DC conductivity of silica xerogels

ELSEMER

Journal of Non-CrystallineSolids 194 (1996) 241-255

DC conductivity of silica xerogels H. Sodolski

*,

M. Kozlowski

Department of Applied Physics and Mathematics, Technical University of Gdatisk, Narutowicta

II / 12,80-952

Gdaiisk, Pokmd

Received5 January 1995;revised 25 July 1995

Abstract

DC conduction of silica xerogels has been investigated in an equilibrium state with the atmosphere. and under decreased pressure (down to p = 4 X 10m3 Pa). The results obtained indicate conduction of ionic character, determined by the state of internal surfaces of xerogel pores. This state may be modified by the sorption/desorption processes of water vapour and thermal treatment of gel in vacuum. Changes of xerogel structure accompanying these processes have been detected in infrared spectra. In equilibrium with the atmosphere, the conduction of xerogels is ohmic due to strong sorption of H,O molecules. Under decreased pressure, the conductivity, u, of xerogels decreases about eight orders of magnitude (from u= lo-’ R-’ cm-’ to UN IO- I4 a-’ cm-‘) and non-ohmic and polarization effects occur. These effects can be explained in terms of the field-enhanced mobility ‘theory taking into account internal polarization of xerogels or, under certain assumptions, in terms of the Onsager theory.

1. Introduction

Among the increasing number of publications on the physics of xerogels, there are papers concerning their electrical propertie&-71. There are at least two reasons to stimulate this direction of research. First of all, silica xerogels have a unique amorphous structure with a high degree of porosity, and the mechanism of electrical conduction of these structures is not well known. The study of the electrical properties of gel matrices is also important because of their function as host structures [4-61. The porous structure of gels can be easily modified by chemical or physical methods and, thus, the

Corresponding author: Tel: +48-58 472 704. Telefax: +4858 472 821. E-mail: [email protected]. ??

0022-3093/%/$15.00 0 1996 SSDI 0022-3093(95)00505-6

influence of the gel structure on the electrical properties of gel matrix or gel with guest molecules may be examined. In the case of silica gel, one of the ways of modifying the structure is to add glycol during gel preparation procedure. The addition of ethylene glyco1 (CH,OH), can strengthen dried gel [8]. It is particularly important, while investigating the properties of xerogels under decreased pressure, to avoid cracking due to capillary forces. The purpose of this work is to establish the mechanism of dc conduction in SiO, xerogels. The object of particular studies is the change in conductivity caused by the sorption and desorption of water vapour and the influence of electric field and temperature on the conductivity of SiO, xerogels. It seems that the knowledge of electrical properties of the gel matrix should be the first step in the investigation of complex doped gel structures.

Elsevier Science B.V. All rights reserved

242

H. Sodolski, M. Kodowski/Journal

of Non-Crystalline Solids 194 (19%) 241-255

2. Experimental In carrying out our measurements of dc conduction, two types of gel have been examined: basic gel (A) without glycol, and gel with the addition of glycol (B) in the molar ratio, 0.66:1 of (CH,0H),:Si(GC,H5)4. The basic gel has been prepared from the mixture of Si(OCzH& H,O and HCl in the molar ratio, 1:24.6:0.59. TEOS was mixed intensively with Hz0 for 5 min, until a suspension was obtained. Concentrated HCl was dropped slowly (a drop per minute) into the continuously mixed suspension. After dropping in 0.5 ml of HCl, a gradually increasing clarity of sol was observed. Additionally, an increase of sol temperature, due to chemical reactions, was also observed. Clarity of the sol was obtained after dropping in about 1 ml of HCl (30% of the total HCl amount). Then, the prepared sol was mixed for another 2 h and, after that time, the sol was poured into polyethylene vessels, which were placed in a heater under cover. Glycol was introduced into the mixture before hydrolysis. Drying of the gels was similar to the procedure described in Ref. [8] and consisted of the following steps: (i) gelation (T= 323-328 K, r = 5 h), (ii) drying (T = 368 K, t = 15 h), (iii) hardening (T = 393 K, t = 3 h> and (iv> a vacuum test (T= 393 K, p = 50 Pa, f = 1 h). The aim of a vacuum test is the elimination of sample cracking under decreased pressure at higher temperatures. The cracking is probably due to the presence of closed pores in some of the samples. Passing the vacuum test guarantees that the samples will not crack during evaporation of electrodes or upon measurements of conduction at decreased pressure. Some samples were additionally heated in vacuum (p = 4 X 10e3 Pa, t = 1 h) at the temperatures of 423, 473 and 523 K. These samples are referred to as Bl, A2, B2 and B3, respectively, in the text below. Samples of the xercgel were in the form of slabs with surfaces and thicknesses within the range of 0.5-1.0 cm2 and 0.01-0.1 cm, respectively. Gold vacuum evaporated electrodes were used. Sample conductivity was evaluated from the measurement of the current (Keithley Electrometer Model 614) flowing through the sample under dc voltage (up to 3000 V>. Temperature was stabilized with the accuracy of 0.1 K by a temperature controller operat-

ing in the PID correction system. The temperature of a thermostat was registered by a platinum sensor. Sample temperature was determined on the basis of signals from a thermocouple located in the immediate vicinity. Both sensors and the sample itself were placed in a copper measurement chamber. The chamber’s heating circuit was connected with the temperature controller. The measuring electrodes were teflon insulated. The measurement set was placed in a vacuum system. The dielectric constant of gels was determined from measurements of the capacitance of gel samples by the ac method using a semi-automatic precision bridge (BM 484) working at constant frequency, f= 1591.5 Hz, and a capacitance measuring assembly (1620-AP) (50 Hz-10 kI-Iz). The diffusion coefficient of water vapour in gel was estimated from the mass increase of gel due to sorption of H,O. Infrared spectra were measured with a standard measurement set, including a monochromator working in the range from 0.2 to 3.2 p,m, capable of vacuum measurements. Between the measurements, all the samples were stored in the same atmosphere in closed containers. Between the electrical measurements, the samples were briefly short-circuited. 3. Results 3.1. The influence of moisture on conductivity Significant influence of moisture on the electrical conductivity of polymers is known from experiment [9-121. Such influence may also be expected in relation to SiO, xerogels due to their strong hydrophility. The relation between moisture and the conductivity of xerogels was examined through the investigation of the influence of sorption and desorption of water vapour contained in air on the electrical conductivity of SiO, xerogels. Fig. 1 shows a decrease of conductivity as a function of desorption time of gel under decreased pressure (at the temperature, T = 293 K). Variation of pressure during desorption is shown in the inset of Fig. 1. As shown in Fig. 1, desorption of gel induced by pressure less than the water vapour pressure (p = 2 X lo3 Pa at T = 300 K) causes a decrease of electrical conductivity of the samples.

