摘要:

GENERAL DISCUSSION Prof. K. J. Laidler (University of Ottawa) said: Prof. Herzfeld has made reference to our hypothesis 1 that transfer of energy does not readily occur between modes of different symmetry. It is important to emphasize that this suggestion was put forward in connection with a very different type of situation than that considered by Prof. Herzfeld. Our work has been with reference to unimolecular processes where the molecules are energized to a sufficient extent that there is a possibility of chemical reaction-dissociation or isomerization-taking place. In such cases the potential-energy surfaces relating to certain normal modes (those that are of the same symmetry species as the reaction co-ordinate) are distorted so that the corresponding vibrations are anharmonic; there is therefore more flow between these modes than the others. The case considered by Prof.Herzfeld, that of the vibrational states of carbon dioxide, cannot really be expected to show the effect that we have postulated; the dissociation energy of this molecule is so large that the distortions to the potential- energy surfaces will hardly be felt in the low levels considered. The fact that there is double dispersion of sound, or two relaxation times, in certain molecules (e.g., C2H6, CH2C12, CH2Br2, SO2) suggests that there are certain classes of vibrations between which flow cannot occur, and a classification based on sym- metry would appear to offer the most plausible explanation. No satisfactory theor- etical treatment seems, however, to have been worked out.Prof. T. L. Cottreii (University qf Edinburgh) said: I should like to comment on Prof. Herzfeld’s reference to the spectrophone experiments of Slobodskaya. If the results in the paper quoted by Prof. Herzfeld are taken at their face value, they imply that nitrogen molecules are much less efficient than carbon dioxide molecules in de-exciting any of the vibrations of carbon dioxide. This seems improbable for the lowest frequency, at any rate, and suggests that there may have been phase lags in the apparatus caused by other effects than vibrational relaxation. Slobodskaya 2 has more recently carried out a further investigation of the spectrophone experi- ment, in which some of these extraneous phase lags were removed, but even so the spectrophonic results for relaxation time can hardly be said to be reliably established.It still seems possible that the discrepancy between the spectrophone and other experiments may not be real. Prof. A. R. Ubbelohde (Imperial Coll., London) said: Can Prof. Herzfeld’s theories of transfer of translational to internal energy on collision between two gaseous molecules be extended to the collision between a gaseous vibrator and the surface of a solid? With modern techniques the probability of such transfer could probably be measured quite accurately if the theoretical background made this worthwhile, and the interpretation might be simpter than with bimolecular collisions of polyatomic molecules. The use of viscosity/temperature data to compute the repulsion forces which control the transfer of internal energy in gaseous collisions becomes less straight- forward with polyatomic molecules, because of the marked anisotropy of such forces, even for a symmetrical molecule such as neopentane.1 Gill and Laidler, Proc. Roy. SOC. A , 1959, 251,66. Wojciechowski and Laidler, J. Chenz. SOC., 2 Slobodskaya and Gasilevich, Optika Specktr., 1959, 7, 58. Spec. Publ., no. 17, 1962. 8586 GENERAL DISCUSSION Prof. K. F. Herzfeld (Catholic Univ. of America) said: The calculated transition probability depends very sensitively on the scale factor of the force (called here I, elsewhere often Z/a). The only source for 1 which is independent of thermal relaxa- tion measurements are the transport properties and their temperature dependence. For the theory presented here, it is assumed that each atom in the molecule exerts an exponential-type force.The theory of the transport properties (in par- ticular for viscosity), however, has been developed in a form here useful only for spherically symmetrical forces. To get around this difficulty, the following procedure has been chosen.* The interaction energy is given by interactions of exponential form between pairs of atoms. The total interaction energy is divided into two parts, one independent of vibra- tional co-ordinates, the other, the perturbation energy, containing the first power of the vibrational co-ordinates, Both parts are angle dependent, as is the wave function used. It is, however, assumed now that energy changes due to rotational transitions can be neglected.It is then possible to take average values over the angles making use of the addition theorems of spherical harmonics. The average value of the first part of the interaction energy is then identified with that energy which determines the " elastic " collisions important for viscosity (they are not truly elastic, since rotational transitions are allowed), while the average (over the angles) of the perturbation energy is identified with a spherically symmetric per- turbation energy providing vibrational transitions, including vibrational-rotational transitions. The outcome of the calculation is a steric factor 1 / 2 0 = c S 0 = 1/3 for longitudinal vibrations, and sin20 = 2/3 for bending vibrations. Dr. H.-J. Bauer (Tech. Hochsch., Stuttgart) said: The detection of the difference between a single relaxation process and a more complicated one by ultrasonic means is possible only if the several relaxation times are sufficiently different and each relaxation process has a considerable relaxation strength.For the reactions Prof. Herzfeld listed in his paper, which are parallel or in series to reaction (l), this second condition does not hold. Therefore it seems difficult to derive, from the shape of the absorption curve, different transition probabilities which one could compare with the calculated ones. But at least the influence of several simultaneous reactions can be shown. Ultrasonic measurements in He + COa mixtures, taken in Stuttgart, gave evidence of a slight composition dependence of the apparent vibrational specific heat.This perhaps may be understood by the fact that some of the reactions oc- curring in pure CO2 do not occur with He as the colliding atom and other reactions have different transition probabilities. This results in changes of an " effective " relaxation strength with composition. Dr. G. Szasz (G.E. Co., Zurich) said: At room temperature very long vibrational relaxation times are predicted for carbon monoxide by the theory of Schwartz and Herzfeld. Also, extrapolation of the shock-tube data of Matthews leads one to expect a collisional deactivation time of about 5 sec for CO gas at 1 atm pressure. These expectations have recently been borne out in a series of experiments by R. C. Millikan of the General Electric Research Laboratory. He has observed vibrational fluorescence from a flowing stream of carbon monoxide gas that was excited by ab- sorption of infra-red light.When the gas was made sufficiently pure, vibrational fluorescence was observed for as long as 0-2 sec after the excitation was cut off. This means that a measurable part of the vibrational excitation has survived more than 109 collisions without conversion into translational or rotational energy. This vibrational fluorescence is quenched by minute traces of polyatomic impurities. An initial account of this work has appeared in Physic. Reu. Letters, 1962, 8, 253. * This is still unpublished. The treatment of this problem in our book is now considered wrong.GENERAL DISCUSSION 87 Dr. A. B. Callear (University of Cambridge) said: It might be argued that the flash photolysis of nitric oxide + inert gas mixtures results in the formation of ground- state molecules with v > 1 but due to fast vibrational exchange processes of the type, NOX2II(v = n)+NOXZIl(v = o)-+NOX2n(u = n-l)+NOXZII(v = l), only molecules with v = 1 are observed, even at the shortest delay times.In my opinion, although exchange of vibrational quanta between molecules at near resonance is fast compared to vibration-translation relaxation, vibrational exchange is not fast enough to account for the observation at the shortest delay times that the vibrationally excited molecules are almost entirely in the first vibra- tional level. Evidence for this conclusion was obtained recently by Basco and Norrish in their study of the flash photolysis of NOCl1 which produces NOXW with v up to about 11.At short delay times, addition of nitric oxide caused a marked reduction in the concentration of molecules with the highest vibrational quantum numbers but had less effect on the concentration of molecules with v = 2, 3 and 4. With 1 mm of NOCl and 220 mm of nitrogen, the (0,2) band was still observed strongly in the presence of 32.3 mm of added nitric oxide. The (1,7) band was still observed with up to 12.4 mm of added nitric oxide and the (3,lO) band with up to 4.7 mm of nitric oxide. Furthermore, although vibrational exchange is, of course, very rapid, in the NOCl experiments the (0,l) band showed no appreci- able enhancement with up to 1-15 mm of added nitric oxide. The effect of added nitric oxide is greatest on the higher quantum states because the rate of exchange with NOX2IT(v = 0) should increase linearly with the vibrational quantum number.If molecules are observed with v = 1 (and a very small and barely detectable population with v = 2) in the flash photolysis of 1-2mm of NO with inert gas, then this is the initial distribution; molecules are produced almost entirely in the first vibrational level by the collisional deactivation of NOATZCf by NOXZII. As pointed out in my paper, the vibrational excitation of NOXW with 2 mm of NO is predominantly due to self-quenching because the half pressure is less than 1.0 mm.2 This view is slightly different from that expressed in my paper where I suggest that the detection of molecules with = 1 only, is “ possibly ” due to vibrational exchange.After examination of the results of the NOCl photolysis, I believe that possibility can now be ruled out. I was very interested in the comments of Dr. Keck on the work of Nikitin 3 and Wray.4 Robben’s explanation of the fast self-relaxation due to the interaction potential of the N202 dimer does not appear to me to be satisfactory because it requires a ‘‘ sideways on ” interaction and the use of an abnormally small value of ro. I have suggested in my paper, because of these difficulties, that a special theor- etical treatment might be required for NO because of the spin-orbit splitting. Robben obtained the first quantitative data on NO relaxation; his theory was developed in order to interpret his measurements of the fast self relaxation and appeared at that time to offer a plausible explanation.However, if there is resonance between vibration and the 3X and 1C. states corresponding to two NO molecules, as suggested by Nikitin, it provides a much more satisfactory explanation than that given by Robben. Prof. R. G. W. Norrish (Cambridge University) said : It would appear to me to be unrealistic to suppose that fluorescence from the A2Z+ state to the ground state X2Il of nitric oxide will occur exclusively to the levels u = 1 and v = 0. The Franck- Condon curves of the two states lie vertically above each other and transitions to a 1 Basco and Norrish, Proc. Roy. SOC. A , 1962, 268, 291. 2 Callear and Smith, to be published. 4 Wray, J. Chem. Physics, 1962,36, 2597. 3 Nikitin, Optics Spectr., 1960, 9,8.88 GENERAL DISCUSSION whole range of vibrational levels from u = 0 to v = n must initially occur.That this is so is clearly shown in the fluorescence photograph of Basco, Callear and Norrish shown in fig. 1 of Dr. Callear’s paper ; vibrational levels of the X2l-I state up to u = 5 are readily seen. If, alternatively, it is argued that the u = 1 level of the ground state is populated mainly by collisional deactivation of the A2Z+ state to the exclusion of all other vibrational levels, it still does not appear realistic. I suggest, therefore, that vibrational (and rotational) relaxation is extremely rapid, and more rapid than can at present be observed by kinetic spectroscopy, as indeed has been suggested as a possibility by Dr. Callear. This might be explained as due to the near resonance between two closely associated vibrational levels, so that the reaction is highly efficient (and indeed more efficient than reactions between more widely separated values of 0).If a complete spectrum of vibrational levels is initially popu- lated, the successively repeated operation represented by eqn. (1) must inevitably lead exclusively to the final production of an over-population of NO-1, which can only disappear slowly by collisional deactivation (see fig. 1). Dr. B. Brocklehurst (University of Shefield), said: Dr. Callear, in his paper, does not mention vibrational relaxation in the excited state of nitric oxide by col- lision with NO molecules in the ground state. This might be very efficient because of the probable strong “ resonance ” interaction between like molecules when one is excited (e.g., He* and He).While working at A.E.R.E., Harwell, I studied a parallel case-the deactivation of the nitrogen second positive bands (C311U+B3TIg) excited by electron bombardment of pure nitrogen. The probability P of quench- ing of the emission was 0.04 per collision for the u’ = 0 bands and 0-1 1 for the u‘ = 1 or 2 bands. These are highly excited levels (more than 11 eV) and they are known to be perturbed, so that interpretation of these results is rather uncertain. If the difference between the P values is due to vibrational relaxation, then the relaxation is much faster than that predicted theoretically (see fig. 9 in Callear’s paper ; Av = 337 cm-1 in this case). Dr. A.B. Callear and Mr. I. W. M. Smith (University of Cambridge) said : Brockle- hurst described experimental data on a study of the interaction of N2C;(u = 1 ) with N2XCBf, where the quenching is very marked and vibrational relaxation may be a good deal faster than given by fig. 9 of the paper by Callear. Part of our study of the fluorescence of nitric oxide has required examination of the processes which occur when NOA2X+(u = 1) interacts with NOX2Il(u = 0). The probability of quenching per gas kinetic collision is approximately unity and the probability of vibrational relaxation is about 0.3. This abnormally fast relax- ation is probably due to a strong chemical interaction between the two species ratherGENERAL DISCUSSION 89 than resonance, and a similar explanation may be applicable to the case given by Brocklehurst.Our data on the interaction of NOA~C+(U = 1) with NOX4 W(U = 0) are in agreement with preliminary measurements reported by Carrington.l.2 Dr. J. Keck (AVCO Res. Lab., Mass.) said: In his paper on vibrational relaxa- tion in NO, Callear cited a theory due to Robben in which the abnormally fast self-relaxation rates in NO are interpreted using the interaction potential for the N202 dimer in the equations of Schwartz, Slawsky and Herzfeld. Although Robben’s theory is in satisfactory agreement with experiment, we should like to point out that it involves the assumption that binding occurs in all electronic states and in all relative configurations of two NO molecules. This seems extremely unlikely. It is much more probable that only one of the sixteen possible electronic states of two NO molecules is bonding and that the force is only strong when the NO mole- cules are side by side.When one takes these factors into account, it is no longer possible to fit the experiments using Robben’s theory. T X 10-3 (OK) FIG. 1 .-Experimental (solid curves and points) and theoretical (dashed curves) transition prob- abilities for de-exciting the first vibrational level of NO. The dotted line is the sum of the prob- abilities given by the adiabatic (SSH) theory and the non-adiabatic (Nikitin) theory. An alternative and apparently satisfactory explanation of the fast self-relaxation rates has recently been given by Wray 3 in a paper in which he reports the results of shock-tube experiments on vibrational relaxation in NO in the temperature range from 1500 to 7000°K.Wray’s interpretation is based on a theory due to Nikitin 4 in which a vibrational transition is accompanied by a change in the electronic state of the two NO molecules. At low temperatures this theory predicts relaxation rates several orders of magnitude larger than those given by the Schwartz, Slawsky and Herzfeld equations due to the occurrence of a resonance between the energy 1 Carrington, this Discussion. 3 Wray, Avco-Everett Res. Lab., Research Report 96 (June, 1961) ; to be published J . Chem. 4 Nikitin, Optics Spectr., 1960, 9, 8. 2 Broida and Carrington, unpublished results. Physics, May, 1962).90 GENERAL DISCUSSION of the vibrational transition and the spacing of the intermolecular potential curves corresponding to the 3C and 1C states of two NO molecules approaching along a line.The analysis made by Wray using the Nikitin theory is shown in fig. 1. It in- cludes, in addition to his own results, those of Robben, of Bauer, Kneser and Sittig 1 and of Basco, Callear and Norrish.2 It can be seen that at low temperatures the Nikitin theory fits the experimental results quite well while at high temperatures the Schwartz, Slawsky and Herzfeld theory using Van der Waals force constants gives good agreement. By simply adding the contribution of the two theories? the results may be fitted over the entire temperature range. Dr. J. B. Hasted (University CoZZege, London) said : Further evidence of fast deactivation down to vibrational level v = 1 by exchange processes of the type 0 2 + 0 2 + 0 2 + 0 2 v = 2 v = o u = l u = l is provided by the interpretation of electron attachment measurements in oxygen afterglows excited by microwaves.The rates of attachment are found to be several orders of magnitude smaller than those observed in drift tubes, or in afterglows excited by pulses of relativistic electrons. Processes of the type, 0,- + 0 2 + 0 2 + 0 2 + e are known to proceed fast in either direction at sufficiently high particle densities; if it is assumed that an equilibrium is maintained, then the deactivation collision number of the 0 2 v = 2 level can be calculated from the rate of electron attachment. The result is encouragingly close to the curve (fig. 9) of variation of probability of vibrational exchange with energy discrepancy given by Callear.Dr. E. E. Nikitin (Acad. of Sci., Moscow) said: In considering the semiclassical approximation we must, before passing to the limit h+O, replace A by hm and keep the parameter cr)z constant. The condition COT = const.9 1, where z is the collision time, accounts for the adiabatic nature of collisions both in quantum and classical mechanics. The first term in the exponent always is the Landau-Teller term x. But the semi-classical approximation is also liable to give the first correction term. Of course, it need not always be of the form D/kT, as shown in some papers; 33 4 e.g. for the Lennard-Jones potential it is (16D/3x2kT)*~* instead of DlkT.1 Besides, the semiclassical approximation can give the next correction term hm/2kT and this is quite independent of the exact form of the potential, because symmet- rization yielding this term affects only the leading Landau-Teller term.Thus, semiclassical approximation can give all three terms in (1.1) and the neglected terms are of order A2/(kT>2x as shown in my paper.5 Prof. T. L. Cottrell (University of Edinburgh) said: I should like to ask Prof. Widom for his views on the following apparent discrepancy between his general results and the results of a particular numerical calculation of relaxation time in nitrogen using the semiclassical treatment, with symmetrized velocity and the Lennard-Jones intermolecular potential.6 The results were in general agreement with experiment and also with those of the Herzfeld-type calculation. If the correc- tion terms to the Herzfeld-type treatment introduced by using a Lennard-Jones potential were important, we would not expect this agreement. 1 Bauer, Kneser and Sittig, J.Chern. Physics, 1959, 30, 1119. 2 Basco, Callear and Norrish, Proc. Roy. SOC. A , 1961, 260, 459. 3 Nikitin, Optika i Spektr. Russ., 1959, 6, 141. 4 Parker, Physics Fluids, 1959, 2, 449. 6 Blythe, Cottrell and Read, Trans. Faraday SOC., 1961, 57,935. u = 2 u = o v = o 5 Nikitin, this Discussion.GENERAL DISCUSSION 91 Prof. B. Widom (Cornell University) said: In reply to Prof. Cottrell, there is no doubt that a Lennard-Jones potential introduces large correction terms in addi- tion to those given by Schwartz, Slawsky and Herzfeld. If, in a particular example, the additional terms seem not to matter, it can only be due to accidental cancellations among them.Prof. K. J. Laidler (University of Ottawa) said: The calculations by Dickens, Linnett and Sovers on reactions of the type, Na*(2P) + BC-Na(2S) + BC-f-, lead to rates that are much smaller than the observed ones. Their calculations, as they point out, relate to the transition probabilities between the potential-energy surfaces for Na* . . . B . . . C and Na . . . B . . . C, these surfaces being treated as parallel to one another. Some time ago I discussed 1 on the basis of the semi-empirical method the potential energy surfaces for various systems, including Na . . . H . . . H. Such surfaces can conveniently be plotted in terms of energy against r1 and r2, the former being the Na-H distance and the latter the H-H distance.A section through such a surface is shown schematically in the accompanying figure. It is to be seen that the curves Na . . . H2 distance FIG. 1. for Na*H2 and NaH2 run roughly parallel to one another, so that the probability of a direct transition will be small; this is essentially the situation considered by Dickens, Linnett and Sovers. A mechanism for a more rapid transition becomes evident, however, when one considers ionic states. The curve corresponding to the approach of Na+ to H2 is shown as CDE in the figure, and it is seen to cross the other curves at the points D and E. The complexes are all of the same species (2Z:f) so that resonance splitting occurs at each of the crossing points, as shown.The course of the quenching of Na*(2P) by H2 may, therefore, be regarded as represented by the dotted line in the figure. Initially the ionic species F is formed; this will undergo a number of vibrations and eventually there may be a transition 1 Laidler, J. Chem. Physics, 1942, 10, 34.92 GENERAL DISCUSSION to the lowest surface with the formation of Na+ H2. This process will occur much more rapidly than the direct transition between the upper and lower surfaces. Dr. T. Carrington (Nat. Bur. Stand., Washington) said: I should first like to make two brief comments. One is that the collision efficiencies I have given for transfer of energy from electronically excited NO in NO* + NO collisions are still preliminary values, and subject to change by factors of 2 or 3.The second concerns the transfer of energy from vibration of one molecule to vibration of another, a process in which there seems to be considerable interest here. I wish to point out that Shuler 1 has shown that the energy transport equation for this process, assuming identical perfect harmonic oscillators, can be simply linearized. This means that the statistical treatment of such processes is no more difficult than the intrinsically linear problems in which isolated molecules interact with a heat bath. I also have a comment on the paper by Dickens, Linnett and Sovers. One often wonders just how valid optical selection rules or transition probabilities are in molecular collisions, and I believe their paper gives some information on this point. In this connection I should like to ask Dr.Dickens about the significance of the factor U0n which appears in the expressions for the collisions cross-section. It would appear that if one uses their factored potential, eqn. (9), U0n is a product of a factor which is the matrix element for spontaneous radiation by the atom, and a factor which is, at least approximately, the matrix element for spontaneous radiation in a vibration-vibration transition of the molecule. If this is the corrsct meaning to be attached to UOn, its appearance as a factor in the expressions for the cross-section means that radiative selection rules will be obeyed in collisions for which the approximations used in deriving the cross-sections are appropriate. I should like to have Dr. Dickens’ comments on this point.Dr. P. G. Dickens (University of Oxford) said: In reply to Dr. Carrington, it should be emphasized that the factorization occurring in the expression for the cross- section in our paper is a direct consequence of the assumed factorization of the inter- action potential. In this case as Dr. Carrington says, uora is the product of electronic and vibrational matrix elements which are similar to those governing the correspond- ing radiation processes. In vibrational excitation in a head-on collision, such factor- ization arises naturally. Suppose a bound atom, of vibrational amplitude x,gwhose equilibrium position is a distance X from a colliding atom, undergoes a collision along the line of vibration. The interaction potential will depend on the instan- taneous separation of the two atoms, X - x .If the vibrational amplitude is much smaller than the closest distance of approach, then we can develop V( x - x) x V(X) - x( a Ypx), = 0. Hence where $0 and $% are oscillator wave functions. That is, the final expression for the cross-section will contain the factor I J$ox$,dx I 2 which is identical with the matrix element controlling the intensity of dipole radiation for a simple harmonic oscillation. No such simple argument is valid for electronic excitation since the exact interaction potential will not, in general, be linear in the electron co-ordinate. In special cases of the electronic excitation of an atom through high-energy colllisions with ions or electrons, it can be shown that similar “ optical ” matrix elements for the electron co-ordinate appear as factors in the corresponding expressions for the total cross-section.1 Shder, J. Cheni. Physics, 1960, 32, 1692.GENERAL DISCUSSION 93 Dr. A. B. Callear (University of Cambridge) (partly communicated) : We have recently carried out an experimental study of the process Hg 6(3P1) + AB+Hg 6(3Po) + AB by flash spectroscopy.1 The molecule AB is probably vibrationally excited in certain cases though this has not yet been established experimentally. If the AB species was either carbon monoxide or nitrogen, Hg6(3Po) atoms were observed by ab- sorption spectroscopy. However, flashing mercury + nitric oxide mixtures did not produce a detectable concentration of metastable atoms and from the sensitivity of the method the yield of metastable atoms can be estimated at less than 2 % of the total quenching rate.On the other hand, the water molecule is very efficient in causing the spin-orbit relaxation. Mr. G. Marl and Prof. J. C. Polanyi (University of Toronto) (communicated): We have undertaken some experiments which relate to the questions raised by Callear and Norrish’s experiments. These questions concern the nature of the excitation in the stable molecule AB after it has been involved in a quenching col- lision with Hg 6 (3P1), and also the identity of the lower state to which Hg 6 (3P1) is transferred. A mixture of AB and mercury vapour is irradiated at low pressure (lo-1-10-3 mm Hg total presswe) and room temperature, by a continuous source of mercury 2537 A radiation.When AB is CO or NO the reaction mixture is observed to emit infra- red radiation in the region of the CO or the NO first overtone. We have not yet obtained any information concerning the distribution of AB among vibrationally excited states, and can only say that AB is excited to v>2. If this excitation of AB occurs in one step then the excited mercury must be quenched directly to its ground state since the transition Hg 6 (3P1)-+Hg 6 (3P0) would not yield sufficient energy to promote CO or NO to 1122. Dr. J. D. Lambert (University of Oxford) said: If the mechanism proposed in our paper is correct, the measured vibrational relaxation time of A in heteromolecular collisions corresponds with the rate of processes (4) and (5), and not that of (3), the transfer of vibrational energy from A to B, which is of greater interest.But we can say something about the rate of (3), since it must be faster than either (4) or (5). The rates of (4) and ( 5 ) for all the systems involving C2F4 and CH30CH3 represent values of 2 1 0 < 10 collisions, so that 210 for the vibration-vibration transfers must in all cases be <lo collisions, probably 2 or 3. The vibrational energy dis- crepancies Av between A and B vary between exact resonance (Av = 0) and Av = 35 cni-1, and it must be concluded that under these circumstances vibrational energy transfer is very rapid. This is in accord with Carrington’s measurement of reson- ance transfer between two NO molecules, where collision efficiency is 0.5, but not with Callear’s observation that vibrational energy transfer between NO and N2, where Av = 12 cm-1, required some 500 collisions. It is interesting that the slope of Callear’s experimental line relating loglo 210 with Av (his fig.9) is almost identical with that of the empirical Lambert-Salter plot 2 relating loglo Z10 with the lowest fundamental vibration frequency for polyatomic molecules containing no hydrogen ; but the intercept, giving the value of loglo 2 1 0 for exact resonance, is 2-5 for Callear’s as contrasted with zero for Lambert-Salter’s line. The value of Zlo predicted by the Lambert-Salter plot for a frequency of 35 cm-1 is, in fact, about 3, which is in accord with our experimental results for the mixtures, if Av for vibration-vibration transfer is equated with Vmin for vibration-translation transfer. 1 Callear and Norrish, Proc.Roy. SOC. A , 1962, 266, 299. 2 Lambert and Salter, Proc. Roy. SOC. A , 1959, 253, 277.94 GENERAL DISCUSSION Dr. A. B. Callear (University of Cambridge) said: Dr. Lambert showed that vibrational exchange occurs at practically every collision between molecules under the conditions of their experiments and points out the discrepancy between these conclusions and the results of Callear and Smith 1 who conclude that the process, required roughly 500 collisions, the energy discrepancy being only 12 cm-1. He points out that the reaction, NO. A(v = l)+NO. X(u = 0) = NO. A(u = O)+NO . X(v = 1 or 0), (ii) which has a probability of about 0.3 per gas kinetic collision, is more consistent with their experimental data.I suggest that the difference between Dr. Lambert’s observed rates of vibrational exchange and those given in fig. 9 of my paper arise largely because the rate of vibrational exchange at exact resonance depends on the square of the vibrational frequency. The exchange processes studied by Lambert et al. involve vibrational quanta which are much smaller than 2359cm-1, the vibrational frequency of the N2 molecule and in any case, under their conditions it is doubtful if the exchange processes are sufficiently elastic for the theory to be valid. Process (ii) was not included on my fig. 9 because there is probably a strong chemical interaction between NO . A and NO . X preventing the application of the theory of Herzfeld and co-workers. There should not be a strong chemical inter- action between NO.A and N2X because N2X does not quench the y fluorescence appreciably and the theory should be applicable for this case. The slopes of the Lambert-Salter2 plots may be similar to that of my fig. 9 because the magnitudes of all the slopes are dominated by the largest term in the exponential factor contained in the rate equation for energy transfer. This term depends on v3 for vibration translation relaxation and A v ~ for exchange, so that plots of log 2 against v in the former case would give similar slopes to plots of log 2 against Av in the latter case. The theoretical prediction given on fig. 9 of my paper was calculated on the basis of energy discrepancies between NO . X (1904 cm-1) and another species of similar mass (i.e., N2, CO) and diameter, with Elk = 100°K.The Lambert-Salter intercept is zero for v = 0, but this cannot be related to the rate of exchange of vibrational quanta between molecules at exact resonance since the experimental results were obtained from studies of vibration-translation relax- ation. If the Lambert-Salter plot extrapolated to small v does appear to give satis- factory values for the rates of vibration exchange between polyatomic molecules, then such agreement is probably fortuitous and cannot be generally true, since the rate of exchange at exact resonance (v = 0) should depend on v2. Mr. A. J. Matheson (University of Edinburgh) said: Dr. Lambert 3 has found that C2H4 + SF6 collisions are substantially more effective than SF6 + SF6 collisions in deactivating vibrationally excited SF6.An explanation of this may be that energy is being transferred from the vibrational mode of SF6 to the rotational mode of C2H4. Since the moment of inertia of C2H4 is much lower than that of SF6, C2H4 has a much higher rotational velocity. The lowest fundamental of SF6 is a bond bending, and it is possible that energy transfer from this vibration to a rapidly rotating C2H4 molecule may take place in a collision more rapidly than direct vibrational-translational energy transfer. C2H4 + SF6 collisions would thus be more effective than SF6 + SF6 COlliSiOnS, as observed. NO . A(u = l)+N2X(u = 0) = NO. A(u = O)+N~X(U = 1), (i ) 1 Callear and Smith, to be published. 2 Lambert and Salter, Proc. Roy. Soc. A, 1959, 253, 277. 3 Lambert et al., this Discussion.GENERAL DISCUSSION 95 Dr.Callear 1 mentioned that addition of a small partial pressure of NH3 or H20 to NO increased the rate of decay of vibrationally excited NO about 20 times. Other workers2 have observed that NH3 and H20 greatly increase the rate of de- activation of vibrationally excited 0 2 . Both NH3 and H20 have low moments of inertia and high peripheral velocities of rotation, and if energy transfer takes place preferentially from vibrationally excited NO to rotating NH3 or H20 molecules, then the rate of decay of vibrationally excited NO or 0 2 would be increased by the addition of small amounts of NH3 or H20, as observed. " Sticky " collisions will undoubtedly play a considerable part in such interactions, but it is interesting to note that in the H20+C02 and D20+C02 systems, the more rapidly rotating H20 is more efficient than D20 in deactivating CO2.2 H2O has also been found to be more efficient than D20 in deactivating vibrationally excited C2H4 3 and N20,2 strongly suggesting that vibrational-rotational energy transfer is occurring in these systems.Prof. A. R. Ubbelohde (Imperial ColZ., London) said: We have obtained some- what similar results to Lambert et al. in comparisons of the catalytic efficiencies of isotopic molecules. It seems definite that molecular rotations can intervene quite markedly in the transfer of internal energy. However, it is not clear whether rotation during a collision brings the steric factors nearer to unity by enhancing repulsive effects, or whether it merely extends the range of conditions for which the energy difference AE is small and hence the probability of vibration-vibration exchange still is large in the process A* + B + A + B* v1 + n p AE = h[(vl + n,co) - (v, + n2c01)]. If the repulsive forces are markedly anisotropic, rotation of B on average could give more weight to orientations for which the repulsions are strongest, and could thus increase the steric factor.Dr. J. D. Lambert (University of Oxford) said: Ubbelohde's suggestion that the special efficiency of rapidly rotating molecules in promoting vibrational energy transfer may be steric in origin recalls the observation made by Corran et aZ.,4 that some strongly polar molecules show a reversed temperature dependence of vibra- tional relaxation time at lower temperatures, p being smaller at 30°C than at 100°C.This was interpreted on the view that the lack of rotational energy at lower tem- peratures resulted in the majority of collisions taking place in a strongly preferred and favourable orientation, due to dipole interaction. For a non-polar anisotropic molecule such as ethylene, there is no such orienting tendency, and rapid rotation might have the converse effect of increasing the chance of the most favourable orien- tation for energy transfer being attained during the collision. Dr. E. E. Nikitin (Acad. of Sci., Moscow) said: I should like to ask Mr. Davison if he has considered the possible effect of strong coupling between rotational states with the same j and different m. Mr. W. 33. Davison (University of Cambridge) said: In answer to Dr.Nikitin, transitions in which only the magnetic quantum numbers change can be expected to occur fairly readily, and their contribution to the total elastic cross-section can be investigated using the theory I have described. On the other hand, such transitions, preceded or followed by a Aj = 2 transition, provide a second-order correction to 1 Callear, this Discussion. 2 Cottrell and McCoubrey, Molecular Energy Transfer in Gases (Butterworths, London, 1961). J Hudson, McCoubrey and Ubbelohde, Proc. Roy. Sac. A, 1961,264,289. 4 Corran, Lambert, Salter and Warburton, Proc. Roy. Soc. A, 1958, 244, 212. v2 + n 2 0 f96 GENERAL DISCUSSION the inelastic cross-sections I have discussed; I would expect this correction to be small, though not altogether negligible.It should soon be possible to give a fuller answer to this question, when programmes to carry out the distorted wave procedure to second and higher orders have been completed. In treating the inelastic collision of heavier molecules in this more extended scheme, some insight may also be gained into the correct semi-classical limit of the quantum-mechanical theory. Dr. J. P. Toennies (Physik. Inst. der Universitat, Bonn) said: In recent months we have measured directly inelastic collision cross-sections for transitions between specified rotational states. The operating principle of the apparatus is shown in fig. 1. With the first state selector (an electrostatic four-pole field I), TlF molecules, Molecular Stote Velocity : Rotational: Vibrational: 11 F ----------- I Mechanical ' Velocity Setcdor (after Fizcau ) --- --- -- - - - Electrostatic Rotational State unchongod unchanged *---------- Gas Filled Battering Chombcr ---------- - - Eledrostatic Rotation01 State Analyzer e g J-2 M,-0 _---------- 1 2 3 J Beom Detector ( Langrnuir-Toybr Detector-Mass FI kler- Mu LtiPt ler unchanged unchonged unchanged unchanged FIG.1 .-Block diagram of molecular beam apparatus. in one specified rotational state designated by (j,m), are separated out of a mole- cular beam and are focused into a gas-filled scattering chamber in which a homo- geneous electric field is present. Those molecules which have been scattered by less than 1" are then refocused by a second state selector located directly behind the scattering chamber and are analyzed for their rotational state.From the pressure dependence of the intensity in the daughter state (j',O) it is possible to determine the collision cross-section CT for the single collision process TlF(j)+X-+TlF(j') +X, where X is an atom or molecule. In addition, by measuring the pressure dependence of the intensity in the parent state ( j , O ) a total cross-section is obtained corresponding 1 Bennewitz, Paul and Schlier, 2. Physik, 1955, 141, 6.GENERAL DISCUSSION 97 to the sum of the elastic cross-section (at a resolving power of 1") and the sum of all inelastic cross-sections involving transitions out of the parent j-state : In these experiments no direct information on m-transitions can be obtained since the scattering molecules strike from all directions relative to the electric field direction in the scattering chamber. TABLE RESULTS OF INELASTIC CROSS-SECTION MEASUREMENTS FOR TlF ( j = 2) AND VARIOUS SCATTERING PARTNERS, X.ALL VALUES ARE IN 1$2 type of scatterer atom spherical top X He Ne Ar Kr CH4 SF6 non-polar molecule H2 0 2 air 3 7 9 6 20 244 515 3 63 266 343 polar molecule asymietric top symmetric top N20 53 525 J 3 2 0 48 61 5 CF2Cl2 120 865 NH3 375 2140 N D 3 375 2140 * These measured results must be corrected upwards by a f,-:ntor which takes account of the fact that the second-state selector only collects those j' = 3 molecules which are in the rn = 0 sub- state and which are scattered through an angle less than 1". This factor appears to be about 2 and should be independent of the scattering partner. The results of these preliminary experiments with various scattering molecules are shown in table 1.At the preselit time, it is only possible to discuss these results in general terms. For TlF molecules in the j = 2 state the time for one rotation, ~ l p , is greater than the time of collisional interaction t - (l/g) J G / 2 n ) (g is the rela- tive velocity) ; however, this is not always true for the other collision partner. For the atoms, the spherical top molecules, and non-polar molecules, the interaction pro - ducing transitions is, in any case, a weak one (V(r)-il-6) since they do not possess a dipole moment. Although the molecules N2Q and H20 do possess permanent dipole moments, ZX< t, so that the dipole is smeared out in the course of the collision and the interaction is also of the weak type.For CF2ClZ zx"t so that dipole alignment should bs possible, resulting in a stronger interaction (V(r)-+r-3) and a largcr cross-section. For NH3 there is a strong interaction (V(r)-r-3) since this molecule has a dipole niomcnt along its figure axis which is oriented in the electric field. The results for otot also seem to be consistent with this interpretation. The large value of crtot for NH3 is particularly interesting since it is twice as large as the scattering cross-section obtained without state selection but with a high angular resolution. In the latter case the average rotational level is j"50 so that T T ~ F < t, resulting in a weak interaction and a smaller cross-section. NH3 and Ni33 have the same inelastic cross-sections for the j = 1 -+j = 2 transition, which is in approximate98 GENERAL DISCUSSION resonance with the inversion vibration. This result would seem to indicate that resonance exchange? in this case, is a comparatively improbable process. Finally, other experiments indicate that the j = 3-j = 1 cross-section is less than one-tenth as large as the j = 3+j = 2 cross-section for T1F colliding with NH3. This result is in agreement with the Aj = 1 selection rule calculated by Anderson.1 In another experiment we have measured the elastic scattering cross-section of a TlF molecule in the (j,m) = (1,O) rotational state when struck by a rare gas atom in a direction parallel to 011 and perpendicular to ol, an applied electric field direction.2 The measured ratio of the cross-sections obtained in this way is oL/o,l = 1 -0 14 2 0.002. To interpret this result we have assumed a potential of the form V(r,e) = r-6 (a- b cos28), where r is the distance between the centres of mass of the collision partners and 8 is the angle between the internuclear axis and r. Using the “high-energy ap- proximation ” 3 for the elastic scattering cross-section for an anisotropic potential and comparing with the experimental result we have found b/a = 0.43 in agreement with a crude classical estimate. In conclusion I would like to emphasize that it now seems possible to provide a more rigorous test than hitherto available of the various theoretical methods discussed in Mr. Davison’s paper. This work was done together with Dr. H. G. Bennewitz and Dr. K. H. Kramer. We wish to thank Prof. W. Paul for his inspiring encouragement. 1 Anderson, Physic. Rev., 1949, 76, 647. 2 Bennewitz, Kramer and Toennies, 2nd Int. Con$ Physics of Electronic and Atomic Collisions (Benjamin, New York, 1961), p. 113. 3 Schiff, Physic. Rev., 1956, 103, 443.

