R. J. Campbell Lighting Research Laboratory General Electric Co. Neia Park Cleveland, Ohio 441 12
I
II
Gas Phase Energy Transfer Processes
Although much literature and several excellent hooks have been published on gas phase energy transfer processes (1-6), the subject is ignored in most standard curricula for either the beginning or advanced student of physical chemistry. This isunfortunate since an understanding of gas phase energy transfer and the types of processes that occur is essential to the understanding of a broad range of chemical problems, such as the study of flames, electric discharges, or even lasers. The fundamental processes of vital importance in determining the overall macroscopic changes are the collisions which occur among the atoms, molecules, ions, and electrons present in the gas. The physical understanding of these collisions can be based on models which utilize the basic principles of several disciplines included in physical chemistry, including quantum mechanics, statistical mechanics, chemical kinetics, spectroscopy, and thermodynamics. The purpose of this article therefore will he to present the basic model or point of view which is used to classify the types of energy transfer processes and a few examples that will illustrate the various types of energy transfer. The intention will be to give the student, at all levels of physical chemistry, some idea of the relative probability of the various kinds of energy transfer processes. The emphasis will he entirely on the measurement of actual collisional energy transfer efficiencies, rather than on a discussion of the very complex nature of the individual collisions themselves. No effort therefore will be made to go into the details of interpreting the experimental results beyond what is necessary to understand the basic principles, nor will there he any attempt to give an exhaustive listing of all the recent work on microscopic energy transfer processes. What is hoped is that a selective review of recent work should provide a very good illustration of the specific types of energy transfer which occur.
Table 1.
Chart Indicating Ten Different Types of Energy Transfer Pracesses Trans.
Translational Rotational Vibrational Electronic
Rot.
Vib.
(3)
(6) (6)
(8)
(4)
(71
(9)
Elec.
(1) (2)
(101
In general, energy transfer processes will occur via a very complicated combination of these energy transfer processes. It will therefore be convenient to limit ourselves to the specific process symbolized in reaction (I), where we have restricted ourselves to nonreactive intennolecular energy transfer processes between neutral species. Molecule (or atom) A undergoes a collision with molecule (or atom) B which has excitation energy, denoted by the asterisk, which is transferred to A as a result of the interaction, without any overall chemical changes occurring. I t should be clear that the advantage of studying gas phase systems is that individual interactions between pairs of atoms or molecules can he isolated as implied by eqn. (1). Relaxation Measurements
One of the most extensively used techniques for studying energy transfer has been the absorption and dispersion of ultrasonic waves (7). The velocity of a sound wave through a gas is given by
Outline o f the M o d e l
The basic assumption which will he used is that all the energy which is available for gas phase energy transfer must he stored as translational, rotational, vibrational, or electronic energy. Although it is of course not strictly correct to speak of these modes as being independent, it would not he germane to this discussion to worry about this distinction. What is imnortant to realize is that with these four kinds of energy storage in a gas, there are ten possible types energy transfer processes among these four modes, as shown in Table 1. This review was initiated st Northwestern University, Evitnston, Illinois.
156 / Journal o f Chemical Education
where R is the universal gas constant, T is the temperature, M is the molecular weight, and C , is the heat capacity of the gas. It can he seen from this relation that the rate of energy transfer through a gas has an inverse dependence on the effective heat capacity of the gas. If the period of the sound wave is long enough for equilibrium to he established between all modes, then the heat capacity will be given by Cv = Gel...
