DIELECTRIC BEHAVIOR AND PROTON CONDUCTION IN SOLIDS
2573
Dielectric Behavior and Proton Conduction in Solids. I.
Borax
by E. W. Giesekke and L. Glasser’ Department of Chemistry, University of the Witwatersrand, Johannesburg, South Africa Accepted and Transmitted by the Faraday Society
(April 18, 1966)
The dielectric behavior of compressed powder and of single-crystal borax over an extensive range of frequencies and temperatures is described. The dielectric behavior is a sensitive function of the ambient humidity and of the age of the powder, but this is much less evident for the single-crystal material. The effects of “doping” and of varying the thickness of the sample are reported. Transport measurements of other workers have been repeated and extended and show borax to conduct electric currents a t least partially by the motion of protons. A hypothesis of motion of charge carriers and neutral water molecules is utilized to explain the two dielectric absorptions observed in the powder: a low-frequency absorption due to space-charge polarization and a higher frequency absorption arising from orientation of water molecules adsorbed on the surfaces of powder particles.
I. Introduction
centered at about 50 cps was interpreted as a space charge polarization in terms of the theory due to Sodium tetraborate decahydrate, N5t2B407.10H20 Macdonald;8 the third contribution arose from the dc (more correctly,2 Na2[B40b(OH)4J’ 8H20), commonly conductivity of the sample and resulted in a nearly known as borax, and lithium sulfate monohydrate, linear increase in tan 6 values with decreasing frequency Li2S04.H20,have been shown to exhibit proton confrom frequencies lower than 10 cps. The results for duction under static electric fields by Maricic, et ~ l . , ~ single crystals were not so readily analyzed. who collected over mercury the gas evolved at the The present study has repeated and extended the excathode of an electrolysis cell; subsequent chemical perimental work of Maricic, et al., and of van Beek, analysis proved the gas to be hydrogen. Consistent with measurements being made on both compressed with the observed anisotropy of the dc conduction, powders and single crystals. The solid-state electrolwhich was greatest along the b crystallographic axis, a ysis has been examined up to the highest possible path for proton conduction was proposed along the b voltage gradients before breakdown, the frequency axis, involving the water molecules of crystallization. range has been extended toward both higher and lower The absence of proton conduction below about 20” frequencies, while the effects of sample thickness, could not be explained satisfactorily. aging, temperature, and “doping” with appropriate The dielectric properties of borax have been investigated by Kiriyama and Saito4 and by Burton and (1) To whom all correspondence should be addressed at Department TurnbulljS but their results are incomplete and inof Chemistry, Rhodes University, Grahamstown, South Africa. adequate for further analysis. During the progress (2) N. Morimoto, Mineral. J . Sapporo, 2, 1 (1956); J. D. Cuthbert and H. E. Petch, J . Chem. Phys., 38, 1912 (1963); 39, 1247 (1963). of the present study van Beek reported on the di(3) (a) 9. Maricic, V. Pravdic, and Z. Veksli, J . Phys. Chem. Solids, electric properties of compressed powders6 and of 23, 1651 (1962); (b) S. Maricic, V. Pravdic, and Z. Veksli, Croat. single crystals’ of borax. For compressed powders, Chem. Acta, 33, 187 (1961). he observed a broad maximum in tan 6 a t about 50 (4) R. Kiriyama and T. Saito, BUZZ. Chem. SOC. Japan, 26, 531 (1953). cps which he subdivided into three separate contribu(5) E. F. Burton and L. G. Turnbull, Proc. Roy. SOC.(London), tions by a curve-fitting procedure : one contribution A1.58, 182 (1937). of the Debye-relaxation type was centered at about 400 (6) L. K.H.van Beek, Physica, 29, 215 (1963). cps and was attributed to the motion of protons over (7) L. K. H.Beek, ibid., 30, 1925 (1964). molecular distances; a second Debye-type contribution (8) J. R. Macdonald, Phys. Rev., 92, 4 (1953).
