J . Phys. Chem. 1986, 90, 6358-6362
6358
to variations in the water content of the membranes. 2. Cu2+ ligated to bound water is immobilizcd, on the time scale of the ESR experiment, even at 298 K; the complex which represents ligation of Cu2+to mobile water tumbles fast on the same time scale and averages the g and hyperfine anisotropies above 250 K. 3. Preferential solvation of Cu2+ in the hydrophilic phase is observed as the concentration of Cu2+ increases. 4. Heat treatment at 435 K for 10 h at Torr removes the mobile water but not the bound water in the Nafions studied. 5 . Cu2+-Cu2+pairs are observed when the Cu2+concentration in the cation mixture is 10% and above. The upper limit of the interion distance in the pair is 5.5 A.
Acknowledgment. This research was supported by the Research Corp. and by an N S F Grant DMR-8501362 for the purchase of
the Bruker ESR spectrometer. We thank Dr. Robin Hood of Wayne State University for the use of the Varian ESR spectrometer, where the initial spectra were measured. We are grateful to Dr. L. L. Burton of Du Pont for sending us the Nafions used in this study.
Note Added in Proof. As this study was being typed for publication, a quantitative method for determination of the absolute water content in Nafion-H membranes by proton NMR was published (Bunce, N . J.; Sondheimer, S. J.; Fyfe, C. A. Macromolecules 1986,19,333). This study is in agreement with our conclusions that Nafion properties have to be characterized for a known water content or for specified conditions of relative humidity. Registry No. CuS04, 7758-98-7; ZnS04, 7733-02-0; Nafion 117, 66796-30-3.
Dielectric Relaxations in the Liquid and Glassy States of Glucose and Its Water Mixtures R. K. Chan, Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada
K. Pathmanathan, and G. P. Johari* Department of Materials Science & Engineering, McMaster University, Hamilton, Ontario L8S 4L7, Canada (Received: March 24, 1986; In Final Form: July 7 , 1986)
The permittivity and loss of anhydrous glucose and its 10, 15, and 30 wt % water mixtures have been measured from 77 to 350 K in both the glassy and liquid states over a frequency range 1-105 Hz. Two relaxation regions were observed: one above and the second below T,. The T > Tgrelaxation follows the Vogel-Fulcher-Tamman equation and the T < T,, the Arrhenius equation with an activation energy of -60 kJ mol-’. These features are similar to those observed for amorphous polymers. Addition of water raises the strength of the sub-T, relaxation and lowers its rate. On dilution with water the relaxation regions approach each other for two reasons: (i) a decreased glass-transition temperature, and (ii) a decreased rate of the sub-T, relaxation. The increase in the strength of the subT, relaxation peak is attributed to an increased orientational correlation of dipole moments in the localized, high volume, high entropy regions of an otherwise rigid glassy matrix, where molecular reorientation continues to occur.
Introduction Vitrification by supercooling of aqueous solutions is currently receiving much attention for potential use in cryobiological apIn particular, a large number of aqueous solutions, mostly of inorganic solutes, have been vitrified, with varying degree of success, by cooling them at different rates3 Aqueous solutions of organic substances, on the other hand, seem to have been overlooked, despite the greater ease with which they vitrify and their undoubtedly greater relevance to cryobiology and other applications. One objective of this study was to determine the changes in the characteristics of glass transition of a hydrogenbonding organic substance of biological importance when water is added to it. Addition of a fluid solute usually lowers the glass transition temperature, Tg,of the substance. This effect is particularly well-known as ”plasticization”, in amorphous polymers: where the dissolution of a small amount of water or another organic solute in an organic polymer substantially lowers the T, of the polymer. The effect is interpreted on the basis of increased free volume and a weakening of the interchain interactions and it is assumed that interactions in such plasticized polymers are (1) Angell, C. A. Annu. Rev. Phys. Chem. 1983, 34, 593, and references therein. (2) Adrian, M.; Duoochet, J.; Lepault, J.; McDowell, A. W. Nature (London) 1984, 308, 42. Also in Trends Biol. Sci., in press. (3) Angell, C . A.; Sare, E. J. J . Chem. Phys. 1970, 52, 1058. (4) Ferry, J. D. Viscoelastic Properties of Polymers; Wiley: New York, 1980.