H. Sodolski, M. Kodowski/ Journal of Non-Crystalline Solids 194 (19%) 241-255

_F

243

lo8

E

0 g

10”

0

1o-l0 lo-l2

100

0

0

50

100

150

200

300

t [min.] Fig. 1. Decreased electrical conductivity, CT,of SO, xerogels during their &sorption under lowered pressure (A, sample A, 0, sample B; 0, sample B2). Temperature of measurement is T = 293 K. Changes of pressure are shown in the inset.

Electrical conductivity in the quasi-equilibrium state is six to eight orders of magnitude less than its initial value. There is also a significant difference in the behaviour of samples with (B) and without (A) glycol, heated at the standard temperature (T, = 393 K). The desorption-induced decrease in the conductivity of B samples is slower and about three orders of magnitude smaller than that of the type A gel. It can also be seen that additional vacuum heating of samples with glycol (B2, T,= 473 K> causes an approach of the dependences obtained for type A and type B2 gels. After obtaining steady state conductivity (p = 4 X 10e3 Pa, f = 10 h), air (humidity RH =: 85% and temperature T = 293 K) was introduced into the measuring chamber. After equalization of pressure to the atmospheric value, variation of xerogel conductivity due to air sorption was measured (see Fig. 2 for results). In the curves obtained, one can distinguish two areas: an increase of conductivity in the range, f = 50-70 min, and a much slower increase beyond this range. Good repeatability of experimental results is shown in the example of type A samples. In order to avoid effects connected with the operation of an electric field, the results from Figs. 1 and 2 were obtained from measurements of current recorded after t = 15 s from the application of the electric field E < lo3V/cm. Between the measurements, the samples remained in short circuit. Variation of the dielectric constant seems to be important for the possible processes of molecule dissociation inside gels, caused by addition of water

400 t [min.]

200

Fig. 2. Increased electrical conductivity, (r, of SiO, xerogels due to sorption of air of humidity, RH = 85% (A, sample A; 0, sample B; 0, sample B2; A, repeated measurement of sample A; T = 293 K).

due to water vapour sorption [9]. The variation of the effective dielectric constant of SiO, xerogels observed during the sorption of air (humidity RI-I = 85%) was measured for a few samples (results are shown in Fig. 3). The effective dielectric constant was determined from measurements of the capacitance of gel samples at the frequency f= 1591.5 Hz. In Fig. 3, as in the previous figures, we note a difference in behaviour between type A and type B gels. The sorption-induced increase of the dielectric constant of gels with glycol (B) is weaker by comparison with the type A samples. Fig. 1 shows a strong influence of the temperature, T,,of gel heating in vacuum on the change in gel conductivity during the process of vacuum desorption. Fig. 4 shows a similar dependence for four temperatures, T,:393,423, 473 and 523 K. After heating in a vacuum, all samples remained under &en

40 30

20 10

o0

100

200

300

400

t [min.] Fig. 3. Variation of effective dielectric constant, Q, during sorption of air of humidity, RH I: 85% (0, sample A, ??, sample B; T = 293 K). Dielectric constant, Q, was determined at fre+ quency, f = 1591.5 Hz.

H. Sodolski, M. Kodowski/Journal

244

0

50

100

150

ofNon-Crystalline Solids 194 (19%) 24X-23

200

t [min.] Fig. 4. Influence of temperature, T,, of vacuum heating of xerogels on variation of their conductivity during desorption kunple ?,T,=423K,., ? T,=473K; W,T,=523 B; O,T,=393K; K). For desotption conditions, see Fig. 1.

atmospheric pressure for a few days, obtaining a state of equilibrium with the atmosphere. The above figure shows that, only for T, = 393 K, a quasi-equilibrium state at the level of cr = lo- l2 0-i cm-’ has been obtained. For temperatures T, 2 423 K, the state of low conductivity (0~ lOTI5 n-i cm-‘) is the final stage of vacuum desorption. The rate of decrease in the conductivity of gels with glycol significantly increases with increasing temperature,

p = 2.5 Pa to the steady state at the atmospheric pressure with electric field still applied. The purpose of this experiment is to show that the repeated equilibrium state at the atmospheric pressure is obtained with a value of current about three times less than the initial equilibrium state. The above property is relevant to virgin samples, used in experiment for the first time. Obtaining the equilibrium state under decreased pressure is shown in Fig. 5(b), taking, for example, a type B sample. Before measurement, the sample was placed in vacuum (p = 4 X low3 Pa, T = 213 K) for t = 20 h, without electric field. Then the j =f dependence for E = lo3 V/cm and E = lo4 V/cm was determined. It is noticeable that the equilibrium state was obtained much faster than in Fig. 5(a), and that process is slower for higher values of E.

T,. 3.2. From non-steady to steady state The steady state of conductivity of SiO, xerogels, which may be obtained when the electric field is still being applied, depends on several factors, such as the electric field, E, pressure, temperature and gel structure. The rate of establishing an equilibrium state between the process of charge carrier generation and the processes of recombination is a complex function of the above parameters and depends on experimental conditions. Fig. S(a) shows examples of obtaining the equilibrium state for type A samples at the electric field, E = 10’ V/cm. The upper curve was obtained at the temperature, T = 293 K, in equilibrium with the atmosphere. The observed initial decrease of current and its steady value is a result of the applied electric field. After obtaining the steady state, the pressure inside the measuring chamber was decreased to p = 2.5 Pa and, after some time, returned to atmospheric pressure. The lower curve shows the transition from the steady state at

.

“; 2.5*10””

-....

.

??

.

.

b)

9 d ‘-

1.540-10

5.10-” 0 0

5

10

15 t [min.]

Fig. 5. Examples of achieving the equilibrium state of electrical cohduction, j, in silica xerogels. (a) 0, reaching the equihbrium state at atmospheric pressure; H, transition from the equilibrium state at pressure, p = 2.5 Pa, to the equilibrium state at atmospheric pressure. Both curves are obtained for an A sample at E = 10’ V/cm and T = 293 K. (b) Achieving the equilibrium state in vacuum at p= 4X 10e3 Pa and T = 293 K for a B sample (0, E = 10’ V/cm; W, E= lo4 V/cm). Before measurement, the sample stayed in vacuum for T 2 20 h without electric field.