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Volume 71I Number 8
July 1967
E. W. GIESEKKEAND L. GLASSER
2574
materials have been studied. These latter measurements are useful for the information they give on the nature and behavior of ionic defects in the solid, as in the investigations of the dielectric properties of ice and the effects of doping by Steinemann and Granicherg and by Steinemann.lo
11. Experimental Section The frequency range of 15 3lcps-0.01 cps was covered by three instrument systems, with all measurements being made by substitution methods: (a) 15 Mcps-600 kcps, an Advance Type T2 “Q” meter; (b) 300 kcps-30 cps, a General Radio 716 C capacitance bridge, a Heath Co. sine-square generator AG-10 with an output of 10 v, and a Heath Co. oscilloscope 0-12 U of sensitivity 10 mv/cm, connected as a bridgebalance detector. The oscilloscope was connected in a mode originated by Lamson” and described by Czech,12 vix., the output signal from the oscillator is applied to the X amplifier of the oscilloscope, as well as to the bridge, while the unbalance signal from the bridge is applied to the Y amplifier of the oscilloscope. Connected in this way the oscilloscope serves as a frequency-selective balance detector for the bridge. The oscilloscope sensitivity was perfectly adequate for the discrimination of the bridge to be fully utilized. (c) 1 kcps-0.01 cps, a Hewlett-Packard low-frequency oscillator A202 served as generator; a Tektronix oscilloscope 560, also connected as described in (b) above, served as detector for the frequency range 1 kcps-20 cps, while a potentiometric recorder (Kipp Zonen Micrograph BD1, full-scale deflection, 50 pv), connected only to the bridge output, was used as balance detector in the frequency range 3-0.01 cps; the bridge used was a development of one described by Schreiber,la details of which have been published elsewhere.l4 The dielectric sample holder was constructed with parallel electrodes of which one was fixed and the other attached to a micrometer movement to control the electrode gap. The design followed that of Hartshorn and Ward,15 but the electrode system was surrounded with a water jacket through which water from a thermostat was circulated in order to control the sample temperature between 25 and 80” (but with a maximum of 50°, in the present case, since borax dehydrates at higher temperatures). Unless otherwise stated, all materials used were of AR grade. The AR borax was recrystallized from deionized water, dried in the laboratory atmosphere, finely ground in a mortar and pestle, and then placed in a die where pellets 2 in. in diameter were pressed a t 750 kg ern+ for 15 min. Smaller pellets, when reThe Journal of Physical Chemistrg
quired, were pressed in a standard 13-mm diameter KBr pellet press at 11,500 kg cm-2 for 1 min. Some pellets were coated with a thin aluminum foil attached with a film of Vaseline; these pellets are denoted “coated” pellets, while those without the Vaseline coating and foil are “bare” pellets. Measurements on the pellets were commenced 15 min after pressing unless otherwise stated. The compressed pellets had a density of 1.3-1.4 g ern+ compared with the value of 1.73 g ~ m for - ~single crystals.l8 In order to indicate this discrepancy, the dielectric properties of compressed pellets are written with a suffix signifying “apparent”, e.g., egpp’. Single crystals of borax, (2 X 1.5 X 0.5) ern3, were grown over 2 weeks’by the slow evaporation of a saturated solution at room temperature.” These were cut with a wet cotton threadl8 and polished on various grades of abrasive paper in preparation for the electrical measurements.
III. Results ( a ) Aging Phenomena. At high relative humidities, about 70-80%, the dielectric properties of the compressed pellets of borax powder were found to be independent of their age. However, for any lower value of the relative humidity the results were time dependent, the dielectric constant decaying fastest a t the lowest relative humidities, accompanied by a small (0.25%) weight loss (Figure 1). The dielectric effects were reversible and if an aged pellet with a reduced dielectric constant was exposed to a high humidity it regained its original high value of the dielectric constant. Figure 2 represents the frequency dependence of log eaPp” for a borax pellet, both freshly pressed and 6 hr later, when subjected to a relative humidity of 57%. This figure clearly indicates that the decrease in egpp’ shown in Figure 1 arises from the shift of the whole absorption curve toward lower frequencies. If the frequency in cycles per second corresponding (9) A. Steinemann and H. Granicher, Helv. Phys. Acta, 30, 553 (1957). (10) A. Steinemann, ibid.,30, 581 (1957). (11) H. W. Lamson, Rev. Sci. Instr., 9, 272 (1938). (12) J. Czech, “The Cathode Ray Oscilloscope,” Philips, Eindhoven, The Netherlands, 1957, pp 157 and 160. (13) D. J. Schreiber, J . Res. Natl. Bur. Std., C65, 23 (1961). (14) E.W. Giesekke, J . Sci. Instr., 43,123 (1966). (15) L. Hartshorn and W. H. Ward, Proc. I n s t . Elec. Engrs. (London), 79, 597 (1936). (16) “International Critical Tables,” Vol. I, p 153. (17) A. N. Holden and P. Singer, “Crystals and Crystal Growing,” Heinemann, London, 1961. (18) R. Maddon and W. R. Asher, Rev. Sci. Instr., 21, 881 (1950).
