INFORMATION TO USERS
This manuscript has been reproduced from the microfilm master. UM1 films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer.
The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed through, substandard margins, and improper alignment can adversely affect reproduction.
In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion.
Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand corner and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book.
Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9” black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order.
University Microfilms International A Ben & Howell information Company 300 North Z eeb Road Ann Arbor. Ml 48106-1346 USA 313/761-4700 800 521-0600 Order Number 0427099
The investigation of the processes of fragmentation and solvation using cluster ions
Cowen, Kenneth Andrew, Ph.D.
The Ohio State University, 1994
UMI 300 N. Zeeb Rd. Ann Arbor, Ml 48106 The Investigation of the Processes of Fragmentation
and Solvation Using Cluster Ions
A Dissertation
Presented in Partial Fulfillment of the Requirements for
the Degree Doctor of Philosophy in the Graduate
School of the Ohio State University
By
Kenneth A. Cowen
* * * * *
The Ohio State University
1994
Dissertation Committee: Approved by
James V. Coe
C. Weldon Mathews
John Parson Aovisor Chemistry To my parents
ii Acknowledgements
The completion of this document would not have been possible without the
help of a large number of people. I am deeply indebted to these people. It is
impossible for me to adequately express the appreciation I have for the tutelage
provided to me by Professor James V. Coe. His advice, leadership, and
companionship have made the generation of this document a rewarding and
enlightening experience. My coworkers on this project also deserve special
recognition. In particular, I would like to thank Bob Plastridge and Deron Wood for
their help in the development of the Wien filter fragment detection scheme and for
their individual roles in the collection of the data reported in this document. I am
also thankful for the willingness each exhibited in making or fixing pieces of the apparatus in the Machine shop. The "machine shop guys" (Jerry Hoff, John
Herlinger, and Kevin Tewell) should recieve acknowledgment for their help in the completion of this project. Without their expert craftsmanship and the pride each takes in his work, these experiments would have been impossible.
The remainder of the Coe group, past and present, must also be credited with helping in the completion of this dissertation. I would like to thank Cindy Capp for her stabilizing influence on this sometimes volatile research group and for her friendship over the past several years. In addition I would like to thank Mike
Tissandier and Mike Cohen for their support through the writing of this document.
As for past group members, I would like to acknowledge Dr. Garrett Van Cleef,
Mike Mearini, J. J. Wood, and Brian Su. Each of the group members should be commended for recognizing my frequent mood swings and taking appropriate precautionary measures.
As for outside influences, I would like to thank "the flood crew": Pat Fleming,
Chris Carter, and Dr. Tim "the Git" Wright. Their willingness (or reluctance) to play some sack and have an occasional beer has helped greatly in finishing this work.
I must also express my sincere appreciation to Kathy (Smith/Cowen)and would simply like to say "I love you!"
Finally, I must thank my family for the support and encouragement they have shown over the years. Special thanks is expressed to my parents to whom this document is dedicated.
Thanks! Vita
November 5, 1966 ...... Bora - Chicago, Illinois
1988 ...... B. S., University of Connecticut Storrs, Connecticut
1988-1992 Graduate Teaching Associate Department of Chemistry The Ohio State University Columbus, Ohio
1991 ...... M.S., The Ohio State University Columbus, Ohio
1992-Present ...... Graduate Research Associate Department of Chemistry The Ohio State University Columbus, Ohio
1993 ...... Lecturer, General Chemistry Department of Chemistry The Ohio State University Columbus, Ohio
Fields of Study
Major Field: Chemistry Studies in Fastast IonIon BeamBeam StudiesStudies ofof Cluster Ions
Dr. James V. Coe
v Publications
Ronald J. Mattson, Kahnie M. Pham, David J. Leuck, and Kenneth A. Cowen, An Improved Method for Reductive Alkylation of Amines Using Titanium (IV) Isopropoxide and Sodium Cyanoborohydride, J. Org. Chem., 55, 2552 (1990).
K. A. Cowen and J. V. Coe, A New and Simple Time-of-Flight Mass Filter for CW Ion Sources, Rev, ScL Instrum., 61, 2601 (1990).
Kenneth A. Cowen, Christopher J. Frank, and James V. Coe, Beam Voltage Manipulation for Time-of-Flight Mass Analysis of Continuous Ion Beams, Anal Chem., 63, 990 (1991).
Patrick A. Limbach, Lutz Schweikhard, Kenneth A. Cowen, Mark T. McDermott, Alan G. Marshall, and James V. Coe, Observation of the Doubly Charged, Gas-Phase Anions CM2' and C702', J. Am . Chem. Soc., 91, 6795 (1991).
Kenneth A. Cowen, Bob Plastridge, Deron A. Wood, and James V. Coe, The Importance of High Impact Parameter Interactions in the Collision Induced Dissociation of Protonated Water Clusters by Argon using a Wien Velocity Filter, J. Chem. Phys., 99, 3480 (1993). Table of Contents
D edication ...... i
Acknowledgements ...... ii
V ita ...... iv
List of F ig u res ...... viii
List of T ables ...... xi
Chapter
I. Introduction ...... 1
1. Spectroscopy ...... 1
2. Solvation E nergetics ...... 3
3. References ...... 5
II. Wien Filter as Fragment Detector ...... 7
A. Theory ...... 8
1. Wien Filter ...... 8 2. Fragment Detection ...... 19
B. Experimental Apparatus ...... 26
1. Ion Beam Apparatus ...... 26 2. Circuits for Ion Optical Elem ents ...... 31 3. Vacuum System ...... 33 4. Glow Discharge Ion Source ...... 35 C. Experimental Procedure ...... 37
1. Pressure Calibration ...... 37 2. Cross Section Measurements ...... 38 3. High Pressure Studies ...... 40
D. Results and Analysis ...... 40
1. Demonstration of Wien Filter as Fragment Detector ...... 41 2. Total Attenuation Cross Sections ...... 48 3. Collision Induced Dissociation Cross Sections ...... 51 4. Multiple Collision Analysis ...... 59 5. Discussion ...... 84
E. References ...... 88
III. Determination of the Free Energies of Solvation for Single Ions at Bulk Using Cluster Ion Data ...... 91
A. Introduction ...... 91
B. Free Energy of Solvation for Single Ions at B ulk ...... 93
C. Connecting Cluster Data to Bulk ...... 106
D. The Ion-Ion Recombination Approach to Solvation ...... 109
E. References ...... 113
IV. A ppendices ...... 115
A. Fortran Programs ...... 115
B. Mathcad Templates ...... 154
C. Related Publications ...... 174
V. List of References ...... 183
viii List of Figures
Figure Page
1. Velocity spectrum recorded by varying the electric field in the Wien filter. These ions were produced in a nozzle filament ion source from electron bombardment of an expansion of neat ammonia ...... 12
2. Peak position (Wien filter voltage) vs. /m for the peaks in the mass spectrum shown in Figure 1. The best fit line is also shown ...... 14
3. Illustration of the dispersion of an ion beam by a Wien filter ...... 18
4. Schematic illustration of the experimental apparatus ...... 27
5. Wiring scheme employed to enable the voltage programmable mode of the Hewlett Packard 6209B power supply used to generate the electric field in the Wien filter ...... 30
6. Voltage dividing circuits for the ion optical elements. (a) circuits for lenses, (b) circuits for quadrupole and parallel plate deflectors ...... 33
7. Isolation scheme used to float the discharge power supply ...... 37
8. Wien filter velocity spectrum of hydrated hydronium cluster ions produced in a glow discharge ion source ...... 38
9. Demonstration of the Wien filter as a means of fragment separation. In trace (a) VDR=0 V, in trace (b) VDR= +198 V. Both traces were recorded with 5 mTorr of argon in the chamber ...... 43
ix 10. The intensity of the one water loss fragment from H50 2+ vs. argon pressure. The collision chamber pressure for each scan was (a) 0.6 mTorr, (b) 1.7 mTorr, (c) 3.3 mTorr, and (d) 4.9 m T o rr ...... 44
11. The position of the one water loss fragment from H50 2+ ...... 46
12. The ratio of the total fragment current to the parent current vs. collision chamber pressure. These data were fitted to Equation 19 to obtain the curves ...... 55
13. The attenuation and glancing CID cross sections for H +(H20) b vs. cluster size ( n ) ...... 57
14. Calculated PC(E) distributions for various combinations of ion mass and beam energy (from Reference 3 0 ) ...... 63
15. Sketch of the approximate PC(E) distribution for H50 2+ showing the threshold energy for the loss of 1 water molecule. The shaded are corresponds to the value of ^ ...... 70
16. A plot of the normalized fragment ion current, I / I p,o> vs. the normalized parent ion current, Ip/IP t0 ...... 76
17. The probability of dissociation and formation of excited parents from collisional activation of HsO ,+ ...... 77
18. The probability of dissociation and formation of excited parents from collisional activation of H70 3+ ...... 79
19. Schematic illustration of the apparatus used to investigate infrared fluorescence from collisionally excited beams of hydrated hydronium cluster ions ...... 82
18. Infrared fluorescence signal observed from a beam of hydrated hydronium cluster ions which has been attenuated by 35% ...... 84
19. Stepwise free energies of neutral water cluster (from Kell and M cLaurin) ...... 98
20. Solvation free energy vs. n'1/3 for various ions in water clusters. Filled symbols correspond to positive ions and
x open symbols correspond to negative ions ...... 101
21. The standard deviation, o, between the bulk data and the cluster data, as given by Equation 11, as a function of potential values for the bulk solvation free energy of Na+ ...... 107
22. Stepwise solvation energies for various ions as shown in Figure 19. The connection from the cluster data to bulk is provided by dielectric sphere slopes which have been included in this p lo t ...... 109
23. Plot of the free energy and enthalpy of the products and reactants vs. cluster size for the reaction of Na+(H20)j cluster ions with 0H '(H 20) k cluster ions ...... I ll
xi List of Tables
Table Page
1. Comparison of the assigned and calculated masses for the peaks in the velocity spectrum in Figure 1 ...... 15
2. Comparison of the calculated vs. observed values of the ratio of fragment ion peak position to parent ion peak position in a Wien velocity spectrum ...... 47
3. Absolute values for the total attenuation cross section for collisions of hydrated hydronium cluster ions with arg o n ...... 50
4. Absolute values for the collision induced dissociation cross section for glancing collisions of hydrated hydronium cluster ions with arg o n ...... 54
5. Branching ratios for the loss of water molecules from hydrated hydronium clusters by glancing collisions ...... 58
6. Comparison of the glancing CID branching ratios with hard sphere CID branching ratios ...... 58
7. Free energy of solvation (AG°twt1er) to place a pair of oppositely charged ions into water at 25° C ...... 94
8. Table of differences in bulk solvation free energies ...... 95
9. Average differences in the bulk solvation energies ...... 96
10. Partial sums of the stepwise free energies for the solvation of various ions (rA n_,iB) in kj/mol ...... 99
11. Individual bulk solvation energies (k /m o l) ...... 105
xii Chapter I
Introduction
The gas phase chemistry of molecular ions has been studied for many years1.
The development of several powerful techniques over the past several decades
combined with recent technological advances, including lasers and high resolution
mass spectrometers, have resulted in a growing interest in gas phase ions. This
heightened interest in the chemistry and physics of molecular ions has motivated a
flurry of activity in the study of these fundamentally important species. A
comprehensive overview of the body of work reported in the literature on gas phase
molecular ions is beyond the scope of this document. However, a brief summary is presented of some of the primary areas of research receiving considerable interest
in the study of ions. This summary will serve as a justification of the motivation for the studies presented in this document.
1. Spectroscopy
Perhaps the field that has profited most by recent technological advances is high resolution molecular spectroscopy. With the advent of high resolution lasers, as well as high resolution Fourier transform spectrometers, the spectroscopy of
1 2 molecular ions has blossomed in the recent years2,3. The development of velocity modulation techniques4’5,6 has made it possible to observe the spectra of molecular ions despite the high ratio of neutrals to ions found in most experiments. Our interest in spectroscopic studies of cluster ions has led to the development of an ion beam apparatus similar to that used to observe the infrared spectra of several gas phase ions in direct absorption7 experiments.
It is likely that several of the cluster ions of interest will dissociate upon absorption of an infrared photon. This has encouraged an interest in the development of high signal to noise techniques for the detection of photofragmentation processes. This interest has motivated the development a novel technique for the separation of fragment ions from a parent ion beam. This technique employs a Wien velocity filter8 to separate fragment ions from parent ions on the basis of a difference in velocity between the two. We have used collision induced dissociation to demonstrated that this technique is useful in the separation of fragment ions, and has the potential to be a powerful toot in the detection of photofragmentation events.
Collision induced dissociation (CID) has been used extensively over the last several decades9 in the study of molecular ions, and several reviews have been written on the subject10,11,12,13. This technique has proven to be a valuable tool for a variety of applications including structure determination and bond strength measurements14. Studies have been performed to determine the effects of beam energy15, and projectile mass, as well as the nature of the target gas and the 3 pressure in the collision region.
The process of collision induced dissociation is thought to occur in two steps.
The first step involves conversion of translational energy into internal energy of the projectile ion, followed by the dissociation of the excited ion.
AB* + neutral - AB" + neutral ^ AB " ~ A* + B
This mechanism is known10,12 to compete with a wide variety of other collisional processes including charge exchange, charge stripping, and scattering.
We have investigated the CID resulting from glancing collisions (i.e. high impact parameter) for collisions of hydrated hydronium cluster ions, H +(H20)n n= 1-4, with argon. These studies have determined that there is a significant increase in the importance of these high impact parameter collisions with increasing cluster size. We have observed that a large fraction of the attenuated parent beam can be recovered at the end of the beamline in the form of fragment ions. In addition, using the multiple collision theory of Kim16,17, it is predicted that of the undissociated parent beam, an appreciable fraction is internally excited. These predictions have suggested a variety of experiments to measure the degree of excitation occurring from the collisional attenuation process.
2. Solvation
The study of aqueous solvation of electrolytic molecules has traditionally been approached from bulk. However, this approach leads to ambiguous results concerning the contributions of the individual electrolytes. Bulk solvation of 4 electrolytes necessarily involves the formation of a pair of oppositely charge solvated ions. Although thermodynamic properties can be measured at bulk for the solvation of a pair of ions, the individual ion solvation energetics are not known.
Clusters are particularly interesting species since they link the gas and condensed phases. Mapping out the properties of clusters from monomer to bulk should provide insight into the physical and chemical properties of the species being studied. Cluster ions provide a unique opportunity to study solvation since an individual ion can exist in the gas phase. Solvation of gas phase ions can be achieved by successive additions of solvent molecules.
Several techniques18,19 have been developed to determine thermodynamic properties of gas phase ion-solvent clustering reactions. These techniques have been used extensively to provide a large body of information concerning the energetics of solvation of cluster ions20. Using cluster ion data, the thermodynamics of the solvation of individual ions can be determined.
The bulk solvation free energy of individual ions has been calculated. The method used was originally developed to determine the enthalpy21 associated with the solvation of individual ions at bulk but has been modified to determine the appropriate values of the free energy of solvation. The method builds on an established technique22 and includes a number of improvements over the previous method. From these calculations, a number of predictions are made about the process of solvation resulting from the gas phase recombination of positive and negative cluster ions. 5
References
1. H. E. Duckworth, R. C. Barber, and V.S. Benkatasubraminian, Mass Spectroscopy (Cambridge University Press, Cambridge 1986).
2. J. P Maier, Ed., Ion and Cluster Ion Spectroscopy and Structure, (Elsevier, Amsterdam, 1989).
3. A. Carrington and Richard Kennedy, / Chem. Phys., 81, 91 (1981).
4. C. S. Gudeman, M. H. Begeman, J. Pfaff, and R. J. Saykally, Phys. Rev. Lett., 50, 727 (1983).
5. E. Schafer, M. H. Begeman, C. S. Gudeman, and R. J. Saykally, / Chem. Phys., 79, 3159 (1983).
6. M. W. Crofton and T. Oka, / Chem. Phys., 79, 3157 (1983).
7. E. R. Kiem, M. L. Polak, J. C. Owrutsky, J. V. Coe, and R. J. Saykally, / Chem. Phys., 93, 3111 (1990).
8. W. Wien, Ann. Phys. Chem. (Leipzig), 8, 224 (1902).
9. K. R. Jennings, Int. J. Mass Spectrom Ion Phys., 1, 227 (1968).
10. R. G. Cooks, Collision Spectroscopy, (Plenum Press, New York, 1978).
11. J. L. Holmes, Org. Mass Spectrom., 20, 169 (1985).
12. J. Bordas-Nagy and K. R. Jennings, Int. J. Mass Spectrom. Ion Proc., 90, 105 (1990).
13. R. N. Hayes and M. L. Gross, Meth. Enzymol, 193, 237 (1990).
14. C.-X. Su and P. B. Armentrout, / Chem. Phys., 99, 6506, 1993.
15. S. A. McLuckey, C.E.D. Ouwerkerk, A. J. H. Boerboom, and P. G. Kistemaker, Int. J. Mass Spectrom. Ion Phys., 84, 85 (1984).
16. M. S. Kim, Int. J. Mass Spectrom. Ion Phys., 50, 189 (1983).
17. M. S. Kim, Int. J. Mass Spectrom. Ion Phys., 51, 270 (1983). 6 18. A. J. Cunningham, J. D. Payzant, and P. J. Kebarle, 7. Amer. Chem. Soc., 94, 7627 (1972).
19. K. Hiraoka, S. Mizuse, S. Yamabe, J. Amer. Chem. Soc.,88, 3943 (1988).
20. R. G. Kessee and A. W. Castleman, J. Phys. Chem.Rev. Data , 15,1011 (1986).
21. J. V. Coe, Submitted to J. Chem. Phys., 1994.
22. C. E. Kiots, J. Chem. Phys., 85, 3585 (1981). Chapter II
The Wien Filter as a Fragment Detector
In a Wien filter1,2, an ion beam is simultaneously exposed to electric and magnetic fields which are perpendicular to one another as well as to the ion beam axis. A charged particle travelling through the Wien filter emerges undeflected if the electric and magnetic forces on that particle are equal in magnitude and opposite in sign. The force exerted on a charged particle in an electric field is identical for all particles with the same charge and the same beam energy. However, the force exerted on a charged particle in a magnetic field is dependent upon the velocity of the particle. Since velocity is a function of particle mass, the relation between magnetic force and velocity is exploited in a Wien filter to allow mass separation.
Wien filters have been used for years in various experiments as a simple, but effective, means of mass separation3,4,56.
The ability of this device to separate species of different mass has been exploited further as a means of separating various fragment ions from a parent ion beam7. This work presents a novel approach to fragment detection using a Wien filter. A theoretical basis which governs the behavior of this technique is presented and is experimentally verified. Demonstration of the device’s utility as a fragment
7 selector is presented as well as a detailed analysis of the observed ion intensities
resulting from a series of collisionally induced dissociation studies.
1. Wien Filter Theory
In these experiments, ions are created in an ion source that is held at a fixed
potential with respect to ground ( Vt) so all the ions are nominally created with the
same energy. Since the kinetic energy for the ions is identical, it follows that different mass ions will have different velocities. The kinetic energy can be expressed in the following manner,
|m v J - qV," (1) in which Vacc is the acceleration voltage and is equal to the difference in the actual potentials applied to the ion optical element at which the ion was "born" (which is generally the anode of the ion source) and the element in question. For parents, the element in which the ions are bom is the anode of the source, therefore, the birth voltage is given by the ion source float voltage (Vc). Since the right hand side of this expression is constant for a beam of parent ions, it is apparent that different mass ions with the same kinetic energy must assume different velocities.
For a monoenergetic beam, the description of the Wien filter as a mass analyzer is a straightforward matter. Assuming the ions in an ion beam have the same beam energy, they will all react in the same fashion to an electric field. The force on a charged particle due to an electric field ( £ ) is given by
8 F - qE <2)
where q is the charge. Similarly charged particles in an electric field will all be
affected in the same manner independent of particle mass. On the other hand, the
force exerted on a charged particle by a magnetic field (f?) exhibits a mass
dependance rendering the device useful for mass analysis. The magnetic force is
given by the following cross product
F = qv x B (3)
where v is the particle velocity.
Only when the electric and magnetic forces on a given ion are equal will an
ion pass through the Wien filter undeflected. In this case
E - vB (4)
Rearranging Equations 3 & 4, and substituting one into the other, we see that the
ion velocity can be expressed as
v = — = M e (5) B \ m
Under a given set of experimental conditions (i.e. beam energy, magnetic Held and electric field) only ions with a specific velocity will emerge from the device undeflected.
To be generally useful as a mass analyzer at least one of the experimental parameters listed above must be variable. Since changing the beam energy generally 10 requires the ion optics to be refocussed, the beam energy is frequently fixed in these experiments. Therefore, the normal mode of operation involves varying either the electric or magnetic field. Since the acceleration potential is equal for all the parent ions in the beam, it is apparent (from Equation 5) that varying one of the fields with respect to the other will allow different mass ions to be detected on axis. Therefore, a scan of either of the fields will result in a separation of ions with different velocities.
Typically, one of the fields is fixed and the other is varied. Either configuration (i.e. fixed magnetic field with variable electric field or vice versa) has advantages and disadvantages in terms of its capabilities. Depending on what the requirements of the experiment are, one or the other configuration is chosen.
In commercial Wien filters, the magnetic field is frequently the parameter which is varied to allow mass separation. From Equation 5, the magnetic field is directly proportional to Jm and is inversely proportional to the ion velocity. In this arrangement, light ions (fast ions) will emerge from the Wien filter at low magnetic fields and heavy ions (slow) will emerge at high magnetic fields. The range of masses which can be detected extends upward from 0 amu. The upper limit is determined from the largest magnetic field which can be generated by the power supply which is limited by the current output of the power supply running the magnet. In this configuration, the spectrum obtained will be of constant resolution.
Scanning the electric field also results in mass separation, however, in this configuration, the scanning parameters provide a very different spectrum than one 11 obtained by scanning the magnetic field. Since the electric field in the Wien filter is directly proportional to the velocity (hence the device is called a velocity filter) and is inversely proportional to Jm , heavy ions will emerge at low electric fields and light ions will appear at high electric fields. An attractive feature of this configuration is that the electric field can be scanned much more rapidly than the magnetic field and requires almost no current. With this arrangement, the peak widths in the velocity spectrum are constant throughout the scan.
Figure 1 shows a velocity spectrum recorded by varying the electric field of the Wien filter. The voltage applied to the electric field plates in the Wien filter is plotted on the x-axis. Since this voltage is directly proportional to velocity and inversely proportional to ,/m, the higher mass ions appear at lower voltages and appear closer to one another than the low mass ions.
Assignment
Assignment of the peaks in a Wein filter spectrum is a relatively straightforward procedure. In these experiments, the electric field is scanned and, therefore, the voltage applied to the Wein filter electrodes relates to mass in the following manner,
y*r - "F ♦ » (6) yjm in which a and b are constants. In theory, b should equal zero since there is no electric field when the Wien filter voltage is zero. In this case, knowledge of the 12
NH,
cCO CO OT c NH o
X 1 0 0 N*
0 50 100 150 200 250 300
Wien Filter Voltage
Figure 1. Velocity spectrum recorded by varying the electric field in the Wien filter. The ions were produced by electron bombardment of an expansion of neat ammonia. mass of a single peak would be all that is necessaiy to allow a definitive assignment of a mass spectrum. In practice, however, b is generally found to be slightly non-zero
(either positive or negative). This is attributed to misalignment between the beamline, the Wein Alter, and the faraday cup. Off-axis trajectories of the ions that are still detected in the mass spectrum will result in an non-zero intercept in the At 13 of the mass spectrum.
A Mathcad™ template (Appendix 1) can be used to assign the Wien filter mass spectra. In this procedure, tentative assignments are made for the masses of at least two peaks. A linear least squares analysis fits the tentative mass to the corresponding position of each of the peaks using the expression above and generates mass assignments for the remaining peaks in the spectrum. The results of the least squares analysis is checked to ensure that the mass determinations are consistent with what can be expected to be produced from the ion source in use. For this reason, a certain understanding of the chemistry likely to take place in the source being used is quite helpful when assigning mass spectra. (Since the positions of the peaks are highly correlated to the beam energy as well the ion optical focussing of the beam, peaks will frequently not appear in the same position from day to day. Therefore, a permanent calibration of the mass spectrometer is not available unless identical conditions are used on a day to day basis. The ability to predict what species are likely to be observed in a mass spectrum becomes a valuable asset.) If the initial guesses at the masses are incorrect the resulting fit will generate mass assignment that should be obviously erroneous. When a misassignment is made, iteration of the initial assignment process is continued until an acceptable fit is obtained.