ISSN:0366-9033    

DOI:10.1039/DF9623300085

出版商:RSC    

年代:1962

数据来源: RSC

摘要:

II. COLLISION PROCESSES INVOLVING CHEMICAL REACTIONS Vibrational Excitation in Photochemical Processes BY N. BASCO* AND R. G. W. NORRISH Dept. of Physical Chemistry, University of Cambridge Received 26th January, 1962 Various ways of producing disequilibrated populations of vibrationally excited molecules and (1) vibrational excitation of the ground state involving prior electronic excitation ; (2) photolysis followed by reactions of the type, radicals are described. The main processes considered are : A+ BCD +AB* + CD ; (3) direct production of vibrationally excited molecules in reactions of the type, ABC+/iv-+AB*+C. The energy distributions resulting from these types of reactions, the study of vibration-translation and vibration-vibration energy transfer in these systems, and the chemical properties of the vibra- tionally excited species are also discussed.The techniques of flash photolysis and kinetic spectroscopy make it possible (in theory at least) to study the physical and chemical properties of vibrationally excited species and the nature of the processes in which they are produced. This paper describes to what extent these possibilities have so far been explored. Experimentally, a suitable molecule in the presence of an inert diluent (usually nitrogen) is subjected to an intense flash of visible and U.V. radiation. This is of 20-50 p sec duration and is produced by discharging 1500-5000 J, stored in a bank of condensers at 10-20 kV, through an inert gas (&,A) in a quartz tube. The absorption spectra of the products are then taken at various known time-intervals measured in microseconds by means of a second much less powerful but even shorter flash, and recorded photographically. In the systems to be considered, these spectra reveal the presence of molecules or radicals possessing up to 20 quanta of vibrational energy though in all other respects at room temperature.Since it is not normally possible, at room temperature, to detect the presence of molecules even with only one vibrational quantum, the degree to which the vibrational levels are overpopulated is evidently extremely marked. EXCITATION INVOLVING AN EXCITED ELECTRONIC STATE The simplest way of producing some vibrationally excited molecules would be by flashing with infra-red radiation, but this does not yet seem to have been done.A somewhat similar method is available for diatomic molecules with discrete intense absorption in the visible or U.V. The molecule is electronically excited and then, either by fluorescence or by collision quenching, returns to various vibrational levels of its ground electronic state according to the Franck-Condon principle. In suitable * Department of Chemistry, University of Sheffield, Sheffield, 10. 99100 VIBRATIONAL EXCITATION cases, the population of the first few excited levels can be interested several hundred- or thousand-fold by this method-sufficient to allow direct observation of the excited species. This type of excitation has been achieved in the case of nitric oxide 1 which, when flashed in the presence of a large excess of inert gas (to ensure isothermal conditions), undergoes the following reactions : electronic excitation fluorescence NO.X ~ I I ( U = O)+h-+NO. A~X(V = 0,1,2) NO. A ~ Z ( U = 0,1,2)+NO. X~II(U = 0,1:2. . .)+hv NO. X ~ I I ( U = ~)+NO.X~IT(U = 0)+2NO. X~II(U = 1). or collisional quenching These lead, almost exclusively, to a several hundred-fold overpopulation of the first vibrational level of the ground state, the relaxation of which could then be followed quantitatively in the presence of various other molecules. An extension of this method makes possible the vibrational excitation of free radicals which are produced by photolysis and then excited in a similar way to that described above. Both the photolysis and the subsequent excitation can be achieved by the same flash and, provided the radical is sufficiently stable and absorbs radia- tion strongly, several vibrational levels can be sufficiently overpopulated to permit observation.An example of this type is the excitation of the cyanogen radical produced in the photolysis of cyanogen and the cyanogen halides.;! Following the photolysis, in which the radicals are produced with no vibrational excitation, the CN radical under- goes electronic excitation to the B2Z and A2Il states. On returning to the ground state (X2I=), about 15 % will possess one or more vibrational quanta. The radical absorbs so strongly that this process can be repeated many times during the period of the photoflash and each time the number of vibrationally excited radicals is in- creased. Thus, theoretically, an infinite vibrational temperature can be produced in the absence of dissociation or relaxation. In practice, only the first six excited levels can be observed directly because of the experimental difficulty in resolving the close sequences which make up the violet system of CN.For the same reason, quantitative measurements are only possible up to the fourth excited level, but the relative populations of these five levels can be measured as functions of, for example, time 2nd pressure. These measurements show that the theoretically predicted distribution is in fact closely realized in that the levels which can be observed are found to be approximately equally populated. Evidence that higher Bevels are also occupied is provided by the observation that, under certain conditions, the popula- tions of the fourth excited level (and probably of the fifth also) can greatly exceed that of the lower levels.This situation arises as a result of a partial relaxation from the predicted distribution and the fact that up to 90 % (or even more) of the radicals are in various vibrationally excited levels opens up the possibility of studying their properties. This may be contrasted with nitric oxide where only about 5 % of the molecules are observed to be excited and virtually all of these to only the first excited level. The production of vibrationally excited carbon monosulphide in the flash plioto- Iysis of carbon disulphide 3 is, very-probably, another example of this type though, so far, other mechanisms have not been excluded.The sulphur atoms produced at the same time give rise to sulphur (S2) which is also observed to be vibrationally excited. The recombination of atoms theoretically provides a method for the production of vibrationally excited molecules with energy up to the dissociation limit. The experimental difficulty in producing atoms in a simple system of flash photolysis and NO . A2X(v = 0,1,2) + M-NO . X2II(u = 0,1,2 . . .) resonance exchangeN. BASCO AND R . G. W. NORRISH 101 the vibrationally excited molecules produced does not seem to have been In principle, the presence of these vibrationally excited species could be short time delays with, for example, bromine and iodine. in detecting over come. detected at REACTIONS BETWEEN ATOMS AND MOLECULES There is a large group of reactions of the type A+ BCD+AB* + CD in which the exothermic reaction between an atom and a molecule produces a vibra- tionally excited molecule AB*.In some cases the exothermicity is provided by the electronic energy of the atom.4 This class of reaction, proposed by McGrath and Norrish 5 has been reviewed by Polanyi,6 Smith7 and ourselves 8 and it is only necessary here to mention two of the outstanding problems of interest. The most striking features of these reactions are the very large degree of excitation observed and their apparent specificity, in that only the molecule AB containing the newly formed bond has been observed to be vibrationally excited. In all reactions, however, there were good reasons why CD* might have escaped detection even if it were produced.In the last year, two exceptions to this have been reported and both support the original conclusion. We 9*1* studied the reaction under conditions where NO* would have been detected had it constituted about 5 % or possibly less of the total NO produced, but could detect none. C1+ ClNO+ Cl2 + NO A similar reaction, viz., H + ClNO+HCl+ NO was studied by Cashion and Polanyill They observed emission in the infra-red from both products, but that from NO* was <l/lOth of the total. Since, because of the relative slowness of vibrational relaxation, vibrational disequilibrium should result from any exothermic reaction, these results show that equipartition is not the rule in reactions of this type. The extent to which the molecule AB can be vibrationally excited is not also finally settled, though the evidence strongly suggests that at least some molecules are produced with the entire exothermicity of the reaction in the form of vibration.In fact, in one case, 0; from N02,89 12 the vibrational excitation has been observed to exceed the exothermicity. The most interesting problem of whether all the molecules are initially produced with the maximum degree of excitation as proposed by Folanyi 6 or whether there is a finite probability of individual molecules being produced with any degree of excitation as suggested by us 8 still remains open. Of course, because of relaxation and the limited time resolution of present techniques, a distribution of energy among all vibrational levels will be observed in practice, whatever the initial distribution.Improved techniques, with increased sensitivity allowing the use of much lower pressures, will be required before the question is finally settled, and some progress is already being made in that direction. The fact that the relative populations of excited levels have not been observed to change greatly with time, suggests to us that the initial distribution, in those systems, is one in which all levels are populated in the initial reaction with an increasing probability of excitation towards lower levels. This implies that the distribution observed in flash photolysis experiments may be fairly close to the initial distribution unless a very much more rapid relaxation process occurs before observation is possible. This could only be resonance exchange and even if this occurred on every collision, it is doubtful whether it could lead to a very marked change in the distribution in the time available.The effect of nitric102 VIBRATIONAL EXCITATION oxide on NO* and oxygen on 0,' has been studied 10y12 and the results seem to support the view that, generally, the concentration of excited species is likely to be too small for resonance reactions to be of such importance in comparison with the other mechanisms. DIRECT VIBRATIONAL EXCITATION DURING PHOTOLYSIS In principle, whenever a molecule dissociates following the absorption of radiation of shorter wavelength than that corresponding to the strength of the bond broken, the fragments may carry part of the excess energy in the form of vibration. This possibility is in fact so obvious that it may be surprising how little real evidence there is to substantiate it.The presence of vibrational energy in a molecule can sometimes be inferred from the exceptional chemical reactivity of the molecule itself or of products formed from it. That this reactivity is due to vibrational rather than translational energy is deduced from its ability to survive a relatively large number of collisions. In this way, evidence has been obtained that the methyl radical produced in the photolysis of methyl iodide with 1849 1$ radiation,l3 the methylene radical produced from diazomethane 14 and several halogen substituted methyl radicals produced from various po ly- halomet hanes 15 arc vibrat ionally excited.As far as the primary process is concerned, the evidence which can be obtained in this way, though valuable, is necessarily indirect and limited. To study the precise extent of the vibrational excitation in various molecules and its variation with the wavelength of the radiation absorbed as well as the corresponding change in chemical reactivity it is highly desirable to observe the excited species directly. This will, of course, be essential where the degree of excitation is insufficient for chemical reaction and this may very often be the case. As we have seen, there are many examples of the direct observation of vibrationally excited species in flash photolysis experiments but in only three of these has it been suggested that they could have been produced in the primary photolytic process. These are the reactions 16,179 99 10 CHZCO + hv+CO(v<2) + CH2 NOCl (or NOBr) + hv+NO(v< 11) + Cl(or Br) To these we may add, for further consideration, the reactions 0, + hv+O; + 0 cs, + IZV-,CS* + s in which the production of the vibrational species observed is ascribed to other mechanisms.33 18 In all of these reactions, several mechanisms are possible and it is difficult to prove beyond doubt which is in fact responsible in a particular case.Only for the nitrosyl halides and cyanogen and the cyanogen halides have serious attempts been made to do this. When nitrosyl chloride or bromide is flash-photolyzed, nitric oxide molecules with up to 11 quanta of vibrational energy are observed in absorption, though the system is maintained at room temperature by the addition of a large (up to 7000-fold) excess of inert gas.Both compounds absorb strongly in the U.V. and thus, with a quartz apparatus, up to 110-120 kcal/mole of excess energy are available. The results show that up to at least 55 kcal of this can appear in vibration and it seems probable that with improved experimental techniques the presence of even moreN . BASCO AND R. G. W. NORRISH 103 highly excited molecules will be revealed. In these systems there are good expei- mental and theoretical reasons for believing that the excited NO is produced directly in the photolytic process. The most interesting alternative is a sequence of reactions involving a singlet and a triplet excited state of NOCl(and NOBr) and the 411 state of NO.This mechanism cannot in fact be entirely excluded, but, using light filters, it was possible to show that it restricts the energy of the 4l-I state to not more than about 3.5eV above the ground state. Most of the present theoretical and experi- mental evidence points to a value 1 eV higher than this. The main experimental difficulty with this system is the decreasing absorption coefficient of the nitrosyl halides towards longer wavelengths, so that, at present, radiation below about 2600 A must be used in order to produce a detectable amount of decomposition. When this restriction is removed (and an improvement in sensi- tivity by a factor of ten is already practicable) it should be possible to study the variation of the degree of excitation with wavelength and, at the same time, to resolve the question of whether the 4l-I state of NO is involved.Regarding the other possible examples of this type, the most general alternative mechanism to be excluded is the electronic excitation process This very probably occurs in the case of CS* (as suggested by the authors 3) so that demonstrating the simultaneous occurrence of another mechanism may be difficult. Apparently the least complicated is ketene where the photoflash radiation transmitted by quartz is not capable of exciting CO. The case of SO* is of interest in another important connection in that an alternative mechanism involves its production as an excited SO molecule in the reaction This was one of the few possible sources of evidence against the postulate that only the AB bond is excited.o(%) + 0, -+ 0: + o2 0 + so,-,o2 +so*. The reaction has for some time now been one of the most striking examples of its type. However, it now seems necessary, in the light of our work on the nitrosyl halides, to reconsider the mechanism by which vibrationally excited oxygen molecules are produced in the ozone system. Ozone absorbs U.V. radiation strongly with a maximum extinction coefficient around 2500A. At this wavelength, 90 kcal/mole of excess energy are available over that required to produce an atom and a molecule of oxygen both in their ground electronic states. At the effective limit of transparency of the quartz apparatus, the excess energy is about 125 kcal/mole-sufficient in fact to dissociate the oxygen molecule, while the highest degree of vibrational excitation so far observed (20 quanta 8 ) corresponds to only 76 kcal.Thus, on purely energetic grounds, the direct reaction could easily explain the experimental facts. Arguments against this mechanism and favouring the reaction between the oxygen atom and the ozone molecule may be summarized as follows. (i) The small change in the bond length.18 This would apply equally to the pro- duction of NO* from NOCl and NOBr. In our view, an overall change in bond length is not a necessary condition though it may favour vibrational excitation. (ii) It has been shown beyond doubt that the photolysis of ozone with U.V. radia- tion produces 1D oxygen atoms3 18 It would therefore be necessary to postulate an additional primary process. 0 3 + h v + 0 2 .3z;(~%0)+03~1 04 VIBRATIONAL EXCITATION (iii) The suppression of the 0; spectrum by the addition of a sufficient excess of H20, H2, HCl, CH4 and NH3 and the appearance of the OH and OH* spectrum 4 , 1 8 is well explained by the competing reactions and O'D + HR-, OH* + R O'D+ 0 3 + 0; + 0,. This implies that the second reaction is almost exclusively respomble for the pro- duction of 0;. Though for this to be a complete proof, the possibilities that RH, R or reaction products are efficient at removing 0; should also be considered. The reaction scheme 0% + 03-' 0; + o2 O:(v> 17)f 03+20, + 0 ' D 0 'D 4- H2 0 -+20H OH+ 03-+H02 + 0, HO2 + 03+20, +OH explains the observed quantum yields for the photolysis of dry and wet ozone with visible and U.V. radiation.(iv) The fact that, under certain conditions, there is an optimum flash energy for the production of the strongest 0; spectrum12 as is to be expected if 0 2 is produced in the reaction between an oxygen atom and an ozone molecule. The rate of this reaction evidentIy depends on the concentrations of both species and, obviously, if all the ozone is destroyed by the flash itself, there is none left to react with the oxygen atoms. A much more detailed study of the variation of the observed 0; concentra- tion with flash energy at various ozone pressures is required to test this argument ; but there are various complications and the mathematical treatment of the results will be difficult. (v) The production of 0; when NO2 or C102 are flashed is accounted for by the reactions 0 +N02-+O: +NO By analogy, the reaction of an oxygen atom with ozone should likewise produce 0; and the existence of many other reactions of a similar type strongly supports this mechanism.We conclude that there is no experimental support for the idea that the reaction 0 + c102-+ 0; + cio. 0, + hv+O: + 0 contributes significantly to the observed production of 0;. In our study of the photolysis of cyanogen and the cyanogen halides,2 the pos- sibility that the vibrationally excited CN radical observed was produced directly was investigated in detail. The compounds all absorb radiation of the shortest wave- length available and the excess energy lies between 40 and 90 kcal/mole-again sufficient to account for the degree of excitation observed. Using various light filters, we were able to show that the production of CN* in the process where R is either CN, Br or I, if it occurred at all, accounted for not more than 6 % of the total CN* observed.This may be compared to NOCl where, under certain conditions, about 50 % of the nitric oxide is observed to be excited. It appears that the direct production of vibrationally excited species may not, after all, be so obvious RCN+hv-+R+CN . X2C(v>O)N. BASCO AND R. G. W. NORRISH 105 and we believe it merits much more attention both from the theoretical and from the experimental points of view. We have already mentioned most of the known examples of the exceptional chemical reactivity of vibrationally excited species.13-15 The outstanding example of reactivity towards other molecules is the reaction O;(u> 17)+ 03+202 + OID postulated by McGrath and Norrish to explain their observations and the high quantum yield for ozone decomposition by U.V.radiation. Evidence for the reaction NO*(o> 8)+ NOC1+2NO + C1 has been sought by Wayne and ourselves,l9 but without success. Further information on this aspect would be of great interest. BEHAVIOUR OF VIBRATIONALLY EXCITED SPECIES The opportunities for vibrational relaxation studies provided by the systems described have so far been little exploited. Lipscomb, Norrish and Thrush20 followed the decay of the fifth, sixth and seventh vibrational levels of the excited oxygen produced in the flash photolysis of NO2 and C102. From half-life measure- ments they found that about 2,000collisions between 0; and C10 were required to remove a vibrational quantum.In a detailed theoretical paper, Schuler 21 showed that the analysis of relaxation data in terms of half-lives loses its meaning when more than two levels are involved in the relaxation process. To obtain information on energy transfer in multilevel systems, it is therefore necessary to follow in detail the time behaviour of the population of several (and preferably all) the energy levels. In many systems it may be difficult to make complete studies of this kind and it is therefore worth pointing out that reasonably accurate relaxation data could be ob- tained more simply from those multilevel systems in which the populations of the vibrational levels decrease towards higher levels. Even where it is not possible to measure the relative populations of two or three adjacent levels, it should be possible to detect changes in the distribution.If the change in the relative populations is small over a period of one or two apparent half-lives, then the required conditions hold. To illustrate this argument, consider a system in which the populations of the adjacent vibrational levels A, By C . . . are X,O, Xg, X,O . . . at time t = 0 and Xa, Xb, Xc . . . at time t and where A is the highest level present. Assuming step- wise degradation with equal probabilities for each level, it can be shown that the relative populations after n half-lives of level A are given by . . . etc. and can easily be calculated. It is immediately obvious from this that the larger the ratios Xg/Xz and X z / X z , the less the distribution changes with time and the closer the measured half-lives are to the true values.The error will not greatly exceed an order of magnitude provided that these ratios are greater than unity and the result may be very much better than this for higher values. Applying these calculations to the relaxation of 0; in the C102 and NO2 systems, we see that the fact that the half-lives for the seventh, sixth and fifth levels were not greatly different is inconsistent with the estimate that the levels were equally populated.106 VIBRATIONAL EXCITATION In fact, when the population of the Mth level had fallen to half its initial value, the ratio of the populations of the fifth and seventh levels (i.e. Xc/Xa) would have been about seven compared to the initial value of unity.While it is possible that an estimate of the relative concentrations could have been considerably in error, it seems much less likely that a '7-fold change in relative concentrations could have been missed. We conclude that the seventh, sixth and fifth levels were probably populated to an increasing extent and that the relaxation results need not have been in error by much more than a factor of two. On Schuler's analysis the error is by a factor of ten. Re-investigating the NO2 system, we 87 12 showed that all levels up to the thirteenth are populated but the previous treatment 20, which assumed that higher levels than the eighth were absent and that the population of the eighth itself was negligibly small, can easily be extended to cover this situation.However, our tentative estimate of the populations suggests that they decrease by about a factor of three towards higher levels and this, if confirmed, would support the argument presented above. A detailed account of the relaxation of nitric oxide studied by kinetic spectroscopy has been published,l the relaxation of the cyanogen radical has been studied2 and direct evidence for resonance energy transfer has been obtained. The reaction has already been mentioned,l and the similar reaction NO(u = n)+NO(u = O)-+NO(u = n-l)+NO(Y = 1) has been shown to occur in the NOCl system when nitric oxide is added3 10 Finally, when NO+CO are flashed the presence of CO(u = I) very probably arising from the reaction can be detected in the vacuum u.v.22 Quantitative measurements on this and the NO* + N2 exchange reaction are in satisfactory agreement with the theory of Herzfeld and Litovitz.23 Summarizing, one need only say that serious studies of the various problems discussed in this paper have virtually only just begun and that very much interesting work remains to be done. NO(u = 2) + NO(u = 0)+2NO(u = I) NO(u = l)+CO(u = O)+NO(u = O)+CO(U = 1) 1 Basco, Callear and Norrish, Proc. Roy. SOC. A, 1961,260,459. 2 Basco, Nicholas, Norrish and Vickers, to be published. 3 Callear and Norrish, Nature, 1960, 188, 53. 4 Basco and Norrish, Proc. Roy. SOC. A , 1961,260, 293. 5 McGrath and Norrish, 2. physik. Chem., 1958, 15, 245. 6 Polanyi, J. Chem. Physics, 1959, 31, 1338. 8 Basco and Norrish, Can. J. Chem., 1960,38,1769. 9 Basco and Norrish, Nature, 1961, 189,455. 7 Smith, J. Chem. Physics, 1959,31, 1352. 10 Basco and Norrish, Proc. Roy. SOC. A, in press. 11 Cashion and Polanyi, J. Chem. Physics, 1961,35, 600. 12 Basco and Norrish, unpublished results. 13 Harris and Willard, J. Amer. Chem. SOC., 1954,76,4678. 14 Frey, Proc. Roy. SOC. A, 1959, 250,409. 15 Simons and Yarwood, Trans. Faradar SOC., 1961, 57, 2167. 16 Norrish and Oldershaw, Proc. Roy. SOC. A, 1958,249,498. 17 Herzberg, Proc. Chem. SOC., 1959, 116. 18 McGrath and Norrish, Proc. Roy. SOC. A , 1957, 242,265. 19 Basco, Norrish and Wayne, to be published. 20 Lipscomb, Norrish and Thrush, Proc. Roy. SOC. A, 1956,233,455. 21 Schuler, J. Physic. Chem., 1957, 61, 849. 23 Herzfeld and Litovitz, Absorption and Dispersion of Ultrasonic Waves (Academic Press. New 22 Basco, Callear and Norrish, to be published. York and London, 1959).