2575
DIELECTRIC BEHAVIOR AND PROTON CONDUCTION IN SOLIDS
Time (days)
Figure 1. Decay of eaPp’ of a “coated” powder pellet with time (0),together with the weight loss ( 0 )suffered by the sample, of weight ca. 13 g. Temperature, 18’; relative humidity, 40%; frequency, 100 cps.
Frequency
(CIS)
for borax powder pellets over the whole Figure 3. available frequency range. The full line with circles refers to a “coated” pellet, the broken line with crosses to a “bare” pellet. The symbols refer to the different instrument General systems used: (a) Q, “Q” meter; (b) 0 and Radio bridge; (c) 0 and X, modified Schreiber bridge. Temperature, 20’ ; relative humidity, 60%; pellet thickness, 0.506 cm.
+,
Figure 2. Shift on aging of the epPp’) curve of a “bare” borax powder pellet, measured 15 min (0)and 6 hr after pressing (0). Temperature, 25’; relative humidity, 57%.
to the maximum value of eappl’ is denoted by fmax, then the relaxation time a t the center of the distribution, ro,is defined as 70 =
1/2nfmax
(1)
For a freshly ground borax pellet, TO was 4 X sec, which increased to 4 X lo-‘ sec in the period of 6 hr. ( b ) Frequency Dependence. The apparent dielectric constant, eapp’, and loss, eaPp”, for a compressed pellet of borax are shown in Figures 3 and 4, respectively. The full lines correspond to the results obtained from the “coated” pellets and the broken lines to those from the “bare” pellets. for freThe values of e.pp” are approximately quencies greater than 100 kcps. Since such small values cannot be measured accurately with the “Q” meter, they are not shown in Figure 4,while the values obtained for eappl in this frequency range, being more reliable, are shown in Figure 3. These results indicate
Frequency (c/o)
Figure 4. espp’l for borax powder pellets over the whole available frequency range. The broken straight line a t -45” depicts the possible contribution of dc conductivity to the dielectric loss. Refer to Figure 3 for meanings of symbols and experimental conditions.
the absence of any dielectric dispersion in the frequency range 105-107 cps in agreement with the results of Burton and Turnbulls and of van BeekS6 The data are replotted as a complex polarizability (a) plot (see section IVa of this paper) in Figure 5. The results indicate the presence of a high-frequency (30 cps-100 kcps) relaxation and another a t lower frequencies (-10 to less than lov2cps). Even a t the lowest frequency there is neither the maximum in eaPp” nor the tailing-off of eappl which is so characteristic of the termination of a relaxation process. There is an Volume 7 1 , Number 8 July 1067
E. W. GIESEKKE AND L. GLASSER
2576
2or
\
increasing W
(b)
I
1 I10
\
\
Figure 5. Polarizability (a)plot of the data of Figures 3 and 4; refer to Figure 3 for meanings of symbols: (a) plot for the “coated” pellet; (b) a plot for the “bare” pellet. x , low-frequency dispersion semicircle center, which lies on the a’axis. The discrepancies between the results of the two instrument systems are emphasized by this plot; the origin of these discrepancies is discussed in ref 14.
indication of a maximum in tan ,6 (not shown) for the “coated” pellet which suggests a very large static dielectric constant and a relaxation time longer than 16 sec at the least. At frequencies below 1 kcps there appears to be a significant difference between “bare” and “coated” pellets (Figures 3,4, and 5 ) . Measurements on powder pellets of different thicknesses showed that the dielectric constant has a nonlinear dependence on the thickness at low frequencies, but this dependence generally disappears toward the high-frequenc y dispersion region. ( c ) Temperature Dependence. The dielectric relaxation time is often found to depend on the absolute temperature according to the relation
A exp(H/RT) (2) where A is a constant, H an activation energy, and R the universal gas constant. 7 0 can be evaluated from ) the maximum in eq 1 or from the frequency ( f ~ of tan 6. A plot of log 2 T f D us. 1/T should yield a straight line, the slope of which will give H. Such a plot for a “bare,” freshly pressed pellet of borax gave a good straight line from which H was found to be 14.3 kcal/ mole for the high-frequency relaxation. ( d ) Single Crystals. JIeasurements of the dielectric properties of single crystals of borax of different thicknesses were conducted a t room temperature, 20” in the frequency range 30 cps-30 kcps. The dielectric properties of single crystals hardly changed with time. The results obtained for the dielectric constant of “bare” crystals along the b and c axes 70
=
The Journal of Physical Chemistry
I
lo*
I
I
lo’ 10‘ Frequency, (c/o)
;05
Figure 6. 6 ’ for various thicknesses of single crystals of borax, measured parallel to the b (unique) axis. Results a t 25’ on “bare” crystals: 0 , 0.165 cm thick; 0, 0.391 cm thick; x, 0.594 cm thick.