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predominantly intramolecular, or conformational? although the intermolecular interaction between the molecular segment and solvent molecules may be appreciable. The added substance also affects the strength of dielectrically observed secondary relaxations, or the number of molecules, or their segments, capable of undergoing thermally excited motions in the glassy state of the polymer. Recent studiesSv6have shown that neither the thermodynamic nor the relaxational characteristics of amorphous polymers differ from other glasses despite the differences in the strength of interactions and/or the nature of disorder among them. Therefore, it seems that “plasticization” of organic molecular glasses with water may affect their relaxation characteristic in a way similar to that in organic polymers. The second objective of this study was to investigate the effect of such addition on the localized molecular motions in the glassy state. We describe a calorimetric and dielectric relaxation study of the liquid and glassy states of anhydrous glucose, and of its mixtures with water and compare the results with those of pure alcohols and with amorphous polymers. Experimental Methods Analytical grade anhydrous D-(+)-glucose obtained from the British Drug House (Canada) Ltd. was studied without further treatment. The aqueous solutions were prepared by weighing. ( 5 ) Johari, G. P.Ann. N . Y.Acad. Sci. 1976, 279, 117. (6) Johari, G. P. J. Chem. Phys. 1985, 82, 283.
0 1986 American Chemical Society
T, for Glucose and Glucose-Water Mixtures
The Journal of Physical Chemistry, Vol. 90, No. 23, 1986 6359
30
1 260
Figure 1. The complex plane plots of c” for (a) pure glucose at 325.3 K and (b) a 10 wt % water-glucose mixture at 278.4 K. The number next to the data point is the frequency in kHz.
300 T/ K
340
Figure 2. A plot of eo against temperature for (a) pure glucose, (b) a 10 wt % water-glucose mixture, and (c) a 15 wt % water-glucose mixture.
A General Radio Model 1615A capacitance bridge was used for the measurement at frequencies from 100 to 2 X lo4 Hz, and a General Radio Model 716C capacitance bridge was used for measurements from 2 X lo4 to 5 X lo5 Hz. For low-frequency measurements (0.1 to 100 Hz) a bridge similar to that described by Cole and Berberian was used. The dielectric cell consisted of a threeterminal guarded parallel plate condenser, based on the type used by Johari.’ This was constructed from stainless steel with teflon spacers. The cell had a stray capacitance of less than 0.001 pF and a nominal geometrical capacitance of 18 pF. It required less than 6 mL of liquid sample. The geometric capacitance of the cell increased with decreasing temperature. This increase which was due to the contraction of the teflon spacers was largest at high temperatures. From 77 to 150 K, the increase was about 3%. The change of cell constant was accounted for in all calculations. The glass transition temperature was measured with a Perkin-Elmer differential scanning calorimeter, DSC- lB, at a heating rate of mid.
Results The calorimetric glass transition temperature, T,, of anhydrous glucose is 302 K and of its 10, 15, and 30 wt % water-containing mixtures are 251, 246, and 201 K, respectively. Mixtures containing less than 10 wt % water required melting at temperatures > 373 K. This caused evaporation of water and thus a substantial uncertainty in the composition. Therefore, only those compositions which did not require melting above 373 K were studied. Typical complex plane plots of permittivity, d, and loss, d’, of pure glucose and 10 wt % water mixture are shown in Figure 1, at temperatures for which their respective ratio, TIT, = 1.1. Both the high- and the low-frequency parts of the curves were well resolved at several temperatures for each substance. As seen in Figure 1, the plots for both pure glucose and 10 wt % water mixture appear highly skewed at the high-frequency end. Within the experimental error the data could be fitted equally well to both the Davidson-Cole8 equation with @ = 0.34 and 0.23 for pure glucose and 10 wt % water-glucose mixture, respectively, and the Kohlrausch-Williams-Watts9 empirical equation with @ = 0.47 and 0.37, respectively. An attempt to fit the data to Havriliak-Negami equationlo was made. The standard deviation of the fit was greater than that in the other two cases. The limiting low-frequency permittivity, eo, obtained from the intercept of the complex plane plots is plotted against temperature in Figure 2. In the temperature range of overlap, of the mixture at 298 K increased with water content, approximately according to the equation co(mixture) = (1 - x)co(glucose) + xco(water) where x is the weight fraction of water at 298 K. The value of err of the pure glucose and its water mixtures at 1 kHz is plotted against temperature in Figure 3. It is clear in Johari, G. P. Phil. Mug.1982, 46, 549. (8) Davidson, D. W.; Cole, R. H. J. Chem. Phys. 1951, 29, 1484. (9) Williams, G.; Watts, D. C.Trans. Furuduy SOC.1970, 66, 80. (10) Havriliak, S.; Negami, S.J . Polym. Sci. 1966, 14, 99. (7)
XI0
280 320 240 T/K Figure 3. A plot of e’’ against temperature at 1 kHz for (a) pure glucose, (b) a 10 wt % water-glucose mixture, and (c) 15 wt % water-glucose mixture. Arrows indicate the glass transition temperature.
