J. Phys. Chem. 1981, 85, 2292-2298
2292
Trapped-Electron Capture by Steroid Molecules with Two Distinct, Reactive Groups. A Test of the Long-Range Tunneling Mechanism R. Kurt Huddleston and John R. Mlller” Chemistry Division, Argonne National Laboratory. Argonne, Illinois 60439 (Received: February 19, 198 1; In Final Form: April 20, 1981)
A quantitative test of the tunneling mechanism for trapped-electron scavenging in low-temperature glasses is described. Kinetics of reactions of trapped electrons with steroid molecules having two electron accepting groups rigidly held -10 apart were studied in organic glasses at 77 K. A model for trapped-electron scavenging by such difunctional molecules, based on the long-range tunneling mechanism, is presented. The model predicts that a difunctional molecule can be a considerably less effective electron acceptor than two independent monofunctional molecules when the separation between the two reactive groups is a substantial fraction of the tunneling distances. The experimental results show that the tunneling model does, in fact, quantitatively predict the kinetics for the reaction of e< with difunctional steroids from two pieces of information: (1)the measured kinetics for reaction with monofunctional model compounds and (2) the known distance between the two reactive functional groups. An alternative hopping model might plausibly provide a parametric fit to the data but cannot make a definite prediction. The results provide strong evidence for the long-range tunneling mechanism.
a
I. Introduction nature of the reactants and solvent as reflected in the reaction exothermicity, rearrangement energies of the Several different mechanisms have been proposed to reactants and solvent,12 and the intervening electron explain the reaction of trapped electrons (eJ with scastates18J9 determine the tunneling rate constant. In advengers in low-temperature glasses. A commonly accepted dition, dielectric relaxation through solvent-molecule remechanism is that et- capture occurs by tunneling from orientation can alter the energetics and thus the kinetics a localized, stationary site (trap) to an acceptor in a single of the electron transfer process as time p r o ~ e e d s . ~ J ~ J ~ J ~ ~ t e p . l - ~Such a mechanism requires tunneling through Another category of mechanisms proposed for e; scatens of angstroms of inert solvent. A large mass of data venging in low-temperature glasses revolves around the consistent with this electron tunneling mechanism is now idea that the e; might reach an acceptor by moving avai1able2-l4 for intermolecular electron transfer reacstepwise through a series of intermediate trapping sites, tions7J3J4as well as electron scavenging. Experiments have thus generating a diffusive motion. Such mechanisms have verified predictions of the tunneling model such as the been put forth where individual steps are postulated to exponential dependence of scavenging efficiency on acoccur by hopping (Hamill and Funabashi20-22)or by trapceptor c o n ~ e n t r a t i o nthe , ~ ~log ~ (time) kinetics of both to-trap tunneling (Buxton and K e m ~ l e y ~ ~ -Similar ~~). scavenging and intermolecular charge transfer,&14and the physical concepts underlie these two models, and we will lack of dependence of the rate of the intermolecular refer of these models as hopping. The Hamillelectron transfer on neutral donor c ~ n c e n t r a t i o n . ~ ~ J ~ JFunabashi ~ to both model is an extension of the continuous time The results of experiments interpreted according to the random walk (CTRW) theory developed by Scher and tunneling model have been found to be consistent with Montrol126to explain room-temperature charge transport modern theories of electron t r a n ~ f e r . ~ , ~ J ~These - ’ ~ J ~results in polymer films and amorphous semiconductors. Such have also shown that the factors controlling rates of models apparently have the capability of reproducing the electron transfer in rigid media are more complex than form of the kinetics observed for e; scavenging in lowpredicted by a simple barrier penetration m ~ d e l . ~ -The I~ temperature, rigid media. However, the viability of the underlying physical process-migration of the trapped (1)A. I. Mikhailov, Dokl. Akad. Nauk SSSR, 197, 136 (1971). charge among similar trapping sites-has not been dem(2) K. I. Zamaraev, R. F. Khairutdinov, A. I. Mikhailov, and V. I. Gol’danskii, Dokl. Akad. Nauk SSSR, 199, 640 (1971). onstrated in low-temperature matrixes. (3) J. R. Miller, J . Chem. Phys., 56, 5173 (1972). The present study was undertaken as a unique, quan(4) J. Kroh and C. Stradowski, Int. J . Radiat. Phys. Chem., 5, 243 titative test of the long-range tunneling mechanism for e; (1973). scavenging in rigid media. Previously, the lack of depen(5) S. A. Rice and M. J. Pilling, Prog. React. Kinet., 9, 93 (1978). (6) J. R. Miller, Chem. Phys. Lett., 22, 180 (1973). dence of the rate of electron transfer on neutral donor (7) J. R. Miller, Science, 189, 221 (1975). (8) J. R. Miller, J . Phys. Chem., 79, 1070 (1975). (9) A. Barkatt, C. A. Angell, and J. R. Miller, J. Phys. Chem., 82,2143
(1978). ~~(10) K. I. Zamaraev, R. F. Khairutdinov, and J. R. Miller, Chem. Phys. 1;ptt.., 67. _ ,311 - - (1978). ~ - -, -. (11) J. R. Miller, J . Phys. Chem., 82, 767 (1978). (12) J. V. Beitz and J. R. Miller, J. Chem. Phys., 71, 4579 (1979). (13) J. V. Beitz and J. R. Miller, “Proceedings of the Sixth International Conference on Radiation Research”, 1979, p 301. (14) A. Kira, Y. Nosaka, and M. Imamura, J . Phys. Chem., 84, 1882 (1980). (15) R. K. Huddleston and J. R. Miller, Radiat. Phys. Chem., in press. (16) J. V. Beitz, R. K. Huddleston, and J. R. Miller, to be submitted -I
for publication. (17) See ref 12 for references to electron transfer theory.
