J. Phys. Chem. 1988, 92, 4191-4196
4191
Electronic Energy Partitioning in the Reactions of Mg" (3P) and Ca* (3P,'D) with SF,, TeF,, and WF, Andrzej Kowalskit and Michael Menzinger* Department of Chemistry, University of Toronto, Toronto, Ontario M5S 1A I , Canada (Received: September 4, 1987)
Absolute cross sections were measured for chemiluminescenceand chemiion production as well as metastable beam attenuation for the reactions of metastable Mg('P) and Ca(3P,'D) with group VI hexafluorides RF6, where R = S, Te, and W.
whenever CI is more exoergic than CL.
Introduction
Alkaline-earth atoms (M) are known to react with dihalogens and halogen-containing molecules through several electronic channels producing neutral products in a variety of electronic states as well as chemiions.' Although the yields of excited products were found insufficient for pumping a chemical laser, the electronic branching problem is interesting in its own right. For metastable metal atoms, an experimental method2s3exists that yields absolute channel cross sections and branching ratios with relative ease. Electronic branching in these systems was once thought to be governed by statistics, but the Mg(3P) and Ca(3P,'D) X2 reactions have shown4g5that the electronic energy partitioning is characterized by substantial deviations from prior expectation and nonlinear surprisal plots, indicating the dynamical individuality of the different reaction channels. In this paper we report the absolute cross sections for all electronic product channels in the reactions of metastable Mg*(3P) and Ca*(3P,1D) atoms with the hexafluorides sF6, TeF6 and WF6. The known reaction channels are M* RF6 MF(X) + RF,, ground state (1) MF*(A,B,C) + RF5, chemiluminescence (2)
+
+
--
-
+
MF+ RF5-, chemiionization (3) where R stands for S, Te, and W. Our work is intended to give a better insight into electronic energy partitioning in chemical reactions and it follows similar efforts for M* + X2 reaction^.^^^ All evidence points to the fact that the reactions (1-3) are initiated by an electron jump (harpooning). The RF6 series studied here offers an interesting possibility to examine how the reaction cross section depends on a crucial parameter in the harpooning mechanism, i.e., the electron affinity (EA) of the target molecule since it varies from 20 kcal/mol for s F 6 to more than 115 kcal/mol for WF6. The large number of degrees of freedom makes the dynamics of reactions involving RF6 more complex and statistically biased than in an atom-diatom case, and we shall try to find out whether the dynamics is governed by the total product phase space or only by a fraction thereof. Indeed, some features of the dynamics can be captured by a simple, two-dimensional (energy vs reaction coordinate) picture, where RF, is treated as a structureless particle. The information theoretical analysis indicates that many vibrational modes of RF, are inactive. The Ca SF6system has previously been studied elsewhere: chemiluminescence spectra from Ca* SF6 have been published:-* reactivity of selected fine structure states s t ~ d i e dand ,~ chemiluminescence (CL) photon yields measured.'O In this work we present electronic state-to-state cross sections as well as photon and ion yields (branching ratios) for the reactions M* + RF,. We find that the CL photon yields are generally low (less than a few percent), although they exceed prior expectations involving the full product phase space by as much as 3 orders of magnitude. Chemiionization (CI) cross sections, on the other hand, are generally higher, of the order of 10 A, and they exceed ucL
+
+
'Permanent address: Institute of Physics, University of Gdansk, Gdansk, Poland
0022-3654/88/2092-4191$01.50/0
Experimental Section
The experimental method is an extension of the original ~ o r k ~ , ~ which has been described in detail previ~usly.~ Briefly, an atomic beam is excited in a pure metal vapor discharge and only ground-state and metastable atoms arrive in the scattering chamber located 8 cm above the beam source. The fraction of metastables in the beam was not measured, but comparison with other metastable sources4 suggests a yield of about 20%. This estimate and the absolute C I yields derived from it are believed to be reliable within a factor of 2 while the relative yields are accurate within a few percent. The transition probabilities of the spectral lines used for monitoring the number density of the metastables are, for Mg, A(3P,-'S) = 455 s-' (average of several literature value^'^-'^) and, for Ca, A(3Pl-'S) = 2270 s-l (average ~ the last two values fromI3-l5) and A('D-IS) = 40 s - ' . ' ~ ' From and the measured line intensities, we obtain the ratio of Ca metastables: n('D)/n(3P) = 0.08. Reactions of magnesium involve only one metastable state, and the analysis is therefore relatively ~ i m p l e .In ~ the case of Ca* reactions, however, two metastable states contribute and it is necessary to identify which one of the two is the dominant precursor of a given product., To this end one must compare the total cross sections uTCLobtained from A-X, B-X, or C-X chemiluminescence attenuation, with q ( 3 P ) and q ( ' D ) obtained from the attenuation of atomic fluorescence 3P,-'S0 and 'D2-'So by scattering gas. Chemiionization is always attributed to the Ca*(3P) as the dominant precursor, since no difference was found between CI, D(3P) and Ca('D) attenuation.