ISSN:0366-9033    

DOI:10.1039/DF9623300099

出版商:RSC    

年代:1962

数据来源: RSC

摘要:

Energy Distribution Among Reaction Products Part 1 .-The Reaction Atomic Hydrogen plus Molecular Chlorine BY P. E. CHARTERS AND J. C. POLANYI Dept. of Chemistry, University of Toronto, Toronto Received 18th January, 1962 Infra-red chemiluminescence from the reaction Hf Cl2 +HClt+ Cl (HClt is vibrationally ex- cited HC1 in its ground electronic state) has been examined with improved resolution at roughly two orders of magnitude lower HCl pressure than heretofore. Under stationary state conditions the rotators in vibrational levels 1 to 4 appear to be in thermal equilibrium (135175°C) up to J = 7. There is, however, an excess of rotators in rotational levels J = 9, 10, 11, . . . of v = 2, 3 and 4 (v = 1 was not measured to J>9). This could be the residue of an even greater rotational excess present in the newly-formed HC1.The stationary state vibrational distribution is markedly non- Boltzmann, being characterized by " temperatures " ranging from 8000 to 2930°K. Relative rates of reaction, Rv, into the various vibrational levels of HClt, have been calculated from the observed stationary state distribution, in several ways. The rate of reaction is always found to be greater into lower vibrational levels, the rate into u = 3 being approximately 35 times that into u = 5. If the heat of a chemical reaction is sufficient to form products in various vibra- tionally and rotationally excited states, then there should exist a " fine-structure " to the reaction rate consisting in the specific rate constants for reaction into each vibrational and rotational level of the products.In the simplest exchange reaction the products have only three internal degrees of freedom, one vibrational and two rotational, all vested in the new molecule AB. There has existed for some time a substantial body of evidence indicating that in certain reactions of the type A+BC, almost the entire heat of reaction goes into vibrational energy of AB. The reactions in question are X+NaZ-,NaX+Na and Na + XM+NaX+ M, where X is C1, Br or I and M is Cd or Hg.13 2 Two avenues are at present being explored in the hope of extending this early data on energy distribution among the products of reactions A+ BC. A preliminary study has been made of the reaction K+BrH-+KBr+H in crossed Maxwellian molecular beams.3 It has been shown that it should be possible to calculate the recoil energy of the KBr product from its angular distribution.By subtracting the recoil energy from the total energy available (i.e., the heat of reaction plus the activation energy, Q+Ea) a value will be obtained for the total internal energy, rotation+vibration, of the KBr.4 As yet, no results are available for this system. A second approach depends upon the investigation of infra-red emission arising from the reactions H+Xz-+HXt+X(X = C1 or Br) in which the emitter HXt is a vibrationally excited molecule in its ground electronic state.5.6 In principle, it should be possible to obtain the " fine-structure " of the reaction rate, for a Max- wellian distribution of reagents, from measurements of the initial vibrational and rotational excitation of the product.The recoil energy could then be obtained by difference; this is the reverse of the procedure in molecular beam experiments. The two techniques should complement one another. The present paper presents some results obtained by the infra-red chemiluminescence technique. A+BC-,AB + C (1) 107108 ENERGY DISTRIBUTION AMONG PRODUCTS In the earlier work on both the systems H+X2, product HXt has been detected with vibrational energy up to and including the level having energy equal to the entire heat of reaction. For H+Cl2, an analysis has been made of the partially- resolved fundamental and first overtone en1issions.7~ * This analysis revealed that the stationary state distribution of HClf in the reaction vessel, at ca. 0.2 mm Hg pressure, deviated only slightly from a 2700°K Boltzmann distribution.From this stationary distribution a calculation was made of the rate of chemical reaction directly into each vibrational level of HClt, on the assumption that HClt had achieved the observed distribution through radiation and collision, but not by transferring vibra- tional energy among themselves. The rates of reaction derived in this way were found to be progressively larger into successively lower vibrational levels. This result ran counter to the general expectation that reaction A+BC would proceed most rapidly into the highest accessible vibrational states of AB.9-11 The most persuasive experimental evidence for the expectation of higher reaction rate into higher vibrationd levels in reactions A+ BC, came from the quantitative results on the systems X+ Na2-+NaX+ M, referred to above.The spectroscopic identification of highly vibrating AB among the products of several reactions A+BCD+AB+CD further strengthened this expectation.129 13 The presence of highly vibrating AB was fully established in this work but the precise extent to which this species was formed directly by chemical reaction remained in doubt. Quantitative evidence came from studies of infra-red emission arising from the reaction of H+03+ OH? + 0 2 , which yielded roughly comparable rates of reaction into all the 9 accessible vibrational levels of OHt,14 and H + NOCl-+HClt +NO, which gave progressively larger rates of reaction into successively lower vibrational states.15 Earlier work on H+C12 appeared to suffer from two major defects.In the first place, resolution, especially in the overtone region of the spectrum, was poor, and analysis had to be made from overlapping partially-resolved bands. Secondly (this criticism could apply also to the results cited above for H+O3 and H + NOCl), the observation of a Boltzmann, or nearly-Boltzmann, distribution of the excited product among vibrational states suggested that, in the interval between product formation and emission (- 10-2 sec), the vibrational energy might have been to some extent randomly redistributed among vibrational states as a consequence of collisions between product molecules, ABt and AB. In a general way it is clear that this randomization would tend to destroy the " memory " that thevibrationallyexcited species had of their original distribution.More precisely, the result would be to invalidate the argument by which stationary state distribution in the reaction vessel is translated into rates of chemical reaction into the various vibrational levels.8 These considerations point to the need for a fresh analysis of the infra-red emission arising from the reaction H+Cl2, at lower partial pressures of HClt (to reduce the likelihood of HClt + HCl exchange), and at the same time, with improved resolution. In order to achieve this, a system with greatly improved " light "-gathering power is required. An apparatus with 120 times the reaction volume of that used in our earlier work on H+Clz, and with internal mirrors to collect the radiation, has already been described in connection with an investigation of the system H + 02.16 A preliminary investigation of the reactions H + Cl2 and H + NOCl in this apparatus 17 showed that at - 10-2 mm Hg total pressure ( N 10-1 times the total pressure used in the earlier work) the stationary distribution of HClt in the reaction vessel was markedly non-Boltzmann. Emission previously observed from the highest vibrational levels was no longer observed at the low pressure.This emission may have been due to secondary processes occurring at higher pressures of HClf. The new observationP. E. CHARTERS AND J . C. POLANYI 109 had the effect of strengthening the conclusion regarding the relative rates of chemical reaction arrived at on the basis of the earlier work, namely, that the rate of reaction is greater into the lower vibrational levels in the system H + C b In the present work this result is supported by further, quantitative, evidence.The fact that the result is in contradiction to the information concerning the only other reactions A+ BC for which data are available (X+Na2 and Na+XM), need not, of course, be taken to mean that one or the other result is wrong, since the reactions are of quite different types. RESULTS The apparatus has been described previously.16 In the present work, in addition to coating the reaction vessel with phosphoric acid, a phosphoric-coated Pyrex lining was placed inside the vessel in the hope of decreasing the loss of H atoms at the wall. The four discharge tubes were drawn down to 3 mm at their tips.The reaction vessel was at room temperature. Internal mirrors were front-surface coated with gold. The spectrometer was a model 112G Perkin-Elmer double-pass grating instrument. FIG. 1.-Trace of the emission in the region of the HCI fundamental ; slit width 0.30 rrm. Fig. 1 shows an actual trace of the fundamental region of the HCl emission (approx. 3.2-3-7 p). A further region (to 4.0 p) was traced at 0.50 mm and 2.00 mm slits. The majority of lines exhibit partial isotopic splitting. Fig. 2 shows a trace of the first overtone emission (approx. 1.7-2-0 p). The times required to trace these spectra were lt h for the fundamental and 1 h for the overtone. In order to check on the constancy of the emission a central portion of each spectrum was traced immediately prior to and subsequent to the recording of the spectrum itself.Flow rates of reagents were 60 p moles/sec of hydrogen through the discharge tubes, and 285 p moles/sec of chlorine into the reaction cell. Total pressure in the cell was 1.4 x 10-2 mm Hg. These spectra constitute the raw data of expt. 2. Expt. 1, an overtone trace made 5 months earlier, provided (along with similar data for H +Noel), the basis for our preliminary conirnunication.17 The results of the detailed analysis of expt. 1, as it related to H+C12, are presented here along with the results of expt. 2. The H+Cl:! first-overtone trace of expt. 1 is not reproduced. Reagent flows were the same as in expt. 2. Relative peak Resolution was similar to that in fig. 2.110 ENERGY DISTRIBUTION AMONG PRODUCTS heights differed from those of fig.2 since a different setting was used for the potassium bromide prism in the fore-prism monochromator ; this has a marked effect on the transmissivity against wavelength curve for the spectrometer. FIG. 2.-Trace of the emission in the region of the HCl first overtone ; slit width 0-25 mm. In both expt. 1 and 2 the areas under the peaks in the recorded spectra were corrected to uniform spectrometer transrnissivity by comparison with a trace, made over the same spectral region at the same slit width, using a black body emitter asP. E. CHARTERS AND J . C . POLANYI 111 source. This corrects at the same time for varying response of the PbS detector, with changing wavelength. The agreement between the overtone traces of expt.1 and 2 after correction for transmissivity (see table 2) attests to the validity of this method of correction, as also does the consistency between relative populations (table 2) taken from the fundamental and those derived from the overtone of expt. 2 ; transmissivity corrections within the fundamental differ considerably from those within the overtone. No correction has yet been made for any variation with wavelength of the reflectivity of the gold mirrors in the reaction cell. Somewhat different reflectivity is to be expected between the fundamental and the overtone regions. However, this would not affect our results since we have only made use of relative intensities within the fundamental, and within the overtone. The data obtained from these two sources, as already remarked, are consistent.This implies either that the re- flectivity of the gold is changing in an identical fashion over the spectral region covered by the fundamental as over the spectral region covered by the overtone or, more probably, that the reflectivity is not changing markedly in either region. i at\ J’(J’+ 1) FKG. 3.-Stationary-state distribution of HClt among rotational states of vibrational levels and 3, as calculated from the fundamental emission. 0 from v(1-0), 0 from v(2-1), A v(3-2). Filled-in points from P branch lines, the remainder from the R branch. 1, 2 from That the latter supposition is correct is suggested by the fact that the ratio of P line to R line intensity within a band does not show the anomaly (enhancement of P) which would be expected if the mirror reflectivity were changing markedly, nor do the Boltzmann plots of fig.3 and 4 show the expected downward curve of R line values. Variation in reflectivity during an experiment, due to chemical attack on the mirrors, cannot be important, since the observed emission intensity changed by no more than 10 %/h.112 ENERGY DISTRIBUTION AMONG PRODUCTS If there is a Boltzmann distribution among the rotational states of HClt present in the reaction vessel, then log (IJ/o.$SJFJ) plotted against J’(J’+ 1) should yield a straight line of slope -Bhc/kT. Here, rJ is the relative emission intensity of a rota- tional line within some vibrational band, COJ is the wave number frequency of that line, SJ = J’ (the upper state rotational quantum number) for an R branch line and SJ is equal to J’+ 1 for a P branch line.FJ, which varies by a factor of 3 in our range of J’, is defined as FJ = 1 -4yem, where y is the frequency ratio of rotational S(S+ 1) FIG. 4.-Stationary-state distribution of HClt among rotational states of vibrational levels 2, 3 and 4, as calculated from the overtone emission. 0 from o(2-0), A from 4 3 - l), V from 44-2). Filled-in points from P branch lines, the remainder from the R branch. to vibrational motion, 8 is close to unity for HCI, and m is an integer equal to +J’ for R branch lines and - (J’ + 1) for P lines.18 The constants in - Bhc/kT have their usual meanings; values used for B were taken from Rank, Eastman, Rao and Wiggins.19 Rotational Boltzmann plots for three fundamental bands of expt.2 are reproduced in fig. 3, and those for three overtone bands in fig. 4. Table 1 lists rotational temperatures taken from the slopes of the lines in fig. 3 and 4 in their linear regions. TABLE 1 .-STATIONARY-STATE ROTATIONAL TEMPERATURES fundamental overtone band temp. (OK) band temp. (OK) 1“ 507 2-1 470 2-0 379 3-2 450 3-1 358 4-2 439P. E. CHARTERS AND J . C. POLANYI 113 Relative stationary-state populations in the various vibrational levels can be calculated by two methods. One method involves summing the intensities of all the lines arising from the same vibrational upper state, I;; = CI;;”’, J’ whereupon N,. oc I~;/(courVAut,). Here coVfv can be taken as the band origin frequency ( u ) ~ ) ~ , ~ . A1)tV cc (oo)$, 1 R;’ 12, where Ri’ is the transition moment for the (forbidden) transition between the rota- tionless states v’, J’ = 0 and v, J = 0 (the values used for this constant were those of ref.(15)). Eqn. (2) implies that the total emission intensity for a particular band bears a fixed relation to the total number of molecules in the upper vibrational state for that transition, irrespective of the rotational distribution within that upper state. This result, which is due to an accidental cancellation of effects in the HCl molecule, is derived in ref. (18). In earlier work we have been obliged to calculate N,, from eqn. (2) since, in the overtone region of the spectrum from which we obtain most of the information concerning relative populations, individual rotational lines could not be resolved.As a consequence, only total emission intensity I:: could be obtained. In the present work, improved resolution permits us to test the ac- curacy of eqn. (2) by calculating our relative populations also from the general expression, which requires a knowledge of the individual rotational line intensities I:!’. Relative populations calculated from eqn. (3) agree with those taken from eqn. (2) to within experimental error. TABLE 2.-sTATIONARY-STATE VIBRATIONAL POPULATIONS N, EXPRESSED RELATIVE TO N4 ; TEMPERATURES Tv CALCULATED FROM NllN, o = l v = 2 v = 3 v=4 u = 5 expt. 1 Nu (overtone) - 13.7 5.4 1.0 ca. 0.2 expt. 2 Nu (overtone) - 13-0 5.9 1.0 ca. 0.12 - - N , (fundamental) 21.5 (1 3-0) 5.1 Tv (OK) - 8000 5450 * 3770 2930 6050 t * from the fundamental of expt.2. t from the overtone of expt. 2. I The values obtained for the stationary-state populations N,, expressed relative to N4 = 1, are listed in table 2 for expt. 1 and 2. Relative populations in the funda- mental of expt. 2 have been brought to the same scale as the overtone by equating N2 in each series. If the distribution of HClt among vibrational levels were Boltzmann, then where N is the total population of HCl in all levels (including v = 0), and Go(v) is the energy of level v relative to the zeroth level. If this expression holds, then a plot of log (N1/Nv) against Go(u) - Go( 1) (cm-1) will yield a straight lineof slope 0-625/T. Fig. 5 shows such a plot for the results of expt. 2. The distribution deviates markedly, and systematically, from Boltzmann, in the sense that the population falls off more and more rapidly (corresponding to lower and lower “ temperatures ”) towards higher vibrational levels.114 ENERGY DISTRIBUTION AMONG PRODUCTS DISCUSSION In previous studies of H+C12 chemiluminescence we have only been able to ob- serve the rotational distribution within the 1-0 band.In the present work, improved intensity and resolution have enabled us, despite roughly two orders of magnitude lower reagent pressure, to make similar measurements on the 2-1 and 3-2 bands of the fundamental and the 2-0, 3-1 and 4-2 bands of the first overtone. The form of the Boltzmann plots (fig. 2 and 3) suggest the following observations, (a) The rotators in any given vibrational level are in thermal equilibrium up to roughly J’ = 7.(b) The rotational “ temperatures ” which characterize the rota- tional distribution in this region of J’ = 0-ca. 7 are similar for all vibrational Go(u)- Go(l), cm-1 of vibrators at the temperatures indicated would give points lying along the solid lines. FIG. 5.-Stationary-state distribution of HClt among vibrational states. A Boltzmann distribution levels, = 1-4. The differences are not great enough to merit discussion at the present time. All are about 100°C above room temperature (falling in the range 135+75”C). It is possible that this is the temperature of the Pyrex sleeve within the reaction vessel, since the sleeve is in poor thermal contact with the metal walls. (c) The measured intensities are not seriously affected either by self-absorption or by change in mirror-reflectivity with wavelength, since either of these effects would cause the Boltzmann plot to curve, starting at J’ = 0.For self-absorption the curvature would be most marked in the fundamental bands (for which the extinction coefficient is greatest), for reflectivity change the curvature would be most marked in the overtone (since reflectivity alters more rapidly in the near infi-a-red). No systematic deviation of this sort is evident. (d) For J’ = 9, 10 . . . there is an excess of rotators in all vibrational levels for which data are available. This excess isP. E. CHARTERS AND J . C. POLANYI 115 real, and not a consequence of faulty analysis, since it is not observed in experiments at 1-2mm pressure employing the same spectrometer and method of analysis.20 Despite the fact that the average emitter has suffered -103 collisions with C12 (the major constituent) since its formation, this excess rotational population may be a residue of an even larger excess present when the HClt was originally formed.Sufficient energy is available for this excitation. For example, HClt in u = 4, J = 20 requires 31.2 + 11 -7 kcal/mole whereas energy liberated per mole of HClt formed is 47.5 kcal. In general, a few collisions suffice to bring about rotational transfer J'+ J' - 1.22 However, this need not necessarily apply to high rotational states for which the rotational jump, AJ = 1, approaches in magnitude that of a normal vibrational jump. Moreover, many transfers could be required to convert an unorthodox rotational distribution into a Boltzmann distribution showing no trace of the original anomaly.Relative rates of chemical reaction, R,, into each vibrational level u have been calculated from the observed relative stationary state populations Nv on the assump- tion that vibrational transfer among HCl's can be neglected owing to the low partial pressure of HC1 (estimated to be -10-4mm). Though the total pressure in the reaction vessel is only an order of magnitude less in the present work than in our earlier experiments,g the partial pressure of HCl is two orders of magnitude less since the partial pressure of H2 is -2 x 10-3 mm whereas previously it was N 1 x 10-1 mm. Furthermore, the percentage dissociation of H2 will be lower in the present case owing to the tube and nozzle separating the discharge from the reaction vessel, and the metal surfaces within the vessel.If, despite the low pressure of HCl, HCl+ HC1 vibrational exchange were still of importance in determining the stationary- state distribution, we should expect the observed distribution to vary from one experiment to the next owing to changed H-atom pressure and hence changed HC1 pressure. We have not observed any such effect. R, has been calculated from the relation Rv = ( C A V U + czpvu + zp:o + 7 - l > N V - ( C A W V N W + C Z P W V N W ) ( 5 ) (5') U U W W = ( A + B + C + D) - ( E + F ) , where u < v < w, 2 is the number of gas-collisions per second suffered by the average molecule ( N 105 at 0.01 mm pressure), z is the number of wall-collisions with metal surfaces (360 per sec in our vessel), A,, is the Einstein radiational transition prob- ability (&, of eqn.(2)), Puu is the analogous gas-phase collisional transition prob- ability, PJo is the collisional transition probability for " quenching " (1130) at a metal surface, and z is the residence time in the reaction vessel (2-22 x 10-2 sec). Table 3 lists the values calculated for each term in eqn. (5). The first four terms in the equation give the total rate of transfer of HClt out of level u ; the remaining two terms give the rate of transfer into v, with the exception of direct chemical forma- tion. The difference is the rate of chemical formation R,. The first term A in eqn. (5') gives the total rate of radiational transfer out of level u.The secondand sixth terms, Band F, give the total rates of collisionaltransfer out of and into t). In table 3, R,' and R1:' assume B = 0, F = 0. RL1 and Riv assume B = maxi- mum, F = maximum. Comparison of R,' with R!, and R1;I with RLv, shows that col- lisional deactivation in the gas is not important at our pressures. We have been able to place an upper limit on B and I; from the observation that the system H + Cl2 at 1 mm pressure gives rise to HClt in a distribution which approaches a 3500°K Boltzmann distribution.20 The total vibrational energy per mole at this temperature is equiv- alent to about 10 % of the energy made available by the reaction forming HCl.I16 ENERGY DISTRIBUTION AMONG PRODUCTS It follows that even if the entire heat of reaction goes into vibration, collisional deactivation at 1 mm pressure (107 collisions per second per HClt) cannot remove more than 90 % of the energy.Writing Pvu = cA,, (according to the Landau- Teller theory 22) and solving the 6 stationary-state equations when only R6 is sig- nificant, one obtains a set of Nu in terms of an undetermined c. These Nu substituted in eqn. (6), c EUNU >Oslo, (6) ~ = 1 - 6 (Q+EJ c N , u=O-6 yield a value of ~ ~ 3 . 3 x 10-6. It follows that Ploy for example, is > 1.1 x 10-4, i.e., on the average >9.1 x 103 collisions are required to transfer HCl from u = 1-+0. This is a reasonable lower limit.21 TABLE 3 . D ” L A T N E RATES OF REACTION, &, INTO SPECIFIC VIBRATIONAL LEVELS OF HCl R: = (A+ D) - E R’,’= (A+ B + D) - (E+ F) RIL1= (A + C + D) - E Riv=(A+ B I- C + D) - (E + F) v Nu A B 5 0.12 16.7 < 5.4 <#*4 5.6 0 0 0.15 0.16 0.13 0.13 4 1.00 115 <37-2 <358 45-2 14.2 < 4.6 1.00 1-00 1-00 1-00 3 5.50 501 <163 <I970 249 104 <33*9 4.43 4.34 5.19 5.11 2 13-04 835 <271 <4670 589 476 <155 6.51 5.97 11.15 10.69 1 21.5 729 <237 97700 972 841 <273 5.91 4.62 17.0 15.9 The third term gives the total rate of “ quenching ” by collision with metal sur- faces.There is experimental evidence that a metal surface is very efficient in re- moving vibrational energy.23 (Pyrex has a low collision efficiency, - 5 x 10-4.23) In calculating R;I and RIV we have made the crude assumption that HClt is trans- ferred to v = 0 at every collision with metal surfaces, i.e., P,fo = 1.In calculating R: and we have gone to the opposite limit and assumed no quenching; P& = 0. More refined assumptions, for example, P;4 - 1 combined with P;uccAuu (this re- quires the introduction of a term, -czP$,N,,,, on the right-hand side of (5)) lead to series of R, somewhat similar to those obtained on the assumption that P$o = 0 . Thus, for P;4 = 1, PZu~Avu, we obtain R5 = 0.16, R4 = 1.00, R3 = 4.10, Rz, = 4.50, R1 = 1.10. Examination of table 3 shows that, under our experimental conditions, the de- cisive term in the calculation of relative rates of chemical reaction into levels 21 = 5, 4 and 3, is the rate of radiational decay. In order to reverse the trend in R, it would be necessary for the radiational transition probabilities to be altered to values well outside the estimated limits of error in theoretical and experimental determina- tions of these quantities.24 The feature that is common to all four series of R,, calculated under various limiting assumptions, is a rise in rate of reaction into successively lower vibrational states u = 5, ZI = 4, u = 3, 21 = 2. In passing from ZI = 5 to v = 3 the increase in rate amounts to a factor of roughly 35. WP. E . CHARTERS AND J . C. POLANYI 117 If (contrary to our expectation) HCl+HCl vibrational transfer is occurring to a significant extent in our system, this would have the effect of increasing the relative population in high vibrational levels under our stationary conditions. We would then have underestimated the increase of reaction rate into successively lower vibra- tional levels.The authors wish to express their thanks to Dr. B. N. mare for assistance with these experiments. They are grateful to the National Research Council of Canada, the University of Toronto Advisory Committee on Scientific Research and the Imperial Oil Company of Canada, for financial assistance. One of them (J. C. P.) thanks the Alfred P. Sloan Foundation for the award of a Fellowship. 1 Polanyi, Atomic Reactions (Williams and Norgate, London, 1932). 2 Evans and Polanyi, Trans. Furaduy SOC., 1939, 35, 178. 3 Taylor and Datz, J. Chem. Physics, 1955, 23, 1711. Greene, Roberts and Ross, J. Chem. 4 Datz, Herschbach and Taylor, J. Chem. Physics, 1961, 35, 1549. 5 Cashion and Polanyi, J. Chem. Physics, 1958, 29, 455. 6 Cashion and Polanyi, Proc. Roy. SOC. A, 1960, 258, 570. 7 Cashion and Polanyi, J. Chem. Physics, 1959,30, 1097. 8 Cashion and Polanyi, Proc. Roy. SOC. A , 1960, 258, 529. 9 McGrath and Norrish, 2. physik. Chem., 1958, 15,245. Physics, 1960, 32, 940. 10 Polanyi, J. Chem. Physics, 1959, 31, 1338. 11 Smith, J. Chem. Physics, 1959, 31, 1352. 12 McKinley, Garvin and Boudart, J. Chem. Physics, 1955, 23, 784. 13 Norrish and co-workers ; for ref., see Basco and Norrish, Can. J. Chem., 1960, 38, 1769. 14 Garvin, Broida and Kostkowsky, J. Chem. Physics, 1960, 32, 880. 15 Cashion and Polanyi, J. Chem. Physics, 1961, 35, 600. 16 Charters and Polanyi, Can. J. Chem., 1960, 38, 1742. 17 Charters, Khare and Polanyi, Nature, 1962, 193, 367. 18 Cashion and Polanyi, Proc. Roy. SOC. A , 1960, 258, 564. 19 Rank, Eastman, Rao and Wiggins, J. Opt. SOC. Am. 1962, 52, 1. 20 Findlay and Polanyi, to be published. 21 Herzfeld and Litovitz, Absorption and Dispersion of Ultrasonic Waves (Academic Press, New 22 Landau and Teller, Physik. 2. Sowjetunion, 1936, 10, 34. Montroll and Shuler, J. Chem. 23 Schiff, private communication. 24 Benedict, Herman, Moore and Silverman, J. Chem. Physics, 1957, 26, 1671. York, 1959). Physics, 1957, 26, 454. -

ISSN:0366-9033    

DOI:10.1039/DF9623300107

出版商:RSC    

年代:1962

数据来源: RSC

摘要:

Studies of Vibrationally Excited Nitrogen Using Mass Spectrometric and Calorimeter-Probe Techniques BY J. E. MORGAN, L. F. PHILLIPS AND H. I. SCHIFF Dept. of Chemistry, McGill University, Montreal, Canada Received 22nd January, 1962 Isothermal calorimeter-probe measurements showed that " active " nitrogen contains excited molecules with excitation energy corresponding to 6 kcal/mole of totaf gas. These molecules were deactivated mainly on the walls with an efficiency of 4-75 x 10-4. The collision efficiencies for the gas-phase deactivation by N20, C02, A and N2 are 1.38 X 10-4, 4.3 X 10-5, 1.5 x 10-6 and 3.3 x 10-8 respectively. This method was also used to show that the vibrationally-excited N$ molecules formed in the reaction N+NO+N;+O have an average energy of 21 5 5 kcal/mole.A mass-spectrometric method showed that 75f5 % of the NJ formed from this reaction have sufficient energy to decompose 0 3 . The rate of deactivation of N$ by unexcited N2 to vibrational levels below the fourth was found to be 3.5 x 10-16 cm3 molecule-1 sec-1 and by N20 to be 1.3 x 10-15 cm3 molecule-' sec-1. Convincing evidence has been obtained for the presence of energetic molecular species in " active " nitrogen. Kaufman and Kelso 1 found that the addition of N20 to a stream of discharged N2 resulted in a marked temperature rise in the neighbourhood of the mixing point. They were able to show that the energy release was not due to an acceleration of atom recombination and ascribed the effect to deactivation of vibrationally excited N2 by the N20.Although this experiment was largely qualitative, they estimated the energy release to be about 2 kcal/mole of total N2, and the lifetime of the excited molecules to be about 50 msec. Dressler 2 studied the ultra-violet absorption spectrum of discharged N2 and showed the presence of N2 in the first vibrational level of the ground state. From the space-average concentration of the excited molecules over the length of the flow tube, he was able to establish a lower limit of 10 msec for the half-life. In the present work it was possible to study the excited molecules by means of an isothermal calorimetric probe.3 This probe measures the total heat content of all the energetic species in the gas stream, i.e., both atoms and excited molecules. The heat content of the atoms can be calculated from the atom concentration and the dissociation energy of N2.It is therefore possible to determine, by subtraction, the heat content of the excited molecules. The N-atom concentration was determined by the NO-titration technique.4-6 The reaction (1) (2) (4) N+NO = N2+O k = 2.2 x 10-11 cm3 molecule-1 sec-1,7.8 k = 6 x 10-32 cm6 molecule-2 sec--1,9-11 k = 5 x 10-33 cm6 molecule-2 sec-1.13. 14 is much more rapid than the subsequent reactions : NO+O+M = NO2+M, NO + 0 = NO2 + Av, k = 3 x 1017 cm3 molecule-1 sec-1,12 (3) N + 0 + M = NO + M + hv, 118J . E. MORGAN, L . F. PHILLIPS AND H . I . SCHIFF 119 Reaction (3) produced chemiluminescence in the presence of excess NO and reaction (4) in the presence of excess N. The end-point is readily determined, since there is no chemiluminescence when reaction (1) is stoichiometric.Some evidence has been obtained 1 to indicate that part of this energy appears as vibrational excitation of the N2 produced. Two methods were used in the present work to study quan- titatively the Nl excited in this way. First, the heat content of the energetic species present in the gas stream after the titration could be compared with the calculated heat content of the 0-atoms produced by the reaction. (The titration also permits an evaluation of the number of 0-atoms produced.) Secondly, the NZ formed by reaction (1) was found to be sufficiently energetic to decompose 0 3 . This reaction was therefore investigated with a mass spectrometer. Reaction (1) is exothermic to the extent of 75 kcal/mole.EXPERIMENTAL ISOTHERMAL CALORIMETRIC-PROBE MEASUREMENTS Molecular nitrogen was dissociated to the extent of about 1 % in a flow system by a microwave discharge operated at 2450 Mc/sec. Descriptions may be found elsewhere of the movable probe,3 the titration techniques 15 and other experimental details.16 FIG. 1 .-Probe measurements on discharged nitrogen at p~~ = 4.10 mm Hg and (p& = 0-03 13 mm Hg. A, Hexpt. measured by cobalt plated probe ; B, Halc. from atom concentration at t = 0 and afterglow intensity ; c, In (Hexpt.--Hcalc.). The N-atom concentration at one point was determined by NO titration. The NO flow was then stopped and the decrease in the atom concentration along the reaction tube was followed by photometer measurements of the " afterglow ", the intensity of which has been shown 17 to be proportional to m]2.The results of a typical experiment are shown in fig. 1. Curve A shows H, the rate of heat liberation to the probe, from the " active " nitrogen. as a function of t h e along the reaction tube. Curve B shows a plot of H120 STUDIES OF VIBRATIONALLY EXCITED NITROGEN calculated from the known N-atom flow rate, while the logarithm of the difference AH is shown as C. The half-life of the species responsible for this energy difference is 80msec. It seems reasonable to conclude that " active " nitrogen contains a relatively large fraction of excited N2 molecules, which will subsequently be denoted by N;. The degradation of the energy from N; to kinetic energy with subsequent loss to the wall can be represented as occurring in the gas phase by N; +M -+N, +M: and on the walls by N,*E%N,.The observed first-order rate constant k, obtained from the In (AH) against t plots, can be written as k = k5[M] + k g . The value of k was found to be independent of the nitrogen pressure within experimental error. It can, therefore, be concluded that k5 is close to zero when M = N2. From a series of such measurements, it was found that k6 = k = 8.7 f0.2 sec-1. 4 FIG. 2.-Probe measurements of discharged nitrogen at different linear flow rates (f.r.). 0 f.r. = 200 cmlsec, p~~ = 2.3 mm, ( p ~ ) o = 00188 mm; 0 f.r. = 165 cmlsec, p~~ = 2.95 mm, (pN)o = 0.0229 mm ; 0 f.r. = 126 cmlsec, p w = 4-10 mm, ( p p . ~ ) ~ = 0.0313 mm; 0 f.r. = 110 cmlsec, PN2 = 5.84 mm, (p& = 0-0405 mm.If the value of AH could be extrapolated to the discharge tube, it would be possible to calculate the energy of the excited molecules leaving the discharge. Unfortunately, the geometry of the tubing between the discharge and the reaction tube made such an extra- polation unreliable. The magnitude of AH at any position along the reaction tube will depend upon the elapsed time from the discharge and on the molar flow rate of N2, h2 For sets of experiments with different linear flow rates, plots of log (AH/&*) against time will have the same slope but will be displaced with respect to one another due to the differ- ence in elapsed time from the discharge to the point of measurement. However, if log (AH/fNJ is plotted against distance along the reaction tube for different linear flow rates, the slopes will also differ due to a change in time scale.Since the dis-J . E. MORGAN, L. F. PHILLIPS AND H. I . SCHIFF 121 charge is a fixed distance from the reaction tube, these plots should all intersect at the effective discharge position. Such plots are shown in fig. 2, where d = 0 is an arbitrary position in the reaction tube. The value of AH/fN2 at the intersection corresponds to a value of 6.03 kcal/mole. This can be taken as the average energy of the nitrogen molecules emerging from the discharge. This does not, however, preclude the possibility of other energetic species with lifetimes much shorter than the time required for the gas to flow from the discharge to the measuring region. In fact, Beale and Broida have recently shown 18 that under certain conditions a very energetic species may be formed with a lifetime of about 2 msec. The addition of about 10 % N20 to the gas stream after the discharge resulted in complete deactivation of N; within the 30msec time delay between the N20 inlet and the first measuring position.The agreement between the heat measured by the probe and that calculated for the atom recombination indicates that the probe quantitatively measured the contribution of the atoms to the heat content of the gas. Separate experiments, in which a second similar probe coil was placed in the reaction tube above the measuring probe, showed that no heat was liberated on the latter. This indicated that the probe measured the entire heat content of the gas and consequently was capable of giving quantitative values for the contribution of N;.I I I I 1 5 I I I I 1 50 100 150 200 msec FIG. 3.-Probe measurements of discharged nitrogen with Pyrex wool plug after the discharge tube ; p~~ = 2-00 m Hg. 0 heat measured by probe ; 0 heat calculated from atom concentration at t = 0, and afterglow intensity. Smaller amounts of N20 were added to the " active " nitrogen stream to determine the value of k5 in the presence of this gas. Similar experiments were performed with the addition of A and C02. The results are shown in table 1. TABLE 1 M kS collision k6 cm3 molecule-1 sec-1 efficiency 01 N2 8.7 sec-1 6 . 5 ~ 10-18 3.3 x 10-8 CO2 8.7 ,9 7 . 5 ~ 10-15 4.3 x 10-5 NZO 8.7 ,Y 2 4 x 10-14 1 . 3 8 ~ 10-4 A 8.7 ,¶ 2.5 x 10-16 1 .5 ~ 10-6 u ~ I G A 0.02 1 29 92122 STUDIES OF VIBRATIONALLY EXCITED NITROGEN As mentioned above, the value of k5 for M = N2 was zero within experimental error. The value given in table 1 represents an upper limit only based on the uncertainty in the measurement of k. The value of kg will be seen to be unaffected by the addition of other gases. The wall- deactivation coefficient, calculated from kg, the radius of the tube and the molecular velocity, was 4.75~ 10-4. The corresponding efficiency of the wall to nitrogen atom recombination is 2x 10-5.199 20 Thus, it should be possible to remove N; preferentially by increasing the surface area. It was found that the insertion of a loose plug of Pyrex wool into the tube after the discharge removed all the N$, but reduced the atom concentration by only 25 %.Fig. 3 shows the agreement between the measured heat content (open circles) and that calculated from the 0-atom concentration (closed circles). msec FIG. 4.-Probe measurement of " filtered " discharged nitrogen titrated by NO. PN = 2.6 mm Hg ; po = 00219 ~llm Hg. A, Hexpt. measured by cobalt plated probe ; B, Hcdc. from titration value of [O] and known decay rate of 0-atoms ; c, In (Hexpt. - Hcalc.). Such a " filtered " system was used to study the @ produced by reaction (1). Curve A in fig. 4 shows a plot of the measured H for the gas as a function of time after the titration. Curve B shows a plot of H due to the 0-atoms, calculated from the titration value of the atom concentration, the known recombination rate and the heat of dissociation of 02.The difference shown in curve C can be ascribed to the NI formed by reaction (1). It should be pointed out that the accuracy of such an experiment is low since (a) AH repre- sents a rather small difference between two relatively large quantities, and (b) the " noise " level of the probe amounts to about 1-2 mcal/sec which is an appreciable fraction of AH. A number of such experiments indicated that the average value of the energy of @ is 21 f5 kcal/mole. MASS-SPECTROMETRIC MEASUREMENTS The flow system and mass spectrometer used to study the reaction NJ+ o,+N,+ O,+O (7) has been described previously.8 Nitrogen atoms were titrated by addition of NO through a fixed inlet to form O-atoms+N$ The end-point of the titration was determined massJ .E. MORGAN, L . F . PHILLIPS AND H. I . SCHIFF 123 spectrometrically. Ozone was added through a movable inlet located between the NO- inlet and the mass-spectrometer “leak”. The distance between the NO-inlet and the movable 03-inlet could be related to the decay time of the NZ formed by reaction (l), while the distance between the movable 03-inlet and the ‘‘ leak ” could be related to the time available for the reaction of N$ with the 0 3 . When the discharge was off, 0 3 was consumed by the reaction, NO+ 0 3 = NO2+ 0 2 , k = 2-5 x 10-14 cm3 molecule-1 sec-1. When the discharge was excited, 0 3 was consumed by the reaction, O+ 0 3 = 202, k = 2.1 x 10-14 cm3 molecule-1 sec-1, and by reaction (7). I I 15 30 45 t, mec FIG. 5.-Change in 0 3 consumption when discharge is excited.0 p~~ = 0.56 111111, (p0,)o = 2.2 x 10-2 mm, PNO = 1.31 x 10-2 rtl~; (D P N ~ = 0.40 mm, (po3)o = 2.5 X 10-2 mm, p NO= 1.08 x 10-2 mrn ; 0 p~~ = 0.35 fll~ PO,)^ = 1-7 X 10-2 111111, p ~ o = 6.2 X 10-3 111111 ; (> p~~ = 0.31 mm (po3)o = 1.45 x 10-2 mm, NO = 5-5 x 10-3 mm. Note:pNo is the amount of NO required for stoichiometry of reaction (1). The rate constants of reactions (8) and (9) are almost identical. Thus, if reaction (7) did not occur, the 0 3 concentration at any time t would, as a first approximation, be the same whether the discharge was on or off. Any additional consumption of 0 3 when the discharge is excited can then be attributed to reaction (7). Fig. 5 shows a series of curves, at different partial pressures of N2, of the decrease in the 0 3 concentration upon excitation of the discharge, as a function of time from the 0 3 - inlet to the “ leak ”.Each curve tends to a plateau value of [AOJ which corresponds to1 24 75 f 5 % of the NJ formed by reaction (1). This figure can be interpreted as the percentage of N$ formed initially by the reaction with u>4, Le., with energy equal to, or greater than the 24 kcal/mole required to dissociate 0 3 . In this set of experiments, the flow rates were too fast to detect any decay of NZ along the reaction tube, in the absence of 0 3 . To study the deactivation of N;, a number of experiments were performed in which the linear flows were reduced by “ throttling ” the pump. A large excess of 0 3 was added through the movable inlet, so that reactions (7) and (9) went to completion before the “ leak ”.This procedure essentially titrated the NZ, with ~2-4, remaining at various times after its initial production. STUDIES OF VIBRATIONALLY EXCITED NITROGEN log A03 t, msec FIG. 6.-Decay of N$ measured by 03-decomposition. 0 pN2 = 0.60 m; 0 P N ~ = 0-69 mm, p ~ ~ o = 0 1 1 mm; @ pN2 = 0.62 mm, pN20 = 0.23 IWll. Some plots of log w2], determined in this manner, as a function of time after its formation, are shown in fig. 6. The lower two curves show the more rapid decay when small amounts of N20 were added to the system. The decay can be represented in the simplest terms, by the processes : NI + M+N; + M”, (11) where Ng and M” have energies less than 24 kcal/mole. The observed first-order rate con- stant ko can then be represented by ko = kllCMI+kl29 and a plot of the slopes of the log mi] against f curves against [MI should be a straight line.Such a plot is shown in fig. 7, where M = N2. It yields a value of k12 which cor- responds to a wall-recombination coefficient of 1 . 9 ~ 10-4 and a value for kll of 3.5 x 10-16 c m 3 molecule-1 sec-1. The value of kll when M = N20 was found to be about 1-3 x 10-15 cm3 molecule-1 sec-1. The rate constant for reaction (7) was found-to be 54x 10-13 cm3 molecule-1 sec-1.J . E. MORGAN, L. F. PHILLIPS AND H. I . SCHIFF 125 DISCUSSION An attempt may now be made to compare the results obtained by the two techniques. The probe method showed that the Nl produced in reaction (1) has an average energy of 21 rt5 kcal/mole, while the 03-decomposition methcd indicated that 75 f5 % are formed initially with excess energy equal to, or greater than, 24 kcal/mole.From these results some deductions may be made about the energy distribution among the approximately evenly-spaced, vibrational levels of Ni. Let us first consider whether a Boltmann distribution is possible. The upper limit of 26 kcal/mole for the average energy would then correspond to a temperature of 13,000"K. Since the vibrational spacing E is close to 6 kcal/mole, the fraction of NI with energy equal to or greater than 24 kcal/mole is e-4n = 0-40, where x = E/RT. I I I I I 't 1 PN2, mm FIG. 7.-Slopes of In";] against t plots as a function of N2 pressure. If it is further assumed that Ni molecules with excess energy248 kcal/mole and those with excess energy 272 kcal/mole can decompose 2 and 3 molecules of 0 3 respectively, the fraction of the NJ capable of decomposing 0 3 would be e-4s+e-8x+e-12x - 0.62, compared with the observed value of 0.75f0-05.This observed value may, however, be somewhat too high. The NJ was formed in these experiments by NO-titration of " unfil- tered ", discharged nitrogen. The probe experiments indicated that the discharged nitrogen would contain about 3 kcal/mole of excess energy at the titration point. If this energy is also in a Boltzmann distribution, calculations show that about 3 % of the observed 0 3 decomposition may be attributed to the discharged nitrogen. This leaves 72*5 as the percentage of the N$ formed by reaction (1) capable of decomposing 0 3 .The difference between the observed and the calculated figures suggests that the dis- tribution is not Boltzmann, unless the magnitude of the experimental errors are greater than indicated. Thus, it would only be necessary to raise the average excitation energy to 28 kcal/mole to obtain a calculated value of 72 % 03-decomposition. Alternately, and perhaps more likely, the N l molecules are not formed with a Boltzmann energy dis- tribution, but have a relatively higher population at, or sIightly above, u = 4.126 STUDIES OF VIBRATIONALLY EXCITED NITROGEN DEACTIVATION OF N; AND Ni The wall-deactivation coefficient of N; measured by the probe method agrees, within a factor of 2, with the wall deactivation of NI measured by the 03-decomposition method.This agreement can be considered satisfactory in view of the difference in apparatus and experimental conditions used. It also suggests that N; and NI are basically similar species which differ only in the extent of their vibrational excitation. On the other hand, there are considerable differences between the homogeneous de- activations of the two species. Thus the value of k5 for N; is at least 50 times lower than kl1 for NJ when M = N2. The reason for this djfference may be understood if consideration is given to the processes measured by the two methods. The calorimeter-probe technique measured the total excitation energy of the gas and, therefore, will not detect any exchange of vibrational energy between molecules. It can only follow the rate at which vibrational energy is lost from the system, i.e., by an exchange from vibrational to kinetic energy which is subsequently lost to the walls.Because of the close matching of vibrational levels, an unexcited nitrogen molecule should be a very efficient collision partner for vibrational exchange, and therefore a poor one for transferring vibrational to kinetic energy. The 03-decomposition method measures the rate at which the energy of the N$ molecules are degraded to vibrational levels below the fourth. Such a system has been examined theoretically by Shuler 21 who showed that the rate of energy loss from a small number of excited oscillators in, effectively, a constant temperature bath of unexcited molecules, will be exponential regardless of the initial distribution. This loss may occur either by vibrational-vibrational or vibrational-kinetic energy transfer to the heat-bath molecules.Normal nitrogen should, by vibrational exchange, be very effective in lowering the excitation of N$ below the fourth level. When M = N20 the value of k5 for N; was found to be 20 times higher than kll for NI. The value for kll was calculated from the rate equation The rate of change of 0 3 decomposition will also be equal to the rate at which the NS molecules cross the fourth vibrational level. If vibrational energy is lost principally by single quantum jumps, the rate can also be expressed as -d[AO,]/dt = k'[N!(v = 4)], where k' is the rate constant for loss of a single vibrational quantum. Equating the two rate expressions gives Thus, the observed rate constant will be less than that for a single quantum jump by the ratio of the number of molecules in the fourth level to the sum of those in the fourth and higher levels.For a Boltzmann distribution at 13,000°K, this ratio is approximately 1/5. The rate constant k5 represents the degradation of one vibrational quantum to kinetic energy, whereas k' represents the transfer of one vibrational quantum either to kinetic or to vibrational energy. Therefore, in this case, k5 could be, at most, higher than kll by a factor of 5, compared with the observed factor of 20. This again suggests that there is a higher proportion of NJ near = 5 than is given by a Boltzmann distribution. Acknowledgements are gratefully made to the Defence Research Board of Canada, and to the U.S.A.F. Cambridge Research Laboratories for financial assis- tance, and to the National Research Council of Canada for two Fellowship awards to J. E. M.J . E. MORGAN, L . F . PHILLIPS A N D H. I . SCHIFF 127 1 Kaufman and Kelso, J. Chem. Physics, 1958, 28, 510. 2 Dressler, J. Chern. Physics, 1959, 30, 1621. 3 Elias, Ogryzlo and Schiff, Can. J. Chem., 1959, 37, 1680. 4 Kistiakowsky and Volpi, J. Chem. Physics, 1957, 27, 1141. 5 Kaufman and Kelso, J. Chem. Physics, 1957,27, 1209. 6 Harteck, Reeves and Mannela, J. Chem. Physics, 1958, 29, 608. 7 Herron, J. Res. Nat. Bur. Stand.lA, 1961, 65, 411. 8 Phillips and Schiff, J. Chem. Physics, 1962, 36, 000. 9 Kaufman, J. Chem. Physics, 1958, 28, 352. 10 Harteck, Reeves and Mannela, J. Chem. Physics, 1957, 26, 1333. 11 Ogryzlo and Schiff, Can. J. Chem., 1959, 37, 1690. 12 Fontijn and Schiff, Chemical Reactions in the Lower and Upper Atmosphere (Interscience, 1962), 13 Barth, Chemical Reactions in the Lower and Upper Atmosphere (Interscience, 1962), p. 303. 14 Mavroyannis and Winkler, Can. J. Chem., 1961, 39, 1601. 15 Morgan, Elias and Schiff, J. Chem. Physics, 1960, 33, 930. 16 Morgan and Schiff, J. Chem. Physics, in press. 17 Berkowitz, Chupka and Kistiakowsky, J. Chem. Physics, 1956, 25,457. 18 Beale and Broida, J. Chem. Physics, 1959, 31, 1030. 19 Herron, Franklin, Bradt and Dibeler, J. Chem. Physics, 1959, 29, 230. 20 Wentink, Sullivan and Wray, J. Chem. Physics, 1959, 29, 231. 21 Shuler, J. Chem. Physics, 1957, 26, 454. p. 239.

ISSN:0366-9033    

DOI:10.1039/DF9623300118

出版商:RSC    

年代:1962

数据来源: RSC

摘要:

Lifetime and Reactions of OH Radicals in Discharge-Flow Systems BY FRANK P. DEL GRECO AND FREDERICK UUFMAN Ballistic Research Laboratories, Aberdeen Proving Ground, Maryland, U.S.A. Received 22nd January, 1962 The decay of OH was studied in a flow system of high pumping speed. Water discharges are unsuitable as sources of OH because OH is produced throughout the flow system. When produced by the very fast reaction H+N02 -+ OH+NO (1), OH was found to decay very rapidly by the steps 20H+ H20+0 (2), and O+OH+ Oz+H (4), with (2) rate-controlling and k2 = 2-5h0.6x 10-12 cm3 molecule-1 sec-1. This decay corresponds to a half-life of OH about 100 times shorter than has previously been reported. The decay of OH was found to be unaffected by He, Ar, N2, 0 2 , NO and H20, but an increased rate in the presence of excess H2 was ascribed to OH+H2+H20+H.No vibrationally excited OH was found and it is concluded that such species are not major re- action products. An $value calculated from the measured light absorption on the basis of re- action (1) and assuming thermally equilibrated OH is in fair agreement with recent estimates. Though the spectra and structure of the OH molecule are known with great accuracy,1-3 studies of the kinetics of OH reactions near room temperature are still in a state of general confusion, because in such studies, the products of electrical discharges in water vapour have been used as reactants. These products are capable of further reactions which continuously generate OH, and thereby falsely give the appearance of a long lifetime (0-1-0-3 sec) for OH,2.4 and lead to erroneous estimates for the kinetics of its di~appearance.4~ 5 This confusion prompted us to investigate OH formation and decay processes in a discharge-ffow system of high pumping speed, so designed that OH concentrations could be measured locally by light ab- sorption across the flow tube anywhere along its full length.We soon found6 that water discharges are poor sources of OH and that the observed OM was pro- duced not in the discharge, but rather throughout the flow system, probably by the reactions H + 0 2 + M-,H02 + M, and H + H02-+2QH.7s 8 A more useful source of OH was found in the reaction H +N02+OH+NO. (1) Its use in the present study has permitted us to measure the rates of several fast OH reactions, to clarify the inechanism of its decay, and to search for vibrationally excited OH as a primary reaction product.The detailed study of water vapour discharges will not be discussed here. EXPERIMENTAL FLOW SYSTEM A diagram of the apparatus is shown in fig. 1. The quartz flow tube of 3.0 cm int. diam. and 150 cm length is connected through a large trap and metal ball valve (3.8 cm int. diam.) to a two-stage Roots pump (Consolidated Vacuum Corp. model VP-R-l52A, manufactured by W. C. Heraeus G.m.b,H., pumping speed of 50l./sec at pressures up to 10mmWg) which is backed by a mechankal pump (Cenco Hypervac 25) of about one- tenth the speed of the Roots pump. Near its upstream end, the quartz tube was fitted with four inlet tubcs of varjous size and purpose. The largest inlet A was a quartz tube of 10 mrn int.diam. which served as the principal discharge tube and was connected to a 128F. P. DEL GRECO AND F. KAUFMAN 129 manifold from which up to four gases could be added through calibrated flowmeters. A second quartz tube B could serve as an auxiliary discharge for double discharge experiments. The third inlet C was there only for addition of diluent gases. Through the fourth inlet D, 16 cm downstream of the principal discharge tube, NO2 or other gaseous " titrants " were introduced. After many mixing experiments utilizing the extinction of the air after- glow with NO2 and of the nitrogen afterglow with NO, it became apparent that for fast mixing of the titrants a multi-perforated inlet tube was required. Two types were made and used.The earlier one was a glass tube of 3 mm ext. diam. which traversed the flow FIG. 1 .-Diagram of apparatus. tube from its bottom to nearly its top inside surface. This thin tube had 10 holes of about 0-1 mm diam., 5 on each side, equally spaced from bottom to top. For moderate gas addi- tions, this inlet tube was successful, but it was later replaced by an improved version con- sisting of a loop plus a straight section of Teflon tubing (2 mm ext. diam.), both sealed into the glass tube by means of Teflon wax and polyethylene tape. The loop was perforated with 26 equally spaced little holes and the straight tube with 5 holes, and all holes pointed against the direction of the gas flow. The flow tube was fitted with two additional inlets, one at the upstream and one at the downstream end, connected to a mercury manometer, oil manometer, and calibrated McLeod gauge.With full pumping at tube pressures of about 1 to 5 mm Hg, an average linear gas velocity of 4000 cmlsec was attained. The main discharge was excited by a microwave power generator (Raytheon PGM-100, 2450 Mc/sec, continuous wave, up to 800 W of microwave power) protected against excessive power reflection by a ferrite load isolator (Microwave Associates, Model MA-171). Micro- wave power was coupled to the discharge by a tapered, slotted cavity. When necessary, a second microwave discharge was excited, in tube B, using a Microtherm unit (Raytheon Model CMD-4, 2450 Mclsec, up to 125 W microwave power) and a cylindrical cavity designed by Dr.H. P. Broida. Large ball joints were sealed to each end of the quartz flow tube, and the corresponding socket joints were fitted with 2-in. diam. quartz windows ; these made possible the measure- ment of small amounts of NO2 by light absorption along the length of the tube. For this purpose a mercury discharge light source was provided at one end, with the 4358A line isolated by Corning glass filters ; at the other end was a photomultiplier tube whose photo- current was recorded by a pen recorder. Cylinder gases of best commercial grade were used throughout. Experiments in which highly purified NO and NO2 were substituted for the commercial grades gave identical results. OH CONCENTRATION MEASUREMENT The heart of the experimental method was the measurement of the OH concentration, by light absorption, in specific rotation-vibration states of the ground electronic state (SII), with good space (and thereby time) resolution.The optical components of the light ab- sorption system, a light source emitting OH radiation ( A 2 P - SII), a set of front-surfaced E130 REACTIONS OF OH mirrors and quartz lenses, and a grating monochromator (Jarrell-Ash, model 82-000, photo- electric, recording, 0.5 m Ebert mount) were mounted on a platform movable along the full length of the flow tube, and the components were so arranged that the light from the source made three traversals across the middle of the quartz tube before being focused on the entrance slit of the monochromator. The three traversals gave a path length of 9 cm and were completely contained in an overall width of 1.3 cm in the direction of flow, cor- responding to a time resolution of + msec under steady-state flow conditions.The light source was a low power microwave discharge (Raytheon Microtherm, model CMD-4) in flowing Ar+H20 mixtures in a quartz tube, with large excess of Ar, and at a pressure of 18 mm Hg. Such discharges had been reported 9 to emit the low rotational members of the various branches of the (0, 0) band, A2C+-X2II with a low rotational " temperature " corresponding probably to the gas kinetic temperature. Analysis of the relative intensities of members of the Ql and P1 branches in several discharges indicated a rotational temperature of 400 to 440°K and such temperatures were used in calculating the Doppler width of the emitted radiation.In the measurement of absorption by OH molecules in specific rotational states, the monochromator serves to isolate a line corresponding to a particular transition, but since its resolution in the vicinity of 3000 A is approximately 0.2 A whereas the Doppler widths of the emitted or absorbed lines are near 0.01 A, it does not resolve line shapes. Therefore, when the monochromator is set at the maximum of an emission line and observed readings of I0 and I are obtained in the absence and presence of absorbing OH, thequantity AB = (Io- I)/Io is given by A, = where AVE and AVA are the Doppler widths of the emitted and absorbed line, a0 is the true absorption coefficient at the centre of the line VO, and I is the path length. The implicit assumption that both the emitted and absorbed lines have Doppler shapes is sure to hold with good accuracy.This expression has been evaluated 10 for different ratios p = AVE/AVA and its use permits the calculation of a0 and thereby of the relative concentration of OH from I0 and I. For small absorption, i.e., Io/I<1.5, Beer's law is obeyed for P t 2 , and In (Io/I) = aol/l/l+P2. The absolute determination of OH concentrations from ab- sorption measurements requires the knowledge of the fivalue of the transition and will be discussed later. The value of p in these experiments was 1.1 to 1.2 as determined from measurement of AVE from the rotational temperature of the emitting molecules, and of AVA from two sources: the rotational temperature of the absorbing molecules by the relative absorption of different rotational lines, and the kinetic temperature of the mixed gases by glass-enclosed thermocouple probes. Depending on the amount of NO2 added, which determines the total heat release, and the dilution of the OH formed, the temperature of the absorbing OH molecules was found to be in the range 310-380°K.Though the absorption of various OH lines was used throughout, most kinetic experiments were done using the Q1-4 line at 3083.278 A (whose satellite Q21-4 at 3083-374A was not resolved) and unless otherwise stated, all values of lo, I and COH are based on these lines. RESULTS MIXING AND OH DECAY OH radicals were generated as follows. The products of a discharge (normally in tube A) in H2 * greatly diluted with He or Ar were further diluted with inert gases * In most experiments the H2 was saturated with H20 at O"C, i.e., contained about 0.6 % H20.This did not affect the OH decay in any way, but increased the yield of H-atoms several-fold even in the presence of a 50-fold excess of He in the discharge.F. P. DEL GRECO AND F. KAUFMAN 131 (at B) which had bypassed the discharge; NO2 was added through tube D; and observation of OH absorption was begun within a few mm of D and continued further downstream. Two results were immediately apparent. Much larger OH con- centrations could be produced this way than are found in water discharge products ; and the decay of OH was very rapid. This is illustrated in fig. 2. Curve A shows a typical decay of OH formed from reaction (1).Curve B clearly shows OH increas- ing for about 20 msec in the downstream gases from the H20 discharge. Had only 0.033 mmole/sec H20 rather than 0.28 mmole/sec H20 been used for B, OH would FIG. 2.-Plots of OH decay. Flows in mmoles/sec, pressures in mm Hg. A : 0.033 H2, 3.30 He, 1.94 mm. B : 0.28 H20, 3-70 He, 2.18 mm. n 2 .'Oo0 - 5 0 -0800 . 3 t -06 0 0 0 4 8 12 16 20 24 time, msec not have been detectable at any point along the flow tube. The decay of OH ap- peared to follow a second-order rate law with good accuracy over concentration changes of a factor of 10, and several pieces of evidence may be adduced to support the belief that the second order decay is real. (1) Mixing apparently was sufficiently fast to be neglected in the interpretation of the decay.This could be substantiated in five ways. (a) Visual titration reactions.-The extinction of the air afterglow by added NO2 11 and of the nitrogen afterglow and blue nitric oxide afterglow by NO 12 were both used. The former reaction, O+NO;!+NO+02, was found to be appreciably slower than the latter, N + NO-+N2 + 0, as has recently been found quantitatively by Phillips and Schiff,l3 who report for the latter reaction a k value of 2-2 x 10-11 cm3 molecule-1 sec-1, in fair agreement with the value of 3.5 x 10-11 reported by Clyne and Thrush.14 With the Teflon mixing tube, mixing was virtually complete within about 3 cm, i.e., within 1 msec. (b) If the discharged gas containing H-atoms were inhomogeneous, different decay characteristics would be expected as more or less He diluent would bypass the discharge, entering the flow tube through tube B.Keeping the total He flow constant but varying the fraction going through the discharge had no effect on the decay (fig. 3, curves A and B).132 REACTIONS OF OH (c) Similarly, when the auxiliary discharge was used to produce the H-atoms and diluent He was added through A, the decay of OH was unchanged (fig. 3, curve C). (d) If the mixing of H and NO2 were too slow, diffusion would be important. Large differences should then be expected if He were replaced by Ar, in which binary diffusion coefficients are much lower. No real change was found in the decay (fig. 3, curves D and E). t I f I 1 I I J OC, ; 2 3 4 5 6 7 8 time, msec FIG. 3.-second order plots for OH decay. Flows in mmolelsec ; pressures in mm Hg.A : 0.050 H2 and 0-67 He main discharge, 3-80 He bypass, 2.68 mm ; B : 0050 H2 and 3.80 He main discharge, 067 He bypass, 2-68 mm ; C : 0042 H2 and 2.22 He auxiliary discharge, 2.22 He bypass, 2-70 mm ; D : 0.050 H2, 2-90 Ar, 2.02 mm ; E : 0.050 H2, 4.50 He, 2-66 mm ; D and E are displaced 1 mFec. (e) Similarly, diffusion controlled mixing should be pressure-dependent since the diffusion coefficient is inversely proportional to total pressure. Yet, no appreciable dependence of the OH decay on total pressure was observed (fig. 3, curve E ; fig. 4, curves A and B). (2) The importance of wall reactions of OH could also be ruled out. Here, dif- fusion is necessary to bring the radical to the wall and a dependence on the nature of the diluent gas (1, d, above) and on total pressure (1 , e, above) should be observed.Moreover, the decay was excessively fast for a bimolecular reaction occurring at the surface. (3) The possibility that metastable He or Ar atoms play a role also could be ruled out. Were this the case, the decay should depend on the fraction of diluent( a ) ( b ) FIG. 3.-(u) Photograph of paramagnetic resonance spectrum from [IrC1# - complex. (6) Reconstruction assuming Cl-Ir-C1 hyperfine structure. The spacing between adjacent peaks is the C1 structure constant. [To face page 132.F. P . DEL GRECO AND F . KAUFMAN 133 gas which goes through the discharge (1, b, above), and it should be different in the experiments where H-atoms were produced in the auxiliary discharge (1, c, above), because the microwave power was a factor of 6-8 lower than in the normal discharge.In all, over 80 kinetic experiments were recorded, each consisting of 6-10 points at distances up to 60 cm downstream of the point of mixing. The error of each point was due mostly to fluctuations of the light source so that higher concentrations of time, msec FIG. 4.-Second-order plots for OH decay. Flows in mmole/sec, pressures in mm Hg. A : 0.042 H2, 0.41 He, 0.52 mm ; C and D : 0.058 H2, 6-26 He, 3-87 mm ; C and D differ only in the amount of NO;! added ; D and E are displaced 1 msec. B : 0.050 H2, 5.0 He, 2.86 mm ; E : 0.032 H2, 3.58 He, 2.08 mm ; OH (Io/l = 1.1 to 1-3) were probably accurate to a few percent whereas low con- centrations (lo/l< 1-05> might be in error by 10 to 20 %.The slope of the second- order plots was reproducible to +15 %. The absolute concentrations of OH which are used throughout these plots are based on the amounts of NO2 reacted as determined by the light absorption of the added NO2 along the 150 cm path when the discharge was turned off. This was further calibrated against the weighed loss of NO2 from a tube containing liquid N02+N204 in steady flow experiments of long duration. All experimental evidence supports the conclusion that reaction (1) is indeed very rapid, as has been reported by several investigators.13-15 With large initial OH concentrations (roll> 1.4) deviations from a linear l / C o ~ against time plot were observed and there are three likely causes for this. (i) Rapid134 REACTIONS OF OH mixing is an increasingly difficult problem when large amounts of NO2 are used; (ii) the destruction of OH is so rapid that an appreciable fraction has disappeared within 1 msec, i.e., within the zone of mixing ; (iii) reaction (1) is exothermic (AH288 = - 29.1 8 kcal/mole) as are subsequent reactions of OH, and large temperature changes will affect the concentration measurement.Even in 100-fold dilution with He, temperature rises of 60-80°C can be expected and actually were observed by probing the mixing zone with glass-sheathed Pt, Pt/lO % Rh thermocouples. These experi- ments also showed that the discharged gas stream was only slightly above room temperature upstream of the NO2 addition tube. 1000 - 900 - 800 - 700 - 7 600- - x" @ 500- W / / 2 3 4 5 6 7 time, msec FIG.5.-Second-order plots for OH decay. Flow in mmolelsec, pressures in mm Hg. A : 0.042 H2, 4-50 He, 0.25 NO (bypass), 2.73 mm ; B : 0-050 H2, 4-25 He, 0.21 0 2 (bypass), 2.64 mm ; C : 0.050 H2, 4.25 He, 0.17 H20 (bypass), 2.44 mm ; D : 0.050 H2, 2-46 He, 2.50 N2 (bypass), 286 mm ; D is dispIaced 1 msec. The independence of the decay on initial COH is shown in fig. 4, curves C, D and E. The decay is thus not only second order within one experiment, but con- sistently gives the same rate constant at different initial concentrations. This also shows that the presence of excess H-atoms has no effect on the decay. EFFECT OF ADDED GASES Moderate additions (1-5 % of total flow) of NO, 0 2 and H20, when added to bypass the discharge, also had no appreciable effect on the rate constant as is shownF.P. DEL GRECO AND F. KAUFMAN 135 in fig. 5, curves A, B and C. Large additions (up to 50 % of total flow) of N2 (bypass) were similarly ineffective (fig. 5, curve D). The addition of large amounts of H2 (bypass, 10 to 50 %) produced a surprising acceleration of the decay (fig. 6A). The reaction Hz+OH-+H20+H is reported 16, 17 to have an activation energy of 10 kcal/mole, a value which would make it too slow to be observable on our time w O 0 1 2 3 4 5 time, msec time, msec FIG. 6.-Plots of OH decay. Flows in mmole/sec, pressures in mm Hg. 6A, 0 : 0.042 H2, 4-50 He, 2-72 mm ; 0 : 0.042 Hz and 2.25 He discharge, 2.25 HZ (bypass), 255 mm ; 6B, 0 : 0.042 H2 and 2-25 He auxiliary discharge, 1.12 He and 1.04 N2 (bypass), 2.56 mm ; 0 : 0.042 H2 and 2-25 He auxiliary discharge, 1-12 He and 1.04Nz main discharge, 0-atom (from N+NO)Zinitial OH = 0.007, 2.56 mm.scale. Careful experiments with low initial COH and therefore with small tem- perature rises resulted in decays which could be interpreted as simultaneous (pseudo) first-order and second-order process and thus yielded a rate constant of 7+2 x 10-15 cm3 molecule-1 sec-1 for the H2+OH reaction at an average temperature of 310°K. STOICHIOMETRY OF THE PRIMARY REACTION The rapid, second-order decay of OH can only be due to one of the following two primary reactions : 20H+H20 + 0, (2) or 20H+H2 + 0 2 . (3) Experiments were therefore performed to decide between (2) and (3) by trapping condensible reaction products at - 77°C. Flow conditions were held constant for periods from 30 min to 2 h, the consumption of NO2 was measured and the condensed product from the large trap at the downstream end of the flow tube was weighed and identified.The product was water and its yield was 75 % uncorrected for losses due to the collection of a small amount (1.35 g) in a very large trap, for136 REACTIONS OF OH vaporization losses upon warm-up, and for incomplete trapping at high pumping speed. With a reasonable estimate of losses, a yield of 90-100 % is indicated. This yield is based on reaction (2) followed by the still faster reaction OH + 0 + 0 2 + H for which further evidence is presented below. As expected (2) rather than (3) is the principal primary step. (3) is a four centre reaction whose intermediate is likely to be of appreciably higher energy than the reactants.In the course of these trapping experiments the OH concentration was measured along the tube in the usual manner, and no trace of OH remained unreacted near the upstream end of the trap; it is evident that all of the water was formed in gas reactions at room temperature in the flow tube and not in surface reactions in the cold trap. (4) DOUBLE DISCHARGE EXPERIMENTS The role of reaction (4) in the decay of OH was ascertained in two ways. First, the air afterglow, which must be emitted strongly if both 0 and NO are present at appreciable concentrations, was feeble. Since the presence of NO as a major product of reaction (1) is assured, the weakness of the afterglow which was observed down- stream from the mixing region indicated a low concentration of 0-atoms, i.e., a very fast reaction (4), but it was difficult to obtain quantitative information from the intensity of the afterglow without careful consideration of the concurrent afterglow due to HNO.14 Second, reaction (4) was investigated directly by double discharge experiments.These were done by producing 0-atoms in tube B (fig. 1) in excess of the OH formed by reaction (1) and noting the change in the rate of disappearance of the OH. 0-atoms were produced by two different methods: by a microwave discharge in 0 2 in tube B, or by the addition of NO to the products of a microwave discharge in N2, i.e., by the reaction N+NO-+N2+0. In either case, the decay of OH was greatly accelerated as is shown in fig.6B. In this experiment, the 0- atom concentration was estimated by the NO-flow required to extinguish the nitrogen afterglow and the blue NO afterglow.12y 18 Two conclusions can be drawn : (a) the fairly small decrease of initial COH when the auxiliary discharge is started shows that reaction (4) is slower than (l), though not much so. The O+NO2 reaction is reported 13-15 to be much slower than (1). (b) The greatly accelerated decay of OH shows that (4) is much faster than (2). The normal decay of OH in the absence of excess 0-atoms can therefore be approximated by (2) + (4), with (2) rate-controlling and with the observed rate of disappearance of OH equalling 3/2 times that of step (2). VIBRATIONAL EXCITATION A repeated search was made for vibrationally excited OH(X2II) in the states v” = 1 and v” = 2 under various conditions and in various rotational states.None was ever detected, either in the mixing region or further downstream. This means that the concentration of OH, 0’‘ = 1, could not be greater than 2 % of that of v’’ = 0, whereas OH, d’ = 2, could not be present in concentrations greater than 5 of OH, u” = 0. These limits take into account the increasing noise levels of the lines from the (1, 1) and (2, 2) bands which were used for the attempted absorption measurement, and the lower transition probabilities of these bands. These were the Ql, 2 and Ql, 4 lines and a blended line consisting of Ql, 3 ; PI, 1 ; and R2, 1 for the (1, 1) band, and the Q1, 2 line for the (2, 2) band. Unsuccessful attempts at finding vibrationally excited OH in absorption were also made at lower dilution with He (He: H2 = 10 : I, P = 0.5 mm Hg), and without added He (P = 0.07 mm Hg).F .P. DEL GRECO AND F. KAUFMAN 137 DISCUSSION The principal results of the kinetic experiments can be summarized as follows. When OH radicals are generated by the extremely fast reaction (l), they decay by the rapid, bimolecular reaction 20H+H20 + 0, (2) followed by OH+0+02+H. (4) k2 is found to be 2-5$-0-6 x 10-12 cm3 molecule-1 sec-1, and k4 is estimated to be about 1 to 2 x 10-11 cm3 molecule-1 sec-1. In the absence of other fast OH reactions, the half-life of OH due to steps (2) and (4) is 2/(3k2Co~), e.g., for 0-01 mm Hg of OH, 1112 is slightly less than 1 msec, more than 100 times shorter than has previously been reported.** 4 Their decay is unaffected by the presence of NO, 0 2 , H2O or N2, but in the presence of much H2, a faster disappearance of OH is observed.This cannot be explained by the reaction of kinetically “ hot ” OH radicals from reaction (1) because the accelerated rate persists throughout the course of the reaction, i.e., through many thousand collisions. Nor can it be explained as a reaction of vibra- tionally excited OH 14 because no measurable concentrations of that species were found. The acceleration must, therefore, be due to the reaction OH + H2-+H20 + H, but this interptetation is in conflict with the results of Fenimore and Jones 17 and Avramenko and Lorentso.16 These authors report a kq of 2-8 x 10-10 exp (- lO,OOO/RT) cm3 molecule-1 sec-1, a value which is not compatible with the present results.If the reported pre-exponential factor-which is close to the gas kinetic collision frequency-is retained, an activation energy of 6.5 rather than 10.0 kcal/mole is indicated. Another major result-and perhaps the most surprising one-is the absence of measurable concentrations of vibrationally excited OH. The AH; of reaction (1) is -29.27 kcal/mole,lg barely sufficient to produce OH with v” = 3 (29.19 kcal/ mole above v” = 0). If atom-molecule reactions generally produce vibrational excitation in the newly-formed bond, large concentrations of OH, v” = 3 and 0’’ = 2, should be made initially. These should relax either by the “ ladder ” pro- cess of vibrational equilibration (Y” = 3+u” = 0 -+ v” = 2+v” = 1, etc.) or by vibration-translation and vibration-rotation relaxation processes.In either case, molecules with 1 or 2 vibrational quanta should be produced, and in particular those with v” = 1 should persist, since they cannot relax by the “ ladder” process and other relaxation processes are likely to be inefficient. Yet, it is found that immediately upon reaction of H and N02, ground state OH molecules are at least 50 times more plentiful than OH, v” = 1, and at least 20 times more plentiful than OH, v” = 2. Under typical experimental conditions, P E PHez’2 mm Hg, POHE 0.006 mm Hg, and each OH molecule makes about 40 collisions with other OH molec- cules per millisecond. With time resolution of 3 msec it would require complete relaxation of vibrational energy at every collision to remove all excited OH by OH+OH collisions if it were a major reaction product.This is most unlikely. Under the same conditions, each OH molecule undergoes about 16,000 collisions with He atoms per msec, and one must also consider this possibility of vibrational relaxation. Yet, experiments with much less He or with none a t all, at corres- pondingly lower pressures, gave the same negative result and this explanation is thereby also ruled out. The only plausible interpretation of these experiments is ( 5 )138 REACTIONS OF OH that vibrationally excited OH molecules are not formed as a major reaction pro- duct.* The implication of the frequently encountered statement that the energy liberated in fast atom-molecule reactions goes largely into vibrational excitation is that it does so for most of the reacting molecules.Such an implication appears to be incorrect for this reaction. Finally, one may compare the observed OH concentration, based on the amount of NO2 used and on a small extrapolation of the bimolecular decay to the point of mixing, with one calculated from the observed light absorption and thef-value of the particular transition. There are several published estimates of F=f(2J+ ~)/AK where J is the rotational quantum number of the lower state and AK is the rotational transition probability,l F ranging from 1-5 to 3.2 x 10-4. With proper correction for the newer values of the thermodynamic properties of OH,19 this range is widened to one of 1.2 to 3 . 2 ~ 10-4.There is, however, a recent, as yet unpublished, value of 1 . 7 4 ~ 10-4 by Bennett 20 which is obtained by the direct measure- ment of the radiation lifetime of the upper state and should be accurate to f10 %. When the present results are cast in the form of an F-value by assuming thermal equilibrium among all rotational states of OH(X2IJ) a value of 1.4+0.3 x is obtained. This again indicates that the observed light absorption satisfactorily accounts for all the OH in the ground vibrational state and that large concentrations (in whatever form of excitation) have not escaped detection. We would like to thank Dr. D. M. Golden for help with the determination of f-values and rotational temperatures. * It must be borne in mind, of course, that the equilibrium ratio OH, v” = 1/OH, v f f = 0 is about 10-7 at 320°K and that large relative excesses of excited OH are not ruled out. Nevertheless the present results indicate that ground-state OH is the only major product of the reaction. 1 Dieke and Crosswhite, The Ultra-uiolet Bands of OH (Bumblebee Report No. 87 ; The Johns 2 Dousmanis, Sanders and Tomes, Physic. Rev., 1955,100, 1735. 3 Radford, Physic. Reu., 1961,122, 114. 4 Oldenberg, J. Chem. Physics, 1935, 3, 266. 5 Oldenberg and Rieke, J. Chem. Physics, 1939,7,485. 6 Kaufman and Del Greco, J. Chem. Physics, 1961, 35, 1895. 7 Foner and Hudson, J. Chem. Physics, 1955,23, 1974 ; 1956,25, 602. 8 Charters and Polanyi, Can. J. Chem., 1960, 38, 1742. 9 Carrington and Broida, J. MoZ. Spectr., 1958, 2, 273. Hopkins University, 1948). 10 Mitchell and Zemansky, Resonance Radiation and Excited Atoms (McMillan Co., New York, 11 Kaufman, Proc. Roy. SOC. A, 1958, 247, 123. 12 Kaufman and Kelso, J . Chem. Physics, 1957 27, 1209. 13 Phillips and Schiff, private communication. 14 Clyne and Thrush, Trans. Faraday SOC., 1961, 57, 1305. 15 Rosser and Wise, J. Physic. Chem., 1961,65, 532. 16 Avramenko and Lorentso, Zhur. Fiz. Khim., 1950,24,207. 17 Fenimore and Jones, J. Physic. Chem., 1958, 62,693. 18 Morgan, Elias and Schiff, J. Chem. Physics, 1960, 33, 930. 19 JANAF Interim Thermochemical TabZes (Dow Chemical Co., Midland, Michigan, 1960). 20 Bennett, private communication. 1934), p. 323.

ISSN:0366-9033    

DOI:10.1039/DF9623300128

出版商:RSC    

年代:1962

数据来源: RSC

摘要:

Mechanism of Chemiluminescent Reactions Involving Nitric Oxide-the H +NO Reaction BY M. A. A. CLYNE AND B. A. THRUSH Dept. of Physical Chemistry, Lensfield Road, Cambridge Received 23rd January, 1962 The kinetics of overall combination and light emission (due to excited HNO) in the reaction of H with NO are closely similar to the kinetics of the combination of 0 with NO and its associated " air after-glow " chemiluminescence. Both reactions were studied by measurement of the in- tensities of their respective light emissions in a fast flow system at 1-2 mm Hg total pressure. Pre- liminary work has been extended and shows that in both OfNO and H+NO reactions there is a significant dependence of emission intensity and combination rate upon the nature of the carrier gas used as third body.Negative temperature coefficients for both the O+NO and H+NO emission intensities were observed, and the dissociation energy of the ground state €€NO molecule was thus determined as 48.6 kcal/mole. In a previous publication 1 it has been shown that the kinetics of the nitric-oxide- catalyzed recombination of hydrogen atoms can be represented by the reactions, H+NO + M-+HNO + M H + HNO -+ H2 + NO, where reaction (3) is rate determining. These reactions were studied by following HNO emission, the intensity of which was proportional to hydrogen atom and nitric oxide concentrations, where 10 is independent of total pressure. The kinetics of light emission and of combination in the reaction, are analogous.3 In this work, values of combination rate constants and of absolute emission intensities and their dependences upon temperature and the nature of the inert gas (M) were determined for the O+NO+M and H+NO+M systems. From these data, information regarding the nature of the reactions was obtained.In a forthcoming publication, results relating to the chemiluminescent combination reaction, will be presented. (3) (4) I = ~o[Hl"Ol, O+NO +M+NO2+ My 0 + CO + M-+CO2 + M, EXPERIMENTAL THE REACTION SYSTEM The experiments were conducted in a fast flow system of 28 mm int. diam. Pyrex tubing and similar to those previously used.1 The flow tube had several inlets along its length for admission of nitric oxide from calibrated capillary flowmeters. Hydrogen atoms were produced by a radio-frequency electrodeless electric discharge in the pure dry molecular gas or in mixtures of hydrogen (1-10 %) with purified argon, neon or helium carrier.With both arrangements, hydrogen-atom concentrations from the discharge were +-2 % of total flow. Measurements were made with total flow rates of 50-200pmole/sec and at total 139140 CHEMILUMINESCENT REACTIONS pressures of 0.7 to 3 mm Hg, corresponding to linear flow rates of the order of 1 mlsec. For experiments at low temperatures (220-290°K) the flow tube could be totally immersed in an insulated brass trough containing alcohol and solid carbon dioxide. The atomic hydrogen from the discharge passed through 30 cm of cooled reaction tube before entering the reaction zone. Observations of emission intensity were made through a double window of Pyrex placed normal to a 5 cm length of reaction tube using a 9558-B photomultiplier cell.The photomultiplier was carefully screened from scattered light emitted by the dis- charge. Ten cm downstream from the observation window was an isothermal wire calori- meter 1 for measurement of hydrogen atom concentrations. The decrease in the HNO emission intensity in passing over the isothermal calorimeter was at least 90 % in every experiment, indicating the high efficiency of the detector. THE PHOTOMULTIPLIER CELL The 9558-B photomultiplier cell was operated from a stabilized power supply at potentials between 800 and 1300 V with a constant potential of 200 V between the photocathode and first dynode. Under these conditions the dark current was very much less than the photo- electric currents due to the €€NO emissions observed in this work.The spectral response of the cell was determined from 5000 to 8000A, using Wratten filters 61, 45, 29, 88A and 74+ 29, which transmit different relatively narrow bands in this wavelength region and a tungsten strip filament lamp operating at 2800°K. Using the known distribution of radiant energy from such a source, the relative sensitivity per incident photon of the photo- multiplier was computed from the photocurrents observed with the various filters. The relative quantum efficiency of the cell is shown in fig. 1, which also shows the corresponding data for the 1P28 cell used in the earlier work.1 FIG. 1.-The intensity distribution (full line) of the H+NO and O+NO emissions as a function of wavelength.The relative quantum efficiencies (dotted line) of the photomultiplier cells are also shown. A, H+NO emission bands, this work; B, O+NO emission, this work and data of Fontijn and Schiff ; 4 X, 1P28 cell ; Y, 9558-B cell. DETERMINATION OF THE ABSOLUTE VALUE OF 10 FOR THE HNO EMISSION Before the absolute value of 10 = I/[H]mO] can be computed, it was desirable to in- vestigate the intensity distribution of the most intense bands in the HNO emission spec- trum. The relative intensities of the 6272, 6925, 7625 and 7965A bands were selected for investigation. Measurements of the same HNO emission from the H+NO reaction were made using the photomultiplier fitted with various filter combinations, selected toM. A . A . CLYNE A N D B . A . THRUSH 141 give sharp discrimination between these bands.The intensity distribution of the €€NO bands is shown schematically in fig. 1 and is in agreement with the work of Clement and Ramsay.2 No dependence of distribution on [HI, WO] or [MI was observed, nor was there any difference between systems in which hydrogen and helium respectively were used as carrier gases. There was no detectable radiation below 6000A. Fig. 1 shows that a large fraction of the emission intensity resides in the 7625 A band. The absolute intensity of the air-afterglow emission (NO+ O+ M-+N02+ M+hv) has been determined actinometrically between 4000 A and 6200 A.4 The absolute intensity of the HNO emission can, therefore, be determined by a comparison of the I0 values for the two chemiluminescent processes using the same reaction tube and photomultiplier arrangement.lo-values for the HNO emission due to the 7625 A and 7965 A bands were determined with the photomultiplier and an 88 A infra-red transmission filter when nitric oxide was added to H+H2 mixtures under conditions of negligible HNO emission decay. It was assumed that 20 % of the total €€NO emission resides in bands above 80008, and the 7625A and 7965A bands then contribute 55 % and 5 % of the total HNO emission respectively. On this assumption, the overall HNO emission intensity was determined using the known sensitivity of the photomultiplier at these two wavelengths. The photomulti- plier, now fitted with a 61 filter, was then used to determine the photocurrent due to the air-afterglow spectrum when nitric oxide was added to a stream of oxygen atoms with argon carrier under the same conditions.Oxygen-atom concentrations were measured by NO2 titration.3 Using the obtained value of 10 = I N o , / [ O ] ~ O ] , the transmission character- istics of the 61 filter, the known intensity distribution of the air-afterglow spectrum from 4000 A to 6200 A,4 and the photomultiplier sensitivity over this wavelength range, the total emission intensity of the air-afterglow spectrum in this region was computed in the same units as the value obtained for the HNO emission intensity Io. Using our determined relative values of I0 for A and H2 as third bodies and Fontijn and Schiff's 4 value for I; from 4000 to 6200 A, a value of 10 = (3.2fl-5)x 105 cm3 mole-1 sec-1 at 293°K was ob- tained for argon as carrier, as compared to 16 = 1.0 x 107 cm3 mole-1 sec-1 (4000-6200 A) for the same carrier at 293°K.It was also of interest to determine the relative intensity of the air-afterglow emission in the near infra-red, since it is known that the infra-red emission contributes considerably to the overall air-afterglow emission. Using the known photomultiplier sensitivities at various wavelengths from 5000 8, to 8000 A, the photocurrents from the air-afterglow emis- sion were measured using several filters under different conditions. The filters used were Wratten no. (74+29), 88A, 29 and 61 which when used with the 9558 photomultiplier had peak transmissions at about 7800, 7500, 6300 and 5300 A respectively. These data showed that the intensity of the emission in the near infra-red from 6200A to 80OOA is consider- able, and the approximate form of the variation of intensity with wavelength is shown in fig.1. Thus, the overall intensity of the air-afterglow emission is probably about 4 times greater than that observed in the region 4000-6200 A and we shall adopt a value for the total 16 of 4 x 107 cm3 mole-1 sec-1. RESULTS KINETICS OF HYDROGEN ATOM REMOVAL In this work, as previously, the rate of removal of hydrogen atoms in the presence of nitric oxide was determined by measurement of the rate of decay of the HNO emission produced. However, whereas in the earlier work measurements were made using the weak bands at 6272 and 6453 A, the superior red sensitivity of the 9558-B photomultiplier used in the present work enabled intensity measurements of the principal emission band at 7625 A to be made.The intensity I of this band was found to fit the rate law, with I0 independent of total pressure, as for the intensity of the shorter wavelength bands. I = ~o[Hl"Ol,142 CHEMILUMINESCENT REACTIONS The intensity I of the 7625 A band was found to obey the same rate equations as that of the 6272 and 6453A bands, where [NO] is the concentration of added nitric oxide, t the reaction time, and [HI0 is the concentration of hydrogen atoms at the photomultiplier housing in the absence of nitric oxide. Values of k3 obtained in this way at 293°K were identical to those obtained previously, within the experimental error of the determinations. Measurements of the rate of hydrogen-atom removal were also made at tempera- tures down to 231°K.Experiments to determine the conservation of nitric oxide during the combination reaction, using the two-inlet method described previously,1 were made at 2 mm Hg pressure and at temperatures of 226"K, 237"K, 246"K, 250"K, and 270°K. In each case the steady-state concentration of HNO was found to be less than 0*2[NO] and thus at all temperatures from 226 to 294"K, kq>5k3[M], leading to a lower limit of k4 >3 x 1010 cm3 mole-1 sec-1 at 226°K. It follows that the activation energy of reaction (4) is less than 4 kcal/mole. Since nitric oxide was conserved down to 226"K, measurements of the rate of decay of HNO emission intensity under these conditions enabled values of k3 to be calculated from eqn. (1).The values obtained at 231 and 265°K are given in table 1, together with previous data for higher temperatures. Fig. 2 shows the variations of k3 with temperature from 231 to 704°K. The observed negative temperature co- efficient can be expressed as an Arrhenius activation energy of - 0.6 & 0.2 kcal/mole, or as k3 = 1.5 x 1016(T/273)[-0'9*0*31 c m 6 mole-2 sec-1 over this temperature range. WlIENOI) = 1n(1o[HIo) - 2k3[NOl[M1t9 (1) TABLE 1 THE VARIATION OF I0 AND k3 WITH TEMPERATURE FOR M = H2 I0 (cm3 mole-1 sec-1) T (OK) k3 (cm6 mole-* sec-1) T (OK) 23 1 (2-04 f0.20) x 1016 224 265 (1 -45 f 0.20) 239 294 (1.48 f0.15) 248 340 (1.49 f0-15) 257 433 (1-17 &0*15) 268 704 (0.75 f0-10) 28 1 296 318 333 (7.8 f0.4) x 10s (7.6 f0.4) (6.6 f0-3) (5.6 f0.3) (5.0 -f 0- 3) (4.0 f0-2) (3.6 f0-2) (2.9 50.1) (4.4 f0.2) The absolute valms of 10 given in table 1 and 2 are based on the determination (for M = H2) at 293°K as described in this paper.The standard deviations of l o given in the tables are thus those of determinations of the relative values of 10. DETERMINATION OF THE TEMPERATURE COEFFICIENT OF 10 Measurements of the HNO emission intensity were made at nine temperatures from 224 to 333°K for several concentrations of added nitric oxide, the hydrogen- atom concentrations being simultaneously determined at the isothermal wire calori- meter. The pressure in the flow tube was 0-80 mm Hg, under which conditions the rate of removal of hydrogen atoms was negligible. In each determination the intensity of HNO emission 10 cm downstream from the isothermal calorimeter was also measured.At this second observation point the temperature of the gas was always within 2 deg. of that of the room. At each reaction temperature used the emissionM. A . A . CLYNE AND B . A. THRUSH FIG, 26, 3 FIG. 2.-The logarithmic variation of 10 and k3 with temperature. 10 is expressed in c m 3 mole-1 sec-1 and k3 in cm6 mole-2 sec-1. 143 FIG. 2a.144 CHEMILUMINESCENT REACTIONS intensity at the second observation point was less than 5 % of that at the low tempera- ture observation point, and it was found that I/[NO] measured at the second observa- tion point was accurately proportional to the heat liberated on the calorimeter wire. It follows that the efficiency of the isothermal calorimeter was high and accurately constant in runs performed at different temperatures.It has been found that I is given by I = Io[H][NO], whcre I0 is independent of total pressure. Using the known efficiency of the isothermal calorimeter for hydrogen-atom recombination, values of [HI were determined for each temperature at which I/[NO] had been measured at the first observation point. Fig. 2 shows the variation of I0 = I/[H][NO] with tempera- ture. These data lead to a negative temperature coefficient, expressible as an activa- tion energy of - 1-4+0.3 kcal/mole or in the form I0 = 4 x 105(T/273) [-2'8f0*4] cm3 mole-1 sec-1. VARIATION OF I. AND k3 WITH THE NATURE OF M Values of I0 = I/[H]mO] were determined at 293°K for mixtures of hydrogen atoms with A, Ne and He at a total pressure of 1 mm Hg.Measurements of k3 at pressures of 1-5-3 mmHg and at 293°K were also made for similar mixtures. There was no significant difference between the distributions of HNO emission bands (6272, 6925 and 7625 A) for hydrogen and helium as carrier gases. The data are shown in table 2. The absolute values of I0 given in the table are based on the determination of 10 (for M = H2) at 293"K, as described in the experimental section of this paper. The standard deviations given in tables 1 and 2 are thus those of determinations of the relative values of l o . TABLE 2 THE DEPENDENCE OF k3 AND 10 ON THE NATURE OF M AT 293°K M k3 (cm6 mole-2 sec-1) 10 (cm3 mole-1 sec-1) H2 (1.48 f0.15)~ 1016 (4-3 fo-3) x 105 A (0.87 &0-15) (3.2 f0-3) Ne (0.72 f0-10) (2.0 f0.4) H e (0.66 -+0*10) (2.4 f0.2) DISCUSSION The observation that Io, the proportionality constant for light emission, depends on the nature but not the pressure of the carrier gas which provides the majority of the third bodies in this reaction, indicates that the carrier gas must be involved in the formation and quenching of excited HNO, but in such a way that the pressure de- pendences cancel.This point is also brought out by the similarity of the variations of k3 and I 0 with the nature of the carrier gas. On this basis we can write the follow ing mechanism for the recombination. H + NO + M = HNO + M (non-radiative) H + NO + M = HNO*(lA") + M HNO"(1A") = HNO(1A') + h~ HNO"(1A") + M = HNO(1A') + M H+HNO = Hz+NO In this scheme the reverse reaction of (3b) has been omitted, since light emission occurs predominantly from levels far enough below the dissociation limit that the rate of redissociation will be lower than the rate of quenching.M.A. A. CLYNE AND B . A . THRUSH 145 Applying the stationary-state hypothesis to HNO* we obtain and to HNO,1 Of these rate constants, k5 can clearly be identified with A, the Einstein probability of spontaneous emission which is a constant in these experiments, whilst k6 the rate constant for quenching will depend on the nature of M and should increase slowly with temperature (with T* if k6 depends only on the collision number). Since table 1 and fig. 2 show that 10 has a slightly larger negative temperature coefficient than k3, k3,& and k3b must have very similar negative temperature dependences of the type frequently encountered in third order recombinations.Since the HNO(lA”-+lA’) emission spectrum in the H + NO reaction breaks off at an energy of 48.6 kcal/mole above the ground state, corresponding to the onset of predissociation in the absorption spectrum 5 the absence of an activation energy for this emission shows clearly that this energy corresponds to the dissociation energy of HNO into H (2s) + NO(2II). As the vibrational levels of the 1A” state of HNO continue above this predissocia- tion limit, it is clear that this state cannot correlate with ground state H and NO except via an appreciable potential maximum, and excited HNO must therefore be formed by a different path. As k3 has a small negative activation energy, it is prob- able that HNO is formed in a state from which it can readily cross into the 1A” state.Evidence for the existence of such a state from which crossing to the 1A” could readily occur is provided by the presence of marked perturbations in various vibrational levels of the 1A” including the lowest.5.6 This state is probably responsible for the onset of predissociation in the 1A” state which occurs close to the dissociation limit and must therefore be caused by a state which is not entirely repulsive. Spectroscopically, the only known electronic states of HNO are 1A” and 1A’ states, whereas the combination H(2S)+N0(2ll) can lead to 1A’, 1A”, 3A’ and 3A” states. Molecular-orbital considerations 7 suggest that the three lowest states of bent HNO would be 1A’, 3A” , 1A”.Thismay also be deduced by comparison with the three lowest states of the isolectronic molecule 02, from which the following states of bent HNO would be expected to be derived: 3A” (from the 3C; ground state), lA’+lA’‘ (from Id,) and 1A’ (from 1X:). Repulsion between the 1A’ states explains the observed 1A’ ground state but the 3A” state would be expected to lie below the 1A” state and to correlate with ground state H+NO. It is suggested that the radiative combination H + NO proceeds via this state and it is this state which is responsible for the perturbations and predissociations of the 1A” state, a view which is consistent with the weakness of the observed predissociation. A representation of the potential energy of suggested low-lying states in terms of r(H-NO) is given in fig.3. It is assumed that the 3A’ state derived from ground- state products is entirely repulsive, since it is related to a more highly excited state of 0 2 . The potential maximum in the 1A’ state of HNO is explained in terms of an avoided crossing. The negative temperature coefficient observed for 10 shows that no such potential maximum can exist in the 3A” state, but it is possible that the 1A’ ground state has one. If this were the case k3a would be very much less than k3b and combina- tion would occur almost exclusively in the excited 1A” state. If data were available146 CHEMILUMINESCENT REACTIONS on quenching of fluorescence of the 1A” state of HNO, the ratio kS/k6 could be evaluated and k3b determined. Such data are, however, available for the closely related combination reaction, 0 +NO + M+N02 + M, (3‘) which has a similar overall rate constant (kj = 2 x 1016 cm6 mole-2 sec-1 at 293°K for M = 02).For this reaction the quantity l o (denoted I;) is also independent of the pressure of inert gas 3 and exhibits a small negative temperature dependence.* Fontijn and Schiff have determined 1; to be 1-0 x 107 cm3 mole-1 sec-1 at 293°K with M = 0 2 I \ / \ / \ \$ ,’ internuclear distance Y (H-NO) FIG. 3.Potential energy curves of electronic states of HNO in the H+NO reaction. for wavelengths up to 6200A. Our measurements of the intensity distribution of the air-afterglow spectrum up to 8000A. indicate that the total I; is about 4 x 107 c m 3 mole-1 sec-1 which is about 100 times larger than for H+NO. The potential curves concerned in the NO2 emission 9 are closely similar to those for HNO, and it is reasonable to assume that 0 and NO approach on a relatively shallow stable potential curve and are stabilized by a third body into this state or the corresponding vibrational levels of the excited electronic state responsible for the absorption, fluorescence and afterglow spectra of N02.As in the HNO system, crossings between the states will occur readily due to perturbations and it is to be expected that at a similar pressure and temperature, the relative probabilities of radiation and quenching of an excited NO2 molecule having an energy a little below the dissociation limit would be independent of whether it was formed from Q+NO and stabilized at that energy by a third body or whether it was excited to that energy by absorption of a quantum of light.Since the dissociation limit of NO2 corresponds to a wavelength of approx. 3975 A, fluorescence quenching of Hg4047 and 4358A light is relevant to this discussion and this fluorescence spectrum appears to have a similar distribution to the air-afterglow emission.10 Baxter’s data 11 on the quenching by 0 2 of NO2 fluorescence excited with these wavelengths gives k;/ki = 3.34 x 10-9 mole c m - 3 , and hence k;b = 1.2 x 1016 cm6 mole-;! sec-1. This shows that approximately half the recombination proceeds via an excited electronic state of N02, and it is tempting to infer from this that the dis- tribution between stable electronic states of the NO2 molecules formed in this reactionM. A.A. CLYNE AND B. A. THRUSH 147 is largely statistical. The accuracy of the combined measurements is not sufficient to exclude the possibility of all the molecules being formed in the excited state which leads to radiation. In the H +NO reaction, the value of 10 is a hundred times lower than for O+NO, whilst the overall rate constant k3 of combination for similar third bodies is only reduced by a factor of two. The value of one or more of the constants k3a, k5, k6 for H+NO must differ by at least an order of magnitude from its value in the 0 +NO system. For the excited state of NO2 which we have considered, k; = 2.3 x 104 sec-1,10 and k; = 9 x 1012 cm3 mole-1 sec-1 for M = 0 2 , corresponding to a collision diameter of 0.7 A for quenching.11 The corresponding rate constants for HNO (]A”) are not known, but an indication of the probable magnitude of k5 can be made by comparison with values for the characteristic red absorption bands of monomeric organic nitroso-compounds which lie very close to the HNO transition.Thef-values of these transitions are close to 5 x 10-4 for aliphatic and aromatic nitroso-com- pounds 12 and about 2 x 10-4 for perfluoro-alkyl derivatives,l3 giving values of k5 of 5 x 104 and 2 x 104 sec-1 respectively which are close to that for NO;. Whilst the transition probability for HNO could be much lower than this, alternative explana- tions of the low I0 must also be sought. It has been shown that reaction (3a) involves no energy barrier, and it would therefore be expected from the data on the O+NO reaction that the process, ~ ( 2 s ) + N O ( ~ ~ I ) + M = HNO(~A”) + M, (34 would account for a large fraction of the recombination rate.The lower value of I0 is therefore associated with either slow crossing from the 3A“ state to the 1A” state or with an additional quenching process since it is unlikely that electronic quenching (reaction (6)) is much faster for HNO (1A”) than for NO,*. The presence of several strong perturbations in the 1A” state of HNO make the former explanation unlikely, since the crossing rate would be much higher than the collision rate of 107 to 108 sec-1 in these experiments. The vibrational-energy distribution in the 1A” state would then be similar to that in the corresponding energy levels of the 3A” state from which it is populated.Since the observed emission spectrum is predominantly from the lowest vibrational level of the 1A” state, most of the electronically excited HNO molecules formed must have lost at least 10 kcal of vibrational energy within the radiative (and electronic quenching) life-time of the 1A” state. It follows that a large number of molecules in the 3A” state will have lost more than this amount of vibrational energy, and as a result are below the (O,O,O) level of the 1A” state and cannot therefore cross into the 1A” state to radiate. This effect would not occur in the O+NO reaction, where the minimum of the excited state arising from normal reactants is believed to be above that for the radiating state.9 It is clearly not possible to distinguish between vibrational energy lost in the initial stabilizing process (3c) and that energy lost in subsequent collisions, but available data indicate that vibra- tional energy exchange occurs in most collisions for excited electronic states 14,15 and for levels near the dissociation limit.16 Such processes therefore have about ten times the collisional efficiency of the electronic quenching of NO2 and so vibrational quenching of HNO (3A”) is probably the dominant process in limiting the light emission in the combination reaction H+NO, even if more than one collision is normally needed to remove the critical amount of energy to prevent radiation.To summarize, in the combination reactions H + NO and 0 + NO stabilization by a third body to an electronically excited molecule makes a major contribution to the total reaction rate. In both cases these excited molecules undergo rapid radiationless transition into the state from which emission occurs and which does not148 CHEMILUMINESCENT REACTIONS dissociate directly into unexcited products. In the case of NO; the emission in- tensity is governed by competition between radiation and electronic quenching of this state, but for HNO* vibrational quenching of the non-radiating excited state (3A") to levels below the minimum of the radiating state (1A") is the dominant quenching mechanism. The authors thank Dr. D. A. Ramsay for sending them the manuscript of an unpublished paper and thank the D.S.I.R. for a maintenance grant to one of them (M. A. A. C.). 1 Clyne and Thrush, Trans. Firaday Soc., 1961,57, 1305. 2 Clement and Ramsay, Can. J. Physics, 1961, 39, 205. 3 Kaufman, Proc. Roy. SOC. A, 1958,247, 123. 4 Fontijn and Schiff, Symp. Upper and Lower Atmosphere Chemistry (Stanford Research In- 5 Bancroft, Hollas and Ramsay, J. Chem. Physics, 1962, 40, 322. 6 Dalby, Can. J. Physics, 1958, 36, 1336. 7 Walsh, J. Chem. SOC., 1953,2288. 8 Clyne and Thrush, Proc. Roy. SOC. A , 1962, 269,404. 9 Broida, Schiff and Sugden, Trans. Faraduy SOC., 1961,57,259. 10 Neuberger and Duncan, J. Chem. Physics, 1954,22, 1693. 11 Baxter, J. Amer. Chem. SOC., 1930, 52, 3920. 12 Keussler and Luttke, 2. Elektrochem., 1959, 63, 614. 13 Mason, J. Chem. Sac., 1957, 3904. 14 Rossler, 2. Physik, 1935, 96, 251. 15 Durand, J. Chem. Physics, 1940, 8, 46. 16 Pritchard, J. Physic. Chem., 1961, 65, 504. stitute, 1961).