+ Grot + Cvlb
where Ct,.,, Grot, and Cvlbare the translational, rotational, and vibrational heat capacities, respectivelv. If the period between waves is'gradudly decreased, a point is reached at which energy cannot he transferred in and out of the vibrational modes rapidly enough to
maintain equilibrium. If the velocity of the sound wave is measured as a function of its period, an inflection will be observed in this region. Thus, the period of the wave at this point is a measure of the vibrational relaxation time of the gas which is in turn a measure of the efficiency of translational-vibrational energy transfer during the molecular collisions. If the period is decreased still further, the translational-rotational energy transfer efficiencies can also be measured in a similar manner. Although these experiments measure r e laxation times, the time required for a particular mode to return to equilibrium, it will be convenient in this discussion to speak of a collision number, 2, which is defmed as the number of collisions required for a particular energy transfer process to occur. These two quantities can be related by using the kinetic theory of gases to compute collision rates for the system of interest. Another device which has been particularly well suited for studying the same types of energy transfer is the shock tube (8). This device basically involves producing a plane shock wave in a long tube and observing the shock front as it passes down the tube. Very high temperatures are produced, 1000-5000°R, within the front; and thus the various internal modes will be produced in much higher energy distributions than typical room temperature distributions. By measuring the relaxation times, ameasure of the relative efficiency of the various energy transfer processes can be obtained. It turns out that because of the very wide range in efficiencyfor the various processes, energy distributions are produced in each mode which are not necessarily in equilibrium with each other. Thus, since there may be very efficient transfer within a particular mode, a lLlaxwel1 Boltzmann distribution may be quickly established which can be characterized by a unique temperature. However, transfer of this energy into another mode may require several hundred or several hundred thousand collisions per molecule, and thus this other mode may be characterized by another temperature. This means that in general we may be able to speak of four temperatures for a gas, one for each mode. In practice we will usually observe less than this since the relaxation of these modes may be too fast for us to detect dierent temperatures forkach mode. The results in Table 2 indicate the collision numbers obtained for the transfer of translational-rotational enerev for various airs of collidina wartners, and ~ a b i3l gives some iypical results for (he transfer of vibration to translation.
Table 3.
Typical Vibrational Collision Numbers for Nitrogen, Oxygen, and Chlorine-
Vibrational frequency (em-') Z at 300°K Z rtt 1000DK
2330 -10~0 4 X 10'
1556 645 2 x 10' 4 x lo4 5 X 10" 400
'Taken from Rsf. (IS).
The most important point to note in these results is the order of magnitude of the results shown for each of the two processes. For rotational-translational transfer from 4 to 300 collisions are required for the transfer of one quantum of rotational energy, whereas translation-vibrational transfer may require up to a billion collisions per vibrational quantum transferred. These numbers demonstrate the single most important criterion for determining energy transfer efficiencies: energy matching between the donor and acceptor molecules must be very good in order for efficient transfer to occur. This accounts for the large differences between rotational and vibrational energy transfer collisions numbers as well as the differencesbetween HI and 0 2 or NPfor rotational energy transfer. Hydrogen has a much smaller moment of inertia and thus considerably larger energy separations than oxygen or nitrogen. Similarly there is an even more pronounced dierence between Nl, 02,and CIZfor vibrational energy transfer which can be related to the very large differences in the size of the vibrational quanta. Likewise at much higher translational energies, -100O0K, the efficiency of vibrational-translational transfer is considerably enhanced. It, of course, can be safely assumed that translationaltranslational transfer can occur on every collision. The major disadvantage of these two techniques is that the relaxation times are very sensitive to impurities. For instance, a t 2500°K 27, water vapor added to nitrogen will reduce the translational-vibrational relaxation times by a factor of two (8). The reason for this is probably related to an energy matchmg between the colliding partners which permits efficient transfer between the vibrational mode of nitrogen and the modes of water. Examples of vibrational-vibrational energy transfer will be considered in more detail later. The impurity problem is particularly acute in all of these studies and has been blamed for the differences in the data obtained in dierent laboratories. Rotational Energy Transfer Processes
Table 2. Typical Rotational Collision Numbers for Nitrogen, Oxygen, and Hydrogen, at R w m Temperature Molecule
-Techni Ultresonic
ue----8hock Tube
Ref.
