8954
FFRANCON WILLIAMS [COXTRIBUTIOS FROM
THE
DEPARTMEKT O F CHEMISTRY, c X I V E R S I T V
OF
Vol. EXi
TENNESSEE, KSOXVILLE, TENKESSEE 379163
Kinetics of Ionic Processes in the Radiolysis of Liquid Cyclohexane' BY FFRANCOK ~YILLIAMS RECEIVED MAY8, 1964 Ammonia-d3 has been used as a proton scavenger in the radiolysis of liquid cyclohexane. The kinetics of proton transfer from cyclohexane ions have been studied by measuring the yield of H D as a function of S D 3 concentration. In agreement with other work, the G-yield of free ions is 0.08. The majority of ions undergo geminate recombination, b u t it is estimated that the lifetimes of about half these ions lie in the range 10-9 to 10-7 sec. Ionic reactions can therefore proceed in the presence of high concentrations of a very reactive scavenger. A simple diffusion model of geminate ionic recombination predicts a lifetime for the ion pair which varies as the cube of the initial separation distance. Calculations according to this model are in semiquantitative agreement with the experimental results
Introduction
terized by rate constants in excess of 1 0 9 .If-' sec - l , l * an investigation of exothermic proton transfer from Previous work has demonstrated that ionic intercyclohexane ions to S D s appeared to be feasible, esmediates are responsible for the radiation-induced polymerization of i s o b ~ t y l e n e , ~a~- m e t h y l ~ t y r e n e , ~ pecially in view of the fact that ion-molecule reactions of this type are known t o occur for hydrocarbon ions in and ~ y c l o p e n t a d i e n e . ~From a study of the latter systhe mass spectrometer. l a Neglecting any isotope effect, temj5i t has been deduced t h a t while the individual ion the neutralization of SD3H product ions is assumed to lifetime during propagation is of the order of lOP3sec., give D atoms with a statistical probability of 3 : 4, folthe yield of ionic initiators is rather low, and correlowed by hydrogen atom abstraction from the cyclosponds to a 100-e.v. yield (G-value) of about 0.2. Rehexane solvent to form H D . Accordingly, the extent cently, conductivity and mobility measurements on of proton transfer can be evaluated from the fraction of radiolytic ions in saturated hydro~arbons6,~ have proH D in the hydrogen gas produced during radiolysis. vided two determinations of the G-yield of free ions,8 Preliminary results5 on this system showed that the v i z . , 0.09 0.04 (Allen and Humme16) and ca. 0 . 2 order of magnitude of H D formation could not be ac(Freeman'). The similarity between the G-values for counted for in the absence of reactivity transfer from the initiation of ionic polymerization and for free ions cyclohexane to ammonia. The possibility t h a t signifsuggests a common identity, and this proposition is icant amounts of H D could arise by some means other supported by calculations on the lifetime of these ions. than proton transfer seems remote; ammonia is relaThe clear implication of the low G-value for free ions tively unreactive to hydrogen atoms'? and apparently in liquid hydrocarbons is t h a t most ions (G ca. 3) does not attach electrons in a saturated hydrocarbon undergo fast geminate recombination,6 but the imglass, while positive charge transfer from cyclohexane portant question remains as t o the time scale of this to ammonia would be endothermic.6 process. Even if the mean lifetime, T , of an ion with respect t o geminate recombination is much less than Experimental sec., the ion will react with a scavenger molecule Eastman Spectrogrdde cyclohexane was passed through a present in a concentration [SIwith a probability excolumn of activated silica gel and degassed on a vacuum line. ceeding 0.5 provided 7 1:'kS[SIjwhere ks is the rate Subsequently, the cyclohexane was distilled twice zn tlacuo onto fresh sodium mirrors; after t h e liquid had been left in contact constant for the ion-molecule reaction. Thus, inforwith the sodium surfaces for periods of hours, a sample was finally mation bearing on the kinetics of geminate ionic redistilled into a cylindrical Pyrex glass ampoule of about 30-mi. combination can be obtained by the use of a very reaccapacity. These ampoules were fitted with a diaphragm breaktive scavenger,l0 and this paper reports a study along seal a t the closed end and the join to the vacuum line was suitably these lines. constricted. Ammonia-& (Merck Sharp and Dohme of Canada Ltd.) was freed from traces of air and moisture by pumping on the The choice of a suitable system was influenced by condensed solid after trap-to-trap distillation onto sodium metal several considerations. Since our previous experience surfaces For each experiment, a prescribed volume of ammoniahad already indicated the potency of ammonia as a reda was measured in a calibrated Toepler pump under standard tarder of radiation-induced ionic p o l y m e r i ~ a t i o n , ~ ~ conditions '~ and then admitted into a n ampoule containing frozen cyclohexane a t -196'. T h e sample was sealed off a t the conand because proton transfer reactions are often charac-
