4009
J. Phys. Chem. 1983, 87, 4089-4092
Nanosecond Time-Resolved Conductivity Studies of Pulse-Ionized Ice. 1. The Mobility and Trapping of Conduction-Band Electrons in H,O and D,O Ice Matthljs P. de Haas, Marlnus Kunst, John M. Warman,’ Interuniversity Reactor Insthute, Mekeiweg 15, 2629 JB Delft, The Netherlands
and Johan B. Verberne Blophyslcs Department, Free University, De Boelelaan 108 1, Amsterdam, The Netherlands (Received: August 23, 1982; I n Final Form: January 13, 1983)
The properties of electrons in the conduction bands of HzO and DzO ice have been investigated by ionizing the media with short pulses of high-energy radiation. Nanosecond time resolution dc and microwave conductivity techniques are used to detect the transient high-mobility electrons formed. Information on the mobility and the kinetics of the reaction of electrons with point defects in ice is presented and discussed. Introduction The electronic properties of crystalline solids have been the subject of intensive study for many years. Until recently these studies were limited to perfect lattice systems of atomic entities. In the past decade or so, however, interest in more complex molecular solids and in amorphous materials has gradually evolved. Despite this, information on the behavior of excess electrons in hydrogen-bonded molecular solids is lacking. Ice, with its lattice ordering of oxygen atoms but complete disorder in proton positioning, would seem to be a system particularly worthy of study. Apart from the unusual lattice characteristics of ice, its pervasive presence as a major constituent of many heavenly bodies, not least of which the earth, together with its frequent use as a model compound in discussions of charge and energy transport in hydrogen-bonded biological systems lend additional weight to the need for an understanding of the electronic and electrical properties of this compound. The involvement of the present authors in studies of the electronic and, indirectly, the electrical properties of ice stems from an interest of radiation chemists in the behavior of excess electrons in molecular media in general and in aqueous systems in particular. Because of the large bandgap of ice (ca. 10 eV1) its electronic properties can only be studied by applying an external stimulus to excite bound valence electrons to the conduction level. For this purpose we have subjected crystalline ice samples to short pulses (ca. 1 ns) of highenergy, ionizing radiation (3-MeV electrons or X rays). During the short time that the conducting state is populated ( S O + s) the properties of the excess electrons are probed by measuring the transient conductivity changes resulting from the ionizing pulse. Both dc and microwave conductivity detection techniques have been applied. It has been determinedZ8that highly mobile, conduction band electrons in ice have a mobility of 25 f 10 cm2 V-’ s-l which is temperature independent, within the error limits, from -60 to -120 O C . For comparison, this mobility is lo4 times greater than that of the proton in ice. The formation and decay kinetics of conduction electrons have been found to be quite well described by the reaction mechanism: (1)M.Seki, K. Kobayashi, and J. Nakahara, J.Phys. SOC.Jpn., 50, 2643 (1981). (2) J. B. Verberne, H. Loman, J. M. Warman, M. P. de Haas, A. Hummel, and L. Prinsen, Nature (London),272,343 (1978). (3)J. M. Warman, M. P. de Haas, and J. B. Verberne, J . Phys. Chem., 84, 1240 (1980). 0022-3654/83/2087-4089$0 1.50/0
--- + + - + + + + -
H20+ e-
H,O
Hz0’ e-
H2O
k,
H30’
OH.
H ~ O H.