(1) Menzinger, M. In Gas Phase Chemiluminescence and Chemi-lonization; Fontijn, A,, Ed.; Elsevier: New York, 1985. (2) Dagdigian, P. J. Chem. Phys. Left. 1978, 55, 239. (3) Telle, H.; Brinkmann, U. Mol. Phys. 1980, 39, 361. (4) Kowalski, A.; Menzinger, M. J . Chem. Phys. 1983, 78, 5612. (5) Kowalski, A,; Menzinger, M., submitted for publication in J . Phys. Chem. (6) Kiang, T.; Estler, R.C.; Zare, R.N. J . Chem. Phys. 1979, 70, 5925. (7) Kiang, T.; Zare, R. N. J . A m . Chem. SOC.1980, 102, 4024. (8) Berneike, W.; Loffler, H. J.; Neuert, H. Z. Naturforsch., A : Phys., Phys. Chem., Kosmophys. 1980, 36A, 173. (9) Campbell, M. L.; Furio, N.; Dagdigian, P. J. Laser Chem. 1986,6, 391. (10) Verdasco, E.; Rabanos, V. S.;Aoiz, F. J.; Urena, A. G.,private communication. ( 1 1 ) Ross, U.; Meyer, H.-J.; Schulze, Th. Chem. Phys. 1984, 84, 359. (12) Boldt, G. Z. Phys. 1958, 150, 205. (13) Furcinetti, P. S.; Balling, L. C.; Wright, J. J. Phys. Lett. A 1975, 53A, 75. (14) Luc-Koening, E. J . Phys. B 1974, 7 , 1052. (1 5) Giusferdi, G.; Minguzzi, P.; Strumia, F.; Tonelli, M. Z. Phys. A 1975, 274, 279. (16) Pasternack, L.; Silver, D. M.; Yarkony, D. R.; Dagdigian, P. J. J. Phys. B 1980, 13, 2231. (17) Fukuda. K.: Ueda. K. J . Phvs. Chem. 1982. 86. 676. (18j Bauschlicher, C. W.; Langhbff, S. R.; Jaffe, R. L.; Partridge, H . J . Phys. B 1984, 17, L427.
0 1988 American Chemical Society
4192
The Journal of Physical Chemistry, Vol. 92, No. 14, 1988
Kowalski and Menzinger
r-----
-I
L-
CaFIXI t RFs
Figure 1. Energy diagram for the title reactions. Zero on the energy scale corresponds to M
+
+
+
RFS F fragments. Reactant states (with E,, Ein, included) are drawn to the left and possible products (even if not observed) to the right of the dotted line, respectively. Accessible product states lie below the relevant reactant state. Uncertainties from EA or Doare marked by the dashed lines.
Molecular Data Some molecular constants that govern the energetics of the title reactions are collected in Table I, and the energies Eiof all the reaction channels are summarized in Figure 1. For the SF5-F bond dissociation energy the value given in ref 6 is presently widely recommended (see e.g., ref 49),despite the fact that it was later
(19) Bott, J. F.; Jacobs, T. A. J . Chem. Phys. 1969, SO, 3850. (20) Modica, A. P. J . Chem. Phys. 1973, 77, 2713. (21) Kay, J.; Page, F. M. Trans. Faraday SOC.1964, 60, 1042. (22) Hildenbrand, D. L. J. Phys. Chem. 1973, 77, 897. (23) Lyman, J. L. J . Chem. Phys. 1977, 67, 1868. (24) Lifshitz, C.; Tiernan, T. 0.;Hughes, B. M. J . Chem. Phys. 1973, 59, 3182. (25) Compton, R. N.; Cooper, C. D. J . Chem. Phys. 1973, 59, 4140. (26) Hammond, P. R. J . Chem. Phys. 1971, 55, 3468. (27) Page, F. M.; Goode, G. C. Negative Ions and the Magnetron; Wiley: New York, 1969. (28) Chaney, E. L.; Christoforou, L.; Collins, E.; Carter, J. J. Chem. Phys. 1970, 52, 4413. (29) Chen, E.; George, R. D.; Wentworth, W. E. J . Chem. Phys. 1968,49, 1973. (30) Compton, R. N.; Christophorou, L. G.; Hurst, G. S.; Reinhardt, P. W. J . Chem. Phys. 1966, 45, 4634. (31) Harland, P. W. Ph.D. Thesis, Edinburgh University, 1971. (32) Leffert, C. B.; Tang, S. Y . ;Rothe, E. W.; Cheny, T. C. J . Chem. Phys. 1974, 61, 4929. (33) Hubers, M. M.; Los, J. Chem. Phys. 1975, IO, 235. (34) Compton, R. N.; Reinhardt, P. W.; Cooper, C. D. J . Chem. Phys. 1978, 68, 2023. (35) Hildenbrand, D. L. Int. J . Mass Spectrom. Ion Phys. 1977, 25, 121. (36) Griffing, K. M.; Kenney, J.; Simmons, J.; Jordan, K. D. J . Chem. Phys. 1975, 63, 4073. (37) Curran, R. K. J . Chem. Phys. 1961, 34, 1069. (38) Cottrell, T. L. The Strengths of Chemical Bonds; Butterworth: London, 1958. (39) Harland, P. W.; Thyme, J. C. J. Inorg. Nucl. Chem. Lett. 1973, 9, 265. (40) Compton, R. N.; Reinhardt, P. W.; Cooper, C. D. J . Chem. Phys. 1974, 60, 2330. (41) Lacmann, K.; Dispert, H., private communication, 1975.