For the velocity spectrum shown in Figure 1, the mass assignments were facilitated considerably from a previous knowledge of the ionization characteristics typical of nozzle filament ion sources. The pattern of 5 peaks at the right hand side of the spectrum was used as a starting point for the analysis. Since the source gas 14
g 7 I
0.10
OJOO •0 100 too too too Wion Fttor Volttgt
Figure 2. Peak position (Wien niter voltage) vs. Jm for the peaks in the mass spectrum shown in Figure 1. The best flt line is also shown. was neat ammonia (30 psi), the presence of large quantities of impurities in the mass spectrum was improbable. Knowing that electron impact ionization frequently results in the formation of stable, closed-shell cluster ions, the presence of NH4+ in the spectrum was expected. This observation, coupled with the peaks corresponding to successive H atom loss from NH3+, made the assignment of the five peaks at the right straightforward. Once these peaks had been assigned it was relatively trivial to make assignments for the remaining peaks. A least squares analysis of the peak positions (as determined by the technique described in the Mathcad template in
Appendix 1) was performed. The assigned mass and the calculated mass of each 15 peak is listed in Table 1 along with the error range expected for the peaks as determined from the least squares analysis. Figure 2 shows a plot of the square root of the assigned mass for each the peaks in this spectrum vs. peak position (Wien filter voltage).
Table 1 Comparison of the Assigned and Calculated Masses for the Peaks in Figure 1
Ion Assigned Calculated Difference Range Mass Mass N + 14 13.93 -0.07 0.10 NH + 15 14.96 -0.04 0.11 N H / 16 15.99 -0.01 0.12 n h / 17 17.03 0.03 0.13 NH/ 18 18.05 0.05 0.14 N/ 28 28.23 0.23 0.28 N H /(N H 3) 32 31.83 -0.17 0.34 N H /(N H 3)i 35 35.23 0.23 0.39 N H /(N H 3)2 52 52.42 0.42 0.71 N H /(N H 3)3 69 69.32 0.32 1.08 N H /(N H 3)4 86 86.31 0.31 1.50 N H /(N H 3)5 103 102.7 -0.31 1.94 N H /(N H 3)6 120 119.2 -0.77 2.43 N H /(N H 3)7 137 136.3 -0.70 2.97 N H /(N H 3)8 154 151.7 -2.28 3 4 9 16 It should be pointed out that, although the peaks are not resolved from one
another, it is evident that NH4+(NH3)n clusters higher than n = 8 are present in the
velocity spectrum. The lack of peak resolution at high mass results from the fact that
the x-axis is not linear with mass and the peak widths are constant throughout the
spectrum.
Resolution
Although conditions can be set such that only a given mass will emerge from
the Wien filter undeflected, in practice, a broad range of masses may emerge from
the device. Resolution is the degree to which the Wien filter is capable of
discriminating one mass from another. The definition of resolution is given in
Equation 2-7, and is essentially the highest mass for which successive masses are separated at half width.
R - (7) 6m
In this expression, m is mass and 6m is the full width at half maximum intensity
(FWHM) of the peak corresponding to that mass. The resolution is influenced by a number of factors and can be controlled to some degree by varying certain parameters. These parameters include the spot size of the beam and the distance the ions travel after exiting the Wien Alter.
Since ions with similar mass will be deflected to nearly the same degree, ions with masses which are similar to the undeflected ion may be deflected only slightly 17 off axis. The distance (dispersion) that an ion will appear off axis is given by8,
D * x0 * L— (8) v* where x0 is the initial off axis position in the x dimension, vx is the velocity of the ion parallel to the electric field, vz is the velocity of the ion along the beam axis, and L is the distance the ion travels after the Wien filter. Since the dispersion is dependent upon the distance between the detector and the Wien filter, it is necessary to have a field free region after the Wien filter to allow the ions to separate spatially. Figure
3 illustrates how a beam of hydrated hydronium cluster ions will be dispersed by the magnetic field in a Wien filter (the electric field is assumed to be zero). The permanent magnetic field (perpendicular to the page) will bend the beam of ions off axis. A scan of the electric field will bring a particular mass ion back on axis when the velocity of that ion is equal to the ratio of electric and magnetic fields (Equation
5). (For convenience, the trajectories of the ions in the Wien filter are shown as straight lines. The actual trajectories of the ions are sinusoidal in nature8). After emerging from the W.F., the ions will continue in a straight line path until a collision occurs (with a wall, detector, ambient gas, etc.). The distance the ions are allowed to travel strongly influences the degree to which ions with similar mass are separated.
The further the detector from the Wien filter the greater the resolution.
The diameter of the ion beam strongly influences the resolving power of the device. The resolution is a measure of how well the device spatially separates the different mass ions, therefore, the smaller the beam diameter, the easier the 18
HtO* H.O,* HtO,* — H .O / H„0/
Figure 3. Illustration of the dispersion of an ion beam by a Wien filter. separation and the higher the resolution. Ideally, the ion beam is well collimated when it enters the Wien filter. To achieve this goal, the ion beam apparatus was designed with ion optical lenses and corrective deflectors which are used to focus and steer the ion beam. In addition, slits are placed on the entrance and exit of the Wien filter, and on the faraday cup, to help collimate the beam. The widths of the slits can be closed down to increase the resolution of the Wien filter or can be opened up to 19 increase the current transported through the device (high beam transport is one of the most appealing aspects of this means of mass separation). In these experiments, the slit widths were generally kept at 1-2 mm to allow high beam transport while maintaining sufficient resolution to observe fragmentation.
Despite the relatively low resolution typical of these devices, Wien filters are employed in a variety of experiments. Several attributes of these devices make them an attractive means of mass analysis. For experiments in which large mass selected ion currents are necessary, a Wien filter is attractive since it is has high beam transport properties. In general, Wien filters are simple to operate (there are a minimal number of controls), and are relatively inexpensive.
2. Fragment detection
A technique has been developed which allows fragmentation events to be observed by separating fragment ions from parent ions. This separation is achieved simply by adding a variable voltage to a tube in front of the Wien filter.
Theory
At the beam energies used in the present experiments (several hundred volts to several kilovolts), excess kinetic energy from dissociation will be small relative to the beam energy. Therefore, under normal operating conditions a Wien Alter will not separate fragment ions from parent ions since they nominally have the same 20 velocity. In order to be separated from the parents, fragment ions must obtain a different velocity than the parents. This can be achieved rather simply by accelerating (or decelerating) all of the ions. Since the parents and the fragments have the same velocity but have different mass, their kinetic energies necessarily must be different. From conservation of energy arguments, the sum of the kinetic energies of the fragment ion and the neutral fragment must equal that of the parent ion.
Therefore, the fragment ion will have a smaller kinetic energy than the parent. Since the fragment and the parent have different energies and since ions of different energies will respond differently to an electric field, accelerating all the ions in an electric field will effect the fragments and the parents differently.
A single step in which the velocity of all the ions is changed after fragmentation is all that is required for the Wien filter to separate the fragments from the parents. Simply exposing all of the ions (parents and fragments) to an electric field is all that is necessary to change the relative velocities of the ions and thereby allow separation of the fragments.
This is achieved in a very simple and straightforward way by placing a tube
(or drift region) in front of the Wien filter and applying a potential difference (VDR) between the tube and the Wien filter reference voltage (which in this case is ground).
If a dissociation event happens within the drift region in front of the Wien filter, the fragment ion velocity (vf) and the parent velocity {vp) will be equal, assuming that the excess kinetic energy is small relative to the beam energy ( VB). Setting the fragment ion velocity equal to the parent ion velocity, we have, 21
2* (Vm - (9) where mp is the mass of the parent ion, VB is the voltage applied to the ion source
(parent ion birth voltage), and VDR is the voltage applied to the drift region.
Assuming, that the velocity and the mass of the fragment are known, the kinetic energy can be determined. The kinetic energy of the fragment ion in the drift region can be expressed in the following manner by rearranging Equation 9 and multiplying by the mass of the fragment ion ( mf).
- • v ( 10) 2 mp
Note that this expression is similar to the expression for the kinetic energy of the parent ion in the drift region (Eq 1) where (VB - Vm ) has been substituted for the accelerating voltage, Vacc. A comparison of these two expressions shows that the kinetic energy for the fragment ion is smaller than that of the parent ion and is smaller by the ratio of the masses of the fragment and parent ions. This difference in energy will result in a different change in velocity for the fragment with respect to the parent when the ions are exposed to an electric field.
To understand how an ion will react to an electric Held, it is necessary to know the potential at which the ions were created ("birth voltage"). In other words, it is important to have a frame of reference for what the ion sees as attractive or repulsive. For example, a positive ion born at +1000 V with respect to ground will see ground as a 1000 V accelerating potential, whereas if that same ion were born 22 at -1000 V with respect to ground, it would see ground as a 1000 V repulsive voltage.
Predicting the behavior of fragment ions after they leave the drift region requires knowing the birth voltage of both the parent and the fragment ions.
The birth voltage of an ion is defined as the potential at which that ion has zero kinetic energy. The parent ion beam has zero kinetic energy (nominally) when it is created in the ion source. (Assuming a thermal distribution in the source, the kinetic energy is distributed about 0.03 eV.) The ions gain the majority of their kinetic energy during their extraction from the source and subsequent acceleration in the beam. In this work positive ions will have birth voltages which are positive with respect to ground and negative ions will have birth voltages that are negative with respect to ground (unless otherwise noted.) Therefore, the parent beam has a birth voltage that is equal to the potential applied to the ion source ( VB).
The birth voltage for the fragments is somewhat more difficult to describe, since, unlike the parents, when the fragments are created they have an appreciable kinetic energy (typically several hundred eV). If the fragments are born in the drift region, the voltage applied to the drift region effects their birth voltage. For fragment ions bom in the drift region, the birth voltage, VBJRTHf is given by the following relation
> W - mr <” ) Knowing this, an expression can be derived for the velocity of a fragment ion after it has responded to the potential difference between the Wien filter and the drift region. 23
^ (^BJKTH/ ~ V w F sJ ( 12)
Under normal operating conditions the Wien Alter is referenced to ground potential
iVwF,nf = 0)' Considering this, and substituting for VBIRTfift Equation 12 can be
rewritten as
S ^2-3-V _ BIKTU = . yM * - £ V , - i v (13) ntf \ N mf I mp
Note that when Kdk = 0. this expression reduces to the velocity of the parent.
Noting that the voltage applied to the electrostatic plates in the Wien filter is proportional to velocity, a very useful relation is obtained by dividing the velocity of a fragment ion at ground potential (Equation 13) by the velocity of the parent ion at ground potential (Equation 5). In this expression V W F ,f and V wf >p are the voltages
(14)
that must be applied to the Wien Alters electrostatic plates in order for the fragment and parent ions, respectively, to be detected on axis. Given the position of a parent ion in the spectrum and the actual voltages applied to the drift region tube and the ion source, this expression can be used to accurately predict the position of a fragment ion in a velocity spectrum. The position of a fragment ion is predicted to be speciAc not only to the mass of the fragment ion but also to the mass of the 24 parent from which the fragment was produced. In other words, this technique is
capable of separating different mass fragments from the same parent and also fragments with the same mass but from different parents.
Manipulation of the drift region voltage shifts the fragment ion peak such that it can be made to appear any where in a large portion of the mass spectrum.
In theory, this range extends from to the position that the fragment would appear in the spectrum if it were a parent. Equation 13 can be used to calculate the voltages on the drift region which satisfy these endpoints. For a perfectly aligned system, when V ^p-0 only infinitely slow ions will be detected on axis. To determine the drift region voltage necessary to create fragment ions with zero velocity, vf = 0,
Equation 13 is rearranged and solved for Vd*
Knowing the beam energies and the masses of the fragment and the parent, this expression can be used to calculate the voltage which when applied to the drift region will result in fragment ions with zero kinetic energy. For example, an H30 + fragment from a 1000 eV beam of H50 2+ will have zero velocity with -1056 V applied to the drift region.
For positive ions, ^dr must be negative to satisfy this expression since the ratio of the parent ion mass to the fragment ion mass is necessarily greater than one
{pip/mj > 1) for fragmentation processes. Negative voltages (with respect to ground) 25 applied to the drift region will result in a fragment ion velocity which is smaller than
that of the parent ion (v/vp < 1). Therefore, with a negative voltage applied to the
drift region, fragment ions will be detected when at smaller Wien filter voltage than
the parent. In a velocity spectrum, fragments will actually appear at the same positions as higher mass parents.
On the other hand, a positive voltage applied to the drift region will result in a fragment velocity which is greater then the parent velocity and, therefore, a larger
Wien filter voltage is necessary for the fragment than the parent to keep the ions on- axis. In a velocity spectrum, the fragments will appear to have a lower mass than the parents. When the voltage applied to the drift region is equal to the birth voltage of the parent beam, the parents will have no velocity in the drift region. In which case, the fragments will have the same birth voltage as the parents and will appear in a velocity spectrum at the same position that a parent with the same mass would appear. The range of positions in which the fragment may appear can not extend past this point since application of a voltage which is above the birth voltage of the parents would prevent the parents from entering the drift region.
In theory, this technique is capable of separating fragment ions mass specifically within a wide range of kinetic energies (0 to VB). In practice, however, this range is limited by the ion optical system’s ability to transport fragment ions of low beam energy and it's ability to compensate for the focussing effects caused by large voltages on the drift region tube. At low energies, the optical fidelity of an ion beam is severely degraded, since the mutual repulsion of similar charges causes the 26 beam's diameter to "blow-up". These space charge effects make it difficult to maintain a high intensity beam at low beam energies. In addition, at low beam energies, it may be no longer valid to assume that recoil energy of the dissociation products is small compared with the beam energy.
Nonetheless, the ability to move the fragment peak to a wide range of positions in the mass spectrum demonstrates the utility of this technique as a means of fragment separation. Manipulation of the fragment peak position allows processes with small fragmentation cross sections to be observed since the fragment peak can be shifted to where little or no background current is observed.
B. Experimental Apparatus
The ion beam apparatus employed in these experiments is shown schematically in Figure 4. Ions are extracted from the source, pass through a 3.2 mm differential pumping aperture, and enter a second chamber which houses the ion optical components. Once in this chamber, the ions are focussed with a three cylinder einzel lens (L) and directed, with two perpendicular sets of parallel plate deflectors, into a quadrupole deflector910 which bends the beam 90°. This bend serves two primary purposes. Firstly, bending the beam by 90° is a convenient way to coaxially overlap the ion beam with a laser beam in order to do photofragmentation studies. Secondly, the bend effectively eliminates any fragments which were produced between the source and the quadrupole.
After the right angle bend, the ions enter a drift region tube (DR) which 27
gas
QD DR —» WF
OR
Ext
So VB
Figure 4. Schematic illustration of the experimental apparatus.
serves as the collision chamber. Two ports on the tube allow gas to be introduced
into the collision chamber and allow the pressure in the chamber to be monitored.
The critical, but also very simple, addition required to use the Wien Filter as a
fragment detector involves the application of a variable voltage to the drift region
(VDR).
The ions are captured in one of two Faraday cups (FC1 or FC2) at the end 28 of the beamline and the current is read using a Keithley 610 electrometer. The off- axis Faraday cup (FC2) serves two purposes. It allows a laser beam to replace the chamber gas as the source of fragmentation and can be used to achieve additional separation from the parents in the dimension perpendicular to the velocity dispersing direction.
All of the active ion optical elements were made of stainless steel. Previous designs using aluminum were found to be unsatisfactory due to the high secondary electron emission caused from ion-electrode collisions. Care was also taken in the design to eliminate any straight line path for ions to collide with the teflon spacers separating the individual elements. The apertures in the beam line were 0.250" except for 0.125" apertures at the extractor, quadrupole and the drift region.
After the collision chamber, the ions enter the Wien filter (WF). The Wien filter used in these studies is a commercially available Colutron 300 which has been modified by replacing the electromagnets (capable of up to 750 gauss) with a 1000 gauss permanent magnet. The length of the electrodes is 7.6 cm. In order to obtain a magnetic field of the same length and minimize the stray magnetic field outside of the Wien filter, field terminators, similar to those described by Hubner and
Wollnik11, were employed. The field terminators are made of mild steel and are mounted on stainless steel Kimball Physics plates which are held rigidly in place by stainless steel screws mounted in the sides of the magnet faces.
Crossed electric and magnetic fields are known to possess focussing properties2. Wahlin12 has shown that the effects of this focussing can be optimized 29 using electrostatic shims inside the Wien filter. Five pairs of electrostatic shims allow the electric field to be tuned in order to either optimize the current throughput or enhance the resolution of the device. A variable potential is applied independently to each of the sets of shims to tune the field.
The Wien filter is generally controlled by a computer (CompuAdd 286 machine) configured with a Keithly/Metrabyte DASH-16F data acquisition board.
The output voltage of the DAC is used as the input of a voltage programmable power supply (Hewlett Packard 6209B) which generates the electric field in the Wien filter. Figure 5 shows the wiring scheme which enables the voltage programmable mode of the power supply. A program (SCAN2B.FOR listed in Appendix 1) allows the electric field to be scanned by the computer at a variable speed. The program also allows the Wien filter voltage to be set at a given value to allow tuning of a specific ion.
A circuit, which is described elsewhere13, was designed to allow the Wien filter circuit to be scanned rapidly (-1 0 KHz) using a 0-10 V ramp input. When controlled by the computer, the rate at which successive scans could be viewed was limited by the computer’s ability to read and plot the data rapidly. Using the computer, mass spectral scans could be viewed on the screen at the rate of - 1Hz.
Scanning the circuit at this speed was a convenient way to tune the beam since the results of individual touches of the ion optics could be seen almost immediately.
There are several practical advantages to using a permanent magnet rather than an electromagnet in the Wein filter. First, the power required to generate the 30
A1 A2 A3 A4 AS A6 A7 A8 A0 8- - QND + $♦ A10 lololololol
3 kohm
Programming Voltago from DAC
Figure 5 Wiring scheme employed to enable the voltage programmable mode of the Hewlett Packard 6209B power supply used to generate the electric field in the Wien Alter. electric Held necessary for operation of the Wien filter is considerably less than that needed to generate the necessary magnetic field, therefore, a smaller less expensive power supply is needed. Also, electromagnets will frequently exhibit hysteresis when the field is varied, whereas permanent magnets do not exhibit this phenomenon.
There is no hysteresis associated with scanning the electric field, therefore, successive 31 scans of an electric field should be more reproducible than successive scans of a
magnetic field. This means that each of the masses should appear at the same
position relative to one another from scan to scan. This reproducibility is very
convenient when tuning the beam, since it allows one to make an accurate guess at
the position of a peak in the mass spectrum when tuning statically.
The use of permanent magnets also changes the general appearance and range
of the mass spectra. With a constant magnetic field, heavy ions (or, more
specifically, slow ions) will be detected on axis when weak electric fields are generated in the Wien filter. Therefore, this arrangement is a convenient way to observe very heavy ions which would not be seen in an arrangement with a permanent electric field and variable magnetic field. Since this research group has a long term interest in cluster ions, this modification to the Wien filter is attractive.
However, this arrangement does put certain constraints on the beam energy at which the lighter ions of interest can be studied. Nonetheless, the primary ions of interest can be easily observed at relatively high beam energies (up to 2000 eV).
Circuits for Ion Optical Elements
Two power supplies (Fluke 410B) are used to define the ion source potential, and to supply the ion optical voltages. The circuit which provides these voltages consists of several simple voltage dividing resistor chains. In general, only three types of ion optical elements are present in the beamline and only two types of resistor chains are necessary to run all of the components. With the exception of the 32 extractor, the lenses in the beam are three aperture einzel lenses with the two
outside elements defined at ground potential. In this configuration, only one potential is necessary per lens. The lens divider circuits consist of a chain of 10 resistors (300 kn) with a single turn potentiometer (500 kn) available as a jumper across any two successive resistors. The potentiometer is used to allow a continuously tunable potential within the voltage range. The resistors in the chain are arranged in a staggered configuration, as shown below (Figure 6), with a banana jack at each junction of two resistors. This arrangement allows a two prong banana plug to jumper any two successive resistors but not any individual resistor. The resistance of the potentiometer was chosen such that its resistance in parallel with two of the resistors equals the resistance of just one of the resistors in the chain.
The source float voltage ( VB) is applied to the top of this resistor chain and ground is defined at the bottom of the chain. Since an equal voltage drop occurs over each of the resistors, voltages in the range from 0 - VB can be obtained in increments of l/9,h of the total range. The potential that is dialed from the circuit is applied directly to one of the ion optical lenses.
The parallel plate deflectors and the quadrupole deflectors can be run from the same circuit design. The deflector circuit design is similar to that of the lens.
Instead of a single chain of resistors, two resistor chains are arranged in parallel
(maintaining the staggered configuration.) For these circuits, a four prong banana plug which jumpers sets of two resistors in each of the two resistor chains is used.
The beam source voltage was applied to one side of this circuit and the negative 33
a HV
♦HV -HV
>
Figure 6. Voltage dividing circuits for the ion optical lenses, (a) circuits for lenses, (b) circuits for quadrupole and parallel plate deflectors.
"mirror” voltage was applied to the other side. The four prong plug allows a range of positive voltages and a range of negative voltages to be picked off simultaneously.
In this arrangement two potentiometers are used to provide continuously tunable voltages in both the positive and negative ranges. The shafts of the potentiometers are mechanically connected (epoxy) to a plexiglass wheel. By turning the wheel, the 34 potentiometers are changed the same amount but in opposite directions.
Vacuum System
The ion beam apparatus was housed in two stainless steel chambers which are connected by a 3.2 mm differential pumping aperture. The chambers are each pumped by a 5000 L/s oil diffusion pump (Balzers Diff 5000 with Dow Corning 704™ diffusion pump oil) backed by a Welch 1398 mechanical pump (53.1 cfm).
(Presently, the optics chamber is backed by a Welch 1375 mechanical pump (35.4 cfm)). Pressure in the chambers was monitored using an ion gauge (Kurt J. Lesker
G075N Ion Gauge Tubes, MKS Type 290 Ion Gauge Controller). In the source chamber, which houses only the source and extractor, the gas load from the source generally produces a working pressure of ~ 5 X 10'5 Torr. The base pressure in the optics chamber is generally maintained at ~ 2 X 10"* Torr. Foreline pressures were monitored by thermocouple gauges (Varian Type 0531 Gauge, Varian Type 801
Controller). The base pressures were generally below 5 mTorr, and under gas load the foreline pressure on the source side was typically ~ 15 mTorr.
A gas rack was used to introduce the gases into the source and to regulate the pressure in the source. A Welch 1397 mechanical pump was used to pump on the gas lines before they were opened to the vacuum chambers. A thermocouple gauge on the gas rack is used to monitor the pressure in the gas lines at the rack. The gas rack was equipped with needle valves (Nupro) for precise control of the gas flow to the source. The gas flows from the rack to the chamber through several meters of 35 polyethylene tubing (6 mm i.d.). The conductance of the tubing through which the
gas must flow is small, therefore a considerable pressure drop from the rack to the
source is observed. In order to determine the pressure inside the source a number
of parameters of the pumping system have been determined and are reported elsewhere14.
Glow Discharge Ion Source
A number of ion sources are employed in these ion beam experiments. The most frequently used source is a glow discharge ion source. This source is similar to the source used by Saykally and coworkers15 in their experiments with direct absorption infrared spectroscopy in ion beams, and has been used in this laboratory to study beam voltage manipulation16,17. The source consists of two hexagonal steel electrodes 3.7 cm across which are separated by a 4 cm pyrex tube (9 mm i.d.).
Viton O-rings were placed in sunken O-ring grooves to allow a vacuum seal to form between the glass and the electrodes. The use of sunken O-ring grooves effectively eliminates the probability of the O-ring being exposed to the violent conditions of the discharge. The front plate (anode) was 6mm thick and had a 22° conical cut in both the front and the back which tapers to a 2 mm aperture in the center of this electrode through which the ions are extracted. The back plate, which was 18 mm thick, had a 6 mm hole drilled from the side into the center of the electrode. A second hole drilled from the front of the electrode intersected this hole, again in the center of the electrode, and produced a passage through which gas was introduced 36 into the source. Small magnets (2 or 3) were placed across the discharge to increase the total ion current extracted from the source. Thin sheets of Teflon were used to insulate the magnets from one of the electrodes to avoid creating a short circuit between the electrodes.
Hydrated hydronium cluster ions were produced from ~ 0.5 Torr of neat water vapor (as determined by system throughput calculations14). The discharge was run at ~ 1500 V and 1 mA with ~ 500 Kohm of ballast resistance in series with the discharge (Figure 7). Floating power supplies (Hewlett Packard 6525A) were originally used to run the discharge, however, several components in these power supplies were found to be quite susceptible to arcs occurring in the ion beam. To eliminate these problems (and subsequent electronic shop repair charges) several 510
V batteries (Eveready #497) were connected in series and used to run the discharge.