H30’ e-
(1)
T
kT
eT-
(2)
(3)
(4)
The initial ionization process (eq 1) is expected to be followed within a few 0-H vibrations (i.e., on the order of 1ps or less) by the proton transfer reaction 2. In pure ice the conduction electrons, e-, have been found to decay either via recombination with the extrinsically produced H30+ions, the rate of which is temperature independent, or via localization at intrinsic defects, T , in the lattice, reaction 4, with the rate, kTNT, being highly thermally activated. In the present paper, attention is focused on (a) a comparison of the results obtained from the dc and microwave detection methods, (b) the effect of isotopic substitution on electron dynamics, and (c) the relationship between the electronic and the dielectric properties of ice. Experimental Section In Figure 1 are shown schematically the cells used for the dc and microwave conductivity measurements. In the dc measurements the current between the electrodes resulting from a pulse of X rays is measured. The part of the cell containing the ice sample is 5 cm long and has a coaxial electrode geometry with inner and outer electrode radii of 0.085 and 0.27 cm, respectively. In the microwave (X-band) experiments the transient conductivity resulting from pulse irradiation with 3-MeV electrons is determined by monitoring the change in microwave power reflected by the ice sample contained in a short-circuited piece of waveguide. Details of the circuitry and methods of signal monitoring and data analysis have been presented at length in other publication^.^" Both cells could be attached to glass bulbs in which deionized and then triply distilled (to remove organic impurities) water could be degassed on a vacuum line via a grease-free stopcock prior to transfer to the cell. After (4)M.P. de Haas, Ph.D. Thesis, University of Leiden, The Netherlands, 1977. (5)P. P. Infelta, M. P. de Haas, and J. M. Warman, Radiat. Phys. Chem., 10,353 (1977). (6)J. M. Warman, in “The Study of Fast Processes and Transient Species by Electron Pulse Radiolysis”, J. H. Baxendale and F. Busi, Ed., Reidel, Boston, 1982,p 129.
0 1983 American Chemical Society
4090
de Haas et al.
The Journal of Physical Chemistry, Vol. 87, No. 21, 1983
D.C. CONDUCTIVITY
-
50Cl AIR LINE
X - rays 1
'
ice
gloss
MICROWAVE CONDUCT1V l T Y 3 MeV electrons
Woveguide
1 1
1
Ice
Flgure 1. Schematic illustrations of the cell designs used for timeresolved dc and microwave conductivity measurements on pulse-ionized ice.
transfer the water was frozen by gradual immersion of the cell into an ethanol bath at -10 "C. The total dose absorbed by the sample per pulse was 0.5 to 50 rd in the microwave experiments and 20 mrd in the dc experiments. These dose levels result in maximum transient concentrations of conduction electrons of 5 X lo4 and 2 X lo-" M, respectively, i.e., less than 1 ppb in all cases.
Results and Discussion Comparison of dc and Microwave Measurements. In Figure 2, conductivity transients, normalized to the total dose in the pulse, obtained with the two techniques are compared. The absolute magnitudes of the signals and the rates of decay are seen to be in fairly good agreement. It would appear therefore that the same species is being monitored in both cases and that this species is ionic in nature rather than dipolar. The dc data were more subject to noise and oscillations induced by the accelerator pulse, as can be seen in Figure 2, and were in general less reproducible from sample to sample than the microwave data. This is presumably due to a greater sensitivity of the dc technique to imperfections in the crystalline medium. In addition, residual polarization and/or space charge effects made interpretation of dc data difficult for temperatures below -80 "C. Because of the above, the microwave method has been exclusively used for the study of the temperature dependence of the magnitude and kinetics of the conductivity transients. However, apart from providing evidence for ionic transport rather than dipolar relaxation, the dc method is also the only way of gaining direct information about the mobility of the major charge carrier formed and its sign. The sign can be determined for a coaxial cell geometry because inward moving ions give convex and outward moving ions concave current-time curves when the loss of ions is due to discharge at the electrode^.^,^ It was therefore with the dc method that the major charge carrier in pulse-irradiated ice could be identified as an electron and its mobility determined to be 25 f 10 cm2V-' s-l. In addition it has been found, using the dc method, (7) A. 0. Allen, M. P. de Haas, and A. Hummel, J . Chem. Phys., 64, 2587 (1976). (8) J. M. Warman, M. Kunst, M. P. de Haas, and J. B. Verberne, J . Electrost., 12, 115 (1982).