(18) J. R. Miller and J. V. Beitz, J . Chem. Phys., 74, 6746 (1981). (19) R. K. Huddleston and J. R. Miller, to be submitted for publica-
tion. (20) K. Funabashi and W. H. Hamill, Chem. Phys. Lett., 56, 175 (1978). (21) W. H. Hamill and K. Funabashi, Phys. Reu. B, 16, 5523 (1977). (22) K. Funabashi and W. H. Hamill, Can. J. Chem., 57, 197 (1979). (23) G. V. Buxton and K. G. Kemsley, J. Chem. SOC., Faraday Trans. 1, 71, 568 (1975). (24) G. V. Buxton and K. G. Kemsley, J. Chem. Soc., Faraday Trans. 1, 72, 466 (1976). (25) G. V. Buxton and K. G. Kemsley, Radiat. Chem. Phys., 13, 151 (1979). (26) H. Scher and E. M. Montroll, Phys. Reu. B , 12, 2455 (1975).
0022-3654/81/2085-2292$01.25/00 1981 American Chemical Society
Trapped-Electron Capture by Steroid Molecules
concentration has verified the tunneling mechanism for intermolecular reactions.13J6J6 Similar demonstrations in the case of electron scavenging are impossible since the trap concentration is both unknown and uncontrollable. Thus a further test of the tunneling mechanism for scavenging of trapped electrons is desirable. We have experimentally observed the reactions of e c with difunctional molecules, which in the present context are molecules with two distinct functional groups each capable of binding an electron but separated by a rigid, inert molecular framework. Such molecules are equivalent to two reaction centers held a fixed distance apart. The electron-tunneling hypothesis can be used to make a definite prediction of the rate of reaction of e; with a difunctional molecule with three pieces of information as input: the rates of reaction of the two individual functional groups and the distance separating them. In the hopping model, on the other hand, the behavior of difunctional molecules toward electron scavenging would be expected to depend on the presently unknown and unspecified details of electron transport, i.e., step size and jump frequency. In the absence of these details, the hopping model might be capable of fitting the data but is not capable of making quantitative predictions. 11. Experimental Section
The Journal of Physical Chemistty, Vol. 85,No. 15, 1981 2293
CH3
‘c=o
OH
Figure 1. Structural formulas for ketone and enone steroids used as e,- scavengers: 5a-androstane-3,17dione (ADO); 5a-androstan-3-one (A30); 5a-androstan-17-0110 (A170); 4,16-pregnadien-3,20dlone (PDDO); 17~-hydroxy-androst-4-en-3-one (AEO, testosterone); 30hydroxy-5a-pregn-16-en-2O-one (PEO). Also used were the acetate derivatives, AEOA and PEOA, of the alcohols AEO and PEO.