these isochrones that, in addition to a relaxation peak at 330 K observed above T,, a second relaxation peak appears at -210 K in pure glucose. The 10 wt % water-glucose mixture shows a peak a t 280 K ( T , = 251 K) and another at -220 K. 15 and 30 wt % water-glucose mixtures showed no relaxation peak below T,, instead a shoulder below T, appeared in both substances. It seems that the secondary or @-relaxation peak (observed here at T < T,) becomes progressively less separated from the main or arelaxation peak (at T > T,) as the amount of water is increased. Despite this lack of separation in the isochrones, the @-relaxation peak could be clearly observed in the isothermal spectra of E” vs. l o g f i n 15 and 30 wt % water mixtures. Although a greater separation between the a- and @-relaxationpeaks was expected in the isochronal measurements at frequencies of less than 1 Hz, such measurements were not made in view of the fact that the @-peakintensity rapidly decreased with temperature. This limited the accuracy with which the dielectric loss in the @-processregion could be measured below 10 Hz. The err spectra of pure glucose and 15 wt % water-glucose mixture in the @-relaxation region ( T < TJ are plotted in Figure 4 at several temperatures. The data are limited in the frequency range, and the half-width of the plot seems to be appreciably greater than 4 decades a t the highest temperature of measurements. The frequency at which the loss reaches a maximum,f,, in the E’’ spectra of both the a- and @-relaxationis plotted against reciprocal temperature in Figure 5. The plots for the a-relaxation process are curved. The relaxation rate follows the Vogel-Fulcher-Tamman equation,f, = A exp(-B/(T- To))where A , B, and To are empirical parameters. These values are listed in Table
6360 The Journal of Physical Chemistry, Vol. 90, No. 23, 1986
Chan et al.
TABLE I: Summary of Parameters for Glucose and Its Water Mixtures
tan L ( 8 ) /
e",@)/
substances
glucose
+ + +
10 wt % H20 glucose 15 wt % H20 glucose 30 wt % H 2 0 glucose
E,
€'',,,(a) at 1 kHz
0.036 0.045 0.055
T,/K
In A
B/K
To/K
1njJHz
kJ mol-'
302 251 246 201
37.4 49.8 40.1 39.3
2760 5218 3259 1837
242 160 178 158
43.4 35.1 36.9 47.1
61.7 49.8 54.1 64.4
tan &,(a) at 1 kHz 0.18 0.27 0.35 I
T d T,
To/Tg
at 1 kHz
0.80 0.64 0.72 0.79
0.67 0.84 0.88 0.96
'
x341.4K
+ 3 37.7 K
(A)
0
I t
325.3 K
0.1
0
I
x285.8K + 270.4 K
,n\
'I5"'
0
267.4K
/
199,QK
0.2
0'
,
I
1o3 I o5 f/Hz Figure 4. The dielectric loss spectrum of 8-relaxation of (a) pure glucose and (b) a 15 wt % water-glucose mixture. The temperature, in K, are 10
indicated near the curves.
I
10'1
3
4
IO~K/T
5
Figure 5. A plot of the frequency of loss peaks of the a-and 8- relaxation regions against reciprocal temperature: 0,a-relaxation; e, 8 relaxation, (A) pure glucose, (B) a 10 wt % water-glucose mixture, and (C) a 15 wt % water-glucose mixture.
I. The rate for the @-relaxation process follows an Arrhenius equation, f, =fo exp(-EIRT). The values of the preexponential factor, Info, and the activation energy, E, are also given in Table I. Discussion The dielectric relaxation features of pure glucose and its water mixtures are remarkably similar to those observed in the supercooled and glassy states of amorphous polymers" and of rigid molecular substances?.'* Detailed discussions of these similarities and their implications for our concepts of the structure of a liquid and glass have been given earlier, where it is also shown that the (1 1) McCrum, N. G.; Read, B. E.;Williams, G. Anelustic and Dielectric Effects in Polymeric Solids; Wiley: London, 1967. (12) Johari, G. P.; Goldstein, M.J. Chem. Phys. 1970, 53, 2372.