that the effective dielectric constant for geminate electron positive ion recombination is 2.6 f 0.6.8 The Yield-Mobility Product. From the magnitude of the conductivity transients obtained with the microwave technique and the known dosimetry it is possible to determine the product of the electron mobility, p(-), and the initial yield of electrons per 100 eV adsorbed, Go(-). The value for H 2 0 ice has been found to be independent of temperature and equal to 3.4 f 0.3 cm2V-l s-l (100 eV)-' over the range -120 to -60 "C. Over this same range a very slight decrease from 6.0 to 5.1 cm2 V-' s-l (100 eV)-' has been found for D20 ice. This decrease is within the estimated f 10% accuracy of the determinations, however, and for all intents and purposes GO(-)p(-) for D20 can be taken to be independent of temperature and equal to 5.5 f 0.5 cm2 V-l s-l (100 eV)-'. The larger value of GO(-)p(-) in D20 than in H20 could be due to either a greater yield of electrons or a higher electron mobility for the heavier isotope. Optical absorption measurements of solvated electron formation at close to the melting point indicate the electron yields in H20 and D20 ice are closely similarg although this conclusion depends to a certain extent on assumptions about the extinction coefficient of the solvated electron. In water it is known that the yield of electrons is in fact significantly larger for the heavier isotope.1° Since higher escaped yields of electrons are usually associated with higher conduction-band mobilities it is quite probable that the difference in GO(-)p(-) between H 2 0 and D20 ice is due to both Go(-) and p ( - ) being somewhat larger (by 25-30%) for the latter compound. Since the yield of electrons is expected to increase with increasing temperature due to a decrease in the Onsager escape distance, the temperature independence of Go(-)p(-) may be taken to indicate a slight decrease in the electron mobility with increasing temperature. Electron Decay Kinetics. As mentioned in the Introduction, the removal of electrons from the conduction band in pulse-irradiated ice may occur either by reaction with extrinsic trapping sites (mainly protons) produced concurrently by the radiation, or by localization at intrinsic defects present prior to irradiation. The extrinsic and intrinsic decay components can be separated by measuring the effect on the decay rate of changing the total dose in the ionizing pulse.3 In this way it is found that the diffusion-controlled process of recombination with protons, reaction 3, occurs with an effective dielectric constant of t e f f= 2.0 f 0.2. From the electron mobility of 25 f 10 cm2 V-l s-l and the Debye relation for the recombination rate constant
k~ = pe/tOteff
(5)
the value of k R is then found to be 1.4 X 10l6M-ls-l. In anticipation of doping experiments it is worth mentioning that, on the basis of this rate constant, a concentration of only one part per billion of protons would be sufficient to reduce the lifetime of electrons in the conduction band to only 1 ns. The reaction with intrinsic defects is very strongly dependent on temperature. In Figure 3 Arrhenius type plots of the intrinsic trapping rate, kTNT,are shown for H20and D20 ice. Above approximately -70 "C a linear dependence of such plots is observed with a corresponding "activation energy" of 0.55 f 0.05 eV. Below -70 "C such Arrhenius plots are found to flatten out (activation energy close to (9) G. N h o n , H. Christensen, P. Pagsberg, and S. 0. Nielsen, J.Phys. Chem., 76, 1000 (1972). (10) E. M. Fielden and E. J. Hart, Radiat. Res., 33, 426 (1968).
Conduction-Band Electrons in H,O and D,O Ice
The Journal of Physical Chemistry, Vol. 87, No. 21, 1983 4091
I
I
I
I
I
A
t 4
jz t 3 E W
a
0
5
15
IO Time (ns)
Time (ns)
Figure 2. The dose-normalized transient conductivity changes resulting from pulsed ionization of ice at the temperatures shown: (A) microwave measurements with 0.5-ns pulses of 3-MeV electrons: (B) dc measurements wlth 2 4 s pulses of 3-MeV X rays with an applied voltage of 200 V. 1o1O
t
!
:?