Thus far the discussion has been primarily restricted to three of the various types of translational energy transfer, which are probably the most extensively studied of the various energy transfer processes. The situation for rotational energy transfer is a t the other extreme. Except for a few observations of anomalous collisional transfer efficiencies which have been attributed to rotational transfer processes (l7),detailed experimental data has been almost completely lacking until very recently. The d i c u l t y in measuring rotational transfer efficiencies is due to the d i c u l t y in identifying the rotational states before and after a colliVolume 45, Number 3, March 1968
/
157
sion. Such an identification can be made from vibration-rotation spectra; however, rotational energy transfer studies in which pure rotational state changes are observed is very limited indeed. Some elegant molecular beam experiments have been performed by Toennies in which specified rotational states were prepared and studied (6, 18, 19). A schematic outline of the apparatus is shown in Figure 1. The source provides a
I
THERMAL BEAM 0'4,EN
I
Table 4. Rotational Energy Transfer Collision Cross Sections of TIF with Various Types of Collision Partners* Collision Partner
6%) Collision Partner
He 3.7 Ne 4.6 Ar 6.1 KI 6.4 Non-Polar H, 19.4 0% 7 . 8 cule A;, 22fi
Atom
(5) --
~
Spherical Top
CH, 6.3 SFs 6.8 Polar Molecule NO 80.0 Asymmetric Top H.0 70.0 CFZCIZ 115.0 Symmetric Top N& 500.0
MECHANICAL
I
ELECTROSTATIC ROTATIONAL STATE SELECTOR
SCATTERING CHAMBER
polar molecules can substantially increase the effective collision cross section, and thus enhance the probability of rotational energy transfer. Since the sensitivity of the apparatus does not permit crossing two rotationally selected beams, it is difficult to determine which of the different possible types of rotational energy transfer dominate in a particular system. Fluorescence Techniques
I
ELECTROSTATIC ROTATIONAL STATE ANALYZER
BEAM DETECTOR
Figure 1.
Block di0gr.m of molecular beam oppardur
beam of atoms or molecules from which particular rotational states may be selected by a velocity selector and a rotational state selector. This beam is then scattered by the target atoms or molecules, and the product states are with another rotational state selector ~~- then analvzed ~" and a Langmuir-Taylor detector. The rotational state selector consists of four symmetrically positioned cylindrical rods which act as a electrostatic quadrupole focusing lens. The molecules experience a harmonic force toward the axis of the four rods that is determined by its particular rotational state. Since the radial force is quite small the field produced by the four rods must be quite long, approximately one meter, and is limited to beams of thermal energies. Because of the limitations of the detector the technique is limited to studies of either ( a ) HP,D2, or hydrogen containing molecules in collision with alkali atoms or (b) polar molecules containing an alkali atom (or TI) with no restrictions on the colliding partner. Some typical results are shown in Table 4 for collisions of TlF with various collision partners. The units reported should be compared with typical gas Emetic cross sections in which the moJecules are thought of as hard spheres with rr E 20-30 A2. It can be seen that nonpolar molecules require from 1to 10 collisions with TIF for transfer of rotational energy, whereas the polar molecules have cross sections which are much larger than typical "billiard ball" values. This indicates that the long-range forces between two ~
~
~
~
158 / Journal of Chemical Education
Thus far we have been mainly concerned with translational and rotational energy transfer processes. NOW we shall consider the results of fluorescence measurements for which considerable information has been obtained on vibrational energy transfer processes. If a molecule is excited to an excited electronic state, it can then undergo a number of different energy transfer processes. It can release the energy as radiation by a spontaneous emission process with the rate governed by the Einstein coefficient of spontaneous emission. Since it will in general be produced initially in excited vibrational and rotational levels, it can also undergo collisions which remove only vibrational or rotational energy still leaving it in its excited electronic state. If it then undergoes a spontaneous transition to the ground electronic state, the emission will be at a different wavelength due to the radiationless loss of energy as well as due to the Frank-Condon factors. By varying the effective collision rate (i.e., inert gas pressure) and photographing the emission spectrum under different conditions, the collisional energy transfer processes can be analyzed. Although the detailed analysis is much more complicated than suggested above, the energy transfer processes for NO in its excited electronic state, denoted by A2Z+ (v = 1, 2, 3, . . .), have been determined with Nz as the collision partner (16). The results presented in Table 5 refer to the type of process indicated by NO A ' z + (v' = 3)
+ N* ( v = 0)
-t
NO A q " '
=
2)
+ N,("
=
1) ( 2 )
where nitric oxide has been deactivated from the third to the second vibrational level and nitrogen has been excited to the first vibrational level of the ground electronic state. The subscripts to the collision number in Table 5 correspond to the vibrational transitions observed for NO AZZ+and N,,respectively. The number of collisions required for vibrational-vibrational energy transfer is much less in this case than that required for
Table 5.