TABLE I: RF, Molecule Constants Available in the Literature (in kcalhol) molecule
SF6
Do(RFs-F)
ref
EA(RF6)
ref
EV(RF5)
ref
75.9 f 4.0 65.2 85.8 f 3.0 78.0 93 f 3 89.9 f 3.4 91.1 f 3.2
19 20 21 22 23 6 7
>13.8 f 2.3 12.4 f 2.3 13.8 32.9 >29.7 34.3 f 4.6 216.1 225.4 232.3 17.3 f 2.3 11.3 f 2.3 7.4 3.5 10.6 f 4.6 19.8 f 16.0b 77.0 f 3.9 76.1 f 4.6 74.7 f 4.6 79.5 f 6.0‘ 63.0 80.5 f 2.3 85.1 f 4.6 76.0 116.8 >112.9 f 9.2 117.3 - 11.5 4.6 119.9 f 5.0 118.0 f 1.9’
24 25 26 27 28 21 29 30 31 32 33 33 34
264.5 f 4.6 75.9 78.0 84.2
25 35 36 37
62.5 f 4.6 266.8 f 2.3
34 33
TeF,
84.8 f 8.0b 80.6 f 2.3 38 96.8 39
WF6
88.7 f 8.0* 121.0 42 117.6 43
+
119.3 f 2.0’
25 40 41 27 44 43 54 45 46 40
75.2 f 12.0b 100.3 f 11.6 100.3 f 11.6’ 32.2 28.8 f 6.9 581.2 59.2
a
48 43 44 35
47 30.5 f 7.0’
“ T h e value is taken from ref 25 but slightly adjusted to fit a different value of TeFs-F bond strength. ’Values used in this work.
corrected slightly.’ Since a lower bound of the value is based on not observing chemiluminescence from the CaF(C) state (which (42) Hildenbrand, D. L. J . Chem. Phys. 1975, 62, 3074.
Reactions of Mg*(3P) and Ca*(3P,1D) with RF6
The Journal of Physical Chemistry, Vol. 92, No. 14, 1988 4193
TABLE II: Exoergicity -a, (kcalhnol), Total Attenuation Cross Sections UT (A'), Electronic Channel Cross Sections ui, and Quantum Yields ai UT
reactant/product
-AEi
M* attenuation
from MX*
Ul,
a,, ?&
A2
92 f 9
-
Mg*('P) 4- TeF6 MgF(X) + TeF, MgF' + TeF< MgF*(A) Mg' 4- TeF6Mg*('P) + WF6 MgF(X) + WF5 Mg+ + WFc MgF*(A) MgF' + WFC Ca*('P) + SF6 CaF(X) + SF, CaF*(A) CaF+ + SF5CaF*(B) CaF*(C) CaF*(D) CaF*(E) Cat + SF6Ca*('D) + SF6 CaF(X) + SF, CaF*(A) CaF+ + SF< CaF*(B) CaF*(C) CaF*(D) CaF*(E) CaF*(F) Cat + SF6Ca*('P) + TeF6 CaF(X) TeF5 CaF' + TeF5CaF*(A) CaF*(B) CaF*(C) CaF*(D) Cat TeF6Ca*('D) + TeF6 CaF(X) + TeF5 CaF*('P) + WF6 CaF(X) + WF, Ca+ + WFC CaF*(A) CaF*(B) CaF*(C) CaF+ + WFC Ca*('D) WF6 CaF(X) + WF5 Ca+ + WF6CaF*(A) CaF*(B) CaF*(C) Ca+ + WF,
92.8 13.3 6.2 -89.3
0.025 f 0.009 0.53
0.028 f 0.012 0.58
3.9 0.029
3.0 0.022
128 f 10 89.4 23.7 9.9 -32.7
CL too weak
* 0.010
* 0.010
194 f 18
+
60.5 11.1 -19.0 -75.0
10.1
5.0
CL not obsd 68 f 9e
A
-
CL too weak
90.2 43.0 38.8 36.3 3.7 2.3 -7.3 -72.6
0.2 f 0.1' 1.3b
0.30 f 0.15 1.9
not measd
91 f 7 109.2 62.0 57.8 55.3 22.7 21.3 11.7 1.9 -53.6
86 & 7
l l f 2
12
2
92 f 9 92 f 9
0.7 f 0.2 0.03 f 3.01
0.8 f 0.2 0.03 f 0.01
10.0 0.60 0.16 0.026 0.010
6.0 0.35 0.13 0.015 f 0.009
17.0d
8.6
168 f 16
+
87.0 60.7 39.8 33.1 0.5 -0.9 -1 5.8
150 170
*
* 30 * 20
*
*
CI not obsd 191 f 16
+
106.0 205
+
58.1 28.0 10.9 4.2 -28.4 -39.8
* 18
179 f 16
+
77.1 47.0 29.9 23.2 -9.4 -19.8
*
*
150 20 150 f 20
1.2 0.4 0.07 f 0.02