1
0 0
IO6
'
I
I
I
4
5
6
IO~/T
PK-I)
Figure 3. Arrhenius plots of the rate of trapping of conduction electrons at intrinsic defects in H,O, 0,and D20, 0, ice. The dashed lines in the figure are given by 2.50 X 106/7, where T , Is the dielectric relaxation time as reported by Auty and Cole."
zero) with the absolute plateau value of kTNTbeing somewhat irreproducible within the range (2-5) X lo6 s-l for HzOice and somewhat lower for heavy ice. As can be seen in Figure 3, the electron decay rates are slower a t all temperatures for D20 ice by approximately a factor of two. Since the electron mobility in DzO ice, as discussed above, is expected to be, if anything, slightly larger than in HzO ice, the lower value of the intrinsic trapping rate of electrons in DzO would appear to be due to a lower concentration of the defect responsible for trapping. Nature o f the Intrinsic Electron Trap. The optical absorption spectrum of the final, fully relaxed state of the trapped electron in ice9J1J2resembles very closely that of the solvated electron in water with no discontinuity in the (11)V. N.Shubin, V. A. Zhigunov, V. I. Zolotarevsky, and P.Dolin, Nature (London), 212,1002 (1966). (12)I. A. Taub and K. Eiben, J. Chem. Phys.,49,2499 (1968).
position of the absorption maximum at ca. 1.8 eV being found on melting.12 This strongly suggests the same basic microscopic structure for the solvated state in both media. Present opinion, based on theoretical considerations and ESR studies of electrons in low-temperature aqueous glasses,13 tends to favor a cavity model for the solvated electron, Le., a model in which the electron occupies a void surrounded by oriented water molecules. This being the case, the initial localization process in ice must therefore involve trapping at a vacant position in the lattice. The maximum possible value for the rate constant for localization of a quasi-free electron at an uncharged site14J6 is 3 X 1014M-' s- at close to the melting point of ice. This value would result in the requirement of a concentration M of vacancies in order to explain the of at least 3 X 100-ps localization time measured at -5 O C . Until recently this concentration of vacancies, even at close to the melting point, would have been considered excessive since the activation energy for vacancy formation was generally considered to be approximately 0.6 eV.16 Positronium lifetime measurements" in ice and a more detailed consideration of the vacancy controlled diffusion process18 have, however, resulted in a considerable downward revision of the activation energy to approximately 0.3 eV. The above requirement of a vacancy concentration of at least 3 X M at -5 "C is therefore readily satisfied and even concentrations as high as M would appear to be possible. An activation energy of only 0.3 eV for vacancy formation presents, however, a problem since this is 0.25 eV less than the activation energy found for electron trapping. If this extra energy were due to the rate constant for localization, k T , being thermally activated, then the maximum value of kT would be reduced from 3 X 1014to 6 X lo9 M-l s-l at -5 OC. This would in turn result in the requirement of a vacancy concentration of 1.7 M which is outside the realms of possibility. Localization of conduction electrons by interaction with vacancies alone would therefore appear to be excluded. The possibility that Bjerrum type orientational defects may play a role in the initial trapping of electrons is suggested by the remarkably good correspondence found between the electron localization rate and the dielectric re(13)L. Kevan, J. Phys.Chem., 85, 1628 (1981). (14)N. F. Mott and H. S. W. Massey, "The Theory of Atomic Collisions", Oxford Clarendon Press, London, 1975,p 185. (15)J. M. Warman and M. C. Sauer, Int. J. Radiat. Phys.Chem., 3, 273 (1971). (16)P.V. Hobbs, 'Ice Physics", Clarendon, Oxford, 1974. (17)0. E.Mogensen and M. Eldlrup, J. Glaciol., 21, 85 (1978). (18)0.E. Mogensen and M. Eldrup, Phys.Lett. A , 60,325 (1977).
The Journal of Physical Chemistry, Vol. 87, No. 21, 1983
4092
Point ~
Ion,c
Defects
in I c e
Bierrum
might be considered to be ideal centers for the initial localization of conduction electrons. If the net charge of the DV defect is taken to be +0.38 e then an upper limit for the rate constant for reaction with an electron will be given by a modified form of the Debye equation, i.e. 0.38e p ( - )
Vocancy
f ’E
-i
de Haas et al.