Pulse radiolysis experiments were carried out by using 4-40-11s pulses of 15-MeV electrons from the Argonne linac. Transient absorbance measurements were made the estimated standard deviations were determined. The over the interval 10-7-102 s after the pulse. Analyzing light probability P(t)that trapped electrons survive capture by from a xenon lamp passed through a chopper (5% on) and the acceptor was taken as the ratio A / A o ,where A and A. a monochromator before reaching the sample to minimize are (time-dependent) absorbances in samples with and photobleaching effects. Tests in which the light intensity without the added electron acceptor. was reduced by using neutral density filters verified that the analyzing light had no measurable effect on the ob111. Model for Trapped-Electron Scavenging by a served kinetics for even the slowest reactions studied. The Difunctional Molecule samples were frozen by plunging into liquid nitrogen. They The probability of survival of trapped electrons reacting were then transferred to the sample chamber of the with randomly distributed scavenger molecules by a tuncryostat (Oxford CF204) which was regulated to within neling mechanism is given by3 *0.1 K of the set point on a variable temperature controller (Oxford DTC2). All experiments were carried out at 77.4 P ( t ) = exp[-cV(t)] (1) K with an estimated uncertainty of i0.2 K. Temperature calibrations were regularly made with liquid nitrogen in where c is the number concentration of scavenger. V ( t ) is a time-dependent capture volume centered on each the sample chamber a t 1-atm pressure. A more detailed description of the apparatus has been given e l ~ e w h e r e . l ~ t ~ ~scavenger such that only those electrons not initially trapped within the capture volume of any scanvenger will All of the steroids had been specified by the manufacsurvive at time t. Equation 1is valid for moderately low turer (Steraloids, Inc.) as showing one spot in thin-layer scavenger concentrations where the total physical space chromatography and were used as received. Structural occupied by the scavenger molecules can be neglected as formulas, names, and abbreviations for these steroids are being small in comparison with the system volume. For given in Figure 1. Refined grade 5a-androstane was also spherical capture volumes eq 1 may be written as used as received from the American Petroleum Institute Samples Office. 2-Methyltetrahydrofuran (MTHF) was P ( t ) = e~p(-4/~7rc[R(t)]~) (2) distilled from lithium aluminum hydride and stored under argon in the dark over alumina. Anhydrous ethanol where now R ( t ) is a time-dependent reaction radius. The (EtOH) was distilled from sodium borohydride. Samples existence of a definite reaction distance is the major aswere degassed and then sealed under vacuum in 1 x 1 cm sumption required in the derivation of eq 1 and 2. This Pyrex cells. All molar concentrations are given for the approximation is valid because of the steep falloff of the frozen samples at 77 K. electron tunneling rate constant with distance. Modern The experimental procedure was to record the absorquantum-mechanical theories of electron transfer formubance as a function of time at a convenient wavelength late the electron transfer process as a nonradiative trannear Am=. We used 1000 nm in MTHF and 650 nm in sition between electronic and vibrational states of the EtOH. The absorbance curves were normalized by direactants and products.l’ The expression from first-order viding by the dose as measured by the beam current perturbation theory for the electron transfer rate constant passing through the sample and collected on a Faraday at a given distance R is then cup. The results from several shots were averaged, and k ( r ) = (27r/h)lV(R)I2(FCWD) (3) where V(R) is the electron exchange matrix element be(27) J. R. Miller, B. E. Clifft, J. J. Hines, R. F. Runowski, and K. W. Johnson, J. Phys. Chem., 80, 457 (1976). tween the reactants (the donor and the acceptor) and the N
2294
Huddleston and Miller
The Journal of Physical Chemistry, Vol. 85, No. 15, 1981
products and FCWD is the thermally averaged FranckCondon weighted density of states.12 In general, V(R) depends exponentially on distance; it has been found that typically lV(R)I2and hence the rate will decrease by 1order of magnitude for each 1.5-2.0-A increase in the separation R.13 This fact justifies the assumption inherent in eq 1. For a rate constant of the form k(R) = v exp[-2y(R - R,)] (4)
&
R(t) will be given by eq 5.3,6 Thus the reaction radius increases linearly with log (time). 1 R(t) = Ro + - In ut (5)
0 0 P,
2Y
If two electron acceptors are placed at a fixed, relatively short distance apart, the capture volumes for the individual acceptors may now overlap (see Figure 2). In this case, the total capture efficiency is reduced from that expected for the two acceptors acting independently. Consider two electron scavengers Al and A,; these may have different scavenging efficiencies due to different Franck-Condon factors as shown by eq 3. The trapped-electron survival probability Pi(t) in the presence of either acceptor at a concentration ci is Pi@)= exp[-ciVi(t)] (6) where Vi(t) is the capture volume associated with acceptor A,. If both acceptors are dispersed in the same matrix, each at the concentration c, the survival probability will now be
P ( t ) = PlP2= exp(-c[Vl(t)
+ V2(t)]]
(7)
If, however, the two acceptor units are linked so that they are a t a fixed separation a, the probability of a trapped electron surviving at time t is
J',(t) = exp[-cV,(t)I
(8)
where now V,(t) is the net capture volume (excluding overlap) for the difunctional species. It is convenient to define a ratio $ ( t ) by
$(t) = Vn(t)/[Vl(t) = In P,(t)/[ln
+ Vz(t)l Pz(t)l
V,,t/IVl
=
t
VpI
exp(-c,Vii
i
~ 1 2= expi-c12vneti
0
=
1,
0
=
!VI
0
:
ViIVl
t
V2 - V l 2 i / ! V l t
Vpi, V
=
+
Vpl,
MAXIVI, Vpl,
=
(P1P2i0 R1
t
R1
+
IR1
R2< a
R p > a > i R 1 - R2I
-
R2i
R2 + a
4 = V,/(V, + V2)
Pn =
(14) Case 3 will apply only if one scavenger unit is considerably more effective than the other a t capturing trapped electrons and the separation is small. Case 2 is more typical and includes all of the experimental results reported here. It is apparent that if R,(t) and R,(t) are known, e.g., from measurements of scavenging kinetics for monofunctional model compounds, the scavenging efficiency of the difunctional molecule may be predicted at each point in time by using eq 10 and 13, with only the separation distance a required as additional input.
