J. Phys. Chem. 1982, 86,903-908
L.I 3000
3000
1
I
303C
300C
CW-'
i
Figure 4. C-H stretching absorptlons of non-hydrcgen-bonded (A = SnBr:-), weakly hydrogen-bonded (B = Br-, C = HF,-), and very strongly hydrogen-bonded (D = F-) tetramethylarnmonlum ion salts (Fluorolube mulls on NaCl (A, B, D) and AgCl (C) plates).
0bse~ed.8The cation in tetramethylammonium hydrogen ditluoride, however, is much more weakly hydrogen bonded to anion than in the fluoride (Figure 4); the cation-to-anion hydrogen bonding in the hydrogen difluoride is about the
903
same as that in the bromide or perchlorate salts. The large loss of cation-to-anion hydrogen bonding will make m o H . b o n d positive for the formation of tetramethylammonium hydrogen difluoride. Since, in eq 2, both AUo and A H o H . b n d are positive, mol,the actual hydrogen-bond energy, must be negative and larger than -155 kJ mol-l, the experimentally determined value of Mod. It is not possible to quantify the exact value of AHolfor tetramethylammonium hydrogen difluoride at this time. Nevertheless, our observation of a very strong hydrogen bond in tetramethylammonium hydrogen difluoride is not obviated by the measurements of Harrell and McDaniel. Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this work, and to the Oakland University Research Committee, for additional support.
Comparison of Semlempirical Formulas for the Electric Field Dependence of Geminate Recombination Fluorescencet J. K. Balrd,t Health and Safety Research Dlvlsbn, Oak Rldge Natbnal Laboratory, Oak Ridge, Tennessee 37830
J. Bullot, P. Cordler,. Laboratolre de Chlmie physique des Mat6rkux Amptms, Unlverslt6 de Paris Sud, Centre d'Orsay, 91405 Orsay, France
and M. Gauthier ERA 718, Unlverslt6 de Pads-Sud, Centre d'Orsay, 91405 Crsay, France (Received: July 31, 1981)
The probability of recombination of geminate ions produced in photochemistry or radiation chemistry follows the predictions of the Onsager theory. According to the theory, an isolated pair starts from an initial separation r and subsequently executes a Brownian motion which leads either to recombination or to escape. To evaluate the recombination probability for an ensemble of pairs, as occurs in experiment, the Onsager recombination probability is averaged over a distribution function u(r). As the form of this function is not known a priori, various representations for it have been assumed in order to calculate the average. In this paper, we show that a more direct method is to assume an a priori functional dependence of the recombination probability Q(0,E) on the magnitude E of an externally applied electric field. Forms for Q(0,E)are more easily surmised from experimental data than are forms for u(r). Given a representation for Q(O,E), we work backward to obtain expressions for the first k-momenta of the function 477?u(r) exp(-rc/r). Here r, = e2/tkBTis the Onsager length, e is the electron charge, kB is Boltzmann's constant, and t and Tare, respectively, the dielectric constant and absolute temperature of the fluid. As an example of our procedure, we analyze recent experimental data on geminate ion recombination fluorescence using two semiempirically derived representations for Q(0,E). We determine the primary process quantum yield, the dissociation probability of the pair, and the first nine moments of the function written above. We compare our results with those obtained from two popular representations for u(r).
Introduction The fate of electron-ion pairs produced by photolysis or radiolysis of solutions is determined by two effects: (i) diffusion and (ii) drift of the species under their mutual
interaction and/or interaction with externally applied fields. Recent experiments on the electric field quenching of recombination fluorescence in photoionized doped nonpolar solutions have been explained within this
'Research sponsored by the office of Health and Environment Research, U.S.Department of Energy, under contract W-7405-eng-26 with Union Carbide Corporation. General Electric Company, Knolls Atomic Power Laboratory, Schenectady, NY 12301.
(1) J. Bullot, P. Cordier, and M. Gauthier, Chern. Phys. Lett., 64,77 (1978). (2) J. Bullot, P. Cordier, and M. Gauthier, J. Chern. Phys., 69,1374 (1978).
