Electron tunnelling in frozen aqueous solutions at 77 K

Int. J. Radiat. Phys. Chem. 1973, Vol. 5, pp. 243-245. Pergamon Press. Printed in Great Britain

L E T T E R TO T H E E D I T O R

Electron tunnelling in frozen aqueous solutions at 77 K J. KROH and Cz. STRADOWSKI Institute of Radiation Chemistry, Technical University, L6d~, Poland (Received 2 June 1972; in revised form 3 January 1973)

Abstract--The decrease in concentration of stabilized electrons in frozen aqueous solutions at 77 K is described and assigned to tunnelling.

OUR P R E V I O U S investigations m indicated that the stabilized electrons e s- in alkaline ice may undergo tunnelling to adjacent scavenger molecules. Similar conclusions have been reached by Mikhailov t2) and---in the case of organic matrices--by Miller t3). In order to test this hypothesis, the following experiments were carried out. Glassy samples of 8 mol dm -a N a O H with various scavengers NOa-, NO2-, CnHsO-, CHzC1COO- were irradiated with X-rays, and then the absorption spectra were recorded with a Beckman D K 2 A spectrophotometer. In all cases a decrease in optical density (O.D.) was observed in the visible range of the spectrum during storage at 77 K. However, O.D. decays more rapidly at the red end of the spectrum than at the blue end. A typical decrease in absorption for various wavelengths A is presented in a half-logarithmic plot on Fig. 1. An effort was made to explain this

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Fro. 1. Half-logarithmic plot of the decrease of absorption A for electrons stabilized in 8 mol dm -3 NaOH containing 0'05 tool dm -3 NaNOa as measured at different wavelengths. : x 550 n m ; © : 600 nm; + : 650 nm; [] : 700 rim; V : 750 rim. situation in terms of two basic assumptions. Firstly, we believe that excited energy levels of e~- are not bound, and the energy of optical excitation corresponds to the trap depth. Secondly, the experimentally observed optical spectrum of e s - represents a superposition of m a n y spectra of electrons occupying traps with different depths. Hence, the kinetics of absorption decrease should be complex. The rate of decay for 243

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X-T,~ nm-~2 Fig. 2. C o r r e l a t i o n b e t w e e n t h e slope k o f t h e curves o f Fig. 1 a n d t h e wavelength, x : log kl ,~ vs h - t , w h e r e kl is t h e initial slope o f t h e curves f r o m Fig. ] a for 8 m o l d m -3 N a O H with 0'05 m o l d i n -3 N O B - ; O : log k S ,~ vs ~-~ for 8 m o l d m - s N a O H with 0-05 m o l d m -3 N O z - , w h e r e ks is t h e slope o f t h e s e c o n d linear f r a g m e n t o f decay; + : log k2 ,~ vs ,~-~ for 8 tool d m -3 N a O H c o n t a i n i n g 0.025 tool d m -~ N O 3 - ; [] : log k 2 A vs 2~-~ for 8 tool d m -z N a O H with 0-010 tool d m -z N O z - .

Letter to the Editor

245

a given A is the sum of the rates characterized by various rate constants. As was reported by us t4), such kinetics could be approximately considered as composed of two processes with two different rate constants. Thus, one might look for the correlation between the wavelength and the slopes, k 4 and ks, of straight fragments in Fig. 1 ; the initial portions of the curves of Fig. 1, giving kl, are shown in Fig. la. The transparency T of a one-dimensional potential well can be expressed as (1)

T = A exp ( - Ka),

where Kz = 2m/h 2 ( V - E ) ; m is the electron mass, ( V - E ) is the height of the energy barrier, A is a constant, and a is the distance between e s- and the scavenger molecule. The rate constant, k, of tunnelling is proportional to the transparency of the energy barrier and to the frequency of the oscillations of the trapped electron in its ground state, this frequency being, as a first approximation, proportional to the frequency of the light absorbed by es-. Taking our previous assumptions into account one can expect a straight line dependence in the system logkA vs A-~. Such plots for 8 mol dm -z N a O H containing NO3- are shown in Fig. 2. Experimental points fulfil fairly well the expected correlation. Moreover, the slopes of the lines in Fig. 2 are very slightly dependent on [NOz-]. This may be in agreement with equation (1), according to which the slopes should be proportional to [NO3-]-~. A similar log k = f(A)-½ linear dependence has been observed by us for the following aqueous matrices: 50 per cent (CH2OH)2, 5 m o l d m -3 K~CO 3, 8 mol dm -3 NaOH, 8 m o l d m -3 HCOONa, 15 mol dm -3 LiC1 and 8 mol dm -a INaC104. All of these solutions contained 0.025 m o l d m -3 N a N O s. Thus, the tunnelling of e s- to scavenger molecules seems to be a common phenomenon in glassy aqueous matrices. REFERENCES 1. J. KROH and Cz. STRADOWSrd, Radiochem. radioanaL Lett. 1972, 9, 169. 2. R. F. KHAIROATDINOV, A. Y. MIKHAILOV, K. J. ZAMARAEV and W. J. GOLDANSKIJ, Dokl. Akad. Nauk SSSR, 1971, 199, 690. 3. J. R. MILLER, J. chem. Phys. 1972, 56, 5173. 4. J. KROH, J. MAYER and Cz. STRADOWSKI, Radiochem. radioanal. Lett. 1969, 2, 209.

R6sum6---Les auteurs d6crivent la diminution de la concentration des 61ectrons stabilis6s dans les

solutions aqueuses congel~s tt 77 K et attribuent ce ph6nom6ne/~ un effet tunnel. Zusammenfassung--Das A b n e h m e n bei 77 K der Konzentration yon stabilisierten Elektronen wurde festgestellt. Als Ursache wird Turmeleffekt angegeben.

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