OL
1
1o*
10
I
10s Frequency
1cE (c/o)
;os
Figure 7. e ’ for various thicknesses of single crystals of borax, measured parallel to the c axis (normal to the moat prominent face of the usual habit). Results a t 25’ on “barel’ crystals: 0, 0.281 cm thick; 0, 0.398 cm thick; X, 0.529 cm thick; 0.752 cm thick.
+,
are shown in Figures 6 and 7, respectively; the dielectric constants of “coated” crystals are rather larger. The results in general agree quite well with similar data7kindly supplied by Dr. van Beek. ( e ) Doping. The dielectric properties of ice doped with H F provided the data necessary to explain the electrical properties and conduction in ice.1° The fluoride ion has the same diameter as the oxide ion, hence the former can replace the latter in solid solutions with ice. By analogy with their behavior in ice, it was anticipated that H F and NH4F might be able to replace some waters of crystallization in borax to form solid solutions. It was of interest to study such doping dielectrically in order t o elucidate the proton conduction mechanism. No data on solid solution between borax and either of these compounds are available. The doping was achieved by recrystallizing borax from a saturated solution 1 M with respect to NH4F.
2577
DIELECTRIC BEHAVIOR AND PROTON CONDUCTION IN SOLIDS
Since the interference of the borate ion precluded a direct determination of the fluoride ion concentration in the doped borax powder, the purity of the borax was determined by titration against a standard HC1 solution to give the indirect estimate of 5 wt % for the fluoride ion concentration. Figure 8 shows the frequency dependence of tan for compressed powder pellets of pure and of NH4F-doped borax at room temperature. The dc conductivity increased from ohm-' cm-' on doping the 6.6 X 10-lo to 8.0 X borax with NH4F. Similar increases in the conductivity and decreases in relaxation time were found for borax samples recrystallized from aqueous solutions containing NaC1, HF, and NaHC03. (f) Electrolysis oaf Compressed Powders. I n order to confirm the existence of proton conduction in borax, electrolysis experiments similar to those described by * conducted on compressed pellets Maricic, et ~ l . , ~were of borax. This method involves the hydrogen evolved on electrolysis displacing a column of mercury through a horizontal capillary and presents a convenient way of examining the rate of evolution of hydrogen, a matter which received some attention in our study of the proton conduction mechanism. The proton efficiency of the current at field strengths of about 1000 v/cm was about 5% (Figure 9) from 15 to 50", the remainder of the current presumably being contributed largely by electron conduction. This value is considerably lower than the corresponding value quoted by Maricic, et al., who observed neither a drop in current nor a reduction in hydrogen evolution with passage of time, in contrast with the results shown in Figure 9. van Beek6 also found a decrease in dc current with time for borax. He found that, for times longer than 0.5 hr, the empirical relation
i
=
i, exp(-t/T)
(3)
satisfactorily predicts the observed current decrease, with i, being the value of the current after an infinite period and 7 a constant having the value 2 X lo4 sec. Our results are in agreement with those of van Beek. To a first approximation, the proton efficiency remained constant throughout the electrolysis. Consequently, the displacement of the mercury column is simply a direct function of the current. There was some decrease in the efficiency a t the longest times. In some instances the efficiency started from a low value, about 0.5%, reaching a constant value of 5% within 100 min. This retardation could have arisen from dirt in the mercury or on the capillary or some porosity of the sample pellet. For field strengths of 7000 v/cm the proton efficiency increased to 30%.
h
I
10'
io3
1o3
Id
1'04
Frequency (cis)
Figure 8. Effect of "doping" with NHaF on tan sappfor "bare" borax powder pellets: 0 , AR borax; 0, AR borax recrystallized containing 5 wt % NHdF; temperature, 25'; relative humidity, 55%.