*
>
(1) T h i s research is supported by t h e U . S. Atomic Energy Commission under C o n t r a c t S o . AT-(40-1)-2968. ( 2 ) W. H . T. Davison, S. H. Pinner, a n d K . Worrall, Proc. R o y . SOL. ( L o n d o n ) . A262, 187 (1939). ( 3 ) E Collinson, F . S . D a i n t o n , a n d H . A Gillis, J . P h y s . C h e m . , 63, 909 (1939) ( 4 ) 1.V ,F. Best, T . H. B a t e s , a n d F. Williams, T v o n s . Faraday Soc., 68, 1 9 2 (1962). (i) \V. K . Busler, D . H . l l a r t i n , a n d F . Williams, Discussions Faraday Soc., 3 6 , 102 (1963). 6 ) A 0 . .4llen a n d -1.H u m m e l , i b i d . , 36, !45 (1963). ,7J G . I
Vol. 86
and D 2 0 . Also, i t can be concluded t h a t the demonstration of free-ion scavenging by low concentrations of ammonia in cyclohexane provides emphatic support for the interpretation of ammonia retardation in radiationinduced cationic polymerization . 5 Turning t o the dependence of the H D yield a t higher scavenger concentration (>lo-* M), this region obviously corresponds (compare ref. 10) to the situation where ammonia is competing with the geminate recombination of ions. I t is remarkable t h a t the yield increases as the square root of the ND3 concentration, since this result parallels the predictions'0s24for scavenger competition with the geminate recombination of free radicals. For reasons given below, it is felt that this parallelism is merely accidental and without theoretical significance. First of all, a pair of ions will not undergo random diffusive displacements relative to one another because of the superimposition of their mutual Coulombic attraction on the Brownian movement. Secondly, the lifetime of an ion undergoing geminate recombination would be expected to be a rather sensitive function of initial separation distance (vzde znjra), and therefore the kinetics would in turn depend on the detailed statistics of separation Lastly, the situation is further complicated by our complete ignorance of the nature of the negative species. In the model suggested by Samuel and MageejZ5 the ejected electron was considered to be thermalized and recaptured by the parent ion in a time of about sec. However, there are many uncertainties about this calculation, especially in regard to the mechanism of energy loss sustained by the e l e c t r ~ n . ~ ~ ' ~ ' In this connection, the transient formation of negative ion states has been considered as a contributory factor 2fi It is also relevant to recall the experiments of LeBlancC3 on electron-drift mobility in liquid n-hexane. This latter work indicates t h a t electrons can migrate between low energy traps such that the electrons behave neither as free entities nor as true molecular anions. Now, in considering the time scale for geminate recombination, the nature of the negative entity is of obvious significance, and this is especially true regarding the details of the return journey after thermal equilibrium has been attained. Although the problem defies a rigorous theoretical approach, some headway can be made by considering the electron to be trapped as some kind of negative entity with molecular dimensions. The situation now corresponds to the diffusion of ions of opposite charge under the influence of their mutual Coulombic force field. .Application of the Nernst-Einstein relation leads to the equation br/bt
--bE(r)/br
-
D _ kT
where & / a t is the relative velocity a t a separation disstance r , - d E ( r ) 'dr is the Coulombic force = - e 2 ' u2,e is the absolute charge on each ion, E is the dielectric (24) J . C . Roy, R . R . Williams, J r . , a n d W. H. Hamill, J . A m . C h r m . S o c . , 76, 3274 (19.54). (2.5) A . H. Samuel a n d J . L. hfagee, J . C h e m . P h y s . , 21, 1085 (1!?5:3), ( 2 6 ) J . L. >lagee, Discussions F a r a d a y Soc., 36, 247 (1963). ( 2 7 ) > f . h f a g a t , ibid., 36, 256 (1963). (28) 0. H. LeBlanc, J r . , J . C h e m . P h r s . , 3 0 , 1443 (1959). LeBlanc obtained a value of 1 . 4 x 10-3 cm.2, v.-sec. for electron drift mobility in liquid n-hexane, which corresponds t o a diffusion coefficient of 3.5 X 10-6 cm.2 set.-' a t 300'K.
