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Calculation of electron solvation times for several dipolar liquids
lnt. J. Radiat. Phys. Chem. 1974, Vol. 6, pp. 223-226. Pergamon Press. Printed in Great Britain
CALCULATION OF ELECTRON SOLVATION TIMES
FOR SEVERAL DIPOLAR LIQUIDS R. SCHILLERand Sz. VASS Central Research Institute for Physics, Budapest, Hungary (Received 20 June 1973) Abstract--An earlier theory on the kinetics of electron solvation is developed further and evaluated
numerically. Comparing the theoretical predictions with recent experimental results the agreements seem to be reasonable particularly for liquids of fast dielectric relaxation. This finding supports the view that electrons become solvated by self-trapping.
RECENT developments in the technique of pulse radiolysis have made the process of electron solvation in dipolar liquids amenable to experimental kinetic studies. Baxendale and Wardman tl,9"~ were the first to determine a number of solvation rate constants for cold alcohols while Beck and Thomas tS~and Gilles et aL c4Jextended these measurements to room-temperature liquids. These results enable us to compare our earlier theoretical prediction on electron localization kinetics ts~ with directly measurable data. The model underlying the theory considers an electron being characterized by a density distribution p(r, t), where r is some polar coordinate, and t the time, and moving around in a dipolar liquid continuum. The electron polarizes the liquid bringing about a potential well in which it becomes self-trapped. The period of time during which the depth of the potential well attains a value appropriate for stable electron-trapping can be calculated. The liquid is characterized by the macroscopic static and high-frequency dielectric constants es and e~o, respectively, and by the dielectric relaxation time, ~'. The electron-cloud moves on in a certain direction. Some regions of the cloud with a higher density start to polarize their liquid environment. The cloud moves fast in comparison to dielectric relaxation, thus its high-density regions part with their original sites untrapped. The early polarization produced by them, however, might be sufficient for trapping a lower density region of the cloud. The model is apparently meaningful in statistical terms only. This model can be described quantitatively in the following way c5~. Let the volume within which trapping occurs be denoted by V(t). The probability of trapping, p(t), is then
p(t) = fr'~o p(r, t) dr,
(1)
while V(t) is defined by inequality (2),
(2)
p(r, 0) +f~[~p(r, u)/~u] exp (u/O) du <~O,
where 0 ~
223
224
R. SCHILLERand Sz. VASS
The theoretical solvation rate constant kth can be expressed as (3)
kth =
dp(t)/dt.
This derivative is usually time-dependent, while experimentalists (1-4) observe timeindependent rate constants. We regard these latter as time averages of kth. Let t m denote the solvation time, i.e. the period during which p(t) approaches the value 1. Then (4)
kex p = t m -1
(Inl
[dp(t)/dt I dt ~ tm-1.
d0
Thus the solvation time is approximately the reciprocal of the first-order solvation rate constant. The non-stationary charge distribution of the electron during self-trapping cannot be calculated. For the sake of a crude estimate of t m the electron is thought to be a one-dimensional " r o o f "-shaped wave packet which travels with constant width, height and velocity in the + x direction as depicted in the inset of Fig. 1. The equation of its charge density is given by
p ( x - vt) = - A(2A2)-I(x- vt) + h/(2)/~]-1,
(5)
A = sgn ( x -
vt),
where sgn is the symbol for the signum or sign function. ¢n
10 -1
I0"~
~
I0"~
10-~
i
....
v t~-[tU£
lo
7
70-'
x
7o-~
J
~ b ~ - W ~
10-' ,
7o-'
e
W
FIG. 1. The dependence of the solvation time on # for two different electron density distributions. Lower curve: A = Aa; upper curve: A = Ab. Inset: The one-dimensional wave packet. Two alternative guesses are made for parameter A: (a) The electron of thermal velocity v has the characteristic dimensions of the de Broglie wavelength An = h/m e v throughout the whole process. This width of the wave packet is compatible with the uncertainty principle at the beginning of the process but neglects the broadening of the distribution with elapsing time. Thus it is something of a lower bound to the size of the wave packet.