ISSN:0366-9033    

DOI:10.1039/DF9623300139

出版商:RSC    

年代:1962

数据来源: RSC

摘要:

Reactive Collisions in Crossed Molecular Beams BY DUDLEY R. HERSCHBACH Dept. of Chemistry, University of California, Berkeley 4, California Received 26th February, 1962 The distribution of velocity vectors of reaction products is discussed, with emphasis on the re- strictions imposed by the conservation laws. The recoil velocity which carries the products away from the centre of mass shows how the energy of reaction is divided between internal excitation and translation. Similarly, the angular distributions, as viewed from the centre of mass, reflect the partitioning of the total angular momentum between angular momenta of individual molecules and orbital angular momentum associated with their relative motion. Crossed-beam studies of several reactions of the type M+RI+R+MI are described, where M = K, Rb, Cs and R = CH3, C2H5, etc.The results show that most of the energy of reaction goes into internal excitation of the products and that the angular distribution is quite anisotropic, with most of the MI recoiling backward (and R forward) with respect to the incoming K beam. The molecular mechanics of chemical reactions can be studied most directly in crossed-beam experiments. In recent years this prospect has captivated workers in several laboratories, and encouraging results have already been obtained.1-7 Fortunately, there is a large class of reactions of alkali metals with halogen com- pounds which can be studied with almost rudimentary apparatus. The early flame studies of Polanyis demonstrated that many of these reactions have very large cross-sections, even larger than " hard-sphere '' values ; and the surface ionization studies of Langmuir provided a remarkably sensitive and specific detector for alkali atoms and their compounds.9 Even for alkali atom reactions, in a typical crossed- beam experiment the yield at the peak of the angular distribution corresponds to only a monolayer of product molecules per month. The feasibility of such experiments was established in 1955 by the work of Taylor and Datz 2 on the reaction K + HBr+H+ KBr.(1) Although the traditional tungsten surface ionization detector is about equally sensitive to K and KBr, Taylor and Datz found that a platinum alloy is much more effective for K than for KBr, and this enabled them to distinguish the reactive scattering from the large background of elastic scattering.The collision yield (ratio of total KBr detected to K scattered out of the parent beam) was found to be 10-3 and an activation energy of 3 kcal/mole was estimated from the variation of the yield with beam temperatures. In 1960, Greene, Roberts and Ross 3 reported a further study of reaction (l), with the important refinement of a mechanical rotor to select the K beam velocity. This has led, in recent work with Beck,4 to detailed informa- tion about the dependence of the reaction probability on the initial relative trans- lational energy and impact parameter of the reactants. In the experiments at Berkeley,s-7 we have been very fortunate to have the collaboration of G. H. Kwei, J. A. Norris and J. L. Kinsey. Our first aim has been to study the distribution of velocity vectors of the products.This dictated the choice of a reaction which fulfilled certain kinematical requirements, to be outlined below. 149150 CROSSED MOLECULAR BEAMS It was decided to use K + CH3I+CH3 + KI and analogous reactions. The restrictions imposed by the conservation laws make it possible to infer from the angular distribution of alkali halide in these reactions the final relative translational energy of the products as well as the directions in which they recoil away from the centre of mass. MECHANICS OF COLLISIONS ENERGY AND LINEAR MOMENTUM The conservation laws for energy and linear momentum provide geometrical relationships between the velocity vectors in the asymptotic initial and final states of a collision.Newtonian mechanics is rigorously applicable here, as the same relationships hold in quantum mechanics. The total energy available to the reaction products, to be partitioned between their final relative translational kinetic energy E’ and internal excitation W’ (rota- tional, vibrational, or electronic), is given by (3) The constant energy of the centre-of-mass motion is omitted ; E+ W is the initial energy of the reactants, and ADZ is the difference in dissociation energies of the products and reactants (measured from the zero-point vibrational levels). E’+ W’ = E+ W+ AD:. An observer travelling with the constant velocity of the centre of mass, c = ( ~ l V l +m2v2)lm, (4) would see the reactants approach with velocities inversely proportional to their masses and parallel to the relative velocity vector, since momentum conservation requires v = V1-V2 (5) v1- c = (mz/rn)v, ( 6 4 v2-c = -(ml/m>v.(fib) The recoil velocities which carry the products away from the centre of mass are correlated in the same way (see fig. l), v3-c = (mlr/m)v‘, ( 7 4 v4 - c = -(m3/m)v’. (7b) The final relative velocity vector, v’ = v3-v4, may take any direction in space, but energy conservation restricts its magnitude, V’ = (2E’/p‘)*, (9) which is determined by the reduced mass p’ of the products and the final relative translational energy. A convenient way to take into account the conservation laws in analyzing an observed laboratory distribution is to construct a “ Newton diagram ”, as illus- trated below in fig. 6-9.For each of the accessible values of E’, the spectrum of recoil vectors for product m3 can range over a sphere of radius (ma[m)v’ about the tip of c (see fig. lb). The angle x between v and v’ describes the angular distribution, which has cylindrical symmetry about v, as shown later under eqn. (11). Cor-D. R. HERSCHBACH 151 responding vectors for product m4 appear at the mirror image angle - x on a sphere of radius (m3/m)v’. The Newton diagram thus displays the possible recoil spectrum of a product as a set of spheres, one for each value of E’ up to the maximum allowed by eqn. (3). To compare a theoretical model with experiment we must (i) derive from the model the density of recoil vectors per unit area over each sphere in the Newton diagram, (ii) project these distributions on the laboratory co-ordinate system, and (iii) average over the initial velocity distributions in the incident beams.FIG. 1.-Relations among the velocity vectors of (a) reactants and (b) products. Masses are numbered such that rnlGm2 and m3 Gm4. For (i) we require the differential cross-section per unit solid angle, da/do = I(%,E,E’), (10) for which 13(x) = I4(n - x). The partitioning of angular momentum in the reaction strongly influences the form of I(x) and under certain conditions it will favour peaking along the direction of v, as indicated later. When the reactant beams have comparable velocities, the transformation (ii) is much more complicated than that familiar in nuclear scattering,lo and often intro- duces severe distortions in the laboratory “image” of I(x).It is convenient to designate a product as “ fast ” or ‘‘ slow ” according as its recoil velocity (7) is greater or less than the centre-of-mass velocity. As seen in fig. lb, the laboratory distribution of a fast product may range over 4n steradians, whereas that of a slow product is confined within a forward cone about c, regardless of the form of I(x), and in general contributions from two values of x are superimposed at each labor- atory angle. Three cases may be identified in which the relations imposed by (ii) can be used to advantage by choosing reactions with suitable values of AD: and mass ratios. CASE A : 1 vi-c I 2 0-lc. All the KBr formed in reaction (1) is very slow, for example; even for the maximum possible value of E’, it is confined within about152 CROSSED MOLECULAR BEAMS 10" of c.This facilitates measurement of the total reaction cross-section and its dependence on E. The variation of Z(x) with x and E' has practically no effect on the laboratory distribution of product, which is essentially determined just by the spread in c arising from the velocity distributions of the reactants.11, 12 CASE B : I vi - c I 5 10c.-If a product is sufficiently fast over most of the range of E', its laboratory distribution will give the variation of I(x) with x directly, with negligible distortion from (ii). An example is the H atom produced in reaction (1). However, information about the dependence on E' cannot be obtained without a velocity analysis of the product. Also, for this case, important portions of the Z(x) distribution will often fall in regions obscured by elastic scattering or outside the range that can be scanned by the detectors.CIKI FIG. 2.-Transformation relating angle and energy in centre-of-mass and laboratory co-ordinate systems, for the in-plane scattering corresponding to fig. 6. Contours of constant x are shown by solid curves, contours of constant E' by dashed curves. CASE C : 1 vi-c I=c.-For a suitable intermediate case, the laboratory dis- tribution will be strongly influenced by both x and E'. This occurs for the KI formed in reaction (2), as shown in fig. 2. Furthermore, as illustrated later, the main features of the dependence on x and on E' can sometimes be untangled, without resorting to a velocity analysis of the product, by combining data from different ex- perimental configurations. This is possible if the reactant beams have comparable velocities, as in reaction (2).The transformation relations of fig. 2 are then dras- tically altered for out-of-plane scattering and for different angles of intersection of the reactant beams.D. R. HERSCHBACH 153 ANGULAR MOMENTUM Conservation of angular momentum provides that L + J ' = L+J, (1 1) where L and L denote the initial and final orbital angular momentum associated with the relative motion of the collision partners and are sums of the momenta of the individual reactant and product molecules. As indicated in fig. 3a, the initial J vectors are randomly oriented, whereas the L vectors are perpendicular to the initial relative velocity v, with all azimuthal orienta- tions of L about v equally likely. Therefore, the total angular momentum L+ J always has a distribution with cylindrical symmetry about v and (1 1) imposes this symmetry on the angular distribution of products.J = J1+J2; J = J3+J4 (12) FIG. 3 . 4 ~ ) Orientation of initial angular momentum vectors. (b) Distribution of recoil vectors for " sticky collision " model discussed in text. There is another kinematical feature which, under certain conditions, can greatly enhance the correlation between the product distribution and the direction of v. Consider first the limiting case in which orbital angular momentum is conserved, (This holds precisely for elastic scattering in a central potential.) In this limit, the motion of both reactants and products is confined to a plane perpendicular to L.According to classical mechanics, the relation between the scattered intensity per unit angle in this plane, da/dx, and the differential cross-section is where the first factor arises from integrating over the azimuthal orientations of L about v. The situation is illustrated in fig. 3b, for the special case L' = L. (1 3) I(x) = (2n sin x)-l da/dX, (14) da/dX = constant, (1 5)154 CROSSED MOLECULAR BEAMS which distributes the products uniformly over the azimuthal angles about L, like “water spraying off a spinning wheel”. The complete angular distribution is obtained by rotating the diagram about v so that the circle shown in fig. 3b generates a sphere. Thus we see that the recoil vectors of the products will fan out around the equator and accumulate along the poles, as required by eqn.(14). Of course, eqn. (1 5) need not hold in general ; the l/sin x factor in (14) will produce strong forward peaking whenever the planar distribution does not vanish at x = 0”, and backward peaking whenever it does not vanish at x = 180”. This has been called the “ glory effect ’’ in discussions of elastic scattering.13 The peaking can be sup- pressed only when do/dx vanishes sufficiently rapidly at the poles; for example, the angular distribution becomes isotropic only for specular reflection of hard spheres (for which do/dx is proportional to sin x). In reactive scattering, eqn. (13) cannot be expected to hold. However, devi- ations from planar motion will be small when (a) L$ J and (a’) L’$ J’, and the glory effect will then enter prominently.Averaging over the various orientations of J and J’, which tilt the total angular momentum vector with respect to v and v’, merely rounds off the peaking somewhat. As the conditions (16) are relaxed, the glory scattering persists to a surprising extent; calculations show it is still significant when J and J carry over half of the angular momentum.10 It fades away, of course, when either of the inequalities in (16) is reversed ; thus, if L-g J, the distribution of directions of the total angular momentum vector becomes nearly isotropic and hence no longer endows the products with a “memory” of the direction of v. In the analysis of I(x) it is therefore often appropriate to separate three factors : the partitioning of the total angular momentum (i) between L and J, and (ii) between L‘ and J’ ; and (iii) the distribution do/dX.A rough estimate of (i) may be made by comparing the distribution of J, as given by a rotational partition function, with that of L, derived from the classical relation L = pub by compounding the distributions of initial relative velocity and impact parameter. Reaction is assumed to occur for all values of b up to a maximum, which is ap- proximated by equating nb2 to the total reaction cross-section. For most chemical reactions, including (1) and (2), it is found that L is substantially larger than J, and accordingly, (i) does not inhibit the glory effect. For such reactions, factors (ii) and (iii) decide whether the angular distribution of products will show pronounced anisotropy.Several reaction models have been examined which suggest that in many cases (ii) is likely to be the dominant factor.10 For example, the simplest model to treat assumes a “ sticky ” collision complex which lives long enough to make eqn. (1 5) hold ; that is, longer than the relaxation time required for the decay of phase relations associated with formation of the complex. A characteristic feature of this model is that the angular distribution of products must be symmetrical about x = 90”. If it is also assumed that (ii) is fixed by the population of rotational states of the complex (regarded as in thermal equilibrium at the saddle-point of a potential energy surface), the angular distribution is readily calculated in terms of the moments of inertia and rotational temperature of the complex and the total available angular momentum inferred from eqn.(17) and (1 I). For reactions (1) and (2), any reasonable assignment of these parameters predicts L’$J, and hence strong scattering both forward and backward along v.D. R. HERSCHBACH 155 In this brief survey, only a few aspects of the connection between reaction mechanism and angular distribution could be mentioned. Others are developed in a more detailed, quantum mechanical treatment.10 Like the present classical dis- cussion, much of this is adapted from the theory of nuclear reactions.14 Classical theory is usually qualitatively correct for chemical reactions, which typically involve very large angular momenta; however, the infinite peaking at the poles predicted by eqn.(14) and other sharp edges of the classical approximation are smoothly rounded off in the quantum treatment. APPARATUS AND EXPERIMENTAL CONDITIONS As shown in fig. 4, the beams are formed by thermal effusion from ovens mounted on a turntable which is rotated to sweep the angular distribution past the detector. Vertical adjustment of the detector position allows the scattering to be measured out of the plane (angle4, accessible from 0" to 540") as well as in the plane of the incident beams (angle 8, accessible over -30" to 150" from the alkali beam). The detector is similar to that de- scribed by Taylor and Datz ; ~ 1 5 after the initial aging, the tungsten filament is usually operated at 1900"K, the platinum-alloy filament at 1650°K.The two chambers of the alkali oven are separately heated. The temperature of the beam, which issues from the upper chamber, can thus be varied about 300 deg. without affecting the vapour pressure, which is fixed (at about 0.1 mm Hg) by the temperature of the molten alkali in the lower chamber. LSURFACE-IONIZATION DETECTOR ' I FIG. 4.-Sketch of apparatus. Cold shields, collimating slits, shutters to interrupt the beams, and other details omitted. The gas oven is connected to an external barostat by a supply tube (not shown in fig. 4) which passes through the support column in the rotating lid. Cold shields and collimating slits hide both ovens from the scattering centre, and a cold shield also surrounds the detector.The entire scattering chamber is enclosed in a copper box attached to a large liquid-nitrogen trap. For condensable reactants this provides a very high pumping speed (estimated as 200,000 l./sec) and although this apparatus lacks the customary differ- ential pumping of the beam sources, the background pressure remains at lO-7mmHg during runs. For measurements of in-plane scattering " tall beams " are used ; the oven slits are ordinarily made 0.025 cm wide by 1 cm high and the collimating slits adjusted to give beams between 0.05 and 0.20 cm wide at the scattering centre. For measurements of out- of-plane scattering the detector filaments (both 0.005 cm in diameter) and the beams are156 CROSSED MOLECULAR BEAMS made " flat " ; the beams are then only 0-025 cm high and 0-2 to 0-4 cm wide.Increasing the narrow dimension of the oven slits would not lead to increased beam intensity as the pressure within the oven would have to be decreased proportionately to satisfy the con- dition for effusive flow. The distance from the scattering centre to the alkali oven is 11 cm, to the gas oven slit 1.7 cm, and to the detector usually 10 cm in the tall configuration and 4 cm in the flat configuration. Auxiliary experiments showed the detector filaments to be unaffected by alkyl iodides except for a slight increase in noise. It was also confirmed that the tungsten filament is about equally sensitive to M and MI, whereas the platinum alloy was found to be about 50 times more efficient for M than for MI in rough agreement with data in the literature 15.Test runs made with non-reactive materials as the cross beam, such as n-pentane, showed that the relative detection efficiencies of the tungsten and the platinum alloy filaments for M remained constant over the range of intensities of interest for the study of reactive scattering. However, the readings often failed to match in the region close to the M beam (within f25") where the intensity of elastic scattering rises very steeply ; the discrepancies here may be due mainly to insufficiently precise interchanging of the filament positions. These runs also indicated that any " diffusion-pump " action of the crossed beam 16 was negligibly small. In the K+CH31 experiments, the concentration of IC within the volume defined by the intersection of the beams is about 1010 atoms cm-3, equivalent to a pressure of 10-6 mm, and that of CH31 is about 100-fold greater.About lO14K atoms/sec enter the reaction volume, of which roughly 0.1 % react to form KI while about 10 % undergo elastic scattering. In beam experiments elastic scattering always predominates, since quite weak interactions will deflect a moleci.de from the beam. The total cross-section for beam scattering 17 of K+CH31 is about 1400 A2 and implies that encounters in which the K and CH3I pass at a distance of 20A count as collisions; at this distance the intermolecular potential energy amounts to only 0.3 cal/mole. The steady-state concentration of KI in the reaction volume is roughly 107 molecules/cm~3, the pressure 10-9 mm. At the peak of the KT distribution about 107 molecules/sec arrive at the detector.SUMMARY OF RESULTS An example of the data obtained 5 for reaction (2) is shown in fig. 5. The KI distributions are normalized so that the area under the curves gives the collision yield, which is 5 x 10-4 and corresponds to a reaction cross-section of about 7 A2. Variation of the K beam temperature over a range of 250°K gives practically no change in the yield and indicates the activation energy is less than 0.3 kcal/mole. The Newton diagram of fig. 6, constructed from eqn. (3) and (6)-(9), compares the observed angular distribution with that allowed by the conservation laws. In eqn. (3), AD: = 22 kcal/mole; the thermal distribution of initial kinetic energy is peaked at E = 1.3 kcal/mole ; and the CH31 is mostly in the ground vibrational state with a rotational distribution peaked near W = 0.6 kcal/mole. It is seen that the broad peak observed near 83" in the laboratory corresponds to scattering in which an observer stationed at the centre of mass would see KI recoil backward (and CH3 forward) with respect to the incoming K beam.The displacement of almost 35" from the direction of c shows that the main contributions must have E ' s l kcal/mole. Also, as illustrated by the vector labelled a, reactions producing large values of E' can contribute to the peak only if the recoil velocity vector deviates considerably from the direction of the initial relative velocity v (see also fig. 2). Since the recoil vectors must have cylindrical symmetry about v, such contributions can be studied directly by measurement of the out-of-plane scattering.As the KI is found to be peaked about the plane of the incident beams, we may conclude that scattering close to the direction of v with small values of E' is predominant. Experi- ments at various angles of intersection of the beams confirm this. It is found thatD. R . HERSCHBACH 157 the in-plane KI peak shifts to 68" and to 129" for intersection angles of 60" and 135", respectively, in agreement with predictions derived by redrawing the Newton 6 Parent K beam of 5 x 10-8 A attenuated 7 'X bv crossed CHd beam. Readinns on Pt detector (solid circles) normalized to W (open circles) a t parent beam peak. (b) KI distributions ; circles derived from (a), triangles from a replicate experiment (several months later).Area under curves gives collision yield. KI a t 83' ,I o4 cm /sec, 4 4 CH,ct -10" FIG. 6.-Newton diagram corresponding to most probable velocities of reactants in fig. 5 . diagram for these intersection angles (see fig. 9). In order to account for the ob- servations, 50 % of the KI recoil vectors must lie within the doubly-shaded region in fig. 6 and 90 % within the singly-shaded region. These regions were derived158 -30" 0" 30" 60" 90" 120" 150" 66" 25 Cs:521 O K - CH3I: 303°K - (a) - I I -30" 0" 300 60" 6 90" 120" 150" FIG. 8.Results for Cs reaction.FIG. 1.-Photograph of magnetic resonance spectrum of X-irradiated Perspex (5 x lo* r). [To face page 159.D. R. HERSCHBACH 159 by a calculation which combined the in-plane and out-of-plane data and included the velocity distributions in the reactant beams.Also shown in fig. 6 is the estimate of the most probable CH3 recoil velocity implied by eqn. (7) and this analysis of the KI distribution. Velocity selection 18 is essential if the resolution is to be improved, as illustrated by the dashed curve in fig. 5b. This was calculated by averaging over the initial distribution of v vectors, assuming that all of the KI recoiled directly backwards along v (that is, x = 0') with internal excitation W'rsr21 kcal/mole (corresponding to E'- E = 1.6 kcal/mole). -25 -5,A 'Yo FIG. 9.-Test for possible presence of " forward peaking ". From the results for reaction (2), we can predict what to expect for the angular distributions in other M+RX reactions, if we assume the products will show a similar peaking about the direction of v and high internal excitation.The results found for the reactions of Rb6 and Cs atoms with CH31, shown in fig. 7 and 8, have peaks within a few degrees of the predictions. The activation energy is again found to be negligibly small for these reactions. The reactions of K atoms with ethyl, i-propyl, n-propyl and n-butyl iodides have also been studied. Under con- ditions similar to those of fig. 5, all these reactions have KI peaks in the neighbour- hood of 90". This indicates, according to eqn. (7b), that the average E' decreases as the mass of the R group is increased. There is no noticeable effect from " steric interference " as the R group becomes larger ; the collision yield remains about the same as for the CHJI reaction.1 60 CROSSED MOLECULAR BEAMS A question of particular interest, but not yet entirely settled, is the possible presence of '' forward " scattering of the alkali halide, corresponding to recoil angles near x = 180".. As can be seen from fig. 2, for large E' most of this would appear in the region -30"<81(1<30", which is hidden by elastic scattering from the parent K beam (see fig. 5). There is evidence that the recoil distribution is not symmetrical about x = 90", however.7 The dashed curves in fig. 9 (calculated as before with E'-E = 1.6 kcal/mole, and equal intensity at x = 0" and 180") indicate that a prominent shoulder should have been observed in the region 30" <Om < 50", if a forward peak complementary to the observed backward peak were present.DISCUSSION The rather primitive experiments described here may suffice to illustrate both the present linlitations of the beam method and some of its potentialities. Because the products are observed immediately after the collision in which they are formed, even the qualitative results already obtained pose interesting new questions for the theory of chemical kinetics. For all the reactions studied, the average relative translational energy of the products inferred from the angular distributions is comparable to that of the re- actants. Thus, roughly 90 % of the energy of reaction appears as internal excitation. The present results offer no information about the partitioning of this energy among various degrees of freedom, but presumably it is largely present as vibration of the newly-formed bond.In contrast, spectroscopic studies have in several cases pro- vided a detailed picture of both the vibrational and rotational disequilibrium of a reaction product, but not yet under conditions that permit conclusions about the initial excitation.199 20 The spectroscopic results and theoretical models con- cerned with the vibrational excitation of products have recently been reviewed by Basco and Norrish 19 and by Polanyi.21 The observed asymmetric peaking of the angular distribution along the direction of the initial relative velocity vector implies a reaction mechanism with specific properties. The lack of symmetry about x = 90" shows that the decomposition of the collision complex cannot be regarded as independent of its manner of forma- tion (as in the compound nucleus model of nuclear reactions 14) ; the initial phase relations are not entirely " forgotten ".The suppression of x = 180" scattering (thus far established only for E' 2 5 kcal/mole) must be attributed to anisotropy in the planar cross-section, da/dx. However, the prominence of scattering near x = 0" could arise either from the form of doldx or, if' the final orbital angular momentum is large enough, from the glory effect. (This is, incidentally, opposite to the directional preference of the " stripping" collision model for nuclear re- actions.14) Scattering near x = 0" evidently corresponds to a " hard " collision rather than to a " grazing " one, as the M atom, the R group, and the centre of mass of M and I must all reverse direction.It would seem plausible to assume that da/dx is not restricted to be strongly peaked at x = 0", and to interpret the ob- served peaking as mainly due to a gloriously large final orbital angular momentum. According to eqn. (16), the reaction then takes place more or less in a plane, and the picture suggested by the asymmetry is that the complex is likely to decompose before it can rotate through a half-turn. As the rotational velocities estimated from eqn. (17) are very high, roughly half of the complexes would have to decom- pose within about 5 x 10-13 sec, a time not much longer than a vibrational period. Support received from the U.S. Atomic Energy Commission and the Alfred P. Sloan Foundation is gratefully acknowledged.D. R. HERSCHBACH 161 1 Bull and Moon, Disc. Faraday Soc., 1954, 17, 54. 2 Taylor and Datz, J. Chem. Physics, 1955, 23, 1711. 3 Greene, Roberts and ROSS, J. Chem. Physics, 1960, 32, 940. 4Beck, Greene and ROSS, 2nd Int. Coilf. Electronic and Atomic Collisions (Beajamin, New 5 Herschbach, Kwei and Norris, J. Chenz. Physics, 1961, 34, 1842. 7 Norris, Bull. Amer. Physic. Soc., 1961, 6, 339. 8 Polanyi, Atomic Reactions (Williams and Norgate, London, 1932). 9 Langmuir and Kingdon, Proc. Roy. Soc. A , 1923, 21, 380 ; see also Fraser, Molecular Ray: York, 1961), p. 94. Kinscy and Kwei, Bull. Amer. Physic. Soc., 1961, 6, 152. (Cambridge, 1931), p. 43. 10 Herschbach, J. C h z . Physics, to be published. 11 Merschbach, J. C/ienz. Plzysics, 1960, 33, 1870. 12 Datz, Herschbach and Taylor, J . Cizenz. Physics, 1961, 35, 1549. 13 Ford and Wheeler, Ann. Physics, 1959, 7, 287. 14 See, for example, I. Halpern, Ann. Rev. NucE. Sci., 1959, 9, 245. 15 Dcltz and Taylor, J. Chem. Physics, 1956, 25, 395. 16 Wutt and Biddlestone, Nature, 1961, 191, 798 ; Trans. Faraday Soc., 1952, 58, 1363. 17 Rothc and Bernstein, J . Chem. Physics, 1959, 31, 1619. 18 ICwej, work in progrzss. 19 Basco and Norrish, Can. J. Chem., 1960, 38, 1769. 20 Cashion and Polanyi, J. Chem. Pliysics, 1961, 35, 600. 21 PoIanyi, J. Chem. Physics, 1959, 31, 1338. Weisskopf, Physica, 1956, 22 955. Butler, Nuclenr Stripping Reactions (Wiley, New York, 1957).

