1 T3 +0.34282E-1214 EQ. 5:1 This particular expression was derived for the Frank-Condon factors determined by Nicholl (129) but no incompatabilities were found in using those due to Spindler (130).

In order to relate the calculated emissivity for the whole sequence to the fraction (sal) passed by an experimental slit profile, its shape and transmission must be known. Levitt and Famous have given the low resolution spectral distribution, Ix , for the AV = 1 sequence of the B22i+ state, scaled so that fIxdX = 1 . Throughout the course of this work a triangular slit profile of half-width 7*5nm was always 115 applicable (cf. Appendix I). The fraction of the intensity passed by a triangular profile for 1001. transmission of the optical system is given by

sm = (1/tmax) f Ix tx dX EQ. 5:2 where tx is the transmission at a given wavelength X and tmax is the maximum transmission of the monochromator over the given triangular slit profile, where there is no geometrical loss of intensity. This is valid for the relatively wide slits used. The millivolt response (D X) of a photomultiplier monitoring the intensity emitted in the narrow band X to X dX , isolated by a monochromator is given by an expression analogous to the SO2 emissivity

(equation EQ. 3:13),

X i.e. Dx = LV Im sm tmaxG SA [6] EQ. 5:3 using the same nomenclature. The polynomial (equation EQ. 5:1) for logioIm defines a smooth,

10 s slightly curved variation with respect to reciprocal temperature. Log m for the experimental slit profile varies slowly and smoothly with reciprocal temperature but in the opposite sense to log10 Im . To a good approximation, the variation of log10 Im sm may be taken as linear over limited temperature ranges and can be defined by

s = I, exp (—E Im 1 aAT) where I is a constant and E is the mean excitation energy applicable T a for an experimental slit profile and is used as input data to the program

FROFIL. For the temperature range 25C0 to 4.000K Ee = 71°88 kcal mole The values calculated from EQ. 5:1 and 5:2 for Im sm are in absolute

units. It is convenient to recast this in terms of the millivolt signal -1 mole 1. for direct conversion of the experimental kinetic measurements (given in Chapter VI) directly to concentrations. This is simply achieved 116 from the calibration at 421 °5;, obtained using the emission from shock heated SO 2 as an intermediate standard (section 3:4.). Combining equations EQ. 3:13 and 5:3.

D X(s02 DX (CN) _ Lim sm ) -1 CN mv.mol. 1 f t X D0 1 ( P 2 ) x d 2 /p EQ. 5:4 -1 The calculated emissivity in mv. mol. 1. was checked experimentally for a few runs in cyanogen bromide/argon mixtures.

5:3:1 Experimental

The emissivity of CN at 421.5 nm. was checked experimentally at approximately the same temperatures as Levitt and Parsons (66): at lower

temperatures it was indicated that chemical equilibrium is not attained within the time scale of the experimental observation. Shocks into a 5/ mixture of cyanogen bromide in argon, at an initial unshocked gas pressure of

5 torr, were selected to give equilibrium temperatures in the range 3500 K

to 4500 K. The emission was recorded using a slow sweep of an oscilloscope -1 (i.e. 20p.s.cm) to display the output from the photomultiplier.

The shocked gas temperature, pressure, density and composition at equilibrium were calculated from the measured shock velocity using the

HUG (39) computer program. The following species were always included in the computation; BrCN, Ar, Br, N, N2, CN, C, C2, C3, C4, C5, C2N2, C4N4, Br2. Appropriate thermodynamic data was taken from the JANAF tables (37) except for AB:..„ (ON) - cf. section 5:1:3. Io 5:3:2 Results

Figure 5:3 shows an oscilloscope trace for a typical run. The emission char- acteristy rises to a peak value close behind the shock front and subsequently decays exponentially to a lower steady level (Is). The observed emissivity I,,/[01] was corrected for flow non-uniformities in the manner adopted by Levitt and Parsons (66). As indicated in ;.eetion

1:9, corrections to the shocked gas temperature and pressure, due to

117

FIGURE 5:3

THE IMISFjIVITY OF CT AT .421 ,rjn!a: A TYHCA OSCILLOSCOPF]

TRACING

1 E

SHOCK FRONT

Mixture: BreN/Ar; M=0,05 and P1=5 torr

Shock velocity: 2,0877005 cm/sec

118 E i:AISSIVITY OF ON

PLOTT:M IN AFaITRARY 1.',XPIE..:NTAL UNITS

FIGURE 5:4 LOG IE. / [CNi 10

:\\%.4y Solid Line: Calculated from E. 5:1 and EQ. 5:4 for the temperature range 2500 to 4500 K E 1 a(excite) = 71.9 kcal mole

oo F-

Dashed Line: Expt, results from ref. 66

0 M=0.05; Pc 5 mm. BrON/Ar This work

4 2.2 2.5 10 /T2,0 3 119 boundary layer formation at long test times, must be considered though a theoretical treatment for systems where flow and chemical reaction are coupled is not available.

In this work, the condition for applying Mirels' theory (43) was taken to be f = This has been found to be the better approximation, at least in correcting the more drastic time compression effects (35). On

Mirels' theory, the shocked gas pressure, density and temperature have reached their limiting values when f>0.1. The equilibrium measurements were always made at longer test times than indicated by this inequality. For pure argon, at Mach numbers above 6, the ratio of the temperature, density and pressure at f>0.1 compared to those calculated from ideal theory are respectively

1.07, 1.11 and 1.19. Levitt and Parsons (66) have shown that these changes can be simulated assuming that there is no coupling between flow and chemical reaction so that the latter simply adjusts itself to changes in the former.

This is readily accomplished by changing the shock velocity and initial unshocked gas pressure used in the HUG computer calculations for the equilibrium conditions until the temperature and pressure have increased by these ratios.

The experimental emissivity (IXCED, corrected for boundary layer formation as above, is shown in figure 5:4. The results are in good agreement with the experimental determination due to Levitt and Parsons (ref. 66 — dashed line) but fall lower than the predicted line using equation EQ. 5:4. No account has been made, however, for the reduction in the optical path length (and hence the volume of the emitting gas) due to the formation of the boundary layer (cf. figure 1:3:A). It is estimated that this can lead to a further correction of 20% in the direction of the theoretical line.

The kinetic results, derived from the rate of rise of the emission from ON and reported in chapters VI and VII, were obtained using the Itheoreticall line of figure 5:4, calculated for the temperature range 2500 K to 4500 K and reduced to experimental units using the inteniediate calibration against shock heated sulphur dioxide (figure 3:2). The slope of the 7 theoretical1 line gives the mean apparent activation energy for the electronic excitation. 120

CHAPTER VI

THE PYROLYSIS OF CYANOGEN BROMIDE

6:1 Introduction

In this chapter, the results for the thermal decomposition of cyanogen bromide, behind incident shock waves, are reported. Rate measurements from the time resolved emission measurements are detailed and re—cast in terms of an apparent rate constant, Ka , which can be directly compared to the apparent rate constant, Ke , obtained by using the computer simulation techniques outlined in Chapter IV.

The results of the computations are included in the discussion.

In all, three basic reaction mechanisms were investigated; (i) simple dissociation, (ii) a free radical chain mechanism and (iii) an energy chain branching mechanism. In addition, an alternative treatment of

(iii) is presented as Scheme IV. The computations are first discussed in terms of the K /K a c matching and then, when appropriate, in terms of the detailed matching of the reaction profiles. At the introduction to each scheme, estimates for the rate constants and a review of the literature supporting the proposed mechanism are given.

6:2 Results

6:2:1 The emission profiles at X = 4T21 °,

The emission records showed distinct and reproducible character which is dependent upon

(i) the shock front temperature; T20

(ii) the initial shocked gas concentration; [M] 29 ,0

(iii) the initial shocked gas concentration of cyanogen bromide;

[Brq 2,0 . 121

The temperature, pressure and mole fraction ranges are respectively

T2,0 = 2300 - 4300K , P20 = 3-24 torr and m(BrCN) = 0.005 - 0.10 .

Some typical oscilloscope tracings are shown in figure 6:1 and are discussed below; separate photographic records have been accurately traced and superimposed upon each other so that the shock fronts coincide. a) Lean mixtures (m=0.005; 0.01) - Figures 6:1(A) and (B)

At low initial pressures (3 to 10 torr) and at only

moderate temperatures, the emission intensity rises exponentially

from zero at the shock front, steadies to a linear rate of rise

and finally reaches a peak value within a few J.l sec laboratory

time. Photographed using a longer time base (e.g. 20p.sec)

the intensity subsequently decays to a lower steady level,

presumably due to reactions involving CN and the temperature

drop accompanying the overall decomposition. At higher

temperatures (about 4000K) the intensity rises rapidly and

linearly to a peak value from which it again decays. Examples

of these traces, obtained for 3torr 1% initial conditions,

are shown in figure 6:1:A. At lower temperatures (less than

2800K) the signal to noise, ratio becomes unfavourable and noise

tends to obscure the 'structure' of the initial rising portion.

As the pressure (P1) is increased, the emission records

for any given temperature exhibit less exponential curvature in

the initial rise. In other words, the temperature at which

the linear rise from zero becomes predominant is shifted towards higher temperatures. This can be seen by comparing figures _

6:1:A and 6:1 :B.

b) Rich mixtures( ,e 04,5j 0.101:agFren 6:1(D) andiEl

At the lowest unshocked gas pressure of Pi 3 torn and

as the mole fraction of cyanogan bromide is increased to

m(BroN) = 0=05 , the steady curvature, obeerved for the mid-temperature lean mixture runs, gives way to a profile SAKPLE OSCILLOSCOPE TRACINGS FIGURE 6:1 X=421.5nm

1% BrCN/Ar 1% BreN/Ar Pi=3mm Pi=20mm

a1 run 388 a;run 326 b; rr 327 ; " 384 " 2400 C; 328 0 V/cm: a=500 T2 0: C...430606- °K V/cm: a=200 T2 0: a=31d7.bK 9 0 b=3318.3 K b=50 b=2868.5K b=50 0 c=20 o=3135.6°K c=20 c=2732,2 K

Time scale for 3% Bral/Ar Arrows indicate P1 I Figures ABDE run 371 =3mm Shock Front. C M. — tisec/cm=2 V/cm: 20 T2 0: 2869.0 X [isec/cm=59

b

5% 1.1.-CN/Ar 5% BrON/Ar P1=10mm a; run 453 a;run 664

b ; 486 V/cm: a=200 b; 656 0

^.• T2 0: a=3301.7 K c; 654 V/cLa: T2 0: a=3636.9 K V/cm: b=50 T2, a=.502.D.o o 0: 0 b=20 b=3033.20 K c=20 c=2859.2 K 123

FIGURE 6:1

T HE RATE OF RISE OF EMISSION AT 421.5„„,

DUE TO PART OF THE CN VIO LET

BAND; dv -1 SEQUENCE

A TYPICAL ANALYS I S

'SLOPE

z E— 50 mycoy RUN 409

LABORATORY / 1 T IME 211SEC.

3 0.5 BRCN/A 5 525 JJSEC/METRE

T2, 7: 3528-8 K

clI S LOPE D MV LAID,

124

FIGURE 6 : 1 ©8t0

CURVATURE OF EMISSION RECORDS

RUN 182

10 1/

1 2 JiSEC..

10mm. 10% SO2 /A

SHOCK VELOCITY = 1.92680x105 m/sec.

RUN 260

50 cr)V

1 1 2 iiSEC

3 mm. 1 Bps CN IA , SHOCK 1=001 TY = 8)-1160x10 in/sec, 125

apparently composed of two linear and distinct rates of rise.

This can be seen by comparing the traces of figures 6:1 labelled

A(c); C(a) and D(b). These rates are defined by a tprimaryt

and a larger tsecondaryt slope. At longer test times the

emission record slowly decays to a lower level. As would be

expected, this double slope phenomenum is temperature dependent;

the two merging to form a single linear rate of rise at the highest

temperatures (e.g. at 3637K — figure 6:1:D(a)).

Upon increasing either the initial pressure (p1) to 10torr

or m,kIirCN) \ to 0.10, the single linear rise becomes predominant at even lower temperatures (cf. figures 6:1:E(a) and (b)) and is

reminiscent of the pressure effect observed for the lean mixtures. At the lowest temperatures studied (e.g. figure 6:1:E(c)) the traces show an approximately linear primary portion, followed by a Thumpt replacing the secondary slope of the low pressure (3 torr)-

runs; a secondary slope was not measurable for these runs.

6:2:2 The rate of rise of emission at X = 421.5nm The rate of rise of emission was measured directly from the photographs to yield (dVdtlab) in experimental units (mv signal) and laboratory coordinates (cf. figure 6:1:F). Some discussion of this quantity and its relationship to the kinetics of decomposition has already been given in terms of the computer simulated apparent rate (section 4:2:5 and 4:4:1).

For the lean mixtures, this quantity is defined by a tmaximumt rate and is compared to corresponding rates, (dI/dt g)2 1 from the simulations. For those runs where two slopes were measured (i.e. 5% 3 torr), the primary (initial) and secondary (maximum) rates are compared to the computed values (dIa/dts)2, and (dIe/dtg)2 respectively.

(dVdtiab) was corrected for the time compression effect by assuming that the density remains constant behind the shock front, at least for the period of the measurement. Hence, applying ideal shock tube theory 126

(section 1:9)

(di/dts) = cli/atiab)/( P 2,0/P 1)

It is convenient to subdivide the results into sections according

to the initial mole fractions of cyanogen bromide; plots of logs

(dVdt ) vs. 1/T2,0 are shown in figures 6:2 to 6:5.

(a) Lean mixtures (m — 0.005; 0.01)

The temperature dependence of log10 (dI/dtg) is shown in figure 6:2 for the 1-;i runs. For clarity, the results at

different pressures (fitted symbols) are shown arbitrarily

scaled by 0°9 log10 units. Assuming a first order dependence [BrCN and [11] respectively (i.e. second order in ]2,0 2,0 2 overall) the results should scale in P m ' where m is the mole fraction of BrCN . In the lower plot, the values (open

symbols) are multiplied by a factor

(9/P1 2 ). 0.01A0 = 0.09/P12m

i.e. scaled to an arbitrarily selected standard of P1 = 3 torr

and m = 0.01 . The scaled results fall upon a single line 12 (Line C I) confirming the P dependence. To emphasise the

dependence over an 8:1 range in the initial pressure (i.e. 64:1 in scaling) the lines through the filled symbols are drawn

parallel to Line C'. The temperature dependence of log10 (dI/dt) for the 15

runs is shown in figure 6:3, where the results at different pressures (filled symbols) are plotted arbitrarily increased by 2 0'6 log units. These are shown scaled by the ciP factor 10 -1 in the lower plot(open symbols). For simplicity, only the

scaled quantity is plotted for the 20 torr runs. The scaling in Pi holds for the 3 and 5 torr runs (Line C') but 127

FIGURE 612 LOG ccilid

3.0

2.0

z

1-0 >-

Q ALL LINES: Cr 2 H EXPECTED Pon SCALING RELATIVE TO T'iE 3m.m 1% RUNS. 00

Line C :=0.005 P1 mm. Circles: 3 Squares: 5 —1.0 Hexagons: 10 Triangles: 2L

Filled symbols - expt. results shifted by 0.9 Log units. Open syMbols - all results scaled to the 3mm 1% runs (no shifting) •—2.0 Solid line C - s for Figure 6:3 eca....asossawmgmarriarsismuss,wrzummasTrsnanwrgarsiantlaniftlibtrie r 2.3 2.5 3.0 3.5 4.0 4 10/T 210 THE RATE OF RISE OF INTENSITY (log units) VS. RECIPRO= TEMPERATURE FOR AN INITIAL ROLE FRACTION OF CYA!TOGEN BROMIDE CF M=0.00 : X =421.5 nn. 128 FIGURE 6:3 LOG du/d 10

30

2.0

U)

Z •

1.0 >- cc

cc A A ci0 aC 0-0

O

O

D# Line C -1.0 O • 01 M=0.01 F1 mm. A A Circles: 3 Squares: 5 Triangles: 10 Hexagons: 20 -2.0 Filled symbols - exot. results shifted by 0.6.1og units Open symbols - all results scaled to the 3mm runs (no shifting) Solid lines - the expected 1,1-m scaling relative to the 3mm runs.

,....wROORNES6•6•1.1.013T,../SWINMISPRI ORMII•MMUSI...././r11.10...0.11,1=1:1P1SMILLAMMIAGINIMMEe . 2.5 3.0 3.5 4,0 4 10 /T THE RATE OF RISE OF INTENSITY (log units) VS. RgcnorriocAL TEMPERATURE FOR All INITIAL MOLE FRACTION OF CYANOGEN BROMIDE OF M=0.01: A =L21.5 nm. 129

breaks down as the pressure is increased to 10 and 20 torr:

the line C' is the same as obtained for the 1.5 runs (figure 6:2).

!t moderate temperatures the 10 torr runs appear to fall along

a new line D' . However, as the temperature is decreased,

they begin to approach the extrapolation of Line C' to lower

temperatures: at about 2325K these runs eventually scale

with line C'. The 20 torr results also fall low relative to

the runs at lower pressures and lie along the line D' .

In both figures 6:2 and 6:3 Line C' is the same, indicating

at least a partial scaling in gas composition. The activation 102.2 energy for line C is kcal mole ,(EC ) whereas for line D', , this increases to 127'8 kcal mole—1, (ED).

) Rich mixtures (m = 0.005; 0.10) The temperature dependence of logio(dIfdt ), for the 5, 3 and 10 torr runs only, is shown in figure 6:4- (filled symbols). The rates derived from the primary slopes show an apparent

second order dependence on total gas pressure. That is, scaled to the arbitrary standard of 3 torr the results fall upon -1 the single line A' of activation energy152.3 kcal mole (EA)

The secondary slopes yield results which fall slightly higher

(Line B') than the corresponding primary rates and have a lower — 1 , activation energy of 12063 kcal mole as). As was remarked in section 6:2:1(b), it was not possible to measure a secondary slope for the 10 torr runs.

Comparatively few 10% runs were conducted and, for convenience, 9 these are shown already scaled by the A12m factor, together with the scaled 5;"! primary rate results, in figure 6:5. The points (filled symbols) are still a good fit to line A' , confirming

an apparent first order dependence in [BrCd a, u Fart of line C' is also shown in this figure: it is clear that there is a considerable divergence from line A' at lower temperatures. 1X) FIGURE 6:4

ATP= RATE C2 -.1-SE OF Ii 2:SITY (log unitc) VS. RECIPROCAL TENPEaATURE FOR CYANOGEN BRONIDE. X =421.5nm.

-1°C) M=0.05 P1mm. 'Ii5N Circles: 3 Primary slopes 73 --- 1-4 Hexagons: 3 Secondary i i

N:0_, Squares: 10 Primary ii , C) Line A 0-- 0 Filled symbols - unsealed results -2.0 Open symbols - tprimaryt rates scaled by 9/P iCO i.ea relative to 3mm 15 conditions. Lines - see text.

LJ 2.5 219. 3.3 3.7 4 1 0 / T 133.

FIGURE 61;5

THE APP' REM RATE OF RIDE OF INT=ITY (log units) VS. RECIPROCAL TEMPERTURE FOR CYANOGEK BROMIDE;X=h21.5nra. (PRIMARY RATES ONLY; AIL 2 , RESULTS SC LED BY 9/P, 01 )

\Line C'

M=0.05 N=0.10 P, mm. C) 0 3 10

Secondary rate not observable for E=0.10.

La= A — d for i'•.;'-1--C.C) 6 :4 •

2'9 3.3 3 132

(c) Intermediate mixtures. (m = 0.02; 0°03)

The notable feature which arises from the comparison of the lean and rich mixture results is the increase in the apparent activation energy as either a) the initial mole fraction of cyanogen '—omide is increased or b) the pressure is increased.

It is, -)fore, appropriate to check the activation energy at intermediate gas compositions. Consequently, a few runs in 274 and 3 BrCN/Ar mixtures, at an initial pressure of 3 torr were conducted. The temperature dependence of 2 logio (dI/dtg) for these runs, scaled by the 9/P1 m factor, is shown in figures 6:6 and 6:7 respectively.

The rates of rise of intensity for these intermediate mixtures fall between the high rates observed for the lean and the low rates observed for the rich mixtures (dashed lines).

This feature and the appearance of a secondary slope, at the low initial pressure of 3 torr , follows the anticipated progression from lean to rich mixture behaviour. Furthermore, the activation energies, calculated only from the primary rate measurements at this pressure, also fit this progression.

i.e. Etlan and Em = 102°2 kcal mole-1 (7'—c0 \2/-1 -1 E( = 137.8 kcal mole ) -1 E g = 146.0 kcal mole ) -1 E(5%) and E(1%) = 152.3 kcal mole (EA)

As expected, the 2% and 3 results do not scale in m

The pressure dependence was not investigated for these mixtures and, because of the apparent complexity in this region, no attempt was ever made to simulate these experimental reaction profiles on the computer. 133 FIGURE 616

( (0 2.5 LOG ditcPc, ;.,/ Pi co 10

2.0

›- CC cc Lean Mixtures: (M=0,005 to 0.01 cc P1 =3 to 10 mm.) 0,0 •Rich Mixtures: (M=0.05 Co 0.10 P1 =3 to 10 mm.)

a Primary slopes 0 Secondary slopes 1.0 (M=0.020 P1=3mm) Scaled to 3mm 1%'runs - Figure 6:3 Dashed lines — Linea Al and C' taken from figures 62 and 6:3 1.5 ; .__...--R.orr4:,!ewa.rr-avar.acarwa=,ro..-,raqk,Aanliritr-aiknIIItaIr,on ata.CIVSII:ITXeanCra-TE•ararm,.EZV,nfcr&ZIK.L,,ai,9•2 V.( :..1-itr,=..Sklia0MICIMIT 2.5 • 3.0 4 4 .C- 1 0 / T20 THE APPART RkTi;; CP RISE OF INTEHSITY (log units) VS. RECIP7ZOCAL TEI.TATURE FOR CYANOGEll :BROMIDE X11.21..5nm. 134

L 0 G (d i/d 9.(Pi2m) FIGURE 6:7 2.0

U) z 1.0

CC

CC F- 0 CC Lean Mixtures: Ns\(M=0.005 to 0.01 P1-3- to 10 mm.) 0'0

Primary slopes Secondary slopes <:„ (M.0.03; P =3 m) Scaled to 3mm 1/0 runs - Figure 6:3 17(\;\

Dashed lines - Lines A' and C' taken from Figures 6:2 and 6:3

2.5 3.0 3.5 4 / T 4.0 1 0 2,0 THE APPARENT RATE OF RISE OF INTNSITY (log units) VS. RECIPROCAL TEMPERATURE FOR CYANOGEN BROMIDE

=421.5nm. 135

Before attempting a kinetic analysis, it is important

to check that this complex variation of the apparent rates with

composition is real and not due to some other artefact. The

only feasible sources of systematic error which could represent

a significant contribution to the overall rate (besides

contamination effects which are discussed later in section

6:L..:2) arise from problems associated with inadequate time

resolution and/or optical thickness.

(d) Time resolution

If the shock transit time across the observation slit

is long compared to the emission rise time, then the

oscilloscope trace can exhibit curvature of the initial rise

due to

(i) the monitoring of reflections, etc. before the

arrival of the shock front.

(ii) the time required to fill the integral volume V

'seent by the photomultiplier (cf. appendix II. ref. 35).

The time resolution was checked experimentally using the

sharp rise of intensity due to shock heated sulphur dioxide

(55, 56 and see section 3:4). The rise time for the emission

fromshockheatedBrWAriscomparedtothatforsO,Arin 4 figures 6:1:G and 6:1:H. The shock velocities are similar and

typical of the mean conditions of this work.

The SO2 emission reaches a peak value within illsec

(rise-time (10-901 = 0.5[Isec). This rise-time is long

compared to the equilibration of energy among the degrees of

freedom (including electronic) available to SO and is, 2 in fact, just that expected from the optical geometry. The

emission from BrCN/Ar , however, shows the pronounced curvature

characteristic of the mid-temperature, lean mixture decomposition.