Calculation of electron solvation times for several dipolar liquids
225
(b) T h e e l e c t r o n d i s t r i b u t i o n is t h o u g h t t o b e o f t h e w i d t h it w o u l d a t t a i n at t m i f its initial v a l u e is Am a n d t h e f o r m a t i o n o f t h e p o t e n t i a l w e l l d o e s n o t l i m i t its b r o a d e n i n g . T h i s gives Ab = (A~2 + 1 6 h 2 tm~/me 2 Aa2)½
(6)
2% b e i n g t h e u p p e r b o u n d t o t h e size o f t h e w a v e p a c k e t . C o m b i n i n g e q u a t i o n s (2) a n d (5) o n e o b t a i n s x 1 2A2 4 x/(2) A By t m e v e n t h e o f t h e a p e x at x = x m, t = t m thermal energy Ab, o n e o b t a i n s
v 2A 2 tg[exp (t/O) - 1] ~<0.
a p e x o f t h e w a v e p a c k e t b e c o m e s s o l v a t e d . H e n c e w i t h the a b s c i s s a t h e m o m e n t o f s o l v a t i o n b e c o m i n g c o m p l e t e , x m e q u a l s vtm. F o r the above expression turns into an equality. Attributing average to t h e e l e c t r o n , m e v 2 = 3kT, a n d i n s e r t i n g t h e e x p r e s s i o n s f o r Aa o r the f o l l o w i n g a l t e r n a t i v e e q u a t i o n s f o r tm
(7a)
e x p (tmJt9) - ( t m J O ) - ( 0 1 0 ) - 1 = O,
(7b)
e x p ( t m b / t 9 ) -- ( t m b / / 9 ) - - [(6)//9) 2 + 87r--~(tmb/~9)2] ½ = 0,
w h e r e 6) = x/(2)h/3kT. O f t h e t w o e x p r e s s i o n s , e q u a t i o n (7a) r e n d e r s a l o w e r b o u n d , (7b) a n u p p e r b o u n d t o tm. B o t h e q u a t i o n s w e r e s o l v e d n u m e r i c a l l y , t h e s o l u t i o n s b e i n g p l o t t e d in Fig. 1 as a f u n c t i o n o f ®/~9. A s 6)/va increases, tmoJ~9 a p p r o a c h e s tmb/tg, t h e r a n g e f o r t h e prediction of solvation time becoming more and more narrow. At extremely low v a l u e s o f 6)/v~, i.e. in t h e cases o f s l o w l y r e l a x i n g dielectrics, t h e t w o b o u n d s b e c o m e far a p a r t a n d t h e e s t i m a t e is u n c e r t a i n . O n e feels s t r o n g l y , h o w e v e r , t h a t i f t9 a n d h e n c e t m is m u c h h i g h e r t h a n 6) (this l a t t e r b e i n g a b o u t 10 - l a s a r o u n d 200 K), t m is b e t t e r a p p r o x i m a t e d b y tmb w h e r e t h e effect o f e l a p s i n g t i m e h a s b e e n a l l o w e d for. TABLE I. COMPARISON OF THE OBSERVED SOLVATION TIMES tm(eXp) WITH THE THEORETICAL ESTIMATES (tmatmb) t
Substance Methanol Ethanol n-Butanol iso-Propanol n-Propanol n-Propanol Methanol Ethanol n-Propanol H20 * Ref. (2).