Vibratianal Collision Numbers for the the N O Excited State (A%+).
Table 7. Electronic, Vibratianal, and Rotational Collision Numbers for Various Gases with the Excited Iodine Molecules 1/20
Gas
vibrational-translational transfer. The extremely close matching of vibrational energy spacing for NO A%+ (2371 cm-I) and N2 (2359 cm-') is responsible for this very efficient transfer. It was also shown in these studies that other molecules with a much less favorable matching of energy levels can require more than an order of magnitude more collisions than N2. It should be emphasized that these results refer to energy transfer efficiencies of NO in its excited electronic state. Energy transfer has also been measured by a flash photolytic technique in which NO is produced in excited vibrational levels of the ground electronic state. Relaxation from these excited vibrational levels is then followed with absorption spectrophotometry. Some typical results are shown in Table 6.
Table 6. Vibrational Collision numbers for the N O Ground Stote (X2n)m Molecule N O (X2s) Nz CO HsO Kr
Frequency (em-') -
&-o
2.82 2.5 4.0 1.4
X X X X
>
10P 10' 10" 10' 108
1876
2330 2143 1595
...
Also included in this table are the vibrational energies of the various colliding partners. I t has been suggested that some of these relatively large transfer efficiencies are due to the formation of a collision complex which can permit much more efficient transfer of vibrational energy than a simple physical model would indicate. Thus it is probably not strictly correct to speak of these processes as nonreactive collisions since we have produced species which may have lifetimes (lo4 sec ?) sufficient to be called chemical entities. These results, nevertheless, illustrate another factor, chemical affinity between the colliding partners, which is important in determining the probability of collisional energy transfer processes. Recently a very detailed analysis of the iodine fluorescence in the presence of several d i e r e n t deactivating gases has been performed in which the iodine has been excited to the V' = 25, J' = 34 level of the excited electronic state B37r.,+ ($0). It is very tempting to get into a very detailed discussion of some of the points raised in this work, however, an effort will be made to restrict ourselves only to a very general description of the system and the conclusions reached on several points. The iodine molecule was produced in its excited
1/Z,
1/Zn
'Reference (90).
electronic state with precisely defined vibrational aud rotational excitation from which it was then observed to undergo three types of collisional transfer processes for which collision numbers were obtained. The eollision numbers given in Table 7 refer to direct electronic quenching, Z,, such that fluorescence was completely quenched; vibrational energy transfer to the V = 23, 24, 26, or 27 levels from which fluorescence was then observed, Z,; and rotational energy transfer from the J = 34 level to levels corresponding to transfer of up to 50 units of rotational energy, Z X . I t should be noted that collisional energy transfer efficiencies are much larger in this system forvibrational energy transfer than what we observed previously. This can be accounted for by the very much narrower vibrational energy spacing, -80 em-', compared to the vibrational spacing previously considered. It was established from the results in Table 7 that there is a rough correspondence between quenching efficiency and polarizability of the colliding partner, although it has also been suggested that the formation of transient intermediates may play a role in the quenching mechanism. The vibrational energy transfer appeared to be most efficientwhen the collision time of the colliding partners just matched the period of a vibrational oscillation, but this conclusion may have been due to a fortuitous combination of the competing transfer processes. A fuller discussion of this point would require a deeper understanding of the theoretical interpretation of translational-vibrational energy transfer processes than is appropriate in this review. Needless to say, there is a large active interest in understanding these processes more fully. The rotational energy transfer efficiencies agree with the conclusion of Toennies quoted earlier that long range forces are significant in determining rotational energy transfer, even though the collision is in this case with the nonpolar 12. I t was also indicated in these studies (although it is not shown in Table 7) that the size of the rotational energy jump is a function of the size of the vibrational energy transfer jump. The two fluorescence systems already discussed involve fluorescence emission of excited electronic states. It would appear that measurement of vibrational euergy transfer processes would be possible by studying the fluorescence from excited vibrational states, i.e., IR Volume 45, Number 3, March 1968