This curvature lasts for some 2211sec continuing to approximately 136

2070f of the peak emission and cannot be due to the rise-time of the apparatus. The latter, however, does represent a limit to the time resolution of kinetic measurements and determines the upper temperature, for any given gas composition, at which reliable rate measurements can be made. The lower temperature limit is set by the signal to noise ratio and the shape of the emission profiles. At the lowest temperatures studied, for all mixture compositions, it became difficult to resolve a linear rate of rise in the emission profiles.

(e) Optical thickness

The choice of monitoring the A v = -1 sequence of the

CN violet bands has already been discussed (section 5:2:3) in terms of the onset of optical thickness for other seauences.

The fall-off in the apparent rate of rise of intensity with increasing initial concentration of cyanogen bromide is also reflected in the dependence of the peak height upon the gas composition. It was thought possible that for large concentrations of BrCN , large concentrations of CN could be formed and optical thickness could become a problem.

The largest concentration of BrCN used in this work was for the 1 20 torr runs. A few runs were conducted under these conditions in the temperature region where the falloff in the apparent rate occurs (cr. figure 6:3) with a 905 reflecting mirror placed over the window opposite the central observation station. Within the experimental scatter, the results confirmed that the gas was optically thin.

Furthermore, if the fall-off in the apparent rate of rise of intensity were due solely to optical thickness, it would be exnected that the 5 and 10;,/, runs would not scale in

[BrCd 2,0 ; however, the rates do scale (figure 6:5). 137 Further evidence for optical thinness is available from the

equilibrium study of the emissivity of CN behind incident

shocks by Levitt and Parsons (66) and the agreement between this

work and the absorption measurements for C1CN/Ar shocks by

Bauer et al (85) — discussed in Chapter VII.

6:2:3 The apparent second order rate constant (Ka) The experimental rate constant (Ka) is defined in the same manner as .0 (section 4:4:1) in terms of the rate of formation of ground state CN and hence the rate of rise of intensity at X = 421•5nm. Taking the results for the rich and lean mixture sets independently, the overall 2 second order scaling (P1 m) fit is appropriate (figures 6:2 to 6:5).

To a first approximation, therefore,

(d [CN] /dt ) = K [BrCN] g a 2,0 [M] 2,0 EQ. 6:1

More precisely, the apparent rate constant is defined by

Ka = (dlidtlab)/ [BrCN] 2,0 ["] 2,0 (P2,0/P1)

EQ. 6:2 where I is in the experimental units and is the emissivity (I/ [0] ) at the shock front temperature T2 0 ' evaluated from the calibration graph (figure 5:4).

The apparent second order rate constant is plotted, as log 10 Ka , against reciprocal temperature 2, 0) in figure 6:8 for the rich (1/T mixtures only. The temperature dependence for the lean mixtures is shown in figure 6:9. The solid lines represent the ?trend? lines adopted for the various mixture compositions (i.e. trend line A of the apparent second order rate constant is derived from line A' of the rate of rise of intensity (figures 6:4 and 6:5). Similarly, trend' lines B, C and D for

Aa are derived from lines B' , C' and D' respectively. These trend lines are used later in the computer matching of Ka and K . The activation energies are summarised in Table 6:1 over. 138

7.5 FIGURE 6:8

THE APPARENT SECOND ORDER RATE CONS.= (as log Ka) FOR THE DISSOCIATION OF BrUN IN RICH MIXTURES; M=0.05 AND 0 M=0.10. ALL WITH ARGON AS DILUEKT.

7.0

Secondary Slopes TREND LINE B

cs 00 O

_J 6.0 N=o. 05 m=0.10 Pi mm. o 0 3 Primary O 3 Secondary 10 Primary Primary Slopes TREND LT. 1TE A

5.5 SECONDARY RATE CONSTANT O_TLY OBSERVABLE FOR THE 3mm 5% RUNS.

2.6 3.0 3.4

139

FIGURE 6:9 L OG 8.0 10 NOTATION IN TEXT. O

\STE LINE K =P(ZT°•5/ )(D/RT)2exp(-EiRT) d 2 7.5 P=1.1

7,A Ti 0 \ LINE LEAN MIXTURE 7.0 TREND LINES C AND D

LINE C

6.5 RICH MIXTURE A TREND LINES A AND B

LINE A

60.J

LINE D PG LINE Xa =2• Ox109T"5exp(-90500/RT)

5.5

2.5 3.0 3.5 4.0 I 0/T

THE APPARENT SECOND ORDER RATE CONSTANT (AS LOG Ka) FOR THE DISSOCIATION OF BreN IN LEAN MIXTURES; M=0.005 AND M=0.01 ALL WITH ARGON AS DILUENT.

INITIAL TOTAL GAS PRESSURE MM 11=0.005 (P1) M=0.01 0 3 0 5 0 10 A 20 0 fa 2h - ALL LINES - SEE TEXT 140.

TABLE 6:1

The Apparent Activation Energies

Mixture Trend linem P (BrCN) 1 torr Ea kcal mole-1

A(primary) 0'005; 0.10 3•• 10 82.1 RICH B (secondary) 0.05 3 47'8

C 0.005 3 - 24 28 LEAN 0°01 3 and 5 .

D 0'01 20 64°6 (and high T; 10 torr) " 1

The dashed lines of figure 6:10 represent the rate constant for the bimolecular dissociation of cyanogen bromide: (1) as measured by Patterson and Greene (PG Line — ref. 102) where

9'3 1 .1 kd = 10 T2 exp(-90000/RT) 1.mol.— s. EQ. 6:3

The dissociation energy of cyanogen bromide was taken to be 90.5 kcal mole and is based upon the heat of formation of cyanogen deduced by Knight and

Rink (133). This corresponds to the high range of A H (CN) discussed fo in section 5:1 :3.

(ii) as calculated from the theoretical prediction due to Keck and

Kalelkar (i Line — ref. 108) obtained by a statistical approach to

unimolecular decomposition. In these calculations, D(BrCN) was taken -1 to be 83 kcal mole based upon the enthalpy of dissociation of cyanogen

observed by Bauer et al (85) and, therefore, in close agreement with the lower concensus value for A Hfo(CN) adopted in the present work. 141

The bimolecular rate constant (kd) was calculated from the predicted quasi-unimolecular rate constant (kuni.) assuming that

kd = k(uni) [M]

holds over limited pressure and temperature ranges. For a mean

experimental temperature of T2,0 = 3300K , for [141 = 1074687 and 6.8 -1 -1 m = 0.8 k = 10 d 1.mol. s. The temperature dependence as plotted is taken directly from the calculations. of Keck and Kalelkar; i.e. -1 Ea = 63 kcal mole (iii) as estimated from the rate constant for the dissociation of the

analogous compound, C1CN , Schofield Tsang and Bauer (STB Line - ref. 85)

have measured kd(C1CN) using A HfoCN=99°4 kcal mole-1 for the temperature range 2000 - 2800K.

f = exp(- 91500/RT)1.mo1: EQ. 6:i. kdk C1CN) 1013.53 1 s:1

Re-writing the Kassel equation (EQ 1:8) for the dissociation rate constant of XCN N nk-1 P( rv)Z0()XCN)/ItT) exP(-D(X0N)/1111) k d(XCN) = X4- EQ. 6:5 (nK-1

Equating EQ. 6:4 and EQ.6:5 and taking /ix equal to the maximum number

of vibrations for the linear XCN molecule (i.e. nK = 3), the rate constant for C1CN and BrCN can be calculated. Assuming a collision

kcal mole-1 P,C1CN) = 1.1 diameter of 3A , then for D(C1CN) = 95.5 k at the mean temperatures of the experimental investigation (T201 (mean)

2600K). To a first approximation

13, = p, (BrCN) kC1CN)

can be estimated from equation EQ, 6:5, where Di and k (BrCN) kBrCU) = d -1 82.5 kcal mole . The corresponding temperature dependence given by EQ. 6:5 and represented by the curve STB fits a simple Arrhenius expression over 142 1 the experimental temperature range with E 74. a = kcal mole • It can be seen that the magnitude and temperature dependence of

K a for the rich mixtures is similar to that predicted by simple dissociation; especially the RRK expression. However, measurements

of K a alone cannot distinguish between a simple dissociation (Scheme I) and a chain mechanism (Scheme II) discussed in detail below.

6:2:4. Errors

The major sources of systematic error are as follows:

(i) Pressure measurements, using the double manometer techniques,

could always be made to within I 2% ; this is small compared to other

sources of error.

(ii) The error in the calculation of the shocked gas temperature

is essentially determined by the accuracy of the shock velocity measurements.

It is estimated that T2 ,0 is known within — 30K or approximately 1% for the mean conditions of this work.

(iii) The largest error arises from uncertainties in the initial

absolute calibration of the photomultiplier response to incident radiation.

Levitt (4.7) and Sheen (35) have discussed the sources of error in applying

equations like EQ. 3:13. The'luminous /slug? of gas, between the shock front and the contact surface, acts as a diffuse light source with

ill—defined boundaries. As a consequence, uncertainties are introduced

into the calculation of the volume of the hot gas tseent by the

photomultiplier. It has been estimated that errors from this source

could be as high as ± 50% in individual values of the absolute intensity

with 120% in the variation with wavelength. The more recent absolute

calibration due to Levitt and Parsons (66, 135) indicates that this is

an over—estimate and that the error is probably less than t 30% in

the absolute intensity.

The major source of random error is in the measurement of an apparent

rate rise of intensity; for some runs it was difficult to discern a linear rising portion in the experimental record, from which an apparent 143 rate of rise of intensity would be made. It is estimated that the absolute value of the experimental apparent rate constant at any given temperature is not known to better than — 50% . The interpolation techniques employed, however, will reduce this by at least a factor of two.

6:3 Scheme I — A 'Simple' Dissociation Mechanism

The simplest scheme to adopt fo'r the initial computer simulations is to restrict reaction to the forward bimolecular dissociation and its reverse

kd

BrCN + M Br + CN + M (R :1) k r In the present study, contributions to the total rate due to different collision efficiencies of the various collision partners are not included because a) at the low mole fractions of cyanogen bromide used the concentration of all other species, except the diluent argon, are small within the experimental time scale and b) a preliminary investigation (67) of the pyrolysis of BrCN dilute in argon and nitrogen respectively, indicated that the rate of reaction is independent of the collision partner. Scheme I is similar to that proposed by Patterson and Greene (102) for this temperature regime.

Initial estimates for k d , as used in the computer simulations, were taken either directly from Patterson and Greenees measured rate constant, or from analogy with the cyanogen chloride results of Bauer et al (85) i.e. P, ‘,BrCN) = 1.1 °

6: Discus ion — The computer 7eredictions for Scheme I

The computed and experimental apparent activation energies and the

and K absolute values of K0 a at the mean temperature of 3300K are compared in Table 6:2. The trials quoted are representative of all those undertaken. For each trial value for kd , the emission profiles were constructed for the pressure range P1 = 3 -- 20 torr and for six TABLE 6:2 THE COMPARISON OF THE COMPUTED AND EXPERIMENTAL RATE PARAMETERS FOR SCHEME I

(T20 = 3000K; P1 = 3 to 20 torr)

Trial ka m Trend log10 Ka log10 Kc Ea T.:0 1 -1 -4 -1 1 -1 No. 1.mol. s. (BrCN) Line 1.mol:1s71 1.mol. s. kcal mole kcal mole 0.05 A 6-24 4•55 82.1 91.4 0.05 B 6.61 • 47°8 i 109.3 T0.5exP(-4554)c/T) 0.01 C 7.29 4.55 28 91.6 0.01 ' D 6.83 4-55 64.6 91.6 0.005 C 7.29 4-55 28 91.6

o-o5 A 6.24 6.20 82.1 89.7 0.05 B 6.61 47-8 10.63T 2 10 0-5exp(-455 1I1,/T) 0.01 C 7.29 6.22 28 90.4 0.01 D 6.83 6.22 64.6 90•5 0.005 C 7.29 6.22 28 90.4

0.'05 A 6.24 6.20 82.1 80.2 0'05 B 6°61 4.7.8 3 1011'57 m0.5exp(-41491/T) 0.01 C 7.29 6.22 28 81.4 0'01 D 6683 6.22 64.-6 81.6 0 .005 C 7.29 6.22 28 81'4 Table 6:2 contd , E E Trial ka, m.Trend log10 Ka logi0 Ka a c 1 I -1 -1 -I -I -1 -1 No. 1.mol. s. (BrCN) Line 1.mol. s. 1.mol. s. kcal mole kcal mole 0.05 A 6.24 7.42 82.1 70.0 0.05 B 6.61 47'8 4. 1018.77 T-1.5exp(-41491/T) 0.01 C 7.29 7.48 28 70.4 0.01 D 6.83 7'48 64.6 70.4. 0.005 C. 7.29 7'48 28 70.2

0.05 A 6.24. 6.4.8 82.1 73.0 0.05 B 6.61 47'8 5 1017.73 T-1.5exp(-4.14.91/T) 0.01 C 7.29 6.48 28 73'8 0.01 D 6.83 6.4.8 64-6 73.8 0.005 C 7.29 6.48 28 73'8

Notes:- Trial No. k" d from Patterson and Greene 002) 99 Trial No. 2 - Dissociation energy, D(BrCrT), adjusted to comply with Hfo(C = kcal mole 1.1 Trial No. 4 - 7stimate from Bauer et al (85) where P(C1CN) = P(BrCN) 146

temperatures approximately covering the experimental range. The

values of K and K a c were obtained by the method of interpolation and the computed apparent activation energy was calculated applying an

Arrhenius expression to the temperature dependence of K c . The results are discussed by grouping the results into the natural categories

of RICH and LEAN mixtures.

a) Rich mixtures

The activation energy observed for the 'primary' rate constant (i.e.

derived from the primary rates of rise of intensity) could be approximately

matched in Trials 1 and 2, if the high activation energy observed by

Patterson and Greene (102) is adopted (i.e. E .1 a = 9045 kcal mole ). In trial (3), kd is adjusted by taking Greene and Patterson's measured

rate constant at 3300K and recasting the equations using a more realistic 1 -1 activation energy of 8245 kcal mole based upon AHfo Cr. = 99 kcal mole The fits to the apparent activation energy for the primary rate constant

(and the absolute values at 3300) are improved (cf. Table 6:2 no. 3).

However, the computer profiles for Scheme I never matched the

experimental records, particularly at low temperatures. The computer

profiles always rose linearly from zero at the shock front, eventually

falling—off to a plateau region, due to the effects of the reverse step

(R:1), the depletion of reactant and the temperature drop accompanying

the dissociation. It was not possible to simulate the secondary rising

portion observed for the 50 3 torn runs.

It is appropriate to note that Patterson and Greene employed slower

oscilloscope time bases to record the emission history. In effect, this

will tend to obscure any secondary rising portions and the measurements

will correspond to an average rather than an initial or maximum rate.

As can be seen from Table 6:2, the computed activation energy was

always close to that expected from the dissociation energy and the type

of expression used for kd . This simply indicates that, in the computed profiles, the contributions to Kc from temperature and reagent depletion 147

effects are small. Also from the computer print-out of the forward

and reverse reaction rates, the latter was always relatively slow and

played little part in the decomposition within the time scale of the

experimental measurement. b) Lean mixtures

Simulations for the lean mixtures were, similarly, inadequate in

matching the shape of the emission profiles and Kc . Indeed the

discrepancy in Elc was even more marked as is evident from the apparent

activation energies computed for these mixtures (cf. Table 6:2). The

computer simulations could never predict the anomolously low experimental

activation energy observed for trend line C (figure 6:9).

6:4 Scheme II - I Simple Chain Mechanism -1 k A kcal mole d Ho

(R:1) BrCN + M -{-----4- Br + CN + M 82.5

(R:2) BrCN + CN --->- Br + C N -42.3 --4--- 2 2

(R:3) BrCN + Br _It:. Br2 + CN 37.0

C N (R:4) 2 2 + M _.<._.-÷- 2CN + M 124.7

(R:5) Br2 + M qt 2Br + M 45•5

(R:6) 2BrCN Z Br2 + C2N2 5'4 considered but not effective

This scheme is essentially the analogue of that proposed by Bauer

et al (85) for the decomposition of C1CN : Bauer et al, however, did

not include the reverse steps in their analysis.

L1)71121111.2,1e1 estimates for the rats constants

Reaction R:1 (kA; BrCN + Br + CN + M

Prom the results and discussion of scheme I, a Kassel type

equation was always used for the dissociation rate constant, 148

where nk = 3 . For comparison, the P factors for the dissociation of molecules containing two to four atoms are reviewed in Table. 6:3.

Compared to the other triatomics where P is of the order of 1/20 the result for C1CN is high. It would be expected

that the cyanogen halides would be intermediate between the

diatomics and the polyatomics in behaviour. Strong collision

theory should apply, because of the probable rapid relaxation of vibrational energy via the low bending frequencies present,

and contributions to the pre-exponential from entropy terms

should be insignificant (i.e. AS4* 0 ; cf. section 1:30). However, it is to be noted that the P factor for the

dissociation of the linear C 2 N2 molecule is high compared to that of the halogens. It has been suggested (95) that the

C » N group, although strongly bonded, does not act as a rigid

body and the C - C bond becomes elongated in the transition state, destroying the linearity of NC - CN and, consequently, introducing entropy terms from the increased degrees of freedom

(i.e rotation). The cyanogen halides possess only one -CN

group and contributions to the pre-exponential from entropy terms are unlikely to be significant.

It is to be emphasised, however, that the comparison of P

factors can only yield an order of magnitude estimate for the rate constant because,

(i)the collision diameter (cr) required for the calculation of Z o (1Q. 1:2) is rarely known (ii)the determination of the temperature dependence

Tm = T" . T(mk-i) of the pre-exponential by fitting observed and calculated activation

energies cannot normally define n to better than - 7-2 . For 149

TABLE, 6:3

THE COMPARISON OF THE P FACTORS FOR THE

DISSOCIATION OF SOME SMALL MOLECULES

kd = A T1- (D exp(-DIRT) RT

Molecule Collision -n Cr a P—A Temperature Ref. Partner ~ 70 Range

2 4.2 0.3 1550 - 2650K (9) Cl2 Cl2 0.75 (b) Cl2 Ar 2.087 3.42 0.03 1000 — 1200K (c) Br2 Ar 1.97 3.42 3.64 (a) 02 02 3 0.07 3000 — 5000K (e) 02 M 2 3.64 0.21 2800 - 5000K C1CN Ar 2+ 3.0+ 1.1 1000 - 2800K 85 2.85 0.085 2600 - 3700K 134 CF2 Ar 3'42 0.62 Ar 2+ ' 3.0+ 0. NO2 5 20 03 ' Ar 1.75 3.04. 0.052 1400 --2300 (f) Ar 2 3.0+ 0.05 SO2 58 2.35 3.0 0.5 1400 - 2000 (g) NF2 Ar ONC1 Ar 3.43 3.0 0.29 880 — 1350 (h) 0.33 1700 — 2500K 95 C2N2- Ar 5.5 4.0

rotes :-

+ indicates an assumed value. 150

NOTES TO TABU 6:3

(a) HIRAOKA, H; HARDWICK, R; J.Chem.Phys. 2.) 1715 (1962)

(b) JACOBS, T.A; GEIDT, R.R; J.Chem.Phys. 39 744 (1963)

(c) PALMER, H.B; HORNIG, D.F; J.Chem.Phys. 26 98 (1957)

(d) MATTHEWS, D.L; Phys Fluid. 2 170 (1959)

(e)LOBB, R.K; 'Hypersonic Flow' Ed. A.R. CALLAR; J. TIMER (Butterworth Scientific Pal. (LOTT) 1965 p.45)

(f) JONES, W.M; DAVIDSON, N; J.Amer. Chem.Soc. 64 2868 (1962)

(g) MODICA, A.P; HORNIG, D.F; J.Chem.Phys. 24_3 2739 (1965)

(h)DECKLAU, D; PALMER, H.B; .8th Symposium (Int) on Combustion, • p.139 (1962) 151 example, the dissociation of CF2 (134) has been fitted with

n = ± 0°64 . This uncertainty is reflected in the determination of the P factor even ignoring the effects due to (i) above. If entropy terms are indeed unimportant, then from the P factors for other triatomic molecules, such as NO2 (54) and SO2 (58; and refs cited), a lower value of P, kBrCN) of about 1/20 is indicated. It seems likely, therefore, 1 that P(BrCN) lies within the approximate range /20 to unity. As in initial estimate the lower value was sP1 ected;

i.e. k = 2•5 x 1017 T-1'5 d exp(-41491/T)1.mol:13:1

Reaction R:2 (k2); BrCN + CN --->- C2N2 + Br

This is a metathetical (transfer) reaction which may be treated as

A + BC —4-- AB + C where A and B represent semi-rigid ON radicals. Radical/ molecule reactions of this type frequently possess (i) activation energies which are only a small fraction of the bond to be broken and (ii) P factors in the range 10-3 to 101 . Typical reactions have been summarised in standard texts on kinetics (3, 4, 71) and tables (136).

Of particular interest, however, are the reactions of CN radicals with various molecules. Some are detailed in Table 6:4; all the reactions quoted are exothermic. The activation energy for such reactions is frequently termed the

Itruet activation energy and is expected to be of the order of -1 a few kcal mole . Indeed Sernenov (71) has reviewed the activation energies for 65 exothermic reactions and finds that

± r. - Ea 5 kcal mole. The low rate constant obtained by Paul and Dalby (100) TABLE 6:4 REACTIONS INVOLVING THE CN RADICAL

(AHfo(CN) = 99 kcal mole 1)

) REACTION -1 1 AHo (kcal mole k(l.mo1.1s. - ) Ref.

(1)0 721. + 02 ----)-- NCO + 0 -24 109'64(1'0'3) exp0)f /hn:11) 96 (2) CN + CH ---*- HCN + CH3 4 k2/k1 = 0.15 98 CE + H -->-- HCN2+ H -17 k k = 0.05 (3) 3/ I 98 CN + NO --±- CO + N2 k4/k = 0 06(t0.05) (4) -148 1 98 (5)CN + NH ---4- HCN + NH k /k = 1 2±0.2 98 3. 2 -81.6 5 1 10 (6)CN + H2 ---÷- HCN + H -18 10 exp ( -7000/RT) 98 (7)CN + C1CN---*-- C2N2 + Cl 109.0 exp( --6000/RT) 85 (8)CN + C2N2 -->- products+ - 107.86exp (-2100 T ) 100 (9) CE + C1CN--)- products - 106.33 exp( •-•,2100/RT) 100

products not identified ++ estimated from the measured rate of (9) and the activation energy of (8) . 153 for the reaction CN + C N 2 2 (No. 8 of Table 6:1+) has been criticised by Boden and Thrush (99), who estimate a rate 100

times larger at 678K in their discharge flow experiments.

Paul and Dalby have also reported a rate measurement for the

CN + C1CN reaction (No. 9 of Table 6:1+) but did not investigate the temperature dependence. However, assuming that the

activation energy is the same as was determined for the -1 CN + C2N2 reaction (i.e. Ea = 2'1 kcal mole ) then a low rate constant for CN + C1CN is indicated. Unfortunately, Paul and Dalby did not positively identify the products of this

reaction and the thermochemistry cannot, therefore, be calculated.

But extrapolating the rate constant for C1CN , derived in 6416 the above manner, to 2500K k = 10 • This is approximately 1/200 of that given by Bauer et alts (85) shock tube study 8-48 at this temperature; i.e. k = 10 • This discrepancy is similar to that found between Paul and Dalby (100) and Boden and

Thrush (99) for the CN + C2N2 reaction.

Boden and Thrush have also measured the rate constant for

CN +02 —4-NCO + 0 and- have determined the rate of CN + X where X = CH , 4 H2 and NO , relative to this reaction. Using a collision diameter of 3R , these reactions have P factors in the range 2.5 x 10-3 to 5 x 10-2 . As a preliminary estimate for k 2 , the higher value determined by Bauer et al (85) and Thrush et al (99) were 1 used; i.e. P 110 .