Time (min)
Figure 9. The electrolysis of a borax powder pellet, showing that the volume of gas generated follows the current flow closely. Temperature, 40.2' ; pressure, 65.8 cm; field strength, 3750 v/cm; radius of capillary, 0.055 cm.
For fresh pellets of borax, dielectric breakdown occurred at field strengths of approximately 2000 v/cm. For older pellets, those which showed no dielectric absorption at frequencies above 100 cps, the dielectric breakdown occurred at field strengths of the order of 30,000 v/cm. However, even for older pellets, proton conduction was never absent, but required higher fields, of about 10,000 v/cm, for its observation instead of the 1000 v/cm required for a fresh specimen. The temperature of the solid, as measured with a fine thermocouple placed in a well drilled into the pellet, remained unchanged on application of the electric field, even a t field strengths close to breakdown. The evolution of hydrogen is therefore not associated with a decomposition or a dehydration as a result of a temperature rise in the borax except, possibly, in very localized positions. As mentioned earlier, Maricic, et al. , found proton conduction to be absent for borax a t temperatures below 20". This was not confirmed, as proton conVolume 71 Il'umber 8 July 1967 ~
E. W. GIESEKKEAND L. GLASSER
2578
duction was even observed for certain pellets at 15’. The difference may arise from the fact that we sought for proton conduction at the highest voltage gradient which we could apply without breakdown, while Naricic, et al.,3aused a voltage gradient “at the limit of the ohmic range,” which suggests a value of about 1500 v/cm for fresh pellets. h final comment should be made with regard to negative charge carriers. A yellow stain was observed at the contact between the mercury and the borax on the anodic side of the conductivity cell, possibly owing to the formation of HgO by the discharge of oxygen. It is not believed that oxygen transport through the borax could contribute significantly to the current flow; discharge of oxygen localized at the electrode would, however, reduce any permanent polarization which might have been expected and which was observed for partially hydrated hemoglobin.1g
IV. Discussion ( a ) Conduction and Polarization. The dielectric properties of borax might be discussed in a number of ways, but since Xaricic, et al., have shown that at least some of the charge carriers are protons and, further, since the results for polycrystalline borax are so close to those for polycrystalline ice,g an interpretation involving protons is reasonable. As already mentioned, van BeeP has used this approach, subdividing the dielectric absorption for a powder specimen into three separate contributions. From this analysis he drew quantitative conclusions about the proton mobilities and concentration. If his conclusions are correct, a limiting value of 575 should have been observed in the dielectric constant below 5 cps. van Beek anticipated, but never observed, such a result. The results in Figure 3 show no such tendency and his analysis is not confirmed. However, qualitative comparison with van Beek’s6 results and those of Steinemann and GranicheP for ice strongly suggests that the low-frequency dispersion is due to space charge polarization arising from blocking of charge carriers, as opposed to a dc conductivity loss suggested by van Beek.6 These charge carriers could be protons, but electrons cannot be excluded. It is unfortunate that even at 0.01 cps esPp’ shows no tailingoff and tapp”shows no maximum since only from such limiting values can one draw quantitative conclusions about the mobility and concentrations of the protons using 1Iacdonald’s theory of space charge polarization.8 Xeasurements at still lower frequencies than the very low frequencies used in this investigation are required; relaxation methods probably provide the only solution to this difficulty. Rlacdonald’s theory The Journal of Physical Chemistry
predicts a linear dependence of the static (low-frequency) value of on the sample thickness. This linearity could also not be verified for borax. It is important to note that the dependence of E ~ on~ the ~ sample thickness for borax disappears at higher frequencies, suggesting that the high-frequency relaxation is a molecular process rather than a polarization process. The significant difference between “bare” and “coated” specimens requires consideration. If the reduction in capacitance for the ‘lbare” pellet relative to the “coated” pellet were due to a series air gap capacitance*O it would have influenced the whole frequency range, not only those values below 1 kcps. Special care was taken in preparing pellets with faces as parallel as possible; the micrometer electrode system employed in the sample holder was designed to ensure parallel movement of the electrodes. Since this decrease in capacitance is only observed at low frequencies, where space charge polarizations are most likely to occur, it is suggested that the difference arises from a difference in the polarization effects at the interfaces of “bare” and of “coated” specimens. We suggest that coating the pellet with Vaseline (an insulator which covers the surface entirely) causes the electrode to act more nearly like a blocking electrode than is the case for the “bare” pellet with its direct contact with the electrodes. Consequently the space charge polarization effects in the former case are more pronounced than in the latter. The space charge polarization overlaps, to some extent, the high-frequency relaxation and the relative reduction of the polarization effect for the “bare” pellet makes such pellets more useful in discussing the high-frequency relaxation. The dispersion is most conveniently represented on a polarizability (a)plotz1of the real and imaginary values of the polarizability, a’ and a”, respectively, plotted against one another. These are the real and imaginary values of the frequency-dependent complex polarizability, a(.)
