Langmuir 1995,11, 2173-2178
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Dielectric Behavior in the SrF2-H20 System. 2. Measurement at Low Temperatures Yasushige Kuroda" and Yuzo Yoshikawa Coordination Chemistry Laboratories, Institute for Molecular Science, Myodaiji-cho, Okazaki 444, Japan
Tetsuo Morimotot Department of Chemistry, Faculty of Science, Okayama University, Tsushima, Okayama 700, Japan
Mahiko Nagao Research Laboratory for Surface Science, Faculty of Science, Okayama University, Tsushima, Okayama 700, Japan Received October 20, 1994. I n Final Form: March 6, 1995@ Dielectricproperties ofwater adsorbed on the SrF2 surfacehave been investigatedunder various conditions. A small relaxation was found at 33 kHz, 159 K, and a coverage of 0.74, besides a large relaxation observed at 298 K which had been described in part 1 of this series. This small relaxation is observed only when the physisorbed water molecules are present. Furthermore, the chord length of Cole-Cole plots for this relaxation is found to be a function of the coverage. These findings are interpreted in terms of the Debyetype rotational polarization of the adsorbed water and therefore confirm that the relaxation observed at 298 K is ascribed to the Maxwell-Wagner-type relaxation. An activation energy for the dipole rotation is also calculated from the variation of frequency corresponding to a maximum in the dielectric loss curve with temperature. This result suggeststhat the rotation ofthe water molecules condensedtwo-dimensionally is expected to be more hindered than that of bulk liquid water, though not so much as in ice. The state oftwo-dimensionallycondensed water on SrFz is discussed on the basis ofthe concept oflateral interaction.
1. Introduction Dielectric measurement of the adsorbed species is, in principle, vital to characterize the state of the adsorbate on the solid surface.l-1° However, there are some difficulties in this method. One of the difficulties is to determine which process is responsible for the observed dielectric relaxation, the Debye-type or the MaxwellWagner-type. In the Debye process, the dielectric dispersion is due to a rotation of dipolar molecules in the applied electric field and hence is characteristic of the molecular structure of the adsorbate.ll On the other hand, the Maxwell-Wagner process is caused by an inherent heterogeneity of the dielectric system and it originates in the differences in conductivities of the adsorbate, substrate, and electrode.12 Both processes give a similar dependence of the dielectric constant and loss on frequency,
* Author to whom all correspondence should be addressed.
Presentaddress: Department of Chemistry, Faculty of Science, OkayamaUniversityof Science,1-1Ridai-cho, Okayama 700, Japan. @Abstractpublished in Advance ACS Abstracts, May 15, 1995. f
(1) McIntosh, R. L. Dielectric Behavior ofPhysicalZy Adsorbed Gases; Marcel Dekker: New York, 1966. (2) Nair, N. K.; Thorp,J. M. Trans.Faraday SOC.1966,61,962;974. (3) Hall, P. G.; Williams, R. T.; Slade, R. C. T. J.Chem. Soc., Faraday Trans. 1 1985,81, 847. (4) Hall, P. G.; Kouvarellis, G . K. Trans. Faraday SOC.1968, 64, 1940. ( 5 ) Nelson, S. M.; Newman, A. C. D.; Tomlinson, T. E.; Sutton, L. E. Trans. Faraday SOC.1959, 55, 2186. (6)Kaneko, K.; Serizawa, M.; Ishikawa, T.; Inouye, K. Bull. Chem. SOC.Jpn. 1975,48, 1764. (7) Morris, B. J.Phys. Chem. Solids 1969,30, 73; 103. (8) Jones, G.; Davis, M. J. Chem. SOC.,Faraday Trans. 1 1975, 71, 1791. (9) Jones, G. J. Chem. SOC.,Faraday Trans. 1 1975, 71, 2085. (10) Ozeki, S.; Masuda, Y.; Sano, H. J.Phys. Chem. 1989,93,7226. (11)Debye, P. PolarMolecules; The Chemical Catalog Co.: NewYork, 1929. (12)Van Beek, L. K. H. Prog. DieZectr. 1967, 7, 69.