*
0022-3654/82/2086-0903~01.25/0 0 1982 Amerlcan Chemical Society
904
The Journal of phvsical Chemistry, Vol. 86, No. 6, 1982
Given an isolated electron separated from a positive ion by a distance r, the probability of dissociation of the pair can be calculated from the Smoluchowski equation.68 In actual experiments, however, there is an ensemble of electron-ion pairs with an isotropic distribution u(r) of separations r. The dissociation probability in the ensemble is given by the Onsager result6 averaged over a(r). Little a priori information on the form of u(r) exists, however. In practice, a physically reasonable closed form a(r,X) is choseng and the theory is fitted to photocurrent data by adjusting the parameter X.lo This suffices to determine the ensemble averaged dissociation probability P(E) as a function of the externally applied electric field E. Next, if photocurrent measurements are combined with measurements of the recombination fluorescence, the free electron quantum yield @,(E)is obtained. The quantum yield @ip for formation of the electron-ion pair in the absence of the external field is determined from the ratio @&O)/P(O).A more detailed description of this method is given in ref 3-5. Recently, a different approach has been applied.'l A physically reasonable function with one free parameter was chosen to represent P(E). The value of the parameter w&s adjusted to obtain the best fit to the recombination fluorescence data. From this, momenta of the distribution a(r) were calculated. This technique was numerically simpler than the earlier method. Moreover, by comparison with theory, the technique permitted ready assessment of the differences between chemical scavenging and electric field scavenging of electron-ion pairs. In this paper, we generalize this approach to arbitrary P(E). As an illustration, we compare results obtained with hyperbolic and exponential representations of P(E). Theory In solution at room temperat~rel-~ a molecule M such as N,N,N',"-tetramethyl-p-phenylenediamine (TMPD) can be raised to a highly excited state M** by absorption of a photon whose energy is larger than the ionization threshold. This excited state relaxes to generate either an electron cation pair [M+,e-] or a singlet state M* with respective yields @ip and (1 - @ip). The pair [M+,e-] can either dissociate into free charges M+ and e- or recombine to give the singlet state M*. The singlet state can emit fluorescence or return to the ground state M by a radiationless transition. The probabilities for [M+,e-] dissociation or recombination are, respectively, P and (1- P). The effect of an external electric field of strength E is to impede the recombination of [M+,e-]and quench the ensuing neutralization fluorescence. The decrease in fluorescence intensity F appears as an increase in the collected current i. According to this mechanism it has been shown that the relative current ratio2t3can be written as i P(O,E) - =(1) io m , O ) (3)J. Bullot, P.Cordier, and M. Gauthier, J. Chem. Phys., 69,4908 (1978). (4)J. Bullot, P.Cordier, and M. Gauthier, J.Phys. Chem., 84, 1253 (1980). (5) J. Bullot, P. Cordier, and M. Gauthier, J.Phys. Chem., 84, 3516 (1980). (6) L.Onsager, Phys. Reu., 54, 554 (1938). (7)M.Tachiya, J. Chem. Phys., 69,2375 (1978);70, 238 (1979). (8)Yu. A. Berlin, P. Cordier, and J. A. Delaire, J. Chem. Phys., 73, 4619 (1980),and references therein. (9)A. Mozumder, J. Chem. Phys., 60,4300,4305 (1974). (IO) J. Casanovas, Thesis, UniversiG de Toulouse, 1975. (11) J. K.Baird, J. Bullot, P. Cordier, and M. Gauthier, J. Chem. Phys., 74, 1692 (1981).