'Estimated by using the data of ref 9, that 80% of chemiluminescence comes from Ca*(lD). Ca*(3P) rather than Ca(lD). CReference10 gives 55 A*. dFor Ca('S) + WF6, ucI < 0.005 A2. we do observe in a similar experimental arrangement), and the previous work6,' did not account for Ca*('D), as pointed out in ref 9, we treat the result from ref 7 as all the rest and use average (43) Dispert, H.; Lacmann, K. Chem. Phys. Lett. 1977, 45, 311. (44) George, P. M.; Beauchamp, J. L. Chem. Phys. 1979, 36, 345. (45) Burgess, J.; Haigh, I.; Peacock, R. D.; Taylor, P. J . Chem. SOC., Dalton Trans. 1974, 1064. (46) Mathur, B. P.; Rothe, E. W.; Reck, G. P. J . Chem. Phys. 1977,67, 377. (47) Peacock, R. D.; Burgess, J.; Haigh, I. J . Chem. SOC.1971, 26, 977. (48) Cooper, C. D.; Compton, R. N. 22nd Annual Conference on Mass Specrrometry, Philadelphia, May 1974; paper V7. (49) CRC Handbook of Chemistry and Physics; Weast, R. C., Ed.; CRC Press: Boca Raton, FL, 1985.
0.8 f 0.2 0.05 f 0.02
was assumed that all chemiions derive from
value of Do(SF5-F) equal to (84.8 f 8.0) kcal/mol (the value of ref 20 was neglected in the averaging, since it lies too far from others). For Do(TeF5-F) and Do(WF5-F) the averages used are (88.7 8.0) kcal/mol and (1 19.3 2.0) kcal/mol, respectively (the errors cover the data taken into account). The values of electron affinities used are also averages of literature data, except that we neglect upper and lower bounds in the averaging (the EA value of SF6is therefore probably slightly underestimated). The electron affinities used for SF6 and TeF6 are (19.8 16.0) and (75.9 6.0) kcal/mol, respectively. The electron affinities of WF6 reported in the literature concentrate around two values (the result from ref 14 does not fit into any of them); the data of ref 25, 31, and 33 give the average of (1 18.0
*
*
*
*
4194
Kowalski and Menzinger
The Journal of Physical Chemistry, Vol. 92, No. 14, 1988
TABLE HI: Harpooning Cross Sections (in A*) covalent curve
ionic curve
Mg*(’P) + SF6 Mg+ + SF6Mg*(3P) + TeF, Mg+ + TeF6Mg*(’P) WF,5 Mg+ WF.5Mg+ + WF6-* Mg+*(’P) WF6Ca*(3P) + SF6 Ca+ + SF6Ca*(’D) 4- SF, Ca+ + SF6Ca*(’P) + TeF6 Ca+ + TeF6Ca+*(2D) + TeF; Ca*(’D) + TeF, Ca+ + TeF6Ca+*(*D) + TeF6Ca*(’P) + WF6 Caf WF6Ca+ + WF6-* Ca+’*(’D) + WF6Ca+*(’D) + WF6-* Ca+*(’P) + wF6Ca*(’D) + WF6 Ca’ + WF6Ca+ + WF6-* Ca+*(ZD)+ WF6Ca+*(2D) + WF6-* Ca+*(’P) + WF6Ca+*(*P) + WF6-*
a h (ohmin,ahmax)‘
UT
92 f 9 128 f 10 194 f 18
40 (30, 54) 253 (206, 316) m
(-,
m)
312 (240, 421) 36 (34, 38) 68 f 9 (55)b 60 (48, 86) 91 k 7 108 (79, 177) 168 f 16 817 (576, 1250) 97 (86, 111) 191 f 16 105 (104, m ) 211 (175, 259) 205 f 18 ( m , m) 1210 (750, 2300) 1010 (800, 1320) 110 (94, 131) 130 (119, 143) 179 f 16 ( m , a) (IOs, -) m (IO5,m ) 253 (200, 330) 325 (284, 377) 71 (62, 81)
--
ouhmlnand ahmax are harpooning sections calculated for the lowest and highest values of EA(RF6) given in the literature (see Table I). bFrom ref 10.