(s)
T (K)
tam (s)
tmb (s)
(tnmtmb)½ (s)
tm(eXp) (s)
3 x 10 -1° 5 x 10 -a 4 x 10 -8 3.5 x 10 -8 7.5 x 10 -7 3.3 x 10 -8 9 x 10 -12 3 x 10 -11 8.1 x 10 -11 2 x 10 -la 6-2 x 10-1s:~
181 166 184 186 152 176 296 296 296 296 296
2.70 x 10 - n 3.68 x 10 -11 9.92 x 10 -11 9.24 x 10 -x1 9"37 x 10 -1° 9.21 x 10 -11 1.15 × 10 -12 2"11 x 10 -12 3.49 x 10 -12 1.52 x 10 -la 2"84 x 10 -is
3.51 x 10 -1° 5.85 x 10 -° 4"68 x 10 -8 4.09 x 10 -8 8.77 x 10 -7 3.86 x 10 -s 1.05 x 10 -11 3"51x 10 -11 9"48 x 10 -11 2.44 x 10 -la 7-32 x 10 -is
9.73 x 10 -11 4.68 x 10 -l° 2.13 x 10 -9 1.94 x 10 -a 2.87 x 10 -8 1-89 x 10 -a 3"47 x 10 -12 8.61 x 10 -12 1.82 x 10 - n 1"92 x 10 -la 4-59 x 10 -is
1 x 10 -9* 2 x 10 -9* 4 x 10 -a* 7 x 10 -9* 6 x 10 -8* 5 x 10 -9* 2.2 x 10-12 t 10 x 10-12 t 1.3 x 10-11"t"
t Ref. (4).
:~ Ref. (9).
< 2 x 10-11 t
All other ~9 values cited after Refs. 2 and 4.
I n T a b l e I, tma a n d tmb v a l u e s are listed f o r d i f f e r e n t s u b s t a n c e s t o g e t h e r w i t h t h e e x p e r i m e n t a l s o l v a t i o n times, i.e. t h e r e c i p r o c a l s o f s o l v a t i o n r a t e c o n s t a n t s . A l c o h o l s have two or three distinct relaxation times; we used the highest ones throughout our
226
R. SCHILLER and Sz. VASS
calculations, since it is the slow relaxation which corresponds to the overwhelming part of polarization. This is borne out by the fact that as the dielectric constant changes with the frequency from e~ to e~ some 90 per cent of this increase proceeds with the slowest relaxation time (v). The geometrical mean values of tm~ and tmb predict the experimental data adequately for room-temperature liquids. Here D is always low which brings the two bounds close to each other. The predictions for cold alcohols are certainly poorer, but even here the (tm~tmb) ~ values agree with the observed data within a factor of 2-4, with the sole exception of liquid methanol. It is apparent, however, that for the low temperature cases, tmb is usually nearer to tm(exp) than tm~. The present calculations based on the crude model of an electron wave packet travelling in a continuous liquid medium can be regarded as a rough first approximation only. Nevertheless, we are of the opinion that the reasonable numerical agreements obtained without any adjustable parameter for a number of systems and temperatures offer an argument in the self-trapping vs. pre-formed trap issue (s) in favour of the self-trapping mechanism. Acknowledgement--The authors express their thanks to Dr. J. W. Hunt for the manuscript of his unpublished paper. REFERENCES J. H. BAXENDALEand P. WARDMAN, Nature (Lond.) 1971, 230, 449. J. H. BAXENDALEand P. WARDMAN,J. chem. Soc. Faraday I, 1973, 69, 584. G. BECK and J. K. THOMAS, J. phys. Chem. 1972, 76, 3856. L. GILLES, J. E. ALDRICH and J. W. HUNT, Nature phys. Sci. 1973, 243, 70. R. SCHILLER, Nature (Lond.) 1968, 217, 1141. R. SCHILLER, J. chem. Phys. 1965, 43, 2760; J. chem. Phys. 1967, 47, 2278; Chem. Phys. Lett. 1970, 5, 176. 7. E. g. R. H. COLE and D. W. DAVIDSON, J. chem. Phys. 1952, 20, 1389; W. DANNHAUSER and R. H. COLE, J. chem. Phys. 1955, 23, 1762. 8. B. WEBSTER and G. HOWAT, Radiat. Res. Rev. 1972, 4, 250. 9. R. P. AUTY and R. H. COLE, J. chem. Phys. 1952, 20, 1309.
1. 2. 3. 4. 5. 6.