0743-746319512411-2173$09.00/0
though the Maxwell-Wagner relaxation appears in the relatively lower frequency region, whereas water has its dipolar relaxation in much higher frequency region. The assignment of the relaxation observed in the adsorption system is still controversial. Actually, McCafYerty et al.13J4 studied the dielectric behavior in the a-Fe203-HzO system at room temperature and they assigned the relaxation observed at ca. 10 Hz to the Debye-type relaxation caused by the orientational polarization of adsorbed water. We have also observed a similar relaxation, though it was assigned to the interfacial polarization arising from a heterogeneity of the system.15-17 Thus there is confusion in assigning the relaxation observed in the powder sample. These difficulties can be overcome by discussing the dielectric properties ofthe adsorption system as a function of the coverage in a wide range of frequencies and Through these investigations, it is possible to discuss the assignment of the observed relaxation and the state of adsorbed species. We found a step in the adsorption isotherm of water on SrF2 at 283 K that was ascribed to the two-dimensional condensation ofwater on the homogeneous surface of SrF2. This adsorption anomaly has been investigated by several (13) McCafferty, E.; Pravdic, V.; Zettlemoyer, A. C. Trans. Faraday
SOC.1970, 66, 1720.
(14)McCafferty, E.; Zettlemoyer, A. C. Disc. Faraday SOC.1971,52,
229
(15) Morimoto, T.; Iwaki, T. J . Chem. SOC.,Faraday Trans. 1 1987, 83, 943. (16) Iwaki, T.; Morimoto, T. Langmuir 1987, 3, 282. (17) Kuwabara, R.; Iwaki, T.; Morimoto, T. Langmuir 1987,3,1059. (18) Kondo, S.; Muroya, M. Bull. Chem. SOC.Jpn. 1969,42, 1165. (19) Hoekstra, P.;Doyle, W. T. J . ColZoidInterface Sci. 1971,36,513. (20) Kondo, S.;Muroya, M.; Fujiwara,H.;Yamaguchi, N. Bull. Chem. SOC.Jpn. 1973, 46, 1362. (21)Biquard, F.; Guermeur, R.; Jacolin, C. J.Chem. Phys. 1990,93, 6779.
0 1995 American Chemical Society
Kuroda et al.
2174 Langmuir, Vol. 11, No. 6, 1995 nc,
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Figure 1. Adsorption isotherm of water on SrFz at 298 K. V, indicates the monolayer capacity of water.
methods.22-26In part 1of this series to investigate the dielectric properties of the SrFZ-HzO system, we reported that the large dielectric dispersion observed in the vicinity of 298 K is attributable to the interfacial polarization arising from a heterogeneity of the system.26 If our interpretation is true, one might expect another relaxation resulting from the orientational polarization of adsorbed water. In the present work we measured the dielectric properties of a SrFZ-HzO system as a function of coverage a t lower temperatures and in the range of 0.1 Hz-5 MHz in order to find the orientational polarization of adsorbed water, and the adsorbed state of two-dimensionally condensed water is also discussed. 2. Experimental The sample and sample cell (dielectriccell) used in this study were the same as those in the previous work.26 The adsorption isotherm was measured by the same method as described previously.2'2 Prior to the dielectric measurement, the amount of water adsorbed on SrFz was controlled on the basis of the adsorption data at 298 K. After the attainment of adsorption equilibrium at a certain pressure of water vapor and at 298 K, the sample cell, the dead volume ofwhich is known, was promptly cooled to 273 K and then very slowly cooled to 228 K to avoid the desorption of water from the sample and its simultaneous adsorption onto the inner wall of the cell. Following this, the temperature of the cell was successively lowered to 201, 179, 159, 149, and 77 K. At every stage the dielectric permittivity and dielectric loss were measured in the frequency range from 0.1 Hz to 5 MHz by using impedance bridges (TR-4and TR-lOC, Ando Electric Co.). An establishmentof the equilibrium,which was ascertained by checking the E' value, took about 12 h every successive cooling. The measurement of the enthalpy of adsorption was carried out by the use of an adiabatic adsorption calorimeter connected to the volumetric adsorptionapparatus.25 3. Results and Discussion
The adsorption isotherm of water on SrFz evacuated a t 298 K is illustrated in Figure 1. This isotherm is essentially the same as that obtained in the preceding work;26the adsorption of water proceeds on the active sites a t lower pressures, followed by adsorption on the (22) Kuroda,Y.;Kittaka, S.;Miura, K.; Morimoto,T.Langmuir 1988, 4 , 210.