ISSN:0366-9033    

DOI:10.1039/DF9623300149

出版商:RSC    

年代:1962

数据来源: RSC

摘要:

Atomic Oxygen and Nitrogen Density Measurements with E.P.R. BY C. A. BARTH, A. F. HILDEBRANDT AND M. PATAPOFF Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, U.S.A. Received 1st February, 1962 The peak signal height, the line width, and the doubly integrated signal were measured at different modulation amplitudes for the J = 1 atomic oxygen line, the J = 2 composite line, and the atomic nitrogen line. It was found that the composite line at large modulation amplitudes, as well as the others, obeyed analytical expressions that were derived for single, well-resolved Lorentzian lines. This realization makes it possible to measure atomic oxygen densities in the pressure range above 1 mm Hg without the necessity of a double integration of the e.p.r.signal. The density of atoms in the gas phase may be measured with an electron para- magnetic resonance spectrometer if the atom is capable of exhibiting a Zeeman effect. Resonance spectra possess the unique advantage that different atomic species may be quantitatively compared with one another without the necessity of the f-number calculations associated with the electronic wave functions. Measurements of mixtures of nitrogen and hydrogen atoms at various pressures have been made by Hildebrandt, Barth, and Booth.132* In order to compare quantitatively the different atomic species at different pressures, it was necessary for the resonance spectra to have well-resolved, non-overlapped Lorentzian line shapes and for the modulation amplitude to be small compared with the line width.Since the spectra of atomic oxygen overlap at pressures above 1 mm Hg pressure, this technique could not be directly applied at such pres- sures. In their work on atomic oxygen, Krongelb and Strandberg3 were able to measure relative oxygen-atom densities at single pressures, but to compare atoms at different pressures and to calibrate their atomic oxygen signal it was necessary to integrate numerically the overlapped spectrum. The recent work of Wahlquist on the modulation broadening of Lorentzian lines 4* has obviated the necessity of using small amplitude modulation when doing quantitative work. In the present work, it was discovered how to measure oxygen atoms at varying pressures above 1 mm Hg without resorting to the cumbersome double integration technique.THEORY The energy absorbed in an electron paramagnetic resonance line per unit time is equal to the product of the number ATi of species involved in the transition, the Einstein absorption coefficient B, the radiation density p , and the energy of the transi- tion hv (cf. paper I) : E = NiBphv. (1) The Einstein absorption coefficient for transitions between magnetic sublevels is proportional to the square of a matrix element which involves the change of only angular momentum quantum numbers : * ref. (2) will be referred to as Daper I and ref. (4) as paper I1 throughout the rest of this work. 162C . A. BARTH, A . F . HILDEBRANDT AND M. PATAPOFF 163 The total and magnetic angular momentum quantum numbers are J and M, and L and S are the orbital and spin angular momentum operators.For atoms in which only a pure Zeeman effect occurs, such as nitrogen, the square of this matrix element is proportional to the square of the Lande g factor and an algebraic combination of the angular momentum quantum numbers : where po is the Bohr magneton. For atoms such as oxygen, the magnetic field used in e.p.r. spectrometers is sufficiently large to produce a quadratic Zeeman effect or the beginning of a Paschen- Back effect. This deviation from the weak field case produces a second-order term in the energy splitting of the sub-levels and a change in the transition probabilities between the various sub-levels. A calculation of these transition probabilities using perturbation theory showed that the square of the matrix elements between the per- turbed levels differed from what their values would have been neglecting the quadratic effect by terms involving (,uoH/AE)2 and higher powers. The A23 in the denominator is the energy difference between different levels of a given atomic state.For atomic oxygen, which was examined in the present work at a magnetic field of 4430 gauss, (,uoH/AE)2 was of the order of 10-6 and hence may be disregarded in intensity measure- ments. Thus, eqn. (3) is applicable to atomic oxygen as well as atomic nitrogen. Since in a magnetic resonance transition, stimulated emission as well as absorption may take place, the number iVi of species involved is equal to the population difference of the adjacent magnetic sublevels. For splittings that are small compared to the thermal energy, where N is the total number of atoms in the level.coefficient gives the following expression for a single resonance line : The product of the number Nt of atoms available and the Einstein absorption N h v g2( J + M)( J - M + 1) NiB = - c, kT (25 + 1) ( 5 ) where C contains the numerical and atomic constants. of the sublevels of a single level, the following expression is obtained : When this expression is summed over all of the transitions occurring between all Nhv kT Nil3 = - g2J(J+ l)C. For e.p.r. spectrometers which employ a fixed-frequency of incident microwave radiation and slowly vary the d.c. component of the magnetic field, such as that used in these experiments, the intensity of the absorption line, I(H), is a function of the magnetic field.The intensity is obtained by introducing G(H), the shape function of the absorption line with its dependence on the magnetic field intensity : The following function describes a normalized unsaturated Lorentzian absorption line (cf. paper 11) : I ( H ) = dEjdH = N,BphvG(H). (7) 9H& ( 4 ~ ~ ) ~ +(H - H , ) ~ ’ G(H) =I64 E.P.R. ATOM MEASUREMENTS where H+ is the half-width or the difference in magnetic field intensity at the half- intensity points and HO is the field intensity at which resonance occurs. This function is normalized so that G(H)dH = 1. Atoms in the gas phase undergoing magnetic resonance transitions exhibit Lorentzian line shapes since the lifetime of the atom in any one magnetic sublevel is limited by collisions.When the expressions for the Einstein coefficient, the number of species, and the line shape are substituted into eqn. (1) and the absorbed intensity is integrated ovei the entire line or lines from a single level, the following expression is obtained : rm co v2Ng2J(J+ I)p = Id(H- H,) = C , T Y -m (9) where the constant Cl contains all of the fundamental constants. For a fixed- frequency spectrometer, v is also a constant. Hence, the amount of energy absorbed in an e.p.r. line is proportional to the number of species present, the square of the Lande g factor, the square of the total angular momentum, the incident microwave power, and inversely proportional to the temperature. The behaviour of the e.p.r. signal with respect to the incident microwave power is discussed in paper I.In the experinients reported here, the temperature is allowed to remain constant. In the electron paramagnetic resonance spectrometer employed in these experi- ments, the magnetic field is modulated at frequency w as its d.c. component is being slowly swept through the resonance line. The absorption signal is then measured with a phase sensitive detector. The signal S(H), measured by the spectrometer is the integral of the detection signal times the line shape function G(H), which now contains the modulation signal (cf. paper I and 11) : S(H) = 5s’ G(H) cos wtd(wt), where C;! is a constant involving instrumental factors as the atomic system that are contained in eqn. (9). n -lL (10) well as the parameters of where HB = H - HO is the d.c. value of the sweep magnetic field and H, is the modula- tion amplitude (cf.eqn. (8) and paper 11.) The usual way of integrating eqn. (10) is to expand G(H), eqn. (1 l), in a Taylor’s series and to retain only the first term of the series resulting from the integration.5 The result is only valid for small values of H,/H*, less than 0.1. The spectrometer signal is then proportional to the modulation amplitude and to the derivative of the line function with respect to the magnetic field : The superscript Tis used with S to indicate that this expression comes from the Taylor’s expansion and is only valid for small values of H,/H+. The parameter that is conveniently measured is the value of the signal at one of the peaks of the derivative curve : where AH is the measure of the magnetic field between the maximum and minimum peaks of the derivative curve and is equal to H4/J3 (cf.paper I). The area underC. A. BARTH, A. F. HILDEBRANDT AND M. PATAPOFF 165 the absorption curve described by I(H) is a measure of the number of atomic species as has been shown in eqn. (9). The double integration of the instrumental signal, eqn. (12), is straightforward and yields the following : H YT = dHJ ST(IT)dH’ = C2H,. (14) -co Hence, the double integration of the instpument signal needs to be divided by the modulation amplitude Hw, and the various constants normalized in order for it to be made equal to the area under the true absorption curve. The constant C2 is then equal to the instrumentation constant C3 times the atomic parameters : and Ng2J(J+ 1)p T ’ c, = c, where C3 = Clv2.In paper 11, Wahlquist showed how to obtain an analytic solution of eqn. (10). His results are valid for all values of Hw/H, and allow experimental measurements to be made with their full intrinsic sensitivity without any fear of loss of accuracy. The spectrometer signal is proportional to the quantity a1 in paper I1 : (16) H, cos otd(wt) S w(H) = C,%a,(H+,H,,H,) = 27c +(Ha + H , cos The superscript Win this case indicates that this result comes from the closed analytic solution and hence may be used for all values of H,/H+ (cf. eqn. (16) with eqn. (12)). The magnitude of the signal at the peaks of the spectrometer signal is also obtained from paper I1 : The magnitude of the the signal peak, eqn (17), is proportional to the reciprocal of H+ times a function of H,/H, which depends on the ratio Hco/H, : When H,/H+ is small, eqn.(17) reduces to the following : w 343- H , s,, = c2- - 2n (Ht)2’ which is identical to eqn. (1 3), the small modulation broadening approximation. At maximum modulation broadening, when H, = H+, the peak signal is166 E.P.R. ATOM MBASURBMENTS The double integration of the signal magnitude SW(H) from eqn. (1 6) is as follows : 9,= d H r Sw(H’)dri’ = 5 Jrn d H r d H ’ r H , cos c;otd(cot) -03 2n2 -03 - l L ($H+)2 + ( H , + H , cos = C2H,. (21) Hence, the double integration of the spectrometer signal is directly proportional to H,, the modulation amplitude, for all values of H,/Ht.* : Eqn. (22) shows the dependence of 6, on all of the relevant atomic and instrumental parameters.The ratio of the values of the double integration to the peak signal height at maximum modulation is the square of the half width times x : The relationships between the half-width, the modulation amplitude, and the measured line width may also be obtained from paper 11. At maximum modulation, the amplititude is equal to the half-width and the measured line width is equal to J3 times the half-width, where AH is the peak width between the inflection points of the spectrometer signal. These results apply to atoms undergoing the simple Zeeman effect. They may also be applied to atoms with a nuclear spin provided that the signal intensity is summed for all the hyperfine components. This may be done by multiplying the signal intensity of one of these components by 21+ 1.These equations may also be used with atoms undergoing an incipient Paschen-Bach effect if the signal intensities of all the now-degenerate lines are summed for each level. Alternately, eqn. ( 5 ) may be used to determine the intensities of the transitions between the various sub-levels. EXPERIMENTAL The instrumentation that was used in this work was a Vaxian 4500 spectrometer and 401 2-B high-resolution electromagnet. The modifications that previously were made to this instrument are described in paper 1. In the present experiments, the spectrometer output was displayed on one channel of a dual channel recorder. The output was also integrated twice using two Philbrick integrating amplifiers and displayed on the second channel of the recorder.This experimental arrangement allowed the simultaneous measurements of the peak signal height S, and the doubly integrated signal 6. The oxygen and nitrogen atoms that were measured in these experiments were produced in a low-pressure flow system. Fig. 1 shows a schematic diagram of the apparatus. The gas enters from the left at pressures varying between 0.1 and 6 mm Hg. It is pumped through the 12.5 mm int. diam. flow tube at flow rates varying between 1 and 12 cm3 sec-1 measured at atmospheric pressure. The oxygen or nitrogen gas is dissociated in the microwave discharge into atoms producing concentrations up to 12 % for oxygen and 1 % for nitrogen. Nitric oxide is added through the titration nozzle when it is necessary to calibrate either the nitrogen or oxygen atom density.6 Fig. 1 also shows the e.p.r.resonant cavity where the atom densities are measured, the spectrometer, and the double integrator. * This integration was performed by H. Wahlquist.C. A . BARTH, A. F . HILDEBRANDT AND M. PATAPOFF 167 At pressures in the vicinity of 0.1 mm Hg, the e.p.r. spectrum of atomic oxygen consists of four well-resolved J = 2 lines and two well-resolved and well-separated J = 1 lines.7 At pressures above 1 mm Hg, the four J = 2 lines overlap forming one composite line even when the modulation amplitude is very small. Above 3 mm Hg pressure the J = 1 lines broaden and overlap so as to become indistinguishable. Spectra that were obtained at 0.13 mm Hg and 1.1 mm Hg at small amplitude modulation are shown in fig.2 to illustrate this. The magnetic field sweep rates were the same for the two spectra so that the line CAVITY , GAS INLET- FIG. 1.4chematic diagram of atom flow system and e.p.r. spectrometer. Atoms are produced in microwave discharge and pumped through e.p.r. resonant cavity. k I I I ,! ___) PUMP l t - ‘ . I OXYGEN. 0.13 rnrn Ha \ ‘-.____-I 1-85 gauss L- 10.7 gauss OXYGEN, 1.10 rnrn Hg / / x’ FIG. 2.-E.p.r. spectra of atomic oxygen at 0-13 and 1-1Omm Hg pressure at low modulation amplitude. The J = 2 lines overlap at the higher pressure while they are resolved at the lower pressure. separations may be compared directly. The splittings of the two J = 1 lines, 10.7 gauss, and the two outermost J = 2 lines, 1.85 gauss, are taken from the original paper 7 and ad- justed to the microwave frequency used in this experiment.The experimental programme consisted of measuring the dependence of the peak signal height S,, the line width AH or 2(H& and the doubly integrated signal 8, on modulation amplitude H, for both nitrogen and oxygen atoms. Nitrogen was measured at 4.0 mm Hg pressure. The J = 1 line of oxygen was measured at 0.1 mm Hg and the J = 2 line at pressures from 1-0 to 5.4 mm Hg.168 E.P.R. ATOM MEASUREMENTS RESULTS The J = 1 atomic oxygen line at 0.1 mm Hg pressure is an ideal spectral line to test the relationships contained in eqn. (10)-(24). The atomic nitrogen line has the difficulty that its natural half-width is so narrow that the line width of 100 milligauss that was measured with the present instrumentation was determined by the inhomogeneity in the magnetic field.The difficulty with the J = 2 oxygen lines is that above 1 mm pressure, the line is a com- posite of four overlapped lines. These characteristics of the three different types of e.p.r. lines under investigation suggest that the J = 1 line at low pressures should obey the theor- etical equations while it is not known a priori what the behaviour of the atomic nitrogen and atomic oxygen J = 2 lines will be. The measurements of the variation of the doubly integrated signal 8 with modulation amplitude for each of the three types of lines resulted in straight lines in all three cases for H,IH& ratios that varied from 0.1 to 1.2. As suggested in the previous paragraph, since eqn. (21) predicts that 8 is proportional to H,, it is to be expected that the J = 1 line obeys I I"*' FIG.3.-Variation of the peak signal height and line width with varying modulation amplitude for the J = 1 oxygen line at 0.104 mm Hg pressure. this relationship. It 3s also to be expected that the J = 2 composite line also follows this relationship, since S(H) in eqn. (16) is a Fourier transform and since that, being a linear operation, the transform of a sum is equal to the sum of the transforms. Hence, the in- tegration of a sum is equal to the sum of the separate integiations and is also proportional to the modulation amplitude H,. It is interesting to find that the double integration of a magnetically inhomogeneous line such as nitrogen also is directly proportional to modulation amplitude.The measurements of the variatim of the peak signal height S,, and the measured line width with changing modulation amplitude for the J = 1 atomic oxygen line at 0-104 mm Hg are plotted in fig. 3. The theoretical curves are drawn from Wahlquist's relation- ships, eqn. (17). The vertical scale for peak signal height and the scale for line width are independently normalized to the experimental data. The horizontal scale for modulation amplitude is uniquely determined for both sets of measurements. A s was to be expected in this case, the agreement between the theoretical expressions and the experimental points is good. The measurements for the J = 2 line at 1.0 mm Hg pressure are presented in fig. 4. The peak signal heights can be fitted to the theoretical curve and the measured line widthsFIG.1.-The three atomic deuterium lines and central broad line in H2S04 diluted with D20 and irradiated at liquid nitrogen temperature. [To face page 168.C. A. BARTH, A. F . HILDEBRANDT AND M. PATAPOFF 169 can be fitted for values of modulation amplitude for HJH+ greater than 0.5. For values less than 0.5, the measured line width falls much more slowly than the curve described by eqn. (17). The same effect is observed for the J = 2 line at 2.0 and 3.0 mm Hg pressure H,IHt FIG. 4.Variation of the peak signal height and line width with varying modulation awlitude for the J = 2 oxygen line at 1-0 mm Hg pressure. FIG. H,IH+ 5.Variation of the peak signal height and line width with varying modulation amplitude for the oxygen line at 5.4 mm Hg pressure.except that the measured line width begins to follow the analytical curve at progressively lower H,/H& ratios. At 4-1 and 5.4 mm Hg, the measured line width follows the curve for all values of H,/H+. The data at 5.4 mm Hg are plotted in fig. 5. In all cases, the peak signal height data falls on the appropriate analytical curve.1 70 E . P . R . ATOM MEASUREMENTS The measurements of the line width of the atomic nitrogen line are also similar to the data in fig. 4. They fall along the analytical curve for high values of HJH4 and at low values the line widths assume a constant value equal to the magnetic inhomogeneity. These results suggest that when the composite J = 2 oxygen line or the inhomogeneous nitrogen line are sufficiently modulation broadened their properties may be described by analytical expressions that were derived for a modulation-broadened, single Lorentzian fine.pressure, mm Hg FIG. 6.-Measured values of line widths at small amplitude modulation of the J = 2 line at pressures from 1-0 to 5.4 mm Hg. The values of the J = 1 line width at small modulation and 0-1 mm Hg pressure and the splitting of the outermost J = 2 lines are included for comparison. 0 1 2 3 4 5 6 pressure, mm Hg FIG. 7.Values of half-width of the J = 2 line of oxygen as measured from the maximum modula- tion amplitude and the line width at maximum modulation amplitude over the pressure range 1.0 to 5.4 mm Hg. The behaviour of the measured line widths of the J = 2 oxygen line is explored further in fig.6 and 7. The measured line width at small modulation amplitude A H is plotted at each pressure from 1.0 to 5.4 mm Hg in fig. 6. The line width of the J = 1 line at 0.1 mm Hg pressure is shown for comparison. The measured line width decreases with decreasing pressure approaching a limit that is set by the splitting of the outermost J = 2 lines. This also may be seen in the spectra shown in fig. 2 where the splitting of 1.85 gauss is indicated.FIG. 3.--The high field atomic H line in irradiated HC104 showing weak satellites. [To ,face page 170.C. A. BARTH, A. F. HILDEBRANDT AND M. PATAPOFF 171 At the modulation for maximum signal height, the measured line width, (AH)m, is a linear function of pressure. This may be seen in fig. 7 where (AH)m, is a linear function of pressure. This may be seen in fig.7 where (AH)m/d3 is plotted at pressures from 1.0 to 5.4 mm Hg. Fig. 7 also gives further evidence that a modulation-broadened J =2 line has the properties of a modulation-broadened Lorentzian line. Eqn. (24) states that at the modulation amplitude for maximum peak signal height, the modulation amplitude ( c m ) m , is equal to the half-width H+, and the measured line width (AH)m is equal to the 4 3 times the half-width. In fig. 7, the half-width is determined by these two separate measurements over the range of pressures. Since the line width and modulation amplitude measurements agree at each pressure, the analytical formulation again appears to be applic- able. The calculated half-width being proportional to the pressure gives credence to this quantity being a collision property of the atom.pressure, mm Hg FIG. &-Measured values of the square root of the ratio of the doubly integrated signal to the peak signal height at maximum modulation amplitude and pressures from 1.0 to 5.0 mm Hg. The ratio of the doubly integrated signal to the peak signal height is proportional to the half-width squared at maximum modulation amplitude as stated in eqn. (23). In fig. 8, the square root of the measured values of the doubly integrated signal and peak signal height of the J = 2 is plotted against pressure. The variation is linear. If the half-width is interpreted to be proportional to pressure, then these data show that the ratio of the integral to the signal height is proportional to the half-width squared by analogy with eqn.(23). The half-width is expected to be proportional to pressure for collisions with a given constituent. Both the nitrogen and oxygen atom densities were calibrated by means of the nitric oxide titration.6 Care was taken to avoid the production of additional active species such as were found by Schade in pure nitrogen afterglows.8 The number of nitrogen atoms at the beginning of the titration was measured and compared to the number of oxygen atoms at the end of the titration by the double integration of the two signals and the use of eqn. (22). With this calibration, the double integrator was used to obtain the oxygen atom densities at the pressures studied in these experiments. They are plotted in fig. 9 along with the flow rates at each of the pressures.172 E .P . R . ATOM MEASUREMENTS DISCUSSION The results of the previous section show that the density of oxygen atoms may be measured at different pressures without resorting to the double integration of the spectro- meter signal. The procedure is as follows : (i) at each pressure determine the modulation amplitude that produces the maximum signal height ; (ii) measure the line width and peak signal height and apply eqn. (20). It is stilI necessary to calibrate the number of oxygen atoms at one pressure by an independent technique such as the nitric oxide titration. This is because these experiments have established the proportionality implicit in eqn. (20) but have not determined that the numerical constant is the same for composite modulation- broadened lines as it is for single Lorentzian lines. It may be, but the present work gives no information on this problem. U L I I 1 I I I I OO I 2 3 4 3 pressure, mm Hg FIG. 9.-Oxygen atom density at various pressures and flow rates as measured by the double integration of the output signal. The results of this work also establish that the ratio in eqn. (23) is proportional to the square of the half-width for a modulation-broadened composite line. The present experi- ments do not determine whether or not the constant derived in eqn. (23) is applicable to the composite line. The relationship depicted in this equation suggests, however, the manner in which this may be studied. The authors appreciate the many discussions with H. Wahlquist concerning this work. This research was supported by the National Aeronautics and Space Administration under contract No. NASw-6. 1 Hildebrandt, Booth and Barth, J. Chem. Physics, 1959,31, 273. 2 Hildebrandt, Barth and Booth, Proc. Con$ Physical Chemistry in Aerodynamics and Space 3 Krongelb and Strandberg, J. Chem. Physics, 1959, 31, 1196. 4 Wahlquist, J. Chem. Physics, 1961, 35, 1708. 5 Andrew, Physic. Rev., 1953, 91, 425. 6 Kaplan, Schade, Barth and Hildebrandt, Can. J. Chem., 1960,38, 1688. 7 Rawson and Beringer, Physic. Rev., 1952,88,677. Rawson, Ph.D. Thesis (Yale, 1952). 8 Schade, Ph.D. Thesis (Univ. of Calif., Los Angeles, 1961). Flight (Pergamon Press, London, 1961), pp. 194-203.

