J. Phys. Chem. 1989,93, 357-366
357
High-Frequency Dlelectric Relaxation of Water Bound to Hydrophilic Silica Gels Takeshi Sakamoto,+ Department of Physics, Faculty of Science, University of Tokyo, Bunkyo, Tokyo 113, Japan
Haruki Nakamura, Protein Engineering Research Institute, Furuedai, Suita, Osaka, 565 Japan
Hatsuho Uedaira, Research Institute for Polymer and Textiles, Tsukuba, Ibaraki 305, Japan
and Akiyoshi Wada* Department of Physics, Faculty of Science, University of Tokyo, Bunkyo, Tokyo 113, Japan (Received: March 14, 1988)
Dielectric and calorimetric properties of water bound to hydrophilic silica gels with and without ionized groups were investigated in partially hydrated powder states of several water contents, over the temperature range from -100 to 23 O C . Dielectric measurements were performed by time domain reflectometry (TDR) in the frequency range from 1 MHz to several gigahertz. Calorimetric measurements were performed by differential scanning calorimeter (DSC). The hydration water of the nonionized polar gel can be clearly classified into tightly and loosely bound water dynamically. The former has a dielectric relaxation time near 1.5 ns, whose saturation content is similar to the thermally unfreezable water content and is estimated to cover the gel surface just by one layer. The latter has a relaxation time of 50-100 ps and is assigned to the secondary layer. The dielectric relaxation of the hydrated ionized gel is multidispersive described mainly by the Cole-Davidson function, indicating that the hydration water has continuously distributed mobility according to the interaction with the ionized groups. The apparent dielectric constant of hydration water is about 10 for the nonionized gel and 50-70 for the ionized gel.
1. Introduction Hydration of biological macromolecules has been investigated by many experimental and theoretical methods.'" The importance of the interaction between biopolymers and surrounding water molecules has been recognized on a molecular level, such as folding, stability, and function of p r o t e i n ~ , ~and , ~ - ~structural polymorphism of DNA.6*10-'2 Physical properties of hydration water are different from those of bulk water in the sense of both statics and dynamics. Relaxation methods are powerful and effective techniques for the study of water dynamics7 Among them, dielectric relaxation measurement provides unique and quantitative information on the heterogeneous nature of the rotational relaxation of hydration water. Moreover, dielectric measurement gives us the dielectric constant of hydration layer, which is essential in understanding electrostatic effects on a biopolymer surface. Measurements of the dielectric spectra (or constants at specific frequencies) focused on the hydration of biopolymers have been made for protein solution^,'^-'^ protein powders,lb2' D N A solut i o n ~ , ' ~and , ~ ~D-N~A~gels.25 Though dielectric measurement of aqueous solution has the advantage of ease of sample preparation and of data reproducibility, it poses severe difficulty for evaluation of the contribution of bound water from that of bulk water, because the former is usually below the noise level of the dominant bulk water signal. On the other hand, measurement in a hydrated powder state gives full information on the dielectric properties of hydration water and their hydration content dependence and is not disturbed by bulk water. In the powder sample, however, there are several difficulties in fixing the experimental conditions such as hydration content and packing density. We have recently developed the dielectric measurement system based upon time domain reflectometry (TDR) which overcomes the above difficulties;26 precise dielectric spectra of partially hydrated powder sample have been observed in the frequency range from megahertz to several gigahertz and in the temperature range from -100 O C to room temperature. Present address: Advanced Research Laboratory, Hitachi, Ltd., Kokubunji, Tokyo 185, Japan.
0022-3654/89/2093-0357$01.50/0
Time domain reflectometry (TDR) is a measuring technique of dielectric spectra in the time Its effectiveness is due to its short measuring time with wide frequency coverage (a (1) Water, A Comprehensive Treatise; Franks, F., Ed.; Plenum: New York, 1975-1982; (a) Eagland, D., Vol. 4, p 305; (b) Berendsen, J. J. C., Vol. 5, p 293; (c) Finney, J. L., Vol. 6, p 47; (d) Derbyshire, W., Vol. 7, p 339. (2) Water in Polymers; Rowland, S . P., Ed.; American Chemical Society: Washington, DC, 1980. (3) Biophysics of Water; Franks, F., Mathias, S. F., Eds.; Wiley: ChiChester, 1982. (4) Kuntz, I. D.; Kauzmann, W. Adu. Protein Chem. 1974, 28, 239. (5) Edsall, J. T.; McKenzie, H. A. Adu. Biophys. 1978, 10, 137; 1983, 16, 53. (6) Saenger, W. In Principles of Nucleic Acid Structure; Springer-Verlag: New York, 1984; p 368. (7) Rupley, . . J. A.; Gratton, E.; Careri, G. Trends Biochem. Sci. 1983,8,
18. (8) Finney, J. L.; Poole, P. L. Comments Mol. Cell. Biophys. 1984, 2, 129. (9) Ooi, T.; Oobatake, M. J. Biochem. 1988, 103, 114. (10) Saenger, W.; Hunter, W. N.; Kennard, 0. Nature (London) 1986, 324, 385. (1 1) Prive, G.; Heinemann, U.; Chandrasegaran, S.; Kan, L.-S.; Kopka, M. L.; Dickerson, R. E. Science (Washington, D.C.)1987, 238, 498. (12) Tao, N. J.; Lindsay, S. M.; Rupprecht, A. Biopolymers 1987,26, 171. (13) Buchanan, T. J.; Haggis, G. H.; Hasted, J. B.; Robinson, B. G. Proc. R . SOC.London, A 1952, 213, 379. (14) Pennock, B. E.; Schwan, H. P. J . Phys. Chem. 1969, 73, 2600. (15) Mashimo, S.; Kuwabara, S.; Yagihara, S.; Higashi, K. J. Phvs. Chem. 1987, 91, 6337. (16) Kent. M. J. Phvs. D 1970. 3. 1275: 1972. 5. 394. (17j Harvey, S. C.; Hoekstra, P. J. Phyk Chem.'1972, 76, 2987. (18) Bone, S.; Pethig, R. J. Mol. Biol. 1982, 157, 571; 1985, 181, 323. (19) (a) Careri, G.; Careri, M.; Rupley, J. A. Proc. Natl. Acad. Sci. U.S.A. 1985,82, 5342. (b) Careri, G.; Giansanti, A,; Rupley, J. A. Proc. Natl. Acad. Sci. U.S.A. 1986, 83, 6810. (20) Poglitsch, A,; Kremer, F.; Genzel, L. J. Mol. Biol. 1984, 173, 137. (21) Bone, S. Biochim. Biophys. Acta 1987, 916, 128. (22) De Xammar Oro, J. R.; Grigera, J. R. Biopolymers 1984,23, 1457. (23) Takashima, S.; Casaleggio, A,; Giuliano, F.; Morando, M.; Arrigo, P.; Ridella, S. Biophys. J . 1986, 49, 1003. (24) Gabriel, C.; Grant, E. H.; Tata, R.; Brown, P. R.; Gestblom, B.; Noreland, E. Nature (London) 1987, 328, 145. (25) Bonincontro, A.; Di Biasio, A.; Pedone,F. Biopolymers 1986,25, 241. (26) Sakamoto, T.; Nakamura, H.; Wade, A. Jpn. J. Appl. Phys. 1988, 27, 912. (27) Van Gemert, M. J. C. Philips Res. Rep. 1973, 28, 530. (28) Cole, R.H.Annu. Rev. Phys. Chcm. 1977, 28, 283.