(9)
IV. Results
so that
This is expected to obtain at short times when the capture radii are small. As time proceeds, the capture spheres may begin to overlap and case 2 (that of partial overlap) applies. Then (12) 4(t) = ( V , + v2 - V12)/(Vl + V2)
Figure 3 gives decay curves for the surviving fraction of e; in MTHF in the presence of 0.05 M of steroids having either one or two saturated ketone groups. The dione ADO has ketone functional groups positioned at opposite ends of a rigid steroid hydrocarbon framework. The centerto-center distance between the two carbonyl bonds, as measured from molecular models, is 10.0 A. The two model compounds A30 and A170 were used to provide data on scavenging kinetics (reaction radii as a function of time) for the two ketone groups separately. The fact that the steroid framework is inert toward reaction with the trapped electron was verified by the observation that no loss of e; absorption occurred in an MTHF sample containing 0.025 M of the hydrocarbon 5a-androstane. Reactions of e; with cyclopentanone and cyclohexanone were practically indistinguishable from reactions with the corresponding steroids. The ketones of six-membered rings were slightly better electron acceptors than those of fivemembered rings, which may correlate with the fact that cyclohexanone is more easily reduced by 0.03 V.,' These reactions of e; with saturated ketones are weakly exo-
where Vlz is the volume common to both spheres. The value of 4 may be readily calculated from eq 13
(28) A. Albisson, G. Mousset, and J. Simonet, C. R. Hebd. Seances Acad. Sei., 272, 646 (1971).
Pn(t) = [Pl(t) Pz(t)I""
(10)
The quantity $(t)is a measure of the degree of overlap of the capture volumes of two correlated reaction centers. It gives the scavenging efficiency of the difunctional species A,-Az relative to the individual acceptor units located a t random distances from each other. For spherical reaction volumes the quantity $(t)can be evaluated in a straightforward manner. There are three cases to consider depending on the relative sizes of the two reaction radii and the separation a: (1)R1 + R2 < a, (2) R1 + R, > a > IR1 - R21, and (3) a < IR1 - RzJ. In case 1 the spheres do not overlap and 4(t) = 1 (11)
The Journal of Physical Chemistry, Vol. 85, No. 15, 198 1 2295
Trapped-Electron Capture by Steroid Molecules
e i t 005 M MONO OR 01-KETO I o1
I
ACCEPTORS IN MTHF AT 77 K
,
I
1
t t
OOL
e; t 00125 M
STEROIDS IN MTHF AT 77K
I
'
1
10-6
"
1
'
10.~ TIME,sec-
'
1
I
'
,
" 102
Figure 3. Decay kinetics for the e,- in MTHF at 77 K in the presence of the Indicated ketones at 0.05 M. The vertical axis corresponds to the e; survival probability calculated from a ratio of the absorbance at 1 pm for sample containing the ketone to that in a sample of pure MTHF under the same conditions ( A I A o ) . The curve was calculated by using the data for A30 and A170 and eq 10 and 13.