R6sum6--On d6veloppe, et 6value par le calcul num6rique, une th6orie ant6rieure de la solvatation des 61ectrons. La comparaison des pr6dictions th6oriques avec des r6sultats exp6rimentaux r6cents conduit h un accord raisonnable, en particulier dans le cas des liquides h relaxation di61ectrique rapide. Ce r6sultat corrobore l'id6e que les 61ectrons sont solvat6s par un processus d'autopi6geage.
Zusammenfassung--Eine friihere Theorie der Elektronsolvatisierungkinetik wird weiterentwickelt und numerisch ausgewertet. Beim Vergleich der theoretischen Voraussagen mit kiirzlich erhaltenen experimentellen Resultaten ergibt sich eine annehmbare [3bereinstimmung, besonders im Falle von Fliissigkeiten mit r6scher dielektrischer Relaxation. Dieser Befund unterstiitzt die Ansicht, dass die Elektronen durch Selbsteinfangen solvatisiert werden. P e 3 i o M e - HpOBOIIHTCfl ~an~,He~tuee pa3BFITMe Teoprlrt, raca~otue~ca KHHeTI4qeCKOFO noBe~/eHH~ CO7IbBaTFIpOBaHHOI'O 9IIeKTpOHa, I,I ~aeTcn qI,ICJIeHHa~ otteaKa. CpaBHeH~leM TeopeTI,IqeCKHX npe~/nocb~noK c 6once HO3~HFIMFI 9KC[lepl,IMel-ITaJIbHblM!4pe3yYrbTaTaMn ~OCTMFHyTayZ[OBIleTBOpl,lTeYlbHa~l COFYracoBaI-IHOCTb, Oco6eHHo ~t3Ifl )Krlj/KOCTe~I C Ma.rlblM BpeMeHeM )i~i932eK'rp14qecKoi~penaKcauH~. Taro~ pe3y3IbTaT nojiTBep:~)laeT npejIrIo510~eHHe, tlTO COYIbBaTI,IpylOTC~I 9.rleKTpOHbI Hocpe~CTBOM CaMO3aXBaTblaaI-lYl~l.
CALCULATION OF ELECTRON SOLVATION TIMES
FOR SEVERAL DIPOLAR LIQUIDS R. SCHILLERand Sz. VASS Central Research Institute for Physics, Budapest, Hungary (Received 20 June 1973) Abstract--An earlier theory on the kinetics of electron solvation is developed further and evaluated
numerically. Comparing the theoretical predictions with recent experimental results the agreements seem to be reasonable particularly for liquids of fast dielectric relaxation. This finding supports the view that electrons become solvated by self-trapping.
RECENT developments in the technique of pulse radiolysis have made the process of electron solvation in dipolar liquids amenable to experimental kinetic studies. Baxendale and Wardman tl,9"~ were the first to determine a number of solvation rate constants for cold alcohols while Beck and Thomas tS~and Gilles et aL c4Jextended these measurements to room-temperature liquids. These results enable us to compare our earlier theoretical prediction on electron localization kinetics ts~ with directly measurable data. The model underlying the theory considers an electron being characterized by a density distribution p(r, t), where r is some polar coordinate, and t the time, and moving around in a dipolar liquid continuum. The electron polarizes the liquid bringing about a potential well in which it becomes self-trapped. The period of time during which the depth of the potential well attains a value appropriate for stable electron-trapping can be calculated. The liquid is characterized by the macroscopic static and high-frequency dielectric constants es and e~o, respectively, and by the dielectric relaxation time, ~'. The electron-cloud moves on in a certain direction. Some regions of the cloud with a higher density start to polarize their liquid environment. The cloud moves fast in comparison to dielectric relaxation, thus its high-density regions part with their original sites untrapped. The early polarization produced by them, however, might be sufficient for trapping a lower density region of the cloud. The model is apparently meaningful in statistical terms only. This model can be described quantitatively in the following way c5~. Let the volume within which trapping occurs be denoted by V(t). The probability of trapping, p(t), is then
p(t) = fr'~o p(r, t) dr,
(1)
while V(t) is defined by inequality (2),
(2)
p(r, 0) +f~[~p(r, u)/~u] exp (u/O) du <~O,
where 0 ~
223
224
R. SCHILLERand Sz. VASS
The theoretical solvation rate constant kth can be expressed as (3)
kth =
dp(t)/dt.