8.7 i.e. k(2) = 10 T2 exp (-1000/T)1.mo1:1 s:1

Reaction 11.1 Oc ; arm Br-4— + CN

This is the simple form of the metathetical reaction, where the collision involves only atomic and molecular species. 154

These reactions typically have P factors of the order of 1 1 to /10 and activation energies close to the heat of reaction (Table 4:41 ref. 4). To a first approximation, therefore, k was chosen so that E = AH and P 1/6 3 3 T

i.e. k = 109 T2 exp(-14595)1.mol:1s.1 3 T

Reaction R:4 (1/4) ; C2N2 + + M

The rate constant for R:4 is known from the shock tube study of the dissociation of cyanogen due to Tsang, Batter and

Cowperthwaite (95). This was confirmed to within 5% (well within the experimental error) by Schofeild Tsang and Bauer (85).

Fishburne and Slack (73, 97) have combined their high temperature emission results with the low temperature absorption results due to Bauer et al to yield

8 : (E/ -E -1 1 k = 3.71 x 103 T1 exp ( /RI') 1.mol. s. where E = 129 kcal mole ; the combined temperature range was 1700 - 4000 K . However, the analysis in terms of a reaction half-life neglects the effects of side reactions and temperature changes. Furthermore, the need to employ 18 square terms in the expression seems unduly high. In the analysis of the present emission profiles k was regarded as a known quantity and the value obtained by

Bauer et al (95) was used.

r -4 -1 i.e. k, = 1033'45 T-5e0 exN-02907/T)1.mols.

Reaction R:5 (k5) ; Br2 +N 2Br + N

The rate constant, k5 , is known from the precise and detailed shock tube study of the dissociation of bromine by 155

Warshay (137). The activation energies and relative collision efficiencies for argon, neon and krypton were determined, over the temperature range 1200 - 2000K. Throughout the course of this work the diluent was always argon and

k = l08.34 T1 e 5849/T)1.moit1 s 1 5 was always used.

It is to be noted, however, that Warshay (138) has re-analysed his results, carefully allowing for flow corrections.

Although the results are slightly different (i.e. lower activation energies) the discrepancy will not cause a large difference in the calculated bromine atom concentration because, at the temperatures of this study, equilibrium between bromine molecules and atoms lies far to the dissociation products.

Reaction R:6 (k6) ; 2BrCN 2 C2N2

For completeness, reaction R:6 was always included in the proposed reaction mechanism. The reaction is only slightly

= 5.5 kcal mole . However, bimolecular endothermic; Ali`fo reactions of this type, which proceed via complex transition states, frequently possess activation energies which are a large fraction of the dissociation energy or the bond to be

In this case, E was chosen to be 60ra of D(BrCN). broken. a Because of the complexity of the collision such reactions normally have low P factors. In this work, P = 5 X 10-2 was selected and probably represents an over-estimate.

0 i.e. k6 = 1 00°40 exp(-25164/T) 1.1,101.1s7/

The computer simulations confirm that, due to the low concentrations of BrCN used, reaction R:6 is unimportant in the overall decomposition. The rate constant was never adjusted 156

in obtaining the final fit of the rate parameters, either in

this or subsequent mechanisms and k, is, therefore, not

determined by this work.

6:4:1 Discussion — The computer simulations for Scheme II a) Rich mixtures

Some of the simulations conducted for the rich mixtures are detailed and indexed in Table 6:5. For convenience, the trials are divided into four groups and are shown plotted as log10 KC against reciprocal temperature in figures 6:10 to 6:13. The simulations were always constructed for the 5%1 3 torr initial unshocked gas conditions; in addition the pressure dependence was checked for those trials which were close to the apparent rate constant , K a . Unfortunately, due to the onset of mathematical instability in the integration for some of the igro trials, the scaling in [Bra]2 0 could not always be checked. ,

(i) Figure 6:10

Based upon the initial estimates for k k and k (Trial 6:10:A), d , 2 3 the computer simulations predict curves for the primary and secondary rate constants (KC 4 and KC" respectively) which fall lower than the corresponding experimental curves Ka ' and Ka" (dashed lines where the superscripts have the same meaning). Although the shape of the profiles is qualitatively reproduced (i.e. two slopes), the time scale for the simulation is long compared to experiment. The K curves fall low partly because the possible chain branching steps R:4. and R:5 are not effective within the time scale of the measurement. After only a few lisec. gas time reaction R:2 removes

Cr,: to form C N 2 2 at a rate comparable to the initial dissociation. Also, because of the low activation energy for this step, the effect is most pronounced at low temreratures. It is notable that Bauer et al (85) were required to propose that a partial steady state in [Cril is rapidly 157 formed in the initial stages of the decomposition of C1CN at low

temperatures.

i.e. [Cl,] k /k2 pzs d. [ii]

Because of the failure of trial 6:10:A and other attempts to reproduce

the reaction profiles for [0] pss this is not applicable, in such

a simple form, to the decomposition of BrCN .

The time scale of the simulation is particularly sensitive to the

value chosen for ka . However, the secondary rising portion of the

simulations generally becomes less pronounced and tends to merge with 1 the initial linear rate of rise. For example, at /T200 -1 2'85 x 10' K , the simulated profile for trial 6:10:B reaches a

peak value in intensity in less than 1 lisec laboratory time, whereas from experiment 8.5 ILL are required. However, if R:2 is fast, then large concentrations of Br atom

will be rapidly generated and this can promote the formation of CN

via the consecutive reaction R:3. Furthermore, if R:2 is fast similarly

large concentrations of C2N2 will be formed and this may contribute to

GPI formation, at least in the later stages of reaction, by dissociation

via PA..

Attempts were, therefore, made to promote the rates of R:3 and R:)4.

relative to R:2. In order to accommodate for the rapid depletion

of CN via R:2 at low temperatures and yet retain a lcw value for k d 1 (i.e. P /20) , the activation energy (E3) for reaction R:3 was

reduced by about 2RT. This must be regarded as a lower limit to E3 ,

for there is little justification in removing greater than 2RT and, indeed,

it is far more common for E3 to be slightly higher (not more than 105)

than the endothermicity. 158

ENERGY -1 mole

REACTION COORDINATE.

This was done in Trials 6:10:C and 6:10:D: in addition, however, k2 was reduced. (It is to be emphasised at this point, that in matching

and K normally only one rate constant at a time was adjusted - ka c the effect of any given change is, therefore, the more recognisable).

Although Trial :10:C is promising in both the magnitude of K c and the apparent activation energy, it was noted that under these conditions the reverse reaction R:-3 becomes important as [Dr21 and [C n] increase. The bulk of the molecular bromine at long test times is removed via this reverse rather than the simple

dissociation R:5. In effect R:3 and R:-3 tend to equilibrate earlier as k is increased; at this stage there is of course no net formation 3 of CN via reactions involving Br atoms and the promotion effects of

R:3 disappear.

(_ii) Figure 6:11

For these simulations, in order to avoid the onset on equilibration

between steps R:3 and R:-3 the rate constant for the initial dissociation, k,a , is increased by a factor of two. The original value for E3 was re-adopted for all the simulations of figures 6:11. However, as long

as R3 is restricted to reasonable values of the steric factor

(i.e. R. < 1) , a secondary slope was only observed if the initial rate of bromine atom formation, due to reaction R:3, is high compared

to the initial dissociation. 159

The most striking feature of this series of trial fits is the

excellent agreement between the primary apparent rate constants, Kat

and K t , observed for trial c 6:11:11. Furthermore, the computed primary rate also scales in pressure (3-10 torr) and mole fraction

(0.05 0.'10) However, the secondary character for the 5% 3 torr

conditions is not reproduced. It is tempting to suggest that the

failure to simulate a secondary rate in the emission profiles is due,

not to incomplete fitting of the rate constants kd , k and k 2 3 , but to further reactions as yet not included in the reaction scheme.

In support of this, it is pertinent to note that even when an

experimental secondary slope is observable, the duration of the primary

(initial) rise is typically 15 Ii sec gas time or more.

Figure 6:12

Before further modification of the proposed reaction mechanism was

undertaken, further attempts were made to reproduce the secondary portion

(K a") solely on the basis of scheme 2. The relative contribution of step R:3 to the overall reaction

mechanism can be achieved by reducing F (as in trials 6:10:D and C). ' 3 To further facilitate such contributions, at low temperatures and in

times comparable with experiment, the activation E 2 , is increased. In agreement with the considerations of section 6:4(a), an upper limit -1 to F of approximately 10 kcal mole (i.e. E 2 2A = 5 X 103) is used. However, because of the excellent fit of primary rate constants for

trial 6:11:H0 the pre—exponential factor for k2 was increased so that

at approximately 4000K the rate of removal of CN is the same as

predicted by trial 6:11:H i.e. for this change in E3 the pre—expcnential

factor must be increased by 2.7 for a match at about 4000K.

However, because of the competitive nature of R:2 and R:3 and the

approach to a quasi—equilibrium between R:3 and R:-3 at longer test

times, this nanoeuvre alone is of limited success (cf. trials 6:12:A to C): 160 indeed the match is improved if the rate of R:2 is reduced at low temperatures (trial 6:12:D). The major limitation, however, is the

R:3, R:-3 equilibration; for example, from trial 6:13:G, the rates 1 -4 for these steps at /T220 = 3•3 X 10 K are close to a quasi» equilibrium at only 35% of the reaction (defined in terms of CN formation by equation EQ. 4:7).

(iv) Figure 6:13

It is possible to shift the position of the quasi-equilibrium between R:3 and R:-3 to longer test times by reducing the rate of removal of BrCN via reaction R:1. For the trials of figure 6:13, an intermediate value for k between those of the previous simulations, d , and k3 were adjusted in was chosen. The rate constants for k2 accord with observations similar to those already outlined. The "best fit' is obtained for trial 6:13:D and, using the present scheme, no further attempts were made to improve upon it. . It should be noted, however, that simply matching Ka and K does not conclusively determine the rate constants or the reaction mechanism. For the reasons previously discussed, Trial 6:11:H cannot be excluded for the values of ka , k2 and k3 . It is necessary to explain the complex dependence of the rate constant upon gas composition and to fit the emission profiles in more detail. b) Lean mixtures

A representative sample of the simulations, for m = 0.005 and

0.01 and mainly for the pressure range, P1 = 3 to 10 torr (a few simulations were also constructed for P.1 = 20 torr) , is shown in

terms of log10 KC against reciprocal temperature (figures 6:14 and

6:15). The range of rate constants used for ka k2 and k3 are summarised in tables beneath these plots. For reference, some of the

trial values, adopted in the rich mixture computations, have also been integrated; the correlation is shown in Table 6:5.

FIGURE 6:1 8.0 The computed rate constant (as logloKc against re4procal temperature: trial fits for .20071.17, 2 (RICH NIXTURES ONLY)

(Bt),), 7.0

0 6.0 Dashed lines: Rich mixture ?trend? lines for Ka (cf. Figure 6:10) Solid lines: Trial fits i.e. computed dependence for Ice f denotes rate from primary slope i(Af) t? secondary slope t-a rn 5.0 DESCRIPTION OF RATE CONSTANTS USED GIVEN IN TABLE T i-s

2.5 2.6 2.8 3.0 3.2 3.4 FIGURE 6:11 The computed rate constant (as logioKe) against reciprocal

Ka2 temperature: trial fits for SCHEME 2 uo• (RICH MIXTURES ONLY) 0 7.0

K a U Q9' 0

6.0 Dashed lines: Rich mixture 'trend' lines for Ka A'') (cf, Figure 6:10) Solid lines: Trial fits i.e. computed ( A to H ) dependence for Ke. JP) denotes rate from primary slope A? fl is secondary slope. ' 4, DESCRIPTION OF RATE CONSTANTS USED GIVEN IN TABLE 6:5 10/T 5.0 20

2.5 2.6 2.8 3.0 3'2 3.4

The computed rate constant (as logioK0) against reciprocal temperature: further 163 FIGURE 6:12 trial fits for scheme 2 A 75

K ' U) a (RICH MIXTURES ONLY) 0 70

ft ,,. a

ttg., U Dashed lines: Rich mixture 'trend' -L..% Liu %,. 0 lines for Ka® N. (9 (cf. Figure 6:10) 0 Solid lines: Trial fits i.e. computed __I 6 0 dependence for KC. ' denotes rate from primary slope

f secondary slope

10 4/ T 1102•061625STVIINTAAMMOCNRIMPLi.C.GLI 0

26 2 7 29 31 33

FIGURE 6:12 7.5 B

• (RICH MIXTURES ONLY) U) TJ 0 7.0

K tt a U 0 t. 0 6.0 =OM AS ABOVE. DESCRIPTION OF RATE COESTALTS USED IN TRIALS A TO G GIVEN IN TABLE 6:5 4 5.5 10 /Ton 2.6 2.7 2.9 341 3.3 354

THE COMPUTED RATE CONSTANT (AS LOGio Kg) AGAINST RECIPROCAL TEMPERATURE: FURTHER TRIAL FITS FOR e.0 FIGURE 6:13 SCHEME 2. RICH MIXTURES ONLY.

7.0

6.0 . K • U) a

I J 0 2 7.0

U C") B") O

6.0

7.0

Dashed lines: Rich mixture 'trend' lines for Ka. (cf. Figure 6:10) Solid lines: Trial fits i.e. computed 6.0 dependence for K 4/ ( A to D ) g. 10 T I 2p 2.5 2.6 2•8 3.0 3.2 3.4 NOTE* denotes rate from primary slope i t f2 secondary slope DESCRIPTION OF RATE CONSTANTS USED IN TRIALS A TO D GIVEN IN TABLE 6:5 9.0 L Q G 1

j o ; FLO TT AGAINST VT:7 .,0 -- 171,1E1 2 - LE AN I4-1 XTURES ONLY:„

..10/10.4.inwaamot.

8.0

(J)

K - TREND LINE C a

4*431t2ta (Figure 6:10) 7.0

•••••••••• M(BrcN)=0.005; 0.01 1)1 mm. . 3 to 10

10/T 6.0

2.3 '2.5 3-0 3.5 4°0

INDEX OF RATE CONSTANTS USED IN THE ABOVE SIMULATIONS. SCHEME 2 - LEAN MIXTURES.

-1 _1 _1 _1 ...J. -1 k 1 mol. s. k2 1. mol, s, k3 1. mol. s. TRIAL A d . n E/R A n E/R A n E/R 1 9 a 1.36x10 -1.5 41491 5.0x10 0.5 1000 1.0x10 0.5 14595 J 18 7 10 2.00x10 IT If 5.0x10 tt n 1.0x10 n II K 18 8 1,00X10 II If 200X1 0 " It If tt II L 17 8 54,00X10 II If 3.0x10 tt tt 1.3x10 9 " 8303.6 M 8 IT •II If 2.0x10 " It It If ft N 18 8 3.30x10 If II 105X10 " " It If It 0 17 10 3.307.:10 II It It II IT 6.0X10 " It P 9 II It IT IT If If 6. Ox10 " ft Q 33 -5 k4„-.2.8324x10 T exp(-62907/T) 0.5 ...1 ... 1 k5=2.18x108T exp(15849/T) 1. mole so ±0 , ke.--2.5x10 exp(-25164/T)

265

LOG KMOL S'i C " FIGURE 6 :1 4 THE OWTUTED RATE CONSTr.7a (as R-0 LOGio K PLOTTED AGAINST 1/T,90 -SCHEME 2 - LEAN MIXTURES.

X -TREND LINE C 7.0 (Figure 6:I0 r

M(BrON =0.005, 0.01 P1 mm. = 3 to 10 0- , G) cs- (A: (A:1%) 0.5% k ) 6.0 (C) B 4 (D) E 10/T20 .1511Waliksmams!IMMalt 2.3 2.5 3.0 3 .5 4.0

INDEX OF RATE CONSTANTS USED IN THE ABOVE SIMULATIONS. SCHEME. 2 - LEAN MIXTURES. k2 .• k3_ -, 1. mol. s. 1. molt` s. . A n E/R A n E/R TRIAL 8 9 5003[10 0.5 1000 1.0x10 0.5 14595 A 8 10 ft If it It 200X10 14,0X10 B 8 9 160X10 ft II 5.0x10 n fl C e 10 5.0x10 ft It 1o0X10 11 It D 8 10 It It 460X10 If II 2.0x10 E 7 10 5.0x10 it it 1.0x10 it tt F 10 t: II it 5,0x10 It It G 11 It If If 1o0X10 it It H

17 ...1 k =5.0x10 T exp(-41491/T) d 33•5 k4=2.8324X10 T exp(-62907/T) 8 OsS 1. mot. s. k5=2.18x10 T exp(-158149/T) l o k5=2.5x10 exp(-25164/T)

TABLE 6:5

THE INDEX OF RATE CONSTANTS USED FOR THE TRIAL SIMULATIONS FOR SCHEME II - RICH MIXTURES -1 1 (only ka , k2 and k3 are varied: units - 1.mol. s. )

k 1033'45 T-5.° exp( -62907/T) = 0•5 k, = 108-34- T exp (-15849/t) 0.0 k6 = 101 exp (-25164/T)

k k k +Trial Lean Mixture d 2 3 Correlation

101744- T-145 exp(-41491M 108.7 T°.5 exp(-1000/T) 1094° T°.5 exp(-14595/T) 6:10:A 1 p'8-3 " n n n It 109'7 IT it 6:10:B

It 8- .8 n it 1017-4 n 10 4 109.41 T0.5 exp(-830306/T) 6:10:C .11 n ti It 108 .0 . n 109 t' n 6:10:D

0 0.5 1017'7 T-1'5 exp(-41491/T) 108.7 T°°5 exp'-1000/T) 109"- T exp(-14595/T) 6:11:A 6:14:A

It It II II I 109.4 " 6:11:B

n 108 "Q 10'0.6 6:11:C

Table 6:5 contd

+ + k k k Trial Lean Mixture d 2 3 Correlation

1017'7 T 1 .5 exn(-41491/T) 108.° T0.5 exp(-1000/T) 109.4 T0.5 exp(-14595/T) 6:11:D n It ee re 109.7 " 11 6:11 :E 6:14:0 n 108.3 It u 1010 n n 6:11:F 6:14:B .6 0.3 It 108 f

11 108 .7 11 u 101000 " u 6:11 :1-1 6:14:D

1 0. 161 7. 7 T1.5 exp(-414.91/T) 108.9 TC'e 5 exp (-5000/T)10g•l- T -5 exp ( -8303•6/T) 6:12:A it 108'7 'IT r• It II !I 6:12:B .0 ,, u 109 u u H H 6:12:C

u 108'7 , u 1 08. 85 " 9 6:12:D n 108.3 T°.5 exp(-1000/T) 109.11 " tt 6:12:E 6:15:N

It 11 11 1 08'48 " 109.41 " 6:12 :11

109.11 tt It tt It lt ft 6 :12 :G 6 :1 5 :M

Table 6:5 contd

+ k k k +Lean Mxture d 2 3 Trial Correlation

9.6 T0.5 1017'52 T-1.5 exp(-1.14.91/T) 10 exP(-5000/T) 101° T°*5 exp(-8306'6/T) 6:13:A

ft 8.4 tt n 9.26 u H 10 lo 6:13:B

If 8.6 " H .6 , n 10 109 6:13:C

H .18 , H H 108 lo9.11 " 6:13:E

7,7otes:- + The numbers refer to the figure upon which the simulation is plotted. The letter identifies the curve. 170

The major expeeinental features to be reproduced are:—

(i) the anemolously low activation energy observed for trend line C of figure 6:9, and

(ii)the fall—off in rate constant with increasing pressure for the 1% mixtures.

Attempts to accomplish this by either a) rapid CN formation via reaction

R:3 promoting an initially slow rate of BrCN dissociation (cf. figure

6:14), or by b) rapid CN depletion via reaction R:2 retarding an initially fast dissociation, were unsuccessful. Unless otherwise stated (e.g. Trial 6:14:A), the computed apparent rate always scaled in [BrCld 20 and [M] , 2, 0 and the fall—off with pressure could not be reproduced (cf. figure 6:14). The apparent activation energy was never reproduced, even for those trials where kd was increased to large values so that Ka and Ke matched at the mean temperatures of this study (e.g. for Trial 6:15:3 the P factor is approximately 2 which is close to that estimated from Bauer et al (85) where

P(o_crr) — 1.1) . More significantly, the time scales and qualitative shapes of the experimental records could only be reproduced for the results obtained at the highest- temperatures (i.e. > 2+000K) .

6:4:2 Conclusions from scheme 2 simulations — Ccmaricon of computer

and experimental profiles

For the lean mixtures, the failure of the reaction scheme to reproduce the temperature dependence of the apparent rate constant is conclusive evidence that for these mixtures the scheme is inadequate; there is no need to discuss the detailed variation between the computed and experimental profiles. For the rich mixtures, however, the apparent rate constant was well matched by trial 16:13:D and) within certain limitations trial 6:11:H; in thie case detailed comparisons of profile shapes are required to differentiate between the two.

The computer simulations for some of the trial sets of rate constanto 171 which, were applied to the rich mixture results, are compared to experiment in figures 6:16 to 6:20. The profiles are plotted using the CALCOMP facility incorporated in the program CALKIN (section

4:4:2). The points represented by triangles are taken from the experimental records and scaled to computer units as described in section 4:2:2(d); the smooth lines are constructed by joining the individual predicted values at each step in the integration with a straight line. (For a 4" axis this generally implies that somewhere in the region of 200 line segments an inch are used). In each figure the solid curves are labelled alphabetically and correspond to the following trial simulations

Curve Trial

A 6:13:C

B 6:12:G

C 6:11:H

6:10:A

The rate constants for these trials are summarised in Table 6:5.

All the profiles presented correspond to shocks into a 5% mixture of

BrCN in Argon at an initial pressure of 3 torr

The individual experimental records, which are shown, were selected by interpolation along trend line A of figure 6:9. This reduces the random error between successive comparisons of simulated and experimental profiles. From the considerations outlined in section 6:2:4, any

comparison for a successful set of profiles should agree to within about 25% in intensity, at least in early times. (It is to be emphasised that the units are absolute and not arbitrarily scaled as for example in ref. 103). Because the exact position of the shock front could only be determined to within lilsec , the experimental profiles may be shifted, in time, relative to the simulations (of. figure 6:17; photo.462). 172

The simulations, obtained from the initial estimates of the rate constants, are shown as curve D. These are obviously inadequate for the whole temperature range and illustrate the usefulness of the preliminary Ka/Kc matching procedures (compare figures 6:10 and figure 6:19).

Taking the set of simulations as a whole, the set of curves, C are the best fit to the initial rise of intensity. At high temperatures, these curves also reproduce the qualitative shape of the emission records

(cf. Figures 6:16 to 6:18) but at lower temperatures (figures 6:19 and

6:20) the high peak intensity is not reproduced. Part of this discrepancy in peak measurements is undoubtedly due to the neglect of boundary layer and shock attenuation effects. However, the time scale is still relatively short in terms of the former and the time scale compression effect should be more marked than deviations in the magnitude of the peak emission (cf. section 4:3). For the attenuation observed in this study (less than irjo per metre) the total contribution to corrections to the peak height will be only of the order of 1C and cannot account for the discrepancy between experiment and curve C at the low temperatures.

At high temperatures, curve A does not match the shape of the experimental records and consistently predicts larger intensities than are observed. At lower temperatures, however, the peak intensity is more closely matched (cf. figure 6:20). It is to be mmembered, however, that for trials A and B , the rate of the step

BrCN + Br Br, + CN (R:3) was artificially promoted by adopting a low value for E3 (cf. section

6:4.:1 subsections (ii) and (iv)). By comparison, therefore, curves C which reproduce to the more important initial rise with wholly reasonable values for the rate constants (trial 6:11:E) seem the most appropriate.,

However, as indicated earlier, this implies that additional reactions involving CN are important in the secondary rising portion of the FIGURE 6:16

THE COMPARISON OF COMPUTER AND EXPERIMENTAL PROFILES.

A

it,. A A A

,

O

PHOTO 454 PHOTO 459 P1=3mm. 5%BrON; 95%Ar P1=3mm. 5%BrCN; 95%Ar T2,0=3771 K T2,0=3511 K T(eob).3061 T(eqb)2857 K 1.9685E5 cm/s 1.8939e5 cm/s Triangles: expt. Triangles: expt. Simulations A-D summarised in Table 6:5

0,00 0,14 0.28 0.42 0.56 .01.30 0.60 0.90 1.20 LAB TIMER 1 0 -5 LAB. TIMER 10 -5 FIGURE 6:17

THE COMPARISON OF COMPUTER AND EXPERIMENTAL PROFILES.