1o2
I
1
I
IO'
Figure 6. Normalized plots of the a-relaxation spectrum of (a) pure glucose and (b) a 10 wt W water-glucose mixture.
glassy state of orientationally disordered crystals and of the various forms of (mesomorphic) liquid crystals have a remarkable resemblance in their thermodynamic and relaxation characteristics with amorphous p01ymers.I~ Therefore, we are mainly concerned here with the particular features of glucose and with the effect of addition of water to it. The a-and P-Relaxations. Pure water shows a single relaxation time,14 or @ = 1. Therefore, we expect that addition of water to glucose would increase the parameter @ of the a-relaxation process. But the addition of water to glucose decreased the value of the parameter 8, as seen in Figure 1 and more clearly shown in Figure 6, where normalized plots of e'' against log f (Le. ~"/e", vs. log (flf,)) are given. The dimensionless parameter @ in both the Davidson-Cole* equation and the Kohlrausch-Williams-Watts9 equation is a direct measure of the nonexponentiality or, equivalently, the breadth of the distribution of relaxation rates. Smaller values of @ correspond to increased nonexponentiality and are accompanied by an increase in the width of the E" vs. log f curves at half-height of their peaks. The decrease in the parameter @ of the Davidson-Cole equation, or the increase in the half-width of the normalized e" spectra in Figure 6, is large on the initial ' corresponds to 53 mol 7%) to glucose. addition of water (10 wt % Further addition of water has a relatively small effect and is only approximately measurable in our studies. For 15 wt %, or 64 mol %, P of the Davidson-Cole equation is 0.22 at TIT, = 1.1. As shown in Figure 6, the relaxation spectrum of the a-process becomes broader on addition of water to glucose. The half-width of the a-relaxation spectrum increases from 2.3 decades for pure glucose to 2.7 decades for a 10 wt % water-glucose mixture. Similarly, as shown in Figure 7, the relaxation spectrum of the P-process also becomes broader on addition of water to glucose. The half-width of the spectrum increases from 5 decades in pure glucose to 6 decades in a 10 wt % water mixture. The half-width (13) Johari, G. P. Relaxations in Disordered Sysrems, Ngai, K. L., Wright, G. B., Naval Research Laboratory: Washington, 1985; p 17. (14) Hasted, J. B. In Wutei-A Comprehensive Treatise, Vol. 1, Franks, F., Ed.; Plenum: New York, 1972; Chapter 8.
The Journal of Physical Chemistry, Vol. 90, No. 23, 1986 6361
Tg for Glucose and Glucose-Water Mixtures
0.6
1
(C)
6“ €A t
i
0
01
,
I
10‘
1
I
IO2
f/fm
Figure 7. Normalized plots of the &relaxation spectrum of (A) pure glucose and (B) a IO wt % water-glucose mixture.
IC
2 20 240 TfK F m e 9. The amplitude of maximum loss, e“,,,, against temperature for the &process of (A) pure glucose, (B) a 10 wt % water-glucose mixture, and (C) a 15 wt % water-glucose mixture. 180
200
does not follow the inverse temperature dependence of polarization according to the Curie law. The total polarization, i.e. the sum of the strengths of the a-and j3-relaxation processes, follows the Curie law, as the product of T and (eo - nD2),where nDz = 3, for water-glucose mixture remains unchanged with T. Thus the aand &processes are interrelated via a conservation relation, Ae = Aea A€@,with respect to changes in temperature. But most significantly, it qualitatively seems from Figure 8 that, at a certain temperature far above TB(-400 K), the e”, of the a-process would approach the value of zero, but the e”, of the & p r m would increase rapidly and become very large (Figure 9) such that, at that temperature, the contribution to Ae from the a-process would be negligible. Such a temperature has been suggested as one at which the a-and @-processestend to merge. Figure 5 suggests that this temperature is less than 400 K-the discrepancy being mainly due to the large extrapolations involved in the estimates from the nonlinear plots of Figures 8 , 9 , and 5. Above the temperature of approximately 400 K, the requirements of cooperative motion of dipoles giving rise to the a-process is removed as a result of the relatively low density of the liquid. The entire orientational polarization of the liquid then involves a relaxation same in mechanism as the j3-proce~s.~ One may also consider the possibility that the @-processis due to water whose motion has been slowed by vitrification and/or hydrogen bonding to glucose. Although this would be consistent with (i) the intensity of the &relaxation increasing with water content, (ii) the water-induced dielectric secondary relaxations observed in several polymers, (iii) the behaviour of several aqueous electrolytic solutions,” and (iv) the different response of the shift of the @-relaxationpeak to addition of water compared with that of amorphous polymers: we believe that the motion of water molecules in the vitreous state of glucose solution is only partly responsible for the /3-relaxation, as anhydrous glucose also shows a well-separated, although less intense, @-processas seen in Figure 3. Since the height of the @-peakin the anhydrous glucose is approximately half of that in 10 and 