& 1.9) kcal/mol, while the data of ref 29, 32, and 54 give the average (80.5 f 4.5) kcal/mol. Following suggestions from ref 43 and 46, we associated the latter value with experiment yielding electronically excited WF6* molecules. For electron affinities of the SFS, TeF5, and WFS radicals we use (75.2 f 12.0), (100.3 f 11.6), and (30.5 & 7.0) kcal/mol, respectively. The exoergicity -AEi of all relevant reaction channels is summarized in Figure 1 and in the first column of Table 11. Dissociation energies of MgF and CaF are (1 10.4 f 1.2) 5o and (126.4 f 1.6) k c a l / m ~ l , respectively; ~’ ionization potentials of MgF and C a F are (166 & 5 ) 4 and (126.6 f 7.0) kcal/mol,52respectively. The sums of average translational and internal energies are 4.7, 5.2, and 6.9 kcal/mol for Mg + SF,, TeF6, and WF,, respectively, and 5.1, 5.8, and 7.5 kcal/mol for Ca SF6, TeF6, and WF6, respectively. Atomic energy levels and ionization potential data were taken from ref 53. The exoergicities -Mi have sometimes quite large error bars (especially chemiionization channels), which are not included in Table I1 for clarity, but they have been taken into account in the surprisal plots and in Figure 1.
+
Results and Discussion The primary results are summarized in Table 11, where the two types of attenuation cross section gTcLand uT(M*), the individual channel (CL or CI) cross sections gi, and the corresponding channel yields G j = l O o ( ( T j / ( T T ) are listed. From this compilation it can be seen that, for Mg* RF6 reactions, a very weak CL is observed for R = S and Te (and none for R = W, in agreement with the energetics). All three reactions produce ions with considerable yield, and while for Mg*(3P) + SF, and TeF6 chemiionization takes place, for Mg*(3P) + WF6 the only exothermic channel is collisional ionization. The Ca* reactions with RF6 follow a similar pattern: chemiluminescence photon yields are usually much lower than the corresponding ion yields. The latter increase in the order S < Te < W. Observation of ions in the Mg*(3P) WF, experiment allows one to set the lower limit for EA(WF6) I106.9 kcal/mol, in agreement with the l i t e r a t ~ r e . ~ ~ , ~ ~
+
+
(50) Hildenbrand, D. L. J . Chem. Phys. 1968, 48, 3657. (5 1 ) Rosen, B. Donnees Spectroscopiques relatives aux Molecules Diatomiques; Pergamon: Oxford, 1970. (52) Blue, G. D.; Green, J. W.; Bautista, R. G.; Margrave, J. L. J . Chem. Phys. 1963, 37, 877. (53) Moore, C. E. Atomic Energy Levels; NBSRDS, NBS 35; U S . Government Printing Office: Washington, DC, 1971. (54) Bartlett, N. Angew. Chem., Znr. Ed. Engl. 1968, 6 , 433.
Since the electron affinity of RF6 varies from 20 to 115 kcal/mol, the electron-transfer dynamics is expected to differ substantially between the different molecules and states, as the calculated harpooning cross sections in Table I11 indicate. The interaction Hii = (ilm)between the configurations li) and b) and their splitting at the avoided intersection depend exponentially on r , and the diabatic transition probability grows rapidly as rc increases, while the rise of the excitation function at low collision energies’,,’ due to the attraction caused by configuration interaction is enhanced for crossings with small r, relative to long-range crossings. For purposes of Table I11 reactants and ion pairs are characterized by covalent (first column) and ionic configurations (third column) to which the transition takes place. The second column lists the experimental values of the total M* attenuation cross section u T ( M * ) (Table IV), and in the fourth column are calculated values of the primitive harpooning cross section q,, including (in parentheses) upper and lower limit estimates derived from the extreme values of EA in Table I. The harpooning cross sections are calculated from q, = rr: where rc is the crossing radius:ss r, = e*/(IP(M*) - EA(RF,)), and e, IP(M*), and EA(RF6) have the usual meaning. The electron affinities used in this analysis are documented in Table I. They represent adiabatic rather than vertical or reactive values, although the authors are seldom explicit what type of EA they report. While the choice of the particular electron affinity (vertical or adiabatic) has been disputed for many years, adiabatic values give a better agreement with experiment. One notes that with a few exceptions the agreement between crh and the experimental cT is quite poor: Among the Mg(3P) RF, systems, harpooning underestimates the beam attenuation by a factor of 2 in the case of SF,, while for TeF6 it overestimates oT by the same factor, and none of the ground or excited states of the ion pair reconcile this simple theory with experiment. For the Ca(3P,1D) SF6 reactions, however, the agreement is much better, but for the remaining processes the model fails again. For WF,, Ca(’D) TeF6, and some systems, notably Mg* Ca(3P,1D) + WF6 where the simple model involving ground-state ions greatly overestimates the electron-transfer cross sections, consideration of “higher order harpooning”, in which the ion pair is formed in an excited state, leads to a great improvement of the calculation, suggesting that the intermediate ion pair and probably also the product ions are electronically excited. Clearly, the primitive harpooning model in its unmodified form is not suited for the present purposes since it does not consider (a) the degeneracy of the M(3P,1D)reactants and the PES structure arising from it,’q5 (b) the above-mentioned attraction due to configuration mixing which tends to enhance the capture cross section, and (c) the effect of diabatic transitions which tends to diminish the probability of an electron transfer.[ The reaction of Mg* and Ca* with WF, are the most interesting since the molecular electron affinity EA(RF,) exceeds the ionization potential IP(M*) of the excited atom. Consequently, the ground-state ion pair lies below that of the covalent reactants asymptotically as well as at closer range, and an electron transfer involving these configurations will not take place. Instead, excited states of the ion pair must be involved, with the possibility of forming electronically excited ions. Some harpooning cross sections (Table 111) for such “higher order” crossings compare nicely with the experimental results in those cases where they exceed the experimental values. The crossing radii are then so large that it can always be argued that the electron transfer does not occur in every collision due to the diminished overlap of the reactant wave functions. This effect is probably present in the case of Ca* WF6: the experimental gT for Ca*(3P) exceeds that for Ca*(’D), although the primitive harpooning model predicts a reverse ordering. The multitude of relevant crossings documented in Table I11 and the preceding arguments suggest, however, that a monotonic dependence of the observed cross section on the harpooning distance does not have to be the rule. A
+
+
+
+
+
(55) Levine, R. D.; Bernstein, R. B. Molecular Reaction Dynamics: Oxford University Press New York, 1974.