H. Sodolski. hi. Kodowski/Journal

of Non-Crystalline Solids 194 (19%) 241-255

3.3. Ohmic and non-ohmic conduction

lo-l3

_-

The dependences presented above indicate that conductivity of silica xerogels depends on the method of preparation (types A and B), their thermal history (influence of temperature, r,) and conditions of measurement (pressure, etc.). The above factors may influence both concentration and mobility of charge carriers. In order to determine the influence of these factors on the mechanism of conduction in xerogels, dependences of conductivity, u, as a function of the electric field, E, were measured (Figs. 6 and 7). Fig. 6 shows the dependence, log a=fllog E), obtained at the temperature T = 293 K, for xerogels of type B. It is noteworthy that u =flE) is ohmic only in the case of relatively high conductivity, when the gel is in a state of equilibrium with the atmosphere (RH = 85%). Characteristics obtained under

lo-'O

60

0

lJM

“’

E b 0

100

200

300 UM

” b ‘4

6

9 -2

10-l'

IO3

10'

105

E

[v/cm]

Fig. 6. Influence of electric field, E, on conductivity, CT, of xerogels (T = 293 K). 0, sample B in the equilibrium state with the atmosphere (RH = SS%o);+ , sample B in vacuum ( p = 4 x 10V3 Pa); A, sample B2 in vacuum (p = 4X 10e3 Pa). The absence (above) or presence (center and below) of the internal polarization voltage of investigated samples is shown in the insets.

r

245

_______~_~ ._~~..

lo4

5*104

lo5

E [v/cm] Fig. 7. Log D = fllog E) dependence for xerogels of type B3 obtained in a vacuum (p = 4X 10e3 Pa) for three temperatures: 0, 320 K; 0, 377 K; A, 461.5 K.

decreased pressure are non-ohmic; the value of conductivity increases with an increase of the electric field, E. The non-ohmic a=flE) properties obtained for increasing values of E differ from those obtained for the samples initially polarized in high E field, which was then gradually decreased. The results shown in Fig. 6 were achieved using the latter method; the equilibrium current was obtained at E max (U = 3000 V), and the experimental points were determined by measuring the stationary current for gradually decreasing voltage applied to the sample. I = flu> dependences obtained for a few low values of applied voltage are shown in the insets of Fig. 6. The value of voltage corresponding to internal polarization of the investigated samples was obtained by extrapolation. Notably, the non-ohmic effect increases with a decrease of conductivity, (T, caused by increased temperature, T,, (from T, = 393 K to T, = 473 K). The value of internal polarization of samples also increases with a decrease of u. The above mentioned trends are confirmed by the a=flE) dependences shown in Fig. 7. These were obtained for B3 xerogels (T, = 523 K) at three temperatures: 320, 377 and 461.5 K. Values of the polarization electric field obtained by extrapolation decrease with increasing temperature and, for 320 and 377 K, are 1.14X lo4 and 4.9 X lo3 V/cm,

H. Sodolski, M. Kodowski/

246

Journal of Non-Crystalline

Solids 194 (19%) 241-255

respectively. For T = 461.5 K, the internal polarization of sample decays. 3.4. Thermal activation of conductivity Fig. 7 shows that conductivity, o, of silica xerogels depends on temperature. More specific measurements of B as a function of temperature (Figs. 8 and 9) indicate the activative property of these dependences. Fig. 8 shows the dependence log U= fl103/T) obtained for a type A xerogel at two values of electric field, E = lo3 V/cm and lo4 V/cm (p=4X 10e3 Pa). In order to avoid the influence of polarization, conductivity was determined from initial values of current with the electric field, E, applied for a short period of time. Between measurements, when temperature stabilized, the sample remained in short circuit. The experimental dependences, cr =fl103/T>, from Fig. 8 may be described as a superposition of two Arrhenius dependences: (+ (T) = aO, exp( - W,/RT) + gOo2exp( - W,/kT), where W, =(1.13 kO.03) eV, W,=(0.4OfO.11) eV, a,, = 2.3 X lo2 a-’ cm-’ and a,,, = 7 X lo-” R-’ cm- ‘. In the range of the higher temperatures (near T,), a deviation of experimental results from the

10-l’ ‘E .” ,0-‘2 G 0 lo-l3 lo-l4 lo-l5 lo-l6 2.4

2.6

2.6

3

3.2 lO’/T

3.4 [K’]

Fig. 8. Temperature dependence of conductivity of xerogels, (T, obtained in a vacuum (sample A, p = 4X 10m3 Pa) for two values of electric field: ?? , E = 10’ V/cm; A, E= lo4 V/cm. The solid line satisfies the equation, a(T) = a,,, exp(- W, /kT)+ o,,r exp(- W, /kT), where: W, = 1.13 eV, AW, = 0.03 eV, uoI =2.3X lo2 0-l cm-‘, r, = 0.998 and W, = 0.40 eV, AW, = 0.11 eV. corn=7.35XlO-‘o a-’ cm-‘, r2 =0.890 (r,, r2 are correlation coeffkients). The line is drawn as a guide for the eye.

2

2.5

3

3.5 1O”/T [K-l]

Fig. 9. Influence of the temperature, T,, of vacuum heating of glycol doped xerogels on temperature dependences of electrical conductivity. 0, T, = 120°C = 393 K (W = 0.6 eV, AW = 0.01 eV, u,,= 4.27X10d3 R-’ cm-‘, r=0.999 is the correlation coeffkient). 0, T, = 200°C = 473 K (W, = 0.86 eV, AW, = 0.02 eV, uO, = 0.175 a-’ cm-‘, r, = 0.999, W, = 0.29 eV, AW, = 0.05 eV, uo2 =1.49X lo-” n-’ cm-‘, r2 = 0.975). A, T, = 250°C = 523 K (W, = 1.43 eV, AW, = 0.02 eV, q,, = 83.5 R- ’ cm-‘, r, =0.999, W, =0.24 eV, AW, =O.ll eV, a,,, = 1.31X lo-l3 a-1 cm-l , r2 = 0.910). The lines are drawn as guides for the eye.

above dependence was observed, an increase of u with temperature gradually became smaller. The influence of temperature, T,, on thermal dependences of conductivity o (at p = 4 X 10e3 Pa) is shown in Fig. 9, with a glycol-doped xerogel as an example. The value of activation energy, W,, (from the experimental dependence: a(T) = uO, exp( - W,/RT) + a,,, exp<- W,/kT)) significantly increases with an increase of vacuum heating temperature, T,. The values of W, for temperatures T, = 393, 473 and 523 K are 0.6, 0.86 and 1.43 eV (L-0.02), respectively. Although the values of W, have been determined with a higher value of error than W,, within the range of this error, the influence of temperature, T,, on W, cannot be detected. Fig. 9 also indicates that deviation from the Arrhenius dependence for T, = 393 K is apparent much sooner than a similar dependence obtained for A xerogels (compare Fig. 8). 3.5. Structural effects The results presented above suggest that electrical conductivity of SiO, xerogels is mainly determined

H. Sodolski. M. Kodowski/Journal

1.2

1.4

1.6

1.8

WAVELENGTH,

2

2.2

of Non-Crystalline Solids 194 (1996) 241-255

2.4

pm

Fig. 10. Infrared spectrum of A2 xerogel equilibrated with the atmosphere (solid curve) and with a vacuum (dashed curve).