(t’
- l)(d (E’
+ 2) + + 2)Z +
E”2 E”Z
- 3id’
(4)
The plot is similar to the familiar Cole-Cole plot,22 (19) S. Maricic, G. Pifat, and V. Pravdic, Biochim. Biophys. Acta, 79, 293 (1964). (20) S. Ruthberg and L. Frenkel, J . Res. Natl. Bur. Std., A68, 173 (1964). (21) B. K.P. Scaife, Proc. Phys. Sac. (London), 81, 124 (1963). (22) K.S. Cole and R. H. Cole, J . Chem. Phys., 9,341 (1941).
’
DIELECTRIC BEHAVIOR AND PROTON CONDUCTION IN SOLIDS
giving a semicircle for a Debye dispersion, which is depressed if there is a distribution of relaxation times, but de conduction also gives rise to a true semicircle = 1.0, a” = 0.23 with a low-frequency limit at CY’ Figure 5a is the CY plot for the “coated” pellet and Figure 5b for the “bare” pellet. (The value of em obtained from the high-frequency limit, am = (em - 1)/ (ea a),is different in the two cases because it is the apparent values which are plotted and the results for the coated pellet include a small contribution from the coating.) The broad high-frequency dispersion for the “coated” specimen is considerably narrowed for the “bare” pellet, without a change in 70, while there is good resolution of the two dispersion regions for the “bare” pellet. The low-frequency absorption for the “bare” pellet is a true semicircle within experimental error and is ascribed to space charge polarization, as already discussed. Only at the lowest frequencies does the dc conduction contribute to the dielectric loss, as suggested by the broken line drawn at -45” in Figure 4 (the logarithmic scale of the ordinate should be noted) using a dc conductivity for this pure borax ohm-‘ ern-’, measured directly. The of 3 X parameters of the distribution obtained from Figure 5b are given in Table I.
+
Table I : Parameters of the Dielectric Dispersion for “Rare” Borax
_
_
____ High from ColeCole plot
Parameter
+J
0.52 6.0
(ern)ap€IC
52
(es)appC
TO'^ (see) roe (sec)
4
ox
~
-
Dispersion at-frequencyfrom a-plota
0.53
0 41 >>1 3 . 5 x 10-3
6.2 52 4.0 10-6 2 . 7 x 10-4
x
10-4
(calcd. from T ~
-
Low frequency from a-plota
... ‘ )
a plot data derived from Figure 5b. Empirical constant which measures the distribution of relaxation times. c Real dielectric constants a t the high- and low-frequency limits, respectively, of the distribution. d Intrinsic macroscopic relaxation time as defined by Scaife,z1 evaluated a t the center of the cy plot, L e . , a t maximum of a”, according to eq 1. 8 7 0 = [(e, 2)/(em 2)]70’ = macroscopic relaxation time, evaluated at the center of the Cole-Cole plot, i.e., a t maximum of e”.
+
+
( b ) Aging. The magnitudes of the dielectric quantities in the high-frequency relaxation process, starting at about 100 cps and extending to 100 kcps, are critically dependent on the age of the compressed powder and on the ambient relative humidity. The
2579
low-frequency dispersion is also influenced by these factors, but to a much lesser extent; when the time dependence of the dielectric properties of borax is discussed below it is the high-frequency relaxation which is invariably being referred to. For compressed powders of Li2S04.H20van BeekZ4 observed a shift in tan,,,6 with time toward lower frequencies. This he interpreted in terms of a recrystallization as “the sample had lost very little weight.” Time-dependent results were also observed in single alum crystals,25where the dielectric properties did not reach a final steady level even over a few weeks. For borax, however, van Beek found no such behavior. In a personal communication he reports that he “rested his samples (of borax) for a day” in an atmosphere of relative humidity of approximately 50% before commencing measurements, which probably explains the discrepancy since most of the changes we describe occurred during the first day after pressing (Figure 1). A comparison between the results obtained from our ‘(coated” specimens and the results published by van Beek6shows that the general features of the two curves for day-old pellets are in agreement (it is assumed van Beek used “coated” specimensz4); our “bare” pellets show considerable deviation from van Beek’s results with much more detail. In general there are two other types of explanation (in addition to possible recry~tallization~~) presented for aging phenomena similar to those we have defound a decrease in scribed. Thus, Kurosaki, et tan 8app with time for water adsorbed on nonalkali glass cloth even when the sample was kept at a fixed water vapor pressure and interpreted their results in terms of a phase change in the adsorbed water phase, changing from a relatively freely bonded form t o a more tightly bonded form. The second type of explanation is due to Dryden and R l e a k i n ~ ,who ~ ~ have studied dielectrically the effects of grinding and pressing certain ionic salts.