thermic and slow; their rates are expected to be sensitive to small changes in energetics.12 Decay curves for reactions of e; in MTHF with steroid molecules containing a,0 unsaturated ketone functional groups are shown in Figures 4 and 5. The separation a for the difunctional molecule PDDO is 8.8 A, again taken from molecular models. These enone compounds are considerably better e; scavengers than simple ketones. This is consistent with their less negative reduction potentials (--2.15 VZ9vs. -2.8 V,30adjusted to SCE reference) and correspondingly higher electron affinities. The A/Ao ratios were used to obtain P(t) values for all samples which, for the model compounds, were translated into reaction radii by using eq 2. Equations 10 and 13 were then used to calculate a predicted P J t ) for the difunctional molecule, which could be compared to the experimental decay curve. In practice, the simulations were calculated from decay curves ( A / A ovs. log t ) for the model compounds which had been processed by a quadratic smoothing routine in order to reduce fluctuations due to random noise on the signals. The predicted decay curves for difunctional molecules, obtained from the observed decay curves for monofunctional molecules and the distances between the reactive groups, are presented as solid lines in Figures 3-5. Tables I and I1 present observed and calculated values for P(t), R(t),and $ ( t )at two points in time along with the associated errors. The stated errors were calculated by using the estimated standard deviations for the absorbance curves and do not allow for any possible systematic errors. The observed and predicted values agree to within the given errors, which represent one standard deviation. Figures 4 and 5 also show experimental decay curves for samples containing both monofunctional enone steroids (0.0125 M AEO + 0.0125 M PEO in Figure 4; 0.025 M AEOA + 0.025 M PEOA in Figure 5 ) . In these samples the decay of trapped electrons is much faster than with the difunctional molecule PDDO, even though the total concentration of reactive functional groups is the same. This illustrates the effective reduction in scavenging efficiency of the molecule PDDO containing closely associated functional groups with overlapping capture volumes as compared to a random distribution of scavengers acting independently. The e, survival probabilities in the mixed samples (AEO + PEO or AEOA + PEOA) are given ac(29) A. Cohen, Anal. Chem., 35, 128 (1963). (30) P. Kabasakalian and J. McGlotten, Anal. Chem., 31,1091 (1959).
TIME,sec-
Flgure 4. Decay kinetics for the e; in MTHF at 77 K in the presence of the indicated compounds at 0.0125 M. The absorbance was measured at 1 pm. The solid curve was calculated by using the data for AEO and PEO and eq 10 and 13. The dotted curves were calculated by using eq 10 and the lndlcated values of 4 .
ej t 0025 M ACCEPTORS IN MTHF
Q.
L
c
t
0.0
IO-^ TIME,sec
-
Io2
I
Figure 5. Decay kinetics for the e; in MTHF at 77 K in the presence of the indicated compounds at 0.025 M. The absorbance was measured at lpm. The solid curve was calculated by using the data for AEOA and PEOA and eq 10 and 13. The dotted curves were calculated by using eq 10 and the indicated values of 4 .
TABLE I: Electron Scavenging Data for Ketone Steroids in MTHF at 77 K s
0.658 f 14.9 A
A30 0.007
A170 0.650 f 0.011 15.1 A
lo2s 0.352 + 0.005 20.2 A 0.392 * 0.007 19.5 A
ADO Pobsd @ calcd @ob& PCalCd
0.546 i 0.741 * 0.712 ? 0.533 i
0.010 0.002 0.027 0.008
0.262 i 0.686 i 0.674 i 0.257 f
0.007 0.001 0.016 0.004
curately by P = PIPz ( @ ( t = ) l),while in the case of the PDDO samples the observed values of 4(t)range from 0.67 a t lo4 s to 0.61 a t lo2 s. The solid-line simulations shown in Figures 4 and 5 were calculated from the data for AEO and PEO (or AEOA and PEOA) a t each point in time. These appear to provide somewhat better fits than dashed-line simulations presented for comparison, which use fixed, time-independent values for 4(t). But constant 4(t) curves can fit the data within the experimental uncertainty. No significant dif-
2296
Huddleston and Miller
The Journal of Physical Chemistry, Vol, 85, No. 15, 1981
TABLE 11: Electron Scavenging Data for Enone Steroids in MTHF 0.0125 M s
0.025 M
lo2s
P(t) R(t)
0.733 t 0.027 21.4 A
AEO 0.196 i 0.009 37.2 A
P(t)
0.745 i 0.019 21.1 a
PEO 0.212 i 0.011 36.6 A
R(t)
10 s
s
AEOA 0.537 t 0.012 21.4 a
0.056 5 0.001 35.8 a
0.533 c 0.017 21.5 A
0.055 c 0.003 35.8 a
0.450 i 0.651 t 0.638 c 0.443 i
0.033 c 0.592 c 0.590 c 0.033 t
PEOA
Pobsd &alcd
@obsd PCdCd
0.666 i 0.653 c 0.672 i 0.673 *
0.021 0.004 0.072 0.020
PDDO 0.144 i 0.013 0.589 i 0.001 0.609 i 0.030 0.153 * 0.066