A milliammeter was used to monitor the current drawn from the batteries.
Ion currents of several microamperes are routinely extracted from a 2 mm aperture in the anode. Figure 8 shows a typical mass spectrum recorded using this arrangement. This spectrum was taken with a source float voltage (VB) of + 1500 V, a mirror voltage of -1900 V, an extraction voltage of -1100 V (VEXT = +400 V), and a drift region voltage of + 700 V. 37
Ion Beam
a /w w — 1 Discharge Ballast Power Supply Resisitor Beam Power Supply
Figure 7. Isolation scheme used to float the discharge power supply.
C. Experimental Procedures
1. Pressure Calibration
Absolute pressure measurements in the drift region were made using a capacitance manometer (MKS type 127, 0-1 Torr range). The absolute accuracy of this device was verified to be within l%-5% by overlapping measurements with another capacitance manometer (MKS type 222B, 0-760 Torr range) and a mercury 38
H.OH.O H.O
CD C OB W C O
60 90 110 130 150 170 190 210 23070
Wien Filter Voltage
Figure 8. Wien filter velocity spectrum of hydrated hydronium cluster ions produced in glow discharge ion source. barometer.
2. Cross Section Measurements
The total attenuation cross sections for H30 +, H50 2+, H70 3+, H90 4\ and
Hn0 5+ with argon have been determined. Two different methods have been employed to obtain attenuation data. The first of these methods involved recording 39 successive mass spectral scans at various collision gas pressures. The data were collected over a range of parent beam energies as well as a range of drift region voltages. The intensities and widths of all the peaks which were determined using a nonlinear least squares analysis (programs listed in Appendix 1). This body of data was particularly useful in that the attenuation of all the parents was observed simultaneously. These mass spectra were also used to determine the collision induced dissociation cross sections.
In addition to, and as a check of this data collection method, additional data for the total attenuation cross sections was recorded by statically sitting on the individual parent peaks and recording the ion current as a function of collision gas pressure. In these measurements, care was taken to ensure that the total ion intensity returned to it’s initial value (±10 %) when the collision gas was allowed to pump away. This check confirmed that the presence of the target gas had not changed the ion optical focussing of the beam and caused the peak positions to shift slightly. A small change of this type could result in a large change in the maximum current observed.
The static measurement technique was also used to obtain data for the CID cross sections of the parents by alternately measuring the ion current for both the parent and the fragment ions using appropriate Wien filter voltage settings for each.
To avoid ambiguous results due to multiple collisions and three body collisions, care was taken to keep the pressure below 2 mTorr when obtaining data 40 for the total attenuation cross sections. This was estimated to be the cut off pressure below which only single collisions were likely. It will be shown later that above this pressure multiple collisions become important.
3. High Pressure Studies
To investigate the effects of multiple collisions, data was recorded at target gas pressures above 2 mTorr. These studies determine the rj parameter as defined by Kim18,19. The data which was collected included the parent and fragment intensities for HaO + and H50 2+ for parent beam attenuations of up to -95%.
D. Results and Analysis
In the previous section, a theoretical basis for the use of a Wien filter as a fragment detector was presented. The predicted behavior of this device has been tested and the technique has been shown to be a powerful means of obtaining information concerning fragmentation processes. This section presents results which demonstrate the utility of this technique and also describes the method used to analyze the data obtained in order to determine various cross sections. Also, in this section, a discussion of the internal energy of the collision products is presented. In this discussion, predictions are made concerning the degree to which excitation occurs in the glancing collisions studied. The predictions suggest that the beam emerging from the collision cell can harbor a surprising amount of internal energy resulting 41 from glancing collisions.
1. Demonstration of Wien Filter as Fragment Detector
To demonstrate the use of the Wien filter as a means of fragment separation,
a series of studies were performed on the collisionally induced dissociation of various cluster ions. Protonated water clusters were chosen as the species to be studies because of our interest in the process of aqueous solvation.
Since only fragment ions which are not knocked out of the beam are detected by this technique, only a small fraction of the total fragment current is observed at the end of the line. It is useful to have a source which produces high currents to observe an appreciable fragment current using our detection scheme, which consists of a standard electrometer capable of reading 0.01 pA (Keithley Instruments 610C).
The hydronium ion and it’s first several hydrated clusters can be made in abundance using the glow discharge source described in the previous section. Using this source, mass selected currents of several nanoamperes, are easily obtained for H30 +, H50 2+,
H70 3+, and H90 4\
Furthermore, only fragments resulting from glancing collisions are detected; so the energy transferred during these glancing collisions must be sufficient to cause fragmentation. Consequently, the ions to be had to be weakly bound. The water binding energies of the three higher clusters (1.37, 0.846, 0.776 eV, respectively20,21,22) are sufficient to allow large currents to be extracted from the source, but are also small enough to allow glancing collisions to produce fragments 42 that remain in the beam.
Figure 9 illustrates the use of the Wien filter as a fragment detector. Both traces in this figure were recorded under identical source conditions with 5 mTorr of argon in the collision cell. The bottom trace (a) is an expanded view of a
"normal" Wien filter velocity spectrum taken with the drift region at ground potential
(VDR=0). The top trace (b) shows the effect of changing only the voltage on the drift region/collision cell tube to VDR= 198. With the application of a voltage to the drift region, a series of new peaks appear in the mass spectrum. The new peaks
(shaded) correspond to fragment ions which were present in trace (a) but not detected separately until a voltage was applied to the collision chamber. With no voltage applied to the drift region, the fragments remain at the same velocity as the parent beam and therefore are not separated. However, once a voltage is applied to the drift region the fragments assume a different velocity than the parents and are clearly separated from their parent ions in the mass spectrum. To confirm that the appearance of the new peaks is due to fragment ions, the following investigations were performed.
First the pressure in the collision cell was systematically varied while monitoring the resulting intensities of both the parent and fragment ion peaks in the mass spectrum. Since the probability of creating a detectable fragment ion is directly proportional to the pressure of the collision gas, as the pressure is increased the fragment ion intensity should increase as the parent ion intensity decreases.
In Figure 10, the region between the H30 + and the H50 2+ peaks is shown at 43
■ n
c 4) k. 3 o c o
50 100 150 200
Wien Filter Voltage
Figure 9. Demonstration of the Wien filter as a means of fragment separation. In trace (a) VDr=0 V, in trace (b) VDR= +198 V. Both traces were recorded with 5 mTorr of argon in the collision chamber. various pressures. The individual traces in this figure correspond to spectra recorded with a non-zero value of VDR and with target gas pressures in the range from 0.6 -
4.9 mTorr. In these scans, the length of the drift region was 5.0 cm which is twice
the length used for the cross section measurements reported later. The peak shown
corresponds to HaO + which arises from the one water loss fragment from H50 2+ and 44
CM
135 155 175
Wien Filter Voltage Figure 10. The intensity of the one water loss fragment from H502+ vs. argon pressure. The collision chamber pressure for each scan was (a) 0.6 mTorr, (b) 1.7 mTorr, (c) 3 J mTorr, and (d) 4.9 mTorr. is definitively identified as a fragment by the increase in peak intensity with collision chamber pressure. At the highest pressure, the two water loss fragment from H70 3'" can be seen as a shoulder on the H50 2+ peak. In general, fragment peaks are easily identified by their characteristic growth with increasing pressure (at low pressure).
Although distinguishing between parent and fragment ions is trivial, it is more 45 difficult to determine the identity of a fragment ion in terms of it’s mass and the parent from which it was born. Tentative identification of fragment ions can be made from a basic understanding of the theory described previously. Moreover,
Equation 14 can be used to predict the position at which a fragment ion will appear, and therefore, can be used to make definitive assignments of the identity of fragment ions. To confirm the validity of the theory and to demonstrate the use of Equation
14 for fragment identification, a second study was performed.
The second study involved systematically varying the voltage applied to the drift region in an attempt to predict the position of various fragment ions in the resulting mass spectra. Figure 11 shows an expanded view of the region between the
HaO+ and H50 2+ in several mass spectra. By changing the voltage applied to the drift region, the HaO+ fragment ion resulting from one water loss off H50 2+ gradually slides from the H50 2+ position in the mass spectrum to the H30 + position.
Theoretically, when the drift region voltage equals the birth voltage for the parents, the H30 + fragment would appear at the same position as H30 + parent . Under these circumstances the parent beam would have zero kinetic energy and the birth voltage of the fragments would equal the birth voltage of the parents. Ion optically, however, the system is unable to transport the beam (either parent or fragment) at zero kinetic energy. Since the drift region acts as an ion optical lens, the system has problems transporting the beams when the voltage applied to the drift region is a large fraction of the beam energy of the parents at ground.
Since the fragments move away from the parent as VDR is increasingly 46
H.O H.O
■ n < w M c 155 t_ 3 o 196 e o 231
276
120 140
Wien Filter Voltage (V)
Figure 11. The position of the one water loss fragment from H50 2+ vs. the voltage applied to the drift region (VDR).
different than ground, it is usually a simple matter to identify a fragment ion without any calculations if one is familiar with the technique. However, to illustrate it’s use,
Equation 2-14 has been used to predict the position of several fragments resulting from the dissociation of the parent ion beam. Knowing the beam energy of the parent beam and the voltage applied to the drift region, the ratio of the peak 47 positions of the fragment and the parent has been calculated under several sets of conditions. Table 2 lists a comparison of the calculated and observed values for this ratio. These values have been calculated for the H30 + fragment from H50 2+ at various combinations of beam energies and drift region voltages. The agreement between the calculated and the measured values supports the theoretical description of this technique which was presented previously.
Note that the ratio of the fragment velocity to the parent velocity can be greater than or less than unity. Therefore, the fragment peak can be made to appear on either side of the parent peak in the mass spectrum.
Table 2
Comparison of the calculated vs. observed values of the ratio of fragment ion peak position to parent ion peak position in a Wien velocity spectrum.
^WF,f/^WF.p VB ^DR Beam Energy (V) (V) (eV) Calculated Observed 700 357 343 1.2179 ± 0.0014 1.222 ± 0.008 700 237 462 1.1494 ± 0.0014 1.139 ± 0.002 1000 258 742 1.1157 ± 0.0010 1.091 ± 0.028 700 -125 825 0.9115 ± 0.0016 0.9103 ± 0.008 48 2. Total Attenuation Cross Sections
There have been several studies of the collisional fragmentation of
H30 +(H20)n23,24’25’26, however, we have found only one which reports absolute cross sections and fragmentation branching ratios. These studies, by Dawson27, were accomplished with a triple quadrupole at beam energies of about 25 eV. In these experiments, ions are mass selected in the first quadrupole and injected into the second quadrupole where they are confined in an rf field and undergo collisions with the target gas. The products are then mass selected in the third quadrupole.
Dawson’s experiment does not distinguish between high and low impact parameter collisions since essentially all the parent ions which are lost are recovered in the form of fragment ions.
Theory
The attenuation of a fast ion beam analogous to the attenuation of a beam of light by absorption, and therefore can be adequately described by the following expression28 (which is similar to the familiar Beer’s law expression which applies to absorption of light)
/ - >0' / <»> in which Ip is the ion intensity at pressure P, Ip 0 is the ion intensity at zero pressure,
L is the length of the collision cell, and kT is the product of the Boltzman constant and the absolute temperature. 49 To determine the total attenuation cross sections for the hydrated hydronium
cluster ions, data were collected as described earlier. Analysis of the mass spectral
data involved the use of a non-linear least squares routine (fit.for listed in Appendix
II) to determine the intensity, width, and position of each peak in the mass spectra
assuming gaussian lineshapes for the peaks. At low pressures, a global fit of just the
four most intense parent peaks (H30 +, H50 2+, H70 3+, and H90 4+) was sufficient to
obtain the parameters for these peaks. At high pressures, however, the fragment
peaks became significant and were included in the fit. The analysis of the H nOs*
peak was more difficult even at low pressures. To obtain acceptable fits of the
Hn0 5+ peak, special attention was paid to this peak during the fitting procedure.
Since the parameter of most importance in determining the attenuation cross section
is the peak intensity, an effort was made to determine these values as well as
possible. Frequently, this required fixing the width and the position of this peak at given values.
Calculations
The intensities obtained from this fitting procedure were used in the following expression to determine the attenuation cross sections for each parent (op).
In this expression, i is an index denoting data recorded at different pressures, Ip, is the parent ion intensity at pressure /, Ip0 is the parent ion current with zero pressure 50 Table 3
Absolute values for the total attenuation cross section for collisions of hydrated hydronium cluster ions with argon.
Attenuation Cross Section (A2) Ion This Work Dawson27 (300-1000 eV) (25 eV) I H3°+ 11 ± 6 16 h 5o 2+ 25 + 8 29
h 7o 3+ 36+ 11 44 H, in the collision chamber, L is the length of the collision chamber, and kT is the product of the Boltzman constant and the absolute temperature. Data obtained from manually sitting on each of the parent peaks and recording the intensity as a function of pressure was also used in this expression to determine ap. To investigate the energy dependence on the cross section, measurements were taken using both techniques at various beam energies in the range from 300 to 1000 eV. Variations in individual determinations of ap were much greater than any observable beam energy dependence of the total cross section. Table 3 lists the average values of the total attenuation cross sections which were measured. These values represent measurements taken on several different days at several different beam energies. The uncertainties reported are 95% confidence limits determined from multiple runs. 51 For comparison, the values for the total attenuation cross sections reported by Dawson have been included in this table. The values presented here agree well with the values reported by Dawson. It is not apparent whether the deviations from Dawson’s values are due to uncertainties in the two sets of values or whether there is an energy dependence which can be attributed to these differences. 3. Collision Induced Dissociation Cross Sections The detection of fragment ions at the end of the beamline is interesting since after dissociation these ions remain in the ion beam for further experiments. When these fragments are formed in collisions with ambient gas, this indicates that a collision occurred in which enough energy was transferred to dissociate the parent ion but not enough was transferred to knock the fragment out of the beamline. Since the recoil energy is small in comparison with the beam energy, scattering of the collision products off-axis is the primary means of removing the fragments from the beam. Interactions resulting in detectable fragment ions must be glancing (i.e. high impact parameter) collisions. To determine the degree to which these glancing collisions play a role in the overall attenuation of the parent beam, the cross sections for the production of detectable fragment ions from H30 +(H20)n (n=03) have been determined. 52 Theory The observation of fragment ions is governed by two opposing factors. In order for the fragments to be formed, pressure in the collision chamber is required; however, this same pressure will attenuate the fragment ions just as it does the parents. At low pressure (single collision conditions), the formation of detectable fragment ions, Ip within a differential length of the collision chamber, dl, is given by (18) in which acm is the glancing collision induced dissociation cross section which results in detectable ions, and oy is the total attenuation cross section for the attenuation of the fragment. Note that since the fragment ions which are formed also appear as parent ions, the appropriate values for oy have already been determined over a range of beam energies. (For simplification, it is assumed that fragment ions have the same cross sections as the parent with the same mass. This may not be a valid assumption if there is a considerable difference in the cross sections between excited and ground state ions, since it is likely that an attenuated beam will be significantly excited.) This expression is integrated29 over the length of the drift region, /, and evaluated at the end of the drift region ( l= L ). If Equation 17 is solved for Ipo and substituted into the integrated form of Equation 18 the following relation can be derived, Note that this expression depends on the difference of the total attenuation cross section for the parent and the fragment, both of which have already been determined. If the exponential in this expression is expanded we see that, PL (o , - o f 1 + (o, - — + * ------£- - I (20) lJL ' f kT 2 kT CID IM (O, - op At low values of the pressure, P(, it is valid to truncate this expansion at the linear term and this expression simplifies to h i - „ t t (21) I cm kT Note that at low pressure the dependence on (ap - of) vanishes completely. Therefore, the limiting value of the slope of a plot of J vs. P, will determine the CID cross section aCID. Calculations The fragment ion peaks were monitored as a function of collision chamber pressure, as was done with the parent ions. Fits of the mass spectral data were performed using the non-linear least squares fitting procedure used to analyze the parent data. Global fits were not possible in the analysis of the fragment ions since the intensities of the fragment peaks were generally much smaller than those of the 54 parents. For this reason, the fragment peaks were fit individually with the data set truncated at the baseline on each side of the peak. A plot of the ratio of the total fragment ion current to parent ion current is presented in Figure 14 for H50 2+, HA** and H90 4+. In this plot, If i represents the sum of all the fragment ions detected for a particular parent ion. The data for H90 4+ are sparse since only one set of data with a particularly well chosen value of VDR had all three fragments revealed. The fitted curves were obtained using Equation 19 with fixed values of the difference in parent and fragment attenuation cross sections determined from our measurements reported in Table 3. The value used for (ap - of) has only a small effect on the final value of oaD as is demonstrated in the limiting case by Equation 21. The values obtained for oaD are given in Table 4. Table 4 Absolute values for the collislonally induced dissociation cross section for collisions of hydrated hydronium cluster ions with argon. .... Glancing CID Ion cross section (A2) h 3o + 0 h 5o 2+ 0.62 ± .08 h a + 4.3 ± 0.2 h 9o 4+ 9.1 ± 1.2 55 0.20 0 .1 5 a \ 0.10 0.0 5 H.O 0.00 « 0.0 0.5 1.0 1.5 2.0 2.5 Pressure (mTorr) Figure 12, The ratio of the total fragment current to the parent current vs. collision chamber pressure for several cluster ions. These data were fitted to Equation 19 to obtain the curves. In these studies, only H30 +(H20) n_m fragments were detected which suggests, as expected, that the weak intramolecular bonds break preferentially to the strong O-H bonds. No evidence for the formation of the H+ fragment from any of the parent ions was observed. Since 7.22 eV of energy is required to form H + from H30 +, it is not surprising that no evidence for the formation of this fragment from 56 glancing collisions is observed. At the beam energies used in these experiments, collisions which could provide > 7 eV of collisional energy must be low impact parameter collisions which knock the fragment out of the beamline. In addition, from the recoil energy of the dissociation, it is less likely for the H + fragment to remain in the beam than it is for more massive fragments. In Figure 13, the attenuation and the CID cross sections for H 4(H20) n have been plotted vs. cluster size (n). The attenuation cross sections have also been plotted in this figure for comparison. It is interesting to note the evidence for solvent shell structure on going from n=4 to n=5. In both data sets, a jump in the cross section occurs at Hn0 4+. This jump can be attributed to the fact that H30 + has three available ligand sites which can bind water molecules quite strongly. An additional water molecule will be held less tightly and will be more susceptible to fragmentation during a collision. Branching ratios for the glancing collisional activation process have been determined by examining the distribution of fragment ion intensities vs. the number of waters lost in the dissociation process under single collision conditions. These average branching ratios are given in Table 5 along with the energies required to break the corresponding number of weak bonds. The process of one water loss seems to dominate in all of these clusters as it does with hard sphere collisions as demonstrated by Dawson. Compared with the hard sphere collisions, the glancing 57 8 0 M < 6 0 o 4> 4 0 CO <0 <0 20 O h. o CN> 0 0 1 2 3 4 5 6 Figure 13. The attenuation and glancing CID cross sections for H^HjO), vs. cluster size (n). collisions result in a higher fraction of the