15 wt % water-glucose mixtures (Figures 3 and 4), it is unlikely that our “anhydrous” glucose (whose purity was established by measuring its melting point which agreed with that of anhydrous glucose, 421 K, and by the lack of weight loss on keeping at 373 K for 3 h) contained sufficient water to cause such a large @-peak. The Relaxation Rates. The relaxation rates for both the aand &processes in the three substances, seen in Figure 5, clearly show that the two processes become progressively less separated both in the temperature and in the frequency planes as water is added to glucose. Since the glass transition temperature is associated with the cessation of the a-process at a time scale of 104 s, it follows that, at a constant frequency, the @-processbecomes progressively closer to Tg. This is evident in Table I where the ratio T8(1 kHz)/ Tg rapidly increases with the water content in ’ (or >81 mol a)the @-process glucose. It implies that at >30 wt %
+
:E 6 0
2
260
300
340
T/ K Figure 8. The amplitude of maximum loss, e”,, plotted against temperature for the a-pocess of (A) pure glucose, (B) a 10 wt % waterglucose mixture, and (C) a 15 wt % water-glucose mixture.
of the &process in amorphous solids generally increases with decreasing temperat~re.’~ However, the normalized loss against frequency plots of water-glucose mixtures in Figures 6 and 7 show that the half-width of both the a-and 8- processes remain nearly constant with changing temperature. The relative heights of the @- and a-relaxation peak at an f, of 1 kHz are given in Table I. The value [e”,(~)/e”,(a)]Iwz increases on the addition of water to glucose, which means that an increasing fraction of the total number of dipoles, either due to an increase in the number or in the dipole moment of the molecules (or both), is involved in the &relaxation. The ratio [tan 6,(@)/tan 6,(a)Ilmzis in the range 0.18-0.35, which is comparable to that observed in other molecular glass-forming substances.” This ratio increases on the addition of water in approximately the same ratio as [e”,(@)/e”,(a)]. The maximum dielectric loss, t-”,, obtained from the isothermal spectrum for the a-process is plotted against temperature in Figure 8 and for the &process in Figure 9. The addition of water is seen to decrease e’/, for the a-process but to increase et‘, for the @-processat a constant temperature. This conclusion is partly based on a short extrapolation of the anhydrous glucose data to T = 290 K in Figure 8. An increase in temperature has a remarkably different effect on the e”, of the two processes. For the a-process, the &,’ for a given substance decreases on increasing the temperature as seen in Figure 8, but for the @-processfor the same substance, it increases rapidly with increasing temperature (Figure 9). This shows that the strength of the &process increases when a glass is heated toward it Tg,and further that the @-process
-
(15) Hodge, I. M.; Angell, C. A. J . Phys. Chem. 1978,82, 1761
6362
J . Phys. Chem. 1986, 90, 6362-6365
may not be easily resolved a t kHz frequencies, or that at temperatures not very far below Tg,the @-processwould also freeze out on a time scale of one's experiment. Thus the possibility of the Occurrence of molecular motions in >30 wt % water-glucose mixtures at T I Tgis much less than it is in more-glucose-containing mixtures. In the Vogel-Fulcher-Tamman equation, f, = A exp(-B/( T - To)),the values of parameters A, B, and To are subject to both the method of analysis and the number of data points available for the a n a l y ~ i s . ' ~ The J ~ values given in Table I represent merely an empirical fit. The only significance is in the ratio T,/T, which decreases on addition of 10 wt % water to glucose. On further addition of water, the ratio increases. This means that In f, vs. 1/T plots for >30 wt % water-glucose mixtures would become increasingly more steep at temperatures near TB. The activation energies for the @-process are in the range of 50-64 kJ mol-I. There is a decrease in its value when 10 wt % water is added to glucose and thereafter an increase on further dilution with water. The change is relatively small and their interpretation within our present knowledge of the origin of @process seems less clear. However, this range of values is similar to that observed for @-processin other glassy materials.6 The presence of a @-processin the glassy state has been suggested to indicate localized high-volume, high-entropy regions, in the otherwise rigid matrix of a glass, where molecular orientation and translational motions persist.13 An analysis of Figure 5 shows that at a constant value of T/T,, the rate of @-process progressively decreases as water is added to it. The decrease in the rate of @-process may involve a closer packing of the highvolume, high-entropy regions allowed by the presence of hydrogen-bonded water molecules, which can also hydrogen bond to the hydroxyl groups of glucose. If such packing involved a greater correlation of dipole vectors of the water molecules or the dipolar (16) Johari, G. P.; Whalley, E. Furuduy Symp., Chem. SOC.1972,6,23. (17) Angell, C. A.; Smith, D. L. J . Phys. Chem. 1982,86, 3845.
