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Hazelwood-FJ-1966-Phd-Thesis.Pdf ktt 1. THE PHYSICO-CHEMICAL PROPERTIES 'OW OF LOW MELTIN SALTS. A thesis submitted to the University of London for the degree of Doctor of Philosophy by FRANK JULIAN HAZLEWOOD, B.A. (Cantab). January, 1966. Department of Chemical Engineering and Chemical Technology, Imperial College of Science & Technology, London, S.W.7. 2. Acknowledgements. The author wishes to express his thanks to Professor A.R. Ubbelohde, F.R.S., for his advice, and for many ideas which have stimulated this work. Many thanks are also due to Dr. E. Rhodes, who has not only been a source of encouragement, but has also provided much valuable practical advice. A maintenance grant from the Ministry of Aviation is also gratefully acknowledged. 3. Abstract. A survey of the salts of organic acids was made in order to assess their stability in the molten state, with a view to investigating their properties as ionic melts. Acetates of the group IA metals proved the most suitable. A range of physical properties was measured for the sodium and potassium salts, and for some mixtures. In the absence of detailed crystal structures for the solids interpretation of the results in terms of a structure of the melt was somewhat hindered. However a simple lattice model was advanced for the melt which was compatible with the observed data. In part IV a report is given of an investigation of a transition in crystalline potassium nitrite at 40-50°C. This part of the work has been published as a paper, con- jointly with Dr. E. Rhodes and Professor A.R. Ubbelohde, F.R.S. and a copy is bound in at the end of the thesis. 4. Table of contents Page No. Acknowledgements 2 Abstract 3 List of symbols 6 PART I • INTRODUCTION. 7 CHAPTER 1 Theories of the liquid state. 7 - CHAPTER 2 Theories relating to transport processes in 26 ionic melts. CHAPTER 3 The thermodynamics of the solid state I relating to the structure of the solid. CHAPTER 4 Survey of previous work on the physical, structural - and thermodynamic properties of salts containing organic anions. PART II EXPERIMENTAL AND RESULTS. - rrt, CHAPTER 5 Preliminary investigation of the stability 12 of organic salts. CHAPTER 6 General experimental techniques. RG CHAPTER 7 The Measurements of the freezing points of 04. the melts. CHAPTER 8 The Measurement of the electrical conductance 02 CHAPTER 9 The measurement of VlscosIty. CH =ER 10 111-)4, measurement of the molar volume of **A i3o the solids. CHAPTER 11 The measurement of the molar volume of the melts. CHAPTER 12 The me&s14.11L-picnt of the volume change on 15'1 fueon. CRAFTER 13 The measurement of ultra-violet spectra. 1? 5. Contents - contd. Page No. PART III : DISCUSSION. I7s- 216 CHAPTER 14 The general properties of acetates as melts. t7 5 CHAPTER 15 The transport properties of molten acetates. CHAPTER 16 The structural and thermodynamic properties 211 of acetates. PART IV : THE THERMAL TRANSITION IN POTASSIUM NITRITE. 227 -2ki Chapter 17 17.1 Introduction. 227 17.2 Experimental. 2-21 17,3 Discussion. 237 List of symbols used This list is not comprehensive but covers those symbols which constantly recur throughout the work. Where symbols are used infrequently, they are explained on their introduction. A Helmholz free energy G Gibbs free energy ) per mole V Volume k S Entropy Subscripts 1, 2 refer to components 1,2; refers to partial molar quantities 4 G1 Partial molar free energy of component 1. In Natural logarithm (base e) log Common logarithm (base 10) Z Molar partition function. f Molecular partition function. Subscripts tr, r, v refer to translation, rotation and vibration, respectively. No Avogadro's number. k Boltzmann's constant. Faraday's constant. e Charge on 1 electron. z Valency. Viscosity. Specific conductance. A Equivalent conductance. Fluidity. D. Diffusion coefficient of species i. T Temperature. Tf Temperature of fusion. (Of etc. Heats of fusion. kcm-1 Thousands of wave numbers. 7 CHAPTER 1 THEORIES OF THE LIQUID STATE The exact evaluation of the physical properties of liquids, in terms of their molecular parameters is hindered by the large variation in the properties of the liquid, between its freezing point, and its critical point. At the critical point there is a continuous transition between the liquid and vapour phase, with a continuity of properties. At present, no liquid is known which exhibits a solid/liquid critical point. However, the Uscontinuous step in properties between the solid and liquid, is normally much less than that between the liquid and vapour (when far from the critical region). Thus a theory of the liquid state must account for a nearly regular structure at low temperatures passing into a nearly random structure at temperatures near to the normal boiling point. In many cases more detailed theory has been worked out for the so called "dense gases", than for liquids at the higher densities characteristic of molten salts. 