loss of a single water. This would seem to be due to the smaller amount of energy transfer in glancing collisions. Dawson also reports branching ratios for the various water loss channels in the CID of these clusters, however, his measurements do not distinguish between high and low impact parameter collisions. Table 6 compares the branching ratios 58 determined in this work with those obtained by Dawson. Since the collision products formed in his experiment are collected with near unit efficiency the glancing collisions are not separable from the hard sphere collisions. Table 5 Branching ratios for the Loss of Water Molecules from Hydrated Hydronium Clusters by Glancing Collisions Number of waters lost Ion 1 2 3 Prob. Eb (eV) Prob. Eb (eV) Prob. Eb (eV) h 3o + 0 7.22 h 5o 2+ 1.00 1.37 0 8.59 h 7o 3+ 0.91 0.85 0.09 2.22 0 10.21 I h 9c v 0.78 0.78 0.18 1.62 0.04 2.99 Table 6 Comparison of the Glancing and Hard Sphere Branching Ratios for the Loss of Water Molecules from Hydrated Hydronium Clusters This Work Dawson27 | Species 1 2 3 1 2 3 I h 3o + 0 1.0 h 3c v 1.00 .83 .17 HtCV .91 .09 .73 .27 H , After seeing that a large fraction of the initial beam could be recovered as fragment ions at the end of the beamline, it became apparent that glancing collisions play an important role in the collisional dissociation dynamics of these clusters. These glancing collisions will result in a fragment ion if the energy transferred in the collision is greater than the weakest bond in the parent ion. If less than this threshold energy is transferred in the collision, internal excitation of the parent will occur. This has led to different definitions of collisional activation (CA) in the literature. Some authors30 have defined the collisional activation cross section, as that arising from detectable fragment ions and therefore equal to the presently reported values of aaD. Others prefer a more general definition of a^ which relates to the conversion of collisional energy into internal energy. For the present discussion of collisional energy transfer and for the multiple collision analysis, the definitions adopted by Kim18,19. Using these definitions, the total collisional cross section, aT for the ion can be separated into two distinct components, ° T * ° L * ° CA The ion loss cross section, oL, accounts for all processes in which no ion is detected at the end of the line. These processes include neutralization processes as well as collisions which scatter ions out of the collection angle for detection. The collisional activation cross section, o ^ , includes all collisional processes which allow an ion to be detected. Collision induced dissociation is included in this group of processes, 60 therefore, the detection of ions is not limited to parent ions but also can include fragment ions. These definitions clearly separate the collisional processes into two distinct groups, one which results in the attenuation of the total ion current, and one which does not. From this definition of a^ collisional activation can be defined as the transfer of kinetic energy to internal energy without the loss of total ion current. This internal energy may or may not lead to dissociation depending on how it compares with the dissociation energy of the weakest bond. At low target gas pressures, the probability of a single ion suffering multiple collisions is small. However, as the number density of the target gas increases, multiple collisions become more likely. It is apparent that processes such as collision induced dissociation are strongly effected by multiple collisions, since each collision results in the transfer of some energy to the collision partners. The effect of multiple collisions on collisional activation is a function of the amount of energy transferred in each collision. Two separate channels can be imagined when considering the role of multiple collisions on CA18. On one hand, a series of dissociation steps via sequential collisions can be imagined as in Equation 23. A*{B)m - A *(£)„_, + B - A 'iB ) ^ + 2B - . . . (23) On the other hand, when sequential collisions transfer less than the bond dissociation energy, the series of excitation steps can be imagined. 61 A'W. - - (/••(B).)" - . . . - A '(B),., * B (24) In the first case, each collision with a target gas molecule has sufficient energy to break a bond, therefore, each collision results in a dissociation. In the second case, the collisional activation energy which is transferred is less than the weakest bond dissociation energy and internal excitation of the ion results. Of course, it is improbable that collisional activation will proceed along either of these channels exclusively. In fact, it is quite likely that a large number of combinations of these two processes take place during CID. The second sequence is analogous to the technique of multiphoton dissociation which is a commonly used spectroscopic procedure. Although the collision and the spectroscopic processes are similar in that each process has a series of steps which result in the transfer of energy to the species of interest, the two processes are significantly different in one primary aspect: the amount of energy transferred per event. The multi-step spectroscopic experiments involve the transfer of discrete packets with a specific amount of energy. In collisions, however, the amount of energy transferred covers a broad range which can be described by a probability function, PC(E). It would be useful to have some idea of the collisional energy transfer probability, PC(E), since knowledge of this probability distribution coupled with a known bond dissociation energy could be used to predict the probability that a single collision will lead to dissociation. For this reason, there have been several attempts to both theoretically predict and experimentally measure this distribution. 62 Theoretical Predictions of Pf(E) Although considerable work has been performed on the prediction of energy deposition distributions for diatomics31,32, the author is aware of only one set of calculations for PC(E) for systems involving polyatomic ions. This discussion will be limited to that work since the present work involves polyatomic clusters. Making several simplifying assumptions, Kim and McLafferty33 were able to use Massey’s "adiabatic criterion"18,34,35 to calculate approximate energy transfer distributions for a variety of molecular weight species at several beam energies using previously reported charge transfer data. The distributions calculated by Kim and McLafferty are shown in Figure 14. Massey’s adiabatic criterion predicts that the amount of energy transferred in a collision (£") can be related to the velocity (v) of the ion by (25) in which h is Planck’s constant and a is the adiabatic parameter. The charge transfer data used in these calculations provided an experimental measure of the probability of transferring a given amount of energy at various velocities. Kim and McLafferty used this data to determine the energy transfer distribution at a given velocity. These calculations showed that the energy transfer probability functions for high energy collisions was a smooth function which had a low energy maximum and a high energy tail. The presence of the high energy tail indicates that a finite probability exists for the transfer of a large amount of energy. Both of these features were predicted irrespective of the collisional energy and the projectile mass. 63 Colllclonol Energy Transfer Probability (a*4&) 100, 3.9 KV; «Mt 000, 31KV \m/g 100, 7.6 KV, m/e 400, 31 KV 15 £ I \mAe tOO, 31 KV, m/e 25. 7.6 KV | o 0.4 m/e 25, 31 KV (TV Q 2 - 6 6 10 " 12 14 16 ifl Energy Tronsfered. eV Figure 14. Calculated P((E) distribution from Reference 30. Experimental Determinations of Pr(E) A variety of experimental investigations of collisional energy transfer have been published. Griffiths, et. al.36, have studied the collisional dissociation of n- butyl benzene and n-pentyl benzene in the range from 2-8 keV. By measuring the branching ratios for the two most probable fragmentation channels, the collisional excitation energy was determined by comparison to photodissociation data. At low collision gas pressure, these studies indicated that in the range from 2-8 keV, the maximum in the collisional excitation energy distribution remained relatively constant 64 at 2.4 eV when argon was used as the collision gas. However, when the collision gas was changed to nitrogen, the collisional excitation energy was found to increase from 2.2 to 2.5 eV within the same projectile energy range. The difference in collisional energy transfer suggests that the nature of the target gas influences the shape of the PC(E) curves. This paper also showed that the maximum in the energy transfer distribution is independent of pressure at low pressures but increases rapidly with increasing pressure, suggesting that multiple collisions can be an effective means of transferring large amounts of energy. To compliment the high energy studies, Dawson and Sun37 performed low energy CID studies on n-butyl benzene ions. The results of these studies differ considerably with those of Griffiths36, suggesting that the energy transferred in low energy collisions can actually be greater than in high energy collisions. Using the same technique of comparing branching ratios at various collision energies to photodissociation data, Dawson and Sun found that the excitation energy profile has a maximum at - 9 eV (center-of-mass) corresponding to a peak in the excitation energy distribution of between 2.8 and 3.3 eV depending on the collision gas. These studies indicate that at low energies the conversion of translational energy to vibrational energy is much more efficient than at high energies. This phenomenon has been attrributed to a more efficient transfer of translational energy to electronic excitation at high collision energies. Using an magnetic deflection mass spectrometer, Nacson and Harrison38 were able to measure the charge transfer cross sections for a variety of n- 65 alkylbenzene molecular ions, including those studied by Dawson and Sun37, and Griffiths, and coworkers36. These charge transfer cross sections were used to determine the amount of energy transferred in both low energy and high energy collisions. By monitoring the branching ratios for the two primary fragmentation channels as a function of collision energy they were able to determine the average energy transfer by comparison to the charge transfer data. For the n-butyl benzene molecular ion, the maximum in the energy transfer profile was found to be 4.6 eV with either argon and nitrogen as the collision gas. The energy transfer profiles were also determined for a variety of other n-alkyl benzene molecular ions. It was found that the maxima in these distributions increased with an increase in the size of the alkyl portion of the ions. In fact, a linear relationship exists between the maxima and the number of vibrational degrees of freedom of the ion. Cooks and coworkers39 have studied the internal energy distributions resulting from a variety of activation processes. In these studies, W(CO)6+, Fe(CO)5+, and (CjH^Si* were collisionally dissociated and photodissociated. These species were chosen because each has several sequential dissociation steps, therefore, a reasonable determination of the collisional energy transfer distributions can be measured almost directly. Knowing the appropriate bond energies, one can surmise the amount of energy transferred in a collision by measuring the ratio of the various fragments. These measurements were made for collisions at both low and high energies and the resulting PC(E) curves were compared with similar curves obtained from photodissociation data as well as data obtained from collisions with 70 eV 66 electrons. At low collision energies, the energy transfer profiles were similar for each of the ions. At higher energies, the energy distributions were different for each of the ions but they each exhibited the features predicted by Kim and McLafferty33. The primary differences between the profiles was in the height of the high energy tail. In addition, two of the profiles had an indication of structure in the high energy tail. Comparison of these profiles with those obtained by other methods showed little or no resemblance between the CA processes. In addition to these studies, the effects of target pressure on low energy collisions was investigated. In agreement with earlier studies36, this investigation found that the average amount of energy transferred increases significantly with target gas pressure. Under multiple collision conditions, a factor of 3.5 could be gained in the maximum of the energy transfer distribution over single collision conditions. This evidence clearly suggests that multiple collisions can play an important role in collisional activation, and can be used as a means of depositing a great deal of internal energy into an ion. Multiple Collision Probability The probability for a single ion to undergo multiple collisions has been described previously. As was first shown by Todd and McLafferty30, and later by Kim18, a Poisson distribution can be used to approximate the probability , P„, for an ion to experience n collisions and still be detected. This probability can be given as the product of the probability of suffering n collisions and the probability of staying within the collection angle of the detector. Ions which reach the exit of the collision 67 chamber will suffer n collisions, where n is the number of target gas molecules within the volume swept out by the ion, V,. This volume is given by the product of the total cross section for the ion, a„ and the length of the collision chamber, I. Vt - oTl The probability of finding n molecules in the volume Vt can be approximated by t ' aa* q* “ nt where a is the product of the number density of the target gas, p, in the collision chamber and Vr Using the cross section definitions given previously, the probability of an ion, either parent or fragment, suffering a collision and remaining in the beam and being detected is given by the ratio of the collisional activation cross section to the total cross section, 3 . — (28) a T From this and the probability of suffering n collisions, the probability that an ion suffers n collisions and is detected is P. . (29) If this probability is summed for all values of n, the overall probability for the detection of an ion is, 68 ,e"*a* (30) n.O rt! Substituting for s and a, this expression becomes, CA (31) ' x - £ M-0 n! Evaluation of the sum gives, ° caP1 1 + o-.pl + (32) = g - ° T Ple *CA P* Recalling that oT = oL + a ^ , this expression reduces to, PT ‘ e ’°Lp' (33) This expression gives the probability of the detection of an ion whether it be a parent or a fragment. To interpret the results presented previously it is important to distinguish between the parent ions and the fragment ions. It would be helpful if this total probability could be broken into the sum of the probability of detecting a parent ion and the probability of detecting a fragment ion. In order to do so, it is necessary to know the probability that a collision will result in a dissociation. The probability of dissociation can be predicted from the collisional energy transfer distribution and the multiple collision probability. Unfortunately, the exact PC(E) curve is generally not known. However, Kim18 has developed a theory to describe the effects of multiple collisions on the process of collisional activation. This theory can be used 69 to determine the probability of suffering a collision (or multiple collisions) without dissociating. Effects of Multiple Collisions on Collisional Activation Kim18,19 defines the parameter r, as the probability of a parent ion suffering a single collision and being detected as a parent ion, that is, without dissociating. This parameter accounts for all collisions in which the parent ion remains in the beam and the collisional energy transfer is less than the threshold energy for fragmentation. As shown in Figure IS, this parameter can be depicted graphically on a PC(E) curve. It is apparent that the value for this parameter depends quite heavily upon the shape of the energy transfer distribution. Furthermore, Kim defines rH as the probability of suffering n collisions without dissociating and without being knocked out of the beam. From these definitions, the following expression gives the probability for a parent ion to be detected as a parent ion. • E (3 4 ) *•0 In this expression, it is assumed that no unimolecular dissociation occurs (i.e. r0 = 1). (In our experiments this assumption is valid since the quadrupole deflector removes any ions which have undergone unimolecular decay.) The probability for a fragment ion to be detected is somewhat more complicated to describe since a& and aL for the fragment ion are likely to be different than for the parent. 70 >» TH 0 . V > •«-> © cc o 1 2 Energy Transferred (eV) Figure 15. Sketch of the approximate PC(E) distribution for Hs0 2* showing the threshold energy for the loss of 1 water molecule. The shaded area corresponds to the value of rr Effect of Fragment Ion Cross Section The derivation presented above assumes that the values for and oL are the same for the parent and the fragment ions. However, Tables 3 and 4 indicate that this is not a good assumption for the hydrated hydronium cluster ions. Therefore the differences in the cross sections of the parent and the fragment must be taken into 71 account when determining the probability of ion detection. The probability that a fragment ion will be detected is given by the product of each of the following steps: 1) a parent ion travels distance x without dissociating, 2) the parent then suffers a dissociating collision in the differential length dx, 3) the fragment ion remains in the beam to be detected. The probability that a parent ion travels a distance x through the collision chamber can be derived from Equation 30, by substituting 0 for /t, and x for /. P0 - s % (35) Again using Equation 30, the probability of suffering a single collision in the region from x to dx is P. - e - ' ^ o r f d x (36) ° T Assuming dx is very small, this expression becomes, P, - “ o ,pdx (37) - o a pdx From Equation 16, the probability that a fragment ion formed at distance x in the collision chamber will be detected as an ion is given by, 72 (38) The probability of a fragment ion being detected is given by this product evaluated at all values of x from 0 to /. P, - /[« '* * ■“] [oa ,P This derivation assumes only one collision occurs for the parent and that this collision results in dissociation. However, if the multiple collision probability is incorporated into this derivation, the probability for detection of a fragment ion is p/ “ / e "°t/p(,'*> J2 (r„ - rB+1) [j"*J [ o ^ p dx] (40) This expression has been simplified by Kim to the following, (41) in which -l ’CA* (42) The values for A„ are determined from the following recursion relation. («p r (43) where 73 i _ _^4i _ ^ P = Tj> pi (44) Equation 26 can be used to calculate the probability of detecting fragment ions from the following three parameters: o^p/ojp, <*L,/a and r,. Determination of rj The multiple collision theory of Kim has been used to determine the parameter r7 for H50 2+ and H70 3+. Using the glancing CID and attenuation cross sections determined previously, Equations 42 and 34 have been used to generate theoretical plots of (If / l p0) vs. (Ip/ l p0). However, since the definitions for the cross sections made by Kim are not the same as what has been determined in this work, a relationship between the two sets of definitions is necessary. As described by Ouwerkerk et. a i40, the CID cross section as measured here can be related to the CA cross section of Kim in the following manner. (Note that if r,=0 all the parents dissociate and - aclD. These conditions define the "two step model" in which every collision results in excitation followed by dissociation of the parent.) As defined by Kim, all processes reducing the total ion current are included in the ion loss cross section, oL. In these experiments, the cross section for collision induced dissociation is determined separately from the parent attenuation cross section, ap. The ion loss without reappearing fragment ions is given 74 by the difference in the parent attenuation and the CID cross sections, °L * " °C £ D <4 6 > Since the fragment ions which are formed in collisional dissociation are also present as parent ions, values for op and aaD for the fragments have been determined, therefore, values of oL are readily determined. For the fragment ions it is reasonable to wonder whether the values for the attenuation and CID cross sections differ with internal excitation since all of the fragments have been formed from a collision. However, Dawson27 has determined very similar attenuation cross sections for the fragment and parent ions of the same mass. This observation has been verified in this laboratory by measuring the attenuation cross sections for a beam of H50 2+ after it had been attenuated by 60%. Under these conditions, it is expected that of the emerging beam approximately 30% is internally excited. However, no change in attenuation cross section was observed indicating that excited H50 2+ has approximately the same cross section as ground state H50 2+. Figure 16 shows the normalized fragment ion intensity (If / I p0) has been plotted versus the normalized parent ion intensity (IPti/I Pio) for H50 2+ and H70 3+. This data has been modelled using the multiple collision theory to determine rt values of 0.90 and 0.60 for H50 2+ and H70 3+, respectively. The modelled fits are included in the plot for comparison. Since the determined values of r; are non-zero, a fraction of the collisions result in excitation of the ion without dissociation. A cross section for excitation of the parent without dissociation, ap., can be defined as, The relationships between the cross sections and the values of r} have been used to determine ap. values of 5.6 and 6.5 A2 for H50 2+ and H t0 3+, respectively. If the current of excited parent, lp*, is considered distinguishable from the total parent current, lp, the kinetic energy expression for the production of excited parent in the single collision pressure regime will be very similar to the expression for the production of fragment ion. The fraction of the beam which becomes excited can be determined from Equation 19 by substituting p m for / in the subscripts. Using this expression, at the end of the single collision regime (33% attenuation), the fraction of the emerging parent H50 2+ beam that is excited is 11%. These calculations can be extended past the single collision regime using Kim's theory for the probability of multiple collisions. The fraction of the emerging ion current which is excited can be determined if ap. is substituted for acu> and if it is assumed that the cross sections for ground state and excited parents are the same. This model predicts that a 65% attenuation of the parent beam results in excitation of 29% of the emerging beam. Although these numbers should not be taken too seriously, these results do indicate that passing an ion beam through a collision gas can be an efficient means of excitation. Using multiple collision theory, the branching ratios for the formation of excited parent with respect to dissociation have been calculated as a function of the attenuation of the parent ion beam. The probability curves for the two forms of collisional activation have been plotted versus the parent ion intensity for H50 2* and H70 3+. To illustrate the effects of single and multiple collisions on the collisional 76 0 .0 7 5 0 .0 5 0 0 .0 2 5 H.O 0 .0 0 0 0.00 0.25 0.50 0.75 1.00 1.25 ■ A .o Figure 16. A plot of the normalized fragment ion intensity, 1^/1^ vs the normalized parent ion intensity, Ip/Ip^ Modelled fits of the data are also shown. activation processes, these two curves have been separated to show the individual contributions of the various number of collisions. The single and double collision curves, in addition to the overall probability curves, are shown for each process. In these figures, the probability of formation of excited parent is represented by the solid lines and the probability of dissociation is represented by the dashed tines. 