Baird et al.
and the relative decrease of fluorescence as @ i D [ P ( O , E ) - P(O,O)] FO - F where P(0,E) is the dissociation probability at zero scavenger concentration and at field E while P(0,O) is this probability at zero concentration and at zero field. The fluorescence intensity in the presence of the applied field is F and in the absence Fo. The difference (Po- F) will be written hereafter as AF. The main problem is now to find a closed expression for P(0,E). In the absence of field but in the presence of a scavenger at low concentration cat the solution12of the steady-state Smoluchowski equation leads to an expression for the dissociation probability which can be written in terms of an infinite series depending upon a single dimensionless variable V related to c,. Now in the presence of both scavenger and external electric field, the solution' shows that the expression for the dissociation probability is formally identical with that found in the zero field case except that the variable V is replaced by the combination (VZ W)1/2where W is a dimensionless variable related to E. Such an expression, however, is only valid for small values of the V and W.'J1J3 In terms of physical and chemical parameters, the dimensionless variables can be written
+
V = (k,c,r,2/D)1/2
(3)
W = yrJ3
(4)
r, = e 2 / t k E T
(5)
y = e/2kET
(6)
with
In these relations k, is the rate constant for the electron capture by the scavenger at the concentration cg, D is the mutual diffusion coefficient of the electron and of the cation moving in a liquid of static dielectric constant E at the temperature T, rc is the Onsager distance, kB is Boltzmann's constant, and e is the magnitude of the electron charge. For large V in the absence of field, the dissociation probability has generally been approximated by a semiempirical function P(c,,O).'~J~ This and the arguments in the preceding paragraph suggest that for finite V and W, P(c,,E) can be represented at least approximately by a function of the form P ( c , 3 ) = 1 - [1- P(O,O)lcp[P(Vz + W)1'21 (7) where
cp
is a function such that $40) = 1
and cp(m)
=0
and where /3 is an adjustable parameter. The associated electron cation recombination probability therefore can be written Q(c,,E) = 1 - P(c,,E) (10) Applied to a scavenger free solution experiencing an electric field strength E eq 7 and 10 reduce to P(O,E) = 1 - Q(o,o)cp(PyrJ3) (11) Q(0,E) = Q ( O , O ) c p ( W J 3 ) (12) (12)J. L. Magee and A. B. Tayler, J. Chem. Phys., 56,3061 (1972). (13)J. K.Baird, J. Chem. Phys., 72, 5289 (1980).
Geminate Recombination Fluorescence
The Journal of Physicai Chemlstry, Vol. 86, No. 6, 1982 905
Assuming that p(PrrJ3) can be determined, eq 11 expreset3 P(0,E) in closed form. Then substituting eq 11 into eq 2, the relative decrease of fluorescence intensity can be written as
On the other hand, according to the Onsager theorye and its subsequent de~elopment,'~ the dissociation probability averaged over a normalized distribution function u(r) can be expressed by a convergent series in powers of E, i.e.
+
P(0J) = 4 r S - d r r2u(r) exp(-r,/r) 0
4*
P=l
(-1)~"
P
OD
n-1
+
(n - j ) -rd+l x
(p - n)!(n l)! j=o (l
(2rE)p:l
+ l)!
dr ?u(r)rPj-l exp(-r/r,)
J m
k
apk
= C (-I)'+(j j=O
+ I)/[& - j ) ! ( p - k + j + I)!@ - k)!]
(22) where p runs from 1 to N and k from 0 to ( N - 1). Through eq 17 or 19 it can be seen that the matrix A is independent on the closed form of &W). Numerical values of the apk elements have been listed in Table I for future developments. We now apply eq 20 and 21 to specific forms for P(0J). We consider in the next two paragraphs a hyperbolic form and an exponential form, respectively. For the case of zero applied electric field, the hyperbolic form has been used extensively experimental1y"j and compared'' with the results of the Smoluchowski theory.12 It can be written simply as
(14)
where all2 = B(k,r,2/D)1/2. Using eq 11 and 21 and applying the transformation suggested in eq 7, we find P ( 0 J ) = 1 - Q(O,O)/(1 + B W ) (24)
The first term of the right-hand side of eq 14 is obviously equal to the zero-field dissociation probability P(0,O)and also represents the norm of the function 4rr2u(r) exp(-r,/r). Let (rk) be the k moment of the function 4rr2u(r) exp(-rJr), that is 4* (rk) = dr r2a(r) I.k exp(-r,/r) (15) P(0,O) 0 Then introducing eq 15 into eq 14 the ensemble averaged dissociation probability is P(0J) = P(0,O) P(0,O) P (-1)p" n-1 (n - j ) . C(2YE)P5p- n)!(n l)!/-O(l -r:+l l)! (rPj-l) (16)
0, = (1/2)(-/3/2P-1 (25) Numerical values of the first few moments ( rh) obtained with this function have recently been published." The exponential function18can be written P(c,,O) = 1 - Q(0,O)exp(-a1/2c,1/2) (26)
This result suggests' that we expand also eq 11 in a Mac-Laurin series in powers of E and compare it term by term with eq 16. This leads to the basic relation of the moment procedure, i.e.