(23) Kuroda, Y.;Morimoto, T. Langmuir 1988,4 , 425; 430. (24) Kuroda, Y.;Yoshikawa, Y.; Yokota, Y.; Morimoto, T. Langmuir 1990,6,1544. (25) Kuroda, Y.; Matsuda, T.; Nagao, M. J. Chem. SOC.,Faraday Trans. 1993,89, 2041. (26) Kuroda, Y.;Yoshikawa, Y.; Morimoto, T.;Nagao, M. Langmuir 1995,11, 259.
0 0.1
1
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1
10 100 l k 10k lOOk 1M 1 Frequency/Hz
'
100
10
1
t 0.1
0.0 1
E
0,001 0.1
Figure 2. Dependence of (a)dielectric permittivity, E', and (b) dielectric loss, E", on frequency for adsorbed water on SrFz at 0 = 0.92. Temperatures of measurement are 298 (01,273 (01, 228 (a), 201 (@I, 179 (01,159 (e),and 149 K (0).
specific homogeneous surface, giving rise to a step in the isotherm at the relative pressure of 0.03. The appearance of such a step was ascribed to the two-dimensional condensation of water on the solid surface.22 The monolayer capacity for water is estimated to be 0.4 cm3 (standard temperature and pressure, STP) mT2by the "point B method,27being larger than 0.35 cm3(STP) m-2 obtained on the basis of the molecular area of water.28 The dielectric permittivity, E', and loss, E", for the present SrFZ-HzO system, which were obtained by using blocking electrodes in the temperature range from 298 to 149 K, are plotted against the frequency in Figure 2. E' obtained at 298 K is approximately 300 a t lower frequencies, and it decreases steeply and then gradually with increasing frequency to give a constant value of 2 beyond 5 kHz.The E" curve for the same temperature reveals a maximum a t 2 Hz. In the region where the dielectric dispersion appears, there exists a correlation between E' and E". E" has a characteristic frequency dependence corresponding to the variations in E'; E" passes through a maximum value at the frequency where dundergoes its maximum change in the variation with frequency. The frequency where E" gives a maximum value corresponds to a characteristic (27) Ross, S.; Olivier, J. P. On Physical Adsorption; Interscience: New York, 1964. (28) McClellan, A. L.; Harnsberger, H. F. J. Colloid Interface Sci. 1967,23,577.
Langmuir, Vol. 11, No. 6, 1995 2175
Dielectric Behavior in the SrF2-H20 System 100
10
1 W
0.1
0.01
0.1
1
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0.001 0.1
1
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Frequency/Hz
d
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Figure 3. Dependence of dielectric loss, c”, on frequency for various coverages: (a) 8 = 0, (b)8 = 0.26, (c) 8 = 0.74, and (d) 8 = 1.26. Temperatures of measurement are 298 (01,273 (01,228 (81,201 (@I, 179 (e),159 (e),and 149 K (0).