0 1989 American Chemical Society
358 The Journal of Physical Chemistry, Vol. 93, No. I , 1989
Sakamoto et al.
TABLE I: Characteristics of Hydrophilic Silica Gels'
particle gel no.
1 2 3 4
gel name TSK gel SP-2SW TSK gel G-2000SWb TSK gel G-2000SWb TSK gel G-4000SW
diameter, pm 5-8 5-8 12-15 12-15
mean pore diameter, A
density, g/mL
120 120 120 -450
0.25-0.28 0.25-0.28 0.25-0.28 0.18-0.22
--
surface area, m2/g 400 f 50 400 f 50 400 f 50 250 f 50
surface modifier hydrophilic polymer and propylsulfonic group hydrophilic polymer hydrophilic polymer hydrophilic polymer
'Kato, Y.,personal communication. bThe difference between gels no. 2 and no. 3 is a particle diameter alone. few minutes, from 1 M H z to 10 GHz). Many high-frequency dielectric spectra of liquid sample have been observed by using this method.15,24,2e32 The TDR technique is also suitable for measurements of hydration water because (1) most of the frequency range where the dielectric relaxation of hydration water occurs is covered by this method and (2) short time measurement is essential for the powder state sample whose condition is not as stable as solution. Temperature dependence of the dielectric relaxation gives us thermodynamic information on the relaxation phenomena such as activation enthalpy and entropy. In addition, dynamic behavior of hydration layers below 0 O C may alter around the freezing point of each layer. From this motivation, low temperature dielectric spectra were observed down to -100 OC. The correlation between the dynamic relaxation behavior and the static liquidsolid phase transition of the hydration water is also of physical importance. Therefore, in parallel with the dielectric measurements, calorimetric measurements of the same hydrated powder sample below 0 OC were also performed, monitoring the fusion of frozen hydration water bound to the powder surface.33 In order to obtain unequivocal information on the dielectric properties of hydration structure, the surface of the hydrated material should be as homogeneous as possible. In the present study, four kinds of hydrophilic silica gels having different particle sizes, pore sizes, and chemical modifications were investigated for the model system of hydration structure. 11. Experimental Section 1 . Sample Preparation. The four kinds of hydrophilic silica gels used in this study were gifts of Toyo Soda Mfg. Co., Ltd. They are materials for high-performance liquid chromatography (HPLC) columns. Characteristics of these gels are summarized in Table I and for convenience they are numbered from 1 to 4 (first column in Table I). The most important point is that gels 1 and 2 are different only in terms of surface charge; gel 1 has an anionic (SO,-) surface, while gel 2 is neutral. The four kinds of gels were used without any further purification. Counterion (Na+) condensation remained for anionic gel 1. Each gel was partitioned into several vials to prepare samples with various hydration contents. They were dried for 10 h at abopt 90 OC in an environment of low relative humidity controlled by P2OSand were weighed, so that the zero point of hydration content was determined. Then they were transferred in desiccators in which the relative humidity was controlled by the supersaturated solutions of several standard salts. After equilibration a t 22 OC, the samples were weighed again, and the water content bound to the dry powder was determined. 2. Dielectric M e a ~ u r e r n e n t . ~Here, ~ , ~ ~the TDR dielectric measuring system is described briefly. The sample cell is a brass open-ended coaxial line passed through a silver-plated copper block. Temperature reduction inside the sample cell was performed by soaking part of the copper block (29) Cole, R. H.; Mashimo, S.; Winsor, P., IV J . Phys. Chem. 1980, 84, 786. (30) Nakamura, H.; Mashimo, S.; Wada, A. Jpn. J. Appl. Phys. 1982,21, 461; 1982, 21, 1022. (31) (a) Dawkins, A. W. J.; Grant, E. H.; Sheppard, R.J. J. Phys. E 1981, 14, 1429. (b) Gabriel, C.; Dawkins, A. W. J.; Sheppard, R. J.; Grant, E. H. J . Phys. E 1984, 17, 513. (32) Imamatsu, K.;Nozaki, R.; Yagihara, S.; Mashimo, S.; Hashimoto, M. J . Chem. Phys. 1986,84,6511. (33) Mrevlishvili, G. M. Sou. Phys.-Wsp. (Engl. Traml.) 1979, 22, 433.
in liquid nitrogen in a Dewar vessel. Both the copper block and the sample cell can be cooled down to about -180 O C . The decreasing rate inside the sample cell was about -4 OC/min on an average. When the Dewar vessel was removed and the whole system was surrounded with styrene foam, the increasing rate was about 0.5 OC/min around -100 O C and about 0.2 OC/min around -20 OC. It is necessary to perform dielectric measurement at several fixed temperatures; therefore the measurements in the present study were performed in the process of increasing temperature where the temperature change was small in the time period of each TDR measurement, less than 1 min. The measurement procedure was almost the same as that described e l ~ e w h e r e . To ~ ~ obtain , ~ ~ a dielectric spectrum by TDR, it is necessary to observe a set of three reflected signals from air [R,(t)],reference liquid [R,(t)],and the sample of interest [R,(t)]. Before sample filling, R,(t) and R,(t) were observed in several time ranges of the sampling oscilloscope. Then, the prepared hydrated powder sample was filled in the sample cell and was capped by a Teflon round rod so that no space remained in the cell. The Teflon rod was made to be best fitted to the outer conductor so as to strictly isolate the sample to the external atmosphere. The weight and volume of the filled sample were measured to estimate the packing density. The sample cell was cooled by liquid nitrogen down to about -100 OC. Then the whole system was covered by styrene foam and R,(t) in several time ranges was observed with increasing temperature up to room temperature. During the measurement, dry nitrogen gas was flowed into the styrene foam box so as to protect the outside of the sample cell from frosting. The observed time domain signals R,(t), R,(t), and R,(t) for several temperatures were Fourier transformed and analyzed, giving the dielectric spectrum in the frequency domain.30 3. Calorimetric Measurement. A differential scanning calorimeter (DSC) (SSC-56OU; Seiko Instruments and Electronics, Ltd.) was used to obtain the heat of fusion of the frozen water adsorbed on the hydrophilic silica gels. An empty cell was used as a reference cell. Both sample and reference cells were first cooled to about -90 OC by liquid nitrogen and then were heated at a rate of 1.85 OC/min. The enthalpy change of the sample is in proportion to the area surrounded by the thermogram and the base line. By use of the area of the thermogram of the pure water as standard material = 79.8 (cal/g), the of known enthalpy change of fusion, enthalpy change of the hydrated powder sample was determined. Heating rate dependence of the peak area and the peak temperature in the DSC thermogram was verified by measuring the same sample at different heating rates. The peak area was found to be independent of the heating rates within the error of 3%. The relation between the observed peak temperature Tpat the heating rate of 1.85 OC/min and the calibrated peak temperature Tcp,the extrapolated temperature to the limit of zero heating rate, was found to be Tcp= Tp - 0.8 ("C) 111. Results 1. Ionized Gel (Gel No. I). Dielectric spectra measurements
of hydrated ionized silica gel no. 1 were performed for four hydration levels: h = 0.08 g of water per 1 g of dry powder [controlled by 66% relative humidity (RH) using a supersaturated solution of NaN02],h = 0.16 g/g [81% RH, using (NH4)2S04], h = 0.43 g/g (88% RH, BaCl2.2Hz0), and h = 0.54 g/g (92% RH, Na2C,H406.2H20).
