4093
J. Phys. Chem. 1983, 87,4093-4095
Nanosecond Time-Resolved Conductivity Studies of Pulse-Ionized Ice. 2. The Mobility and Trapping of Protons Marinus Kunst and John M. Warman" Interuniversity Reactor Institute, Mekelweg 15, 2629 JB Delft, The Netherlands (Received:August 23, 1982; I n Final Form: January 13, 1983)
Above -40 "C conduction electrons formed on ionization of ice become completely immobile due to trapping at defects in the lattice within a time of approximately 1ns. Much longer-lived conductivity transients which remain after electron trapping are attributed to mobile protons. By studying these transients using the time resolved microwave conductivity technique, we have obtained information about the mobility of bare protons and the equilibrium kinetics of proton trapping by complex formation with L defects.
Introduction As pointed out in the previous paper of this series,' the mobility of conduction electrons in ice is several orders of magnitude larger than even the highest values which have ever been suggested2 for the mobility of protons in this medium. An investigation of the properties of protons formed on pulsed ionization of ice via
-+ -
H20
H 2 0 ++ e-
H20+ H 2 0
H30+ + OH.
(1) (2)
can therefore only be carried out if electrons are very rapidly immobilized by trapping at lattice defecb prior to their undergoing the recombination reaction e-
+ H30+
-
H20
+ H.
(3)
It may be considered fortunate that nature does in fact provide sufficient trapping sites in ice to result in the localization and solvation of electrons within 1 ns for temperatures above approximately -40 OC. As a result of this, when a relatively long, 50-11s ionizing pulse is applied, the electron concentration reaches a constant, equilibrium level within the pulse and decays rapidly following termination of the pulse. after electron decay a conductivity transient with a half-life of tens to hundreds of nanoseconds remains and it is this which has been ascribed to the presence of mobile protons. In the present paper we pay particular attention to the kinetics of trapping of the initially "bare" protons. Experimental Section All of the measurements reported in the present paper were carried out with the microwave conductivity technique described p r e v i ~ u s l y . ~ -The ~ sample preparation procedure was the same as that used for the electron studies. The total dose in the 50-11s pulses used was on the order of 1 krd which would be expected to yield a concentration of approximately lo4 M of protons at -5 "C and a factor of ca. 3 less at -40 "C. (1) M. P. de Haas, M. Kunst, J. M. Warman, and J. B. Verberne, J. Phys. Chem., this issue. (2) P. V. Hobbs, 'Ice Physics", Clarendon, Oxford, 1974. (3) M. P. de Haas, Ph.D. Thesis, University of Leiden, The Netherlands, 1977. (4) P. P. Infelta, M. P. de Haas, and J. M. Warman, Radiat. Phys. Chem., 10, 353 (1977). (5) J. M. Warman in 'The Study of Fast Processes and Transient Species by Electron Pulse Radiolysis", J. H. Bagendale and F. Busi, Ed., Reidel, Boston, 1982, p 129.
Results a n d Discussion In Figure 1are shown the conductivity transients which remain after a 50-11s pulse of irradiation for temperatures in the range -5 to -40 OC. Since conduction electrons are known to have become completely localized on a time scale much shorter than these observation^^^' via e-
+T
-
eT-
-+
esoi
(4)
it is concluded that the conductivity observed results from the presence of mobile protons. If the transients were in fact due to a small thermal equilibrium concentration of electrons in the conduction band state then a marked decrease in the height of the signals with decreasing temperature would have been expected. As can be seen, if anything the signal height tends to display a temperature dependence in the opposite direction. It can be seen from the data in Figure 1 that the proton signal decreases after the pulse over a time scale of tens to hundreds of nanoseconds with the decay rate becoming slower as the temperature is lowered. Furthermore, the conductivity is seen not to decay completely to zero but to approach a plateau value. The decay rate is found to be independent of the dose in the pulse indicating that bare protons are being trapped by an intrinsic defect in the lattice rather than by reaction with other products of irradiation. Complexing of protons with L defects has been proposed by several authors in the past and we believe that this process is responsible for the decay observed in the present case. The reverse reaction of thermal dissociation of the complex is taken to be responsible for the fact that the decay is incomplete: H3Of.l
-
+ 15 H30+.12 k-i
(5)
If the trapped proton is taken to be immobile, it is apparent that the final plateau conductivity signal relative to the initial conductivity will be a measure of the fraction of protons in the mobile state a t equilibrium. It is of interest to note that while the end-of-pulse conductivity signals tend to be almost equal (see Figure l),the equilibrium level reached a t long times (see Figure 2) is significantly lower at the lower temperatures. This is as would be expected for an equilibrium trapping situation as represented by (5). On a time scale of several microseconds the conductivity signal which appeared as a plateau on the faster time scale (6)J. M. Warman and C. D. Jonah, Chem. Phys. Lett., 79,43 (1981). (7) J. M. Warman, M. Kunst, and C. D. Jonah, J . Phys. Chem., this issue.