ferences in reactivity toward the e t in MTHF between the hydroxy and acetate derivatives of the compounds were detected. The agreement between the predictions of the tunneling model in section I11 and the experimental results for both the simple ketone and enone steroids in MTHF is very good. Also, the observed values of &) agree within the experimental error for the two concentrations of the enone compounds (Table 11). Figure 6, a and b, and Table I11 display data on e; scavenging by 0.025 M of enone steroids (AEO, PEO, PDDO, etc.) in EtOH a t 77 K. These reactions are considerably slower than the corresponding reactions in MTHF (Figure 5), because trapped electrons are much more strongly solvated in the highly polar EtOH glass. This strong solvation both decreases the reaction exothermicity and increases the rearrangement energy so that the reaction with enones is weakly exothermic and slow. Also, it is apparent that there is significant difference in reactivity in EtOH between the compounds with a carbon-carbon double bond in the 4 position and a carbonyl group in the 3 position (AEO, AEOA) and the 16-en-20-one compounds (PEO, PEOA), as well as smaller differences within each class. The origin of these effects is unclear. Polarographic data in the literaturem indicate that the two enone functional groups of PDDO are simultaneously reduced a t almost exactly the same potential required to reduce several structural analogues of AEO. Since these reactions are weakly exothermic in EtOH, they are expected to be far more sensitive to small changes in exothermicity than in MTHF, but the effect is larger than anticipated considering the reduction potentials. Simulations for the PDDO decay curve in EtOH were calculated by using data for the four obvious combinations of model compounds: AEO and PEO, AEO and PEOA, AEOA and PEO, and AEOA and PEOA. In each case the results were in agreement with the observed data for PDDO within the experimental uncertainties. (The worst agreement is found with AEO and PEO to yield P,(t) values of 0.564 f 0.007 at lo4 s and 0.279 f 0.009 at lo2 s.) Thus, the observed differences in reactivity within the two classes of compounds are small enough to neglect for present purposes, and the results shown in Figure 6 and Table I11 were calculated by using averages of the decay curves for AEO and AEOA and for PEO and PEOA. However, these results must be considered somewhat less conclusive than the results for the same compounds in MTHF, since small systematic effects may contribute to
0.010 0.001 0.026 0.011
e; t 0.025 M
IO-
0
0.004 0.001 0.023 0.001
ACCEPTORS IN E t O H AT 7 7 K
ibi
-
< . 4
00
"
"
"
"
"
The Journal of Physical Chemistry, Vol. 85,
Trapped-Electron Capture by Steroid Molecules T A B L E 111: Electron Scavenging Data f o r E n o n e Steroids in E T O H
s
l o 2s
AEO 0.634 i 0.006 19.3 A
0.324 i 0.015 26.1 A
AEOA 0.657 i 0.005 18.8 A
0.366 r 0.008 25.2 A
PEO 0.673 * 0.010 18.4 A
0.415 i 0.010 24.1 A
PEOA 0.708 i 0.006 17.6 A
0.457 i. 0.007 23.2 A
PDDO Pobsd @J
calcd
@Jobsd
PCalCd
0.583 0.677 0.668 0.579
?
0.012
k
0.002 0.028 0.006
i i
0.303 0.639 0.630 0.298
i i
i i
0.015 0.003 0.029 0.007
in each of the cases considered. It should be emphasized that the theory contains no adjustable parameters; only data for suitable model compounds (tunneling distances) and the separation a are required to predict the scavenging kinetics of the difunctional compound. Thus the present experiments provide convincing evidence for the correctness of the long-range tunneling mechanism for electron transfer in low-temperature organic glasses. One might expect deviations from the model in section I11 to be due to two sources. Tunneling reaction volumes may be nonspherical because of orientation effects on the rate of electron transfer. Such an effect might be expected to be more important for the somewhat elongated enone functional group than for a simple ketone. A second possible source for deviations from the model in section I11 would be direct electronic interactions between the two functional groups at opposite ends of the molecule. This sort of interaction would be expected to be very small eV) for large separations. The results in section IV provide experimental evidence that both of these effects are small in the systems under consideration. Evaluation of Hopping Mechanism. General Considerations. As stated in section I, the detailed predictions of a hopping mechanism for electron scavenging by a difunctional molecule are model dependent. However, a few general conclusions are possible. A diffusive (or hopping) mechanism for electron transport involving fixed reaction ) be time independent. radii would imply that @ ( t should In the limit of small reaction radii relative to the separation a, one would expect that the two electron-accepting groups will act independently and 4 will approach unity. This limit will never be precisely realized since a portion of incoming diffusive flux for one functional group will fall within the solid angle subtended by the other end of the molecule and be intercepted. The present results show @(t) significantly less than 1 and provide some, although not conclusive, evidence that 4 ( t )is actually time dependent. The fact that 4 ( t ) C 1 is observed could conceivably be explained by a diffusive mechanism if the encounter radii and/or step size were of the proper dimensions, since the data can be satisfactorily fitted by time-independent 4's. However, it would be necessary to invoke a special coincidence to explain the data, in the absence of any more detailed hopping model. Comparison with Diffusion i n Liquids. It is impressive that the experiments show that two reactive groups centered roughly 10 A apart can be barely more effective at