can be derived. In the next section, we compute the ( rk) by combining electron-ion recombination fluorescence data with eq 20,22, and 28. The results obtained will be compared with those published previously for the hyperbolic function."
-
-S +
OD
and in like fashion the results P ( 0 J ) = 1 - Q(0,O) exp(-PW)
+ C +
P-1
-
F P!
($.p
~(090)d P p ( b m ~ (17) P(0,O) d(Bu3P Bw-o
In particular, for p = 1, this equation yields
P(O,O)/Q(O,O) = -8P(O) (18) Substituting eq 18 into eq 17, commuting the summation signs, and changing indices,16we arrive at the final result P1 (rk) (-1)Wj + 1) k=o :r j=o (k - j)!(p - k + j + 1)!(p - k)!
-
c-c
The first ( N - 1) moments are obtained by solving the linear system AR = (20) where R is the vector of component (rk)/r,k, @ is the vector of component ap
= (1/2P!)(8/2)p-l(~l(0)/(P[11(0))
(21)
and A is the matrix of element apk (14) J. Terlecki and J. Fiutak, Radiat. Phys. Chem., 4, 469 (1972). (15) To obtain eq 19 from eq 17, put k = p - j - i, commute summation signs, and then put j = n - p + k.
ap= (1/2p!)(-P/2)Pl
(27) (28)
Numerical Results In order to facilitate computations for the exponential function, it is convenient to write the fluorescence-field relation (13) in the form AF/Fo = S [ 1 - exp(-PW)] (29) ;here S and 0are two adjustable parameters which can be determined by a best-fitting program. Then it is easy to obtain the P(0,O) value from eq 11 and 18, i.e. the
$ip
P(0,O) = P/(1 value from eq 13 and 30
+ P)
and the zero-field electron yield $eo from $eo = $i$(O,O) = PS/(l + PS)
(30)
(32)
For use in the next section we recall that for a hyperbolic function (24), the S and parameters can be obtained from the equation (33) (16) S. J. Rzad, P. P. Infelta, J. M. Warman, and R. H. Schuler, J. Chem. Phys., 52, 3971 (1970). (17) J. A.Crumb and J. K. Baird,J. Phys. Chem.,83,1130 (1979),and references therein. (18)A Hummel, J. Chem. Phys., 49,4840 (1968).
906
Balrd et al.
The Journal of phvscal ChetnlsW, Vol. 86, No. 6, 1982
0 rl
X
ooooooooom 0000000000 ooooooooom
i
0151
0 0 0 0 0 0 0 0 0 ~ I
c,
cI
OlOj-
00
I
A *
x x oooooooo(Dtoooooooomeu oooooooot-* ooooooooojr;
0
0
-
I
,
,
00 5
000 rl*rl
x x x
Flgurr 1. Relative decrease of fluorescence Intensity AFIF, as a function of (1 - exp(-BW)) for TMPD solutions In TMSi at dlfferent photon energies: (0)6.05 eV; (0) 5.90 eV; (0) 5.61 eV; (+) 5.39
eV. I
!
,
,
0000 rl*rlrl
x x x x
ooooooom(Dw oooooow*w(D oooooo*weutoooo0onidr;cd
ooooo*omoo
o o o o o w ~ ~ m m oooooa*'(D*(o ooooorit-'o;Gd I
I
I
I
I
Flgurr 2. Relative decrease of fluorescence Intensity AFIF, as a functlon of (1 exp(-j3W)) for TMPD solutions In DMB at different photon energies: (0)6.2 eV; (0) 6.05 eV; (0) 5.9 eV; (+) 5.77 eV.