77 0 .0 8 total 0 .0 6 >. « g 0 .0 4 o k_ CID total CL 0.02 0.00 0.00 0.20 0 .4 0 0 .6 0 0 .8 0 1.00 » A o Figure 17. The probability of dissociation and formation of excited parents from collisional activation for H502+. A great deal of information can be obtained from these plots. Figure 17 illustrates that, for H50 2\ the process of parent excitation is more effective than dissociation at moderate parent beam attenuations, but becomes less effective when the parent beam is attenuated by more than ~ 95%. At low pressure (small parent attenuation), parent ions suffering only a single glancing collision are more likely to 78 result in parent ion excitation than dissociation. However, ions suffering two collisions are more likely to dissociate. Only a small fraction of the ions which suffer two collisions remain in the beam without dissociating. For dissociation, the contributions of one and two collisions are comparable throughout much of the range. It is interesting to note that when the parent beam is attenuated by more than ~ 70 %, it is more probable for fragmentation to occur after suffering two collisions. In Figure 18, the probabilities for dissociation and for the formation of excited parents are plotted vs. parent ion attenuation for H70 3+. Unfortunately, the approach used in the calculation of these curves does not include the possibility of HaO+ fragment formation from H70 3+. Therefore, the curves shown for the CID are slightly lower in intensity than would be expected if the two water loss channel is included in the calculation. Although these curves are not rigorously correct, the figure does illustrate some interesting features. For H70 3+, this figure illustrates that the processes of fragmentation and excitation are of similar importance in collisional activation throughout much of the parent attenuation range. From the calculated rt value for H ^ * (which is 0.60), of the ions which suffer a single collision and remain in the beam, 40 % dissociate and 60 % become internally excited. At small attenuations, the parent excitation channel is more efficient than the channel for dissociation. However, the opposite effect is observed at approximately a 40 % attenuation of the parent. Since H70 3+ has a weaker bond strength than H50 2\ it is expected that CID will be more facile for H7Oa+ than Hs0 2\ This is confirmed 79 0 .0 8 0 .0 6 CID total p* total « 0 .0 4 h_ 0.02 0.00 0.00 0.20 0 .4 00 .6 0 0 .8 0 1.00 Figure 18. The probability of dissociation and excited parent formation from collisional activation vs. parent ion attenuation for H703+. from a comparison of the CID cross sections and can be seen from a cursory inspection of Figures 17 and 18. These figures suggest that dissociation is more probable (by a factor of ~3) for H^Oj*. For both activation processes, the effect of the single collision are large in comparison with the effects of multiple collisions. Parent ions are likely to dissociate 80 with a single collision since 0.85 eV is required to remove a single water, and, on average -0.7 eV of energy is transferred in collisions. Therefore, the single collision curve for CID is approximately the same intensity as the excitation curve and is considerably more intense than the multiple collision curves. The double collision curves indicate that parent ions which suffer two collisions are much more likely to dissociate than become more excited. As with H50 2+, the maxima in the two collisional activation processes occur at different beam attenuations, with parent excitation being less important at higher pressures. This is primarily a result of the difference in the attenuation cross sections for the parent and fragment ions. Although these plots illustrate the fraction of the beam which has become internally excited, the excitation covers a range of energies, and therefore, the amount of energy deposited in the beam is not known. However, with an accurate description of the energy transfer distribution, an average value can be determined for the amount of energy per ion suffering a non-dissociating collision. It should be possible to determine the PC(E) from: 1) branching ratios of the various water loss channels 2) energies required for the removal of water molecules and 3) measured r} values The investigation of larger cluster ions would be extremely helpful in determining these energy transfer distributions. Studies performed at higher beam energies might 81 also provide information concerning the position of the distribution maximum as a function of collision energy. Infrared Fluorescence The results of the multiple collision analysis have indicated that a fair fraction of a beam emerging from a collision chamber can be excited internally. The fact that an ion can remain in the beam after suffering a glancing collision which imparts an eV or so of energy suggests the possibility of a variety of experiments on the excited beam. One such experiment which is presently ongoing in this laboratory involves the detection of infrared fluorescence from the excited beam. The energy transferred during a collision is likely to be deposited into vibrational excitation of the ion, suggesting that when the ion relaxes, it may do so by emitting an infrared photon. The apparatus used in the preliminary studies of infrared fluorescence is schematically illustrated in Figure 17. Ions are extracted from a glow discharge ion source and focussed with an ion lens (LI). The beam is steered, with two sets of parallel plate deflectors (D1 & D2), through a drift region (DR) into a collision cell (CC). The beam is attenuated with argon by 25%, and the ions impinge on a stainless steel plate which is at a 45° angle with respect to the ion beam axis. A polished aluminum tube was used to catch the light and direct it towards the detector. An indium-antimonide, InSb, detector (Cincinnati Electronics), whose response curve peaks in the O-H stretch region, was used to monitor the light emitted from the collisions with the surface. Since the detector has a very low 82 CC LI D2 fl U Ext D1 DR V Figure 19. Schematic illustration of apparatus used to investigate infrared fluorescence from collisionally excited beams of hydrated hydronium cluster ions. response efficiency in the visible, any signal observed can be assumed to be infrared radiation. To eliminate the large background due to blackbody radiation, the ion beam was modulated using a 20 V square wave applied to the first deflector in the beam. This modulation scheme effectively produces pulses of ions which are injected into the collision chamber and subsequently impinge upon the stainless steel surface. 83 The IR signal was then demodulated at the frequency of the square wave using a lock-in amplifier (Stanford Research SR510). To further differentiate between background signal and fluorescence signal, the field of view of the detector was manually blocked after a fluorescence baseline had been established. Figure 18 shows an example of the demodulated signal obtained from this procedure. The "unblocked" signal corresponds to conditions in which the detector was allowed to view the region into which the ions were injected; for the "blocked" signal, the detector’s field of view was covered. This difference between the blocked and unblocked signal corresponds to a power of approximately 2 pW. Ideally, this experiment should be done by passing the beam in front of the detector and monitoring the fluorescence from the beam. To optimize the observable signal one would like to maximize the time the ion spends in front of the detector. Unfortunately, at high beam energies, the velocity of an ion is such that the amount of time that an ion spends in front of the detector is small in comparison with the radiative lifetimes of vibrations. Conversely, at low beam energies, space charge effects causes a rapid expansion of the diameter of an ion beam and results in the loss of the ion from the field of view of the detector. Limited by these constraints, it seems the best way to increase the signal to noise of the fluorescence signal is to reduce the noise. At present, an attempt is being made to keep everything in the field of view of the detector at liquid nitrogen temperatures. This should reduce the blackbody radiation by ~ 7 orders of magnitude, presumably reducing the noise several orders of magnitude also. 84 (•.••I Qai On Oat On € < s <•«> I «• oit Figure 20. Infrared fluorescence signal observed from a beam of hydrated hydronium cluster ions which has been attenuated by 35%. 5. Discussion Fragment detection using a Wien filter In this chapter, a novel technique for the use of a Wien filter has been demonstrated. Separation on the basis of fragment ion velocity manipulation has been demonstrated to be effective and versatile. A relationship has been derived to illustrate the operation of this technique and can be used to provide unambiguous identification of fragment ions with respect to both the mass of the fragment and the 85 mass of the parent ion. The relation can be used to predict the position of a fragment ion in a velocity spectrum under any given set of experimental conditions. This is an attractive feature since it allows a fragment peak to be moved to a position in a velocity spectrum where there is little or no background from parent ions. When searching for indications of fragmentation processes which have small cross sections, this may prove to be particularly useful. This configuration is not meant to be a replacement for the much used multisector techniques41,42,43 for studying high beam energy (keV) collisions. Instead these studies were motivated by a long term interest in the development of high signal-to-noise techniques for detecting fragment ions in spectroscopic experiments. Attenuation Cross Sections The absolute attenuation cross sections for collisions of H +(H20) n (n = l-4) with argon have been measured using this ion separation technique. The values obtained in this work agree very well with those previously reported by Dawson27 even though two very different techniques and beam energies were employed. Excitation from Glancing Collisions There are a number of experiments which can imagined to exploit the fact that passing an ion beam through a collision gas can result in a beam with a large degree of internal excitation. Stable, mass-selected, fragment ion beams have been observed as a result of glancing collisions. The total fragment currents can be made 86 to be at least 6% of the original parent ion intensity (in the case of H70 3+). It has been shown that the importance of these glancing collisions increases with increasing cluster size. Although the experimental results presented here involve the observation of fragmentation, there can be little doubt that parent ions suffer collisions without dissociating. The data has been modelled to determine the fraction of the parent beam which has suffered a non-dissociating collision without being knocked out of the beam. These non-dissociating collisions almost certainly result in some internal excitation of the parent ion beam. The results of this analysis suggest that 50% of the emerging beam has suffered at least one collision when the total current has been attenuated by 50%. This excitation is significant and should be detectable in a variety of experiments. These results suggest that glancing collisions are an efficient means of excitation and can be used to deposit a large amount of internal energy into an ion beam. Although the experiments performed here involve cluster ions, the use of monomer ions with much stronger bond energies than clusters could result in a greater degree of non-dissociating excitation. A variety of experiments are being performed to investigate the role of glancing collisions on internal excitation. Preliminary studies involving infrared fluorescence of collisionally excited beam have been performed. These experiments will be extended to allow molecular spectra of vibrationally excited molecules to be recorded by using a circular variable filter for wavelength discrimination. Other experiments include the investigation of the form of the collisional 87 energy transfer distributions. Using a bolometer, the effects of oollisional excitation on the beam can be determined from a comparison of attenuated and unattenuated beams which have been decelerated to - 1 eV. The difference in the energies of the two beams can be normalized to the total ion current in each beam to determine the average excitation per molecule at various pressures. This data in addition to glancing CID branching ratios and fitted values of rt should be sufficient to map out the PC(E) curves for these cluster ion species. 88 References 1. W. Wien, Ann. Phys. Chem. (Liepzig), 8, 224 (1902). 2. H. E. Duckworth, R. C. Barber, and V. S. Venkatasubramanian, Mass Spectroscopy (Cambridge University Press, Cambridge, 1986). 3. R. A. Dressier and E. Murad, J. Chem. Phys., 100, 5656 (1994). 4. H. W. Sarkas, J. H. Hendricks, S. T. Arnold, and K. H. Bowen, J. Chem. Phys., 100, 1884 (1994). 5. J. Ho, K. M. Ervin, and W. C. Lineberger, J. Chem. Phys., 93, 6987 (1987). 6. J. Ho, M. L. Polak, K. M. Ervin, and W. C. Lineberger, J. Chem. Phys., 99, 8542 (1993). 7. K. A. Cowen, Bob Plastridge, Deron A. Wood, and James V. Coe, J. Chem. Phys., 99, 3480 (1993) 8. J. V. Coe, Ph. D. Dissertation, The Johns Hopkins University, Baltimore, MD, 1986. 9. H. D. Zeeman, Rev. Sci. Instrum., 48, 1079 (1977). 10. J. W. Farley, Rev. Sci. Instrum., 56, 1834 (1985). 11. H. Hubner and H. Wollnik, NucL Instrum.Metfu, 86, 141 (1970). 12. L. Wahlin, NucL Inst. Meth., 27, 55 (1964). 13. D. A. Wood, Master’s Thesis (in preparation), The Ohio State University, 1994. 14. K. A. Cowen, Master’s Thesis, The Ohio State University, Columbus, OH, 1991. 15. E. R. Kiem, M. L. Polack, J. C. Owrutsky, J. V. Coe, and R. J. Saykally, J. Chem. Phys., 93, 3111 (1990). 16. K. A. Cowen and J. V. Coe, Rev. Sci Instrum., 61, 2601 (1990). 17. K. A. Cowen, C. J. Frank, and J. V. Coe, Anal. Chem., 63, 990 (1991). 18. M. S. Kim, Int. J. Mass Spectrom. Ion Phys., 50, 189 (1983). 89 19. M. S. Kim, Int. J. Mass Spectrom. Ion Phys ., 51, 279 (1983). 20. L. 1. Yeh, M. Okumura, J. D. Myers, J. M. Price, and Y. T. Lee, J. Chem. Phys., 91, 7319 (1989). 21. R. G. Keesee and A. W. Castleman, J. Phys. Chem. Data, 15, 1011 (1986). 22. Y. K. Lau, S. Ikuta, and P. Kabarle, J. Amer. Chem. Soc., 104, 1462 (1982). 23. M. Depaz, J. J. Leventhal, and L. Friedman, J. Chem. Phys., 51, 3748 (1969). 24. I. Dotan, W. Lindinger, and D. L. AJbriton, J. Chem. Phys., 67. 5968 (1977). 25. H. Udseth, H. Zmora, R. J. Beuhler, and L. Friedman, J. Phys. Chem., 86, 612 (1982). 26. H. Kambara and I. Kanomata, Int. J. Mass Spectrom. Ion Phys., 25, 129 (1977). 27. P. H. Dawson, Int. J. Mass Spectrom. Ion Phys., 43, 195 (1982). 28. R. D. Levine and R. B. Bernstein, Molecular Reaction Dynamics and Chemical Reactivity (Oxford, New York, 1987). 29. A. Van Lumig and J. Reuss, Int. J. Mass Spectrom. Ion Phys., 27, 197 (1978) see p. 208, Eq. (8). 30. P. J. Todd and F. W. McLafferty, Int. J. Mass Spectrom. Ion Phys., 38, 371 (1981). 31. J. Bordas-Nagy and K. R. Jennings, Int. J. Mass Spectrom. Ion Proc., 90, 105 (1990). 32. A. Russek, Physica, 48, 165 (1970). 33. M. S. Kim and F. W. McLafferty, J. Amer. Chem. Soc., 78, 3279 (1978). 34. R. G. Cooks, Collision Spectroscopy (Plenum Press, New York, 1978). 35. H. S. W. Massey, Rep. Prog. Phys., 12, 248 (1949). 36. I. W. Griffiths, E. S. Mukhtar, R. E. March, F. M. Harris, and J. H. Beynon, Int. J. Mass Spectrom. Ion Phys., 39, 125 (1981). 37. P. H. Dawson and W. F. Sun, Int. J. Mass Spectrom. Ion Phys., 82, 51 (1982). 38. S. Nacson and A. G. Harrison, Int. J. Mass Spectrom. Ion Phys., 63, 325 (1985). 90 39. V. H. Wysocki, H. I. Kenttamaa, and R. G. Cooks, Int. J. Mass Spectrom. Ion Phys., 87, 181 (1987). 40. C. E. D. Ouwerkerk, S. A. McLuckey, P. G. Kistemater, and A. J. H. Boerboom, Int. J. Mass spectrm. Ion Phys., 56, 11 (1984). 41. J. A. Laramee, D. Cameron, and R. G. Cooks, J. Amer. Chem. Soc., 103, 12 (1981). 42. R. N. Hayes and M. L. Gross, Methods EnzymoL, 193, 237 (1990). 43. J. L. Holmes, Org. Mass Spectrom., 20, 169 (1985). Chapter III Determination of the Free Energy of Solvation for Single Ions at Bulk Using Cluster Ion Data 1. Introduction There are many examples of species which exhibit very different physical or chemical properties in the gas phase compared with the properties they exhibit at bulk. One example of this phenomenon involves the solvation of a gas phase electrolyte. In the gas phase, the neutral species will be very stable with respect to it’s corresponding ions, whereas in solution an electrolyte will dissociate and the solvated pair of oppositely charged ions will be more stable than the neutral. The process of solvation results in a complete reversal in the tendency of an electrolyte to dissociate ionically. The solvation of electrolytic salts in water is a process of fundamental importance in chemistry and has been studied in detail at bulk. Much less is known about the process of solvation on the molecular level. To help understand the solute-solvent interactions which govern solvation, this research group has an interest in determining the point at which electrolytic dissociation occurs. Experimentally, these problems can be approached by studying cluster ions since these species link 91 the condensed and gas phases. An understanding of the chemistry occurring in these clusters should provide an insight into both phases. Several powerful techniques have been developed to study the chemical and physical properties of gas phase species including clusters. One of the most important of these techniques involves the measurement of gas phase equilibrium concentrations of various ions as a function of temperature. This technique, developed by Kabarle and coworkers,1 involves the mass spectrometric sampling of high pressure ion sources to determine equilibrium concentrations of various cluster ions at different temperatures. From Van’t Hoff plots, the AG and AH of clustering reactions can be calculated. This technique has been used extensively and has provided a great deal of data concerning the thermodynamic properties of gas phase ion-molecule clustering reactions. Kabarle’s data in addition to that of several other groups2,3 provide a reasonably large body of thermodynamic information of gas phase ion-molecule clustering reactions which has been tabulated by Keesee and Castleman4. These data, which extends out to the addition of 8 solvent molecules to a gas phase ion, encompasses the clustering reactions of a variety of cations and anions with several solvents (including H20, CH3OH, etc.). Castleman’s tabulated data, supplemented with more recent data, of the energetics for the stepwise addition of solvent molecules to gas phase ions can be used to determine the bulk solvation energies of these ions. Using available bulk and cluster data, a new approach for the determination 92 93 of single ion solvation enthalpies has been developed3. This method builds upon several established strategies6'7 but is distinguished by: 1) consistency with bulk constraints 2) the use of cluster data from a variety of different ions 3) a least squares calculation with a rigorous error analysis and 4) the use of neutral water cluster data. This new technique is used here to determine the Gibb’s free energy of solvation for various ions at bulk. 2. Free Energy of Solvation for Single Ions at Bulk The determination of thermodynamic data for the solvation of individual ions at bulk is difficult since bulk solutions are generally electrically neutral. The bulk thermodynamic data which is available has been determined from the solvation of electrolytic salts, and therefore, involves the solvation of a pair of oppositely charged ions. The free energy of solvation for an individual ion can be determined if the contributions of each ion to the overall free energy of solvation for a salt is known. However, a direct measurement of these individual contributions is difficult. Bulk Constraints The free energy of solvation to place a pair of gas phase ions into water (AG0,^ ^ ) can frequently be determined from available bulk thermodynamic data. Table 7 lists values of AG°fWller, obtained from Rosseinsky8, for various pairs of 94 oppositely charged ions. To determine the individual ion solvation energies, the fraction of each entry which can be attributed to each of the individual ions must be determined. It is important to note that if the solvation energy of just one ion is determined, the solvation energy for all the ions can be calculated. Table 7 Free energy of solvation (A G \wlhr) to place a pair of oppositely charged ions into water at 25° C Species OHF c r Br* • H + -1524 -1524 -1407 -1393 -1347 Li+ -944.7 -945.2 -828.0 -814.2 -767.8 Na* -844.7 -845.2 -728.0 -714.2 -667.8 -771.1 -771.5 -654.4 -640.6 -594.1 K+ Rb+ -749.8 -750.2 -633.0 -619.2 -572.8 Cs+ -717.6 -718.0 -600.8 -587.0 -540.6 NH/ -769.0 -769.4 -652.3 -638.5 -592.0 | The differences in the rows and the columns of Table 7 are used to determine the bulk solvation energies. For example, the differences in the rows of Table 7 can be added to the guess at the bulk solvation energy of Na* to calculate the solvation energies for the cations. Similarly, the same value for G ^ , is subtracted from the solvation energy of NaOH to determine the bulk solvation energy OH' which can 95 then be related to the solvation energies of the other anions using the differences in the columns in Table 7. Table 8 lists the differences between the single ion bulk solvation free energies for the positively charged ions. Table 8 Table of Differences in Bulk Solvation Free Energies OH F c r Br I- H + - Na4 679 678 679 679 679 Li+ - N a4 100.0 100.0 100.0 100.0 100.0 K+ - N a4 -73.6 -73.7 -73.6 -73.6 -73.7 R b4 - Na4 -94.9 -95.0 -95.0 -95.0 -95.0 I Cs4 - Na4 -127.1 -127.2 -127.2 -127.2 -127.2 Examination of this table suggests that the raw data used to construct the table has been processed to an internally consistent set without report of the individual uncertainties. The lack of uncertainty in these differences is unfortunate in that without the individual uncertainties in the data, the error analysis, which is an important part of this procedure, is invalid. Nonetheless, the average values for the differences in the bulk solvation free energies can be calculated for similarly charged ions. These average values are listed in Table 9. 