groups of glucose molecule, the strength of the @-processwould also be increased. The latter effect has been discussed earlier here and is also seen in Table I and Figure 9. The Effect of Plasticization with Water. The effect of water on glucose, as for organic polymers, is to lower the glass transition temperature. The effect in polymers has been interpreted as due to an increased free volume and the consequent loosening of the interchain and/or intrasegmental motions? and in this sense the effect observed in glucose is similar to that in polymers. But the effect of plasticization by water on the @-processin glucose is quite the opposite of that observed in amorphous polymers. External plasticization of most polymers (for a list of such polymers see ref 4 and 18) does not seem to affect the location of the @-relaxation peak in a temperature plane or its frequency in an isothermal spectrum.18 It also does not affect the height of the @-relaxationpeak. Plasticization of glucose causes the @-relaxation peak to shift to higher temperatures as Seen in Figure 3, or to lower frequencies as seen in Figure 5 . It also raises the height of the @-relaxation peak by more than a factor of two (Figure 9). Clearly, the plasticization effects in glucose are dominated by the directionality of the hydrogen bonds between water molecules and the OH groups of a glucose molecule, as discussed in the preceding section. The Static Permittivity. The strength of relaxation, AE = eo - nD2,where eo is the low-frequency permittivity which decreases with increase in temperature in all cases as seen in Figure 2. The product TAt is found to decrease with temperature for anhydrous glucose but to remain approximately constant at 1.0 X lo4 and 1.2 X lo4 K for 10 and 15 wt % water-glucose mixtures. Thus the orientational correlation of the dipole moments in pure glucose decreases on increasing the temperature while little change occurs in their water mixtures in the relatively narrow temperature range of our study. Registry No. Glucose, 50-99-7. ~
(18)
~~
~~
Heijboer, J. In?. J. Polym. Murer. 1977,6, 11, and references therein.
Interpretation of the "Stokes Radius" in Terms of Hubbard-Onsager's Dielectric Frictlon Theory K. Ibuki and M. Nakahara* Department of Chemistry, Faculty of Science, Kyoto University, Kyoto 606, Japan (Received: April 1 , 1986; In Final Form: July 7, 1986)
The velocity field around the lithium ion in water has been schematically presented according to the solution of the Hubbardansager electrohydrodynamic equation where the coupling of viscous and dielectric frictions is taken into account in the self-consistent manner. The HO velocity field around the ion is found to be much smaller than the Stokes velocity field around the corresponding uncharged sphere as a result of the strong attractive interaction between the ion and solvent dipoles. The often-used concept of the "Stokes radius" and the apparent validity of the Walden rule exceptionally for the lithium ion in water against temperature are successfully explained by means of the HO dielectric friction theory. The failure of the early dielectric friction theory by Zwanzig is ascribed to the incomplete treatment of the coupling of viscous and dielectric frictions on the migrating ion on the basis of systematic comparison of the early and modern dielectric friction theories.
Introduction The purpose of the present study is to promote our understanding of the significance and usefulness of the modem dielectric friction theory developed to an almost final form by Hubbard and Onsager (H0).1*2 At present this kind of work is of great necessity because little proper attention is paid to the modern dielectric friction theory on the experimental side. The conventional pro(1) Hubbard, J.; Onsager, L. J . Chem. Phys. 1977,67, 4850. (2) Hubbard, J. J . Chem. Phys. 1978, 68, 1649.
0022-3654/86/2090-6362$01.50/0
cedure for interpreting the experimental value of the limiting ionic conductance Xo remains in an underdeveloped state basically relying upon the classical hydrodynamic (Navier-Stokes) equation leading to the Stokes-Einstein law or the Walden product as criticized in our previous paper.3 Although the effects of ion size and solvent structure on ion mobility have been discussed with the aid of the classical hydrodynamic equation, this is not reliable because the equation completely neglects the charge effect (3) Nakahara, M.; Ibuki, K. J . Phys. Chem. 1986, 90, 3026.
0 1986 American Chemical Society