0022-3654/83/2087-4093$01.50/00 1983 American Chemical Society
4094
Kunst and Warman
The Journal of Physical Chemistty, Vol. 87, No. 21, 1983 _-_-
__
TABLE I : Proton Yield, Mobility, and Relaxation Parameters in Ice G,-
(H+):
a
temp, "C
(100 eV)-l
-5 -13 -21 -27 -36
1.2 0.76 0.55 0.42 0.30
103~(H+), 10-7 x cmz k,N,,
v-1
s-l
5.3 8.4 11.6 15 21
g
k,N,/
l
k-1
3.0 2.2 1.2 0.7 0.5
6 7 8 12 16
7.6 10.5 12.9 11.5 12.4
Taken equal to the initial yield of electrons, G o ( - ) __-
10-1L--7 7--T--
-
I
-
-0 I
'10 E
-2
N
0
IO0
2 00 TIME (ns)
300
400
t
U
r
L
t
-
m ' L
Flgure 1. Conductivity transients observed following ionization of ice with a 50-17s pulse of high-energy radiation at the temperatures (in "C) shown. The conductMty is considered to be due to mobile protons and the decay to immobilization of protons by complexing with L defects.
-
J
-
0
-
z
-3 IO
=
1
___-
ICr
\,
106
I
40
35 IO~/T
(OK-')
Flgure 3. Arrhenium plots of the bare proton mobility, U(H+),the equllibrium proton drift mobility, p(H+), in H,O ice and the forward rates for complexing of bare protons with L defects in H,O and D20 ice.
0
4
8 TIME
12
16
(,US)
Flgure 2. Conductivity transients observed on a microsecond time scale, using a microwave cavity technique, following ionization of ice with a 50-17spulse of high-energy radiation at the temperatures (in "C) shown. The conductivity is considered to be due to mobile protons in euilibrium with proton-L defect complexes and the decay to recombination with trapped electrons.
of Figure 1eventually decays to zero as is shown in Figure 2. The rate of this long time decay is found to increase with increasing dose in the pulse and is therefore ascribed to the eventual recombination of protons with solvated electrons
-
H30+.l+ ego
(10)C.Jaccard in "Water and Aqueous Solutions", R. A. Horne, Ed., Wiley, London, 1972. (11) V. Eckener, D. Helmreich, and H. Engelhardt, Proc. Int. Symp. Phys. Chem. Ice, 242 (1973). (12)H. Engelhardt, B. Bullemer, and N. Riehl, Proc. Int. Symp. Phys. Chem. Ice, 430 (1973). (13)M. Kunst and J. M. Warman, Nature (London),288,465(1980). (14)P. Gosar and M. Pintar, Phys. Status Solidi, 4, 675 (1964). (15)S.F. Fischer and G. L. Hofacker, Proc. Int. Symp. Phys. Chem. Ice, 369 (1969). (16)G. G. Roberts, N. Apsley, and R. W. Munn, Phys. Rep., 60,59 (1980).
The Journal of Physical Chemistry, Vol. 87, No. 21, 1983 4095
M(H+)/M(D+)k 1.3. This does not change the initial conclusion that the main charge interaction is with the translational mode. It should perhaps be emphasized that M(H+) is the high-frequency mobility of bare protons. For experiments carried out a t low frequencies and under equilibrium conditions account must be taken of the polarization of the medium which occurs on proton displacement and also of the effects of temporary localization which will be discussed in the next session. Proton Trapping. Arrhenius plots of the proton and deuteron trapping rates, klNl, are shown in Figure 3. The straight lines drawn through the points corresponding to
klNl = A exp(-Ee/kBT)
(10)
give for H 2 0 and D20, respectively, A = 1.56 X 1014and 0.84 X 1014 s-' and, E = 0.36 and 0.35 eV. If the rate constant for the forward reaction, kl, is taken to be proportional to M(H+),which would seem reasonable, then the activation energy associated with N,, the L defect concentration, is found to be 0.36 + 0.22 = 0.58 eV. This is similar to the activation energy found for the defect responsible for electron localization' but is considerably greater than the "accepted" literature value of 0.34 eV for L defect formations2 the latter value is based on an estimate of a positive activation energy of 0.24 eV for the mobility of the L defect. If the value of 0.58 eV, derived from the present work, is correct then one would have to conclude that L defect transport occurs in fact with almost zero activation energy. A parameter of further interest is the binding energy, AH1, of the proton-L defect complex which can be obtained from the slope of an Arrhenius plot of the equlibrium constant. The value found is 0.19 eV which gives for the total activation energy for dissociation of the complex a value of 0.19 + 0.36 = 0.55 eV. As mentioned previously, the effective drift mobility of protons under conditions of equilibrium trapping will be proportional to the fraction of protons in the mobile state and will be given by
For pure ice the value of K1 = klNl/k_' is available from the present measurements and from these values the effective proton mobility can be calculated. This is given in the last column of Table I and plotted in Figure 3. As can be seen apart from a possible slight decrease above -10 "C p(H+)can be taken to be independent of temperature and equal to 1.2 x cm2 V-l s-' . On the basis of this, the minimum value of the low-frequency conductivity of ice of 4 X lo* mho/m17 at close to the melting point would correspond to a proton concentration of 3.5 X M. Registry No. HzO, 7732-18-5; H+,12408-02-5. (17)L.Onsager, Proc. Int. Symp. Phys. Chem. Ice, 7 (1973).