/
159
emission. Unfortunately there is a fundamental handicap which has made these studies especially difficult. In order to observe emission one must depend on the spontaneous emission rate from the excited state which is inversely proportional to the cube of the frequency. For UV or visible emission this corresponds to fluorescent lifetimes of the order of 10-810-9 sec. Smce typical intervals between collisions can be varied conveniently over this range the experiments can easily he designed to measure the rates of competitive energy deactivating collisional and fluorescent decay processes. For I R emission, the spontaneous rates correspond to vibrational level lifetimes which are of the order of several milliseconds. This means that a molecule produced in an excited vibrational level will undergo several thousand collisions before it is likely to undergo radiative emission. Therefore, even though these deactivating processes may be very slow on an individual collision basis, they can still dominate the kinetics and prevent I R emission. Reducing the pressure in order to reduce the collision rate also has the disadvantage of reducing the total I R intensity, and thus the lowest pressures are limited by the sensitivity of the detectors. I n spite of these difficulties I R emission studies have been performed on several systems. The reaction of H atoms with CL molecules produces HC1 in vibrationally excited states which have been identified by analysis of the IR emission of HC1 (21). I n addition to the information obtained on the energy transfer efficiencies, considerable information has been obtained on the distribution of energy in the products of a chemical reaction. Another less complicated system which has yielded interesting vibrational-vibrational energy transfer results involves the I R excitation of carbon monoxide immersed in a flowing stream of inert gas to which a known small trace of deactivating gas has been added (22). The CO is produced in its first excited vibrational level ( u = 2143 em-') by the emission from a CHcO1 flame, and the subsequent emission from CO is measured. Results for the transfer of vibrational energy to various colliding partners is shown in Table 8. Note that in
Table 8. Vibrational Collision Numbers for Carbon Monoxide for Various Collision Partnersa
Colliding Psxtner
all cases except for Oz the experimental results are much less than the calculated theoretical values which have been included for comparison (23, 24). The high efficiency of O2 has been attributed to chemical affinity between Ozand CO. Thus, as with NO and 12,the formation of transient "chemical intermediates" can considerably enhance transfer efficiency. 160
/
Journal of Chemical Education
Vibration-vibration transfer from CO has also been observed by measuring the collisional quenching rate of methane with the vihrationally excited CO (26). It was determined that on the average 33,000 collisions are required to transfer one quantum of vibrational energy to methane. The significantly lower efficiency for transfer in this case compared with the NO-N2 transfer cited earlier can be attributed to a much worse matching of vibrational energy spacing for the collidmg partners. The closest methane vibrational level available for accepting the energy is at 1526 em-' which means that the difference in energy, 617 em-', must be converted into relative motion of the separating partners, a process we already know to be much less efficient. I n fact, efforts to correlate the transfer efficiency with the energy match have indicated that the 33,000 collisions required are much less than might have been expected on an energy matching basis. This again has been attributed to an enhancement due to the chemical affinity between the colliding partners. The one last example of vibrational energy which ought to be mentioned is the transfer of large amounts of energy from highly excited polyatomic molecules. It is well known that virtually every collision can be effective in removing vibrational energy with up to 20 kcal per mole of collisions in some cases (26). Since there are many oscillators in a large molecule, the number of energy levels a t high energy is very large, and thus there is always bound to be efficient matching between collidmg partners even when the vibrational energy is converted into translational energy. Efforts to elucidate the nature of these energy transfer processes have been many and are still underway. With the possibility of unit efficiency collisional energy transfer processes, it is easy to see why the effect of very small traces of impurities can be so large. I n many cases the transfer process being studied may be several orders of magnitude less efficient than that of an impurity. This means that exceptionally pure gases must be used to eliminate these unwanted effects. Electronic Energy Transfer