Dielectric Relaxation of Water
The Journal of Physical Chemistry, Vol. 93, No. 1, 1989 359
TABLE I 1 Summary of Dielectric Relaxation Parameters
water content, figure no.
gel no.'
g/g of dry powder
temp., OC
T ~ ns ,
1 2 3 10 11
1
0.16
1 1
0.43 0.43 0.33 0.33
22 -20 23 -20 22
3.45 3.03 2.97 1.67 1.44
2 2
P
At, 2.79 2.27 5.50 0.35 0.32
fitting parameters 72, ns A.c~
a
c,
0.78 1.0 1.0 1.0
2.11 2.38 2.51 1.91 2.77
0.50 0.70 0.31 1.0 1.0
0.08 0.06 0.11 0.05
0.62 0.77 0.23 0.55
'See Table I.
--I
2.0c
t
n
io,.' -2 0.1
" 0
I 6
7
8 9 logiOf (Hz)
10
0.0
-11
-10
-9
(c) E"
0.5
-
log,of (Hz)
3jO
4i9 E
510
O'O
log,,r(sec)
Figure 2. Dielectric spectrum [(a) real part, (b) imaginary part], (c) Cole-Cole plot, and (d) distribution of relaxation time for gel no. 1. h = 0.43 g/g, T = -20 "C. In parts a-c solid lines indicate fitting curves by eq 2. Fitting parameters are listed in Table 11.
Examples of dielectric spectra and Cole-Cole plots are shown in Figures 1-3. Figure 1 shows the result with h = 0.16 g/g and T = 22 OC. In Figures 2 and 3, h = 0.43 g/g together, T = -20 O C and 23 OC, respectively. In each figure, the complex dielectric spectrum €*(a)= e'(o) - id'(w) (a, real part t'; b, imaginary part e") and (c) Cole-Cole plot are shown by filled circles. These dielectric spectra and Cole-Cole plots indicate that the dielectric relaxation of the hydrated silica gel is not simply described by single Debye relaxation. Since the Cole-Cole plots at low frequencies had a semicircular shape, the following model function containing a Cole-Davidson function34was assumed for the dielectric spectra:
where t, is a high-frequency limit of the dielectric constant, Atl and Atz are dielectric increments, T~ and T~ are principal dielectric relaxation times, and a (Cole-Cole parameter, 0 < a I1)35and /3 (ColeDavidson parameter, 0 C /3 I1)34are spread parameters of relaxation times. Curve fitting of ~ ' ' ( uto ) eq 2 was performed (34) Davidson, D. W.; Cole, R. H.J . Chem. Phys. 1950, 18, 1417. (35) Cole, R. H.; Cole, K.S . J . C h e w Phys. 1941, 9, 341.
-
b '
" 0
0.5
0.0
0.0 7
8
logiof(Hz)
b , , T (sed
-1.0
3.0-
0.1
6
-8
Figure 1. Dielectric spectrum [(a) real part, (b) imaginary part], (c) Cole-Cole plot, and (d) distribution of relaxation time for gel no. 1. Water content h = 0.16 g of water/g of dry powder, T = 22 OC. In parts a-c solid lines indicate fitting curves by eq 2. Fitting parameters are listed in Table 11. (a)
1.o
E"
9
10
-11
-10 -9 b i 0 T (sed
-8
Figure 3. Dielectric spectrum [(a) real part, (b) imaginary part], (c) Cole-Cole plot, and (d) distribution of relaxation time for gel no. 1. h = 0.43 g/g, T = 23 OC. In parts a-c solid lines indicate fitting curves by eq 2. Fitting parameters are listed in Table 11.
by use of the program system SALS36 of the Computer Centre of the University of Tokyo. The parameters a and /3 were fixed at unity when the spectrum was expressed by the composition of two single exponential Debye relaxations. Akaike's information criterion (AIC) was used to judge whether or not parameters were fixed." For Figure 1, Ae2 in eq 2 was fixed at zero, so a single Cole-Davidson function was assumed. For Figure 3, a was fixed at unity. For Figure 2, there were no such constraints. Each constraint was determined by searching for the parameter set with minimum AIC. The fitting results are summarized in Table 11. The solid lines shown in Figures 1-3 (a-c) are fitted curves and two deconvoluted e" curves are also shown in part b. Figures 1-3 (d) show the normalized distribution of the relaxation time 7,g(1og 7),obtained from the above fitting procedure. g(1og 7) is expressed as
+
here Attot = Atl At2. g, and gp are calculated a n a l y t i ~ a l l y . ~ ~ In the case of a = /3 = 1, g, and gBare equal to 76(7 - 7 2 ) and 76(~- T ~ ) respectively. , It should be noticed that the curve fitting was made from the data below about 3 GHz, so in Figures 1-3 (d) the distribution shorter than about 50 ps may possibly include large errors. The shape of the spectrum and the Cole-Cole plot in Figure 2 is apparently similar to that in Figure 1, indicating that the dielectric relaxation of the sample with high water content at relatively low temperature (in this case -20 "C) is similar to that of the low water content sample a t room temperature. The dielectric spectrum seen in Figure 3 is greatly dispersed, having a large component in gigahertz frequencies. This tendency is also seen from Figure 3d, in which the distribution has a tail extending to shorter relaxation times. Temperature dependence of the dielectric spectra of hydrated ionized silica gel no. 1 with two kinds of hydration contents (h (36) Nakagawa, H.; Oyanagi, Y . In Recent Developments in Statistical Interface and Data Analysis; Matusita, K.; Ed.; North Holland Amsterdam, 1980; p 221. (37) Akaike, H. IEEE Trans. Autom. Control 1974, AC-19, 716. (38) Battcher, C. J. F.; Bordewijk, P.In Theory ofEIectric Polarization, 2nd ed.;Elsevier: Amsterdam, 1978; Vol. 11, eq 9.55 for g, (ais replaced by 1 - a);eq 9.68 and 9.69 for ge.
360
Sakamoto et al.
The Journal of Physical Chemistry. Vol. 93, No. I , 1989
-
7
I:o
(a)
1.0 L.
0.5 0
Figure 4. Three-dimensional representation of dielectric spectra and Cole-Cnle plots for gel no. I as a function of temperature: (a) real part, (b) imaginary part, and (e) Cole-Cole plots. Water wntent is 0.16 g/g. In parts a and b arrows indicate the amplitude of the ordinate axis.