This derivative is usually time-dependent, while experimentalists (1-4) observe timeindependent rate constants. We regard these latter as time averages of kth. Let t m denote the solvation time, i.e. the period during which p(t) approaches the value 1. Then (4)
kex p = t m -1
(Inl
[dp(t)/dt I dt ~ tm-1.
d0
Thus the solvation time is approximately the reciprocal of the first-order solvation rate constant. The non-stationary charge distribution of the electron during self-trapping cannot be calculated. For the sake of a crude estimate of t m the electron is thought to be a one-dimensional " r o o f "-shaped wave packet which travels with constant width, height and velocity in the + x direction as depicted in the inset of Fig. 1. The equation of its charge density is given by
p ( x - vt) = - A(2A2)-I(x- vt) + h/(2)/~]-1,
(5)
A = sgn ( x -
vt),
where sgn is the symbol for the signum or sign function. ¢n
10 -1
I0"~
~
I0"~
10-~
i
....
v t~-[tU£
lo
7
70-'
x
7o-~
J
~ b ~ - W ~
10-' ,
7o-'
e
W
FIG. 1. The dependence of the solvation time on # for two different electron density distributions. Lower curve: A = Aa; upper curve: A = Ab. Inset: The one-dimensional wave packet. Two alternative guesses are made for parameter A: (a) The electron of thermal velocity v has the characteristic dimensions of the de Broglie wavelength An = h/m e v throughout the whole process. This width of the wave packet is compatible with the uncertainty principle at the beginning of the process but neglects the broadening of the distribution with elapsing time. Thus it is something of a lower bound to the size of the wave packet.
Calculation of electron solvation times for several dipolar liquids
225
(b) T h e e l e c t r o n d i s t r i b u t i o n is t h o u g h t t o b e o f t h e w i d t h it w o u l d a t t a i n at t m i f its initial v a l u e is Am a n d t h e f o r m a t i o n o f t h e p o t e n t i a l w e l l d o e s n o t l i m i t its b r o a d e n i n g . T h i s gives Ab = (A~2 + 1 6 h 2 tm~/me 2 Aa2)½
(6)
2% b e i n g t h e u p p e r b o u n d t o t h e size o f t h e w a v e p a c k e t . C o m b i n i n g e q u a t i o n s (2) a n d (5) o n e o b t a i n s x 1 2A2 4 x/(2) A By t m e v e n t h e o f t h e a p e x at x = x m, t = t m thermal energy Ab, o n e o b t a i n s
v 2A 2 tg[exp (t/O) - 1] ~<0.