No. 15, 198 1 2297
capturing trapped electrons than a single reactive group = 0.59 at lo2s in Table 11; @(t) = 0.5 would mean (e.g., @(t) the difunctional molecule is no more effective than a monofunctional molecule). This is clearly understood in terms of the tunneling model because the tunneling distance (35.8A in the example cited) is much larger than the separation (8.8 A). One might intuitively expect that these results would definitely rule out at least those hopping mechanisms which invoked short reaction radii (e.g., 5-10 A). However, a comparison with diffusion kinetics in liquid solution shows that this expectation is incorrect. We have carried out experiments on reactions of ADO and PDDO with solvated electrons and have shown that small values of 4 (the effectiveness of a reactive group in a difunctional molecule relative to the same group in a monofunctional molecule) are possible for a diffusional mechanism in liquid ~olution.'~Values near to 0.5 are allowed by a model based on treating the difunctional molecules as prolate spheroids and can indeed be observed by pulse radiolysis in fluid solution^.^^ The value of 4 for hopping in a rigid medium might be obtained from 4 for diffusional reactions in fluids if (1) the reaction radii in the liquid and the solid were equal and (2) the hopping step size (length) were small compared to the reaction radii. However such small hopping step sizes would require a very high concentration of trapping sites. For larger step sizes the relative e,- capture efficiency, 4, would depend on the details of e; transport. Fitting with a Hopping Model. From the foregoing it seems plausible that a hopping mechanism could fit the data by appropriate adjustment of (1)the hopping rate and its time dependence, (2) the hopping step size and its time dependence, and (3) the reaction probability as a function of distance and its time dependence. Because none of these has thus far been specified by proponents of the hopping model for electron transfer in glasses, it may even be possible to fit all of the data with mutually consistent sets of parameters. We must emphasize, however, that current formulations of the hopping model have very little predictive power.
VI. Conclusions The relative effectiveness of difunctional vs. monofunctional molecules, 4(t),varied substantially with the nature of the reactive groups, with time, and with the type of solvent. These variations were successfully and quantitatively predicted by the tunneling model with no adjustable parameters. Thus strong evidence for the tunneling mechanism has been obtained. Alternating hopping models are likely to be capable of making fits by adjusting parameters, but not of making quantitative predictions. Experimental evidence is steadily accumulating that electron transfer in low-temperature glasses proceeds by a tunneling rather than a hopping mechanism.'-19 Previously, a number of arguments against hopping as an efficient transport mechanism in low-temperature polar media have been presented.11-13 In the case of intermo(31) I t is interesting to note that a small @J (near 0.5) can occur in diffusion even when the reaction radius is less than the separation distance. To qualitatively understand this, we should note the very different role of the reaction radius in reactions in different phases. In solids the tunneling mechanism predicts that the reaction probability is proportional to the cube of the reaction radius (i.e., proportional to the reaction volume). In gas-phase kinetics the reaction probability is proportional to the square of the reaction radius. But in liquids, diffusion-controlled reaction rates are proportional to the reaction radius to the first power. This remarkable situation is related to the fact that a diffusing particle known to have passed through a given point in space is quite likely to reencounter that same point in space before diffusing far away.
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J. Phys. Chem. 1981, 85, 2298-2303
lecular charge transfer, the evidence in favor of a tunneling mechanism is overwhelming,13J5J6 and the present experiments provide a direct test in the case of e; scavenging. It now seems clear that the available data as well as theoretical descriptions of the electron transfer process are
consistent with a long-range tunneling mechanism. Acknowledgment. This work was performed under the auspices of the Office of Basic Energy Sciences of the U.S. Department of Energy.