by the state of the xerogels’ internal surface. Changes of electrical conductivity during the desorption and sorption processes should be affected by a change of the xerogels’ internal surface structure. Wood and Rabinovich’s work [ 131 suggests that it is reasonable to investigate the structural changes by examining the infrared spectrum of SiO, xerogels in the frequency range from 4000 to 8000 cm-‘. There are overtone and combination absorption frequencies in this region, which are different for H,O and OH groups (in the silanol groups SiOH). It allows us to study, independently, changes of characteristic bands in the IR spectrum occurring during desorption and sorption of H,O vapour in SiO, xerogels. In Fig. 10, examples are shown of IR spectra of A2 xerogels. The spectra have been obtained in equilibrium with the atmosphere (RI-I = 85%) - shown as the full curve - and in vacuum at pressure p = 2 Pa. In the spectrum of the xerogel equilibriated in air, we note three absorption bands: the first near 4340 cm-’ , the second near 5160 cm-’ and the third near 6935 cm- ‘. In agreement with Ref. [13], the bands correspond to H-bonded H,O (5160 cm-’ ) and Hbonded OH (4340 and 6935 cm-’ ). It is worth noticing that, while the composition of the sol used by Wood and Rabinovich differs from the sol used by us, the IR spectra are similar with respect to the energies of the observed bands. The infrared spectrum of the A2 xerogel obtained in vacuum (dashed curve in Fig. 10) shows a decrease in the intensity of the 5160 cm-’ band. This decrease indicates that the greater part of the H,O molecules are weakly bonded with the internal surface of the xerogel. Also, two new bands (4494 and

247

7138 cm-’ > have been created by equilibration in vacuum. A shift of these bands towards higher frequencies indicates that the OH groups are now more weakly bonded than they were in the internal surface state with considerably higher concentration of H,O molecules. Wood and Rabinovich [13] consider the new bands created in vacuum as connected with the presence of free OH groups. These groups result from the small amount of H,O molecules now present on the internal surface, leaving a great part of the SiOH groups not hydrogen-bonded with water molecules. However, we note that not all the H,O molecules have been removed from the internal surface. On the right of both bands, 4494 and 7138 cm-‘, there are residues of the bands related to H-bonded OH groups. Sections 3.3. and 3.4. indicate an influence of vacuum heating temperature, T,, on the electrical properties of xerogels (especially of the B type). The influence of T, on the IR spectra of type B xerogels is shown in Fig. 11. The infrared spectra of B,, B, and B, samples were obtained at atmospheric pressure. By comparison with the spectra of type A samples from Fig. 10, these spectra additionally indicate the following. The 4348 cm-’ band, connected with stronger hydrogen-bonded OH groups, is relatively more intensive than the 5162 cm-’ band. This difference may be due to ethylene glycol (CH,OH), molecules, which may participate in binding relatively larger amounts of SiOH groups with hydrogen bonds. The presence of (CH,OH), molecules in type B xerogels’ structure is marked on

I

I

1.2

1.4

1.6

1.8

WAVELENGTH,

2

2.2

2.4

pm

Fig. 11. The influence of T, temperature on the infrared spectra of the B type xerogels ( , Bl, 7Y,=423 K; ---, B2, T,=473K; . . ..B3.T,=523K).

248

H. Sodolski, M. Koslowski/ Journal of Non-Crystalline Solids 194 (1996) 241-255

the IR spectrum by two broad bands of frequency from 5580 to 5570 cm-’ and about 4790 cm- * (EG in Fig. 11). It is noteworthy that these bands do not change within errors of measurements until T, = 473 K, while, after thermal treatment in vacuum at temperature, T, = 523 K, a decay of the EG bands is observed. A decrease of intensities of all bands can be noted with decreasing intensity of EG bands. Taking into account that base group frequencies of ethylene glycol are < 4000 cm-’ 1141,the EG bands marked in Fig. 11 may be overtones or combination absorption frequencies. Given their breadth and position, they may also be due to hydrogen bonds between H,O and (CH,OH), molecules. The influence of desorption on the IR spectrum of type B samples has also been examined. The vacuum spectra of xerogels with ethylene glycol (type B and T, < 473 K) and without glycol (type A) are similar, save for the EG 4790 cm-i band, which does not disappear completely (namely, its intensity decreased by nearly a half). 3.6. Complementary measurements The measurements described above have been supplemented by the measurement of the internal specific surface of xerogels of types A and B, the temperature dependence of the dielectric constant of both types of gel and the water vapour sorption curve for xerogel A. The measurement of specific surface, S, was made by the Brunauer-Emmett-Teller method, and the following results were obtained: sA = (582 f 12) m’/g for xerogels A and s, = (674 rt 4) m*/g for xerogels B . Variation of the dielectric constant, E = AT), were determined in vacuum at p = 4 X 10d3 Pa, in the range of temperatures 290 K-390 K, at frequencies f= 0.5, 1, 2, 5 and 10 kHz. For both types of gel, a monotonic decrease of E with temperature was observed. In the investigated range of temperatures, the values of E decreased from 6.4 to 5.4 (A> and from 6.4 to 4.6 (B). The sorption curve of water vapour was determined by measuring the increase of the mass of samples with average thickness, d = 0.15 cm, in equilibrium with air of atmospheric pressure and humidity, RI-I = 85%. Prior to sorption, the samples

had been dehydrated in vacuum of p = 2.3 Pa for 20 h. The total increase of the gel mass due to sorption was Am = 0.142 g. The accuracy of weighting was 10M4 g. From the value of time, &, corresponding to a half of the mass increase, Am, the diffusion coefficient, DHzO = 10d7 cm*/s, was estimated.

4. Discussion An analysis of the obtained experimental results indicates that electrical conduction in the investigated silica gels is ionic in character and is determined by the state of pores’ internal surfaces in the gel, which influences the two processes determining the mechanism of conduction: ion generation and mobility. These experimental data indicate that there are several factors that may influence the state of internal surface in the SiO, gel: sorption and desorption of water vapour, thermal treatment in vacuum (influence of temperature, T,) and chemical constitution of sol (gels A and B). The influence of humidity on electrical conduction of polymers [9,15] and some gels [2] is observed as an increase of conduction with increasing concentration of H,O molecules in the volume of the polymer. It is usually assumed that the presence of H,O molecules causes increases of charge carrier concentrations only. The possibility of ion concentration increase through the dissociation of H,O molecules and the influence of a high dielectric constant of water on the dissociation of ionically bound groups present inside the polymer has also been discussed 1151. The authors of Ref. [2] prove that high conduction of vanadium pentoxide xerogel is primarily determined by water content. The experimental data from section 3.1. show the influence of humidity on the electrical conduction of SiO, xerogels to be strong (Figs. 1 and 2). Through the hydration/dehydration phenomena, reversible changes of electrical conductivity in the range of six to eight orders of magnitude are achieved. At the same time, significant changes of the effective dielectric constant of xerogels are observed (Fig. 3). Analysis of infrared spectra of SiO, xerogels indicates the presence of several different interactions between H,O molecules and other molecules or groups of molecules present in the pores. As a