Ln

PHO y 462 PHOTO 458 P =3mm. 5%BrCN; 95%Ar p1.5mm. 5%B C1 95%Ar T2,0=3561 K T2,0=3558 K T(eqb)=2894. X T )=275l K 1.9084e5 cm/s l.8484e5 cm/s Triangles: expt. Triangles: expt.

Simulations A-D summarised in Table 6:5

.00 0.23 0.46 0.69 0.92 0.29 0.58 0.87 1.16 LAB T INFx 10 -5 LAB. TIMEX 10 -5 175

FIGURE 6:18

THE COMPARISON OF COMPUTER AND EXPERIMENTAL PROFILES.

A

lu

Cr) C P i0 477 P1=3mm. 5%BrCN; 95%Ar T2,0.3258 K T(eqb)=2681 K

CD 0: 0 0.41 0.62 1.23 1-64 LRB. TIMEx10

Shock velocity 1.8149e5 cm/s Triangles: expt.

NOTE:- In figures 6:17 to 6:21, the computer profiles identified by the same letter(e.g. A) were obtained using the same values for the rate constants of SHCEME 2. Simulations A--D are summarised in Table 6:5 FIGURE 6:19

THE COMPARISON OF COMPUTER AND EXPERIMENTAL PROFILES.

PHOTO 482 3mm BrON in Ar ti- 1.758 e5 cm/s T2(frozen) 3063 K

PHOTO 482 p1 = 3 mm 5c; BrCN; 95 Ar 1.758 e5 m/s T2 (froz n) = 3063 K m (eqb = 2574 K Triangles : exot. Curv,s: cooputed; step length pardmeter 500; about 600 steps. This is a scale expansion of the diagram opposite.

Simulations A—D are summarised in Table 6:5

r 0.48 0.6 4 0,, , n _4 0:26 0.52 0 78 1 V4 q 3 TIME.4 ItJ LAB L TIME 1 0 FIGURE 6 20

THE COMPARISON OF COMPUTER AND EXPERIMENTAL PROFILES.

•••f• cJ CsJ

Cr cn CD - PHOTO 486 3mm 5BrCIT'9%Ar 1.74 e5 cm/s frozen) = 3034 K T2, CJ PHOTO 486 eqb) = 2558 K • CD i 3mm 5% BrCN in Ar Tr angles: expt. CD 1.748e5 cm/s (frozen) = 3034K T2

This is a scale expansion of the diagram opposite.

Simulations A-D are summarised in Table CD 6:5 CD n nr, 0.54 0.72 C3r, rn .0.45 0 •92 1.3q LP5. .TIMES 10 -4 LAB. TIME:i 10 -5 178 experimental recorde. From the knowledge that the apparent rate of reaction is fastest in lean mixtures, those additional reactions must increase their relative contribution to the overall reaction path with

dilution. The effect of further classical reactions of the type outlined

in Chapter V is discussed, from thermodynamic considerations, in the following section. It will be shown that inclusion of such reactions cannot account for the complexity in the apparent rate which is observed.

In section 6:5 an alternative mechanism, involving the formation and rapid

decomposition of a vibrationally excited intermediate, is presented and

discussed.

6:4:3 Possible modifications to scheme II

In section 5:1:1, it was noted that previous investigators (95 - 102),

working at long test times, have found it necessary to include reactions

involving atomic carbon and nitrogen and/or more exotic (CN)n fragments.

Because of the short time scales involved in this work and the large

enthalpy of dissociation for CN , chains, such as those proposed by

Fishburne and Slack (97, 103; of. R:2 to R:4. section 5:1:1) for C2 formation, will not be important. Patterson and Greene (102) have

found that, at temperatures below 4000K, the rate of C2 formation lags behind that of CN and is not significant during the initial rise in

^Aot the CN omission, up to its peak value. Similarly, C2 formation was found to be important within the time scale of the present experiments:

simultaneous measurements of the emission due to CN and C2 were made for some shocks in the temperature range 4000 - 3000K . Below 3000 K

emission due to C2 could not be detected. Furthermore, inclusion of Patterson and Greenels rate constant for the reaction

2CN C + N • A H ae 2 kcal.mole-1 2 2 o

12.15 ( 1 -1 where k == 10 exp -43000AT)1.mol. a. , does not effect the predicted initial rate of rise of the CN emission profiles to any significant 179 extent. Indeed, at high temperatures and longer test times (viz. at the peak) the computed intensity was only some 10% lower than that obtained from scheme II.

While it has been observed that the formation of (CN) fragments leads to low apparent activation energies, the absolute value of the' apparent rate constant is low because of the small pre—exponential factors involved (95). These effects could not, therefore, account for the large apparent rate constant and low activation energy observed for the

decomposition of lean BrCN/Ar mixtures. a) Possible effects due to contamination

Thrush et al (98, 99) have found that the intensity of emission from

CN , in discharge flow experiments with cyanogen, is considerably

enhanced by the addition of oxygen atoms in the absence of molecular

oxygen. It was proposed (98) that the rate of formation of CN is

promoted by the following reaction steps:—

AHTkcal mole-1

(R:7) CN + C N --*— C N + N —44 2 2 3 2 (R:8) o + C3N —4— CO + C2N 95 (R:9) 0 + C N —4— CO + CN 2 108

However, for this shock tube study, even if quite high leak rates

of atmospheric oxygen are presumed (no impurities could be detected upon

mass spectroscopic analysis of the gas samples prior to admission to

the shock tube), this regeneration cycle is unlikely to be important.

The concentrations of C2N2 formed in the early stages of reaction

are relatively low and the rate, k7 [C2N2] , will be very slow compared to reactions R:1 and R:). Alternatively, R:2 of the reaction

scheme could be replaced by the analogue of R:6, resulting in the

formation of C N + NBr and the possible subsequent reaction with 0 2 atoms via R:9. This is also unlikely because the transition state 180 for CN + BrCN is probably far less comclex than for CN + C2N 2 and the simple metathetical exchange is preferred. In all events, however, the large dissociation energy for oxygen excludes the rapid generation of 0 atoms and it has been found (98) that in the presence of 02 , CN emission is quenched by the reaction

CN + 0 4.4 2 -->- CNO + 0 k = X 109 1.mo1.1371

From similar considerations, the enhancement of intensity, reported for discharge flow systems with CN and N atoms, is unlikely to be the cause of the anomolously high rates of CN formation observed in this study.

6: Scheme III - An Ener v Chain Branchin2; Mechanism

(R:1) BrCN + M --.4.____-"±- Br + CN + M Initiation v (R:2a) BrCN + CN --4- C N ° -<--- 21 2 + Br Propagation

(R:3) BrCN + Br Br2 + CN tt

(R:10) C N ° + M 2CN + M Energy Chain Branching 2 2

(R:4) C2N2 + M 2CN + M

--±- (R:5) Br2 + M ..... 2Br + M

2BrCN --÷- Br + C N (R:6) -÷-- 2 2 2 v o (R:11) C N + M ---->-- Relaxation 2 2 ---<--- C2 N2 + M v (R :12) C o + C 1,1 C N + C N ,I 27C2" 2 2 2 2 2 2 (H :13) + BrCl: C2N2 + BrCN it C2N2 vo where the superscript vo denotes a vibrationally excited species.

6:5 a) General consideration

Below 1000K , it is commonly accepted (139) that chain reactions

take place by elementary steps involving atoms and radicals in the 181 reaction mechanism. The high reactivity of these species is derived from the presence of unpaired electrons which make for strong specific intermolecular forces and low activation energies. However, the integration of such 'Nernst' chain kinetics, in which Maxwell-'Boltzman distributions of energy are assumed to apply (i.e. scheme 2), does not reproduce the most striking feature of the present kinetic study; namely, the anomolously low activation energy of trend line C' . (cf. Table 6:1)

At temperatures in excess of 1000K , it can be necessary, however, to consider the additional participation of energy chains, involving non-equilibrium distributions of energy, in the overall mechanism (139).

The reactivity of the species included in such energy chain reactions is not due solely to specific affinities as in the classical atom/radical systems, but is due predominantly to the possession of energy in excess of the equilibrium conditions. That is, the reactivity of the species is dependent upon the possession of translational and/or internal energy in distributions sufficiently high to overcome (or at least assist in mounting) the energy barrier of the reaction.

It is of particular interest to note that the difference between the expected activation energy for the simple dissociation of BrCN -1 (i.e. 74 kcal mole , calculated on the basis of a Kassel ,expression for k d involving three vibrational degrees of freedom) and the experimental apparent activation energy of 28 kcal mole () is very close to the exothermicity of the reaction

(R:2) BrCN + Br + C2N2; D Ho=-42•3 kcal mole-1

This suggests that part of the exothermicity may be available to the reacting system, not as an overall change in the bulk gas temperature but as a non-equilibrium distribution of energy partitioned between the degrees of freedom (translational, rotational and vibrational) available to the product cyanogen molecule and bromine atom. That exothermic reactions do produce relatively long lived 3132

non—Boltzman distribotions is well illustrated by those summarised in

Table 6:6 and discussed In the following sections. Shuler (139)has given an historical survey of the early theoretical treatments of such

non—equilibrium systems, with particular regard to temperature.

It is proposed, therefore, that at least some of the exothermicity

of reaction (R:2) is partitioned to the vibrational modes of the newly

formed cyanogen; this is written as step R:2a above. The degree of

excitation is discussed in the following sections. In an attempt to

reproduce the observed kinetics for the lean mixtures, it is further

proposed that the concentration of the vibrationally excited cyanogen is depleted,

a)by dissociation via reaction (R:10) to promote a chain branching

mechanism, and

b) by vibrational relaxation where collisions due to M, C2N2 and

BrCN are expected to be of differing efficiencies and are therefore

written as individual reactions steps (R:11, R:12 and R:13 respectively).

These reaction steps were inserted into the reaction mechanism one at

a time in order to investigate the effect upon the apparent rate of

reaction.

The approximations implied, by this much simplified mechanism for

the contribution of complex energy transfer processes to the total rate

of formation of CN and as required to achieve a mathematically tractable

model, are discusecd in the following sections.

vo .6.152 1 - BC > AB + C reactions It 13 convenient at this stage to briefly review the salient points,

arising from past enperAmentel ana theoretical studies of A + BC

exothermic reaction systems.

The early work of 7olanyi and co-worker- (140-142) indicated that

for reactions of the type 183

TABLE 6:6

A+BC --->--ABv +C Reactions

H Highest v Highest v v Maximum of Reaction kcal mole-1 possible observed distribution

H+012---->--HC11r+Cl 47 6 6 2,3 H+B r HBrv 2 —It- +Br 43 6 6 3,4

CS+80 -4--COv+S2 53 10 14 S+52012--->- S2+5012 36 Z 18 12 v v 0+CS2---4--CS +CO 30 9(51 4(50) 8( CS 3(05) 0+110 -->- 0 +NO v 2 2 46 11 13(02) 8 v H+0 --->- OH +0 78 8,9 3 2 9 9

Notes :- v denotes a vibrationally excited species Taken from Table 1 of reference 51 in which a more detailed review of A+BC reactions is given 384

vo M + X -->-- MX + X 2 v M + XH MX ° +X

(M = alkali-metal atom; X = halogen atom) the product molecule, MX , is formed in high vibrational levels.

Preliminary calculations (141), based upon a mass sliding across a potential surface (143), indicated that the energy was liberated to product vibrational energy along the approach coordinate of alkali- metal atom to the X 2 molecule. This mode of energy release was, therefore, termed 'attractive'.

In contrast, however, it has been found that for exchange reactions involving the breaking and formation of essentially covalent bonds

(unlike the M/X systems, in which an ionic bond is formed) the degree 2 of vibrational excitation can be low. The most notable and extensively studied (144-148) is the reaction system

(R:14) H + X2 HXv° + x (x = Br,C1)

Indeed, it has been observed that approximately 8g% of the exothermicity plus the activation energy goes to the relative translation of the products and rotations of the newly formed la molecule. For the similar reaction

vo (R:15) X + HY IBCX + Y (where X and Y = halogen atoms)

Analauf et al (147) have, in contrast to R:14, observed a high degree of vibrational excitation. The former has been interpreted in terms of energy release when the reaction has passed into product (i.e. repulsive) coordinates and the latter, which is apparently intermediate between the purely attractive and the purely repulsive cases, has been described (147) by a tmixod model release (first postulated by Polanyi

(12+9)). The formation of vibrational excited species is not rezitricted to B5 these 'simple' reactions; some othersare summarised in Table 6:6. For example, Smith (150) has produced both CS and SO from the flash photolysis of 02/CS2 systems and has observed vibrational excitation of both product molecules due to the reaction

0 + CS CSvo vo 2 SO

Theoretical calculations of the reaction trajectories over a potential energyhypersurface have been conducted for the H/X systems

(R:14. and R:15). The relative merits of the procedures employed have been critically reviewed by Laidler and Polanyi (151). Normally, the equations of motion for particles moving across a potential surfaces constructed using the London—Eyring—Polanyi and Sato (152), are solved.

From the literature (for example 147, 149, 153) these calculations yield the following conclusions:-.

(i) The vibrational energy of excitation is not sensitive to the initial impact parameters.

(ii) Exchange on an 'attractive' surface enhances high product vibrational excitation.

(iii) Exchange on a purely 'repulsive' surface is inefficient and the product vibrational energy is consequently only a small fraction of the exothermicity.

(iv) The inclusion of a multiple encounter model on an 'attractive' surface can yield low mean vibrational excitation of the product molecule but the vibrational/rotational distribution is broader than is observed experimentally (e.g. H X2 reaction).

(v) The exchange on a 'mixed' mode surface can, however, yield high vibrational activation. The energy release to vibration is more efficient than from a purely repulsive mode because the incipient A — B bond is still under tension due to reactant attraction even as the reaction moves into the prcduct coordinates. 186

(vi) Energy exchange on a repulsive surface is attributed to the low mass of the attacking atom relative to that of the attacked

molecule (e.g. H in H/X2 systems). This singular behaviour is known as the 'light atom anomoly' and is attributed to the rapid approach

of the relatively light atom allowing little time for bond extension in

the reactant molecule (i.e. X — X ) resulting in a reduction of the

energy partitioned to vibrations of the incipient product molecule, due

to 'mixed mode' release. This model is preferred to the multiple

encounter model (iv above) because it reproduces the sharply peaked

distributions observed in experiment.

(vii) The very high excitation observed for the alkali—metal/halogen

systems, results from the increased attraction between the reactants due

to tan electron jump mechanisein which Coulombic forces become important

(154, 155).

(viii) In some cases, the degree of excitation is sensitive to the

height and location of the activation barrier in the reaction coordinate.

However, it should be noted that this is generally of more importance

when considering the reverse endothermic step.

vo e.g. HC1 Cl H Cl 2

Dials and Bunker (156-158) have conducted computations by a slightly

different method. An empiric potential energy surface, capable of

adjustment to represent from moderately attractive to moderately repulsive

conditions, was proposed but with the distinction that, unlike the methods

due to Polanyi and others (153),the particles of the A B....-C transition

state are allowed to move freely in any plane. Numerous trajectories,

selected by a weighted 'Monte Carlo' procedure (159) were performed with

the intention of investigating the relative mass effects (M n, MB and

P.tC ) of the particles involved. For M A>>.MB and ,ITc on an attractive surface, high energy release to vibration was predicted in agreement with the previous studies. The two dimensional study (157) 187 further predicted low product vibration even on an attractive surface if14< < Y and MG A ; this contrasts markedly with (vi) above. This was not, however, repeated when the computations were extended to three dimensions (158) when, indeed, exchange on an attractive surface always yielded high product vibration for all the mass ratios tried.

This is in better accord with the previous findings and further confirms that the light atom anomoly is best described by the repulsive mode of energy release.

6:5:1a) Energy chains - previous investigations

While it is evident that exothermic reactions do produce non-equilibrium distributions of energies among the products, there is a paucity of data exploring the effects (if any) of these distributions upon the apparent rate of reaction. Shuler (139) has emphasised, however, that if the excited species is long lived, then propagation via complex energy chains could be important, particularly at very high temperatures when the rate of chemical reaction becomes comparable to relaxation processes. This is not unreasonable, for it is well established (160, 161) that at elevated temperatures the high vibrational levels of diatomic molecules are rapidly depleted by dissociation and that energy transfer processes become rate determining in the overall dissociation. The experimental evidence for the dissociation of diatomic molecules has been reviewed by Rush and Pritchard (162).

It is worth commenting that non-Boltzman distributions of the

translational/rotational energy of any given species are rapidly relaxed:

the former requiring on average only 3 4. collisions and the latter only

some 6 r-20 collisions (excluding the exceptional cases of H2 and D 2 which are orders of magnitude larger). In effect, therefore, non-equilibrium

distributions initially formed in either one or both of these degrees of freedom (cf. ref. 148) are normally short lived and the system is sufficiently well described by the bulk gas temperature. 188

Although several attempts have been made to find an irrefutable example of an energy chain depending upon vibrationally excited species, success has been limited. Boudart (163) has critically reviewed some of the work in which energy chain mechanisms have been proposed and has noted that in several cases vibrational relaxation times have been over—estimated and that the rate of reaction could be explained by normal classical kinetics.

Slootmaeker and Van Tieglen (164) have proposed that the enhanced rate of removal of chlorine molecules in 112/C1 flames is due to the 2 vo formation and subsequent reaction of HC1

vo i.e. (R:14) H + Cl2 HCI + Cl vo (R:16) HC1 + CI,2 HC1 + Cl + Cl

The exothermicity, H for the analogue of R:14. , where excited T species are not formed, is 45 kcal mole and the dissociation energy of chlorine D(C12) is 57 kcal.mole . Slootmaeker et al found -1 the activation energy of reaction R:16 to be 12 kcal mole or exactly

D(C12) — HT . (This is similar to the results obtained in this study for R:1, R:2 and Er — cf. section 6:5(a)). Slootmaeker et al. took this vo to infer that HC1 must correspond to the molecule excited to vibrational levels up to the thermodynamic limit. Evidence in support of this has been given by Cashion and Polanyi (165) who, by infra—red measurements, observed vibrational levels of HC1 to within 90% of the exothermicity. However, the population of these high vibrational levels

reaction. is very low due to the light atom anomoly effect in the H + X2 Bcudart (163) has based his criticisms of the proposed mechanism in terms of these low populations and suggest that, while R:16 probably does occur, the bulk of the reaction probably proceeds via classical radical/ atom chain kinetics.

If the effects of energy chain reactions are to be observed, clearly the excited species must possess 389

(i) a large excess of internal energy relative to the equilibrium conditions defined by the bulk gas temperature, and

(ii) a long relaxation time.

For these reasons, systems involving vibrationally excited oxygen molecules have been repeatedly investigated in the hope of observing an energy chain.

It has been suggested that the mechanism

(R:17) 0 + 0 ---->— 0 V0 3 2 02 vo (R:18) 0 0 ---*- 0 0 02 2 3 2 where the exothermicity for the analogue of R:17 to normal products is .4 93 kcal mole and the dissociation energy of ozone is only -1 24 kcal mole , is important in the ozone self—decomposition flame.

The vibrationally excited oxygen has been observed to possess 66 kcal .1 mole of the excess internal energy (166) which is substantilly in

excess of D(0 ) . Basco and Norrish (167, 168) have similarly found 3 that the formation and subsequent reactions of 02v are important in the flash photolysis of ozone.

In contrast, however, the energy chain postulate for ozone decomposition

has been challenged by Fitzsimmons and Bair (169) and Benson and Axworthy vo (170). The former authors concluded that the concentrations of 02

found by direct measurement, are too low tobe important in promoting the

decomposition via reaction R:18, while the latter could find no evidence

to support the occurrence of energy chains at the low temperatures of

their study. It is, however, of doubtful validity to extrapolate from

these low temperature studies directly to the high temperature systems

such as flames and_ shock waves. vo Similar experiments on the effect of vibrationally excited e2 vo and OH generated by the exothermic reactions

N + NO -->-- 7..\72 + 0 (171, 172)

and

190

, H 0 OH + 0 (173) 3 2 have shown that vibrational excitation of the collision partner, in reactions analogous to R:18, enhance the rate of dissociation cf ozone.

This lends support to the proposal that vibrationally 'hot' species can be important as chain carriers. Indeed, Schott and Kinnsey (174) have

proposed that their observations cf an enhanced chain branching in the

complex H2/02 system is due to the presence of vibrationally excited

oxygen.

6:5:1(b) Reactions involving vibrationally excited cyanogen

Previous investigators have tended to emphasise the increased collision

efficiency of an excited molecule, accompanied by complex energy transfer

processes (e.g. reactions R:16 and R:18) in promoting energy chains rather

than an increase in the probability that the excited molecule itself will

undergo a chemical change. In this respect, the treatment of vibrationally

?hot' species has resembled that for translationally hot species. In

this work, however, the view is taken that the vibrationally excited

species does possess an enhanced probability for chemical reaction; viz.

the dissociation on collision with an inert gas molecule (reaction R:10).

It is pertinent at this point, however, to consider the effects (if vo any) of alternative reactions of C2n2 especially the reverse of the

initial formation step: i.e. reaction R: -2a.

C N + Br BrCN + Br (R: -2a) 2 2

and the analogous class of reactions typified by R:16 and R:18

vo (R:19) i.e. C2N2 + C2N2 ---*- C2N9 CN + CI' vo C2N2 + Br + Br (R:20) C2lj + Br2

.2rom considerations of the relative concentrations of the various products of decomposition, within the short experimental time scales, the rates 191 of R:19 and R:20 will be slow compared to the steps proposed in this work; namely R:10 and the relaxation processes R:11 to R:13. For these reasons reactions R:19 and R:20 were not incorporated in the proposed reaction scheme. Polanyi (175) has, however, shown that vibrationally excited species can possess what are termed 'extended collision frequencies=

(Z*). These normally lie in the range 1.5 < ZVZ < 3, where Z is the gas kinetic collision frequency for the normal molecule. In the initial stages of reaction, however, the endothermic reverse step,

R:-2a, will also be slow. Furthermore, Wray et al (176) have noted that the reaction

0 + N NO + N 2 is not sensitive to the vibrational energy content of N , whereas 2 N v° is formed by the reverse 2 vo i.e. N + NO -->— N + 0 2

For convenience, therefore, considerations of a ZVZ ratio greater than unity were not included in the Calculation of the rate of R:-2a and

k 2a was simply obtained from the equilibrium constant (EQ. 4:2). For completeness, an enhanced rate for the reverse of reaction

R:6 due to vibrational excitation of C N must also be considered. 2 2

vo N + Br ---4— 2BrCN i.e. C2 2 2

Recently, Spicer and Rabinovitch (177) have surveyed the literature known for this class of reaction. The fractional order with respect to the diluent (usually argon) which is often observed for bimolecular reactions

(e.g. H2/D2 isotopic exchange — refs 178, 179) can only be explained if initial vibrational excitation of one or more of the reactants is a prerequisite to chemical reaction (180). This has been semi—quantitatively explained in terms of the configuration of the transition state for the 192

NH /D 3 2 system (181). A more detailed comparison of experiment and theory has been given elsewhere (182). In this work, however, contributions to the overall rate can safely be ignored because of the low concentrations vn of C2N2 and Br 2 which will be present immediately behind the shock front.

6:5:1(c) The degree of vibrational excitation (a. ) for the reaction: o vo BrCN + CN C N 2 2 + Br

Before detailed computations for scheme III can be conducted the initial degree of vibrational excitation (Ct o) must be estimated. A thorough theoretical treatment, involving the analysis of the quantum mechanics of the collision under the influences of an appropriate potential hypersurfaaa(as outlined in section 6:5:1) is strictly required. vo Unfortunately, such calculations for the BrCN + CN --->— C N 2 2 + Br reaction are not known from the literature and are outside the scope of the present work. However, from comparison of this reaction with those of table 6:6 and the general considerations previously discussed, it is reasonable to assume, (i) that low mean vibrational excitation due to the light atom anomoly effect will not be observed, so that (ii) this moderately exothermic reaction will proceed via a 'mixed mode energy transfer mechanism' to form cyanogen in vibrational levels not far removed from that permitted by the thermodynamic limit.