ISSN:0366-9033    

DOI:10.1039/DF9623300162

出版商:RSC    

年代:1962

数据来源: RSC

摘要:

Statistical Investigation of Dissociation Cross-Sections for Diatoms" BY JAMES KECK Avco-Everett Research Laboratory, 2385 Revere Beach Parkway, Everett, Mass., U.S.A. Received 1st February, 1962 An efficient statistical method for investigating the mechanism and rate of simple chemical reactions has been developed. The procedure involves the random selection of representative systems from the middle of the reaction zone, followed by numerical integration of the equations of motion in both directions to determine the complete course of the reaction. The approach has the important advantage over the usual one of sampling outside the reaction zone that the fraction of systems which react is tremendously increased. The method has been used to investigate the dissociation and recombination of H2,02 and I2 in collisions with argon at temperatures of 0.01 and 0.1 the dissociation temperature D/k.A total of 2400 systems were followed, approximately half of which resulted in a reaction. The cross-section for dissociation as a function of the internal energy H12 of the diatom was found to be proportional to [l +(B-H12)/kT]-3.5, where E is the height of the rotational barrier for the diatom. In a previously published paper,l the author proposed a theory of chemical reaction rates by means of which it is possible to obtain a rigorous upper bound to the reaction rate which can be systematically lowered by a variational technique. Although similar theories were proposed more than 20 years ago by Wigner 2 and Horiuto,3 they apparently failed to attract the attention of theoretical chemists and have been lost in the literature until recently.In these theories, the reacting system is represented by a point in an appropriate classical phase space and an upper bound to the reaction rate is obtained by calculating the flux of trajectories crossing a " trial " surface dividing the reactants from the products. The bomd may then be lowered by adjusting the parameters which define the " trial " surface to produce the minimuiii crossing rate. The reitson this procedure leads only to an upper bound for the reaction rate is that, although in principle there exists a class of surfaces which are crossed only once by any one trajectory, in practice the " trial " surfaces chosen will almost never belong to this class and may be crossed many times by single trajectories.Thus, in the calculations of the reaction rate we will have included some trajectories which do not react at all, as well as others which react only after multiple traversals of the " trial " surface. The present work was initially undertaken to investigate the effect of multiple traversals of the " trial " surface on the calculation of the rate of dissociation and recombination of diatoms in collisions with noble gases carried out in ref. (1). The method involves the random sampling of phase-space trajectories crossing a '' trial " surface tangent to the top of the rotational barrier for the diatom, followed by numerical integration of the classical equations of motion in both directions in time * This work has been supported jointly by Headquarters, Ballistic Systems Division, Air Force Systems Command, United States Air Force, under Contract #AF04(694)-33 and Advanced Research Projects Agency, monitored by the Army Rocket and Guided Missile Agency, Army Ordnance Missile Command, United States Army, under Contract #DA-19-020-ORD-5476. 173174 DISSOCIATION OF DIATOMS to determine the complete trajectories. Given the complete trajectories we can deter- mine not only whether reaction occurred and the number of crossings of the " trial " surface involved, but also the dependence of the reaction probability on the initial configuration of the system.This latter possibility, which is made practical by the large fraction of trajectories which react, opens an extremely interesting field for investigation, the first results of which are the determinations of the dissociation cross-sections as a function of vibrational energy presented in fig. 6 of this paper.MATHEMATICAL FORMULATION Following the methods of ref. ( 1 ) an upper bound Ro to the equilibrium rate of a chemical reaction A+B may be obtained in the form where do is an element of the hypersurface S which divides the reactants A and products B, n is the unit normal to do, v is the generalized velocity of a point in phase space and Pe is the equilibrium density of representative points. To obtain a corresponding expression for the true rate we proceed as follows. Let R(i,j) be the partial rate associated with trajectories which make i traversals of S in the direction of n and j traversals in the opposite direction.By definition, where S(i,j) is that part of S crossed by trajectories in the class (i,j). Since the trajec- tories are continuous curves in phase space and S cannot have any " holes ", R(i,j) = 0 unless j = i,i&l. For a reaction to occur, the number of traversals of S which a trajectory makes in the direction of n must exceed the number it makes in the opposite direction. Hence, j = i- 1 and the true reaction rate R = X(i-')R(i,i-f), (3) i where the factor i-1 has been introduced to correct for the fact that a single trajectory crossing S(i,j) i times contributes i times to R(i,j). In general, it will not be possible to calculate R(i,j) because the surfaces S(i,j) are not known. However, we can obtain a statistical estimate R(i,j) by numerical methods. To do this, we select a random sample of trajectories crossing S with a weight function proportional to the flux pe(v.n). We then follow these trajectories through the reaction in both directions from S to determine their histories. The rate R(i,j) = Ro lim N(i,j)/No , No+ co (4) where NO is the number of trajectories followed and N(i,j) is the number falling in the class (i,j). In practice, the success of this procedure for investigating reaction rates depends on the fraction N(i,i-l)/No of reacting trajectories being fairly large. It is here that the present approach gains an important advantage over similar ones which have been made in the past. By starting the calculation in the middle of the reaction zone rather than outside it as is the usual procedure, the fraction of reacting trajectories is tremendously increased and what was a prohibitive calculation in terms of machine- time becomes quite modest.J . KECK 175 CALCULATIONS OF REACTION PROBABILITY We have applied the method outlined above to the problem of estimating the equilibrium rates for the reactions 2H+A+H2 +A 2 0 +A+02 + A 21 -!- A+I2 +A for values of kT/D equal to 0.01 and 0.1.I I 1 I I I I I I I - 10 -5 0 5 10 vet FIG. 1.-Typical trajectory histories for collisions involving 2H and A at kT/D = 0.01. Shown plotted in dimensionless form are the separation r12 of the H atoms, the separation r3 of A from the centre of the 2H and the difference ( B - H I ~ ) between the instantaneous height of the rotational barrier and the energy of the 2H.ve = 1.3 x 1014 sec-1 is the vibrational frequency of H2 in the ground state, /3 = 1.93 x 108 cm-1 is the decay constant appearing in the Morse potential, z2 is the most probable position of the rotational barrier, and re is the equilibrium separation of H2. The calculations were carried out in the centre-of-mass system for the three particles. As in ref. (1) the interaction potential for the three-atom system was assumed to be the sum of the interaction potentials for the individual pairs of atoms. The Morse potential 4 VM(r) = D([l-exp (-pr+gre)]2-1) was used to represent the interaction between the atoms of the diatom and the Mason- Vanderslice potential 5 K,,&) = DMv exp ( - D , AI76 DISSOCIATION OF DIATOMS was used to represent the interaction between an atom of the diatom and the argon atom.For simplicity, the Van der Waals attraction included in the calculations of ref. (1) was neglected in the present work. The trajectories were started on a surface SB tangent to the toy of the rotational barrier for the diatom. The distribution functions for the initial co-ordinates and momenta were obtained by separating the eleven dimensional integral obtained from eqn. (1) as a product of integrals following the methods of ref. (1). The six coupled equations of motion were written in Cartesian co-ordinates and integrated on an IBh4 7090 computer using a 4th order Runge-Kzrtta method. The trajectories were -4 -5 -1.0 -0.5 0 0 - 5 1'0 vet FIG. 2.-Typical trajectory plots for collisions involving 21 and A at kT/D = 0.1.Shown plotted in dimensionless form are the separation r12 of the atoms, the separation rg of the A atom from the centre of the 21, and the difference (B-Ii12) between the energy of the 21 and the instantaneous height of the rotational barrier. ve = 6.5 x 1012 sec-1 is the vibrational frequency of I2 in the ground state, /3 = 1.86 x 108 cm-1 is the decay constant appearing in the Morse potential, z2 is the most probable position of the rotational barrier and re is the equilibrium separation of 12. followed in both directions from the initial point until the potential of interaction with the argon atom fell below kT/100. As a check on the interval size we required that changes in the total energy E and angular momentum L be limited to values AESkT/100 and AL S L/lOO.The former condition was the more difficult to satisfy. For each case, 400 trajectories were followed making a total of 2400 trajectories and the total computer time involved was about 6 h. All of the 12 co-ordinates and momenta giving the relative positions and velocities of the three particles were printed out at the beginning and end of each trajectory. In addition, a tabulation was madeFIG. 1.-Section of paramagnetic resonance spectrum of 10-5 Mc in cubic ZnS. [To ,face page 176.J . KECK 177 of the internal energy H12 of the diatom, the height B of the rotational barrier for the diatom, the separation r12 of the atoms in the diatom, and the separation r3 of the argon atom from the centre of the diatom. Examples of a few trajectory histories taken from this tabulation are shown in fig. 1 and 2.The cases chosen, 2H-t-A at kT/D = 0.01, and 21+A at kT/D = 0.1, represent the two extremes in the ratio of the collision time to the vibrational period of the molecule. From the plots, one can form a general impression of the character of the particle motions, the duration of the collisions, and the excursions in the energy (B-Hl2). Note that (B-Hl2) TABLE DISTRIBUTION OF TRAJECTORIES WITH RESPECT TO CLASS OF REACTION AND NUMBER OF TRAVERSALS OF THE TRIAL SURFACE. THE PARAMETER 8 = kT/D N(b I i,i I b) N(dE/dt > 0) 2H+A 94 28 60 26 74 8 91 19 119 14 108 16 19 1 26 2 35 4 36 11 1 2 3 0 3 2 0 2 1 0 0 0 1 total 122 89 84 110 135 125 20 28 39 48 total l b class N(fl i:i-l 1 b) N(dE/dt> 0) *o 1 -1 341 55 321 74 20+A 146 33 128 31 81 4 77 14 94 8 100 6 15 0 13 1 12 5 28 2 1 7 & 4 5 3 2 0 0 0 0 0 0 0 0 0 400 400 total 181 159 85 91 102 106 15 14 17 30 total l c class N(fI i,i-1 [ b) N ( f I i,i I f> N(b I i,i I b) N(dE/dt> 0) -01 -1 348 50 346 54 2I+A 256 7 282 4 48 0 44 0 69 1 39 1 0 0 5 0 16 3 25 0 1 2 2 0 0 0 0 0 0 0 0 0 0 0 400 400 total 263 286 48 44 70 40 0 5 19 25 total -0 1 -1 389 11 0 400 395 5 0 400178 DISSOCIATION OF DIATOMS approaches a constant value at the beginning and end of each trajectory indicating that the interaction with the third particle has indeed become negligible.Also note that the vibrational period for diatoms crossing the energy surface (B-Hl2) = 0 is substantially larger than the ground-state vibrational period v, 1.In table I, the results have been catalogued according to the type of transition involved and the number of traversals of the energy surface (B-Hl2) = 0 in each direction. We have expanded the notation N(i,j) of the preceding section to indicate the initial and final state of the diatom. Thus, N(f1 i,i- 1 I b) denotes the number of cases in which a trajectory went from a free state f to a bound state b with i cros- sings of (B-Hl2) = 0 in the directionfjb and i- 1 crossings in the direction b+J Note that there were a small number of cases denoted N(d&/dt>O for which the initial traversal of the trial surface was in the wrong direction. This arose from an approxi- mation made in separating the integral in eqn. (1) in which only the interaction between the third body and its nearest neighbour was taken into account.These cases are to be treated as non-reacting. FIG. 3.-Ratio of number N of reacting trajectories to total number No followed as a function of the ratio P12/(P3+P12), where ~ 1 2 is the reduced mass of the diatom and p3 is the reduced mass for the collision. The upper scale shows the ratio of the mass rn1 of an atom of the diatom to the mass m3 of the third body. A number of interesting features are immediately apparent in table 1. First, and most welcome, is the large number of cases in which a reaction occurred. This implies that our original estimates of the rates based on the variational theory were not far wrong. Secondly, the number of trajectories which cross the trial surface more than once in each direction decreases rapidly as the number of crossings in- creases.Thirdly, within the statistical accuracy of the data there is very little indica- tion of a temperature dependence in the results. Finally, there is a relatively weak dependence of the reaction probability on the mass of the recombining atoms. In fig. 3 the fraction of reacting trajectories NIN, = N,lx(i-l)N(f I i,i-1 I b) I ( 5 ) is plotted as a function of pl2/(pl2+p3), where p12 is the reduced mass of the diatomJ, KECK I79 and ,u3 is the reduced mass of the argon and diatom. The data can be represented by the empirical equation Although the present results give no indication of the dependence of the reaction rate on the mass of the " third body ", there is some evidence in the comparison of theory and experiment made in table 1 of ref.(1) which suggests that when the '' third body " is lighter than the reacting atoms the recombination probability is near unity. Eqn. (6) is in accord with this suggestion. DISSOCIATION CROSS-SECTION As a result of the relatively large fraction of reactions occurring, it is possible to obtain information on the reaction probability as a function of conditions in the initial and final states of the system. Our first effort in this direction has been to investigate the number of reactions as a function of the energy of the bound state of the diatom. The results are shown in table 2 where we have tabulated the number of cases AN in which the ratio E = ( B - H 1 2 ) / k T falls between the values given in the first column.When correlated in this manner, the distribution exhibits very little mass or temperature dependence. TABLE 2.-DISTRIBUTION OF REACTING TRAJECTORIES WITH RESPECT TO THE PARAMETER E = (B-H12)/kT. THE PARAMETER 8 = kT/D case & I @ 0.0-0.25 0.25-0.50 0.50- 1 '0 1 -0-2-0 2.0-4.0 4.0- co 2H+A -01 0.1 42 47 23 11 16 5 8 9 8 2 11 0 20+A 2I+A -0 1 0- 1 *01 0.1 75 67 143 145 27 22 44 50 30 23 30 51 16 20 23 25 9 10 13 11 6 1 6 2 N 108 74 163 143 259 284 The data in tabIe 2 may be used to estimate the cross-section O(E) for the dis- To do this, sociation of a diatom as a function of the parameter E = (B-H12)/kT. we simply equate the differential reaction rate given by the present theory to the corresponding expression which defines the cross- section, to obtain where EX,] and [A] are respectively the concentrations of diatoms and argon atoms, Ke is the equilibrium constant for the reaction X2 -t AeZX + A, kr is the recombination180 DISSOCIATION OF DIATOMS rate constant given by eqn.(45) in ref. (l), v3 is the relative velocity of Xz and A and 83 = p3v3/2kT. For a rotating Morse oscillator, the factor where v is the frequency of the rotating oscillator in the state (B-&)/kT = E, and 22 is the most probable position of the rotational maximum which may be obtained from curves in the appendix of ref. (1). FIG. 4.-Curve of 7 = (v/ve)2D/kT as a function of the parameter E. The curve is approximately valid for 1< @re< 9 and 0.01< kTID< 0.1. For large E, 7 is asymptotic to E.Combining eqn. (6), (9) and (10) we obtain where q = (v/ve)2D/kT is shown plotted in fig. 4 as a function of E and 00 is a cross- section of the order of 10-15 cm2 which may be expressed in terms of parameters defined in ref. (1) as The quantity [F’-+F;-]/4 which must be obtained by numerical methods is plotted in fig. 5 for the cases of interest here. The ratio a(e)/oo computed from eqn. (11) using the data in table 2 is shown as a function of the parameter ( 1 + ~ ) in fig. 6. Within the statistical accuracy of the data, all the points can be fitted by the empirical equation (1 3) Whether or not this particular functional form has any basic significance is not clear to the author. However, it does seem somewhat remarkable that the results which a(E)/a, = 1.5(1 + E ) - ~ ” .FIG.3. [To face page 180,FIG. 4.J . KECK 181 13'' 0 = (kT/D) FIG. 5.--curVe of the function (F$-+F/-)/4 required for computing dissociation cross-section from eqn. (12). I I ! I I L L - ~~ I 2 3 4 5 (1 +El FIG. 6.-Calculated dissociation cross-sections as a function of 1 +E. The reference cross-section a0 is defined in eqn. (12) and E = (B-H12)/kT where B is the height of the rotational maximum and H12 is the internal energy of the molecule. The scatter of the points about the line is com- patible with the statistical errors involved.182 DISSOCIATION OF DIATOMS span so wide a range of conditions can be correlated in so simple a manner. It should be noted that (1 + E ) is the mean energy transferred to the diatom divided by kT.DISCUSSION One of the fundamental reasons for our interest in the dissociation cross-section G(E) is that it is independent of the assumption of equilibrium in the vibrational degree of freedom of the diatom. This is important for practical applications since it is virtually certain that during the process of dissociation or recombination in any experimental situation the vibrational states near the dissociation limit will be out of equilibrium. Unfortunately, direct observation of O(E) will probably be extremely difficult. It is most likely that O(E) will be observable only through its influence on the overall dissociation rate. In this connection a theory of coupled vibration and dissociation is being developed by some of the author’s colleagues and will be published shortly.With respect to the integrated reaction rate, the present work produces little change in the comparison between theory and experiment made in ref. (1). The theory predicts the experimental rates at room temperature well but overestimates the rates at high temperatures by a factor of about 5. The mass dependence of the reaction probability uncovered in the present work should slightly improve the cor- relation of the experiments shown in fig. 15 of ref. (1). It should also make possible correlation of recent data on the dissociation of Hz. Since the theory developed here has the potential of giving considerable detail about the mechanics of simple chemical reactions, a restatement of the assumptions which have been made is well worth-while.The most fundamental of these is, of course, that classical mechanics is valid. The main argument here is based on a comparison of the reduced wavelength 2 = fi/(2MkT)* for the heavy particles with the characteristic distance a0 w 0.5 A over which appreciable changes in force occur. The ratio where me is the electron mass, R is the Rydberg energy, and A is the atomic mass. It can be seen that even for hydrogen at room temperature 2/ao-+, while for all heavier molecules and higher temperatures it is substantially less. This implies that it should be possible to describe the particles by reasonably well-defined wave packets which will follow the classical orbits. The second assumption of importance is that the forces between the particles can be uniquely related to their positions and velocities. This requires that electronic transitions do not occur during the course of the collision and is related to the validity of the Born-Oppenheimer separation in chemistry. The final assumption is that the potential can be described as the sum of the interactions between pairs. While this affects the numerical results, it is not basic to the theory which can be used with any potential. In fact, the coupling of theory and experiment may well be useful for obtaining information about the nature of many-body interactions. 3/ao = (m,/M)*(R/kT)* = (86/AT)*, The author wishes to acknowledge the important contributions made to this work by Benjamin Woznik who blocked out the original IBM programme, Kendrick Ownby who made it work, and Anna Manzi who is currently assisting with the calculations. 1 Keck, J. Chem. Physics, 1960, 32, 1035. 3 Horiuto, Bull. Chem. SOC. Japan, 1938, 13, 210. 4 Herzkrg, Spectra of Diatomic Molecules @. Van Nostrand, New York, 1950). 3 Mason and Vandersiice, J. Chem. Physics, 1958,28,432. 2 Wigner, J. Chem. Physics, 1937,5, 720.

ISSN:0366-9033    

DOI:10.1039/DF9623300173

出版商:RSC    

年代:1962

数据来源: RSC

摘要:

Three-Body Collision Rates in Atomic Recombination Reactions BY FELIX T. SMITH Stanford Research Institute, Menlo Park, California Received 1st February, 1962 A new symmetric representation for 3-body collisions makes it possible to define the 3-body collision rate in terms of the masses and radii of the particles, and the temperature. Comparison with experiment shows that the reaction I+I+A +Iz+A, with A a rare gas, has a collision efficiency between 11720 for He and 1/44 for Xe. The current renascence in the application of modern collision theory to chemical kinetics coincides with a flood of experimental data on atomic recombination reactions, and a lot of theoretical work is being devoted to them. Keck has given both a phase- space, statistical theory and a variational approach ; 1 many authors have studied excitation and de-excitation of the vibrational " ladder ", with dissociation at the top ; 2 Bunker and Davidson, among others, have considered a two-step process with association into a weakly-bound 2-body complex followed by collision with the third active species,3 and Bunker has emphasized the importance of metastable orbiting 2-body complexes in this sort of process.4 The relative importance of essentially simultaneous 3-body collisions as compared to these 2-step, 2-body processes is still uncertain. Even with the development of these and other sophisticated treatments, we shall still have use for the crude sort of information contained in simple collision pictures like the hard-sphere model for 2-body collisions.This note is devoted to a reexamination of the 3-body collision rate from such a point of view.In 2-body collisions, the hard-sphere picture leads to a simple form for the col- lision rate as the product of an average velocity and a cross-section depending only on the particle radii. Three-body collisions do not occur for hard spheres, but they will occur with attractive potentials with a sharp cut-off; such a picture leads to a 3-body cross-section depending only on the radii and masses of the particles. Three-body collision rates have been discussed by several authors.5 Tolman,6 using a modified hard-sphere picture, derived a 3-body collision rate that involves an additional distance parameter besides the particle radii. This parameter is ill-defined, making that theory somewhat unsatisfactory.Moelwyn-Hughes 7 has derived a formula that involves only the radii and masses of the particles, but it is unsymmetrical in the particles. I shall base a renewed discussion on a recently developed symmetric description of 3-body collisions. For a symmetric description of 3-particle motion, the potential is best represented in a 6-dimensional normalized centre-of-mass co-ordinate system, whose origin represents coincidence of the 3 particles.8 The 6-space is traversed by three 3-di- mensional tubes representing the interaction of the particles in pairs. These tubes intersect in a region S around the orgin where all 3 particles interact simultaneously. For a chemically effective 3-body event the trajectory must pass through the central region S.In the region of no interaction, the trajectory is a straight line, which may enter the 3-body region either directly, giving a pure 3-body collision, or indirectly 183184 3-BODY COLLISION RATES by first entering one of the tubes of 2-body interaction and forming a complex which remains together long enough to collide and interact with the third particle. These two processes are, in principle, different, although there is a certain region of overlap between them ; the distinction is particularly clear for long-lived 2-body complexes. The most important of these complexes are the orbiting pairs of Oldenberg and Bunker. These processes, and some others, are illustrated in fig. 1. FIG. 1 . p o m e possible 3-body trajectories. The hatched regions are regions of interaction, where the potential is non-zero.(c) represents two successive 2-body collisions, (d) represents a vibrating molecule AB approaching collision with C, (f) represents 3 particles separating, starting from a region of pure 3-body interaction, (e) shows A and B colliding and revolving about each other long enough to collide with C, (d’) shows a bound molecule BC rotating as it departs from A. If the rate of 3-body reaction between A, B and C is - d[A]/dt = k‘3’[A][B][C], we shall assume that can be approximated as the sum of 4 terms, (2) Here ki3’ represents the contribution of the pure 3-body collisions, represents the contribution of orbiting pairs B . . . C colliding with A, and similarly for k::! (A . . . C+B) and kfii (A . . . B+C).The terms k$ depend on the lifetimes of the orbiting pairs as a function of their angular momentum and energy, and their evaluation requires a consideration of the potentials of the 2-body interactions. These matters will have to be discussed elsewhere. From here on, our attention will be devoted to the estimation of kk3’. To discuss the pure 3-body collision rate, we can take advantage of the fact that chemically reacting particles must move on an essentially straight-line trajectory until they come within reach of the short-range interactions. These short-range forces between particles will be assumed to be cut o f f at a rangepij, which can often be taken k(3) N k(3) (3) k(3)+k(3) - I +krro+ IIh IIC’5 6 4 5 3 4 2 3 1 2 FIG. 2.-Paramagnetic resonance spectra of vanadium ions in aqueous solution (above) and ether solution (below) at 9000 Mc/sec.The spectrum centres fall near 3200 oersteds and the line splittings are approximately 116 and 110 oersteds, respectively (see text). [To face page 184.F . T. SMITH 185 as the sum of the particle radii, pi+pj. It will be our aim to estimate kI3) in terms of the particle masses mi and the ranges pij. The co-ordinate system is very similar to that introduced by Polanyi and Eyring. It is defined by the following equations : x u is the vector from B to A, and xc is the vector from C to the centre of mass of AB. These co-ordinates (CAB, CF) define a 6-dimensional configuration space in which all possible motions of the 3 particles can be described. The fundamental radial distance in this space is defined by Fig.1 shows a projection of various trajectories in the plane (Cf , <:). The statistics of 3-body collisions take a particularly simple form in this normalized co-ordinate system. I have recently developed the basic equations 9 and merely reproduce the most important formulas here. The 3-body reaction rate k(3) can be related to a 3-body reaction cross-section d3) (E) : p2 = ci[(54B)2 + (<9’]. (4) Let us now assume that the reaction cross-section can be approximated by a 3- body collision cross-section, and confine our attention to the pure 3-body collisions contributing to the rate constant ki3). If the collision cross-section is assumed to be independent of energy the rate constant becomes a product of this cross-section and an average velocity : /q3) = 4 3 1 , v = (15n/S)(kT/2zp)*. (6) 0i3) = (8z2r:/15), (7) (8) Further simplification depends on assuming for the collision cross-section the formula appropriate to the hypersphere : which leads to kf3) = n3r@T/2np)* = ( 15n/8)(kT/2np)*o(31.In these formulas, the characteristic temperature dependence is as Ti. This de- dendence arises because of the assumption that the cross-section is independent of energy, and a different dependence would obtain if a more realistic cross-section, falling off at higher energy, were used. To obtain an estimated collision rate it is now necessary to determine the geo- metric cross-section of the central region of 3-body interaction illustrated in fig. 1. The simplest assumption to make is that this region is the intersection region of the tubes of 2-body interaction.To obtain this cross-section is an exercise in geometry in 6 dimensions which I shall short-cut by using the spherical formula, eqn. (7), and an average radius obtained from the 2-dimensional diagram of fig. 1. This average radius will depend on the interaction distances, p i j = pi+pj, and the masses of the particles. The result is only an approximation, since the proper average would be taken over an orientation-dependent d 3 ) of dimension r5, and not simply over Y.186 3-BODY COLLISION RATES For a reaction of 2 identical atoms A and a third body By the geometry of the interaction region is given in fig. 2. In this figure, the important quantities are : si = (PAAIP>'PAA, PAB = mAmB/(mA + mB), s2 = (PABIPPPA~, PAA = l1lAI2, p2 = n12mBK2ntA + nzB), tan y = [(2mA+mB)/mB]+.(9) The interaction region depends on the quantities : ra = s2 sec y, r, = s1 cosec 8 = s2 cosec (y - 8) = cosec y[s: +2sls2 cos y +si]* tan q = (ra-sl)/r& cos 8. (10) The effective size of the interaction region depends on the orientation of the collision trajectory. In fig. 2, the collision radius is ra for a horizontal trajectory and ra cos +a for a trajectory that departs from the horizontal by an angle 4 a as long as O r & l q . FIG. 2.-The geometry of the interaction region : 2 identical particles. From then on, the collision radius is r b cos 4 6 for (-z/2+ rj + 8) 5 4628, with 4b measured from the perpendicular to r6. The average radius of the interaction region is then 9 = (qn)cr, J' cos $d$ + .f coS $d+] 9 + q - x / 2 = (2/n)[sl + 2 cosec 2y(sf cos2 y +2s1s2 cos y cos 2y + sz>f]187 With 3 different atoms, the result is more complicated and will not be given explicitly here.It can be obtained by the following argument based on fig. 3. From the masses and ranges, we know the 3 angles y i and 3 lengths sf. From these the distances ri and angles Bij are determined by solving The three central angles q j follow because From& rj and qk we can find the third side of the triangle ?k and the other angles 4 k i , 4kj- The average radius is then F. T . SMITH ri = sj cosecOji = sk cosec Oki. (12) ?Ij = eji+ejk. (13) 1 cos 4d+ = -Xiri(cos 4ji + cos 4ki). n; FIG. 3.-The geometry of the interaction region : 3 different particles.The 3-body collision rate, and its estimate ki3), are expected to be only an upper bound for the reaction rate. Like a 2-body collision rate, kc," is at least a useful norm for comparison with measured reaction rates. In making this comparison for the reaction A+ A+ B, kf3) as computed by eqn. (8) and (1 1) counts each collision twice, but it is still the appropriate coefficient if the rate measured is the loss of A: - d[A]/dt = 2k'[AI2[B] = k'3'[A]2[B]. (15)188 3-BODY COLLISION RATES In table 1, this comparison is made for the reaction I+I+A+Iz+A, where A is a rare gas atom. The data are taken from Christie, Harrison, Norrish and Porter.10 TABLE 1.-3-BODY COLLISION RATE AND THE REACTION RATE FOR I+I+A+I2+A I H e Ne A Kr Xe PA = PAA (A) 5-2 2-18 2.59 3-64 4.1 6 485 ki3) x 1032 (cm6 sec-1) 484 128 126 121 132 kexp x 1032 (cm6 sec-1) 0-67 0.92 1.89 2-25 2.99 (A) 10.0 8.29 8-52 8-70 9.00 kr3 )/I&, 720 140 68 59 44 The temperature used is 293°K.The recombination reaction occurs with a 3-body collision efficiency between 1/44 and 1/720. The collisions are more efficient when the mass of the third body is close to that of the recombining iodine atoms. I am indebted to Dr. C. R. Gatz for computing table 1. This work has been supported by the National Aeronautics Space Administration and by the National Science Foundation. 1 Keck, J. Chem. Physics, 1958,29,410 and 1960,32, 1035. 2 Pritchard, J. Physic. Chem., 1961, 65, 504. 3 Bunker and Davidson, J. Amer. Chem. SOC., 1958,80, 5090. 4 Oldenberg, Amer. J. Physics, 1957, 25, 94. 5 von Smoluchowski, Ann. Physik (4), 1908, 25, 205. Bodenstein, Z. physik. Chem., 1922, 100, 118. Fowler, Statistical Mechanics (Cambridge University Press, 1935), 2nd ed., p. 691. Rice, 9th Int. Astronautical Congv. Proc. (Springer Verlag, Vienna, 1959), p. 9. Rice, Monatsh., 1959, 90, 330. Bunker, J. Chem. Physics, 1960, 32, 1001. Syrkin, Physik. Z., 1923, 24, 236. Steiner, 2. physik. Chem. B, 1932, 15, 249. 6 Tolman, Statistical Mechanics (Chemical Catalog Co., New York, 1921), p. 245. 7 Moelwyn-Hughes, Physical Chemistry (Pergamon Press, London, 1957), p. 1124. SSmith, Physic. Rev., 1960, 120, 1058. 9 Smith, J. Chem. Physics, 1962, 36, 248.. 10 Christie, Harrison, Norrish and Porter, Pvoc. Roy. SOC. A, 1955, 236, 446.

ISSN:0366-9033    

DOI:10.1039/DF9623300183

出版商:RSC    

年代:1962

数据来源: RSC