Thus far we have covered six of the ten possible types of energy transfer processes, with only transfer of electronic energy yet to be considered. As with other types of energy transfer, there is an abundance of information available on certain types of electronic energy transfer with almost a complete void in other areas. I n particular, electronic-electronic energy transfer has been worthy of many treatises and is still very actively investigated. I n contrast electronic-rotational energy transfer is possible only via fragmentation of an excited molecular species due to angular momentum conservation. Transfer of pure electronic-translational and electronic-vibrational energy must also be considered unlikely due to a very bad matching of energy levels and is therefore limited to special cases. I n fact the only examples of pure electronic-translational energy transfer have been observed when this energy requirement is met (27-29). This occurs for the spin orbit relaxation of various species for which the separation of Russell-Saunders states is not very large. The results in Figure 2 refer to the collision-induced ZPs,, 2P~l,transitions of the alkali atoms for which it can be seen that the efficiency decreases with increasing separa-
+
An example of the reverse process, the conversion of electronic excitation into vibrational excitation, has been studied in detail recently (34). It was found that for the process: Hga
+ CO
-
Hg
+ Cot
(6)
a large fraction, up to 477& of the original electronic excitation energy, was converted into vibrational excitation of the carbon monoxide from which I R emission was then observed. The results have indicated that the formation of a stable chemical intermediate, HgCO*, is probably involved. The one remaining type of energy transfer which has not yet been discussed is that of electronic-electronic transfer. The first known example was reported by Wood (56) in 1923 for the process:
-
Figure 2. The relationship between the crass sections On(%/, 'Palrl and the energy defect AE for collirions between olkoii atom. of like specie,.
(Adapted from ref. 1291.1
tion of the two electronic states. The first example of this type of energy transfer was reported fifty years ago for sodium by Wood (SO). I n this case transfer of energy has been found to occur on every collision due to a separation of only 17 cm-I between the electronic states. Transfer of vibrational energy into electronic energy was first observed by M. Polanyi (31) for the reactions
+
- -+
C1 Nan NaCl* Na NaCI* Na(lS) NaCl
+
+ 70 kcd
+ Na('P)
(3) (4)
NaCl was initially produced with large vibrational excitation which was found to be converted via collision into electronic excitation of the Na from which the familiar yellow D lines were emitted. Evidence that the Na(=P) was produced by reaction (4) rather than directly in reaction (3) was interpreted from the fact that the emission could be quenched by inert gases with an efficiency much greater than could be accounted for by collisional deactivation of the Na(=P) itself (58). Vibrational deactivation of NaCl* by collision would prevent the formation of the electronically excited sodium. It now appears, however, that reaction (4) may occur by an exchange of the alkali metal atom, sodium, and therefore is, in fact, a reactive collision process. This is based on recent molecular beam experiments (33) in which it was demonstrated that the following reaction occurred: KXtfNa-NaX+K*
(5)
where the dagger refers to vibrational excitation, and the asterisk to electronic excitation, and X is an halogen atom. I t has been found that the electronic energy distribution of sodium introduced into flames or shock tubes very closely follows the vibrational temperature, indicating relatively efficient vibrational-electronic transfer in these cases. This has proved to be a very useful tool for measuring the vibrational relaxation of gases in such systems (8).