1.1. The relationship between the macroscopic thermo— Aynarnic_properties and the microscopic properties of liquids. The Helmholz free energy A, of a material can be related to the microscopic properties by the equation 49 A =-kT in Z (T,V) Z 10 the molar partition function of the assembly and is defined by Z(T,V) = exp ( Er kT Er is the energy associated with the rth state of the system. From the first equation the other thermodynamic parameters can be derived by the formation of the appropriate partial differentials. Notably an equation of state can be defined by P - 1 'DV /T atnz 4.1 Thus, the evaluation of the molar partition function is of vital importance in the determination of the equilibrium properties of the material. 1.2. The molar partition function of liquid systems An array of particles distributed over the available energy levels in accordance with a Boltzmann type of distribution law is considered. Quantum— mechanical effects are neglected. Eaah particle is free to move throughout the whole of the liquid volume, provided that it does not overlap with any other particle. In a liquid, as distinct from a gas, this exclusion effect will be important, due to the higher density of the system. For this reason also, the interparticle potential energy cannot be neglected when dealing with liquids. Thus the total energy of the assembly will take the form 57 E = 1 n(px2 py2 Pz2) U(r) + 2m Px,Py, Pz are the momenta of the particles along three orthogonal axes, U(r) is the interparticle potential energy, and I the total potential energy due to internal degrees of freedom. Normally either monatomic particles are considered in which case. I = 0, or alternatively the molecules are supposedly so rigid that I is unaffected by the external field in which the molecule moves. In this latter case the contribution of I to the partition function can be treated independently. If, in addition it is supposed that the trans— lational degree of freedom of the particles can be described by classical statistics the contributions of the kinetic and potential energy terms to Z can be separated, leading to N 3/2 = 1 ( Tr mkT ) exp( __U(r) trans FT! ur h3 kT - drN The term in square brackets is the molecular translational partition function with the volume divided out — ftr V ID Thus the complete partition function of the liquid can be represented by N Z = ftr fv fr f..... 1 - exp(-1:EcH dri...drN 171.! { V The first term contains all the molecular partition functions, and is only dependent on the temperature of the system. The second term contains the additional terms due to the peculiar nature of the liquid system and is normally known as the configurational integral of the system (3 (3 is the most difficult of the two terms to deal with, due partly to our lack of knowledge of the exact form of U(r) and partly to the mathematical complexities of such an integration. Various approximate methods have been used to overcome this difficulty, amongst which are:- 1)Expansion of the integral, in terms of interactions between small numbers of molecules. 2)Use of a physical model for the liquid so defining the relationship between the particles. 1.3. Distribution function theories of liquids Such an approach has been used to predict p—V—T data for fluids in the region of the critical point (1,2,3). An attempt is made to synthesize the configul— ational integral by combining the n—particle distribution St functions. These functions define the probability that a certain number of particles exist in a certain spatial relationship. Assumptions have to be made to relate the pair distribution function to the triplet one, and higher. For example, Kirkwood has supposed that the probability of three particles being in a particular configuration, is the product , the probability of eacb of the three pair configurations occurring independent1 (Super-position, approximation). This approach,,with its attendant mathematical complexities, has been used for Tluids consisting of inert monatomic particles, but not for ioni, melts, where the electrostatic effects will lead to short rany order. 1.4. The use of phygical models to evaluate the configuration integral. Many of the models used particularly for ionic melts take as a basis the structure of the solid state, This is reasonable in view of the data on X-ray diffract- ion of liquids.4 There are indications that short range order is preserved, though long range order disappears. These observations, together with the increase in molar volume on fusion, lead to a simple lattice model. /2 6 1.4.1. Simple Lattice model.
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