The Journal of Physical Chemistry, Vol. 92, No. 14, 1988 4195
Reactions of Mg*(3P) and Ca*(3P,'D) with RF6 TABLE I V Information Theoretical Analysis of Branching Ratios reaction channel Mg*('P) SF6 MgF(X) SFS MgF*(A) MgF* + SF, Mg*('P) TeF6 MgF(X) + TeF, MgF' + TeF, MgF*(A) Ca*('P) + SF6 CaF(X) + SF, CaF*(A) SF, CaF' SF, Ca*('D) f SF6 CaF(X) + SF, CaF*(A) CaF*(B) CaF*(-) Ca*(3P) 4- TeF6 CaF(X) TeF5 CaF+ TeF, CaF*(A) CaF*(B) Ca*(D) WF6 CaF(X) + WF5 CaF*(A) CaF*(B)
+
f;"
+
pioc
-Id
NI=O)
(&,"3
@max)c
0.85 0.93
1.o 0.00028 0.0058
1 .o 8.7 (-14) 2.6 (-20)
21.9 40.0
4.5 1
(3, 6 5) (0, 2.5)
0.0 0.73 0.9 1
0.97 0.030 0.00022
1.o 5.0 (-1 1) 1.0 (-15)
0.0 20.2 26.1
1 4
(0, 2.5) (2, 6)
0.0 0.52 0.57
0.98 0.003 0.019
1.o 1.4 (-5) 1.1 (-7)
0.0 5.4 12.0
9 1.5
(7, 12) (1.0, 2)
0.0 0.43 0.49 0.79
0.87 0.12 0.008 0.0003
1.o 2.2 (-4) 1.9 (-5) 2.4 (1 1)
-0.1 6.3 6.0 16.3
5 7 5.5
(4.5, 5.5) (6, 8) (5, 6)
0.0 0.30 0.54 0.62
0.94 0.060 0.0035 0.00015
1.o 2.6 (-4) 7.3 (-6) 2.0 (-7)
0.0 5.4 6.2 6.6
0.0 0.62 0.71
0.99 0.008 0.0005
1.o 3.1 (-7) 2.1 (-9)
0.0 10.2 12.4
0.0
-
+
-
+
Plb
+
+
0.0
+
+
+
+
-
2:;ri
1
(0.5, 12) (6, 10) (7, 11.5)
8 8.5
+
( 5 , 6) (5.5, 6.5)
5.5 6
"fi = 1 - ( E , / E x ) ,where E, is the total energy available to products in channel i (see ref 4) and E, is the total energy available to ground-state products. = u,/Cu,. = (E,')B, where p = 16 (see eq 4a). d - I = In (p,/p,"). e(&ln/&,,ax) are the minimal and maximal values of /3 that would still yield pto = pI,considering the error of p I o (arising from uncertainties of bond strengths, electron affinities, and ionization potentials) as well as the experimental error of p d . quantitative treatment of the attenuation cross section that includes the above-mentioned effects a-c is planned. The branching ratios for M* RF6 systems were subjected to an information theoretical a n a l y s i ~as~described ~ ~ ~ ~ el~ewhere.~ The only major difference between the M* RF6 systems and the atom-diatom case analyzed previously is the greatly enhanced number of vibrational degrees of freedom. For an RF, product it is equal to 3N - 6 = 12, compared with 0 for the departing atom in the M* X2 reactions. The product-state density p(E,') is proportional to the energy E l available to the products in channels li)
40 0 C o F i A l
40 AMgFiAi ~~~~~~
+
+
30 ACoF'
-1
30 0 CoFiAI 0 CoFiBI
20 IO
lo
+
0
0
10 0
05
05
FL
f,
p(Ei') = (E,')@
(4a)
raised to the power & where
p = u,
+ ub + l/,(ra+ rb + t ) - 1
(4b)
ua and ub stand for the numbers of vibrational degrees of freedom of the products a and b, ra and rb are the numbers of rotational degrees of freedom, and t is the number of translational degrees of freedom. The prior pio is approximately by the R R H O product-state density (4a). This is compared with experimental branching ratio p i in the (negative) surprisal function -I = In (pi/p?). The results of the surprisal analysis are collected in Table IV and plotted in Figure 2. The errors of surprisal and of.