-
O O , " c , e I
I
I
I
I
I
I
0000000 rlrl**rl*rl
x x x x x x x
by use of a linear regression. The quantities P(0,O) and 4eothen follow from eq 30 and 32, respectively. The notation in eq 33 is slightly different from that used in ref 11. In Figures 1and 2 we have plotted the relative decrease of fluorescence intensity AF/F,, as a linear function of (1 - exp(-DW)) for various experimental data6 obtained from 2 X 1od M TMPD solutions in tetramethyhilane ( M i ) and in 2,Zdimethylbutane (DMB). Solutions were irradiated at 295 K with photons ranging from 5.4. to 6.2. eV. There is excellent agreement between the experimental points and the computed straight lines. The correlation coefficients of the linear regression range from 0.9986 to N
0.9997.
In the last four columns of Table I1 we give the p, P(O,O), values obtained from the exponential dissociation function and report in columns 9 to 11 values previously obtained for these quantities from the hyperbolic function. For the sake of comparison, columns 4 to 7 give the P(0,O) and 4i values calculated from the distribution function metkod3 for the case of a gaussian distribution and an exponential one. In column 3 are also listed the zero-field electron yields as determined by the method given in ref 2. Knowing the @ value the first nine moments of the function 4x?u(r) exp(-r,/r) have been computed by solving the system (20) with the vector CP given by eq 28. In Figures 3 and 4 these moments have been plotted on a log scale as a function of their rank k and compared to those obtained from the hyperbolic dissociation function. In
4jP,and
The Journal of phvsical Chemistty, Vol. 86, No. 6, 1982 907
Geminate Recombination Fluorescence
TABLE I1 distribution functionb exponential solvent TMSi TMSi TMSi TMSi DMB DMB DMB DMB a
hvexcd
@eoa
6.05 5.91 5.61 5.39 6.20 6.05 5.91 5.77
0.077 0.076 0.081 0.055 0.039 0.026 0.022 0.030
From ref 2.
P(o,o) 0.155 0.141 0.128 0.137 0.049 0.057 0.043 0.087
From ref 3.
@ig
0.50 0.53 0.65 0.40 0.35 0.46 0.52 0.34
dissociation probability function
gaussian
P(O,O) 0.268 0.246 0.239 0.242 0.128 0.135 0.118 0.187
$ip
0.28 0.30 0.35 0.23 0.18 0.19 0.19 0.16
From ref 11.
hyperbolicC
P(o,o)
P 0.137 0.177 0.127 0.064 0.059 0.055 0.044 0.053
exponential
~ i p
0.121 0.150 0.113 0.060 0.055 0.052 0.042 0.050
0.46 0.41 0.57 0.59 0.53 0.43 0.49 0.47
@eo
0.055 0.062 0.065 0.036 0.029 0.022 0.021 0.024
P 0.258 0.288 0.242 0.116 0.076 0.114 0.091 0.059
P(0,O) 0.205 0.224 0.195 0.104 0.071 0.102 0.083 0.056
@ip
@eo
0.27 0.27 0.34 0.34 0.40 0.22 0.25 0.41
0.056 0.060 0.065 0.035 0.028 0.022 0.021 0.026
Photon energy. TABLE I11
P 0.127 0.044
1
I
I
I
I
2
4
6
8
k
I
Figwe 3. Moment evolution versus rank k computed from escape p-r funcbkn [(X) exponentiel; (0)hypwbok] and from distance dlstributkm function [(0)exponential; (0) gaussian] for a T M W solution In TMSi lrradlated by 5.81-eV photons (r, = 295 A).