a p e x o f t h e w a v e p a c k e t b e c o m e s s o l v a t e d . H e n c e w i t h the a b s c i s s a t h e m o m e n t o f s o l v a t i o n b e c o m i n g c o m p l e t e , x m e q u a l s vtm. F o r the above expression turns into an equality. Attributing average to t h e e l e c t r o n , m e v 2 = 3kT, a n d i n s e r t i n g t h e e x p r e s s i o n s f o r Aa o r the f o l l o w i n g a l t e r n a t i v e e q u a t i o n s f o r tm
(7a)
e x p (tmJt9) - ( t m J O ) - ( 0 1 0 ) - 1 = O,
(7b)
e x p ( t m b / t 9 ) -- ( t m b / / 9 ) - - [(6)//9) 2 + 87r--~(tmb/~9)2] ½ = 0,
w h e r e 6) = x/(2)h/3kT. O f t h e t w o e x p r e s s i o n s , e q u a t i o n (7a) r e n d e r s a l o w e r b o u n d , (7b) a n u p p e r b o u n d t o tm. B o t h e q u a t i o n s w e r e s o l v e d n u m e r i c a l l y , t h e s o l u t i o n s b e i n g p l o t t e d in Fig. 1 as a f u n c t i o n o f ®/~9. A s 6)/va increases, tmoJ~9 a p p r o a c h e s tmb/tg, t h e r a n g e f o r t h e prediction of solvation time becoming more and more narrow. At extremely low v a l u e s o f 6)/v~, i.e. in t h e cases o f s l o w l y r e l a x i n g dielectrics, t h e t w o b o u n d s b e c o m e far a p a r t a n d t h e e s t i m a t e is u n c e r t a i n . O n e feels s t r o n g l y , h o w e v e r , t h a t i f t9 a n d h e n c e t m is m u c h h i g h e r t h a n 6) (this l a t t e r b e i n g a b o u t 10 - l a s a r o u n d 200 K), t m is b e t t e r a p p r o x i m a t e d b y tmb w h e r e t h e effect o f e l a p s i n g t i m e h a s b e e n a l l o w e d for. TABLE I. COMPARISON OF THE OBSERVED SOLVATION TIMES tm(eXp) WITH THE THEORETICAL ESTIMATES (tmatmb) t
Substance Methanol Ethanol n-Butanol iso-Propanol n-Propanol n-Propanol Methanol Ethanol n-Propanol H20 * Ref. (2).
(s)
T (K)
tam (s)
tmb (s)
(tnmtmb)½ (s)
tm(eXp) (s)
3 x 10 -1° 5 x 10 -a 4 x 10 -8 3.5 x 10 -8 7.5 x 10 -7 3.3 x 10 -8 9 x 10 -12 3 x 10 -11 8.1 x 10 -11 2 x 10 -la 6-2 x 10-1s:~
181 166 184 186 152 176 296 296 296 296 296
2.70 x 10 - n 3.68 x 10 -11 9.92 x 10 -11 9.24 x 10 -x1 9"37 x 10 -1° 9.21 x 10 -11 1.15 × 10 -12 2"11 x 10 -12 3.49 x 10 -12 1.52 x 10 -la 2"84 x 10 -is
3.51 x 10 -1° 5.85 x 10 -° 4"68 x 10 -8 4.09 x 10 -8 8.77 x 10 -7 3.86 x 10 -s 1.05 x 10 -11 3"51x 10 -11 9"48 x 10 -11 2.44 x 10 -la 7-32 x 10 -is
9.73 x 10 -11 4.68 x 10 -l° 2.13 x 10 -9 1.94 x 10 -a 2.87 x 10 -8 1-89 x 10 -a 3"47 x 10 -12 8.61 x 10 -12 1.82 x 10 - n 1"92 x 10 -la 4-59 x 10 -is
1 x 10 -9* 2 x 10 -9* 4 x 10 -a* 7 x 10 -9* 6 x 10 -8* 5 x 10 -9* 2.2 x 10-12 t 10 x 10-12 t 1.3 x 10-11"t"
t Ref. (4).
:~ Ref. (9).
< 2 x 10-11 t
All other ~9 values cited after Refs. 2 and 4.