Fortunately,crude guesses from these conclusions can be improved using the semi—empiric method of calculation for a o due to Smith (183). . A 'kinematic' factorj sing p, based simply on the mass ratios of the atoms involved in the transition state, is defined and correlated with the maximum excitation to be expected. 0 is the angle of rotation required to transform reactant coordinates into product coordinates.

Assuming a linear transition state of the A—Ba.0 type for reactions typified by 193

A EC AB 4- C (case 1)

Sint p .3(1.1A 4- EQ. MB MC) / (MA ME) (MB MC) 6:6

Ignoring contributions due to 'repulsive' terms

2 ingn p 0 =-VIB = s EEX° . where E--a is the energy of excitation relative to the 0 = 0 level and 77x0 is the exothermicity available.

Applying linear coordinates to the BrCN CN reaction where CN is treated as a rigid body acting as a stick mass a = 91,0 .

However, Smith (183) has emphasised that deviations from this upper limit are found if the transition state is not linear. Treating the

BrCN CT reaction as an A + BCD type (case 2) a lower degree of excitation is expected. The calculations due to Smith (cases i and 2), for several well known reactions are summarised in table 6:7. Ignoring the last reaction because of the poor fit, the calculated values due to case 1 are 3 to 17% of the exothermicity higher than experiment, and due to case 2 are -8 to 6,71 70 higher. As a first approximation, therefore,

a for step R:2a of scheme 3 is taken to be 87% of the exothermicity.

v, 6:5:2 The thermodynamics of C V 2 9 vo In order to include the vibrationally excited species, C 22 ' in the computer simulations of the reaction profile, a suitable estimate for its thermodynamic properties must be made.

The energy released to product vibration via reaction R:2a will, in the first instance, be located in that vibrational mode corresponding essentially to the C C stretch of the new molecule (cf. Table 6:8).

This energy can subsequently be ranicmised by rapid intra-mclecular energy transfers. For simplicity, therefore, it is assumed that the vo thermcynamic description of C2N2 differs from the normal molecule TABLE 6:7

THE COMPARISON OF THE PREDICTED AND OBSERVED DEGREE OF VIBRATIONAL EXCITATION FOR BIMOLECULAR EXOTHERMIC REACTIONS

[AFTM THE METHOD OF SMITH — Ref. 183]

Observed: E vib 2 2 1 REACTION — — AH E kcal mole-1 Sin p Sin f3 EEXO — -1 vib E kcal mole EXO

H + 0 ---+— HOv + 0 80 75 0.94 0.971 0.961 3 2 v 63 0 68 0.750 0 + 03_ ----›— 02 + 0 93 . 0.667 v 61 0 + 0010 ---*— 02 + Clo 34 0 56 0 656 0 619 v ONO ---7— 0.75 0.766 0 + 02 + NO 46 314. 0-674 Br + 0 -----)-- BrOv + 0 19 8 0.41 0.584. 0.446 3 2 Cl + 0 ----4--clov + 0 ' 40 11 0.28 0.656 0.54.3 3 2

Where the superscript v denotes a vibrationally excited species Sin 2 p is calculated for cas1; A + ABv + C 2 i Sin p is calculated for case 2; A BCD AB' + CD

TABLE 6:8

FUNDAMENTAL FREQUENCIES (from reference 37)

Fundamental Mode ** *Frequency cm- 1 Comments Molecule ascending Order No. Spectroscopic No.

C2N2 V 240(2) V1 5 bending V V 2 4 507.2(2) bending V • 3 1/ 2 850.6(1) essentially C-C stretch V V 4 3 2149(1)

BrCN V 1 ' V2 342.5(2) bending V 2 V1 575(1) essentially Br,-C stretch V V 3 3 2200(1)

Notes :- a) Br-CN length 1079 ; BrC-N length 10152; = 1800 b) NC-ON length 1.382 ; N-CCN length 1.157R; = leo o

c) * ; The number in parenthesis indicates the degeneracy of that mode d) **; Nomenclature used throughout this thesis 3.96 only in its heat of formation from the elements. Janaf (37) data for

C2N2 is, therefore, used throughout except that the heat of formation is adjusted by the mean excess vibrational enervy (EVIB) possessed vo '2 by C2 . For a o 87%

Hfo(C2N2v0) =Alifo(C2N2) + 36.8 kcal mole-1

6:5:3 Estimates for the rate constants

The estimation of all the rate constants, except k2a , k10 and k11 to k13 , have been discussed (section 6:4(a)); the values for the remaining rate constants are given below.

vo (k ) BrCN + CN C2N2 Reaction 2a 2a ' + Br

The forward rate constant (k2a) was modelled upon the classical exothermic equivalent (i.e. reaction R:2), assuming that the formation of a vibrationally excited species has little effect upon the reaction coordinate (cf. points (i) and (viii) of section 6:5:1(a)). That is, a large increase in the height of the activation energy barrier is not expected and, compared to reaction (R:2), only the heat of reaction will be different. vo Reaction R:10 (k10) ; C2N2 + M --4— 2CN + M

Polanyi (175) has discussed the dissociation of vibrationelly excited

species upon collision with an inert gas partner

v A2 + M --4— A + A + M

It was noted that not only should the vibrational levels greater than

v be included but that those less than v should also be considered

in the dissociation. Because of the tcrunchingt up of vibrational

levels towards the top of the potential well, however, the latter should

be included with a relatively reduced probability. vo In this work the dissociation of Ce1 2 was, for Simplicity 197

modelled upon the dissociation of normal cyanogen. The latter constant

for the latter has been measured (2; cf. reaction R:4).

-.5.5 PZ k = o :) exp(—D/RT) 4 5.52

33°45 10 T —5.0 expk-125000/RT)1.mol., 1 s.—i

where D is the dissociation energy of the C C bond. Treating vo the C2N2 as normal C N 2 2 but with the bottom of the potential well -1 (corresponding to Evill kcal mole ) removed, the rate constant is

given by

= 1033'45 T k10 -5.° exp(-0—EvIBVIIT)

1033•45 T-5.0 exp(-44394/T)1.mol71 sf1

Again for simplicity the consideration of extended collision frequencies

(Z*) was not included.

The vibrational relaxation steps; R:11, R:12 and R:13

C N M C2N2 + M (R:11) 2 2 --÷—

C2N2 0 + C N C2N2 + C N (R:12) 2 2 2 2

vo C N + BrCN C N + BrCN (R:13) 2 2 2 2

In order to solve the kinetics for systems involving vibrationally

thott species, all the relaxation equations for the v = v o levels shcifla bespecifically included. This further implies that the dissociation vo N2 of C2 should be computed duly weighted by the energies and populations of these vibrational levels. However, because of the large

number of relaxation eouations which would be required, this approach 3s

not practicable. In this work, the simplification is made that the net relaxation processes can be sLermarisea by single equations yielding average relaxation rates involving many quanta. It is, however, more

convenient to discuss the ramifications of the assumptions implied by

this procedure after the presentation of the computer simulations.

6:5:2 Discussion — The computer simulations for scheme III

Over 1000 simulations were performed for scheme III and the results

presented in figures 6:21 to 6:26 are representative of the dependence

of K upon the values chosen for the individual rate constants. The c rate constants appropriate to the trials are shown in tables 6:9 (lean

mixtures) and 6:10 (rich mixtures).

a) Lean mixtures

Trial A (Figure 6:21)

In order to demonstrate that an energy chain mechanism can reproduce

the low activation energy of ttrendt line C of the lean mixture results,

simulations were conducted for z and 1% mixtures at an initial unshocked gas pressure of 3 torr with a = 87% but with all deactivation steps

specifically excluded from the reaction scheme. As can be seen, the

temperature dependence of Ke follows the experimental curve more closely

than any of the previous trials based on either scheme I or scheme II;

(compare figures 6:21 and 6:14/6:15). However, as the temperature is

reduced, the absolute values of K c begin to fall higher than Ka . Also of note is the failure of the computed apparent rate constant to

scale in rBrCN12 ] least within 0 and [M 2 0 ' at the observed experimental scatter. It is evident, therefore, that vibrational

relaxation steps must also be included.

Trial B (Figure 6:23)

The effect of including vibrational relaxation steps was most marked

at low temperatures. Trials were conducted, where only the (V T)

relaxation (reaction R:11) is included but this, on its own, always failed

to reproduce the low values of Ka obtained for the rich mixtures. THE INDEX OF THE RATE CONSTANTS FOR SOME OF THE TRIAL

SIMULATIONS FOR SCHEME III -1 (only ka lk2a ,k3 , k11 , k12 and k13 are varied: units •- 1.mol. s. 1 )

k = 1055.45 T-5.0 exp( -62907/T) k = 108.54 T°.5 5 exp(-15849/t) k -10 = 1033.45 T-54O exp( -44394/T) k6 = 101064 exp( -25164/T)

TABLE 6:9 - LEA' MIXTURES (m = 00005; 0.01)

1 k k k k k Trial Figure :a 2a 3 11 12 13 . 1017'46 T-1.5exp(-41491/T) 108.7 T0.5exp(-1000/T) 1090 T0• 5exp(-14595/t) A 6:16

If !I !! t! It !I 109.0 P.5exp(-3000/T) 1 07.0T0.5 1 09.3 T°.5 B 6:17

It II It tt !! H 0. .5 9.3 0.5 108'7 T°.5exp(-1000/T) 106 '780T •5 101 °T0 10 T C 6:18 IT n n n n n 1017.76 T-1.5 exP(-41401/t) 106.9P.5 101°.°T°'5 109'3T0'5 D 6:19 TABLE 6:10 - RICH MIXTURES (m = 0605)

k k k k k Trial Figure 'lcd 2a 3 11 12 13

1017.76 T-1.5exp(-414-91/T) 108.7 T°.5exp( -1000/T)109.° T0.5exp(-14595/T) 106.9 T°5 1010.01'0.5 109- . -3T ° -5 A 6:20

1017'70 n I, 8.3 tt ,, 1010.0 H H 11 fl II 10 • B 6:20

H If II 60 " II '0 " H It If It 108 108 C 6:20

It II It It II II II I/ It ft 107.7 " D 6:21

It II It If It II /I II 107.3 " 1 09.7 " E 6:20

1Q17'46 II n n H II n 1 09.0 T0.5eXp("'3000/T) 109.0 109.7 P5 F 6:20 i 261

FIGURE 6:21 -1 -1 L MOL S THE COMPUTED RATE CONSTANT (as 8.0 LOG10 K C LOGI.° Kc) PLOTTED AGAINST 1/T2,o -SCHEME 3 - LEAN MIXTURES.

7'O BrCN) =0.005; 0.01 K a ettoftios. Pi mm. = 3 only. TREND LINE C (Figure 6:10) 4 TRIAL A - RATE CONSTANTS LISTED IN TABLE 6:8 10 /T

2.3 2.5 3.0 3.5 4.0

FIGURE 6:23 -1 -1 8.0 LOG10 L, MOL. S. THE COMPUTED RATE CONSTANT (as KC LOGI° Ke) PLOTTED AGAINST 1/T2,0 -SCHEME 3 - LEAN MIXTURES.

K - TREND LINE C a (Figure 6:10) otafttitc. 7.0 1-1(BrCN )=0.005; 0.01 P1 mm. = 3 only. 1(0.5%)

TRIAL C - RATE CONSTANTS LISTED IN TABLE 6:8 10/T 2.3 2.5 3.0 3.5 4.0

THE COMPUTED RATE CONSTANT (as LOGI.° Ke) PLOTTED AGAINST 1/T210 -SCHEME 3- LEAN MIXTURES. -1 1 8.0 LOG K L. M 0 L. S. FIGURE 6:22 10 C

K - TREND LINE C (Figure 6:10,)

Dashed line: expt. trend line' for the apparent rate constant. Solid lines: computer simulations - TRIAL B: RATE CONSTANTS LISTED IN TABLE 6:8

LOG FIGURE 6:24 1 O KC L M 0[2. S-.1

K - TREND LINE C

t%* a

N

Symbols as above. KaN. TREND LINE D 1(0.%) (Figure 6:10) TRTAL I); RATE CONSTANTS LISTED IN TABLE 6:8. 4 0/T V 2,0 3.0 3.5 4.0 203

As indicated by Boudart (163) the (V — V) resonant transfer of energy must be carefully considered. Inclusion of such a term (reaction

R:12) does indeed reduce the absolute values of Eb , but only to a minor extent, (V — transfers could never explain the dramatic fall of K with a increasing mole fraction of cyanogen bromide. The rate of R:12 was always relatively slow because of the relatively low vo concentration of C2N2 and particularly C2N2 in the initial stages of reaction.

The general matching of Ka and Ko for the lean mixtures, obtained using a P factor of approximately 1/20 for the dissociation of cyanogen bromide together with reasonable values for k2a and k3

(cf. Table 6:8), is encouraging. However, three observations indicate that the scheme requires further modification.

(i) The computed rate constant still does not scale in DrCN]

for the 1% and 1% trials, contrary to experiment. [ 2,0 (ii) Simulations for the rich mixtures (discussed more fully in the following section) yield. Ko values much higher than observed from experiment.

(iii) The scheme breaks down completely at low temperatures.

Trial C (Figure 6:22)

In order to improve the dependence of on [BrCN] b 2, 0 and 2,0 at least at high temperatures the additional relaxation step

(reaction i:13), involving collisions with BrCN , is included.

For trial_ C, the P factor of approximately 1/20 was retained for the rate constant for the initial dissociation of cyanogen bromide.

'trend' Although the matching of Kb to the experimental line is not as close as was obtained for the previous trial, which did not include the BrCN relaxation step, it is important to notice that at low

for the 15 simulations falls off more rapidly temperatures Kc ici does K for the -0 simulations. with decreasing temperature than c 204

Qualitatively, this behaviour reproduces the complexity observed (cf. figure 6:9).

However, if P=1/10 is retained for kä the Ka/k.c match is not improved to any significant extent simply by adjusting other reaction

rates (e.g. k2a and k3). Similarly, the lean mixture ke scaling

in [BrCN] 2 0 [Id 2 0 is not improved while retaining an absolute Ka/kc match, particularly at high temperatures.

Trial D (Figure 6:210

Increasing kd by a factor of two •1 e° P(BrCN) 1/10) and ° vo using a larger net rate of relaxation of C2N2 by increasing k11

(the V — T step) by a factor of 4/3 , greatly improves the [BrCN] 2,0 [ 2,0 scaling at least at the high temperatures. If k is increased still further, the fall—off in E is shifted to 11 lc correspondingly higher temperatures; if it is reduced the scaling in

[Bra] 2,0 [M] 2,0 begins to break down at low temperatures. The fall—off observed for K c is identified not with the failure of the vibrationally excited intermediate mechanism but with the

inadequacies of the rather crude mathematical model employed. The fall—off is sensitive to the ratio of the rate of dissociation of vo C21N2 to the rates of the relaxation processes. For the lean mixtures.) where the V — T process (R:11) is the most important, this

simplifies to the ratio of the rate constants kin/k11 . This is discussed in more detail in section 6:5:5.

1)) Rich mixtures

Simulations for the rich mixtures for 3 torr initial conditions are shown in figures 6:25 and 6:26 as log10 Ke vs. 1/T2 0 . The rate constants, employed for the various trials, are summarised in Table 6:10.

Trial A corresponds to the simulation based upon the final set of

rate constants determined for the lean mixtures (i.e. corresponds to

,205 TEE CONPUTED RATE CONSTANT (as LOGio Ke) PLOTTED AGAINST 1/T2,0 -SCImi 3 - RICH MIXTURES. 8.0 -I 1 L. MOL. S. FIGURE 6:25

(B)

7.0 K'a TREND LINE A PRIMARY SLOPES (Figures 6:9 & 6:10) TREND LINE B; SECONDARY SLOPES Solid Lines: Computer (Figures 6:9 6:10) Simulations. 104/ T2 ,0 2.5 3.0 3.5

eo LOG K L. MO L.L. S. 1 C FIGURE 6:26 (p)

(E)

7.0

Symbols as above DI-a TREND LINE B RATE CONSTANTS FOR (:) TRIALS k-F LISTED IN TABLE 6:9 K' TRTMD LINE A 10/T 6.0 2,0 1,0161=COSEI SAS ,....uommeUMISZ=W153 2.3 2.5 3.0 3.5 4.0

206

Trial D; Table 6:9; figure 6:24). Although the fall in apparent

rate constant with increasing concentration of BrCN has been

qualitatively reproduced, a quantitative match between K and X a -c is only obtained at low temperatures. It is also to be noted, however,

by K and K " that the two distinct rates of rise, characterised a 1 a is not reproduced. Typically, the simulations possessed an initially

sharply curved portion followed by a single 'maximum' rate. The

K 'A fit could be improved by reducing either k so that a 'c d prCN) 1/20 or changing k2a to the values shown in Table 6:10. P(BrCN) However, this is thought to be an artefact of the inadequate description

of the energy transfer processes rather than an indication that energy

chain kinetics are not applicable to any of the shocked gas conditions.

Conclusions from scheme III

a) Lean mixtures - 3000 to 4300K

The simulations based upon trial D (Table 6:9; figure 6:24) for the

lean mixtures reproduce the observed anomalously low activation energy of

trend line C over approximately a 3000 - 4300K range in temperature.

and Furthermore, the predicted apparent rate scales in [ BrCN] 2,0 [M]2 at least within the experimental scatter. ,0 The P(BrCN) factor of 1/10 for the dissociation of BrCN P

I \ at which scaling in pressure and fixes the lower limit to kdprCN) concentration can be maintained. Only reducing `c(BrCN) by a factor

of two destroys this scaling (cf. the trials for P,PrCN) 1/20).

where scaling was not specifically checked for values of T'3(BrCN) 1/10 but it is apparent from the sensitivity factors P(BrCN) computed by the program FROFIL (section !:2:5) that, at high temperatures

1 *1:2 1/10 , the rate determining step is the initial and even with ID,03rCit) dissociation of BrCN (reaction R:1), If P(BrCN) is increased, then

K should, therefore, still scale in [BrCINT] [Id c 2,0 and 2,0 ' 207

However, as is increased the time scales of the emission profiles P,rCN)P and the absolute match of K and E at high temperatures will be :a :0 destroyed.

In figures 6:27 to 6:32 some of the complete reaction profiles from experiment and by computer simulation (line—printer plots) are compared for results obtained where K and K have been matched using Trial D a c (Table 6:8). As can be seen the match in profiles is good. However, the computer simulation, while quantitatively matching the early portion of the experimental records, typically predicts large peak intensities.

This is probably-due to a failure of the averaging of the energy content vo of C N and unfair weighting to high vibrational levels. It should 2 2 also be noted, however, that as proposed by Patterson and Greene (102) dissociation of CM, at the longer test times of peak emission, may also

be important: this was not investigated because boundary layer formation

and attenuation effects become troublesome at these long test times

(cf. section 4:3). Scheme III was the only mechanism tried which could reproduce the initial structure of the 'exponential' curve in the rise

of intensity particularly characteristic of the mid—temperature 1% 3 torr runs (cf. figures 6:28 to 6:30). The simulations for some 2 3 torr runs are also shown for comparison in figures 6:31 and 6:32.

b Lean mixtures — less than 3000K

As has been noted, scheme III always failed to reproduce the

experimentally observed apparent rate constant at low temperatures.

The apparent activation energy predicted by scheme III became steeper

at these temperatures and resembles that predicted by the more tclassicalt

mechanism — scheme II. In view of the somewhat crude assumptions made

for the energy transfer processes, this is not surprising. The present

scheme, in effect, underestimates the contribution to the overall rate

from dissociation of vibrationally excited cyanogen possessing excess energy other than that defined by the initial partitioning of the 208 -10

e e

G FIGURE 6:27

O 1 7. ; .9..CN/ AR z 0 IA_""' Pi -7- 3 cnrn u 1.992E5 CM/ SEC 0 6,c..: Tzo = 3838.2 K Illi RATE CONSTANTS TABULATED Pf--\ TABLE 6:9 TRIAL D

PHOTO 258

A EXPERIMENTAL

0 COMPUTER PREDICT ION

6 3 9 LAB. TIME 11SEC.

•e U

P H OT_O____) 60 0 EXPERIMENTAL Q COMPUTER PREDICTION 0 4

Mc FIGURE'. 5:_23

A\ 1 •/ ; Ar, P. z 3 rra . • 84:5E 5 SEC T20 z 3317:;•7 K

RATE CC tsSTAr.TS TABULATED TABLE 5:9 - TRIAL D

3 6 9 LAS. TIME µ SEC. 209

1 1 10 0 PHOTO 404 e A EXPERIMENTAL 0 • COMPUTER PREDICTION IT NS TE

I N FIGURE 6:29

1 '/.; CNi

P1 -- 3mm 1.7857E5 CM/SEC. T z 3136 K 20 0,_ 413 ,,azo RATE CONSTANTS TABULATED TABLE 6:9 - TRIAL D.

3 6 9 ' 12 15 LAB, TIME µSEC.

12 10 0 0 0 0 a1-A 0 T 0 401

A EXPERIMENTAL

O COMPUTER PREDICTION

0 SITY N TE

I N 0 FIGURE 6:30 5 - 1% ; B•CN 3 mm 1.7391E5 CM /SEC - 2988 K T2,0 -

RATE CONSTANTS TABULATED TABLE 6:9 L TRIAL D.

r• 1 4 8 12 15 LAB. TIME µSEC,

2.1.0

0

PHOTO 42 5 .

E X PERI1,4E1". T 0 e COMPUTER Pk".71DICT iON

0

F !GU RE 6 : 31 A 'i2 I. ; BCNIAg 3 min P1 1. 9 9 2 E 5 OA/ `DHC 4 59 • RATE. coNsTA NTS TA r_IULATE Ti,eLE 6:9 TRIAL D.

2 4 6

L AF\ TIME µS EE. 1 1

10 FIGURE 6:32

112 ; BRCN/Ait - 3mm T 3529 K >- P1 - H 2 ,0• 1-9048E5 CM/SEC (r) z LU RATE CONSTANTS TABULATED z TABLE 6:9 - TRIAL D.

PHOTO 409

A EXPERIMENTAL LINE - COMPUTER PREDICTION

tl 3 6 9 LAB. TIME 212 exothermicity of reaction R:2a (i.e. dissociation from lower vibrational

N , where v < v is ignored). levels of 2 2 o As written, scheme 3 only allows for the dissociation of cyanogen molecules possessing either the maximum excess internal energy or none at all. Similarly, the deactivation steps are written as 'all or nothing' reactions. In detail, this is obviously unreasonable because the probability, that a collision will result in the transfer of energy to or from internal modes directly to or from translation, is largest for sme11 single quantum jumps (19). As a consequence of this collisional relaxation, the initially sharply peaked energy distribution for the newly vo formed C N will, in time, be smeared out to lower energies. 2 2 From the matching of K and K at high temperatures, it is a evident that for the limit

k10/k11 >>. 1 the rate determining step is not the dissociation but the formation of vibrationally excited cyanogen. However, at low temperatures because

of the inadequate weighting given to lower vibrational levels of cyanogen

an artificial 'bottle-neck' to CN formation is introduced when

k10/k11 << 1 . The characteristic time available for relaxation of

a particular vibrational level, v , is given by the time lapse between

consecutive dissociative encounters. That is

t = 1/k1 [M]

is given for the step where k1 Oa

c N N -4- 2CN + N (R:10a) 2 2

In order to give a more appropriate weighting to vibrational levels in

must be computed as a function of the range v = 0 to v = vo , kl0a the average internal energy at the moment of dissociation: this procedure 213 is adopted in scheme IV of this thesis (section 6:7). c) Rich mixtures

The fall in K a with increasing mole fraction of BrCN is reproduced at least qualitatively by scheme III. However, the simulated profiles

do not exactly match the experimental records. This difficulty is again associated with the crude description of the energy transfer

processes and its failure to give a correct weighting to the energies and relative populations of all the vibrational levels of cyanogen.

If the rate of deactivation of C N 2 2 is fast compared to its

dissociation and k104k11 falls far below unity, then the energy chain kinetics will be suppressed and the reaction mechanism can be adequately

described by normal 'classical' kinetics (i.e. scheme 2). The scaling

of the 5 and 10% experimental rate, derived from the primary portion

of emission records, suggests that this 'classical limit' is appropriate

for the initial rise in intensity for the rich mixtures. The simulations

for the lean mixtures, using energy chain kinetics (scheme III), and

those for the rich mixtures using classical kinetics (scheme II) should,

therefore, yield rate constants for R:1, R:2/R:2a and possibly R:3 in

close agreement. This is discussed with particular reference to the

detailed shape of the comnuter/experimental profiles in section 6:6.

d) The significance of the 'best fit values' of k11 , k12 and k13 .