function hyperbolic exponential hyperbolic exponential
@*
0.1151 0.11 51 0.0943 0.0943
@ 3
@ 4
-0.0049 - 0.0056 -0.0067 -0.0068
should not depend on the form of the dissociation probability. However, the yields obtained from the fluorescence quenching results alone are somewhat smaller than those obtained from previous method based upon simultaneous determination of fluorescence quenching and phot~current.~ Now it is interesting to note that the values obtained from the exponential function are roughly twice those obtained from the hyperbolic function. This fact, at first sight surprising, can be explained as follows. For small field strength E and therefore for small values of the variable W, eq 29 and 33 can be expanded to order W as
AF/FO = S(pW - f/zp2W)
(34)
AF/FO = S(@W- p2W)
(35)
Log(cr,)/r:)
J
respectively. In our experiments2typical values of W range from 0.27 to 2.7 so that j3 W ranges from 0.05 to 0.5. A best fitting procedure will give respectively two pairs of parameters (S’, 8’) and (Srr,p”) such that eq 34 equals eq 35 for any given W. This condition requires that
spy1 - f/zp’w-)= Sttp”(1-
- 2 -
2
L
6
8
k
Flgure 4. Moment evolution versus rank k computed from escape probebwty functkn [(X) exponentiel; (0)hvperbdic] and from distance distribution function [(0)exponential; (0) gaussian] for a TMW solutlon In DMB Irradiated by 5.9-eV photons ( r , = 287 A).
Figure 3, the momenta have been calculated from data on a TMPD solution in TMSi irradiated by 5.91 eV photons. In Figure 4 the data refer to a TMPD solution in DMB. It should be noted that in both solvents all the k moments coincide or are very close each other whatever the dissociation probability function.
Discussion Whatever the dissociation probability function, Table 11shows that the zero-field electron yields +eo are identical. This result is in conformity with the fact that, unlike +ip and P(O,O),the experimentally observable quantity +eo
-0.00047 - 0.00039 -0.00035 -0.00035
p”w)
(36)
As the value does not depend on the dissociation probability function, a second requirement is obtained from eq 32 as B’sr= p”S’I (37) Thus eq 36 will be satisfied whatever W only if 8’ = 2p” (38) As far as the moment evolution is concerned we pointed out that the different k moments do not really differ when using either an exponential or a hyperbolic dissociation function. This result can also be explained by a careful comparison of eq 25 and 28. If we assume eq 38 to be more or less generally obeyed by terms in W of order higher than 2, then the components apare numerically nearly equal for both dissociation probability functions. The solution of eq 20 then will yield similar values of (r k )f r,“ whatever the dissociation functions. In Table I11 we give a typical comparison of the apvalues from data used in Figures 1 and 2. The distribution function method, previously used,3 consists of choosing an arbitrary distribution function a(r,X) depending on one adjustable parameter X and then
J. Phys. Chem. 1982,86,908-913
908
of fitting experimental data with eq 1, 2, and 14. This procedure leads to a determination of the P(0,O)and 4ip values which depends drastically on the arbitraryness of a(r,A). In the dissociation probability method described herein, a mathematical form is assumed for P(O,E), and moments of the function 47r?a(r) exp(-r,/r) are obtained from fitting experimental data. The resulting values of P(0,O) and $ip, nonetheless, depend upon the choice of P(0,E). It should be noted, however, that plausible forms for P(0,E)are more easily guessed than forms for &,A). This is because P(0,E) is directly related to the data through eq 1 or 2 whereas by contrast the complex relation eq 14 intervenes when choosing forms for &,A). This observation makes the dissociation probability method easier to use than the distribution function method. As both methods are subject to a certain arbitrariness, however, it appears that the best way of knowing the real distance distribution would be to solve eq 14 despite its peculiar mathematical nature.
Figures 3 and 4 also show that the moment evolutions obtained from the dissociation probability method always differ from those calculated from the exponential and gaussian initial distribution functions. This behavior would suggest that the initial distance distribution might be described by a hybrid function built from a linear combination of both exponential and gaussian distribution. Two main results emerge from this work. First of all, the exponential dissociation function satisfactorily fits the experimental fluorescence data over the same field range as the hyperbolic function does.'l Secondly, with respect to the initial distribution function a(r), the first nine computed k moments are identical for both exponential and hyperbolic functions. A cursory inspection of eq 34 and 35 shows that the relatively low experimental field range makes it difficult to distinguish one function from the other one by a best-fitting procedure. A similar observation has been noted in studiesg of free ion yield data obtained from the @Co radiolysis of liquids.