& arising from EA and Do (Table I), are explicitly given only in Figure 2. This analysis exposes the fact that although the channel cross sections (Table 11) are not excessive, they correspond generally to substantial negative surprisals, i.e., overpopulations relative to prior expectation. It is also worth noting that chemiionization is usually 1-2 orders of magnitude faster than the competing CL channels. This is in sharp contrast to the corresponding reaction of metastable M* with dihalogen molecules X2 (F2, Cl,, Br2).13435 Similar trends were observed by Mariella,60 who notes that (56) Levine, R. D.; Kinsey, J. L. In Atom-Molecule Collision Theory; Bernstein, R. B., Ed.; Plenum: New York, 1979. ( 5 7 ) Ben-Shaul, A.; Haas, Y.; Kompa, K. L.; Levine, R. D. Lasers and Chemical Change; Springer: Berlin, 1981. (58) Tully, J. C . In Dynamics of Molecular Collisions, Part B Miller, W. H., Ed.;Plenum: New York, 1976.
10
0
05 fi
10 0
05
10
fl.
Figure 2. Surprisal plots for M* + RF6. Chemiluminescence and chemiionization for Mg reactions are marked by full circles and triangles, respectively. Similarly, Ca reaction channels are marked by open symbols.
chemiionization cross sections of excited alkali metals and dihalogens (X,) increase rapidly with available energy. In the present reactions, C I is the dominant channel-apart from the ground-state channel, of course-regardless whether CI is more exoergic than CL (e.g., Mg* + TeF6, WF6; Ca(3P) + TeF6, WF6) or whether it is less exoergic (e.g., Mg* and Ca(3P) SF6),demonstrating that the reason must be dynamical rather than statistical. The transfer of two electrons is required to enter the doubly ionic M2+X- RF< configuration corresponding to chemiions, which obviously takes place quite readily, more readily than in the M* X2 systems where ucI rarely exceeds 1 The chemiluminescence cross sections ucL, on the other hand, are This generally less than those of the dihalogens (X,) reactions.'~~*~ may be due to internal quenching of the excited ion pair complex. The large phase space volume of the M*RF6 complex probably causes the lifetime of the collision complex to be significantly lengthened relative to MX2. Similar to what has been elaborated5* for the electronic quenching of O('D) by N2, a trajectory may pass during the lifetime of the complex many times through a region of weak diabatic coupling, causing the cumulative
+
+
+
A2.'s49,
(59) Pechukas, P. In Dynamics of Molecular Collisions, Part B; Miller, W. H., Ed.; Plenum: New York, 1976. (60) Mariella, R. P., Jr. J . Chem. Phys. 1982, 76, 2965. (61) Wren, D. J.; Menzinger, M. Chem. Phys. Lett. 1981, 81, 599.
J. Phys. Chem. 1988, 92, 4196-4200
4196
quenching probability to be appreciable. By the same token, formation of the doubly ionic ground state of the complex and that of chemiions are favored. That the whole of the product and consequently of complex phase space is not actives9 is suggested by the large negative surprisals and the values of @(I=O)in Table IV.
Acknowledgment. This work was performed under the aegis
of the NSERC of Canada. A.K. acknowledges support within the research project CPBP 01.06. Registry No. Mg, 7439-95-4;Ca, 7440-70-2;SF,, 2551-62-4; TeF,, 7783-80-4; WF,, 7783-82-6; MgF, 14953-28-7;CaF, 13827-26-4;MgF+, 21308-25-8;Mg+, 14581-92-1;CaF+,21308-26-9; Ca+, 14102-48-8;SF,, 10546-01-7; SFS-, 3 1140-82-6; SF;, 2503 1-39-4; TeFS, 40678-56-6; TeF5-,32369-53-2;TeF6-, 93081-58-4;WF,, 19357-83-6;WF,-. 6917556-0; WF,-, 41743-04-8.