Adsorption of Fluorocarbon and Hydrocarbon Surfactants to Air-Water, Hexane-Water, and Perfluorohexane-Water Interfaces. Relative Affinities and Fluorocarbon-Hydrocarbon Nonideality Effects Pasupati Mukerjee’ and Tetsurou Handat School of Pharmacy, University of Wisconsin, Madison, Wisconsin 53706 (Received: January 2 1, 198 1)
Surface and interfacial tensions of dilute aqueous solutions of sodium perfluorobutyrate, sodium perfluorooctanoate (SPFO), sodium perfluorodecanoate, sodium octyl sulfate, and sodium decyl sulfate (SDeS) at the air-water (A/W), hexane-water (H/ W), and perfluorohexane-water (p-f-H/W) interfaces have been measured with the objective of determining the relative affinities for the interfaces at low degrees of adsorption. Up to -2 dyn/cm the surface pressures were found to increase linearly with surfactant concentration (activity), in agreement with a thermodynamic model of adsorption. The free energies of adsorption, AG, have been estimated by using the thermodynamic model. From these data the incremental changes in AG, AhG values, on adding a -CH2- group to the hydrocarbon chain and a -CFz- group to the fluorocarbon chain have been calculated. The affinity of a hydrocarbon surfactant for the H/W interface is markedly higher than that for the A/W interface. A fluorocarbon surfactant at the p-f-H/W interface, in contrast, shows a much smaller increase in affinity as compared to the A/W interface. This result is consistent with the expected weaker mutual interactions among fluorocarbons in comparison to hydrocarbons. Although SPFO and SDeS have nearly identical critical micellization concentrations, it was found that the affinity of SPFO for the A/W interface is markedly higher than that of SDeS. This has been ascribed to a much more pronounced role of the chain-water interactions in determining the hydrophobic character of fluorocarbon surfactants. A t the H/ W interface, however, there is a reversal of affinity, that of SPFO being significantly lower. Such data for all of the surfactants adsorbing at the H/W and the p-f-H/W interfaces reveal a pronounced effect of the nonideality of mixing of fluorocarbon and hydrocarbon surfactants at hydrocarbon and fluorocarbon interfaces, respectively. To compare these nonideality effects with nonidealities in liquid mixtures of fluorocarbons and hydrocarbons, we have estimated partial molal excess free energies at infinite dilution of hydrocarbons in perfluorohexane and fluorocarbons in hexane from critical solution data. The calculated incremental changes in the excess free energies per added -CHz- or -CF2- group are in fair agreement with the difference in the AAG of adsorption of -CH2- and -CF2groups between the H/W and p-f-H/W interfaces. The differences in AG of SPFO and SDeS between the two interfaces are also in rough agreement with estimated nonideality effects for perfluoroheptane and decane.
Introduction Adsorptions of surfactants to fluid interfaces are affected by many factors of which two are of great importance, namely, the affinity of the surfactant for the interface and the maximum adsorption possible before micelle formation begins. The word affinity here corresponds to the adsorbability of the surfactant a t low concentrations and low adsorption densities so that interactions between surfactant molecules a t the interface and prablems related to saturation of the surface are negligible. The present study is concerned with the relative affinities of some selected fluorocarbon and hydrocarbon surfactants for air-water (A/W), hexane-water (H/W), and perfluorohexane-water (p-f-H/W) interfaces. It has been shown recently that fluorocarbon and hydrocarbon surfactants show a considerable nonideality of mixing in mixed micelles.’” On the basis of the early observations, it was suggested that such ‘Faculty of Pharmaceutical Sciences, Kyoto University, Sakyo-ku, Kyoto, Japan. 0022-365418112085-2298$0 1.2510
nonideality effects may be widespread, particularly for “surfactants at interfaces where fluorocarbon hydrocarbon interactions are involved”.l A series of investigations on adsorption of fluorocarbon and hydrocarbon surfactants to fluid and solid surfaces over the whole concentration range from dilute solutions to above the critical micellization concentrations (cmc) have been carried out.6 In this paper we present a portion of this work dealing with adsorption from dilute solutions. Aside from estimates of relative affinities of fluorocarbon and hydrocarbon surfactants for various fluid interfaces, comparisons of hydrophobic interactions and the interactions of fluorocarbon and hydrocarbon chains with fluorocarbon and hydro(1) (2) (3) (4) (5) (6)
P. Mukerjee and A. Y. S. Yang, J. Phys. Chem., 80, 1388 (1976). K. J. Mysels, J. Colloid Interface Sci., 66,331 (1978). P. Mukerjee and K. J. Mysels, ACS Symp. Ser., No. 9,239 (1975). N. Funasaki and S. Hada, J. Colloid Interface Sci., 72,425 (1980). K. Shinoda and T. Nomura, J . Phys. Chem., 84, 365 (1980). P. Mukerjee, T. Handa, and R. A. Pyter, unpublished work.
0 1981 American Chemical Society