(23) If the only source of dielectric loss is dc conduction, then the real portion of the dielectric constant is frequency independent, with a value eo. If zc is substituted for c ’ in eq 4 for a’ and a’’ and s”is eliminated, there is obtained
which is an equation for a semicircle in the complex a’, a” plane. If eq 4 with e’ = ec is separated into its real and imaginary parts, it can be seen that when c”do becomes very large, at low frequencies, a’ = 1.0 and a” = 0. (24) L. K. H. van Beek, Physica, 29, 1323 (1963). (25) L. K. H. van Beek, ibid.,30, 1907 (1964). (26) S. Kurosaki, S. Saito, and S. Sato, J . Chem. Phys., 23, 1846 (1955). (27) J. S. Dryden and R. J. Meakins, Satitre, 171, 307 (1953).
Volume 71 Sumber 8 ~
J u l y 1967
2580
They observed a reduction in espp" with time which they attributed to an evaporation of water from mother liquor in the solid which had been set free on grinding and pressing. I n many respects our results are very similar to the findings of Dryden and Meakins and the decrease in espp' and weight of borax with time can be attributed, at least partially, to evaporation of water from the mother liquor. However, the decrease in eapp' and weight should both approach limiting values simultaneously, which is not the case, as Figure 1 shows, for the weight loss continues even after the dielectric constant has reached its limiting value. lIenzelZ8has shown that the water vapor pressure of borax is 14 mm at 25" and so borax should dehydrate below 60% relative humidity a t 25". Thus the abovementioned weight loss arises not only from a desorption of adsorbed mother liquor, but also from a slight dehydration, which accounts for the discrepancy in Figure 1. Both -1Ieneelz8and Bezjak, et have shown that the spontaneous dehydration of borax does not occur to the pentahydrate phase but that the product is an amorphous phase of much lower water content. Allowing for some weight loss owing to an evaporation of adsorbed mother liquor, the amount of amorphous borax present in the samples is something less than 0.25%. It seems then that the high-frequency absorption arises from the orientation polarization of water molecules on the powder surface. On aging the less strongly adsorbed, and so more mobile water molecules either desorb or move to sites of stronger adsorption, accounting for an increase of relaxation times (the absorption peaks move to lower frequencies). Owing to the complexity of the system it is difficult to say whether or not redistribution is more important than desorption or what part, if any, is played by the amorphous phase. One fact remains certain, that owing to the ephemeral nature of the high-frequency relaxation it is not possible to associate this relaxation with an orientation of the water molecules of crystallization in borax. This last fact is further emphasized in a comparison of the results from single crystals and compressed powders of borax. The relative surface area of a single crystal is very much smaller than that of a powder and the amount of adsorption correspondingly smaller. Therefore on the single crystals it is the bulk properties of the materials which are measured, unobscured by the interference of adsorbed water or amorphous material, explaining the substantial differences between the experimental results for powders and for single crystals. The dependence of e' on the sample thickness The Journal of Physical Chemistry
E. W. GIESEKKEAND L. GLASSER
and frequency are strongly in favor of a space charge polarization even in crystals. (c) Doping. The model thus developed accounts well for the doping experiments. The very fact that the F-, C1-, and HC03- ions, which are of various sizes, all induce the same dielectric changes in borax suggests that it is not the incorporation of ions into the regular borax structure which has brought about these changes, but that they produce an enhanced ionization of surface water, observed in the increase in conductivity. Dipolar orientation would be considerably easier in the presence of these ionic states in the surface water, explaining the shift of the maximum in tan 6,,, to higher frequencies, shown in Figure 8.