Oct. 5 , 1964
RADIOLYSIS O F LIQUIDCYCLOHEXANE
constant of the medium, D is the sum of the ionic diffusion coefficients in the medium, k is Boltzmann's constant, and 2' is the absolute temperature. Rearrangement and integration leads t o eq. 4 for the time 7 of recombination from an initial separation distance r .
I t is now of interest to calculate rCfor the separation distance I C ,defined by -E(rC) = e2/'erc = kT, where the mutual Coulombic potential energy E(rc) balances the energy of Brownian motion. T o a first approximation, r r can be identified as the maximum lifetime of a pair of ions undergoing geminate recombination. For cyclohexane as the medium, E = 2.0 and D N 2.5 X 10-5 c m . 2sec. T h e appropriate calculation reduces t o T~ = rcZli3D = 1.1 X lo-' sec. for recombination from rc = 280 A. a t 300OK. Since T is proportional to r3, a recombination time of sec. corresponds t o r = 60 A. Although this treatment based on the NernstEinstein relation may not be valid a t very short separation distancesgg owing to the large forces of attraction which will then apply, it should serve as a useful approximation for r-values of the order of 100 A. which are of primary interest t o the ensuing discussion. Returning to the experimental findings, the onset of scavenger competition with geminate recombination occurs between and M ND3 concentration (Fig. 1) ; this result corresponds to the scavenging of ions with a mean lifetime, 7, in excess of l / k s [ 1 0 - 2 ] or 10-' sec. where ks is taken as before to be lo9 .TI-' set.-'. Thus, the experimental result is in semiquantitative accord with the previous theoretical calculation of rc. Although such agreement does not prove t h a t the suggested model is correct, it is difficult t o conceive of a model based on a free electron which would allow times of this magnitude (lo-; sec.) t o elapse before geminate recombination, If the proposed model is valid, then the results a t 10-1 ,1f (after statistical correction) can be taken t o indicate t h a t a t least 14y0of the total ions achieve separation distances greater than 130 A. 1Vhether all the ions can be "captured" a t high scavenger concentration is a matter of conjecture; this will obviously depend on the radial distribution function P(r) for initial separation distances. Extrapolation of the empirical dependence of yield on the halfpower of scavenger concentration suggests that molar concentrations of a very reactive scavenger would re(29) T h e mean displacement ( d r i f t ) , A?, of a n univalent ion (mass M ) in t h e direction of t h e force during t h e relaxation time ( t = A/(8kT/rM)'/Z 2 lo-'> sec. for mean free p a t h X of 3 b.) between molecular encounters is given b y 4? = I , ' * [ - ( ? I E / b ' , ' M ] P At I = 100 A , , 41is 0.040 b., and t h e increment of energy 3 E acquired under t h e influence of t h e Coulombic force is 2 9 X 10-j e . v Hence A E , k T is of t h e order of 10-8 a t room t e m perature. and t h e excess energy is easily dissipated by subsequent repeated collisions within t h e solvent cage before t h e next j u m p , Deviations from t h e Piernst-Einstein relation might only be expected t o occur when A E 2 kT; i n t h e present case this condition corresponds t o I 19 A.