The majority of polyatomic gases show a single vibrational relaxation

time involving the whole heat content of the molecule. Rapid vibration

to vibration intramolecular energy transfers normally maintain a

continuous equilibrium distribution of the vibrational energy between

the various fundamental modes and the whole energy relaxes with a rate

characteristic of the (V T) transfer via the lowest frequency (184).

The lowest available frequency for polyatomic molecules normally corresponds

to a bending motion. In a theoretical study, however, Dickens and Linnet -(185) have 214 shown that for molecules where there is a large gap between the two lowest modes, the intra-molecular transfer can proceed more slowly than the inter-molecular (V - T) transfers and two different relaxation times can become apparent. Adopting the convention of numbering the vibrational modes by increasing frecuency this condition was found to -1 be met when V 2V For cyanogen V = 26,5cm and 2 '" 1 ' -1 V 2 = 506cm (cf. Table 6:8) and it is expected that more than one relaxation time should be observed.

Dickens (186) has conducted theoretical calculations, based upon. the Swartz, Slawsky and Hertzfeld formulation (cf. Hertzfeld and Litovitz

(187)) and has found that three separate relaxation times involving

and V 3 are predicted for cyanogen. Dickens predicted V1 ' V 2 that the efficiencies for the V - T relaxation via these modes are in the ratio 1 : 1/2.5 : 1/350 respectively, relative to relaxation via the V i mode. Unfortunately, it is not uncommon for theory to predict multiple relaxation times and yet for experiment to yield only one (e.g. CHC1 and CC1 - ref. 163). 3 Initial estimates for the V - T relaxation involving an inert gas collision partner were based upon the Lambert-Salter correlation for polyatomic molecules not containing H atoms (188). (Molecules containing H atoms relax more rapidly than other molecules). During the course of this work, however, Lambert et al (189) published results for the relaxation of cyanogen determined from acoustic measurements.

These were found to be in agreement with the rough estimates based upon

Lambert-Salter correlation and also to some extent with the SSH calculations. It was found that cyanogen does in fact relax with two distinct relaxation times characteristic of the V 4 and V 2 modes

1 ,0 = 18 at 294°K

212 = 220 215 where Z1 0 is the collision number for relaxation via V 1 only and

is that for the relaxation for mode V together with all higher Z12 2 modes through V - V transfers. The vibrational energy levels and

N due to reference 189 are reproduced in figure 6:33. transitions for C2 2 From the simulations, the finally adopted value for k11 is 6 1 -1 -1 8 x 10 T2 1.mol. s. (Trial D, Table 6:8). Recasting this in terms 0 of a collision efficiency (assuming a 4A collision diameter), the relaxation, as written, goes approximately 1 in 1.3 x 103 collisions. Unlike the acoustic results of Lambert et al (189), however, the rate defined by this

collision efficiency does not refer to single quantum jumps but to the

number of collisions required to remove sufficient energy to prevent

dissociation.

For the lean mixtures, where the bulk of the relaxation proceeds via

reaction R:11, and only considering the temperature range over which Ka are matched (cf. figure 6:24 : trial D) then at 3500K , if the and lcC excess energy is reduced by 15% of the exothermicity (i.e. approximately -I 6 kcal mole ) the rate of dissociation of the vibrationally excited

species is only reduced by a factor of 2.'37 . At these high temperatures,

the rate of reaction is not particularly sensitive to such small changes -1 in the rate of reaction R:10. Dropping EvIB by 6 kcal mole corresponds

to approximately 10 quanta of the V1 mode and 5 quanta of the

V 2 mode. The collision number per quanta of the V 1 mode is, therefore,

the Z1 value of 18 (at 284K) found 130. This is not compatible with 0 by Lambert et al (189). The corresponding collision number per quanta

of the V mode is, however, 260 which is in rough agreement with 2 Z12 = 220 from Lambert et al. It is tentatively suggested that the

order of magnitude discrepancy found upon comparing Lambert et alts

Zio value and the collision number calculated here for the V 1 mode,

and the much closer agreement observed between Lambert et alts Z1,2 value and the collision number calculated for the V2 mode, indicate a) that a 6

FIGURE 6:33

THE DOUBLE RELAXATION OF CYANOGEN: THE MECHANISM DETERMINED BY LAMBERT et al. FROM ACOUSTIC MEASUREMENTS.

•••••••••• 1000

BOO 1) - (em 600 uency eq fr 400

200

Y yl )2 3 -Vibrational energy levels and transitions for C2N2.

Zio = 18 AT 294 K Z12 = 220

THE VIBRATIONAL MODES OF CYANOGEN ARE NUMBERED 1N ORDER OF INCREASING FREQUENCY -•-- cf. TABLE 6:11 217 the slow intra-molecule redistribution of energy among the normal modes of cyanogen form a 'bottle--necks to the relaxation of vibrationally 'hot' cyanogen and b) that the bulk of the energy relaxes in a parallel mechanism via the. V 2 mode (cf. figure 6:33). It is interesting to note that at sufficiently high temperatures RRKM theory may no longer be applicable to the dissociation of the quasi-diatomic molecule

C N 2 2 and that this may account, at least in part, for the low activation energy and the large numbers of square terms determined by Fishburne and

Slack (73, 97) for the dissociation of cyanogen behind incident shock waves at temperatures as high as 4000K; Ea = Dfc --71 RT . 2 2i The apparent rate was not sensitive to k13 ; a detailed discussion of the final fit value is, therefore, not warranted. It is, however, worth commenting that k13 for a C2N2v C2N2 (V - V) exchange is approximately 1.3 x 103 times larger than k11 for the C2-N2v+ M relaxation. This must surely represent an upper limit to k13 because, using the approximations already outlined, a collision efficiency of unity, for the removal of 5 quanta of the V mode or 10 quanta of 2 the V1, mode, is indicated. In view of the very low concentrations of C N 2 2 formed immediately behind the shock front, it is not surprising that the (V - V) relaxation with normal C 2N2 is unimportant. It was found, however, that including deactivation by BrCN enables the scaling and fall in the apparent rate constant with increasing concentration to be reproduced. The value finally adopted for k12 is large compared to k11 (i.e. 2 x 109 T2 1.mol. s. ) , suggesting that

(i) BrCN is a particularly efficient collision partner in the removal of small amounts of energy and/or

(ii) BrCN may remove large amounts of energy on a single collision, although the probability may be small.

These points are discussed below.

Lambert et al (189) have emphasised that for gas mixtures the collision number for relaxation by a (V - V) energy transfer increases a 8 exponentially with the difference A V between the frequencies of the exchanging modes: for those exchanges where A V < 100cm- 1 very rapid near-resonant exchanges can occur. For example, it has been observed (189) that the normally doubly relaxing gas, SO2 , relaxes with a single short relaxation time when dosed with the singly relaxing gas, 91321'2 . This is attributed to the near-resonant exchange between the V mode of SO and the V and V modes of CH2F2 , because 2 2 3 4 -1 the difference V is only 35cm-1 and 25cm respectively. This phenomenum, whereby relaxation is 'catalysed' by the addition of a foreign gas, has been fully discussed elsewhere (190). It can be seen from

mode table 6:8 that Av for the \I 2 mode of BrCN and the V 2 -1 of C N is 71cm and rapid near-resonant energy transfers are not 2 2 unreasonable.

Rabinovitch et al (24) have shown that large amounts of energy (e.g. -1 30 kcal mole ) can be removed from vibrationally 'hot' species, on a single collision, depending upon the complexity of the collision partner.

From empiric calculations Rabinovitch and Lin (191) have related this

dependence upon the nature of the collision partner to the coupling between the degrees of freedom of the collision complex. It was also

noted that if the collision partner is complex (e.g. pentene-1) large

amounts of energy can be removed with a higher probability than the low energy (single Quantum) transfers. It should be noted, however,

that the studies due to Rabinovitch (24) are concerned with the

stabilisation of species containing energy in excess of the dissociation

threshold. It is not clear if the direct extrapolation to molecules

containing excess energy below the dissociation threshold is valid.

From this work, however, it is evident that BrCN is some 250

times more efficient, in removing sufficient energy to prevent the

dissociation of vibrationally excited cyanogen, than is argon.

o:o The Comparison of results from Schemes II and III The proposal that the threshold of 'classical kinetics' is approached 719 for the rich mixtures is supported by the agreement in k and d(bru:) A2a determined for schemes II (rich) and scheme III (lean) - the '2 small differences in the former are not significant.

i.e. kdDrON) = 1017.70 T-1.5exio(-4140.0) 870 T2 exp(-1000/T) k2 = k2a = 10 -1 -1 (units: 1.mol. s. ) .

However, a more detailed consideration of the secondary rising portion for the 5% 3 torr runs (cf. figures 6:L and 6:8) must be given. This secondary rate is no longer discernable if the initial mole fraction of

BrCN is increased (i.e.t40%) or if the total gas pressure is increased

(i.e. 10 torr). This is, however, to be expected, if the collisional

deactivation of vibrationally excited cyanogen tends to suppress the

energy chain kinetics. It is, therefore, proposed that residual energy chain contributions, due to residual energy retained by cyanogen, are

still operative in the rich mixtures.

In order to check these proposals, a few simulations using the rate

constants due to Trial 6:11:H (Table 6:5) of scheme 2 were repeated but

with the rate constant k5 for the step

C N M 2CN M (R:5) 2 2

varied. The experimental and computed profiles for some 5% 10 torr

runs are shown in figures 6:34 to 6:37. Unfortunately, the process of

profile fitting becomes more unwieldy as the number of variable parameters

and is increased and a detailed investigation of the dependence of Inc profile shape upon k5 was not undertaken. In order to obtain the

excellent fits shcwn in figures 6:35 and 6:36, it was necessary to

reduce k 3 by a factor of two and increase k by a factor of 2.14 5 At these temperatures, this change in k5 is equivalent to a reduction

in the apparent activation energy for R:5 of approximately 9 kcal mole-1 0

0-';';%-*P -LTER 5 It/ULATION Z:::\ - E/PERIMENTAL RECORD 0 PHOTO 6650 0 0

0 0 0 FIGURE 6:34 1.7762E5 ::i/S 10mm;"5./. BACN IN AA Tzo = 3122.5 K

1 1 RATE CONSTANTS L. MOL. S.

z 1017.70 T 1 5 Kd EXP(-41491/T) 8.70 K =10 TC).5 EXP( - 2 1000/Tj K3 z1d0.00 T °.5 EXP -145951T')

K4 =1033.45 T-5.° EXP -62907/1

K5 :-.108• 34 T0.5 EXP -158491T) K6 =10040 EXP (-2 5164 /1)•

I.E. AS FOR TRIAL 6:11,: H

4 6 8 LAB. TIME p. SEC.

1 1 10 641 AA/6 Az AA 0 0 AL\

C AI&

WITY A TE

N A I 0 A F I GtJRE 6:35

0 A CONDITIONS - AS ABOVE.

RAW CONSTANTS AS ABOVE EXCEPT 33.60 -5.0 K4 =10 T EXP(-62907/T)

0 COMPUTER SIMULATION

A EXPERIMENTAL RECORD PHOTO 660

4 6 LAB. TIME µSEC. 221

AL 2 jr; z 5 z AO Eic2ILRESLI6 A 10mm ; 51. BRCNIN AR T20 3122.5 K 1-7762E5 CM/ S 4411

LS) RATE CONSTANTS-AS FOR FIG 0 6:34, EXCEPT . =10-709-5 0 I K 14595 /T) 3 T E X P' - 33.78 -5.0 1".4 =10 T EXP(- 62907/T)

® -COMPUTER SIMULATION

EXPER IMENTA L RECORD PHOTO 660

2' 4 6 LAB. TIME ;I SEC.

10 11

LK°\ i 1A* Z 3 w \5r' z At\

FIGURE 6:37

10 um) ; 57. BP.CN N AR T 2,0 7- 3024 K 1 7452 E5 CM/S

RATE CONSTANTS -AS FOR FIG 6:34, EXCEPT 9.70 0•5 / K .7-. 10 T EXP\- 1459511) 3 • 33-78 - K4 =10 T -5 0 EXPc62907/1)

0-COMPUTER SIMULATION A- EX PER IMENTAL RECORD PHOTO 656

6 8 LAB TIME µ SEC 222

In other words, the detailed profiles at longer test times are improved -1 if residual energy of about 9 kcal mole promotes a small

contribution to energy chain kinetics.

In the simulations reported for the 50 3 torr runs using

scheme II, it will be remembered that attempts were made to reproduce

the secondary rate of rise of intensity by increasing the relative

contribution due to the BrGN Br step (reaction R:3). At low

temperaturesI this was apparently successful (curve A of figure 6:19)

but at higher temperatures the fit is not as good (e.g. curve A

figure 6:16). Furthermore, the activation energy for the BrCN Br

step is low compared to that anticipated from the literature. However,

from the fit only to the primary rate of rise (Trial 6:11:H - table 6:5)

—1 —1 k = 10lo T12 exp(-14595) 1.moi. s. 3

which is more reasonable. From the attempts to match the profiles of

the 50 10 torr runs by adjusting k5 , it is evident that the 'peaks

nature of the simulated profile can only be removed by reducing k 3 by a factor of two (figures 6:34 - 6:37). The value given for k 3 probably represents an upper limit but even so it is unlikely to be more

than a factor of two out,

6: 6 :1 The comnarison of k/ with the prediction due to Keck and dABrG71

Kalelkar

As was noted in Chapter V the value reported for the rate constant

measured by Patterson and Greene (102) is nearly two orders of magnitude

lower than that predicted by Keck and Yalelkar (108) at 3300K using

RIM calculations. It is gratifying to note that the difference

between experiment and calculation for the present work now lies within

the expected range of values. At 3300K , kd from experiment is 6'8 -1 -1 106.96 1.s.o171 5:1 and from Keck and Kalelkar is 10 1.mo1. s. ;

there is only a factor of 1.45 difference. 223

6:6:2: Uncertainties in the rate constants determined from the

computer modelling

It is important to estimate the extent to which any given rate

constant os a reaction scheme is isolated from the others by the profile /kc matching and the fitting. The uncertainties in the individual elementary reaction steps can be estimated from the

sensitivities computed by the program PROFIL using equations EQ. 4:8

to EQ. 4:11 (cf. section 4:2:5). For the lean or the rich mixtures at

high temperatures, the dissociation (R:1) is the most important step;

the sensitivity factors for schemes II and III are reproduced in figures *6:38 and 6:39 for various temperatures. For an estimated experimental

error of corresponding 125% in the Ka/kc matching, the uncertainty in kd(BrCN) is 3355 at high temperatures. Applying this to the

sensitivities obtained for the low temperatures, where the other

reactions become important, the uncertainties in the values of k and k 2 3 as required to preserve the Ka/kc match to within ±25% are less than

+30%. In this analysis k and k are known from the literature; , 4 5 further notes are given with the figures 6:38 and 6:39.

It is also pertinent to point out that the Ka/Kc matching obtained for the lean mixtures using scheme III at moderate to high temperatures

is not particularly sensitive to small changes in ao (i.e. 70 — 87%). This is reflected in the near zero sensitivities for R:10 to R:13.

6:7 Scheme IV — The Solution by Iteration of the Average Energy of

Excitation (E v) at the Moment of Dissociation

kd (R:1) BrCN + M < % Br + CN + M (R:2b) BrON + CN < ›— C N v + Br 2 2 (R:3) BrON + Br < Br2 + CN (R;10a) C2N2v + 2CN + M

f.2 SCH-TM Il SENSITIVITIES FIGURE 6:38 20_ (for rich mixtures - M=0.05; F1-3 toter; 60- T =3771 K T =3063 K 20, 2,0 40- H 20

VII

-20- 2:1 R:2 R:3 R:4 R:5 R:6 R:1 R:2 R:3 R:4

6 : 3 9 t 1 /t2 SCIEMi] III f;:',SITIVITIES- FIGURE (for lean mixtures - M=0.005; P1 =3 tore)

40- T2,0=3836 K

/0 20-

0

-20 - R:1 R:2a R:3 R:10 R:4 R:5 R:6 R:11 R:12 R:13

40- .,3529 K T2.0 20

0 OMB

-20 - R:1 R:2a R:3 R:10 R:4 R:5 R:6 F111 R:12 R:13

DIAGR%703 OF THE P]ROENTAGE CHANC;] IN THE RATIO (tilt?) AS 1),77,FITf.:D IN SXTION 4:2:5 IN TERMS CF CN FORMATION. Notes:- The uncertainty in ka for reaction R:1 is given by the high temperature and low mole fraction sensitivities where other reactions are of lesser importance. The uncertainties in the remainder can, therefore, be derived from the low temperature, lareer mole fraction results where they become importm From the figures above, R:10,R:11, R:12 and R:13 of scheme III are not important and the uncertainties are not Serived; A:4 and R:5 are known from the literature. The uncertainties calculated for kd, k and k d' 2 -3 are given in the text.

224-

N + 11 ---4- 2CN + M (11:4) C2 2 ----<

(R:5) Br2 + M —4- 2Br + M -4 ---

(R:6) 2BrCN =: Br + C N 2 2 2

In appearance, this scheme is similar to-that of scheme III where

the relaxation steps R:11, R:12 and R:13 have been excluded as specific

elementary steps. However, implicitly R:11, R:12 and R:13 are

accounted for by the definitions of R:2b and R:10a. The superscript v

represents the vibrational level of the excited species containing 1 Ev kcal mole of excess energy, relative to an equilibrium distribution, at the moment of dissociation.

That is v < v where v is defined in scheme 3 to be equivalent o o to the initial degree of excitation due to the complex energy partitioning vo involved in A + BC AB + C exothermic reactions. In this

alternative energy chain mechanism, the deactivation steps are, therefore,

not explicitly written but are implied from the value of Ev .

a) Assumptions

E v is a function of the net rate of relaxation of the excess vibrational energy. The energy (AE) released on average to

translation, within the time scale of consecutive dissociative collisions,

is given by

A E = a o EXO Ev

where, as before, a o is the percentage of the exothermicity ( EEXO) initially partitioned to the vibrational modes of the newly formed

cyanogen.

The simplifying assumption is made that any vibrationally excited

cyanogen molecule can be treated as a unique 'chemical speciest,

characterised by the magnitude of Ev . The contribution of the

exothermicity of R:2 is, therefore, readily incorporated in the bulk 225

gas temperature by solution of the thermodynamics where

(C N ) + E 6:6 A Hf (C2N2v) = A Hf 2 2

In this way due account is made of the 'trickles of energy to translation as a result of (V — T) relaxation.. b) The rate constants For the reasons outlined in section 6:5:3 k2b was taken to be

Al]. the rate constants, except the same as k2a (and hence k2 ). k10a ' were taken directly from the best fit trial to the lean mixtures for scheme 3: i.e. Trial D; Table 6:9; figure 6:24.

The rate constant for reaction R:10a is defined in terms of Ev using a Kassel type equation

i.e. k10a = AT—nexp(—(D—Ev)/RT) where D is the dissociation energy for the normal molecule. For simplicity k10a is modelled directly upon k4 for the dissociation of C N and 2 2 -1 k10a = 103.45 T-5.° exp(-(125000-Ev)/hT)1.mol. s. For clarity the values used for the remaining rate constants are syrmarised below.

k = 1017.75 T-1.5 exp(-41491A) 8.7 / T2 expk-1000/T) k2b = 10

k 3 = 109.° T.2 exp(- 14595M

k = 1033.45 T-5.° exp(-62907/T)

k 8•34- / 5 io T2 expk-15849/T) 10.4 k6 = 10 exp( —25164/T)

It should be noted, however, that 226

v (i) because the heat of formation of C N 2 2 is a function of the average excess energy Ev , the heats of reaction for those steps

involving C2N2 (i.e. R:26 and R:10a) will similarly depend upon the

magnitude of Ev Furthermore, since the reverse rate constants for

R:2b and R:10a are calculated from the appropriate equilibrium constant,

they will also be dependent upon E . That is to say, if E t a E v v o EXO 21) k_2a (i.e. EVIB) then k

(ii) when E = 0 , the important reactions of the present mechanism, v including their reverse steps, reduce to the best fit values obtained for

the simulations of the rich mixture limiting conditions using scheme II

(i.e. Trial 6:11:H; Table 6:5).

c) The computation

Because E is the only variable parameter allowed in the present v scheme, the computer program was reconstructed to automatically iterate

upon values of E until K matched input values of K . (In v :c a practice the logarithm of the apparent rate constant was matched and the

test for convergence was 1% ). The thermochemistry of C2N217 was always adjusted, according to equation EQ. 6:6, after each step in the

iteration. Further details of the computation and the weighting procedures

employed to speed up the iteration are described in Appendix II.

6:7:1 Discussion — The computer predictions of a 0 from scheme IV

This reaction scheme was used to investigate the apparent rate of

reaction at temperatures below 3000K where scheme III fails. Simulations

were conducted for four temperatures covering this region. Values of

for the 1O 3, 5, 10 and 20 torr results, were determined by Ka ' interpolation and values of Ev iterated until K0 matched Ka .

In keeping with the nomenclature used so far, the parameter CX is

defined by

a = Er /E-111X0 7

and is expressed as a percentage. The variation of a with initial unshocked gas pressure (P1) is shown for the four temperatures in figures 6:4.0 to 6:43. As is expected, the degree of excitation (cc ) at the moment of dissociation, which is required to reproduce the

apparent rate constant, falls with increasing pressure.

The value of a at zero pressure corresponds to the initial degree

of excitation due to the partitioning of the exothermicity to vibrational

modes of the product cyanogen; i.e. Ct o . For the lean mixtures, where

the relative concentration of argon is very high, the net rate of

relaxation will proceed predominantly via the (V T) process and is, C therefore, expected to be first order in 2- 2

i.e. -d a/dt = K a

where K is the quasi-unimolecular rate constant. Upon integration

this yields

a = a a exp(-at)

and K is given by

K=kR [M ]

where A is equated with the rate constant for the net rate at which energy is transfered from vibration to translation. Plots of log10 a

against the initial unshocked gas pressure (pi ) should be approximately linear: this is shown in figure 6:44. The plots are linear from 3 to

10 torr but at higher pressures a marked curvature, for all but the

highest temperature (3236K), is observed. Extrapolations to zero pressure

at each temperature give values of a o between 59 and 69% of the

exothermicity. This is to be compared to the value of 87% estimated

from the literature.

The low value of a o = 59,1, was obtained for the highest temperature (3236K) investigated using scheme IV. It is to be noted that this lies

ao 228

Fi GUpE 6:40

60 .--- 2740 K a% 50

40

30

10 20

90

70

60 a'/,

50

40

30

P1 mm

130

70

60 a7, 50

40

30

3 5 10 20 P- mu) *

9C

FIGURE 6:43 70

z- 3236 K 60 1-47u cr.%

50

40

;0

5 10 20 P mm 1 FIGURE 6:44

2.0 LOG a THE DEGREE OF EXCITATION (as logio a) AT THE MOMENT 10 C2N2V DISSOCIATES PLOTTED AGAINST THE INITIAL PRESSURE Pimm. RESULTS FOR SEVERAL TEMPERATURES ARE SHOWN.

T2,0 K SYMBOL. 3236 C3 3012 0 2857 A 2740 Points coincident

P mm 1 230

thin the temperature range (3000 - 4.300K) for whch scheme III (Trial D;

Table 6:9) matches the apparent activation energy of trend line C. For

these simulations, it is emphasised (cf. section 6:6:2) that the computed

activation energy at high temperatures is not particularly sensitive to

small variations in CL 0 , k10 and k11 . That the apparent rate

is not sensitive to the exact degree of vibrational excitation at

temperatures greater than 3000K is seemingly confirmed by the scheme IV

simulations at 3236K (figures 6:43 and 6:44 - squares) where the iterated

values of CL do not fall upon a single smooth curve and the extrapolated

value of 0. is low. 0 It is, therefore, more appropriate to discard the high temperature

Ca iteration and only consider the lower temperature simulations. The extrapolations to P1 = 0 for the remainder cluster between a 0 = 65% and 69% of the exothermicity. This is still somewhat low compared to

the original estimate of 87;o but in view of the approximations involved

is in reasonable agreement. The difference in energy predicted for vo C 19 -1 2 is approximately 7°6 kcal mole which is only about RT. This is probably due to the crude estimation of the dissociation rate

constant for v C2N2 . Because of the approximations involved, further analysis using scheme IV to obtain relaxation rates was not considered

to be worthwhile.