Vibrational Relaxation of Carbon Monoxide in Collisions with Atomic Hydrogen G. P. Glass" and S. Klronde &mmnt of Chmlsiv, Rlce Unkersity, Houston, Texas 7700 1 (Received: August 4, 198 1)
The rate of vibrational relaxation of carbon monoxide has been measured in the presence of a large concentration of atomic hydrogen by using a discharge-flow shock tube. Upper vibrational levels of carbon monoxide were monitored by infrared emission spectroscopy. The concentration of hydrogen atoms prior to shock heating was determined by using a chemiluminescent titration reaction. Napier times for the relaxation of CO dilute in atomic hydrogen were measured, at temperatures between 840 and 2680 K, as In (P7atm s) = (3 f Z ) W 3 - (18.1 f 0.2). The probability of energy transfer per collision, Plo (CO-H), was found to increase from 7.8 X at 1000 K to 1.7 X at 2600 K. The results were interpreted in terms of an intermediate complex mechanism, with energy transfer occurring during the lifetime of a weakly bound HCO complex. The rate of the energy flow within HCO was discussed in terms of this mechanism.
Introduction Relaxation of vibrationally excited molecules in collisions with potentially reactive atoms is unusually efficient. Because of its high efficiency, this type of process plays an important role in chemical laser systems, which often contain high concentrations of atoms which can deactivate laser-active molecules, and in schemes designed to achieve isotope separation as a result of laser-induced chemistry.' As a consequence, interest in this type of process has been high, and many studies of the effects of reactive atoms on vibrational relaxation of diatomic molecules have been undertaken using shock tube,2flash photolysis,3 and laser techniques! Excellent reviews of much of this work have been published."' In spite of the large volume of work devoted to them, relaxation processes involving potentially reactive atoms (1) J. T. Knudtson and E. M. Eying, Annu. Rev.Phys. Chem., 26,225 (1974). (2)K. G h z e r and J. Troe, J . Chem. Phys., 63,4352 (1975),and references therein. (3) H.Webster and E. J. Blair, J . Chem. Phys., 66, 6104 (1972). (4)See, for example: G.P. Quigley and G.J. Wolga, Chem. Phys. Lett., 27,276(1974);(b) D.Arnoldi and J. Wolfnun, ibid., 24,234(1974); ( c ) R. G. MacDonald and C. B. Moore, J. Chem. Phys., 68,513(1978). (5) E. Weitz and G.Flynn, Annu. Rev.Phys. Chem., 25,275 (1974). (6)I. W. M. Smith, Acc. Chem. Res., 9,161 (1976). (7)I. W.M. Smith, Gas Kinet. Energy Transfer, 2, 1 (1977). 0022-3654/82/2086-0908$01.25/0
are still poorly understood. A t least four different mechanisms have been proposed to explain their high efficiency. An early explanation assumed that the usual SSH mechanisma operated but that the short-range repulsive potential responsible for vibrational-translational transfer was steepened in collisions involving reactive atoms by the presence of the longer-range attractive component of the interaction. More recently, Nikitin and Umanskyg have discussed the contribution to the relaxation rate that occurs as a result of electronically nonadiabatic transitions that can take place when one of the colliding partners possesses nonzero electronic angular momentum. Calculations favoring this mechanism have been presented for the systems 02-0,Nz-O, and CO-Fea9 In addition, some experimental evidence supporting a nonadiabatic mechanism for the relaxation of hydrogen halide molecules by halogens and oxygen atomsl0 has been reported. A third mechanism that has been postulated involves the formation of bound intermediate collision complexes, with energy transfer occurring during the complex lifetime." Such (8)R. N. Schwartz, 2.I. Slawsky, and K. F. Herzfeld, J. Chem. Phys., 20, 1591 (1952). (9) E. E. Nikitin and S. Ya. Umanskv. - . Faraday Discuss. Chem. SOC.. 53,7 (1972). (10)R. D. H.Brown, G. P. Glass, and 1. W. M. Smith, Chem. Phys. Lett., 32,517 (1975).
@ 1982 American Chemlcal Society