frequency cfm)for the observed dispersion. On the basis of this consideration, it should be noted that a large relaxation appears in the lower frequency region at 298 K for a coverage (6)of 0.92. As the temperature is lowered, the €’value a t 0.1 Hz becomes smaller (Figure 2a) and the relaxation frequency shifts to the lower frequencies (Figure 2b). At 228 K, a substantial portion of the peak of the E” curve lies within the limiting frequency, 0.1 Hz, of the present measuring system and it disappears when the temperature is lowered below 228 K. On the other hand, below 179 K another relaxation appears a s a peak in the higher frequency region, though the E‘ value for this relaxation is much smaller than that observed a t 298 K, as is shown in the enlarged scale in Figure 2a. Further temperature drop causes a shift of this peak to the lower frequency side. We have concluded that the relaxation observed at 298 K and in the lower frequency region (relaxation I) can be assigned to the interfacial polarization resultingfrom the conductivity difference in the system.26 Therefore, the origin of the relaxation observed at lower temperatures (relaxation 11)is particularly interesting. It should be necessary to elucidate the conditions necessary for this relaxation to appear. At first, we examined the coverage dependence of the observed relaxation. The dielectric losses ( E ” ) obtained a t various temperatures for the different coverages are plotted against the frequency in Figure 3. For zero coverage and 298 K, a
monotonous increase in E” toward the lower frequencies suggests a presence of the relaxation in the lower frequency side. When the temperature is lowered, E” decreases over the whole range of frequencies. Any other relaxations cannot be observed in the entire frequency range examined, even a t temperatures below 201 K, though water molecules exist (15 H 2 0 molecules nm-’3 on the SrF2 surface which are strongly adsorbed and unable to be removed by evacuation a t 298 K.25 As the coverage increases successively to 0.26, 0.74, and 1.26, the maximum in the E” curve appears correspondingly a t 0.7, 1.3, and 14.5 Hz a t 298 K, keeping the maximum E‘‘ values constant. These maxima shift to the lower frequency with decreasing temperature (Figure 3b,c,d). Below 201 K, the E” values a t low frequencies around 0.1 Hz decrease even for the sample with a coverage of 1.26. It is noteworthy that a new relaxation appears in these coverages, a s is shown in Figure 3. From the fact that this relaxation does not appear for zero coverage in the temperature and frequency ranges examined, the physisorbed water seems to be responsible for this new relaxation (relaxation 11). The relaxation frequencies corresponding to the maximum value of E“ shift to the lower frequencies with decreasing temperature and they are, for example, a t 159 K and 68,33, and 840 k H z for the coverages 0.26,0.74, and 1.26, respectively. Figure 3 also shows the coverage dependence of the E” peak height for
Kuroda et al.
2176 Langmuir, Vol. 11, No. 6, 1995
of the Cole-Cole plots is expressed by the following equation:
Figure 4. Cole-Cole plots for various coverages of adsorbed 0.56 (0),0.74 water on SrFz at 159 K coverages are 0.26 (a),
(e),0.92 (e),and 1.26 (e).
0.41
'51 0.3
'
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1.5
Coverage
Figure 5. Chord length, Ae'obsd, obtained from Cole-Cole plots as a function of coverage.
the relaxation 11; the peak height of E" increases with increasing coverage. Taking these observations into consideration, the origin of the relaxation I1 observed a t lower temperatures can be attributed neither to chemisorbed water nor to a n ionic process (migration) on the surface (or bulk) of SrFz but to the physisorbed water. The possibility of an ionic process is excluded also by considering the fact that Evangelakis and Miliotis observed such a process in a much higher temperature region.29 Thus, it may be reasonable to conclude that the relaxation I1 is caused by the orientational polarization of physisorbed water. The Cole-Cole plots for the relaxation I1 a t 159 K are shown in Figure 4 for the sample with different amounts of physisorbed water. The dielectric relaxation for this system is simply described by a single relaxation. It gives rise to Cole-Cole plots with a shallow arc rather than of semicircle. Although the theories on the variation of dielectric constant with frequency have been worked out for a single relaxation time governing the exponential decay, it can be shown that a general description of the variation of polarization with time is possible by means of a superposition of the continuous distribution of relaxation processes with characteristic times varying over a narrow range. In such a case, it is evident that the graphs of the Cole-Cole plots are flatter than those of a single relaxation time. Such a distribution of relaxation times is often encountered. Another apparent feature is seen from Figure 4. The chord length of the relaxation depends on the adsorbed amounts, which is clearly different from the case of the relaxation observed at 298 K.26 A similar trend has been found a t lower temperatures in the TiOz-30 and Zn0-Hz031 systems. The chord length of the Cole-Cole arc, A d o b s d = EO - E.., for the relaxation I1 at 159 K is plotted against coverage in Figure 5, where EO and 6. are the limiting low- and high-frequency permittivities, respectively. A d o b s d increases in proportion to coverage (8)in the measured range. According to Onsager's equation,32the chord length (29) Evangelakis, G. A.; Miliotis, D. Phys. Rev. 1987,B36, 4958. (30) Iwaki, T.;Morimoto, T.J . Chem. SOC.,Faraday Trans. 1 1987, 83, 957. (31) Iwaki, T.;Morimoto, T. Langmuir 1987,3,287. (32) Onsager, L. J. Am. Chem. SOC.1936,523,1486.