Figure 5. Three-dimensional representation of dielectric spectra and ColeCole plots for gel no. 1 as a function of temperature: ( a ) real part, (b) imaginary part, and (c) Cole-Cole plots. Water wntent is 0.43 g/g. In parts a and b arrows indicate the amplitudc of the ordinate anis.
= 0.16 and 0.43 g/g) is shown in Figures 4 and 5 (a, real part
6 h, imaginary part 8'). and that of the C o l d o l e plots is shown in Figures 4c and 5c. In Figure 4h, as the temperature rises, the amplitude of ('(w) increases monotonously without much change in shape. In Figure 5h, the amplitude of t"(w) increases in the same manner as in Figure 4h up to about -10 OC. Beyond -10 OC, the amplitude of e'' a t higher frequencies around 1 GHz increases rapidly, while the main peak around 100 MHz increases little and actually initially decreases to some extent. Figure 6 shows the temperature dependence of the real part of the dielectric constant a t 1 MHz (lowest frequency in TDR measurement), tlMHz. for four kinds of hydration contents. For increases almost linearly lower water content (0 and A), qMHz from -40 OC to rmm temperature. For higher water wntent ( 0 and O ) , sigmoidal curves saturated a t about 0 O C are seen. Curve fitting calculations of 8'(w) a t several hydration contents and temperatures were performed by eq 2. From -105 'C to -45 OC, Ac2 was fixed a t zero. Figure 7 shows temperature dependence of Aft, Af2, and Acm for the hydration contents of 0.16 and 0.43 g/g. Act increases with rising temperature from -50 to -12 OC for both hydration contents. For lower water content (a), Aq increases almost linearly up to rmm temperature, while for higher water content (h), there is a plateau between -10 and 0 OC, and above 0 OC, Aft increases again with comparatively large error bars. On the other hand, Af2 increases with increasing temperature from -40 to -20 OC and is saturated for both hydration contents. The data scattering
w
l
-100
-60
-60
-40
Temp.
-20
("c)
0
20
Figure 6. Real part of the dielatnc constant lor gel no. 1 at i MHz (CIUH.) as a f""Ctl0" of temperature. Water wntcnls arc ( 0 )0.08 g/g. (A)0.16 g/g, ( 0 )0.43 g/g. and
(e)0.54 g/g.
above 0 OC Sccn in Figure 7 may come from the limitation of the curve fitting from the data below 3 CHz alone. Temperature dependence of the parameters a and B for the hydration contents of 0.16 and 0.43 g/g is shown in Figure 8. 0 decreases with increasing temperature for both hydration contents indicating that the spread of relaxation times becomes prominent as the temperature increases. For lower hydration content (a), the change IS gradual. For higher content (b), on the other hand, there is a gap in jat -10 to -I 2 OC. This suggests the possibility
The Journal of Physical Chemistry, Vol. 93, No. 1 , 1989 361
Dielectric Relaxation of Water (a)
2.0-
4 1.01
0.2 0.0 -60
-40
8.0 1
-20
0
20
Ternp.(°C)
Ternp.(°C) T
'
1
6.0 -
4 4.00.2-
I
0.0 -60 Ternp.(°C)
-20
0
20
Ternp.(°C)
Figure 7. Dielectric increments for gel no. 1 as a function of temperature. Water contents are (a) 0.16 g/g and (b) 0.43 g/g. In each figure, 0, A, and 0 mean Atl, At2 (defined by eq 2), and At, (=Atl + At2), respectively.
of structural transition of the hydration layer at this temperature (see section IV-3). a ranges from 0.7 to 1.0 and does not have marked temperature dependence for either hydration content. Figure 9 shows temperature dependence of the principal relaxation times T~ and T~ (Arrhenius plots) for the hydration contents of 0.16 g/g (a) and 0.43 g/g (b). There is apparently little difference in the temperature dependence of relaxation times for the two hydration contents. The longer relaxation time, T ~ has a constant value, 1.3-1.8 ns, below -40 OC, then increases to 3-4 ns, and above -20 OC, it is flat again. Since the actual relaxation time is widely distributed as seen in Figures 1-3 (d), this temperature dependence does not directly correspond to that of 7 (for detail, see section IV-4). The shorter relaxation time, 72,is distributed roughly from 20 to 150 ps and is a decreasing function of temperature. 2. Nonionized Polar Gel (Gel No. 2 ) . Dielectric spectra measurements of hydrated nonionized silica gel no. 2 were performed for a hydration level h = 0.33 g of water per 1 g of dry powder (controlled by 92% relative humidity using a supersaturated solution of NazC4H4O6.2H20)and for a temperature range from -105 to 22 O C . Figures 10 and 11 show examples of the dielectric spectra (a, real part e'; b, imaginary part e"), (c) Cole-Cole plots, and (d) the distribution of relaxation times at -20 and 22 OC, respectively. The most typical point is that the amplitude of lower frequency relaxation around 100 MHz is larger than that of the higher one around 1 GHz at -20 OC and that the order is reversed at 22 OC. Curve fitting calculations were performed by eq 2, and the dielectric spectra were proved to be described well by two Debye functions below 2 G H z with the constraint of a = B = 1. The fitting results are summarized in Table 11. Temperature dependence of the dielectric spectra and C o l d o l e plots of gel no. 2 is shown in Figure 12 (a, real part; b, imaginary part; c, Cole-Cole plot). E"(o) has roughly two peaks in the different frequency range (lower, around 100 MHz; higher, above 1 GHz). The amplitude of the lower frequency peak increases with rising temperature to -14 OC, and then it is saturated. The
-40
,
Figure 8. Cole-Davidson parameters @ (m) and Cole-Cole parameters a (0)for gel no. 1 as a function of temperature. These parameters are defined by eq 2. Water contents are (a) 0.16 g/g and (b) 0.43 g/g. In these figures, several data points (in the case a or @ = 1.0) are partly eliminated. (a) Below -40 "C, fitting of single Debye function with a = 1; from -40 to -24 OC, fitting by eq 2 with fl = 1; at 22 OC, fitting of single Cole-Davidson function. (b) Below -40 OC, fitting of single Debye function with a = 1; from -14 to 23 OC, fitting by eq 2 with a = 1.
amplitude of the higher frequency peak first increases gradually to -20 OC; at -20 OC it increases abruptly, and above -12 O C it exceeds that of the lower one. Curve fitting calculations of E"(w) for gel no. 2 at several temperatures were performed by eq 2. From -105 to -40 OC, the model function including only the single Debye function [ p = 1, Ae2 = 0 in eq 21 was used; above -40 OC, that with double Debye functions (a = 0 = 1 in eq 2) was used. Figure 13 shows temperature dependence of Ae1, At2, and At, increases monotonously to -14 OC, decreases from -12 to 0 OC, and is constant above 0 OC. At2 emerges at about -40 OC, and increases monotonously to -2 OC; its slope is steeper than that of A q . Above 0 OC it has a constant value. The total dielectric increment, Attot, has a sigmoidal shape and is saturated above 0 O C .