I n T a b l e I, tma a n d tmb v a l u e s are listed f o r d i f f e r e n t s u b s t a n c e s t o g e t h e r w i t h t h e e x p e r i m e n t a l s o l v a t i o n times, i.e. t h e r e c i p r o c a l s o f s o l v a t i o n r a t e c o n s t a n t s . A l c o h o l s have two or three distinct relaxation times; we used the highest ones throughout our
226
R. SCHILLER and Sz. VASS
calculations, since it is the slow relaxation which corresponds to the overwhelming part of polarization. This is borne out by the fact that as the dielectric constant changes with the frequency from e~ to e~ some 90 per cent of this increase proceeds with the slowest relaxation time (v). The geometrical mean values of tm~ and tmb predict the experimental data adequately for room-temperature liquids. Here D is always low which brings the two bounds close to each other. The predictions for cold alcohols are certainly poorer, but even here the (tm~tmb) ~ values agree with the observed data within a factor of 2-4, with the sole exception of liquid methanol. It is apparent, however, that for the low temperature cases, tmb is usually nearer to tm(exp) than tm~. The present calculations based on the crude model of an electron wave packet travelling in a continuous liquid medium can be regarded as a rough first approximation only. Nevertheless, we are of the opinion that the reasonable numerical agreements obtained without any adjustable parameter for a number of systems and temperatures offer an argument in the self-trapping vs. pre-formed trap issue (s) in favour of the self-trapping mechanism. Acknowledgement--The authors express their thanks to Dr. J. W. Hunt for the manuscript of his unpublished paper. REFERENCES J. H. BAXENDALEand P. WARDMAN, Nature (Lond.) 1971, 230, 449. J. H. BAXENDALEand P. WARDMAN,J. chem. Soc. Faraday I, 1973, 69, 584. G. BECK and J. K. THOMAS, J. phys. Chem. 1972, 76, 3856. L. GILLES, J. E. ALDRICH and J. W. HUNT, Nature phys. Sci. 1973, 243, 70. R. SCHILLER, Nature (Lond.) 1968, 217, 1141. R. SCHILLER, J. chem. Phys. 1965, 43, 2760; J. chem. Phys. 1967, 47, 2278; Chem. Phys. Lett. 1970, 5, 176. 7. E. g. R. H. COLE and D. W. DAVIDSON, J. chem. Phys. 1952, 20, 1389; W. DANNHAUSER and R. H. COLE, J. chem. Phys. 1955, 23, 1762. 8. B. WEBSTER and G. HOWAT, Radiat. Res. Rev. 1972, 4, 250. 9. R. P. AUTY and R. H. COLE, J. chem. Phys. 1952, 20, 1309.
1. 2. 3. 4. 5. 6.
R6sum6--On d6veloppe, et 6value par le calcul num6rique, une th6orie ant6rieure de la solvatation des 61ectrons. La comparaison des pr6dictions th6oriques avec des r6sultats exp6rimentaux r6cents conduit h un accord raisonnable, en particulier dans le cas des liquides h relaxation di61ectrique rapide. Ce r6sultat corrobore l'id6e que les 61ectrons sont solvat6s par un processus d'autopi6geage.
Zusammenfassung--Eine friihere Theorie der Elektronsolvatisierungkinetik wird weiterentwickelt und numerisch ausgewertet. Beim Vergleich der theoretischen Voraussagen mit kiirzlich erhaltenen experimentellen Resultaten ergibt sich eine annehmbare [3bereinstimmung, besonders im Falle von Fliissigkeiten mit r6scher dielektrischer Relaxation. Dieser Befund unterstiitzt die Ansicht, dass die Elektronen durch Selbsteinfangen solvatisiert werden. P e 3 i o M e - HpOBOIIHTCfl ~an~,He~tuee pa3BFITMe Teoprlrt, raca~otue~ca KHHeTI4qeCKOFO noBe~/eHH~ CO7IbBaTFIpOBaHHOI'O 9IIeKTpOHa, I,I ~aeTcn qI,ICJIeHHa~ otteaKa. CpaBHeH~leM TeopeTI,IqeCKHX npe~/nocb~noK c 6once HO3~HFIMFI 9KC[lepl,IMel-ITaJIbHblM!4pe3yYrbTaTaMn ~OCTMFHyTayZ[OBIleTBOpl,lTeYlbHa~l COFYracoBaI-IHOCTb, Oco6eHHo ~t3Ifl )Krlj/KOCTe~I C Ma.rlblM BpeMeHeM )i~i932eK'rp14qecKoi~penaKcauH~. Taro~ pe3y3IbTaT nojiTBep:~)laeT npejIrIo510~eHHe, tlTO COYIbBaTI,IpylOTC~I 9.rleKTpOHbI Hocpe~CTBOM CaMO3aXBaTblaaI-lYl~l.