7% 7 1
kDV
Dressed V o c o n c y
’p77”i”S7
Figure 4. Nonrandom, linear- and square-lattice representations of the formation of ionic, orientational, and vacancy point defects in ice.
laxation rate, k, = l / ~ , .This is shown in Figure 3 by the dashed lines which correspond to 2.5 X 105k,with k, being obtained from relationship 6 for the dielectric relaxation T,
= A exp(E/kT)
(6)
time by using the literature values of A = 5.3 X and 7.7 X s and E = 0.57 and 0.58 eV for H20 and D20 ice, respe~tive1y.l~ Above approximately -70 “C the dielectric relaxation rate of pure ice is considered to be almost completely controlled by the Bjerrum L defect and is expected to be given by20 om- 0, eLp(L)NL z k, = (7) €o(t, -
em)
€o(t, -- e m )
where eL, p(L), and NLare the charge, mobility, and concentration of L defects. Since the L defect itself is net negatively charged, eL = 0.38 e, it is its partner, the D defect, which would be the candidate most likely to be involved in the process of electron localization. The finding that the dopant NH3 increases the rate of electron localizationZ1tends to lend support to the role of the D defect in the trapping process. It has been suggested by several authors over the years, in particular by Kroger,22that D defects may form complexes with vacancies and if the latter were to be present in sufficient amount that in fact all D defects would be present as such “dressed vacancy”, DV, complexes. (A simple two-dimensional lattice representation of the point defects in ice including the dressed vacancy is given in Figure 4.) Such iiet positively charged, cavity type defects (19) R. P. Auty and R. H. Cole, J . Chem. Phys., 20, 1309 (1952). (20) G. C. Camplin and J. W. Glen, “Physics and Chemistry of Ice”, Royal Society of Canada, Ottawa, Canada, 1973, p 256. (21) M. Kunst, J. M. Warman, M. P. de Haas, and J. B. Verberne, J . Phys. Chem., this issue. (22) F. A. Kroger, “The Chemistry of Imperfect Crystals”, Vol. 2, North Holland, Amsterdam, 1974, Chapter 18.
=
Weff
(8)
Taking teff = 2.0 as found for reaction between electrons and protons and p(-) = 25 cm2V-’s-l gives kDv = 5 X 1015 M-’ s-’. A minimum concentration of DV defects of 2 x lo4 M would therefore be required to explain the electron localization rate at -5 “C. This is certainly compatible with recent vacancy concentration estimates as discussed above and with estimates of the concentration of orientational defects.16 If all D defects are complexed with vacancies then the activation energy of electron localization should reflect the activation energy associated with the D defect, and hence L defect, concentration since the rate constant is expected to be only weakly dependent on temperature via p(-). The value of 0.55 eV found for localization is, however, considerably larger than the 0.34 eV estimated for NL. The latter value is based on dielectric measurements on HFdoped ice samples from which it was concluded that the activation energy for the mobility of the L defect was approximately 0.2 eV.16 If the higher value for the activation energy of formation were correct then one would be forced to conclude that the activation energy associated with p(L) was in fact close to zero. Studies of electron localization in doped ice samples should help to clarify this point. A preliminary, qualitative discussion of such results is given in a subsequent paper.21 On the basis of the rate of electron localization being controlled by the Bjerrum defect concentration it is possible to derive a relatively simple, approximate relationship between the electron trapping rate, kTNT, and the dielectric relaxation rate, k,,as given by ( 7 ) . Thus, from eq 8, the trapping rate will be given by 0.38ep(-)ND/tOteff and since 0.38e = leLl and ND = NL then
From the actual factor of 2.5 X lo5 found and taking t, = 100 and em teff = 2 one arrives at the conclusion that p(L) 31 2 X p(-). Using the value of p(-) = 25 cm2 V-l s-l for the electron mobility determined in the dc conductivity experiments therefore leads to an estimate of a temperature-independent value of the mobility of L defects of approximately 5 X cm2 V-l s-l. This is somewhat higher than previous estimates16 but not outrageously so and, perhaps interestingly, is very similar in magnitude to the bare proton mobility which is discussed in the following paper of this series. Registry No. D20, 7789-20-0; HzO,7732-18-5.