Figure 14 shows Arrhenius plots of the relaxation times T~ and The longer relaxation time, T ~ranges , from 1 to 2 ns, depending little on temperature. The shorter relaxation time, T ~ is, about 100 ps at -40 O C , decreases slightly with increasing temperature to about 0 OC, and then has a constant value, 50 ps. 3. Summary of the Results for Other Gels (Gels No. 3 and No. 4 ) . Dielectric relaxation measurements of hydrated nonionized hydrophilic silica gels no. 3 and 4 were also performed in the same manner as those of gel no. 2. Hydration contents of gels 3 and 4 were 0.38 and 0.23 g/g, respectively, controlled by 92% relative humidity using a supersaturated solution of Na2C4H406-2H20. Their dielectric spectra and related figures are not shown here, but an outline of the comparison with the results of gel no. 1 and gel no. 2 is described below. The dielectric spectra and related parameters (At and 7) for gel no. 3 are almost similar to those for gel no. 2 over the temperature range from -100 to 20 O C . Thus particle size dependence on the dielectric relaxation of hydration water hardly exists in T~
362
The Journal of Physical Chemisfry, Vol. 93, No. 1. 1989
Sakamoto et al.
Temo.('C) 20
0
-20
-40
-60
-80
-100 3.4
E'
E.
3.2
3.0
E'
i 0.02 0.01
4.0
3.5
20
0
-20
4.5 5.0 ?IT ( X I O - ~K-')
-40
Tew.('C) -60
-80
5.5
6.0
Flgure I I . Dielectric spectrum [(a) real part. (b) imaginary part]. (c) C o l 4 o l c plot. and (d) distribution 01relaxation time lor gel no. 2. h = 0.33 g/g. 7 ' = 22 ' C . I n parts a-c solid lines indicate fitting curycs by eq 2. Fitting parameters are listed m Table I I
-100
I
' I
7
6
4.5 5.0 5.5 6.0 1IT (X10-3 K-') Figure 9. Principal relaxation times [r, ( 0 ) .r2(0);defined by eq 21 3.5
4.0
8
9
7
plotted against 1/T (Arrhenius plots) for gel no. 1. Water cnntents are (a) 0.16 g/g and (b) 0.43 g/g. Dashed lines indicate the trace of ( 7 ) = 4 ( e 9~).
Figure 10. Dielectric spectrum [(a) real part, (b) imaginary part], (c) ColtCole plot, and (d) distribution of relaxation time for gel no. 2. h = 0.33 g/g, T = -20 "C. In parts a-c solid lines indicate fitting curves by eq 2. Fitting parameters are listed in Table 11.
the particle size range used in this experiment. As the surface area of gel no. 4 is less than that of other gels (see Table I), hydration content of this gel at 92% RH is also relatively small. Direct comparison of the data for gel no. 4 with other nonionized gels is therefore difficult. Temperature dependence of the dielectric spectra of gel no. 4 is somewhat similar to that of gel no. 2 in that the two peaks exist around 100 MHz and 2-3 GHz in ("(0). Therefore, there may be little pore size dependence on the dielectric relaxation of hydration water in the pore size range used in this experiment. In this case, however, the peak at gigahertz frequencies is not as large as the peak around 100 MHz even at r m m temperature, indicating that the water content contributing to the higher frequency relaxation is lower in gel no. 4 than in gels no. 2 and no. 3. 4. Calorimetric Resulfs. Differential scanning calorimetric (DSC) thermograms of hydrophilic silica gels no. 1 and no. 2 are
0
1 :
100
2."
z.0
3."
3.3
C'
Figure 12. Threedimensional representation of dielectric spectra and Colecole plots for gel no. 2 as a function of temperature: (a) real part, (b) imaginary part, and (c) C o l d o l e plots. Water content is 0.33 g/g. In parts a and b arrows indicate the amplitude of the ordinate axis.
shown in Figure 15 (a; gel no. 1; b, no. 2). These thermograms have endothermic peaks below 0 O C , whose area increases with increasing water content. Therefore, it is clear that the observed peak corresponds to the fusion of frozen water adsorbed on the gel powder. There is an abrupt change in the shape of thermograms; for gel no. 1, between the water content of 0.17 and 0.32 g/g, and for gel no. 2, between 0.12 and 0.34 g/g. For a thermogram of lower water content sample, there are no or few small endothermic
The Journal of Physical Chemistry, Vol. 93, No. 1, 1989 363
Dielectric Relaxation of Water
Temp.(OC)
Figure 13. Dielectric increments for gel no. 2 as a function of temperature. h = 0.33g/g. 0,A,and 0 mean Aq, Ac2, (defined by eq 2), and Attot (=Asl + Ae2), respectively. Temp.('C)
20 0
-40
-20
-60
-00
-100
TABLE III: Calorimetric Results of Hydrated Silica Gels regression of the function AHfu = yW- 8 hydrated 7. cal/g 8, cal/g of Wo, g/g of of H 2 0 dry powder dry powder So, A2 gel no.' 1 79 f 5 10.7 & 1.6 0.135 i 0.021 9 2 10.0 f 5.6 0.127 i 0.075 9 f 3 2 79 f 15
I
g 0.51
*
i
.-
g H,O/g dry powder
g H,O/g dry powder
Figure 16. Plots of integral heat of fusion, AHf-, against water content for (a) gel no. 1 and (b) no. 2. The regression lines are also drawn (fitting parameters are listed in Table 111).
'See Table I. 4
1 0.021 0.011
I
4.5
5.0 5.5 6.0 IIT ( x 1 0 - ~K-') Figure 14. Relaxation times [ q (O), T~ (0); defined by eq 21 plotted 4.0
3.5
against 1/T(Arrhenius plots) for gel no. 2. h = 0.33 g/g. I
1
,
2
sideration of errors shown in Figure 16. Wois defined as the water content at A H h = 0; i.e. Wo= 6 / y . The fitting results are listed in Table 111. y in eq 4 corresponds to the heat of fusion of frozen hydration water, and it is close to that of pure ice at 0 O C , 79.6 cal/g. WO indicates the saturated content of unfreezable water, which interacts with the hydrated material so strongly that structural transition to ice cannot occur even below -60 O C . The WOvalues are roughly in the range of 0.1-0.15 g/g for both samples. Table I11 also lists the mean surface area (So)of the gel occupied by a single water molecule in the case of W = WO.SOis defined as
SO = S / (NAwO/
I
-80
-60
,
-40 -20 Temp.( C1
1
I
0
20
-80
'
-80
-40 -20 TempPC)
0
20
Figure 15. Differential scanning calorimetric thermograms of (a) gel no. 1 and (b) gel no. 2, in the process of heating. Heating rate is 1.85 OC/min. Water contents (g of water/g of dry powder) are as follows: (a) 1, 0.16;2,0.17;3, 0.32;4,0.45;50.47;6,0.50;7, 0.56;and (b) 1, 0.07;2,0.12;3, 0.34;4,0.43;5, 0.52;6,0.82;7.0.94. Arrows indicate the scale of the ordinate axis.