96 Table 9 Average Differences in the Bulk Solvation Free Energies Positive Ions A G ^ l) - Negative Ions A G ^l) - AG# o1(2) A G ^ ) H + - Na+ 679 F - OH’ 0.4 Li+ - N a+ 100 Cl - OH -116.8 K+ - Na+ -73.7 Br - OH -130.6 Rb+ - Na+ -95.0 I’ - OH* -177.0 Cs+ - Na+ -127.1 Note that the relative spacing between similarly charged ions is well established but there is no connection between the oppositely charged sets. The cluster ion data provides this connection. Cluster Ion Data At bulk, solvation is thought of as the addition of a solute to a solvent; the cluster analog of this process is X + (H20)t - X(H20), * (1) However, the cluster data which is available involves the stepwise addition of solvent molecules to the solute, X , as follows, X{H20) ^ ♦ H20 - X(H20) r ; A G ^/X ) (2) In essence, this expression represents the formation of a water cluster around species 97 X. A series of these reactions can be used to build up cluster size and give the product, X(H20)n, in Equation 1. However, one must account for the stability of a neutral water cluster, (H20)n. Therefore, a second process must be considered to account for the formation of a neutral water cluster through stepwise additions of water molecules, ( « A .- I * h 2° - cw,o>. ; (3) The free energy for the solvation of A" can be expressed as the difference in the sums of the stepwise free energies of these two processes, AG^JiX, . £ [AG,.,,® - AG,.u(H20)] M> 1-1 In the limit as n goes to infinity, the sum of the stepwise free energies of solvation becomes the bulk single ion solvation energy and Equation 4 becomes Equation 1. Notice that the determination of the bulk solvation energy of X from cluster data requires knowledge of the stepwise energies for neutral water clusters in addition to the stepwise energies of the aqueous cluster ion. Stepwise Energies for Neutral Water Clusters The free energies for the stepwise formation of neutral water clusters (AGn_,n) have been plotted in Figure 19. These values have been determined by Kell and McLaurin9 from the second virial coefficients of steam and the bulk value for the free energy of vaporization of water10. A linear fit of these data vs. n'1/3 has been used to estimate the free energy for the stepwise addition of water above the 98 10 O “ 3 " ' 2 oCJ c *r -® c o , | Q ...... ■------1------1------1------J ------«L 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.B 0.0 1.0 Figure 19. Stepwise free energies of neutral water clusters (from Kell and McLaurin). tetramer. The best fit line of this data gives n in kJ/mol and can be expresses as, A = -8.56 + 19.24n 1/3 (5) It is important to note that the actual functional form of this curve is not known and the linear fit was used because it seemed to model the data available. In light of the uncertainty in the shape of the curve, the values obtained from this fit should not be taken too seriously. The free energy for the stepwise formation of neutral water cluster has been used with the cluster ion data, obtained from the Keesee and Castleman4 review and 99 supplemental data from other sources, to determine the partial sums of the stepwise solvation energies for various ions. These partial sums were calculated from Equation 4 where the summations have been extended out to n=5 for most of the ions. The results of these calculations are presented in Table 10. Table 10 Partial Sum of Stepwise Free Energies for the Solvation of Various Ions (EAG,,.,^) in kj/m ol n Species 1 2 3 4 5 Li + -113.8 -192.9 -248.5 -279.9 -298.7 I h 3o + -100.8 -148.5 -185.7 -208.3 -224.6 Na+ -78.7 -133.9 -171.6 -196.3 -211.4 K+ -49.4 -86.6 -113.0 -131.4 -144.8 1 Rb+ -41.0 -70.3 -91.2 -107.1 -118.8 I Cs+ -32.6 -58.5 -77.3 -89.9 OH -74.9 -121.8 -154.0 -177.0 -194.6 F -75.7 -125.1 -159.0 -183.7 -202.5 c r -40.0 -67.6 -88.5 -103.6 -116.2 Br -33.5 -57.3 -75.3 -88.7 I -22.6 -39.8 -53.2 -62.8 h 2o 0 6.7 11.3 15.1 18.0 100 Solvation Free Energy vs. Cluster Size (n’1/} Plots) The data in Table 10 has been used to plot the cluster ion free energy of solvation against n'l/\ where n is the number of solvating water molecules, in Figure 20. The choice of as a parameter comes from consideration of the free energy of a charged sphere within a uniform dielectric medium11,12. If the free energy is considered to be linear with respect to the radius of the sphere, the use of n'1/3 can be justified by assuming that the volume of the dielectric sphere is directly proportional to the number of water molecules. The n'xf3 parameter is equal to zero at bulk and equals one when only one solvating water molecule is in the duster ion. Since very small clusters are not likely to resemble uniform spheres with a centralized charge, the use of this theory to model small clusters should not be considered rigorous. However, the use of this parameter provides a straightforward and convenient means of extrapolating from small cluster size to bulk. As the size of the cluster ions gets bigger, the dielectric sphere theory becomes a better model for these systems and should be a useful means of connecting cluster data to bulk. A remarkable feature of this plot is that the ordering of similarly charged spedes is conserved completely from n = 1 to bulk. Also, the ordering of the positive ions with resped to the negative ions is established by n= 1 in this plot. Calculations Klots Method To understand the advantages of the present method of determining single ion 101 o E -100 >* ct- O) Rto- -200 OH C LU •300 ■ U_ -400 c o -500 <9 X+(H20)n-> X(H20) > •000 o 0.0 0.1 0.2 0.3 0 4 0.5 0.6 0.7 0.8 0.0 1 .0 n - 1 /3 Figure 20. Solvation free energy vs. n‘Iyf3 for various ions in water clusters. Filled symbols correspond to positive ions and open symbols correspond to negative ions. solvation free energies, it is useful to examine the method used previously by C. E. Klots6. Although the sum of the bulk solvation free energies of a pair of oppositely charges ions is known (Table 7), to determine the single ion solvation energies, the difference in the bulk solvation energies in needed. By definition, the following relation is true lim - AG^(B )1 - AG^ JA ) - AG^ JB ) (6) From Equation 4, the cluster solvation energies can be converted to summations over stepwise energies, 102 2>G,on - £ a affi-y - ag__h-) - a g ^ jb -) m <-l i-1 Note that the partial sums of the water cluster energies will cancel out leaving, £AGfiA') ♦ £AGf.H2Cf) - £ AGt(B') - £ AG^O) ... i-1 (-1 (-1 i-1 -AG^.04*) - AG^.(B ) Since solvent molecules in the first solvent shell are effected most strongly by the ion, most of the dissimilarity in ion solvation energies comes from the interactions in the first solvent shell. In fact, as cluster ions get large the nature of the charge buried within the cluster becomes less important and the stepwise solvation energies converge to bulk at the same rate. If one assumes that the energy for the stepwise addition of water for n > 5 is the same for all the ions, the partial sums from n = 6 to « cancel and Equation 6 becomes, 5 5 £ AG,(A*) - £ AG.(B ) - AG„,.(A') - AG^ JB ) <») I I - I J l - l Using this assumption, Klots was able to calculate single ion solvation energies. These values are given in Table 11. However, examination of Figure 20 indicates that this assumption may not be a good one. 103 Least Squares Method To avoid the assumption made by Klots, the present approach to determining the individual ion solvation energies involves normalizing the difference in the solvation energies to the sum of the solvation energies, as in Equation 9. (10) A G ^ O n ♦ A G ^SB ) The parameter, j, allows for the fact that the solvation differences are more pronounced at small cluster size than at bulk. This parameter is simply used to scale the cluster data to the bulk data in order to minimize the differences between the two. Observations by Castleman indicate that the value for s may be the same for different ions. Setting the expression up this way means that the stepwise energies for neutral water no longer cancel out. Rewriting the left hand side of Equation 9 in terms of the partial sums of the stepwise energies, the following expression is obtained, E > G ^ -) - '£ A G i(B ) i-1 AG^-04*) - AG^.(B ) AG^CA*) ♦ A G ^SB ) G(A"> ♦ Gffi ) - 2 £ AG/Z/jO) <•1 i-1 i-1 (11) Although the partial sum of water stepwise energies appears in the denominator on the left hand side of this expression, it is smaller than the other two terms. Consequently, the method is not very sensitive to the neutral water cluster data, which is smaller than the corresponding enthalpy term by a factor of 4. Although the inclusion of the neutral water data in this method is an improvement over Klots’ method, it makes only a small correction. Perhaps a more important deviation from the method of Klots is the decision to exclude the data for the larger halides (Cl', Br', and I ) from the calculations. These ions have been left out since calculations by Berkowitz and Perera131415, and Caldwell and Kollman16 have suggested that these ions reside on the surface of small water clusters rather than inside, and therefore, these systems are not a good representation of bulk solvation. A Mathcad template (Appendix 1) was developed to calculate the values for the individual bulk solvation energies. By guessing the absolute bulk solvation energy of one of the ions, the values for all the other ions are determined using the appropriate data in Tables 7 and 10. Once the single ion solvation energies have been calculated, the ratio on the right hand side of Equation 10 can be determined for each pair of oppositely charged ions. The left hand side of Equation 10 is calculated from the cluster ion data listed in Table 10. The parameter s is determined by minimizing the sum of the squares of the differences of the left and the right hand sides of Equation 10 for each pair of oppositely charged ions for each guess of the value for Na*. 105 Various guesses are made at the possible value of the bulk solvation energy of Na* and this procedure is iterated to find a minimum value of a. For these calculations, the data for only the first four alkali metal cations, F*, and OH' have been included. The H30* data has been left out in these calculations since the bulk data has been determined for H* and not for HaO*. (A different approach to this special case is discussed later.) Table 11 Individual Bulk Solvation Free Energies (kj/mol) Ion This work Klots Friedman17 Li* -525.8 -518.8 -516.7 Na* -425.8 -418.4 -411.3 K* -352.8 -345.2 -338.1 Rb* -330.9 -323.8 -320.5 Cs* -298.7 -291.6 -297.1 OH -418.9 -425.9 -379.1 F -419.2 -426.3 -434.3 a* -302.1 -309.2 -317.1 Br‘ -288.3 -295.4 -303.1 r -241.9 -248.9 -256.9 | 106 Figure 21 shows the values of a versus AGlolibll|k(Na+). The minimum occurs at -424 kJ/mol and corresponds to an agreement of < 1% between the bulk and cluster data. This value of A G ^^N a* ) has been used to determine the absolute bulk solvation energies for all the ions listed in Table 7. These results are presented in Table 11. HjO+ An absolute bulk solvation free energy for the hydronium ion could not be calculated from the least squares method described above since bulk data is not available for H30 +. However, since cluster data is available for HaO +, and since the bulk solvation energies for OH' and F have been determined, AGiOl bulk(H30 +) can be calculated from Equation 3-9. This approach gives an average value of -446.5 kJ/mol for the bulk solvation free energy of H30 +. III. Connecting Cluster Data to Bulk Using the values for single ion solvation energies listed in Table 3-4, dielectric sphere theory can be used to model the behavior of cluster ions as they approach bulk. As previously mentioned, dielectric sphere theory can be used in some capacity to model small cluster ions. For clusters with very few solvent molecules, the assumptions made in this theory are not adequate to describe the nature of the cluster. However, as a cluster ion gets larger, the exact nature of the centralized ion 107 0.15 0.12 0.09 D 0.06 0.03 0.00 -470 -460 -450 -440 -430 -420 -410 -400 -390 -380 AG(0liM(Na+) (kJ/mol) Figure 21. The standard deviation, o, between the bulk data and the cluster data, as given by Equation 11, as a function of potential values for the bulk solvation free energy of Na*. becomes less important and the system can be modelled as a central charge within a dielectric medium. In fact, the slope of n'1/3 plots predicted from dielectric sphere theory agree very well (within 5%) with photodetachment studies of electrons solvated in water and ammonia18,19. From dielectric sphere theory, the free energy of solvation of a cluster ion is given by AG 1 - — (13) 2r. where r( is the radius of the solvent molecule, T is the absolute temperature, and Dt 108 is the static dielectric constant of the solvent. This equation predicts that the limiting slope of the free energy vs. n'l/3 curve is the same for all ions. For large clusters, the assumption is valid since the exact chemical nature of the ion has only a small effect on the free energy at large values of n. However, for small clusters (within two solvent shells), the effect of the ion’s volume should be included. This can be done by replacing n'1/3 in Equation 12 with ' , K 3 - O 10 <14> Figure 20 has been replotted to include dielectric sphere slopes drawn from the bulk solvation energies determined by the least squares method. The combination of the bulk solvation energies, the dielectric sphere slopes, and the cluster ion data, characterizes the free energy of solvation throughout the range from the addition of the first solvent molecule (n'1/3= 1) to bulk (n'1/3 = 0). In fact, with the exception of the larger halides, the connection over the whole cluster range is reasonably well modelled by the dielectric sphere slope. Of course, the region of most uncertainty lies in the intermediate (2nd solvent shell) region where solvent shell structure is likely to be important, but the assumptions of dielectric sphere theory begin to become valid. For the smallest ions, this simple electrostatic model gives an excellent zero order picture of the solvation energetics. For the larger halides, the prediction that these ions will exhibit surface states in small water clusters is supported by the trends observed in Figure 22. An ion on the surface of a cluster can be expected to solvate more slowly than internalized ion, 109 o £ 0 “J -100 >s o> •200 Figure 22. Stepwise solvation free energies for various ions as shown in Figure 19. The connection from the cluster data to bulk is provided by dielectric sphere slopes which have been included in this plot. therefore, at small cluster size the trend in AG should have a softer slope for a surface state than for an internal state. If the dielectric sphere slopes in Figure 22 are extended to the cluster data, reasonable continuity is observed for all of the ions but the large halides. The point at which the trend in cluster data intersects the dielectric sphere data can be considered a crude prediction of the cluster size necessary to convert from a surface state to an internal state. IV. The Ion-Ion Recombination Approach to Solvation At present, this research group is actively studying the process of solvation by 110 merging a beam of positive duster ions with a beam of negative duster ions. The AG and AH duster trends can be used to characterize and make predictions about cluster ion-cluster ion recombination reactions. The process of recombination of a positive ion and a negative ion can be written as A'(H 20)j ♦ B (H20) k - AB{H20)hk (IS) The free energy expressions for reactants and the product are given by, * E a g . ^ b -) i-1 i-1 (16) - AGw/4-) ♦ E AG|.,j(HjO) ♦ A G ^/B ) . E AG,.„(»20) (-1 i-1 and * E *G, u These functions have been calculated as a function of the quantity (j+ k)1/s for the recombination of Na+(H20)j and 0H'(H20)k cluster ions. These results, along with the analogous functions for the enthalpy5 of the reactants and products, are shown in Figure 23. From the differences in the enthalpy of the reactants and the products, the number of water molecules expected to boil off the dusters can be predicted at each cluster size. For the first cluster (j + k=2), the reaction is very exothermic and it is I ll N a^O ), + OH-fH.O), R eactants -3 0 0 Reactants Products O - 6 0 0 AG E Products -ooo 1200 ♦ * ♦* - 1 6 0 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.0 1.0 (i + k)-1'* Figure 23. Plot of the free energy and enthalpy of the products and reactants vs. cluster size for the reaction of Na+(H20)j cluster ions with 0H'(H20)h cluster ions. expected that the cluster will have sufficient energy to boil both the water molecules off the cluster (assuming AH^p*44.01 kJ/mol). It is likely that the remainder of the excess energy will be converted to translational energy of the reaction will be converted into translational energy of the reaction products (2 H20 and AB). This translational energy will result in an expansion of the beam diameter of the neutral 112 beam. In fact, it may be possible to determine the amount of excess energy from the spot size of the neutral beam and the number of products created in the reaction. Although these calculations do not predict this phenomenon for these species, it is interesting to consider that at the thermo-neutral point of the recombination of A +(H20 )j and B'(H20)k reaction, a collimated beam of mass selected neutral water clusters can be produced. With no excess energy, the neutral beam should have the same ion optical properties as the ion beams from which it was produced. Theoretically, the diameter of the neutral beam would not expand and therefore the beam could be transported several meters with minimal loss. 113 References 1. A. J. Cunningham, J. D. Payzant, and P. Kebarle, J. Amer. Chem. Soc., 94, 7627 (1972). 2. K, Hiraoka, S. Mizuse, and S. Yamabe, J. Phys. Chem., 92, 3943 (1988). 3. N. F. Dalleska, K. Honma, and P. R. Armentrout, J. Amer. Chem. Soc., 115, 12125 (1993). 4. R. G. Keesee and A. W. Castleman, 7. Phys. Chem. Ref. Data , 15,1011 (1986). 5. J. V. Coe, Connecting Cluster Ions and Bulk Aqueous Solvation: A Determination of Bulk Single Ion Solvation Enthalpies , submitted to J. Chem. Phys. 6. C. E. Klots, J. Chem. Phys., 85, 3585 (1981). 7. N. Lee, R. G. Keesee, and A. W. Castleman, Jr., J. Coll. Int. Sci., 75, 555 (1980). 8. D. R. Rosseinsky, Chem. Rev., 65, 467 (1965). 9. G. S. Kell and G. E. McLaurin, J. Chem. Phys., 51, 4345 (1969). 10. R. C. Weast, Ed., Handbook of Chemistry and Physics, 66,h Edition, (CRC Press, Boca Raton, 1985). 11. R. A. Marcus, J. Chem. Phys., 24, 979 (1956). 12. M. Bom, Z. Phys., 1, 45 (1920). 13. L. Perera and M. L. Berkowitz, J. Chem. Phys., 95, 1954 (1991). 14. L. Perera and M. L. Berkowitz, J. Chem. Phys., 96, 8288 (1992). 15. L. Perera and M. L. Berkowitz, J. Chem. Phys., 100, 3085 (1994). 16. J. W. Caldwell and P. A. Kollman, J. Phys. Chem., 89, 2242 (1988). 17. H. L. Friedman and C. V. Krishnan, "Thermodynamics of Ion Solvation", in Water A Comprehensive Treatise, F. Franks, Ed., (Plenum Press, New York, 114 1973). 18. J. V. Coe, G. H. Lee, J. G. Eaton, S. T. Arnold, W. H. Sarkas, K. H. Bowen, C. Ludewigt, H. Haberland, and D. R. Worsnop, /. Chem. Phys., 92, 3980 (1990). 19. S.T. Arnold, J. G. Eaton, D. Patel-Misra, H. W. Sarkas, and K. H. Bowen, "Continuous Beam Photoelectron Spectroscopy of Cluster Anions", in Ion and Cluster Ion Spectroscopy and Structure, ed. J. P. Maier, (Elsevier, Amsterdam, 1989). Appendix A Fortran Programs 115 116 scan2b.for Scanning program for the Wien filter. This program is capable of scanning to Wien filters independantly. Data can be recorded as a voltage from an electrometer (or any other analog device) or as TTL pulses. c main routine for scanning the Wien filter voltage dimension xx(721 ),yy( 721 ),ysum(721 ),avg( 1000) logical “1 kkey character* 15 fln,spfln,ttl integer*2 idal,idah,iadl,iadh integer *2 iodal,iodah,ioadl,ioadh integer*2 ibyte,iword integer*2 ilow,ihigh,istat c voltage scale real vscale vscale = 300.0 kkey = .false. tv=0 c default scan settings tstart=0 tend=300 nrp = 300 sm=3 c address for D /A data iodall,iodahl,iword/772,773,0/ data iodal2,iodah2,iword/774,775,0/ c address for A/D data ioadl,ioadh,ibyte/768,769,0/ c set gain call oup(0,779,ibyte) 117 c set mux input channel to 0 (use 17 in first parameter c to read from channel 1) call oup(0,770,ibyte) c Choose which mode of operation to run and set up scan parameters 10 call els sel*0 write(5/)The present scan parameters are:’ write(5,*)’ (v)oltage range = \tstart,’ - \tend write(5,*)’ (n)umber of readings per point = \nrp write(5,*)’ (m)agnification = \sm write(5,*)’ write(5,*)’To change a parameter press the letter in parenthesis’ write(5,*)’ ’ writers,*)’ write(5,*)’Would you like to:’ write(5,*)’ (s)can one or both of the beams’ write(5,*)’ (t)une one or both of the beams’ write(5,*)’ (c)ount pulses’ write(5,*)’ (q)uit’ write(5,*)’ write(5/)’ ’ writeCS,')’ ’ write(5,*)’ ’ write(5,*)’ ’ write(5,*)’ ’ write(5,*)’ ’ write(5,*)’ call inkey (key) if(key.eq.ll8)goto 20 if(key.eq.llO)goto 22 if(key.eq.!09)goto 25 if(key.eq.ll5)goto 30 if(key.eq.ll4)goto 30 if(key.eq.99)goto 400 if(key.eq.ll6)goto 500 if(key.eq.U3)goto 999 goto 10 c input scan settings 20 call els write(5,*)’Input start and stop voltages’ read(5, * )tstart,tend goto 10 22 call ds write(5,*)’Input the no. readings on each point’ read(5,*)nrp goto 10 25 call els write(5,*)’Input the screen magnification factor’ read(5,*)sm goto 10 c convert Wien filter voltage to dac units c D /A 1 to 4096 steps for -10 volts results in 0 - vscale V 30 call els write(5,*)'Do you want to scan:’ write(5,*)’ (a) beam A’ write(5,*)’ (b) beam B’ write(5,*)’ (c) both beams’ call inkey(key) if(key.eq.97)reset = 1 if(key.eq.98)reset=2 if(key.eq.99)reset=3 if(reset.eq.0)goto 30 jstart=1 + int(4095. * tstart/vscale) jend = 1 + int(4095.*tend/vscale) nstep = 1 + int((jend-jstart)/720.) npts= int(0‘end-jstart)/(nstep* 1.)) c scanning loop 40 call hggraf basel-318 do 100 i«l,npts c output step to D/A c j is an index for the 4096 D /A steps j = jstart-nstep+ i* nstep idah=int(j/16.) idal = (j-16*idah)* 16 if(reset.eq.2)goto 42 call oup(idal,iodal 1 .iword) call oup(idah,iodahl,iword) if(reset.eq.l)goto 44 42 call oup(idal,iodal2,iword) call oup(idah,iodah2,iword) c read data from A/D 44 y=0. do 60 kk = l,nrp call hgdotw(l,l,l) call oup(iword,ioadl,ibyte) call inp(iadl,ioadl,ibyte) call inp(iadh,ioadh,ibyte) y=y+ 16.*iadh + int(iadl/16.) 60 continue y=y/(l.*nrp) xx(i) = (j-l)*vscale/4095. yy(i)=y iy * int(sm • (y-2048.) *300./2048.) if(reset.eq.3)basel = 159 iy=basel-iy call hgdotw( 1,1,1) call hgdotw(i,iy,l) 100 continue c set D/A back to zero after scan idah=0 idal*0 if(reset.eq.2)goto 120 call oup(idal,iodall,iword) call oup(idah,iodahl,iword) 120 if(reset.eq.l)goto 150 call oup(idal,iodal2,iword) call oup(idah,iodah2,iword) c check keyboard 150 if(key.eq.ll4)goto 200 call chkchr(kkey) if(kkey)goto 200 goto 40 c output data to disk 200 call inkey(key) call hgtext 50 write(5,*)’Would you like to save this scan? (y/n)’ call inkey (key) if(key.eq.ll0)goto 10 if(key.eq.l21)goto 70 goto 50 70 write(*,’(a\)’)’Emer output filename * read(V (a)’)fln open(3,file = fln) do 80 i = l.npts 80 write(3,*)xx(i),yy(i) close(3) goto 10 400 call els sel= 1 write(5,*)’Do you want to tune the beam? (y/n)* call inkey(key) if(key.eq.ll0)goto 700 if(key.eq.l21)goto 500 500 call els write(5,*)’Do you want to tune* write(5,*)* (a) beam A’ write(5,*)’ (b) beam B’ write(5,*)* (c) both beams’ call inkey(key) if(key.eq.97)goto 520 121 if(key.eq.98)goto 530 if(key.eq.99)goto 510 goto 500 510 sel = l 520 iodal = iodall iodah-iodahl write(5,*)’Input approximate initial voltage for beam A’ read(5,*)tv goto 540 530 iodal=iodal2 iodah=iodah2 sel=0 write(5,*)*lnput approximate initial voltage for beam B’ read(5,*)tv 540 write(5,*)’Left arrow decreases voltage by .2 V’ write(5,*)’Right arrow increases voltage by .2 V’ write(5,*)’Space bar increases voltage by 5 V’ writefS/yEnter decreases voltage by 5 V’ write(5,*)’Press escape when done’ write(5,*)’ ’ j = 1 + int(4095.