H. Sodolski, M. Ko~owski/.Journal

of Non-Crystalline Solids 194 (19%) 241-2S5

result of the above interactions, there are not only free H,O molecules and H,O molecules weakly bound with OH molecules by the Van der Waals interaction, but also H,O monolayers strongly bound with gel [13,16,17]. The same analysis suggests that the various ways of H,O molecule adsorption are mainly influenced by the variety of OH groups present on the surface of the pores. The IR spectra shown in Fig. 10 clearly illustrate the changes in the molecular structure of pores surface due to xerogel desorption. These changes, described in detail in section 3.5, are reversible and agree well with the result of Ref. [13]. Good repeatability of electrical conductivity of SiO, xerogels subjected to repeated hydration and dehydration processes in room temperature indicates the decisive contribution of free and weakly bound H,O molecules in the above processes. H,O molecules also determine the value of electrical conductivity of xerogel in equilibrium with the atmosphere. The values of u at p = pat,,, and RI-I = 85% are about 10-s 0-l cm-’ and are independent of the type of xerogels and their thermal treatment. Nevertheless, measurements of o in vacuum show the important role of ions and ionogenic molecules more strongly bound with the internal surface of pores. After the removal of free and weakly bound H,O molecules, the electrical conductivity of SiO, xerogels becomes several orders of magnitude less (Figs. 1 and 4) and changes (Fig. 6). Then, the value of u and the mechanism of conduction depend mainly on ions and ionogenic molecules more strongly bound with the surface of pores in SiO, xerogel. It is particularly evident on the example of gel with glycol (Figs. 1 and 4 and 91, when the influence of temperature, T,, on the value of equilibrium conductivity in vacuum (Fig. 1). the desorption rate (Fig. 4) and temperature dependences (Fig. 9) are examined. Thermal treatment of xerogels in vacuum determined by T, leads to irreversible changes of the state of the internal surface of the investigated gels. An increase of T, causes an irreversible removal of a growing number of ions and ionogenic molecules. This inverse results in a decrease in the value of conductivity in vacuum (Figs. 1 and 91, an increase of the rate of desorption (Fig. 4) and an increase of the activation energy of conductivity (Fig. 9). The above processes also take place in the

249

case of type A xerogels (Fig. 8), although the range of changes in conductivity, u, and activation energy, W, is smaller than that of type B xerogels. Data in Fig. 3 show that, in the case of type B gels, a significant part of the pore surface is covered by molecules of lower hydrophility, not promoting the sorption of H,O, as suggested by a much smaller increase of the effective dielectric constant during the sorption of air of humidity RH = 85%. Before discussing the mechanism of conduction in SiO, xerogels, let us consider potential sources of ions present or generated in the gel. The presented experimental data do not allow us to identify the ions responsible for conduction in SiO, xerogels. In the case of type A xerogels, the most probable candidates are Hf and OH- ions. The presence of OHions is confirmed by the analysis of infrared spectra[l7]. In the case of gels used in the measurements for the first time, there is a possibility of appearance of a small number of ions coming from the catalyst (Cl-). However, such ions are usually permanently removed from the gel (Fig. S(a)) and do not take part in equilibrium conduction in further measurements. In the case of type B xerogels, there is an additional source of ions (or ionogenic molecules) rather strongly bound with the pores’ surface and responsible for increased conductivity (Fig. 1). Only thermal treatment in vacuum at the temperature T, = 480 K decreases the conductivity of type B xerogels in vacuum to that of type A xerogels (Figs. 1 and 4). It is worth noting that the thermogravimetric analysis of gels with glycol indicates [8] that the desorption of glycol becomes significant at a temperature of about 473 K. This desorption allows us to assume that an increase of conductivity in type B xerogels for T, < 480 K is connected with the presence of (CH,OH), molecules. For lower temperatures, glycol molecules manifest their presence indirectly in two new bands of the IR spectrum, shown as EG bands in Fig. 11. The presence of one of these bands after xerogel desorption helps explain the difference in electrical properties between type A and type B xerogels shown in Fig. 1. Only after glycol has been removed at temperatures of T, > 480 K, are the structure of type B xerogels (see Fig. 11) and their electrical properties (see Fig. 1) similar to those of type A xerogels.

250

H. Soablski, M. Kobowski/ Journal of Non-Crystalline Solids 194 (I 9%) 241-255

In a discussion of the mechanism of conduction in the porous SO, xerogel samples, we should pay attention to the fact that the mechanisms for the states of high and low electrical conductivity differ (Fig. 6). In the state of relatively high electrical conductivity, obtained for xerogels (of types A and B) in the state of equilibrium with air of the pressure p = pat,,, and humidity RI-I = 85%, conduction is ohmic (Fig. 6) and even for electric fields E 2 5 X lo4 V/cm no polarization effects have been observed (upper inset in Fig. 6). High values of the effective dielectric constant for xerogels in equilibrium with atmosphere (Fig. 31, connected with a large amount of adsorbed water and the ohmic character of conduction, indicate that conduction is by percolation of ions on the surface of pores through sequential structures of bound H,O molecules. Calculations taking into account the measured value of the specific surface and total amount of adsorbed water (for type B xerogels, S = 582 m2/g and mHzo = 0.091 g/g) show that, for high sorption of H,O, the amount of water is sufficient to cover only 30% of the total area of pores with a monomolecular layer. However, this amount of water is sufficient to establish a network of many conducting paths, built of adsorbed H,O molecules. Combination of measurements shown in Figs. 2 and 3 allows one to obtain the dependence log a =A1 /E), which, according to the dissociation hypothesis [9], should be linear. Assuming the process of water dissociation to be the main source of ions in xerogels’ equilibrium state with atmosphere, the dissociation hypothesis leads to the following expression: u ( E) = const utu/’exp( - U/2eLT),

(1)

where (U/e) is an energetic barrier due to dissociation of H,O molecules and n, is concentration of H,O molecules in gel. The constant value depends on the average mobility of ions of both signs. Neglecting a slight influence of II,, the value of U may be calculated from the slope of the log u = fll/e) dependence, according to Eq. (1). The difficulty of the experimental verification of Eq. (1) for heterogeneous structures consists mainly in estimating the local dielectric constant E,,,_,. In Ref. [9], Eq. (1) was derived by assuming elocal= ?? eff < 15 and neglecting the space distribution of H,O molecules.