peaks below -10 O C . For a thermogram of higher water content sample, there is mainly a single, comparatively large endothermic peak above -10 O C , which clearly corresponds to the melting of hydration water having frozen in the process of cooling. Figure 16 (a, gel no. 1; b, no. 2) shows the plots of integral heat of fusion, AHHn.(cal/g dry powder), against water content, W (g/g dry powder). The regression line
A",,= yw- 6
(4)
was drawn by the linear least-squares fitting calculation in con-
8)
(5)
where S is a gel surface area per 1 g of the dry gel (obtained from Table I) and NA is Avogadro's number. With the radius of the water molecule, 1.4 A, taken into consideration, the obtained So values, 9 A2,suggest that the unfreezable water constructs the primary hydration monolayer with which the gel surface is almost fully covered. From Figure 15, peak temperature Tcpof the two kinds of hydrated gels is roughly estimated at about -5.3 OC for gel no. 1 and -3.8 OC for gel no. 2, calibrated by eq 1. Half width of the peak is also estimated at about 4.3 OC for gel no. 1, h = 0.50 g/g and about 3.2 "C for gel no. 2, h = 0.52 g/g. These results indicate that (1) the melting temperature of hydration water is lower than that of pure water by about 4-5 O C and that (2) the melting process of the water bound to the ionized surface is broader than the nonionized surface.
IV. Discussion 1. Mechanism of Dielectric Relaxation. The relaxation frequencies obtained from the dielectric spectra for hydrated silica gels are distributed from 100 MHz to several gigahertz (see, e.g., Figures 4, 5, and 12), lying between the relaxation frequency of pure water, 20 GHz, and that of pure ice, 2.5 kHz. For completely dry samples, on the other hand, no detectable relaxations were observed in the frequency range from 1 MHz to 10 GHz (data not shown). Dielectric relaxations of pure water and ice are considered to come from the dipole reorientation of water.39 The (39) Hasted, J. B. In Water, A Comprehensive Treatise, Franks, F., Ed.; Plenum: New York, 1972; Vol. 1, p 2 5 5 .
364
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The Journal of Physical Chemistry, Vol. 93, No. 1 , 1989
rotation of water molecules around the silica gels is expected to be more hindered than that of the bulk solvent water, although not as much as in ice. Therefore, the relaxations seen in the present study are most probably the contribution of water bound to the silica gels. Hereafter, possible relaxation mechanisms other than dipolar rotation of hydration water are considered. (1) The contribution of low-frequency conductivity to the dielectric loss (e”) is in inverse proportion to the frequency, and is excluded beforehand in the process of analysis.26 ( 2 ) Maxwell-Wagner relaxation appears in mixtures of materials of different conductivities usually at frequencies below l MHz, so it does not contribute to the results obtained here. (3) The silica gels used in this study have polar (no. 2, 3, and 4) or ionized (no. 1) groups. For the ionized gel no 1, the obtained spectrum is multidispersive; thus the dipolar rotation of ionized groups can be coupled with the relaxation of water. For the nonionized gel no. 2, on the other hand, the spectrum consists of two single dispersions, both of which are considered to be the contribution of water molecules in the different hydration layers as will be described in section IV-2. (4) Ionized gel no. 1 contains counterions (Na’) condensed around propylsulfonic groups, and the dielectric relaxation due to counterion fluctuation can be coupled with water rotational relaxation. De Xammer Oro and Grigerazz investigated dielectric properties of aqueous solution of calf thymus DNA and found the relaxation around 150 MHz. They attributed the relaxation to a counterion fluctuation alone and did not take the rotation of hydration water into account. In the present study, it is difficult to evaluate separately the effects of water rotation, ionized group rotation, and counterion fluctuation from the obtained spectra. In section IV-3, this point will be considered again. From the above considerations, it can be concluded that the observed relaxations in this study are principally due to the dipolar rotation (reorientation) of the water bound to the silica gels. For the ionized gel no. 1, however, the contribution of ionized groups and counterions cannot be neglected. 2. Dielectric Relaxations of Nonionized Polar Gel (Gel No. 2 ) . As shown in Figures 10 and 11, the dielectric spectra of hydrated nonionized silica gel can be decomposed into two single exponential relaxations (in q 2, cy = p = 1) above -40 “C (Figure 13). It is reasonable to assume that there are two types of hydration around the polar gel surface. The water molecules that contribute to the lower frequency relaxation (about 100 MHz) are supposed to be tightly bound to the polar groups of the gel surface and keep the rotational freedom down to -100 O C . The relaxation frequency is similar to that of hydrated lysozyme powderI7 and many biological materials.I5 The water molecules related to the higher frequency relaxation (above 1 GHz) are presumably loosely bound to the gel, in other words, interact weakly with polar groups of the gel, and are hindered from their rotational motion below -40 O C . How can the amount of tightly and loosely bound water be estimated by the dielectric results? When the dielectric loss of the hydrated sample arises from rotational relaxation of hydration water, the Kirkwood-Frohlich f o r m ~ l a t i o nshould ~ ~ be a good approximation A43
(1
+ 2As/e,)
+ Ae/t,)(e- + 2 ) 2
Ngw2 =-
9tokT
(6)
where N and p are the number density and the mean dipole moment of hydration water molecules, g is the correlation factor, to is the permittivity under vacuum, and k is the Boltzmann constant. The hydration content h (g/g) is related to N such as h = (N/NA)(18/d), where d is the density of the dry gel. At room temperature, both Ael and Atz are saturated, having values of 0.32 and 0.55, respectively (see Table 11; Figure 13). In this case, eq 6 derives the following relations: (40) Bottcher, C. J. F. In Theory of Electric Polarization, 2nd ed.; Elsevier: Amsterdam, 1973; Vol. I, eq 6.185.