Electron Hopping in One Dimension: Mixed Conductor Membranes Richard P. Buck Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27.514 (Received: November 19, 1987; In Final Form: March 28, 1988)
Electron transport in mixed conductor (anion and electron charge carriers) redox electrolyte membranes is analyzed by irreversible thermodynamic methods appropriate to electrolyte transport. But in addition, the method of generalized forces is extended to electron transport by using Fermi-Dirac statistics and the gradient of the Fermi level of electrons in electrolyte phases. Applicable systems are thought to be metal ion redox-site membranes, ordinary fixed-site ion exchangers, e.g. Nafion, with redox counterions and possibly organic fixed-site redox polymers containing nonredox counterions in those cases not requiring bipolaron band models. The equation of motion for second-order electron hopping shows diffusion and migration terms, but a different form from the Nernst-Planck equation. For uniform distributionof sites the equation turns out to be a combination of a numerically corrected Dahms-Ruff diffusion term and the Levich migration term. Explicit forms for diffusion and mobility coefficients, effects of activity coefficients on transport, coupling of electron and counterion motions, significance of jump distances, and boundary conditions at electron exchanging and ion exchanging interfaces are described.
Introduction Coupled electron exchange and ion transport in membranes containing both parts of a bound redox pair has attracted the The attention of experimental research groups in recent list of passive membranes that can be simultaneously ion and electron conductors is extensive, and the illustrative example for this paper is an O s ( I I ) ~ ( I I I ) / X -polymer membrane. It appears that the various kinds can be accommodated among the categories of pure ionic conductors already well established in the ion-exchange and ion-selective-electrode l i t e r a t ~ r e . ~ Conventional .~ ion-conducting membranes, bathed asymmetrically in sensor applications, develop useful membrane potentials, and a selection are listed in Table I. Corresponding mixed conductor types exist, or can be predicted by using the same categories, and are shown in Table 11. The two principal categories are fixed-site and mobile-site membranes. The first group contains those membranes with charged functional groups held in place by covalent bonds while the mobile counterions are present to satisfy bulk electroneutrality, and can pass into and out of the membranes. For high site concentrations relative to bathing solution concentration^,^ ions of one sign are mobile except at very high bathing activities when Donnan exclusion failure occurs and complete salts (counterions and coions) are extracted into membranes. In contrast, ideal mobile-site membranes, the second category, contain dissolved salt whose component ions have widely different hydrophobicities. One ion (the mobile site) is ideally trapped in the membrane because of its ideal hydrophobicity (a very negative ionic free energy of transfer into a membrane), while the more hydrophilic counterion can move through the membrane. Generally, mo(1) Buttry, D. A.; Anson, F. C . J . Am. Chem. SOC.1983, 105, 685-689.
(2) Reed, R.; Murray, R. W., unpublished results, 1987. (3) Buck, R. P.Sensors Actuators 1981, 1, 137-196. (4) Buck, R. P. In Chemically Sensitive Electronic Devices; Bergveld, P., Zemel, J., Middelhoek, S., Eds.; Elsevier: Amsterdam, Netherlands, 1981; p 137-196. (5) Lakshminarayanaiah, N. Transport Phenomena in Membranes; Academic: New York. 1969.
0022-3654/88/2092-4196$01.50/0
TABLE I: Ion Exchanger Categories I. fixed-site (covalently bonded, immobile charged groups) A. homogeneous: glass, ion-conducting crystals, sulfonated
polystyrene B. heterogeneous: pressed pellets, zeolites in binders, plasticized charged-site, poly(viny1 chloride) membranes with selective reagents 11. mobile-site (hydrophobic, trapped, organic ions) A. homogeneous: plasticized extractants in poly(viny1 chloride) B. heterogeneous: plasticized liquid extractants in pores of inert supports 111. hydrophobic ion pairs trapped in plasticized membranes TABLE II: Redox Polymer Categories I. fixed-site redox polymer electron/ion exchangers A. polymer radical ion sites: pyridinum-ba~ed,~~~ pyrrole-based1*l3 B. redox ion sites: ferrocene-based,14-16Fe(II/III)," Ru-ba~ed,'~~~" Os-based,21Co-based,22p r u s ~ i a n - b l u e - b a s e d ~ ~ - ~ ~ C . inert, nonredox site: conventional ion exchangers, e.g., Nafion26
redox counterions 11. mobile-site redox electron/ion exchangers A. trapped cation sites: Aliquat2'
bile-site membranes are plasticized to confer liquidlike mobilities to the species. The third, and least interesting category, contains passive membrane with dissolved salt with no special hydrophobic difference for the two ions. The membrane passes ions of both sign and is a form of constrained liquid junction6 In the foregoing categories redox properties of the component ionic species are not specifically considered, either as counterions or as sites in membranes. However, as modified electrode research proceeds, redox ion exchangers have an important place because redox site densities can be controlled electrochemically. At present ion exchangers with redox sites are generated from the polymer or produced by embedding redox ions in a p ~ l y m e r . ' ~ - ~ ~ (6) Buck, R. P. In Comprehensive Treatise of Electrochemistry; White, R. E., Bockris, J. O., Conway, B. E., Yeager, E., Eds.; Plenum: New York, 1984; Chapter 3, pp 137-248.
0 1988 American Chemical Society