0

0.5

1

1.5

1O/Ed

Fig. 12. Log u = fllO/e,,) dependences obtained for A and B xerogels at frequency f = 1591.5 Hz and ?’= 293 K.

Fig. 12 shows the experimental log cr =fllO/+,,,> dependence for type A and B samples, which does not satisfy Eq. (1) and differs from dependences obtained for hydrophilic polymers [9]. Three stages eff of conductivity variation due to the increase of ?? have been observed in the A and B samples. During the first stage, the conductivity, u, increases about four orders of magnitude, with serf increasing from 6 to 8.5. Then the rate of increase of (T becomes less and, finally, in the last stage of ecff increase (from 11 to 33 (gel A)), (T increases only within the range of one order of magnitude. In Fig. 12, the fragments of large and small increases of (T were estimated only formally by Eq. (11, with the relevant values of activation energies given. We assume that the shape of the log u = fllO/e,,,) dependence presented in Fig. 12 is due to the features of the diffusion process of water vapour into the volume of the gel sample limited by Au electrodes. Three stages of diffusion may be observed for the parallel-electrode assembly, with average thickness of samples d = 0.05 cm, average diameter of electrodes 2r = 0.5 cm, and total areas of samples significantly greater than the area of electrodes. During the first stage, the diffusion fronts approach each other from opposite surfaces, partially penetrating the inter-electrode area. At this time, slight changes of ecff may be observed. However, from the point of view of electrical conduction, two virtual electrodes are created in the inter-electrode area, the areas of which are growing and the distance

H. Sodolski, M. Kodowski/ Journal of Non-Crystalline Solids 194 (19%) 241-255

between same is shrinking. These changes lead to an increase of direct current flowing between electrodes. Short-circuiting of virtual electrodes ends the stage of the strong increase of u. The transient stage is of unknown causes but may be connected with expansion of the area of the virtual electrodes’ short-circuiting towards the center of the inter-electrode area. The last stage, via further growth in concentration of H,O molecules, causes a significant increase of the effective dielectric constant and a relatively smaller increase of o. The above hypothesis will be verified by the authors in further investigations of diffusion processes in silica xerogels of various geometries. The conductivity of the xerogel samples in vacuum is different in value and source from the conductivity of the equilibrium state with atmosphere. The value of (+ in vacuum is a few orders of magnitude less (Figs. 1 and 4 and 61, and the nonohmic and polarization effects appear at the same time (Figs. 6 and 7). Typical processes considered to be responsible for non-ohmic ionic conduction are [ 151 field-enhanced mobility (the rate theory), field-enhanced dissociation (Onsager) and space-charge limited conduction. The possibility of fitting theoretical dependences describing the above processes to the experimental data was examined with computer fitting programs. In order to avoid the influence of polarization, fitting

_ 5.1ct4~,

J

I

0

2.1 o4

4*104

6.1 o4 E D//cm]

Fig. 13. Experimental and theoretical electrical conductivity, (I electric field, E, dependences in the absence of internal polarization (sample B3. p = 4X 10e3 Pa, T k 461.5 K): A, experimental results; - - -, IQ. (2); , 4. (3).

251

was made using data obtained for a type B3 sample at temperature T = 461.5 K (Fig. 7). Good fitting of theoretical dependences to the experimental CT=A E) results was obtained only for the Onsager model and the rate theory (Fig. 11). In the case of the Onsager dependence [ 181, j= c,E/m,

(2)

where j is current density, E is the electric field, F(b) = @(E)/@(O) is the relative increase of dissociation constant due to the electric field, c, is a constant value dependent on the mobility of ions and the generation and recombination coefficients; different values of the dielectric constant, e, were introduced into the computer program, at a fixed temperature, T, and, given the experimental CT= fi E) dependence, a search for the minimum of error defined by the parameter xZ _ c?

1

[ i,@eor.)

-ji(expere)12

,= jibper.) was made. The minimum of X~i”= 3.1 X lo-” A/cm2, at Jexper.) in the range of 3.5 X lo-“-2.9 X 10m9A/cm2, was obtained for E= 21. In the case of the dependence from the modified Stem-Eyring rate theory [9],

j = ( A/A)

sinh( chE) ,

(3)

where: A is a constant value dependent on the concentration of ions and the diffusion coefficient, c is a constant value dependent on temperature and A is the hopping distance of ion; the computer program calculated xi,, the parameter A and the average hopping distance of an ion, A, at a fixed temperature, T, and given the experimental u = fl E) dependence. The best fit of the theoretical dependence (3) was obtained for A = 2.6 X lo-I5 A/cm and A = 1.9 X 10m6 cm, at x2,, = 1.1 X lo-” A/cm2 (Fig. 13). For all dependences from Fig. 13, o was determined as j/E, where E = V/d. In the case of experimental (+= fcE) dependences with a significant effect of internal polarization of gel samples (see lower inset in Fig. 6 and dependences for T = 320 K and 377 K in Fig. 71, it is impossible to fit any of the analyzed theoretical dependences without taking into account the electric field of internal polarization in the sample. When

252

H. Sodolski, h4. Kodowski/ Journal of Non-Crystalline Solids 194 (19%) 241-255

I

0

I

2.lo4

4*104

S-lo4 EDllcml

Fig. 14. Experimental and theoretical electrical conductivity-electric field dependences in the presence of internal polarization (sample B2, p = 4. X O-’ Pa, T = 293 K>. Experimental results: A, u = j/E, 0, a,, = j/E,,, where E = U/d and E,, = E VP/d, with VP=100 V and d=4.7X10e2 cm. Theoretical dependences: - - -, Eq. (2) , Eq.(3). both fitted to the ucrr = j/E,, curve.

polarization was taken into account by replacing the electric field, E = V/d, with the effective field, E,,f = E - VP/d, and o with a-, = j/Eeff, again the best fit was obtained for the Onsager model and the rate theory. Experimental data from the lower part of Fig. 6 (B3, p = 4 X 10e3 Pa) have been taken as an example. This curve is plotted again in Fig. 14 (a = fl E) - A). The dependence, q, = fl E,,) (01 and both theoretical dependences (Eq. (21, broken line, and Eq. (31, solid line), fitted by the computer program to the experimental $, = fl E,,) curve, are also shown for comparison. The latter curve was determined with VP = 100 V and the thickness of a sample d = 4.7 X 10v2 cm, both adopted after Fig. 6. The best fit of the theoretical curves was achieved for E = 31, with ,&, = 2.5 X lo-l2 A/cm2 (Eq. (211, and for A = 1.6 X 10e6 cm, with x,& = 7.2 X lo- l3 A/cm2 (Eq. (311, respectively. The a,, = fl E,,) dependences obtained for other samples with VP > 0 (e.g., both lower curves in Fig. 7) have the same character as in Fig. 14, irrespective of sample type. For most of the analyzed experimental dependences, a,, =fl EC,>, the rate theory gave better accuracy of fitting than the Onsager dependence. However, taking into account the results obtained, it is difficult to predict which of the mechanisms proposed by both theories plays the decisive