g l h l p I 2= 0.1 1 f 0.01 Dz, gzhzpzz= 0.23 f 0.02 DZ
where suffixes 1 and 2 indicate tightly and loosely bound water, respectively. In order to quantify these parameters, two possible cases are considered. (1) If the dipole moments of tightly and loosely bound water are the same as that of pure water (pl= pz = 1.85 D) and the dipole correlation does not exist (g, = g2 = l), then h, = 0.03 g/g and hz = 0.07 g/g. In this case, however, the water content that does not contribute to the dielectric relaxation is 0.33 - (0.03 0.07) = 0 . 2 3 g/g. This is much larger than the amount of unfreezable water, W, = 0.13 g/g, and thus this assumption is thought to be unreasonable. ( 2 ) If the dipole moments of tightly and loosely bound water are similar (pl= F~ = p ) and not correlated (gl= gz = 1) and the total hydration content fully contributes to the relaxation ( h = hl h2), then h , = 0.1 1 g/g, hz = 0 . 2 2 g/g, and p = 1.03 f 0.04 D. These assumptions in this case are not evident from the present study alone but can be confirmed by the measurements of samples with various hydration contents. The tightly bound water content h l is similar to W,, which covers the gel surface with the density of one water molecule per 9 Az(Table 111). The mean dipole moment of the hydration water, p , is similar to the effective dipole moment of water bound to bovine serum albumin, 0.79 D.41 When the above case 2 is adopted, the following hydration model can be constructed for the nonionized polar gel. (1) The primary hydration layer is single dispersive in the dynamic sense. Water molecules in this layer are tightly bound to the polar gel surface, and their thermal rotational motion is restricted by steric hindrance; rotational relaxation time is 1.5 ns, 100 times that of pure water. ( 2 ) The hydration water in the primary layer is not completely frozen until -100 OC in the dynamic sense. It is thermally unfreezable above -60 OC. ( 3 ) The secondary hydration layer is also single dispersive in the dynamic sense. The rotational motion of this water is about 10 times as fast as that of primary hydration water and about 10 times slower than that of pure water, indicating that the steric hindrance for this water is much weaker but that the influence of polar groups remains to some extent. (4) The melting point of water in the secondary layer is below -4 OC from the DSC thermograms (Figure 15b). Thermograms are not symmetrical and the tail extends to lower temperatures, indicating the gradual melting of secondary layer water. (5) The rotational relaxation of the secondary layer water appears above -40 O C (Figure 13), preceding the ice-water transition. This may reflect the difference between dynamic and static hydration structural transitions with temperature. In other words, the rotational freedom of loosely bound water is released at lower temperatures than the translational freedom. 3. Dielectric Relaxations of Ionized Gel (Gel No. 1 ) . As seen in Figures 9 and 14, the two principal relaxation times 7 , and T~ for ionized no. 1 gel are respectively similar to single relaxation times T~ and T~ for nonionized no. 2 gel. Thus, by analogy of the nonionized case (section IV-2), the water molecules associated with the lower frequency multidispersive relaxation are supposed to be tightlv bound to the gel surface. and those associated with the higier hequency relaxation are thought to be loosely bound water. In this case, however, the distinction between tightly and looselv bound water is not as clear as that in nonionized gel. As ieen in Figure 6, four types of no. 1 gels with different water ‘Ontent can be separated into two groups from their temperature dependence of tlMHz;lower water content gels (0.08 and 0.16 g/g) are in One group (group I), and the remainder (o.43 and 0.54 g/g) are in the other (group 11). From the calorimetric results of no. 1 gels, the amount of unfreezable water, Wo,is estimated at about 0.14 g/g. Thus, for the samples of group I, almost all of the water molecules are considered to be unfreezable and tightly bound to the ionized gel
+
+
(41) Gascoyne, P.R.C.; Pethig, R. J . Chem. SOC., Faraday Trans. 11981, 77, 1733.
Dielectric Relaxation of Water surface. As a result, c"(w) increases monotonously with increasing temperature (Figure 4b). Atl increases linearly with temperature and Atz contributes little (Figure 7a), which also indicates the lack of loosely bound water. As seen in Table 111, Woand Soof the two kinds of gels are almost the same. Dielectric properties of both gels are, however, different in that the tightly bound water is not single dispersive for gel no. 1. This indicates that the surface of ionized gel is not homogeneous considering the primary hydration layer. From the data of the ion-exchange capacity of about 0.45 mequiv of NaOH/g of dry ionized gel Sp-2SW (Kato, Y., personal communication), the density of ionized group is estimated as one group/ 150 A2. Therefore, interaction between the ionized group and the primary hydration layer water may alter gradually according to the distance between the water molecule and the nearest ionized group. The mean dipole moment of the tightly bound water is estimated by eq 6 in the same manner as section IV-2. The result is, ghpz = 1.40 f 0.48 DZat 22 O C . If all the hydration water, 0.16 g/g, contributes to the relaxation, (gp2)'l2= 3.0 f 0.5 D. This is about 1.5 times that of pure water. Therefore, (1) effective polarization due to dipole correlations of water molecules ( p = 1.85 D and g = 2.5) or (2) polarization of the effective dipole such as ionized groups and counterions should be coupled with the dielectric relaxation. For samples of group 11, part of the hydration water is thermally freezable. The relaxation frequency of ice is about 2.5 kHz, so the frozen loosely bound water should contribute little to the dielectric spectra from 1 MHz to 10 GHz below -40 "C, where the temperature dependence of tlMHzof group I1 is similar to that of group I (Figure 6). elmr of group I1 shows a sigmoidal increase between -40 and 0 "C, indicating the increase of water content contributing to the relaxation. The most characteristic point shown in E"(.) of group I1 (Figure 5b) is the drastic change of the shape between -12 and -10 O C . The absorption peak around 100 MHz decreases somewhat, and the amplitude at higher frequencies increases instead. The newly appeared relaxation at higher frequencies comes from the water having been frozen below -10 O C , which is more mobile than the tightly bound water. Temperature dependence of 0 (Figure 8) also demonstrates this drastic change. For lower water content (0.16 g/g), /3 depends to a small extent on the temperature (Figure 8a). 0 for higher water content (0.43 g/g), on the other hand, has characteristic temperature dependence (Figure 8b); that is, there is a drastic change in the spread of relaxation times at -12 to -10 O C . As seen in Figure 6, the contribution of the freezable water appears above -40 O C for group 11. From -40 to -10 OC, the dielectric behavior of the freezable water (Figures 5b and 8b) is similar to that of unfreezable water (Figures 4b and 8a). Thus, in this temperature range, the rotational mobility of the freezable water is close to that of tightly bound water. Then, at -10 O C , the hydration structure changes abruptly. As a result, the amplitude of t"(w) for the tightly bound water around 100 MHz decreases and the broad higher-frequency component for the loosely bound water increases as seen in Figure 5b. For a sample of group I1 (0.43 g/g), the amounts of the hydration water at -12 and -10 "C are estimated by eq 6: ghp2 = 1.24 D2 at -12 "C; 1.58 DZat -10 "C. If (gp2)1/2= 3.0 D (group I, 22 O C ) is assumed, h = 0.14 and 0.18 g/g for -12 O C and -10 OC, respectively. With the structural transition at these temperatures taken into consideration, the saturated tightly bound water content proves to lie between 0.16 and 0.18 g/g. Hereafter, Wtb denotes this water content range. For group 11, it is difficult to discriminate the tightly and loosely bound water above -10 O C , thus the average hydration structure is considered. At 23 OC, ghp2 = 2.3 f 1.2 DZ,obtained by eq 6. If the entire hydration content (h = 0.43 g/g) contributes to the relaxation, then (gp2)1/2 = 2.3 f 0.6 D, which is smaller than that of group I (3.0 D). This decrement indicates that the contribution of ionized groups and/or counterions is smaller with increasing hydration water content. Hereafter, the following hydration model is constructed for hydrated ionized gels.