6:8 Concluding Remarks

A complex mechanism involving the formation, dissociation and relaxation of a vibrationally 11100 intermediate is required in order to reproduce the complex dependence of the apparent rate of reaction upon

temperature and gas composition. From the quantitative fits for the limiting rich and lean mixture conditions (schemes II and III respectively) the following rate constants are determined (1.mol. units).

BrCN + Br + CN + M; = 1017°7 T-1.5exp(-41491/T) 231

BrCN + CN Br + c2 8. 7 -;1- N •2' k- e = 10 T'exp(-1000/T) 10 BrCN + Br ---4- Br CN; k = 10 T-'expk-14595M 2 3

with an estimated maximum uncertainty of t 50% at the mean temperatures

of this study.

6:8 Recommendations for Future Work

(i) The presence of the proposed vibrationally excited intermediate

should be checked experimentally. However, the direct observation of

non-equilibrium energy distributions in the product cyanogen molecule by

infra-red emission measurements is precluded by the low concentrations of

the excited species behind the incident shock wave. Alternatively, the

BrCMAr may be dosed with foreign gases in the hope of observing enhanced

relaxation rates. From computer simulations, however, for BrC7/C2N2/Ar

mixtures it is apparent that any enhancement of the relaxation due to

C N lb 2 2 2Nv collisions involving rapid (V - V) energy transfers will be masked by the dissociation of the added cyanogen close to the shock front.

Nevertheless, an enhancement of the relaxation rate and a consequent

increase in the experimental activation energy for the lean mixtures is

expected if Helium is used as the foreign gas.

(ii) Because the reaction

ICN CM C N ICN; o 2 AH = -52 kcal mo171 is more exothermic than the BrCN analogue, it would be of interest to

investigate the role of energy chain kinetics in the shock wave

decomposition of cyanogen iodide. 232

CHAPTER VII

THE PYROLYSIS OF CYANOGEN CHLORIDE

7:1 Introduction

In this chapter, the results for the thermal decomposition of cyanogen chloride are reported. Emission measurements at A = 421'5nm from incident shocks in cyanogen chloride/argon mixtures were made in a similar manner to those for cyanogen bromide. The rate of rise of intensity is re-cast in terms of the apnarent rate constant, Ka which is compared to that predicted by the computer simulations, K , using the C1CN analogues of equations EQ. 6:2 and EQ. 4.:14. respectively.

The experimental results are presented only in terms of Ka .

7:2 Results 7:2:1 The emission profiles at X = 421.5nm The temperature, Pressure and mole fraction ranges are respectively

T20= 2667-3704K, Pi =3,10 and 20 torr and m(c1m) = 0.005 and 0'05 .

Some typical oscilloscope tracings are shown in figure 7:1: the separate records have been superposed so that the shock fronts coincide.

Typically, the records resemble those obtained for cyanogen bromide.

However, the curvature of the initial portion is less pronounced for the V 3 torr runs and is replaced by a rapid near linear rise as the total gas pressure or the initial mole fraction of cyanogen chloride is increased.

7:2:2 The apparent rate constant (Ka)

The results for

(i) m = 0'005; P1 = 3, 10 and 20 torr (open symbols)

(ii) m = 0.05; 1 = 3 torr only (filled symbols)

233

FIGURE 7:1

SAMPLE OSCILLOSCOPE TRACINGS. X= 421.5ron.

1/2% C1CN in Ar; Pi=3mm Trace Run V/cm T2;0 a 58L 100 3705 K b 597 10 3138 K

1/2% C1CN in Ar; P1=20mm Trace Run V/cm T2,0 a 601 200 3255 K b 614 100 2942 K c 617 10 2834 K

MARKS THE POSITION OF THE SHOCK FRONT

TIME SCALE: 2 p,sec/cm. 1 cm

5% C1CN in Ar; P1=3mm Trace Run V/cm T2,0 a 643 200 3593 K b 637 20 3246 K 234 are shown in figure 7:2. Ka (in log units) is plotted against the 10 reciprocal temperature at the shock front. For reference, the

dissociation rate constant, kd , determined by Bauer et al (85) for

the step k d

C1CN + M --+— Cl + CN + M (R:1)

= 1013.53 exp(-91500/RT)1.mo171 1 is also shown (dashed where kd s7 line). The close agreement between line A and k in the temperature d regime where the present emission results overlap the absorption results

of Bauer et al. must, however, be regarded as fortuitous until the

computer simulations have been considered. (cf. section 6:3:1).

The solid lines (A, B and C) are taken as the best linear fits to

the data: the corresponding activation energies are tabulated below

TABLE 7:1

The apparent activation energies -4 Gas composition Line Ea kcal mole

A 92

LEAN (m = 0'005)

B 92

RICH (m = 0.05) C , 61

The major features of interest are:

(i) The high apparent activation energy for the Lean mixtures

(lines A and B), which is close to that expected for simple dissociation:

using a Kassel type equation Q. 1:8, where nK = 3 the expected -1 activation energy for reaction R:1 at 3000K is 86.6 kcal mole .

This contrasts markedly to the results obtained for the lean mixture

cyanogen bromide/argon experiments (cf. Table 6:1).

(ii) The distinctive 'kinky in the temprrature dependence of Ka

235

FIGURE 7:2 LOG10_ K a 1 -1 L. M 0 L. S. 9.0

130 53 Kd=10 exp(-91500/RT) (value found by BAUER et al.) 8.0

7'0 LINE C

M=0.005 Pimm. M=0.05 6,0 C) 3 0 0 10 O 20

ARGON AS DILUENT.

5.4 .....¢21.1.1•ANIMS221Max.retaaniezinntaimaaa.601 2'3 2.5 3.0 3.5 4.0 104/ T 2,0

K THE AMR= SECOND ORDER RATE CONSTANT (as logio 0) FOR THE DIS130CF,TION OF CYANOGEN CHLORIDE PLOTTED AGAINST 1/T2,0, 236

and the agreement in slopes of lines A and B for the lean mixtures.

(iii) The apparent scaling in [ 2 0 ' even over the region M] , where the 'kink' in the lean mixture results becomes apparent.

(iv) The failure to scale in [CICI'] 2,0 upon increasing the initial mole fraction of cyanogen chloride from m = 0.005 to

m = 0.05 .

(v) The low apparent activation energy obtained for the rich mixture results. This variation in activation energy contrasts markedly with the cyanogen bromide results (cf. Table 6:1).

The intensity of light emitted from shocks into the Iro gas mixtures was found to be sensitive to the time allowed for evacuation of the shock tube prior to the admission of the test gases. In figure 7:3, the cyanogen chloride results for the lean mixtures, which were obtained for normal evacuation, are replotted (circles) together with results (filled symbols) obtained if the evacuation time is halved (from 90 to 45 minutes). The results now fall upon the line D, which is the extrapolation of the high temperature results, obtained for normal pumping (figure 7:2). No alteration in the intensity of light emitted or the rate of rise of emission was apparent upon increasing the evacuation time beyond 90 minutes.

The curve E of figure 7:3 is the Itrende line used later in matching

Ka and K c for the lean mixtures. The 'kink' has been deliberately smoothed to facilitate the comparison.

7:3 Discussion and Comparison with the Computer Predictions

The computer simulations were conducted, using the reaction scheme proposed by Bauer et al (85) with the addition that all the reverse processes are also included.

k A H kcal mole-1 d o

(R:1) C1C7 + M + CN + M 95.6

(R:2) C1CN + Cif' + C2N2 —29.;

237

FIGURE 7:3 LOG K. 10 THE SENF-J.TIVITY OF Ka UPON TRACE 1 L. MOL. S. IMPURITIES OF WATER VAPOUR. 9-0 OPEN SYMBOLS - NORMAL PUMPING FILLED SYMBOLS - 1/2 PUMPING.-

8.0 'TREND LINE' E

7.0

'TREN D LINE' E

LINE D 0 6-0 O M=0.005; Pimm.=3 to 20 (taken from figure 6:4 )

El M.0.005; Pimm..10 PUMPING TTlv.E HALVED. 1.4.-.0.005; Pimm.=20 5.4.12 2.3 . 2.5 3•0 3.5 4 4.0 1 0 /T, 40 238

(R:3) C1CN + Cl —4-- —<--- Cl2 + CN- 38.5

(R:4.) C2N2 + M ---->— 2C N + M 12407

(R:5) Cl + M ---÷— 2C1 + M 57*0 2 --<--- (R:6) 2C1CN 22=t: Cl2 + c2 N2 9.1.

The thermodynamic data was taken from Janaf (37) except that the heat of formation for CN was taken to be 99 kcal for the reasons outlined in section 5:1:3. Unfortunately due to lack of time only a limited number of computer simulations could be performed.

In order to check the emission technique, computer simulations were conducted for those conditions where the present work overlaps the absorption study due to Bauer et al (85). The values used for the rate constants were those found by the latter authors and are listed below:

1353 -1 -1 kd = 10 exp(-91500/RT) 1. mol. s.

k2 = 1010605 exp(-6000/RT) 1180 k3 = 10 exp-3400/RT)

k = 1014'23 exp(-100400/RT)

k = 1010 exp(-40600/RT) 5 10 k6 10 exp(-60000/RT)

The computed apparent rate constant (K) is a close match to the experimental Ka : (figure 7:4; trial A). The dashed line is the 'trend' line E for the 1,5 results (cf. figure 7:3). The agreement is within the combined experimental error of the two studies in determining the concentration of CM and confirms the accuracy of the emission measurements. At the lowest temperatures of this study, i.e. the highest investigated by Bauer et al, the detailed fit of the experimental and simulated profiles is reasonable. For example at 2741 K the computed

239

FIGURE 7:4

THE COEFUTED RATE CON'iJTLET- (as logo Kc) PLOTTED 1,a=sT IrEcaroon TERATURE. --CYANOGEN CHLORIDE--

L 0 G10 Kr_

TRIAL B 7 • (.0 7J 0 TREND LINE E (cf. Figure 7:3 )

6.0

2.5 3.0 3.5 104 4.0 /T2,0 240 and experimental profiles for m(cic7) = 0•005 and P1 = 20 torr agree for approximately 8 µsec laboratory time behind the shock front.

(figure 7:5). At higher temperatures, however, although the initial rate

of rise is approximately the same, the predicted rate of rise of intensity

begins to fall—off rapidly with time; this is not observed experimentally

(cf. figures 7:6 and 7:7).

For the next trial, some of the rate constants were re—cast in the

ATnexp(^E/RT) form used in the cyanogen bromide investigation. The modified rate constants are:

k = 1018.84 d T-1.5 exp(-46048/T)1.mol:1s:1 8 k2 = 10 T2 exp(-1000/T)

k = 1033.45 T-5°D exp(-125000/RT) (due to ref. 95) 5

The results in terms of logio Ke are shown as Trial B of figure 7:4-. The Ka/kc fit has been improved at low temperatures but falls higher

than Ka at higher temperatures. Although there is a distinct curvature of Trial B, the tkinkt is not reproduced. Furthermore, the shape of

the experimental and computed profiles do not agree even qualitatively.

The discrepancy is shown in figures 7:8 and 7:9: experimentally the

intensity rises texponentiallyt whereas the computed intensity exhibits

the characteristics of depletion due to

(i) reactant exhaustion

(ii) temperature effects

(iii) depletion of OTT via reaction R:2.

The predicted peak intensities are also too large. Repeating the

simulations where only k2 and k3 are ever changed (typically by a

factor of 2) did not improve the detailed fit of the computed and

experimental profiles nor reproduce the tkinkt of trend line E . Only

minor changes in the temperature dependence of K was ever observed. c

241 •C

• CC,VPUTER SIMULATION

LI- EXPERIMENTAL RECORD PHOTO 629

0 FIGURE Z 7:E' lL 0 20mm 1/2 7. CL CN IN Aa 2741 K T2, 0 1.66 3910 CM/S

1 -1‘ RATE CONSTANTS L. MO L. S.)

EX Kt:3=101153 P(- 46048/ T)

K 2 zid0-051--A 3019•5/T) • K3 z1011.°°EXP(- 17111/T)

K4 z1014.23EX P(- 52338/1)

K5=101°."EXP(- 204 3 2/T) K6 zl d000Exp _ 30915/T,

TAKEN FROM BAUER ET AL,

10 P. SEC.

-12 10

0 3

0

If 0 FIGURE 7:5 20mm 1/2 7. CLCN T20 = 2 675 K 1.642x IC CM/S.

RATE CONSTANTS - AS ABOVE.

COMPUTER SIMULATION

(3 L\- EXPERIMENTAL RECORD PHOTO 62

i I I 10 20 • "30 40 50 LAB TIME tiSEC

242

-12 10

0

0

0 6

0 0

z 0 FIGURE 7:7 A 20 mm ; 1/2 7, CLC N I N AR 6 z 120 2834K • 5 1 6 94 9 x10 CM/ S.

RATE CONSTANTS - AS FIG. 7.5

e- COMPUTER SI MULATI ON

A- EXPERIMENTAL RECORD PHOTO 617

8 12 16 20 2.; LAB. TIME µ SEC

243

1012

6

0- COMPUTER SIMULATION

A- E)( PERIMENTAL RECORD PHOTO 599

0 z4 FIGURE I- 0 3 men ; 1/2 */. CLCNua.AR T20= .2980 K , Aix 1.7422)005 CM/S wA RATE CONSTANTS (L. MOLl. S1) .4 Kci= 18.84 I- 5 A 1. EX P(-46046/T) • A K2= 10 8.co 0.5 E X P( - 00/T) 4 • 1C 3=1011.0° EXP (- 1 7111 IT) • A1/4 K4 =10: 0450T-5.0 1 E X P(- 62907/T)

• K5= 10 EXPk- 2 0432/ T) • 10.00 EX F( K - 10 -- 3019 • 6- 5/ 1)

20 40 60 LAB. TIME µ SEC.

-12 0 0

0

0 0

FIGURE 7:9,

1, CLC N IN AR 0 3 rrn ; 1/ 2 I2,0 z 313 8 K 5 1•79 21x 10 CM/S

0 0 RATE CONSTANTS- AS ABOVE.

0- COMPUTER SIMULATIOt:

E X PE R I ME NTAL RECORD PHOTO SU

I . 20 30 LAB. TIME µSEC. 244

7:/4_ Conclusions

It is evident from the extent of the computations undertaken that only tentative conclusions concerning possible reaction mechanisms can be made rather than a detailed examination of the rate constants.

7:1.:1 An energy chain mechanism

In view of the energy chain mechanism found for the lean mixture cyanogen bromide/argon results, contributions to the overall rate due to the formation of vibrationally 'hot' cyanogen, must be considered.

vn .e. C1CN + CN > C N (R:2a) i 2 2 + Cl

From the measurements of the apparent rate constant for the dissociation of cyanogen bromide, it was found that the apparent activation energy 1 increases from 28 kcal mole to 82.1 kcal mole as the mole fraction of cyanogen bromide is increased from 0'005 to 0.10 (cf. Table 6:1).

In contrast, however, the results for cyanogen chloride show a reduction in the apparent activation energy with increasing mole fraction (i.e.

1°(C1CN) =0-005 - 0.05; Ea = 92 - 61 kcal mole-1 ; cf. Table 7:1). While the former is expected on energy chain kinetics, the latter is not. vo The relaxation of a proposed C2N2 intermediate by collisions with

C1CN is expected to be very rapid due to near resonant (V - V) exchanges (i.e. AV = 3V1(C2N2) V1(C1CN) < 100 cm 1 ; refs

189, 190): the frequencies of C1CN are listed in table 7:2.

Furthermore, reaction R:2 is less exothermic than its cyanogen bromide -1 analogue (All -29'1 and -42.3 kcal mole respectively) and the o will be much less for the C1CN/Ar vibrational energy content of C2' N2 v reaction system, even before the onset of vibrational relaxation.

Because of this, the 'classical kinetic limit' is likely to be reached at greater dilutions than was observed for the cyanogen bromide experiments.

This is also indicated by the sealing in total pressure observed for the lean mixture runs. TABLE 7:2 FUNDAMENTAL FREQUENCIES (from reference 37)

Fundamental Mode * 1 Molecule *x. Frequency cm Comments Ascending Order No. Spectroscopic No. V V 240(2) bending 02N2 1 5 V 507.2(2) bending V 2 4 V V 850.6(1) essentially C-C 3 2 stretch V 2149(1) 4 V3 V5 V1 2328.5(1)

ClON V1 V 2 380(2) bending V2 V1 714(1) Cl-CN stretch V V3 3 2219(1)

Notes:- . * The number in parenthesis indicates the degeneracy of that mode ** Nomenclature used throughout this thesis 246

7:4:2 Lean mixtures: *Shuffle' mechanism

The appearance of the 'kink' for the lean mixture results, which yields K a values at low temperatures which are approximately a factor of two larger than the linear extrapolation of the high temperature ):rder results, is strongly reminiscent of the apparent second rate of

decomposition of water vapour, observed by 010schewski et al (192).

At low total gas pressures and for mixtures heavily dilute in argon,

a similar 'kink' in the apparent rate of removal of water vapour (and

the doubling of this rate at low temperatures) was observed. The

effect was attributed to an H atom 'shuffle' mechanism

H 0 + M (R:7) i.e. 2 H + OH + M

0 + H --4— H (R:8) 2 + OH

The apparent rate at high temperatures was identified with the simple

dissociation (R:7). Olgschewski et al (193) also note that a similar

shuffle mechanism occurs in the low pressure/low mole fraction kinetics

of the SO2 and probably NO2 decompositions. The comparable reactions fOr the lean mixture decomposition of shock heated cyanogen chloride are

kd C1CN + M Cl + CN + M (R:1)

C1CN + Cl —4— Cl + CN 2 (R:3)

The contribution to the overall rate from such a mechanism will be greatest at low temperatures, due, in part, to the relative magnitudes

of the activation energies. At high temperatures, however, k > k d 3 and rate (R:1) >> rate (R:3) and reaction R:1 will become rate

determining. If this is indeed the case, the emission results from this study indicate that the value of k = 1012.53 exn(-91500/RT) 1.mo171 s71 found by Bauer et al (85), may be high by a factor of two Presumably, the dependence of the apparent rate constant upon 247 evacuation time is due to residual impurities when the pumping time is halved. For the reasons discussed in section 6:4:3 (sub—section (a)), contamination from atmospheric oxygen and nitrogen (if any) is unlikely to be important. However, Colgan (45) and Sheen (35) have noted that residual water vapour from the plastic diaphragms and shock tube walls can become troublesome. The intensity of emission and the rate of rise of intensity could be quenched by the removal of chlorine atoms upon reaction with trace impurities of water vapour. If reaction R:3 is quenched, the apparent rate will be predominantly determined by the initial dissociation, reaction R:1. That the apparent rate constant for those runs where the pumping time is halved, falls on the extrapolation of the high temperature results, where R:3 is not important, seemingly confirms these proposals.

7:)f:3 Rich mixtures and lean mixtures at high temperatures

The overshoot in intensity predicted at high temperatures could be in part due to the neglect of C2 formation steps (cf. section 5:1:1).

However, inclusion of C2 formation steps are not likely to reproduce the exponential curvature of some of the experimental records (e.g.

Figures 7:1, 7:8 and 7:9) but will simply reduce the computed peak intensity. This was found for the BrCN/Ar reaction system (c.f. section 6:4:3). Furthermore, experimental observation of the C2 emission for the highest temperatures studied indicated that the formation of C lags behind that of CN and is unimportant within 2 the time scale of the experiment (see also ref. 102). The low rate constant observed for the 5% mixtures is then presumably due to the increasing contribution of reaction R:2 with increasing mole fraction of

C1CN . This step also forms Cl atom and at low temperatures, because of its low activation energy, the increased rate of formation of Cl may subsequently enhance the CN formation via reaction R:3 yielding an overall low apparent activation energy. 248

7:5 Recommendations for Future Work

(i) Extension of the rich mixture results to lower temperatures and higher mole fractions and the investigation of the apparent kinetics upon total gas pressure.

(ii) Detailed computer analysis of the decomposition to elucidate the reaction mechanism and to determine, where possible, rate constants for the elementary steps involved.

(iii)Dosage of the C1GN/Ar reaction system with helium and comparison of the results with BrCN/Ar/He systems.

(iv) Comparison of the decomposition of C1CN/Ar mixtures with the expected complex energy chain kinetics of ICN/Ar systems

(cf. section 6:9). 249

PART III

THE EQUILIBRIUM EMISSION FROM

SULPHUR DIOXIDE BEHIND INCIDENT

SHOCK WAVES

In this section of the thesis, a brief investigation of the ultra-violet emission from shock heated mixtures of sulphur dioxide dilute in argon is compared to that from mixtures dosed with oxygen. The work arose out of the initial calibration procedure reported in Chapter III. 250

CHAPTER VIII

THE 0 — SO RECOMBINATION

8:1 Introduction

The early work of Levitt and Sheen (56) indicated that the ultra— violet emission from S02/Ar mixtures, shock heated to temperatures around 3333K , is due to contributions other than thermal excitation

of undissociated sulphur dioxide. The emission was tentatively identified 1 with transitions from the B1 excited electronic state of sulphur dioxide.

Levitt and Fletcher (68) have mapped the spectral distribution

of the emission intensity behind incident shock waves in S02/Ar

mixtures. From equilibrium calculations and a knowledge of the

emissivity of sulphur dioxide (55, 56) they found that the intensity

emitted is between one and two orders of magnitude larger than the

thermal emission from residual sulphur dioxide. The distribution peaks

at 280 nm and was identified with the chemiluminescent recombination

0 SO . The distribution at longer wavelengths is a good fit to

the room temperature profile of the 0 + SO emission observed by

Clynne et al (195) but at shorter wavelengths falls more steeply.

The shock distribution due to Levitt and Fletcher is reproduced in

figure 8:1.

Cohen and Gross (196) have conducted another shock tube study

coupled with the glow discharge technique. The method involves the

generation of relatively large concentrations of 0 and SO in a

discharge flow, a shock wave is passed through the glowing gas and the

intensity before and after the shock front is compared. These authors have mapped the spectral distribution due to the 0 + SO chemiluminescence FIGURE 8:1

IC; • 0-50 GLOW 208°K REF 195

250 300 350 wavelength nin Point: : intensity of equilibrium emission (photons. arbitrary units) against wavelength. REF 68 252 and observe a peak at 320 nm • The prime advantage of this method is that results from room temperature to shocked gas temperatures may be obtained using the same apparatus.

Cohen and Gross (195) have determined the radiative rate constant,

I OA (cf. section 3:3), at room temperature to be 10528 ma:11.s71 -1 -1 in excellent agreement with the value of 105.18 mol. 1.s. found by

Clyne et al (195). For the temperature range investigated Cohen and Gross have found that

105.28 (T/298)-1.57 t10.15 mole-11.3: EQ. 3:1 OA = 1

In contrast, however, Levitt and Fletcher (68), by monitoring the recombination of the dissociation products at 3500K obtained a radiative rate constant of

I = 105.18 (T/298) OA -1.° EQ. 3:2 where their high temperature results have been combined with the room temperature value due to Clyne et al (195).

The analogous air after-flow exhibits a temperature dependence of 1.6 2-1 from a discharge flow study (197) and — from a shock tube study ( 47), which is apparently in better agreement with the high temperature results of Cohen and Gross than Levitt and Fletcher.

Extrapolating the results due to Cohen and Gross (EQ. 3:1) to 3500K 3.6 yields 10A = 10 mole-11.s. 1compared to the mean radiative rate 4.08 constant of 10 deduced by Levitt and Fletcher at this temperature.

The difference of a factor of 3 is just outside the expected combined experimental error and consideration must be given to other sources and anomolous effects in the equilibrium emission from SO/Ar mixtures.