role. In the case of the Onsager model, the difficulties are connected mainly with verification of the value of the local dielectric constant. The fitting calculations according to Eq. (2) - with polarization in Fig. 14 and without polarization in Fig. 13 yielded x&, for a dielectric constant, E, much higher than the experimentally determined effective value, E,.rr. The obtained effective values ecn for type A and B gels are close to 6.4 for T = 290 K and p = 4 X 10e3 Pa and decrease slowly with temperature, reaching eerr = 5.5 (gel A) and err = 4.7 (gel B) for T = 383 K. Employment of the above effective values, +r, in the Onsager calculations makes the accuracy of fitting much worse (increase of x2 by two to four orders of magnitude). On the other hand, it can be assumed that the dissociation processes intensified by electric field take place mainly in local agglomerations of H,O molecules present in the pores at low pressure. This assumption justifies the local value of the dielectric constant in the range 17-33, for which xi,, was obtained. The results obtained by the nuclear magnetic resonance method show [19] that, with small amounts of water in the gel (m 3 X lOi molecules/m2), it is adsorbed in the pores in agglomerations in areas of the highest concentration of OH groups. On the other hand, the analysis of infrared spectra of SiO, gels [131 indicates that, in vacuum, the content of water is less than 0.1 bmol/m2, at the temperature T = 283 K. This content means that, in the samples, concentrations of H,O molecules in vacuum are expected to be lower than the 3 X 1017 molecules/m2 claimed in Ref. [19]. Thus, the condition of gathering H,O molecules in the form of separate agglomerations on the surface of pores is well satisfied. Completing our discussion of the dissociation mechanism of ion generation, we will make a simple estimation. According to Ref. [16], it may be assumed that, after 18 h of pumping, at p = 10m2 Pa and T = 293 K, there are still 4 X lOi H,O molecules/g of gel in the samples. It may also be assumed that the mobility’of ions in gel in the above conditions is not less than in some hydrophilic polymers (e.g., for polyester polymer CL+= CL__ = 2 X lo-” cm*/V s [20]). For p = 10-‘O cm’/V s and g= lo-l5 f12-’ cm-‘, the required equilibrium concentration of ions is IZ~= 6 x lOi cmp3. Consequently, with the density of SiO, xerogel p = 1 g/cm3, the ratio of H,O

H. Soablski, M. Kodowski/Journal

of Non-Crystalline Solids 194 (19%) 241-255

Fig. 15. Model presentation of ionic transport (1 and 3) and polarization (2 and 4) inside silica xerogel pore.

molecules concentration to equilibrium concentration of ions is nHZO/ni = 5 X 10’. This ratio means that participation of one pair of ions with 5 X lo5 H,O molecules is enough to support the equilibrium conduction. On the other hand, when interpretation of the obtained non-ohmic dependences, (T= fl E) and a,, =A&, 9 is based on the rate theory, which results in Eq. 931, there is an additional possibility of explaining the role of internal polarization in gel and the influence of temperature, T,, on the electrical conduction of SiO, xerogels. The modified Stem-Eyring rate theory is based on the assumption that diffusive transport of ions is connected with carriers surmounting successive potential barriers resulting from the interaction of ions with their immediate neighborhood. In the presence of an electric field, the height of barriers is so modified that transport of both positive and negative ions is made easier. This case results in increased mobility of ions with increasing E and, with certain further assumptions [9], leads to Eq. (3). Fig. 15 shows a simple model of an SiO, xerogel pore with some possible positions of ions marked. Given the direction of the effective electric field inside the pore, as marked, only mobilities of ions in positions 1 and 3 may be modified by the field, E,,,. Local potential barriers will be decreased by AW = 0.5Eqh in the marked direction of ion movement, where A is the mean ion hopping distance. The energetic situation of ions in positions 2 and 4 is different. The forces of the effective field exerted on these ions, added to the local ions-gel matrix interactions, hinder their movement inside the pore. The

253

displacement of these ions may occur only by thermal movement. The placement of ions in positions 2 and 4 is relatively stable by comparison with positions 1 and 3. The result of a stable location of ions in positions such as 2 and 4 inside the pores is internal polarization decreasing the effective electric field. The value of the internal polarization field depends on several factors, including the external electric field applied to the gel sample, the state of surface inside the pores and temperature. High field polarization of the gel sample, deep potential wells and low temperatures promote high and durable internal polarization (see u = fl E) dependences from Fig. 7, obtained for lower temperatures T = 320 K and T = 377 K). Fig. 7 also shows that increased temperature, despite the presence of the same barriers (W, = 1.43 eV for gel B3, Fig. 9) and the same polarizing voltage causes a decrease of polarization till its decay at T = 461.5 K. The influence of the depth of the potential wells on internal polarization may be observed while analyzing the insets in Fig. 6. The state of gel surfaces presented successively in Fig. 6 is modified by permanent removal of weakly bound ions from the surface of the pores, leaving the more strongly bound ions. A large amount of adsorbed water and the relatively high conductivity that occurs with it do not promote durable polarization (upper inset). Decreased pressure in pores causes a permanent removal of weakly bound ions, and molecules and potential wells of depths around 0.6 eV become active (compare the upper curve in Fig. 9). The middle inset already indicates a slight polarization effect. Thermal treatment of the gel in vacuum at 473 K causes subsequent elimination of weaker interactions. Consequently, the bonds of average activation energy, W = 0.86 eV, are dominant, which results in an increase of internal polarization voltage up to 100 v. In a discussion of the mechanism of polarization inside gel samples, one should formally take into account the possibility of a connection between the polarization effect and the formation of space charge near the electrodes. However, there are two reasons practically excluding this possibility. First, the polarization effect should also take place for gels in an equilibrium state with moist atmo-