The Journal of Physical Chemistry, Vol. 93, No. I, 1989 365 (1) The amount of tightly bound water, Wtb, is 0.16-0.18 g/g. This is slightly larger that that of the primary hydration layer, Wo= 0.14 g/g, which suggests that the ionized group partly affects the secondary hydration layer. The tightly bound water is multidispersive. Its average relaxation time (eq 9 in section IV-4; dashed lines in Figure 9) is similar to that of the primary hydration layer around the nonionized gel. (2) The tightly bound water is not completely frozen dynamically until -100 O C . As the temperature rises, the tightly bound water progressively recovers its rotational freedom. The water molecules recovering rotational freedom at higher temperature have higher rotational mobility, as verified by the result that 6 is a decreasing function of temperature (Figure 8). (3) For a sample having hydration content over Wtb, there appears an extra relaxation due to the loosely bound water in the gigahertz region above Ttb,defined as the temperature where the amount of hydration water associating with the dielectric relaxation is equal to Wtb. In this case, however, additivity of the dielectric spectra between tightly and loosely bound water does not hold. That is, ~ " ( w )of the tightly bound water becomes broad abruptly by itself at Ttb,indicating that part of the tightly bound water molecules increase their rotational mobilities influenced by the neighboring loosely bound water. Above Ttb, it is difficult to distinguish tightly and loosely bound water from their relaxation frequencies, since the frequencies are distributed continuously and overlapped. (4) From both dielectric and calorimetric results, each categorized hydration water corresponds to each of the others as follows. (i) The tightly bound water includes the unfreezable water. (ii) Part of the freezable water is tightly bound to the gel below Ttb,.and its saturation content is Wtb - W,. (111) Above Ttb,there is no distinct boundary between the tightly and loosely bound water; thus the freezable water has continuously distributed mobility. (5) Thermal melting of freezable water occurs gradually up to -5 O C . The melting profile of the freezable water of ionized gel is broader than that of nonionized gel from a comparison of the half widths of the thermograms. This indicates that the freezable water of the ionized gel starts melting at lower temperatures than that of the nonionized gel. (6) The rotational relaxation of the freezable water appears above -40 "C (Figures 6 and 7), which precedes the ice-water thermal transition. This indicates that the rotational freedom is released at lower temperatures than the translational freedom. This phenomenon is in common with the case of nonionized gel. 4. Temperature Dependence of Dielectric Relaxation Times. Treatment of the rate process42for dielectric relaxation is given here. In this treatment, Debye-type dipolar rotational relaxation corresponds to the reaction through the passage over a molar activation free energy barrier
AG* = AH* - T A P (7) where AH* and aS*are the molar activation enthalpy and entropy and T i s the absolute temperature. The relaxation time is given by h r = - exp(AG*/RT) kT where h, k, and R are Planck's constant, Boltzmann's constant, and the gas constant, respectively. As seen in Figure 14, the longer dielectric relaxation time, T , , for the nonionized (no. 2) gel is almost temperature-independent. This result indicates that the activation enthalpy AH* for the relaxation around 100 MHz is nearly zero. That is, in the process of the dipolar rotation of tightly bound water, the enthalpy change between the equilibrium and the activated state is almost zero. The resulting activation free energy is AG* = 5.3 kcal/mol at 22 "C, calculated by eq 8. This free energy change is mostly due to AS*,in other words, the narrowness of the reaction path. ~~
~~
~~
(42) Kauzmann, W. Rev. Mod. Phys. 1942, 14, 12.
366 The Journal of Physical Chemistry, Vol. 93, No. 1, 1989 The shorter relaxation time, T ~for , the no. 2 gel decreases with increasing temperature, as shown in Figure 14. The DSC thermograms shown in Figure 15b suggest that the melting process of loosely bound water is gradual in the temperature range from -40 to 0 OC as compared with the steep phase transition of pure water. Thus, in the same manner, the rotational mobility of water molecules in the secondary layer may also increase with rising temperature from -40 to 0 OC. The flattening of T~ above 0 O C indicates the same entropy-driven process as described for 7 , . Similar treatment for the dielectric relaxation times for ionized (no. 1) gel is complicated, because the relaxation is not composed of single exponentials but is distributed continuously. The relaxation time T~ for the lower frequency relaxation plotted in Figure 9 is defined as the upper limit of the distribution of relaxation time, gp As seen in Figure 9, T~ seems to be an increasing function of temperature above -40 OC; however, it may be an effect of @ values shown in Figure 8. When the relaxation time is distributed with the function, g@,the average relaxation time ( T ) is calculated to be
(9) As seen in Figure 8, @ is unity at first, where ( T ) = T ~and , above about -40 OC, it is a decreasing function of temperature. Therefore, with regard to ( T ) , such a large temperature dependence as 71 is hardly seen by canceling of @ and (see dashed lines in Figure 9). Thus it can be concluded that the overall relaxation time distribution also has little temperature dependence in the case of ionized gel. 5. Apparent Dielectric Constant of Hydration Water. The static dielectric constant of the pure water is about 80 at room temperature. That of the hydration water, on the other hand, is expected to have different values because of the dielectric heterogeneity of hydrated materials. Here, apparent dielectric constants of the hydration water for nonionized and ionized gels are estimated . For the nonionized no. 2 gel, the effective dipole moment of the hydration water, (gp2)1/2,is 1.03 f 0.04 D at 22 OC (section IV-2). The static dielectric constant % (=e, At) is derived from
+
Sakamoto et al.
eq 6, which contains parameters of the density and t, of the “bulk” hydration water; these cannot be estimated from the present study alone. If the density of “bulk” hydration water is assumed to be 1.0 g/mL, the right side of eq 6 is equal to 1.2 f 0.1. The 2)* uncertainty oft, affects t, greatly because of the term (e, in eq 6. If e, of the hydration water is assumed to be the same as a square of the refractive index of pure water, 1.8, tsis calculated to be 10. In the extreme case, meanwhile, the virtual E, value, 4.3, which accounts for tsand p of the pure water with g = 1$3 gives e, = 26. Therefore, it is essential to accurately evaluate the t- value of hydration water for the precise estimation of the static dielectric constant of hydration water. For the ionized no. 1 gels, the effective dipole moment of the hydration water is 3.0 f 0.5 D for h = 0.16 g/g a t 22 OC and 2.3 f 0.6 D for h = 0.43 g/g at 23 OC (section IV-3). Similar calculations with t, = 1.8 give t, = 73 for h = 0.16 g/g and tl = 46 for h = 0.43 g/g. ts decreases with increasing hydration content, suggesting that the inner hydration layer has an apparently larger dielectric constant than the outer layer by the influence of ionized groups and counterions. The apparent dielectric constant of water bound to ionized gels is about 5 times as large as nonionized gels, which may be due to the effective polarization concerning ionized groups and counterions. This implies that the electrostatic shielding effects are promoted in the environment around charged groups. Heterogeneity of the dielectric constants of the hydration water may be related to the specificity of electrostatic effects. For example, enzymatic reaction usually occurs on a protein surface, which is composed of hydrophobic, hydrophilic, and ionized amino acid residues; thus the electrostatic interaction between an enzyme and a substrate will be greatly influenced by the dielectric heterogeneity of surrounding hydration water.
+
Acknowledgment. This work was partly supported by a grant-in-aid from the Ministry of Education, Science, and Culture, Japan, and a grant from Protein Engineering Research Institute Co., Ltd. (43) Reference 39; Table I11