By s h i i g a mercury lamp on the T1 vapor no fluorescence a t a T1 wavelength was observed unless the Hg vapor was also added, indicating that the mercury must first absorb the radiation and then transfer it by collision to T1 from which the emission is observed. Examples of this type of gas phase energy transfer are virtually unlimited. S f i c e it to say that this process is extremely common and can he found to occur in all types of systems with all ranges in efficiency. A special type of photochemistry, known as photosensitization, relies on this process for the excitation step rather than direct absorption. Excited species can sometimes be produced in much larger yields than would otherwise he possible, if the acceptor molecule does not absorb in a given region where the donor molecule does. For example, the mercury atom is pised to an excited triplet state by absorption at 2537 A and will therefore produce excited triplet electronic states upon collision with another molecule. Since the direct transition from the ground singlet to the lowest excited triplet is optically forbidden, "mercury photosensitization" has proved to be an extremely useful technique for studying the chemistry of excited triplets (36, 37). Summary
It is hoped that this rather general review has succeeded in giving examples of the various types of energy transfer without getting lost in unnecessary detail. It should be emphasized a t this point that the systems discussed are actually much simpler in terms of the number of energy transfer processes occurring simultaneously than what might be observed in a typical chemical system. Much ingenuity has been demonstrated in the choice of systems to study as well as in the techuiques used in order that the various energy transfer processes may he isolated and studied independently. The examples given were chosen because of the extent to which this goal was achieved. Acknowledgment
I would like t o thank E. W. Schlag for originally suggesting writing this review and E. G. Zubler and W.E. Smyser for their helpful comments on the manuscript. Volume 45, Number 3, Morch 1968
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161
Literature Cited (1) COTTRELL,3. T., AND MCCOUBREY, J. C., "M~leculnr Energy Transfer in Gases," Butterworth, London, 1961,-J. O., CURTISS,C. F., AND BIRD, R. B., (2) HIRSCHFELDER, "Molecular Theory of Gases and Liquids," John Wiley & Sons, Inc., New York, 1954, (3) KONDRATIEV, V. N., "Chemical Kinetics of Gas Reactions" (translation: CRABTREE, 3. J., AND C~RRUTAERS, S. N.), Addison-Wesley Publishing Co., Inc., Reading, Mass., 1964, (4) "Energy Transfer in Gases," Solvay Institute, 12th Chemistry Conference, Interscience Publishers (division of John Wiley & Sons, Inc.), New York, 1962, (5) Discussions of the Faraday Society, 33 (1962). "Inelastic Collisions of Atoms and Simple Molecules!' (6) LAIDLER, K. J., ''The Chemical Kinetics of Excited States," Oxford University Press, New York, 1955, (7) HERZFELD, K. F., AND LITOYITZ,T. A., "Absorption and Dispersion of Ultrasonic Waves," Academic Press, Inc., New York, 1959, (8) GAYDON, A. G., AND HURLE,I. R., "The Shock Tube in High Temperature Chemical Physics," Reinhold Publishers, New York, 1963. M., J . Awu8t. Sac. Am., 31,155 (1959). (9) GREENSPAN, (10) GREENE,E. F., COWAN, G. R., AND HORNING, D. F., J . Chem. Phys., 90, 427 (1951). (11) ANDERSEN, W. H., AND HORNIG,D. F., Molemla~Phys., 2, 49 (1959). 3. V., J. Acmat. SUC.Am., 30,297 (1958). (12) CONNOR, (13) GREENE,E. F., AND HORNIG,D. F., J . them. Phys., 21, 617 (1953). (14) VANITPERBEER, A., AND VERDIAELEN,R., Physics, 9, 345
- -- .
11947) \ * ,
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162
/
Journal of Chemical Education
(16) CALLEAR,A. B., Appl. Opt., Supplement 2: Chemical Lasers (1965). R. C., AND OSBWG,L. A,, J . Chem. Phys., 41, (17) MILLIKAN, 2196 (1964). . . (18) TOENNIES. J. P.. P~oc.Intern. Conf. Phvs. Eleotron. At. ~ o l l i s i o k 3 r d , ' ~ n i vColl. . ond don 1963; 1113 (1964). (19) TOENNIES, J. P., Z. Physik, 193.76-118 (1966); ibid., 182,
. ~.
257 11 9651 \--"",.
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. .
". .
767 (1QU1
(25) MILLIKAN, R. C., J. Chem. Phys., 43, 1439 (1965). B. S., AND FLOWEBS, M. C., Quarterly (26) RABINOVITCH, Rev., 18, 122 (1964). (27) PHELPS,A. V., Phys. Rev., 114, 1011 (1959). G. D.. KRAUSE.L.. AND BROCKMAN. I. H.. Can. (28) CRAPMAN.
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KARL, G., K R ~ U ~P.,, AND POLYANYI, J . C., J. Chem. Phys., 46, 224 (1967). CARIO,G., AND FRANCK, J., Z. Physik, 17,202 (1923). CVETANOVIC, R. J., "Progress in Reaction Kinetics," 2, Mscmillsn Company, New York, 1964. GUNNING, H. E., AND STRAUSZ, 0. P., Ad". PhofOchm., 1, 209 (1963).