254

H. Sodolski, M. Kodowski/ Journal of Non-Crystalline Solids 194 (1996) 241-255

sphere. However, it did not occur in the experiments (see upper inset in Fig. 6). Second, measurements of Z = fir> during polarization of gel samples allow us to estimate the value of total polarization charge, qp. For example, the value of qp for type B2 samples, obtained as a result of polarization at UP= 3000 V, is of the order of lop9 C. Using the dependences given in Ref. [21], one can prove that the charge, qp, is too small to obtain, as significant polarization effects as those in our paper, even when the charge is placed in relatively thick layers. On the other hand, the value of qp is sufficient to obtain desired polarization effects when the polarization charge is distributed in particular pores according to the model proposed above (Fig. 15). Several characteristic features of the electric conduction of SiO, xerogels have been discussed above and the rate theory is shown to be adequate for description of the mechanism of ionic transport in the effective electric field of the silica gel porous structure. An unquestionable weakness of the rate theory is the practical impossibility of experimental verification of the parameter, A, obtained from the fitting of Eq. (3) to the experimental a,, = f(E,,) dependence. According to the theory, A is identified with the hopping distance of an ion [9]. The values of A obtained from the fitting of Eq. (3) are in the range H 3.2 X 10e6 cm for gels A and 1.6 X 1O-6 cm for gels B. The above values are higher than those of many polymers (5-25 nm>. The values of A have not been observed to depend on the temperature, T,, or the measurement temperature. The physical reason for different values of A for xerogels of types A and B is not known. At the end of this section, we would like to further elaborate on temperature characteristics of conductivity of SiO, xerogels (Figs. 8 and 9). The influence of the temperature, T,, on the energetic state of ions present on the surface of pores has already been discussed. However, it is worth noting that the amount of ions remaining in potential wells of the depth, W,, determined by the temperature, T,, is limited. With increasing temperature, the conduction may reach a state at which the ion generation begins to decrease as the sources decrease. This decrease is shown in Figs. 8 and 9, when the temperature of measurement approaches the value of T,.

Generally, the temperature dependence of conductivity of SiO, xerogels in a vacuum may be de+ scribed by a(T) = go, exp(- W,/kT) a,, exp<- W&T). The contribution of the term with activation energy, W,, is small and is usually determined with an error greater than W,. It is worth noting that the activation energy, W,, unlike W,, is independent of the temperature, T,. Only the value of a,,, decreases with increasing temperature, T,. On the other hand, the value of W, is, within the range of error, close to the activation energy of water dissociation, W,, = 0.26 eV. The latter was determined using the dependence of the dissociation constant, K,, on temperature known in the literature [22]. It may be assumed that, even after thermal treatment in vacuum at different temperatures, T,, a vestigial amount of free, unbounded water remains in the gels and may contribute to the electrical conduction of xerogels while dissociating. This hypothesis seems to be confirmed by the results of Ref. [ 161where, despite many hours’ dehydration at the temperature T = 473 K, the signal characteristic for unbound water was observed in the infrared spectrum of SiO, xerogels.

5. Conclusions The electrical conduction of SiO, xerogels is ionic and determined by the state of the gel pores’ internal surface. This state may be modified by the sorption/desorption processes of water vapour and thermal treatment of gel in a vacuum. It also depends on the chemical content of the sol from which A and B xerogels were obtained. In equilibrium with the atmosphere, the conduction of xerogels is ohmic due to strong sorption of H,O molecules. The conductivity dependence as a function of the effective dielectric constant, eefr, of xerogels differs from such dependences obtained for hydrophilic polymers because of the specific features of moisture sorption by SiO, xerogels during transition from the state of low conductivity to the equilibrium state with the atmosphere. Under decreased pressure, the conductivity of xerogels decreases about seven orders of magnitude and is non-ohmic. The appearance of internal polarization due to the applied electric field is also con-

H. Sodolski, M. Kodowski/ Journal of Non-Crystalline Solids 194 (19%) 241-255

netted with the above changes. A theoretical analysis of the current-field characteristics allows us to explain the observed dependences in terms of the field enhanced mobility theory, taking into account the internal polarization of xerogels. Analyzing the obtained results, we cannot exclude an influence of electric field on charge carrier generation (Onsager). Temperature dependences of conductivity confirm the importance of the state of pores’ internal surface in generation and transport of ions in SO, xerogels under lowered pressure. An important factor determining the values of conductivity and activation energy is thermal treatment of xerogels in vacuum defined by the temperature, T,.

Acknowledgements The authors would like to thank Professor J.

Godlewski for helpful discussions of conduction mechanisms and Professor W. Bala and Dr P. Bala for inspiring discussion and help in obtaining the IR spectra. Work was supported by KBN under Program No. 2 2383 92 03.

References [l] P. Barboux, N. Baffier, R. Morineau and J. Livage, Solid State Ionics S&l0 (1983) 1073.

255

[2] T. Szon%yi, K. Bali and I. Hevesi, J. Phys. (Pares) 46 (1985) 473. [3] J. Livage, J.P. Jolivet and E. Tronc, J. Non-Cryst. Solids 121 (1990) 35. [4] V. Mehrotra, J.L. Keddie, J.M. Miller and E.P. Giannelis, J. Non-Cryst. Solids 136 (1991) 97. [5] M. Guglielmi, P. bmocenzi, G. Brusatin, F. Caccavale and N. Tombolan, in: Proc. 16th Int. Congr. on Glass, Madrid, Oct. 1992, Bol. Sot. Esp. Ceram. Vid. 31-C 7 (1992) 87. [6] H. Wakamatsu, S.-P. Szu, L.C. Klein and M. Greenblatt, J. Non-Cry%. Solids 147&148 (1992) 668. [7] H. Sodolski, P. Mondalski, J. Gcdlewski and J. Kalinowski, J. Non-Cryst. Solids 147&148 (1992) 663. [8] S. Luo and K. Tian, J. Non-Cryst. Solids 100 (1988) 254. [9] R.E. Barker Jr. and C.R. Thomas, J. Appl. Phys. 35 (1964) 3203. [lo] M. Onoda, H. Nakayama and K. Amakawa, J. Phys. D23 (1990) 211. [ll] T.J. Lewis, J. Phys. D23 (1990) 1469. [12] R.M. Faria, J.S. Nogueira and N. Alves, J. Phys. D25 (1992) 1518. [13] D.L. Wood and E.M. Rabinovich, J. Non-Cryst. Solids 82 (1986) 171. [14] N.L. Alpert, W.E. Keiser and H.A. Szymanski, IR. Theory and Practice of Infrared Spectroscopy (Plenum, New York 1970) fig. 5.32. [15] R.E. Barker Jr., Pure Appl. Chem. 46 (1976) 157. [16] J. Kratochvila, Z. Salajka, A. Kazda, Z. Kadlc, J. So&k and M. Gheorghiu, J. Non-Cryst. Solids 116 (1990) 93. [17] G.D. Thukin and A.I. Apretova, Zh. Prikl. Spektrosk. 50 (1989) 639. [18] L. Gnsager, J. Chem. Phys. 2 (1934) 599. [19] V.I. Kvilividtke, Dokl. AN USSR 157 (1964) 158. [20] H. Sodolski, J. Phys. Cl2 (1979) 3717. 1211 G.M. Sessler, Electrets (Springer, Berlin, 1980) pp. 13-17. [22] D.R. Lide, ed., Handbook of Chemistry and Physics, 74th Ed. (CRC, London, 1993-94) p. 8-48.