V. Correlation of Results Comparison of these results with those obtained by proton magnetic resonance studies on borax is interesting. All investigator^^^-^^ agree that the magnetic resonance curve consists of a broad and a narrow portion. The broad portion30is not of particular interest. A narrow magnetic resonance line, originating from the protonic motions in the solid, has been found by Rlaricic, et u Z . , ~ ~ to be present in Li2S04. HzO, another proton conductor. From quantitative considerations, they concluded that it was unlikely that this narrow portion could arise from adsorbed water. The presence of a narrow line in the proton magnetic resonance measurements indicates that protons or some water molecules in the solid are mobile. It is not unreasonable to relate this fact to the presence of proton conduction in this material. The significance of such a result is important, particularly when the possibility of proton conduction in other compounds is considered. The dielectric and solid-state electrolysis experiments on compressed borax powders indicate the important role played by adsorbed water in the proton conduction. It seems reasonable to relate the proton conduction to the presence of adsorbed water on the borax surface. However, if this alone were correct then a sample of borax which had been dried out sufficiently should not exhibit proton conduction. Al(28) H. Menzel, Z. Anorg. AZZgem. Chem., 224, l (1935). (29) A. Bezjak, I. Jelenic, S. Maricic, and Z. Meic, Croat. Chem. Acta, 35, 295 (1963). (30) G. E. Pake, J . Chem. Phys., 16, 327 (1948). (31) S. S. Dharmatti, S. A. Iyer, and R. Vijayaraghavan, J . Phys. SOC.Japan, 17, 1736 (1962). (32) S. LMaricic, Z. Vekuli, and M. Pintar, J . Phys. Chem. Solids, 23, 743 (1962).
DIELECTRIC BEHAVIOR AND PROTON CONDUCTION IN SOLIDS
though higher field strengths were required for the older pellets than for freshly pressed ones, proton conduction was nevertheless observed. This apparent conflict can be resolved if it is accepted that the proton can travel only a limited distance in the adsorbed water layer before its path is interrupted by a crystallite. I n order to traverse the powder pellet completely the proton must be able to pass through this crystallite, after which it will move again in the adsorbed layer. Eventually, after using successive paths through crystalline material and along adsorbed water layers, the proton will reach the cathode. The freshly pressed pellet contains a larger amount of adsorbed water than the older pellet; consequently, in the fresh pellet a large portion of the total proton conduction path will be in the adsorbed water phase rather than in the crystal, while in the older pellet the proton must pass through crystalline material to a much greater extent. The proton can be expected to experience a much larger resistance to motion in the crystal than in the adsorbed water phase (this is confirmed by the high resistivity of single crystals), explaining why proton conduction is only observed at higher field strengths for older pellets. I n this light, the proton conduction can still be regarded as an intrinsic property of the solid. I n terms of equivalent electrical resistances, the proton path is described by two lumped resistors in series; one, representing the pathway through crystalline material, has a large resistance per unit length of the path while the second, representing the pathway through adsorbed water layers, has a smaller resistance per unit length of the path. As the adsorbed water disappears, the proton path length through crystalline
2581
material will correspondingly increase and so will the total resistance to proton transport. This resistance increase is a logical consequence of the model, since the more favorable paths have disappeared in the older pellet. The low proton efficiency indicates a considerable electronic conduction in the borax pellet. As Rosenbergs3 has shown for proteins, this electronic conduction can be a function of the proportion of water present in the solid and can give rise to a space charge polarization. In general, it is not easy to distinguish dielectrically between electronic and ionic effects. However, electrons would exhibit dielectric absorption, other than due to space charge polarization, at frequencies much higher than the upper limit of 10 kcps observed here; the higher frequency absorption can only be ascribed to the motion of massive or strongly bound particles such as protons or water molecules.
Acknowledgments. The support of this work by the South African Council for Scientific and Industrial Research in the form of grants toward the purchase of capital equipment and by a bursary to E. W. Giesekke is gratefully acknowledged. The authors are indebted to Dr. G. S. Parry, Imperial College, London, for his suggestion of the value of these dielectric studies, to Dr. L. K. H. van Beek, presently of the Philips Research Laboratories, Eindhoven, for the information he supplied and for his interest in the work, t o Dr. P. G. Hall of this university for valuable discussions, and to the Department of Electrical Engineering of this university for the use of a low-frequency generator. (33) B. Rosenberg,
J. Chem. Phys., 36, 816 (1962).
Volume 71 Number 8 J u l y 1967 ~