*tv/vscale) dj=4 550 idah = int(j/16.) idal * (j-l<>*idah)* 16 call oup(idal,iodal,iword) call oup(idahtiodah,iword) 555 call inkey(key) k=0 if(key.eq.27)goto 560 if(key.eq.l3)k»-25 if(key.eq.32)k=25 if(key.eq.52)k*-l if(key.eq.54)k= 1 if(k.eq.0)goto 555 122 j-j+ d j* k goto 550 560 if(sel.eq.l)goto 530 write(5,*)’Do you want to reset either of the DACs to zero? (y/n)’ call inkey(key) if(key.eq.ll0)goto 10 if(key.eq.l21)goto 570 goto 560 570 call els write(5,*)’Which DAC would you like to reset?’ write(5,*)’ (a) beam A DAC write(5,*)’ (b) beam B DAC write(5,*)’ (c) both DACs’ call inkey (key) if(key.eq.97)goto 590 if(key.eq.98)goto 600 if(key.eq.99)goto 580 goto 500 580 sel = 1 590 idah=0 idal=0 call oup(idal,iodall,iword) call oup(idah,iodahl,iword) if(sel.eq.l)goto 600 goto 10 600 idah=0 idal=0 call oup(idal,iodal2,iword) call oup(idab,iodah2,iword) sel=0 goto 10 c pulse counting loop 700 write(5,*)’Enter time delay in seconds’ read(5,*)time write(5,*)’Enter number of time increments (fewer than 1000)’ read(5,*)reps sum=0 123 ave=0 dcv=0 c set clock ready to read do 730 k * l.reps call oup(48,783,0) call oup(255,780,0) call oup(255,780,0) icounts=0 x=0 do 720 j - l.time c 1 second delay loop do 710 i = 1, 18950 x=x+ 1 x=x-l 710 x=x*x 720 continue c read clock and output results to screen call oup(0,783,0) call inp(ilow,780,0) call inp(ihigh,780,0) icounts = 65535-256*ihigh-ilow avg(k) = icounts/time sum = sum+ avg(k) 730 write(5,*)icounts/time,’ Hz’,icounts,ilow,ihigh c calculate the average and standard deviation for the readings ave=sum/reps do 735 j = l,reps 735 dev=dev+ (avg(j )-ave) * * 2 std=sqrt(dev/(reps-l)) write(5,*)’average = ’,ave,’ + /- ’,std 740 write(5,*)’would you like to save this scan? (y/n)’ call inkey(key) if(key.eq.ll0)goto 900 124 if(key.eq.l21)goto 800 call ds goto 740 800 write(5,*)’input filename’ read(V(a)’)fln open(3,fUe =fln) do 810 i - l,reps 810 write(3,*)k,avg(i) close(3) 900 call els write(5,*)’Would you like to scan again? (y/n)’ call inkey(key) if(key.eq.H0)goto 910 if(key.eq.l21)goto 700 goto 900 c reset d /a to zero 910 idah=0 idal=0 call oup(idal,iodal,iword) call oup(idah,iodah,iword) goto 10 999 end 125 csfrag.for This program calculates the fragment ion to parent ion ratio. c c ••********NLLSQ Analysis of Fragment Cross Sections ...... * c c y = {a( 1)/a(2)} * {exp(a(2) *x)-1} c c If/Ip = {CSecid/CSpfdiff} * {cxp(CSpfdiff' P*L/(kT))-l} c c where CSpfdiff is CSparent -CSfragment c dimension x(50),y(50),z(50),yfit(50) dimension sig(50),a(2),lista(2),covar(2,2),alpha(2,2) c c input data to be fit from data file pipif.dat c of the form: c c first line is the no. of points, npts c c then there are npts lines with three entries each for c the pressure (mTorr), the parent intensity, and the fragment intensity c open(2,file * ’pipif.dat’) read(2,*)npts do 11 i = l,npts sig(i) = 1. read(2,*)x(i),z(i),y(i) x(i)*x(i)/1000. x(i) =x(i) *2.5/(1.363e-25*300*760* 1000) 11 y(i)=y(i)/z(i) close(2) ma=2 do 2 j = l,ma 2 lista(j) <= j c read in initial parameters write(5,*)’input a(l), the CSecid (cm* *2)’ read(5,*)a(l) write(5,*)*input a(2), CSp-CSf (cm* *2)’ 126 read(5,*)a(2) c initialize nllsq program alamda=-l c mfit allows some parameters to be fixed, if mfit is less than ma, the c last ma-mfit parameters in the lista array will not be fit mfit=ma-l call mrqmin(x,y,sig,npts,a,ma,lista,mfit,covar,alpha, 1 ma,chisq,alamda) c iterate until parameters get close k = 1 itst—0 write(5,*)’iter. chi* *2 a(l)-a(ma)’ 10 continue write(5,*)k,chisq,(a(i),i = l,ma) k = k + 1 ochisq-chisq call mrqmin(x,y,sig,npts,a,ma,lista,mfit,covar,alpha, 1 ma,chisq,alamda) if (chisq.gt.ochisq) then itst=0 else if (abs(ochisq-chisq).lt.le-7) then itst® itst+1 endif if (itst.lt.2) then goto 10 endif c one more time for final, best values alamda=0.0 call mrqmin(x,y,sig,npts,a,ma,lista,mfit,covar,alpha, 1 ma,chisq,alamda) write(5,*)’nllsq fit finished’ c calculate yfit and the std. dev. in y do 13 i = l.npts xx=x(i) call fgauss(xx,a,yy,dyda,ma) 13 yfit(i)-yy sum « 0. do 15 i« l.npts 15 sum=sum+(y(i)-yfit(i))**2 sigy * (sum/(npts-ma))* * .5 c output parameters open(2,file * ’if.par’) write(2,*)’standard deviation in y \sigy write(2,*)’ ’ 127 write(2,*)’parameter and uncertainty’ write(5, *)’standard deviation in y \sigy write(5,*)’ ’ write(5,*)’parameter and uncertainty’ do 23 j = l,ma write(2,*)’a(’j,’) = \a(j),’+/- \sigy*sqrt(covar(jj)) 23 write(5,*)’a(’j,’) * \a(j),’ + /- ’,sigy*sqrt(covar(jj)) close(2) c output fragment plot and fit write(5,*)’input CSp(cm**2) and IpO’ read(5,*)csp,rip0 open(2,file = ’iffit.out’) open(3,file = ’if.out’) open(4,file » ’ifipf.out’) open(l,file=’ifip.out’) c convert x back to pressure c convert y back to fragment intensity do 33 i = l,npts zz=ripO*exp(-csp*x(i)) x(i)=x(i) * (1.363e-25*300* 760* 1000)/2.5 write(2,*)x(i),yfit(i)*zz write(4,*)x(i),yfit(i) write(l,*)x(i),y(i) 33 write(3,*)x(i),y(i)*z(i) close(2) close(3) close(4) end SUBROUTINE MRQMIN(X,Y,SIGtNDATA,A,MA,LISTA,MFIT, * COVAR,ALPHA,NCA,CHISQ,ALAMDA) PARAMETER (MMAX=50) DIMENSION X(NDATA),Y(NDATA),SIG(NDATA),A(MA),LISTA(MFIT), * COVAR(NCA,NCA),ALPHA(NCA,NCA),ATRY(MMAX),BETA(MMAX),DA( MMAX) IF(ALAMDAXT.0.)THEN KK*M FIT+1 DO 12 J * 1,MA IHTT=0 DO 11 K= l.MFIT IF(USTA(K).EQJ)IHIT=IHIT+ 1 11 CONTINUE IF (IHIT.EQ.O) THEN 128 LISTA(KK) = J KK=KK+1 ELSE IF (IHIT.GT.l) THEN PAUSE ’Improper permutation in LISTA’ ENDIF 12 CONTINUE IF (KK.NE.(MA+1)) PAUSE ’Improper permutation in LISTA’ ALAMDA=0.001 CALL MRQCOF(X,Y,SIG,NDATA,A,MA,USTA,MFIT,ALPHA,BETA,NCA,CHISQ) OCHISQ=CHISQ DO 13 J = 1,MA ATRY(J)=A(J) 13 CONTINUE ENDIF DO 15 J = l.MFIT DO 14 K= 1,MFIT COVAR(J.K) - ALPHA(J,K) 14 CONTINUE CO VAR(J,J) = ALPH A( J,J) • (1. + ALAMDA) DA(J) - BETA(J) 15 CONTINUE CALL GAUSSJ(COVAR,MFIT,NCAtDA, 1,1) IF(ALAMDA.EQ.O.)THEN CALL COVSRT(COVAR,NCA,MA,LISTA,MFIT) RETURN ENDIF DO 16 J = l.MFIT ATRY(LISTA(J))=ATR Y(LISTA(J)) + DA(J) 16 CONTINUE CALL MRQCOF(X,Y,SIG,NDATA,ATRYtMAtLISTA,MFIT,COVAR,DA,NCA,CHISQ) IF(CHISQ.LT.OCHISQ)THEN ALAMDA=0.1* ALAMDA OCHISQ « CHISQ DO 18 J = l.MFTT DO 17 K-1.MFIT ALPHA(J,K) - COVAR(J,K) 17 CONTINUE BETA(J)=DA(J) A(USTA(J)) - ATR Y(USTA(J)) 18 CONTINUE ELSE ALAMDA = 10.* ALAMDA 129 CHISQ = OCHISQ ENDIF RETURN END SUBROUTINE MRQCOF(X,Y,SIG,NDATAtA,MA,LISTAtMFn',ALPHA,BETA,NALP,CH *ISQ) PARAMETER (MMAX=50) DIMENSION X(NDATA),Y(NDATA),SIG(NDATA),ALPHA(NALP,NALP),BETA(MA), * DYDA(MMAX),USTA(MFIT) DO 12 J = l.MFIT DO 11 K= 1,J ALPHA( J,K) = 0. 11 CONTINUE BETA(J)=0. 12 CONTINUE CHISQ=0. DO 15 I = l.NDATA CALL fgauss(X(I),A,YMOD,DYDA,MA) SIG2I = l./(SIG(I)*SIG(I)) DY = Y(I)-YMOD DO 14 J = l.MFIT WT=DYDA(LISTA(J))*SIG2I DO 13 K=1,J ALPHA(J,K) = ALPHA(J,K) + WT"DYDA(LISTA(K)) 13 CONTINUE BETA(J) = BETA(J) + DY* WT 14 CONTINUE CHISQ=CHISQ+DY*DY*SIG2I 15 CONTINUE DO 17 J = 2,MFIT DO 16 K= 1,J-1 ALPHA(IU) = ALPHA(J,K) 16 CONTINUE 17 CONTINUE RETURN END SUBROUTINE GAUSSJ(A,N,NP,B,M,MP) PARAMETER (NMAX=200) DIMENSION A(NP,NP),B(NP,MP),IPIV(NMAX),INDXR(NMAX),INDXC(NMAX) 130 DO 11 J = 1,N IPIV(J) = 0 11 CONTINUE DO 22 1 = 1,N BIG=0. DO 13 J = 1,N IF(IPIV(J).NE.1)THEN DO 12 K=1,N IF (IPIV(K).EQ.O) THEN IF (ABS(A(J,K)).GE.BIG)THEN BIG=ABS(A(J,K» IROW =J ICOL=K ENDIF ELSE IF (IPIV(K).GT.l) THEN PAUSE ’Singular matrix’ ENDIF 12 CONTINUE ENDIF 13 CONTINUE IPIV(ICOL) = IPI V(ICOL) + 1 IF (IROW.NE.ICOL) THEN DO 14 L= 1,N DUM = A(IROW,L) A(IROW,L) = A(ICOL,L) A(ICOL,L) = DUM 14 CONTINUE DO 15 L=1,M DUM = B(IROW,L) B(IROW,L) = B(ICOL,L) B(ICOL,L) = DUM 15 CONTINUE ENDIF INDXR(I)=IRO W INDXC(I) = ICOL IF (A(ICOL,ICOL).EQ.O.) PAUSE ’Singular matrix.’ PIVIN V = l./A(ICOL,ICOL) A(ICOLJCOL) = l. DO 16 L-1.N A(ICOL,L) *A(ICOL,L)* PIVIN V 16 CONTINUE DO 17 L* 1,M B(ICOL,L)= B(ICOL,L) * PI VIN V 17 CONTINUE DO 21 LL= 1,N IF(LL.NE.ICOL)THEN DUM = A(LL,ICOL) A(LL,ICOL)=0. DO 18 L= 1,N A(LL,L)=A(LL,L)-A(ICOL»L)*DUM 18 CONTINUE DO 19 L=1,M B(LL,L)=B(LL,L)-B(ICOL,L)*DUM 19 CONTINUE ENDIF 21 CONTINUE 22 CONTINUE DO 24 L=N,1,-1 IF(INDXR(L).NE.INDXC(L))THEN DO 23 K= 1,N DUM=A(K,INDXR(L)) A(K,INDXR(L))=A(K,INDXC(L» A(K,INDXC(L))=DUM 23 CONTINUE ENDIF 24 CONTINUE RETURN END SUBROUTINE COVSRT(COVAR,NCVM,MA,LISTA,MFJT) DIMENSION COVAR(NCVM,NCVM),LISTA(MFIT) DO 12 J = 1,MA-1 DO 11 I=J+ 1,MA COVAR(U)=0. 11 CONTINUE 12 CONTINUE DO 14 I = 1,MFIT-1 DO 13 J=I+l.MFIT IF(USTA(J).GT.LISTA(I)) THEN COVAR(USTA( J),USTA(I))=COVAR(U) ELSE COVAR(LISTA(I),LISTA(J)>=COVAR(IfJ) ENDIF 13 CONTINUE 14 CONTINUE SWAP-COVAR( 1,1) DO 15 J = 1,MA COVAR( 1,J)=COVAR(J,J) 132 COVAR(JJ)=0. 15 CONTINUE COVAR(USTA(l),USTA( 1)) = SWAP DO 16 J=2,MFIT COVAR(LISTA(J),USTA(J))=COVAR( U ) 16 CONTINUE DO 18 J=2,MA DO 17 I-l.J-1 COVAR(I,J)=COVAR(J.I) 17 CONTINUE 18 CONTINUE RETURN END SUBROUTINE FGAUSS(X,A,Y,DYDA,NA) DIMENSION A(NA),DYDA(NA) y=(a( 1 )/a(2))*(exp(a(2) *x)-l) dyda( 1)=(l/a(2)>* (exp(a(2) *x)-1) dyda(2) = (exp(a(2)*x))*(a( l)*x/a(2)-a( l)/(a(2)* *2)) + 1 a(l)/(a(2)**2) RETURN END 133 peaks.for This program crudely finds peaks in a mass spectrum and outputs a data file such that it can be entered into the nonlinear least squares program fit.for INCLUDE ’FGRAPH FI’ INCLUDE ’FGRAPH.FD’ dimension x(1000),y(1000),xp(40),yp(40),px(40) INTEGER*2 dummy, ix, iy, i c input data to plot open(2,file * ’ms.in*) read(2,*)npts do 10 i = l,npts 10 read(2,*)x(i),y(i) close (2) c find ymax and ymin ymin=y(l) ymax=y(l) do 15 i = l,npts-l if(y(i).lt.ymin)ymin=y(i) 15 if(y(i).gt.ymax)ymax=y(i) write(5,*)’ymax= \ymax,’ ymin= ’,ymin write(5,*)’ ’ c look for peaks c c a point is considered a peak if the change in y changes c sign and the change in y was neg. for three points before c and pos. three point after c c j is an counter for the nmber of peaks open(3,file=’peaks.out’) j« 0 do 12 i=4,npts-4 if(y(i)-y(i-l).ge.O) goto 12 if(y(i-l)-y(i-2).ge.O) goto 12 if(y(i-2)-y(i-3).ge.O) goto 12 if(y(i+l)-y(i).lt.O) goto 12 if(y(i+2)-y(i+ l).lt.O) goto 12 if(y(i+3)-y(i + 2).lt.O) goto 12 j - j + 1 Px0 ) = i xpO)-x(i) ypO')*ymax-y(i) 12 continue write(3,*)’ 2048’ write(5,*)’the number of peaks is ’j c find the peak widths do 17 k=lj i=px(k) yhmax= 2048-.5 *yp(k) n=i 19 n = n + 1 if(y(n).gt.yhmax) goto 18 goto 19 18 xr=x(n) n=i 27 n= n-l if(y(n).gt.yhmax) goto 28 goto 27 28 xl=x(n + 1) xw=xr-xl write(5,100)-yp(k),xp(k),xw 17 write(3,100)-yp(k),xp(k),xw close(3) 100 format( lx,f 10.3,f 15.3,f 10.3) c wait for return read(V ) c plotting part c c VGA screen goes from 0 to 639 along the x axis c and from 0 to 479 along the y axis c (0,0) is in the upper left hand corner dummy = setvideomode( $vresl6COLOR ) dummy=setcolor(3) do 20 i = l,npts * « 1 X * 1 iy * int2(480*(y(i)-ymin)/(ymax-ymin)) 20 dummy = setpixel(ix.iy) c plot peak positions dummy * setcolor( 1) do 29 i = l j ix*px(i) do 29 k» 0,479 iy*k 29 dummy = setpixel(ix,iy) CC This part waits for the ENTER key to be CC pressed, then resets the screen to normal before returning. READ ( V ) ! Wait for ENTER key dummy = setvideomode( SDEFAULTMODE ) END 136 fit.for This program performs a non-linear least squares analysis on a mass spectrum in order to determine the position, width and intensity of the peaks. This procedure assumes the peaks are gaussian. INCLUDE ’FGRAPH.FT INCLUDE TGRAPH.FD’ PARAMETER (ma= 16) dimension x(700),y(700),yfit(700),sig(700),a(ma),lista(ma), 1 covar(ma,ma),alpha(ma,ma) INTEGER*2 dummy, ix, iy do 2 j = l,ma 2 lista(j)=j c read in mass spectrum open(2,file * ’ms.in’) read(2,*)npts do 5 i = l.npts sig(i) = l. 5 read(2,*)x(i),y(i) close(2) c read in initial parameters open(2,file=’fitms.in’) read(2,*)a(ma) do 7 j = l,ma-l,3 7 read(2,*)a(j),a(j + l),a(j + 2) close(2) c initialize nllsq program alamda = -l c mfit allows some parameters to be fixed, if mfit is less than ma, the c last ma-mfit parameters in the lista array will not be fit mfit = ma-l call mrqmin(x,y,sig,npts,a,ma,lista,mfit,covar,alpha, 1 ma,chisq,alamda) c iterate until parameters get close k = 1 itst—0 write(5,*)’iter. chi**2 a(l)-a(ma)’ 10 continue write(5,*)k,chisq,(a(i),i = l,ma) k -k + 1 ochisq=chisq call mrqmin(x,y,sig,npts,a,ma,lista,mfit,covar,alpha, 137 1 ma,chisq,alamda) if (chisq.gt.ochisq) then itst=0 else if (abs(ochisq-chisq).lt.O.OOl) then itst=itst+1 endif if (itst.lt.2) then goto 10 endif c one more time for final, best values alamda-0.0 call mrqmin(x,y,sig,npt$,a,ma,lista,mfit,covar,alpha, 1 ma,chisq,alamda) write(5,, )’nllsq fit finished’ c calculate yfit and the std. dev. in y open(2,file » ’yfit.out’) open(3,file * ’ms.out’) do 13 i = l,npts xx =x(i) call fgauss(xx,a,yy,dyda,ma) write(2,*)x(i),yy write(3,*)x(i),y(i) 13 yfit(i)=yy close(2) close (3) sum=0. do 15 i=l,npts 15 sum=sum + (y(i)-yfit(i))*“2 sigy= (sum/(npts-ma))* • .5 c find ymax and ymin ymin=y(l) ymax=y(l) do 16 i= l,npts-l if(y(i).lt.ymin)ymin *y(i) 16 if(y(i).gt.ymax)ymax *y(i) write(5,, )’ymax= ymax,’ ymin = ’,ymin write(5,*)’ ’ c plotting part c c VGA screen goes from 0 to 639 along the x axis c and from 0 to 479 along the y axis c (0,0) is in the upper left hand corner dummy = setvideomode( $vresl6COLOR ) 138 dummy=set color (3) do 20 i = l.npts ix=i iy=int2(430*(y(i)-ymin)/(ymax-ymin))+25 20 dummy = setpixel(ixjy) dummy=setcolor (1) do 21 i = l.npts ix=i iy=int2(430*(yfit(i)-ymin)/(ymax-ymin))+25 21 dummy = setpixel(ix,iy) CC This part waits for the ENTER key to be CC pressed, then resets the screen to normal before returning. READ (*,*) ! Wait for ENTER key dummy = setvideomode( SDEFAULTMODE ) open(2,file = 'fit. par’) write(2,*/standard deviation in y \sigy write(2,*/ ’ write(2,*/parameter and uncertainty’ write(5,*/standard deviation in y \sigy write(5,*/ ’ write(5,*/parameter and uncertainty’ do 23 j = l,ma write(2,*)a(j),’ + /- ’,sigy*sqrt(covarO'j)) 23 write(5,*)a(j),’ + /- \sigy*sqrt(covar(jj)) end SUBROUTINE MRQMIN(X,Y,SIG,NDATA,A,MA,LISTA,MFIT, * COVAR,ALPHANCA,CHISQ,ALAMDA) PARAMETER (MMAX * 50) DIMENSION X(NDATA),Y(NDATA),SIG(NDATA),A(MA),LISTA(MFIT), « COVAR(NCA,NCA),ALPHA(NCA,NCA),ATRY( MMAX),BETA( MMAX),DA( MMAX) IF( ALAMD A.LT.0. )THEN KK-M FIT+1 DO 12 J = 1,MA IHIT=0 DO 11 K=1,MFIT IF(LISTA(K).EQ.J)IHIT*IHIT +1 11 CONTINUE IF (IHIT.EQ.O) THEN 139 LISTA(KK)=J K K =K K +1 ELSE IF (IHIT.GT.l) THEN PAUSE ’Improper permutation in LISTA’ ENDIF 12 CONTINUE IF (KK.NE.(MA+1)) PAUSE ’Improper permutation in LISTA’ ALAMDA=0.001 CALL MRQCOF(X,Y,SIG,NDATA,A,MA,USTA,MFIT,ALPHA1BETA,NCA,CHISQ) OCHISQ = CHISQ DO 13 J= 1,MA ATRY(J)=A(J) 13 CONTINUE ENDIF DO 15 J = l.MFIT DO 14 K=1,MFIT COVAR(J.K)=ALPHA(J,K) 14 CONTINUE CO VAR( J,J)=ALPH A( J,J) * (1.+ALAMDA) DA(J)=BETA( J) 15 CONTINUE CALL GAUSSJ(COVAR,MFIT,NCA,DA,l,l) IF(ALAMDA.EQ.O.)THEN CALL COVSRT(COVAR,NCA,MA,LISTA,MFIT) RETURN ENDIF DO 16 J = 1,MFIT ATRY(LISTA(J))=ATRY(LISTA(J)) + DA(J) 16 CONTINUE CALL MRQCOF(X,Y,SlG,NDATA,ATRY,MA,LISTA,MFIT,COVAR,DA,NCA,CHISQ) IF(CHISQ.LT.OCHISQ)THEN ALAMDA=0. I* ALAMDA OCHISQ=CHISQ DO 18 J = l.MFIT DO 17 K=1,MFIT ALPHA(J.K)=COVAR(J.K) 17 CONTINUE BETA(J) = DA(J) A(USTA(J))=ATRY(USTA(J)) 18 CONTINUE ELSE ALAMDA = 10.* ALAMDA 140 CHISQ=OCHISQ ENDIF RETURN END SUBROUTINE MRQCOF(X,Y,SIG,NDATA,A,MA,LISTA,MFIT,ALPHA,BETA,NALP,CH •ISQ) PARAMETER (MMAX=50) DIMENSION X(NDATA),Y(NDATA),SIG(NDATA),ALPHA(NALP,NALP),BETA(MA), * D YD A( MMAX),LISTA( MFIT) DO 12 J = 1,MFIT DO 11 K=1,J ALPHA(J,K) = 0. 11 CONTINUE BETA(J)=0. 12 CONTINUE CHISQ=0. DO 15 I = 1,NDATA CALL fgauss(X(I),A,YMOD,DYDA,MA) SIG2I= l./(SIG(I)*SIG(I)) DY = Y(I)-YMOD DO 14 J = 1,MFIT WT=DYDA(LISTA(J))*SIG2I DO 13 K= 1,J ALPHA(J,K)=ALPHA(J,K) + WT*D YDA(LISTA(K)) 13 CONTINUE BETA(J)= BETA( J) + DY* WT 14 CONTINUE CHISQ=CHISQ + DY*DY*SIG2I 15 CONTINUE DO 17 J=2,MFIT DO 16 K=U-1 ALPHA(KJ)=ALPHA(J.K) 16 CONTINUE 17 CONTINUE RETURN END SUBROUTINE GAUSSJ(A,N,NP,B,M,MP) PARAMETER (NMAX=200) DIMENSION A(NP,NP),B(NP,MP),IPIV(NMAX),INDXR(NMAX),INDXC(NMAX) 141 DO 11 J = 1,N IPIV(J)=0 11 CONTINUE DO 22 1 = 1, N BIG=0. DO 13 J = 1,N IF(IPIV(J).NE.1)THEN DO 12 K= 1,N IF (IPIV(K).EQ.O) THEN IF (ABS(A(J,K)).GE.BIG)THEN BIG=ABS( A(J,K» IROW=J ICOL=K ENDIF ELSE IF (IPIV(K).GT.l) THEN PAUSE ’Singular matrix’ ENDIF 12 CONTINUE ENDIF 13 CONTINUE IPIV(ICOL)=IPI V(ICOL) +1 IF (IROW.NE.ICOL) THEN DO 14 L= 1,N DUM=A(IROW,L) A(IROW,L) = A(ICOL,L) A(ICOL,L) = DUM 14 CONTINUE DO 15 L=1,M DUM = B(IROW,L) B(IROW,L)=B(ICOL,L) B(ICOL,L)=DUM 15 CONTINUE ENDIF INDXR(I) = IROW INDXC(I) = ICOL IF (A(ICOmCOL).EQ.O.) PAUSE ’Singular matrix.’ PIVINV = l./A(ICOL,ICOL) A(ICOL,ICOL) = 1. DO 16 L=1,N A(ICOL,L) «A(ICOL,L>* PIVINV 16 CONTINUE DO 17 L=1,M B(ICOL,L)=B(ICOL,L) • PIVINV 17 CONTINUE DO 21 LL= 1,N IF(LL.NE.ICOL)THEN DUM=A(LLJCOL) A(LL,ICOL)=0. DO 18 L= 1,N A(LL,L)=A(LL,L)-A(ICOL,L)*DUM 18 CONTINUE DO 19 L= 1,M B(LL,L)=B(LL,L)-B(ICOL,L)*DUM 19 CONTINUE ENDIF 21 CONTINUE 22 CONTINUE DO 24 L=N,1,-1 IF(INDXR(L).NE.INDXC(L))THEN DO 23 K=1,N DUM = A(K,INDXR(L)) A(K,INDXR(L))=A(K,INDXC(L)) A(K,INDXC(L)) = DUM 23 CONTINUE ENDIF 24 CONTINUE RETURN END SUBROUTINE COVSRT(COVAR,NCVM,MA,LISTA,MFIT) DIMENSION COVAR(NCVM,NCVM),LISTA(MFIT) DO 12 J = 1,MA-1 DO 11 I=J+ 1,MA COVAR(I,J)=0. 11 CONTINUE 12 CONTINUE DO 14 I = 1,MFIT-1 DO 13 J= I + l.MFIT IF(LISTA(J).GT.LISTA(I)) THEN COVAR(USTA(J),USTA(I»=COVAR(I,J) ELSE COVAR(USTA(I),USTA(J)) = COVAR(U) ENDIF 13 CONTINUE 14 CONTINUE SWAP *COVAR( 1,1) DO 15 J = 1,MA COVAR(U)=COVAR(J,J) COVAR(J,J)=0. 15 CONTINUE COVAR(LISTA( 1 ),LISTA( 1)) = SWAP DO 16 J=2,MFIT COVAR(LISTA(J),LISTA(J))=COVAR( U ) 16 CONTINUE DO 18 J=2,MA DO 17 I-U -l COVAR(U)=COVAR(J,I) 17 CONTINUE 18 CONTINUE RETURN END SUBROUTINE FGAUSS(X,A,Y,DYDA,NA) DIMENSION A(NA),DYDA(NA) Y=0. DO 11 1 = 1,NA-1,3 ARG=(X-A(I +1 ))/A(I + 2) EX=EXP(-ARG**2) FAC=A(I)*EX*2.*ARG Y = Y+A(1)*EX DYDA(I)=EX DYDA(I +1) = FAC/A(I + 2) DYDA(I + 2) = FAC* ARG/A(I + 2) 11 CONTINUE Y = Y + A(NA) DYDA(NA)= 1. RETURN END 144 pdflt2a.for This program uses the multiple collision theory of Kim to find the "best" value of the parameter rl from fragment ion intensities. c Program to Analyze Fragment Ion Intensity c c based on the paper by Myung S. Kim c Int. J. Mass Spectrom. Ion Phys. 51, 279-290 (1983). c c parameters c c a - array of the number of scattering molecules in ion path in DR, c directly proportional to pressure c r - array of r(n) determined from r( 1) which is the fraction of parent c ions which do not dissociate c rp - array of pressures in Torr c rpp - array vs. Pressure of Ip/IpO c rpd - array vs. pressure of If/IpO c rpdc - calculated array vs. pressure of If/IpO dimension a(250),r(0:50),rpdc(250),rp(250),rppc(250) data saf,scidf,sap,scidp/25e-16,5.6e-16,25e-16,5.6e-16/ data npts,rplo,rphi/250,0,20/ write(5,*)’ ’ write(5,*)’input rl’ read(5,*)r(l) f=(saf-scidf)/(sap-scidp) s= l/((l-r(l))*(sap/scidp-l) + 1) st= sap-scidp+ scidp/( l-r{ 1)) c st-sap write(5,*)’ f r(l) s st ’ write(5, * )f,r( 1 ),s,st write(V)’ ’ write(5,*)’input new f * read(5,*)f dp=(rphi-rplo)/(npts* 1000.) rp(l) = 0 do 13 i*l,npts rp(i) * rp(i) + (i-l)*dp rppc(i)*exp(-rp(i)*st*2.5/(1.363e-25*760*300* 1000)) 13 a(i)=rp(i)*st*2.5/(1.363e-25*760*300* 1000) c calculate r(2)-r(10) write(5,*)’ the r values ’ r(0)= l write(5/)0,r(0) write(5,*)l,r(l) do 30 n=2,6 n2=2*n call fac(n2,n2f) r(n) = ((2*r(l))-n)/(n2f*l.) 30 write(5,*)n,r(n) alpha=s/( l-f •( 1-s)) c loop through points do 40 i = l,npts beta=(l-f*(l-s))*a(i) c write(5,*)’i= \i/beta = \beta,’ a=\a(i) c write(5,*)’beta-a(i)\beta-a(i) c write(5,*)’exp(beta-a(i)) \exp(beta-a(i)) rpdc(i)=alpha*(r(0)-r(l))*(exp(beta-a(i))-exp(-a(i))) c loop through n terms do 40 n= 1,6 betas=0. c loop for beta sum do 45 k = 0,n call fac(k,kf) 45 betas=betas-(beta**k)/kf rpdc(i) = rpdc(i) + (alpha* *(n + l))*(r(n)-r(n+ l))s(exp(beta-a(i)) + 1 exp(-a(i))*betas) c write(5,*)’n= ’.n,’ rpdc= \rpdc(i),’ betas= betas 40 continue c output loop open(3,file = ’pdcalc.out’) do 50 i= l.npts 50 write(3,*)rppc(i),rpdc(i) close(3) open(2,file - ’pdpp.dat’) open(3,file =’pd.out’) read(2,*)npts do 57 i - l.npts read(2,*)x,y,z 57 write(3,*)y,z close(3) close(2) end subroutine fac(n2,n2f) if(n2.eq.O) then n2f= 1 else n2f=i do 10 i=n2,l,-l n2f=n2f*i endif end cspark.for This program determines the attenuation cross sections for parent ions. c c **********Least Squares Analysis of Parent Cross Sections********* c c y = slope *x + int c c -ln(Ip) = slope*(-P*L/(kT)) + int c c where int = ln(IpO) c dimension x(50),y(50),yfit(50) c c input data to be fit from data file pipif.dat c of the form: c c first line is the no. of points, npts c c then there are npts lines with three entries each for c the pressure (Torr), the parent intensity, and the fragment intensity c open(2,file = ’pipif.dat’) read(2,*)npts do 10 i = l,npts read(2,*)x(i),y(i) x(i)=x(i)/1000 x(i) = -x(i)*2.5/( 1.363e-25 *300*760* 1000) 10 y(i)*log(y(i)) close(2) c c calculate the sums over the # of observations (npts) of c x,y,xypc**2, and y**2 c sumx=0. sumy=0. sumxy=0. sumxx*0. sumyy=0. do 20 i ” l,npts sumx=sumx+x(i) 148 sumy=sumy+y(i) sumxy= sumxy+x(i)*y(i) sumyy * sumyy+y(i) *y(i) 20 sumxx=sumxx+x(i)*x(i) c c use these sums to calculate the slope (slope) and intercept (rint) c slope = (npts*sumxy-sumx*sumy)/(npts*sumxx-sumx*sumx) rint = (sumy*sumxx-sumxy*sumx)/(npts*sumxx-sumx*sumx) c c once you know the slope and intercept calculate y values (yfit) and c determine the standard deviation in y (stdy). This form of error analysis c forces chi square to be 1, i.e. instead of weighting with a std. deviation c for each measurement y(i), the standard deviation is calculated and used c to weight the uncertainties in the slope and intercept. For this to be c rigorously correct the chosen functional form (a line in this case) must c be the right one. c stdy=0. do 30 i * l,npts yfit(i)=slope*x(i) + rint 30 stdy=stdy+(y(i)-yfit(i))**2 stdy = (stdy/(npts-2.))