Levitt and Fletcher have discussed the possibility of emission from other sources at the long test times at which measurement is made and have also noted that flow corrections, not included in their study, may be important. In particular, the S S chemiluminescence and thermal 253 emission from SO and S 2 were discussed. In order to investigate the proposals made by Levitt and Fletcher a short comparative study of the equilibrium ultra-violet emission from incident shocks in S02/Ar and S02/02/Ar was conducted. Because the equilibrium concentrations of 0 S ' S2 , and SO will be markedly different in the two mixtures contributions from other sourcescan be resolved.

8:2 Experimental

The experimental arrangement as described for the pyrolysis of the cyanogen halides was used throughout. The mole fractions of the test gases used was always:

S0 /0 2 2/Ar: 0.05, 0.05, 0.90 respectively

S02/02 : 0'05, 0'95 respectively

The initial unshocked gas pressure was always 6'3 torr . The test gases were shock heated to cover approximately the same temperature range at the shock front and equilibrium for both mixtures. A narrow band of light, centred at about 280 nm, was isolated by a monochromator and the single sweep of an oscilloscope (20 l(,sec) photographed.

8:3 The Emission Records at = 280 nm

A typical oscilloscope trace for the S02/02/Ar mixtures is shown in figure 8:2, together with the shocked gas conditions. The traces for the S02/Ar mixtures at the same temperature are similar. The sharp initial rise of intensity at the shock front corresponds to thermal emission from the undissociated sulphur dioxide (cf. section 3:1) and may be used in the manner outlined in section 3:14.:1 to calibrate the apparatus at this wavelength. The emission record decays from the peak value (Ip) until it reaches a steady or 'equilibrium? level. In agreement with ii. e.tcher and Levitt (194) this final intensity (IF) was always between one and two orders of magnitude larger than that expected from thermally

254

FIGURE 8:2

RUN B17

ENSITY N T

LAB. TIME

S02/02/Ar mixture: T2 0 =4038.3 K; P2,0/131=4.326 5 :5: 90 Tee =3195.4 K; P 2,o/ Pi=5*"° p1 =6.3 mm. Te=3169.5 K; 132,e/ p1=5.716 2.13219e05 cm/sec.

FIGURE 8:3

T 1 OT.

SU I? f

7 BASE LI NE., 255 excited sulphur dioxide.

A qualitative intensity/time history is given in figure 8:3. The experimental record is represented by the full curve I and the TOT expected history for the thermal emission as the sulphur dioxide dissociates and the gas cools is given by ISO . The curve ISUP represents the 2 growth of the intensity superimposed upon the thermal emission as the concentrations of the reaction products increase. These products may themselves either emit due to thermal excitation or due to chemiluminescent recombination reactions.

8:4 The Method of Analysis

Shocked gas conditions at the front were calculated assuming no reaction and using thermodynamic data (36) appropriate to the complete relaxation of the internal degrees of freedom within the shock front.

The hydrodynamic equations were solved using a standard computer program

(appendix I, ref. 35).

Equilibrium conditions were calculated using thermodynamic data from standard tables (37) as input to the HUG (39) computer program.

Calculations were conducted for a proposed 'partial' or a 'full' equilibrium. These were defined by the following set of species.

Partial: SO 2 ' 02 ' Ar 0 SO 9 SO3

Full : as above plus S and S2

Shocked gas temperatures were in the range

T : 2,0 4487 — 3559 K TEe (Partial : 3417 — 3056 K

TE (Full) : 3282 — 3041 K

Fletcher and Levitt (68) and Sheen (35) have indicated that below these temperatures the thermal emission from undissociated sulphur dioxide begins to 'swamp' the contributions from other possible sources. At 256 higher temperatures, they have shown that the emission records become complex indicating further chemical reaction.

The electronics and optical geometry were recalibrated at

X = 280nm from measurements of Ip immediately behind the shock front in the manner outlined in section 3:24.. The plot of the logarithm of the peak intensity, corrected for the shock comnression effect (i.e. divided by the density ratio), against reciprocal temperature is shown in figure 8:24.. The agreement between the S02/Ar and S02/02/Ar results vindicates the assumption of complete vibrational relaxation at the shock front. The background intensity due to residual thermal emission from SO2 could be readily calculated from the knowledge of the absolute emissivity and the concentration and temperature at equilibrium. The equilibrium measurements were, therefore, always corrected for this effect using the following equation.

IET = I ( [ 0 )exp (—E /R (TE 1/TE)) FT 5 2 Er / [SO2] a

EQ. 3:3 where

is the thermal emission at equilibrium from SO2

I is the thermal emission at the shock front from SO FT 2

E is the activation energy at = 2800 nm. a

a is given by Levitt and Sheen (56, 57). The equilibrium measurement is, therefore, corrected by

IE = IE(oBs, EQ. 3:4 ) /ET

Assuming that any other emission results from the 0 4. SO

recombination, the absolute total intensity of emission is determined

in the manner given by Fletcher and Levitt (68) — i.e. integrating the

observed snectral distribution matched to the room temperature results 257

IGURE 8:4

CALIBRATION AT 280-nm-

LOG / P2. / 10 I F

2'4 268 3•0 4 10 /T F

(1z) S02: 02:AR ; M=0.05 0 • 0 5:0'90;13=6'3MM.

23 SO2: AR; 1\47: 0805:0-95; Pi=-6•3 mm. 258

of Clyne et al (195) (cf. figure 8:1).

8:5 Results

The results for the equilibrium emission from S0 2Ar and SO 2A/Ar are reported conjointly to facilitate comparisons. From the definitions of thermal emission (EQ. 3:6, 3:7) and

chemiluminescence (EQ. 3:8), it is apparent the temperature dependence

of the logarithm plots of IE divided by the concentration of a given postulated thermally emitting species or, the product of the concentrations of species undergoing proposed recombination reactions, will be linear,

as long as the radiative lifetimes of the excited states are long compared

to collisional quenching. For the latter case the absolute value, at

any given temperature, is the radiative rate constant I0A

Thrush et al (195) have observed a pressure scaling for the 0 — SO

recombination down to 1 torr . At the shocked gas pressures employed

in this work radiative depletion will be slow.

In figure 8:5, the plot of

logio OA = logio ( IF,/ [S ) I ]

against the reciprocal temperature (TEt), calculated for the tpartialt

equilibrium, is given. The solid line represents the absolute magnitude

and temperature dependency of I0A found by Fletcher and Levitt ( 68.).

In order to investigate the possible dependence of the emission upon

chemiluminescent recombinations other than 0 + SO , plots of log10 . rJ [0] [S] ) and logio(IT/ [S] 2 ) against reciprocal temperature (1/TE) are given in figures 8:6 and 8:7, i.e. for the two or three

body processes.

0 + S (+ M) SO* (+ M)

S + S (+ M) S2* (+ /1)

where denotes an electronically excited species. 259

FIGURE

LOG (1 0 OA

2-7 2.9 3.1 3.3 4 10 /T E CHEMILUMINESCENT RECOMBINATION OF 0 + SO

SO2 02: Ark ; M= 0.05:0.05:0.90; P=6.3mm r. S0 2:Apx; M=0.05:0.95 ; Pi= 6.3mm 10 Pa 5 & lOmm. 1 REF >> Mr. 0.10: 0.90 Pr_ 5m.m A 1 68 260

FIGURE 8:6

0+ S RECOMBINATION

LOG 10 1E /Lois]

10.4

1 0.2

1 0.0

9'8

2.9 3°1 3.3 4 i 10 iTE 261

FIGURE 8:7

S-1-3 RECOMBINATION

1 • 5 0

H

>- cc

Cc

10.5

3.0 3.2 3.4 4 10/T E 262

However, as indicated by Fletcher and Levitt (68 ) both SO and

S emit. The proposed thermal emissivities due to each species 2 are shown in figures 8:8 and 8:9 as logio(IE/ [SC] ) and logio(IE/ [S2] against reciprocal temperature.

The temperature dependencies of the emission at equilibrium, analysed using the above assumptions are summarised in Table 8:1 in terms of apparent activation energies.

TABLE 3:1

APPARENT ACTIVATION ENERGIES

Assumed E act *Mixture -1 Mechanism kcal mole Composition

0 + S recomb. —72.2 A

11 ,1 —45.8 B

S + S recomb —112.1 A

it ti —63.1 B

SO thermal 45.8 A tt II 45.8 B

S thermal —21.9 A 2 42'0 B

Temp. dependence 84 2 A & B

of IE

*Mixture A = S02/02/Ar; M = 0-05/0.05/0.90; P1= 6.3 torr

Mixture B = S02/Ar; M = 0.05/0.95; P1 = 6.3 torr. 263

FIGURE 8:8

THERMAL EMI SSION FROM SO LOG JES 6.0

5.5 U) z

CC

1-F- 5.0 cc

4.5

2.8 3.0 3.2 3.4 4 10 / T E 264

FIGURE 8:9

THERMAL EMISSION FROM S 2

LOG aS 10 2 - 8.5

cn H 9.0 z Y R A R IT B A 7.5

7.0

2.9 3.1 3.3 4 10 iTE 265

8:6 Discussion

Analysis of the equilibrium emission in terms of the 0 + SO

recombination (figure 8:5) yields results in excellent agreement with

Fletcher and Levitt (68). The values of I , calculated for partial OA equilibrium for both S02/02/Ar (mixture A) and S02/02 (mixture B), lie

within the expected experimental scatter. Taking a mean value for both

mixtures, the agreement is better than which is fortuitiously close.

The ratio of the [0] [SO] product for mixture A to that for mixture B

varies only slightly over the temperature range but is approximately a

factor two

[0] i.e. [SO] (MIX A) = 2 01 tS01 L j (MIX B)

The scaling of intensity obtained with the two mixtures with the [0]

product indicates that the major source of emission is indeed the

0 + SO recombination. This is confirmed by the absence of scaling

between mixtures A and B when the analysis is repeated assuming that

the emission arises from othk, sources.

• The S + S and the S + 0 recombinations, at the pressures used

in this study, are most likely to be three body processes. Fair and

Thrush (64) have observed very weak emission from the two body S + S

recombination, and note that the emission from the three body mechanism

is far more intense. As stated in section 3:3, the recombinations under

these conditions should exhibit a small temperature dependency characterised —n by a T term. Cast in terms of an activation energy using an

Arrhenius expression, this implies that recombinations should show a

small negative activation energy not exceeding a few kcal mole:

Inspection of figures 8:6 and 6:7 and table 8:1 for the postulated

mechanisms 0 + S and S + S , shows that the observed apparent negative

activation energies are too large to be reconciled with chemiluminescence. 266

This is confirmed by the lack of scaling between the results for mixture

A and mixture B. At a mean temperature of about 3150K , the discrepancy . in scaling for the 0 + SO recombination is approximately a factor of 2.

At the same temperature, the discrepancy for the S + S recombination is close to an order of magnitude. Furthermore, if the absolute

difference in the observed activation energies for mixture A and mixture B,

obtained for these chempminescent mechanisms, is then

= 49 kcal mole-1 El 0 + 0 AE -1 I I(0 s) 26.4 kcal mole

These large differences confirm that these recombination reactions are

not responsible for the observed emission.

For thermal emission, however, an activation energy not far below the photon energy, at the wavelength monitored, is expected. It has 47,56 been shown that the observed activation energy shOuld, in fact, -1 not be lower by more than 25 kcal mole. At 280nm this sets a -1 lower limit of approximately 78 kcal mole. The apparent activation

energies for the proposed thermal emission due to SO and S2 are shown in table 8:1 for mixture A and mixture B. Compared to the limit of -1 78 kcal mole the activation energies are far too low to be explained

by these mechanisms. Indeed the negative activation energy observed for log io(Li [82] ) for mixture A is conclusive evidence that emission from S2 can be discounted. In view of the excellent scalingbetweennixtures

A andB for IOA' the failure to scale for the IE/ [32] and IE/ [SC] analyses confirms that thermal emission from sources other than

undissociated SO is unimportant. 2

8:7 Conclusion

In summary, significant contributions to the observed emission at

equilibrium can only be reconciled with the chemiluminescent recombination, 267

0 + SO and residual thermal emission from undissociated SO In 2 ' figure 8:3, therefore, Isup represents the rise in intensity as the

decomposition products increase with time and the rate of the recombination

increases to its equilibrium value.

However, the values of I0A obtained in this work scatter about the

mean value of 104.°8 mo1711.s71 , obtained by Fletcher and Levitt (68).

The apparent disagreement with the results of Cohen and Gross could be

due to the neglect of flow corrections to the measurements made at long

test times. The effect of flcw corrections will be to increase the

temperature and pressure and modify the gas composition compared to the

values calculated for 'equilibrium' from ideal shock tube theory.

In this work corrections were therefore applied on the basis of

Mirels theory for that region of the shocked gas where f > 0.1 .

The procedure has been given in section 5:3:2 where it was applied to

the correction of the equilibrium emissivity of the CN radical in the

shock pyrolysis of the cyanogen halides. The equilibrium calculations

were simply repeated until the temperature, pressure and density were

increased respectively by the ratios 1.07, 1.19 and= 1.11.

• The results for IOA corrected in this manner are shown plotted (as log10 units) against reciprocal temperature (14E1) in figure 8:10.

The results due to Levitt and Fletcher (68.) and Cohen and Gross (196)

are also shown (solid lines) extrapolated to the same temperature regime.

As can be seen the flow corrected results and the extrapolation due to

Cohen and Gross now lie within the expected combined experimental error.

The values due to the latter authors were obtained for the approximate

temperature range 298 to 1500 R. Taking the mean temperature of this work

(flow corrected), the covered temperature range is extended to 3600 K. The -1 -1. mean radiative rate constant is at this temperature 103.851.mo1. sec.

Combining this result with the room temperature value due to Thrush et al (195)

gives

/OA= 103'18 (298/4-1'65 1..mol.-1sec.-1 268

FIGURE 8 : 10

The Radiative Rate Constant IOA (flow corrected results)

LOG I 10 OA 7.1 ref. 68

0 A

A

3.0 3 .2 4 , 10 /T E

S02/kr: mso =0.05 ; Pi = 6.3 torr 2 S02/02/Ar: ric.0 = o2 0.05; Pi = 6.3 tore 2 269

Test calculations show that the scaling and activation energy tests, previously described to discount emission from other sources than the

O+SO recombination, are not much affected by the application of flow corrections. 270

APPENDIX I

THE DISPERSION OF THE OPTICA

CFLI. MONOCIMODIATORS

A schematic representation of the optical path for the monochromators is given in figure 2:5 of this thesis. The standard diffraction grating formula is

A = (S/n) (sin a + sin ID A:1:1 where is the wavelength in cm

S is the grating spacing in cm

n is the order of diffraction

CC is the angle of incidence at the grating

is the angle of diffraction at the grating.

For symmetrical operation CC = p . If CC is small then sin a = CC (radians) and equation A:1 :1 reduces to 2sa./n

For a small increment in a the corresponding increment' in wavelength is

AX. 2sAa/n

The angle subtended by a slit of width OJ cm positioned d cm from the grating is simply W/d . A ray at the edge of the entrance slit will just emerge,at the exit slit. The total wavelength spread at the exit slit corresponding to rays at the two edges of the entrance slit is therefore

AA = 2SW/nd 271

This is a base of a triangular slit function for symmetrical optics.

By similar triangles, the halfwidth is simply SW/nd .

The dispersion of the monochromator (D) is defined by the halfwidth divided by the slit width, i.e.

D = S/nd for the u.v./visible grating S = 1/6000 cm (i.e. 600 lines mm-1);

n = 1 ; d = 80 cm : the dispersion is, therefore, 20•85 1/Mm4 yielding a maximum triangular half-width of 7.5 nm for a fully open slit of

5•6 mm. 272

APPENDIX II

SCHEME IV — THE COMPUTATIONAL PROCEDURE

In scheme IV of this thesis, the only variable allowed was theaverege

energy content (Ev) of the vibrationally 'hot' cyanogen at the

moment of dissociation. It is simpler to modify the program, PROFIL ,

to iterate upon values of Ev until Ka and Ke converge than to

conduct many trial values. Because the original code was designed for

multiple simulation processing in one pass of the computer and because

the subroutines are task orientated, this is a relatively simple

procedure. (1) In practice, it is simpler to match the logarithm of the apparent rate constants than any other parameter. The test for convergence

could be varied but was usually ± 0•01 log10 units; well within the

experimental scatter.

• (ii) The iterative step size in energy (,E) is calculated from

the previous trial integration, using a weighting procedure to reduce

the number of iterations required for convergence. A preliminary value

of Ev(i) to begin the iteration is taken from the thermodynamic data.

i . e . A Iff(c2N2v) EQ. A:2:1 Hf (c2N2 ) Ev(n)

For the nth trial value of the excess energy, Ev(n) , a rate

constant for the step

C N v + M ---*— CN + M (R:10a) 2 2

is calculated using 273

1 -1 k = 1033.45 T-5a0 exp(:-(D E 10akn) v(n))/RT) 1.moi. s.

EQ. A:2:2 -1 where D = 125000 kcal mole. The nth integration using this value for yields an apparent k10a(n) :rate constant Ko(n) . In other words,

= f k Kc(n) (10a(n))

Similarly, however, the final value when Ko matches Ka is still a function of k 10a(n) Thus on the mth and last iteration

Ke(m) = Ka = f(kloa(m))

To a first approximation, it may be assumed that these functions are linear and

Ka = k k /(n) 10a(m)/ 10a(n)

Inserting EQ. A:2:2 and re-arranging

E = E E = W(n)RT ln(K ) v(m) v(n) a/Kc(n)

(n) is the weighting factor described in (iii) below. The where W01) n 1 iteration therefore takes the value

, E Evk n + 1) = Ev(n)+ A

The thermodynamic data is re-adjusted according to equation A:2:1 and the procedure repeated until K and K converge to within the desired a c limits. (iii) In order to reduce the number of iterations required and to prevent the onset of oscillations in the solution, the weighting factor

"(n) is introduced. This is simply defined by

W = A E/RTln(Ka/K(n)) n 274

At the start of the integration, W, r-1)1 where n = 1 is set equal to unity. Whenever in Wtc(n) changed sign oscillations wereavoidedbyre—settingW.to unity. 275

APPENDIX III

THE IDENTIFICATION OF REACTION ZONES

IN THE COMPUTER PROFILES

An example profile of the concentration of CN as a function of gas

time was given in Chapter IV (figure 4:2). This was produced by integration of a scheme II mechanism (cf. section 6:4) where the rate

constants used correspond to trial 6:12:G (Table 6:5). The simulation is for a 5 BraT/Ar mixture at an initial unshocked gas pressure of

3 torr. The shock velocity was 1.74'3305 cm/sec. yielding T2,6=3034 K. The regions (1 to 4) marked on figure 4:2 can be readily identified

with individual reactions or groups of reactions from the computer print-out of the reaction rates, species concentrations, etc. for each

point plotted. The reaction rates for this example are given in Table A:3:1.

Region 1 can be identified with the rapid initial dissociation

BrON + M-›- Br + CN + M (R:1)

the reverse step (R:-1) not being important. Approaching region 2,

the removal step

BrCN + CN—>- Br + C d 2 (R:2) becomes important but is quickly counterbalanced by the rapid CM formation step.

BrCN + Br—>- Br2 + CM (R:3)

Region 2 can be identified with the continuing contributions from R:1, R:2 and R:3 but with the addition of the reverse step R:3 and R:-3 apparently pass through a quasi-equilibrium at which point the rate of CN formation falls (i.e. Region 3). This re3ion also shows a drop in CM intensity which is attributed to an increased rate of fall in the shocked gas temperature.

Region 4 is associated with the eventual dissociation of cyanor:-an via TABLE A : 3 : 1 276 Reaction cilfn( CN ) (1) (-1) (2) (-2) (3) (-3) 1 7.31e-02 0.0 0.0 0.0 0.0 0.0 1 7.26 2.02e-11 2.52c-02 4.02e-09 9.83e-03 5.07e-06 2 7.15 1.78e-10 6.18 1.93e-07 3.46e-02 9,53e-05 3 6.73 6.32 1.02e-01 1.41e-06 7.22 5.91e-04 4 6.98 1.51e-09 1.43 4.99 1.6e-01 2.00e-03 5 6.53 2.50 1.74 1.00e-05 1.50 3.93 6 6.30 3.84 2.05 1.76 1.86 6.79 7 6.08 5.34 2.30 2.67 2.17 1.01e-02 8 5.84 7.29 2.56 3.91 2.49 1.46 9 5061 9.44 2.79 5.31 2.78 1.96 10 5.37 1.21e-08 3.01 7.11 3.07 2.57 12 4.92 1.81 3.36 1.12e-04 3.58 3.94 14 4.44 2.64 3.64 1.69 4.05 5.72 16 4.00 3.62 3.83 2.36 4.43 7.70 18 3.57 4.82 3.94 3.15 4.73 9.92 20 3.16 6.22 3.96 4.08 4.95 1.23e-01 25 2.13 1.14e-07 3.61 7.38 5.10 1.91 30 1.16 2.07 2.62 1.28e-03 4.44 2.52 35 2.68e-03 4.38 8.94e-02 2.36 2.15 2.02 40 9.23e-04 6.42 4.10 2.78 1.04 1.12 45 5.08 7.84 2.72 2.85 6.48e-02 7.21e-02 50 3.22 9.03 2.00 2.84 4.41 4.99 55 2.06 1.03e-06 1.47 2.81 2.97 3.40 60 1.33 1.15 1.08 2.75 2.01 2.29 65 9.15e-05 1.25 8.22e-03 2.69 1.43 1.62 70 6.25 1.37 6.21 2.63 1.00 1.12 75 4.29 1.48 4.72 2.55 7.08 7.70e-03 80 3.03 1.60 3.67 2.48 5.14 5.38 85 2.31 1.71 3.04 2.42 4.01 4.06 %fn( CN ) (4) (-4) (5) (-5) (6) (-6) 1 0.0 0.0 0.0 0.0 6.64e-03 0.0 1 4.18e-05 7.31e-08 2.49e-04 1.35e-10 6.59 5.41e-13 2 5.62e-04 4.47e-07 1.89e-03 1.71e-09 6.46 5.55e-11 3 1.92e-03 1.26e-06 6.96 7.71 6.22 7.04e-10 4 4.09 2.62 1.63e-02 2.10e-08 5089 3.55e-09 5 6.12 4.08 2.55 3.73 5.59 8.39 6 8.41 5.97 3.62 6.05 5.26 1.65e-08 7 1.06 8.02 4.65 8.74 4.96 2.69 8 1.29e-02 1.06e-05 5.80 1.23e-07 4064 4.15 9 1.52 1.34 6.89 1.65 4.34 5.82 10 1.75 1.68 8.07 2.18 4.02 7.96 12 2.18 2.41 1.02e-01 3.45 3.47 1.28e-07 14 2.62 3.37 1.24 5.24 2.92 1.91 16 3.01 4.45 1.44 7.52 2.43 2.60 18 3.37 5.68 1.63 1.05e-06 2.00 3.36 20 3.70 7.05 1.79 1.42 1.62 4.15 25 4.38 1.15e-04 2.11 3.02 8.15e-04 6.23 30 4074 1.73 2.16 6.80 2.78 7.67 35 4.21 2.60 1.27 2.22e-05 2.04e-05 5.06 40 3.54 3.63 5.57 3.61 2.97e-06 2.16 45 3.2 4.72 3.05 4.24 9.89e-07 1.15 50 2.98 5.87 1.85 4.60 4.23 6.83e-08 55 2.79 7.26 1.11 4.87 1.83 4,00 60 2.62 8.85 6.71 5.07 8.04e-08 2.34 65 2.43 1.04e-03 4.31 5.20 3.96 1.47 70 2.35 1.22 2.72 5.32 1.91 9.05e-09 75 2.23 1.42 1.71 5.43 3.54 ED 2,11 1.64 1.09 5.52 ne-" 65 2.00 1.86 7.66e-04 5.61 2.93 2,36 277

C N 2 2 + N -->-- 2C/1 + N (R:4) formed via (R:2). This reaction (R:4) is particularly endothermic and accounts in part for the increased rate of fall in temperature further into the shocked. gas.

Detailed considerations of this nature are essential in the detailed matching of the overall intensity profiles where it is normally found that pairs of rate constants require adjustment to improve the fit.

278

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