# *.5 c c from the standard deviation in y determine the standard deviation c in the slope and intercept c stdslo s= stdy • (npts/( npts * sumxx-sumx * sumx)) * * .5 stdrin = stdy • (sumxx/( npts * sumxx-sumx * sumx)) *" .5 c c in some cases you may prefer to compare correlation coefficients, c for instance when there are errors in both x and y c r « (npts*sumxy-sumx*sumy)/((npts*sumxx-sumx*sumx) • ( 1 npts*sumyy-sumy*sumy))**.5 c c output results to both pipif.out and to the screen c open(3,file » ’pipif.out’) write(3,*)’ i x y y-yfit’ c c you should always output the calculated values of y to see if there c are systematic deviations. If the calculated values vary randomly c about the observed, thing are OK c do 40 i= l.npts write(3,100)i,x(i),y(i),y(i)-yfit(i) 40 continue write(3,*)’ ’ write(5,*)’cs(cm**2) = ’.slope,’ + or - stdslo,’ (1st sd.)’ write(3,*)’cs(cm**2) = slope,’ + or - stdslo,’ (1st sd.)’ ripO=exp(rint) ripOh=exp(rint+stdrin) ripOl= exp(rint-stdrin) diff= abs(ripOh-ripOl) write(5,*)’IpO = \ripO,’ + or - \diff,’ (1st std. dev.)’ write(3,*)’lp0 = \ripO,’ + or - \diff,’ (1st std. dev.)’ write(5,*)’standard deviation in y = \stdy write(3,*)’standard deviation in y = ’.stdy write(5, ^ ’correlation coefficient = \r write(3,*)’correlation coefficient = ’,r 100 format(lx,i4,3el5.8) close(3) end 150 cacs.for This program determines the collisional activation (CA) cross section for the parents. dimension rp(50),rip(50),rif(50) dimension y(50),y0(50),dy(50) character* 15 ifn write(5,*)’Enter Input Filename’ read(*,’(a)’)ifn open(2,file=ifn) read(2,*)npts read(2,* )cslp,cscapO,cslf,cscaf do 10 i = l,npts read(2,*)rp(i),rip(i),rif(i) rp(i)=rp(i)/1000 10 y(i)=rif(i)/rip(i) close(2) c Calculate Pressure conversion factor c pcf=2.5/( 1.363e-25 *300* 1000*760) c c sigcs=0 ni=0 15 sdev=0 sumh=0 smsqdy=0 csf=cscapO+ cslp-cscaf-cslf do 20 i-l,n p ts y0(i) - cscapO* (exp(csf* rp( i )* pcf)-1)/csf sdev * sdev+ (y(i)-yO(i))* *2 dy(i)=y(i)*(l/cscap0- l/csf+ rp(i)*pcf) + rp(i)*pcf*cscapO/csf sumh «sumh+dy(i) *(y(i)-y0(i)) 20 smsqdy=smsqdy+dy(i)**2 stdy « (sdev/(npts-1)) * * .5 sigcs *stdy/smsqdy* *.5 cscap=cscapO+ sumh/smsqdy n i- n i+ 1 write(5, * )ni,cscap,sigcs-sigcsO if(abs(sigcs-sigcs0).le.le-20)goto 30 151 cscapO=cscap sigcsO=sigcs goto 15 30 write(5,*)’CA cross section * \cscap,’ +/- \sigcs open(3,file = ’in.out') do 40 i = l.npts 40 write(3,*)rp(i),y(i) cIose(3) open(3,file=’fit.out’) do 50 i = l,npts 50 write(V)rp(i),y0(i) close(3) end pdpp.for c c c input data to be fit from data file pipif.dat c of the form: c c first line is the no. of points, npts c c then there are npts lines with three entries each for c the pressure (Torr), the parent intensity, and the fragment intensity c open(2,file = ’pipif.dat’) open(3,file=’dp.dat’) open(4,file=’pdpp.dat’) read(2, • )npts,ripO write(4, * )npts,ripO do 10 i = l,npts read(2,*)rp,rip,rif write(4, * )rp,rip/ripO,rif/ripO 10 write(3,*)rip/ripO,rif/ripO close (2) close(3) close(4) end 153 ifip.for write(5,*)’input CA cross section’ read(5,*)cacs write(5,*)’input parent cross section difference’ read(5,*)delcs open(2,file= ’ifip.fit’) do 10 i=0, 200 delp=2.5/200 rp=i*delp/1000 rex=exp(delcs* rp *2.5/(1.363e-25 *300* 1000*760) )-l rf=cacs/delcs rifip=rex*rf write(5,*)rex,rf 10 write(2,*)rp,rifip close(2) end ipcalc.for open(2,file * ’ppd.dat’) open(3,file=’pdpp.dat’) read(2,*) npts read(2,*) rip0,cspar write(3,*)npts do 10 i- l.npts read(2,*)rp,rf rip= rip0*exp(-cspar*2.5 *rp/( 1.363e-25 *300* 1000* 1000* 760)) write(5,* )i,rp/1000,rip,rf 10 write(3,*)rp/1000,rip,rf close(2) close(3) end Appendix B Mathcad templates 154 Analysis of Mass Spectrum Working on a Wien Velocity Filter Spectrum 156 The spectrum is called "data" by mead. The spectrum in "file.ext" is identified as the "data" by the associate file subcategory in the file menu, "file.dat" is stored as Vwf vs. Intensity in OAC units. It cannot start with the no. of points. It is read into 'a' which is an Nx2 matrix. a =READPRN(amlOOOfdat) npts =rows(a) j = 0 ..n p ts-l npts * 682 2100 2030 2000 1930 a.-j.l 1900 1830 1800 1730 30 100 130 200 230 *j,o Take a derivative of the spectrum. j = 1.. npts - 2 d. =‘i + M ~ ( 1) 1 aj+ 1 .0 ‘ “j-1,0 130 100 d. } “ 100 -iso 100 130 200 230 157 To find resolved peaks, we look for four consecutive neg. points in the derivative followed by four consecutive positive points. Find peak intesities and check plot to verify that reasonable peaks are being found j =5..npts- 6 gj (4_,>0) (d>0)(4+,*0) (4^0) (d+3<0), 2048 , r ,,0 300 200 t-.)j 100 0 so 100 1)0 200 2S0 300 *j.O Peak positions are linearly interpolated at the cross-over h. = if j (“i-2>0)(di-.>0)'fr°) (di+.<0) di ^r^Tr-0’0 i+ 1 j An index of the peaks is useful hj. = ifj (d. _ 2>0) -(d_ ,> 0) ■ (cl>0) -(d + 1<0) - (d + 2< 0 ) -(d <0),j,0] Count the no. of peaks pj =4 ( V 2 >0) (dJ - l > 0 i (dJ> 0 H dJ+ l<01 (dJ + 2< 0 ) (dj + 3< 0 ) ' 1'0 ' nP S PJ n p = 1 8 j We have been hunting for peaks using column vectors which have zeros for positions not indentified as peak centers. Now we pull the peak center information out of these column vectors for tabulation. ah =8ort(h) shj =aort(hj) dir =reverae(sh) shj - reverse(shj) q =0..np- 1 y =-2048+#/*: 4 V < | ’ 158 Fitting an Assignment of the Velocity Spectrum Construct a column vector that has np elements. Put in your mass assignment or zero Of you do not have a good guess) using the same order as in the table.. position^ - shr^ intensity mass index 281.257002 271.700758 263.006904 255.110673 247 996758 position 199 841267 188.633958 179 677912 148 673085 130.285728 117 552121 108 403815 101.154301 95.102718 90.539257 86.282788 70.104657 6 39262 Go into to the mass column vector and input any assignments you want to make. Remember that the first peak is indexed with zero. massn =14 mass, =15 mass. =16 1£J o i 2 mass} =17 mass4 =18 mass^ =28 mass,6 = 32 mass. 7 = 35 mass I = 52 mass9 =69 mass]Q =86 ma$$u =103 mass]2 =120 mass[3 =137 mass)4 =154 -1.49 r u 0 281.257002 -8.925 15 1 271.700758 -115.285 16 2 263.006904 -243.04 17 3 255.110673 -98.55 18 4 247.996758 intensity " -60.655 mass ” 28 index m 5 position 199.841267 -32.87 32 6 188633958 -283.015 35 7 179.677912 -86.485 52 8 148.673085 -8836 69 9 130.285728 -10204 86 10 117.552121 -41 205 103 11 108.403815 -36.945 120 12 101.154301 -32.895 137 13 95.102718 154 14 90.539257 -24495 -22 1 0 15 86.282788 -1638 0 16 70.104657 -0.61 0 ! 17 6.39262 j Now we must sort out the peaks to be fit. flag^ = if^mass^O,1.0) npfit - flagg npfit = 15 qi =0. npfit- 1 q index = flag-index index - sort (index) index = reverse( index) R <1 R positionfir = position ^ ^ massfit^. = m a s s ,^ .- } 160 90.539257 154 95.102718 137 101.154301 120 108.403815 103 117.552121 86 positionfit: 130.285728 massfit = 69 148.673085 52 179.677912 35 188.633958 32 199.841267 28 247.996758 18 255.110673 17 263.006904 16 271.700758 IS 281.257002 14 We are fitting 1/mA2 to Vwf The fit ymass . slo - slope(positionfit,ymass) slo =0.000979 massfits* inter - intercept( positionfit, ymass) inter = -0.007473 cor = corr( positionfit, ymass) cor =0.999979 calculate the mass of just the fitted peaks calculate the mass of all the peaks ymassfit^. - slo positionfit^ + inter ymasscalc^ = slo position^ +■ inter calculate the standard deviation in y convert the calculated values back to ma 1 1 stdy - ^ ' (ymassfit^. - ymass^. j ‘ masscalc ^npfit- 2 (ymasscalcj V stdy = 0.000467 range (ymtacdC' - «dy) (ynuMck * «dy) diff = masscalc - mass diflf4 = if \(mass 4 «0,0,diff 4' | 161 Fit Results 0.23 0.2 ♦ 0.1 0.03 0 50 100 130200 230 pOMtimfttq. Correlation coefficient cor * 0.999979 Standard deviation in y stdy - 0 000467 13.928728 14 0.097025 -0.071272 14 955084 15 0107944 -0044916 15.990659 16 0119348 -0 009341 17.027353 17 0131141 0.027353 18 050158 18 0.143133 0.050158 28.227544 mass “ 28 range = 0.279917 diff * 0227544 31.831341 32 0.335199 -0 168659 35.231614 35 0.390319 0.231614 52.423852 52 0.708463 0.423852 69.319887 69 1.077243 0.319887 86.31061 86 1 496672 031061 102.692742 103 1.942419 -0.307258 119.230378 120 2.430059 -0.769622 136.298571 137 2.970138 -0,701429 151.715894 154 3.488102 -2.284106 168.581337 0 4.085639 0 267.197885 0 8152935 0 6 799428*10* 0 -1 441732* 106 0 H502KIM.MCD Calculation of parent excitation and CID probabilities for H502+ 262 I is the index for the pressure in mTorr i -0 100 k is the Boltzmann constant, T is the absolute . 23 T . _. , temperature and I is the length of the collision 1 -3uu cell in cm. i 1 10 J Rho is the number density of the target gas in the collision cell. _ 760 ' k T 1000 Input the experimentally determined values for the Attenuation and the CIO Cross Sections for the Parent and the Fragment op = 25 10'16 ocidp = 0.62 10'16 of = 1110'16 ccidf =0 10"16 r1 is the fraction of parent ion beam which has suffered a single collision and remained in the beam without dissociating. This value is determined by fitting to the detected fragment ion data in the multiple collision region (as described by Kim). r, =-9 rO is the fraction of the detected parent beam which has not undergone unimolecular decay ro r(n) is the fraction of the detected parent ion beam which has suffered n collisions and has not dissociated. Calculate r(n) for n»0 to 10 n = l 10 ^-r, J "(2-n)! The ion loss cross section for the parent is alp = op - ocidp alp =2 438*10 15 The collisional activation cross section for the parent is ocap = °C—^ ocap»6.2*10 16 >-ri The sum of the ion loss and the collisional activation cross section is the total cross section for the parent otp = olp + ocap ctp ■ 3.058* 10 The ion loss cross section for the fragment is olf = of - ocidf oLf — 11*10 13 Use IQm theory to determine multiple collision probabilities s is the ratio of the Ion loss and the total cross section for the perent s = otp , olf fj ocap Calculate alpha and beta a a “ 0.31665 dtp alp otp / P; dtpp; 1 dip \ dtp m is an index for the number of collisions m = 0 .9 The A matrix Is initialized by defining . = 0 Use Recursion Relation to calculate A(n) at each P(i) (apj V i 1 A. . =aA l.i 0,i *2.1 raAi (1 + I')! 3+ 1 >4+1 K) K) V i =aV i- (2+ l!)l V. =° \ i - (3+1!)! A. . =a A. . - *■' (4+1!)! 5+1 ,6+1 (.fj- 7+ I Ax . =a-A, .- :a-A, K)' (aPj *•' 5’’ (5+1!)! *7.1 6i (6+1!)! . . =aA, 1.1 7,1 (7+1!)! •+1 ®+i K) iaV A - a - Ag . — — ------V i =“V i- ( 8 + 1!)! 1 ° .' 9 ,. ( 9 T ]|)i Calculate the probability of detecting a fragment ion after 1 ,2 ,3 ,4 collisions 1 collision Ifp, . =aexp(.dtpp. l) [[(rQ- r,) A0 .]] 2 collision IfpJt. =aexp(.dtp-p.l)[[(r1- r 2)-AI>.]] 3 collision **3.1 =* « P ( - * M '[ [ h - r»)-V»]] 4 collision Ifjy. =aexp(.dtpp.-l)[[(r3-r4).A3 .]] Calculate the parent attenuation p. = exp^(-p). op l] Calculate the Ion loss lp. = exp[(- p). dp i] Calculate the probability of a parent ion suffering 1 collision and being detected Ipi,i ■=r1-er«xp(-pb-otp-l)-(p.-otp-l) The probability of detecting an Ion (either parent or fragment) after 1 collision is It,i,i . =IP, ri.i , + Ifp, n,i . 2 collisions (p-otpl)3 Ip, . = r,s ■cq»[(-p).-etp-l]-il-^ ..i It, . = Ip, ; + Ifp, ( 3 collisions , 3 r, , _ (pi otp l) Ip, ( = r, s exp ( p). otpl] — . ^ „ J 3,i 3Ti r3,i 4 collisions lp^_ = v / expr(, p), qtpij (P-^P ) h 4 . =ip4 . + Ifp4 . Calculate the total fragment ion current (sum of the fragments) Calculate the total ion current (sum of the fragments and unattenuated parent) IT. =(Ifp), j+ Ifp, ^ I lp J ^ l l p 4 i + pi Output the data B , =Ifp, . WRITEPRNfrlhS^) = B B 1,0 <1=p r i 1.1 *1,1 WRITEPRN^hS^) =B B1,0 „ =P B i.l , =ifp, 2.1 B. , =T. WRITEPRN(rth5 =B B 1,0 » =P*1 1, 1 1 WRITEPRNfplhS^,) =B B 1,0 n =p r « B 1,1 , =IPi * 1,1 WRITEPRN (p2h5 ^ J =B B 1,0 „ =P r i B 1,1 , =Ip,r 2,i WRITEPRN(pth5 =B B1,0 =P 1 Bi,l =IP2,i+IP.,i 0.1 0.01 0.06 0.02 ■iiiM lttttttlt t t t ± ±J ±- 0.1 0.2 0.3 0.4 0.3 0.6 0.7 0.1 0.9 1 Pi o.oa 0.06 U 0.04 l.i 0.02 40 100 120 140 160 ISO 200 H703KIM.MCD Calculation of the parent excitation and CID probabilities for H703+ i is the index for the pressure in mTorr i =0 100 k is the Boltzmann constant, T is the absolute k = i 3 ^3 . 1 0 '23 T -300 1= 1 5 temperature and I is the length of the collision cell in cm. 1 l 10 3 Rho is the number density of the target gas in the collision cell. _ 760 Pi k T 1000 Input the experimentally determined values for the Attenuation and the CID Cross Sections for the Parent and the Fragment op =36 10'16 ocidp =4.3 10 16 of =25 10'16 ocidf =0.62 10'16 r1 is the fraction of parent ion beam which has suffered a single collision and remained in the beam without dissociating. This value is determined by fitting to the detected fragment ion data in the multiple collision region (as described by Kim). r. = 6 r0 is the fraction of the detected parent beam which has not undergone unimolecular decay ro =l r(n) is the fraction of the detected parent ion beam which has suffered n collisions and has not dissociated. Calculate r(n) for n-0 to 10 n = 1 10 (2 r|)" " (2 n)t The ion loss cross section for the parent is olp = op - ocidp olp ■ 3.17* 10 1 * The collisional activation cross section for the parent is ocap = qc‘d- ocap * 1.075* 10 13 ‘- ri The sum of the ion loss and the collisional activation cross section is the total cross section for the parent otp = olp + ocap otp *4.245*10 The ion loss cross section for the fragment is olf = of - ocidf olf * 2.438* lO-15 Use Kim theory to determine multiple collision probabilities s is the ratio of the ion loss and the total cross section for the parent s = otp ..i \ -1-1 Calculate alpha and beta a = 1 _ oc*p a -0.59491 otp olp otp otpp. 1 olp \ otp m is an index for the number of collisions m = 0 .9 The A matrix is initialized by defining Am, i =0 Use Recursion Relation to calculate A(n) at each P(i) K)' 1+1 V i ■=«p(Pi) - 1 A.1.' . = a A. 0,i .- (“ Pi) V i =aAi,.- (1 + I?)! 5+ 1 <+ I (“•Pi) (“ Pi) \ i = aV r (2 + 1!)! Vi raA3,. (3+1!)! = a A, - (4+1!)! 5+1 ,6+1 (“ Pi) KC \7 + 1 A* . =a A, ---- : a A (“Pi) 3,1 (5+1!)' V i 6J (6+1!)! V i =“Vi (7 + 1!)! 9+ 1 A . =a-A, -i— ------ML (8 + 1!)! (9+ 1!)! Calculate the probability of detecting a fragment ion alter 1 ,2 .3 ,4 collisions 1 collision lfp, . =acxp(-otpp. 1) [[(rfl- r,) A0 .]] 2 collision Ifp2 . =a-exp(-ctp-p.-^[[(r, - rJ-A^.]] 3 collision “V i =a-exp(-otp-Pi-l).[[(r2- r J - A ,.] ] 4 collision Ilp4 . =oexp(-otpp. l) [ [ ( r ,- r 4) A, .]] Calculate the parent attenuation p. = exp[(-p). op l] Calculate the ion loss lp. = exp[(-p). olp l] Calculate the probability of a parent ion suffering 1 collision and being detected IpU =r, * «q>(-|k o*p l) (pj «p l) The probability of detecting an ion (either parent or fragment) after 1 collision is It, . = Ip, . + lip, . i , i r i , i 2 collisions (PiOtpl)2 Ip2 . =r2 s exp[(-p).otpl] ^ It2 . =Ip2 . + Ifp2 . 3 collisions . 3 r, , _ .1 (p;®^1) IPj . -r3 s -exp[(-p). otp I] . ± — L ^ -_lp3i+]fp3i 4 collisions . 4 r, . .1 (Pj ^P'*) p 4,i =r4s exp[(-p).otpl] - It4 . =Ip4>. + lfp4>. Calculate the total fragment ion current (sum of the fragments) Calculate the total ion current (sum of the fragments and unattenuated parent) ITi = Output the data B =p. WRJTEPRN(rlh7datj =B 1,0 r i B >*l . = Mp. 1.1 B. , =Ifp_ . WRITEPRN(r2h7 ^ =B B 1,0n =P 1,1 2,1 B. , =T. WRITEPRN(tlh7 ^ =B B 1,0A =P r i 1,1 1 WRITEPRN(plh7dal) =B B ».0 =P M B ».l, =IP, r l,i WRITEPRN(p2h7da() =B B.i,0 A " riP BU = **.. WRITEPRN(pth7 ^ =B B 1,0„ =P ri Bi,l =,P2.i+IP|.i 0.1 o.oa * 2 .t 0 06 0.02 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.1 0.9 Pi o.ot 0.06 0.04 l,i 0.02 0 20 40 60 •0 too 120 140 1(0 iao 200 i 170 N5NOCL.MCD Calculation of the Individual Ion Solvation Free Energies Free Energy to place a pair of oppositely charged ions into water (H30+ and the -944.7 945.2 larger halides have been left out) i =0.3 -844.7 -845.2 H - 771.1 -771.5 j =0.1 749.8 -750.2 pick an absolute value for Na+ 0 -100 0 0 mepos = mepos, = - 425.8 posdel = mepos. = mepos ] + posdel. mepos. 0 736 5258 0 94.9 425.8 352.2 330.9 0 meneg meneg0 = H, 0 - mepos, negdel = meneg. = menegQ +- negdel meneg, .5 menegQ *-418.9 418.9 419.4 Hme. ^ = mepos. +■ meneg. -944.7 -945.2 -844.7 -845.2 Hme -771.1 -771.6 -749 8 -750.3 (mepos. - mcnegj Hme. *.j mepos. + meneg. Now for the cluster data .1967 .1791 0 113 0.113 .0380 .0198 0.008 0008 HnS = Hme * .1327 .1505 -0.086 -0.087 .2169 -.2343 -0.117 -0.118 171 scaling 3 1 3 1 ___ sumn3 = Z Z Ji1™iJ2 suramc= Z Z J i ^ J 7 i “ 0 j “ 0 i “ 0 j “ 0 «umn3 * 1.168 summc * 0.65 sumn3 sumn3 * 1.796 s ------summc sumine HnS. Hme. . - of = of “ 0.009332 -J2^ ofof“ *0.013 0( uncertainty in Na+ solvation enthalpy calculate Hme for +delta case 8 = 1 0 100 0 0 mepos mepos, =- 419.5 ■+■ 6 posdel = Rmepos. = mepos j +■ posdel. mepos. 0 73 7 519.4 0 , 95 0 , -419.4 345.7 0 0 - 324 4 0 23 meneg 0 menegQ = H, 0 - mepos, negdel = 164 meneg. = menegQ -t- negdel menei 0 menegp * -425.3 198 425.3 0 235 - 402.3 (mepos. - meneg.) mepos. + meneg. 0.1 0.127 -0.007 0.021 Hmep -0.103 -0.076 -0.135 -0.107 172 calculate Hme for +delta case 0 -109.6 0 0 mepos - mepos, = - 466.S - 5posdel = inepos. = mepos, + posdel. mepos. 0 85.2 576.2 0 108.6 -466.6 381.4 0 0 358 0 226 meneg 0 menegQ = H, 0 - mepos, negdel - 164 meneg. - menegQ +- negdel menei 0 menegQ --378 1 198 -378.1 0 235 355 5 ^mepos. - meneg. J Hmen . •-J mepos. + meneg. 0.208 0.237 0.105 0.135 Hmen 0.004 0 035 -0.027 0.004 Hmep. . Hmen. . 3 1 y A - 0 751 £ £ 2 8 i - 0 j « 0 oH = — of oH-0.011 *Ja 173 k =0. 11 V= °k 370 .1352 390 .0858 400 .0617 o.t 410 .0380 420 .0163 424 .0108 426 .0101 ®k 428 .0116 430 .0146 0.0) 440 0358 450 l0591 / / 480 .1472 A. -4«0-460 -440 -420 -400 -3to -360 \ Comparison of my data and Fridman's to Bulk Fpos_ = Fneg. Hme. ^ = mepos. + meneg. ■ 558.6 423 4 H p = Fpos +. Fneg. 443.9 -474 0 '.j J 360.2 340.2 - 338.9 325.9 268.2 I ! E i - 0 j - 0 ______ome ome ■ 13.554188 ome 20 >9.584 E E (»f, (- ^ ) 3 i» 0 j - 0______oF 20 o F - 33 91252 ® L .23 98 Appendix C Related Publications 174 Th« Importance of high Impact parameter Interactions In the collision Induced diesodetion of protonated water dueters by argon using a Wien velocity fitter Kurtngth A. Cowan, Bob Plastndpo. Duron A. Wood, and damns V. Coa D^artmtm t f Ckemuiry, T%t OUvSlM r U m m na j . CWvmSuX. Otuc 43HO-31T3 (Received 10 February 1993; accepted 30 May 1993) High impact parameter, i.*., glanrfag w S w a t, are of particular interest in ion beam tipenmenU because ions experiencing such collisions ramain available fa tbe ion beam Tor further experiments Tbe mllnional activation and dissociation processes far glancing colliaions of protonated water clusters and argon have been studied with a new and simple, single-stage technique to detect fragment ions aaiag a Wien velocity filter Tbe technique is specific with regard to the mass of a fragment ion and the mass of the parent from which it originates A relation is derived and ex penmen tally verified which governs the operation of the device Absolute values of tbe attenuation crass section with argon of 11(6), 33(1). 3601). 47(17). and 66( 10) A have been determined far HjO*. H jO ?, H,Oj+ , H /),’ , and H1tO,*. respectively, at beam energies in the range of 300-1000 eV Absolute values of the glancing collision induced dissociation cross section of 0 62(4), 4.3(1), and 9.1(6) A3 have been determined for the detectable fragment ions of H .O f, HiOj*, and H*0, , respectively Branching ratios upon activation by glancing collisions of 091.009:0 and 0.710.110.040 have been determined for successive loss of waters by H-Oy and K^O,". respectively. The ooe water loss channel pre dominates. A multiple collision analysis was performed which characterises the fraction of parent ions which suffer a glancing callisioo without dissociating or being knocked out of tbe beam. Our results suggest that the ion beam which emerges from a colbtioo cell can harbor a surprisingly large fraction of parent ions that have obtained a large amount of interna! excita tion, perhaps -0.7 cV per ion suffering a glancing oolhttrw INTRODUCTION sections and fragmentation branching ratios. These studies by Dawson were accomplished with a triple quadrupoic at In general, protonated water clusters, H *(H jO ),, baam energies of about IS eV. Dawson’s experiment does can be characterized as hydrated hydronium,' not distinguish between high and low impact parameter H ]0*(H y0),. |, with the exception of s v 3 which is oolKsfont because essentially all lost parent fans are recov thought to be s proton symmetrically bound between two ered in the form of fragment ions. In fast ion baam exper water molecules IJ Considering that even pure water is iments, only high impact parameter coUmom result fa de partially ionized, it is not surprising that hydrated hydro tectable signal due to the inherently small beam angles of nium is fairly pervasive in nature * These dusters are the such systems. We label these detectable, high impact pa prominent ion of any type at 75 km in the D region of the ionosphere4 and they are "end-of-the-food-chain" ions in rameter collisions as glancing- Colhsaon induced dissocia tion of strongly bound molecules is generally assumed to be the ion-molecule chemistry of that region. Hydrated by- dronium dusters can also serve as staple aquaoua models dominated by low impact parameter collisiosw, but the sit for the study of proton solvation uation is different far weakly bound dusters. We were sur The observation of collision induced dissociation prised, fa the case of the largest duster, by the fraction of (CID) fragment ions at the end of as ion beam hne ts quite tbe total attenuation cross section which could be ac interesting because it indicates that a dissociating collision counted far by glancing colInfant The present data and transferred enough energy to dissociate a parent fan, but Dawson’s results are used together to constrain the many not enough momentum to knock the fragment fan out of pa renters of a mahiplt colhrion analysts,1*" which is the fan beam Thsac dtmociative interactions must be used to dettrmine the fraction of parent fans experiencing glancing, low angle scattering high impact parameter col- |innnfaa| ooQjiiaai (ftftd therefore iMtiBil octtttsoa) btfoos. Glancing collisfona are of particular interest be without dissociating or being knocked out of the ion baam cause the exdtad fans (whether Augment or parent) re Our results suggest that the fan baam which rmrrgss from main fa the fan baam for use in hut her experiments We a mllisfand cdl can harbor a surprisingly large fraction of have haen primarily concerned with determining the de parent fans with a large degree of fatenfal excitation (in pendence of colbsfonel activation dynanuca on duster size. this case —0.7 eV per ion suffering s glancing collision) It There have been several previous studfas*-* of eoOi- has hacomt evident that attenuated parent ion beams could siona] fragmentation of HjCM HjO)., however we have be used to ascertain the effect of internal excitation m ion found only one* which reports absolute attenuation cross beam experiments. 34S0 J Chern Phy* SO |S|. i Same"**- ’ SS3 0O}I S6Oe'S3/S»4t)/y*aO/t/SeaO f 1SS3 American MckMt ot Pnyecs 176 Cowan at at. i et amtwwited water duels'* The present experimental configuration it M ■traded A simple equation (Eq. (3)) hat i derived and ex- at » replacement far multisector H d a i p i such w the penmen tally demonstrated which the poeitioe of a much-used arrangement of a coibtioa oafl h m a a B E fragment ion ( Fwr A to that of a p ■t ion ( in a geometry mint a hi|h (k*V.) baam energy.11'” Thar stud Wien filter velocity spectrum. If a occurs in ies were motivated by a long range mteratl hi far develop the drift region tube before the Wi fa n , the fragment ment of high signaJ-lo-noite techniques far A M h | frag ion velocity, ly, will be the tame as i panwt fan velocity. ment Kioa in spectroscopic experiments « M eantfaoous wave laaen wing nearly spaee-chargc b a r d ion —‘—: lie*. A Wien velocity Utcr11 it one of the n p iaat of de- J2g( rf- fun) ty-iy ( 2 ) vicet mad to separate different Bat* tom. Whir the nao- T lution it not very good, the transmission, m n range. and ion optical quality of the transmitted beam an q n u good where mf it the mass of the parent km, Vt it the voltage Therefore, Wien velocity th e n often tad aae in experi applied to tbe ion source, and it the voltage applied to ment! where matt tpectromctry it not an mi in itself the drift region tube The present nee of vnhtges relative to often experiments where ttgnal b at a I*™ 1*" A simple ground requires one to use the appropriate rign for q when modification it dctcribed which allows a Wien filler to de dealing with positive or negative ions. Since the parent and tect fragment ioni in a tingle nage of analyse. Application fragment ions have the tame velocity but different mass, of a voltage to a tube in front of the Wien filter it all that they can not have the tame beam energy (kinetic energy) it necettary to enable the device to detect fragments with Substituting the relation for vf of Eq. (21 into the relation specificity to the matt of both the fragment and parent ion for kinetic energy of the fragment ion gives for dissociations which occur within the tube. I , mj (»