where E is the dielectric permittivity, N the number of molecules in the unit volume, p the dipole moment, n the refractive index, k the Boltzmann constant, and T the absolute temperature. This equation is derived for threedimensional systems, but it can also be applicable to twodimensional systems, because N corresponds to the adsorbed amount in the two-dimensional layer. Therefore, A d o b s d is expected to be proportional to N (adsorbed amount or number of adsorbed molecules), although the values of p, n , and 6 may be different from those for threedimensional systems. Equation 1implies that the chord length is proportional to the number of molecules if the observed relaxation can be assigned to the orientational polarization of physisorbed molecules. The linearity established in Figure 5 supports the validity of equation 1 for the relaxation 11, which leads us to conclude that this relaxation is due to the orientational polarization of the adsorbed water molecules. Therefore, it is said that the relaxation observed a t 298 K is a Maxwell-Wagnertype of relaxation. The static dielectric constant for pure water is about 80 a t 300 K.33 It is interesting to estimate the apparent dielectric constant for water adsorbed on the SrFz surface from the observed data of A c l 0 b s d and adsorbed amount, N. The value thus obtained exhibits the average dielectric constant of 78, being almost the same value as for pure water. This fact implies that the observed relaxation is caused by the orientational polarization of the adsorbed water. The difference in dielectric permittivities between the localized water and the two-dimensionally condensed water cannot be detected in the present case. This is because the observed value of A d o b s d is too small to allow precise discussion of the difference in the adsorbed state of water. Another striking feature is observed in Figure 3: the magnitude of the dielectric loss of the relaxation I1 shows a maximum decrease with decreasing temperature. The same tendency has been found in the system of watersilica gel,2,34for which a dispersion of the MaxwellWagner-type was responsible for such behavior. The qualitative argument was that the conductance, which causes a n ohmic loss of electrical energy as heat, increases with temperature so that the value of a t a particular frequency should also increase with temperature. However, McCaffertP6explained the same effect by molecular relaxation processes having a distribution of relaxation times. Thus this tendency gives no evidence to ascribe the observed relaxation to the Maxwell-Wagner process. The theory of rate processes can be applied to the temperature variation of relaxation times in the form36
1
-AE*
w = - = A exp z RT
where w ( = 2 d is the angular relaxation frequency, z the relaxation time, and AE* the activation energy of the relaxation process, and R and Thave their usual meanings. Plots of In f m against T-l for the relaxation I1 due to the (33) Hasted, J. B.Water; Franks, F., Ed.; Plenum: New York, 1972. (34) Kamiyoshi, K.; Odake, T.J . Chem. Phys. 1963,21,1295. (35) McCafferty, E. J. Phys. Chem. 1978,82, 2044. (36) Glasstone, S.;Laidler, K. J.; Eyring, H. The Theory of Rate Processes; McGraw-Hill: New York, 1941.
Dielectric Behavior in the SrFZ-HzO System
2P 102 106 l*-
100
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: \49
0.4
0.6
u 0.2
0.4 0.6
0.8 1.0 Coverage
1.2
1.4
1.6
Figure 8. Heats ofadsorption and adsorptionisotherm ofwater on SrFz at 301 K.
t , , . , , i
OO
0.5
1.0
Coverage
Figure 7. Activation energy for dielectric dispersion as a function of coverage.
adsorbed water are given in Figure 6. For comparison, the f m values for ice,37 water,38 and adsorbed water molecules on & 0 3 3 9 and on Si0240are also cited. The slope of the straight line in Figure 6 permits a calculation of the activation energy for the relaxation I1 process. AE* values thus obtained are plotted against the coverage in Figure 7. It should be noted that a distinct maximum appears in the AE*curve in the same coverage range for which the step appears in the adsorption isotherm. Furthermore, the relaxation frequency a t 298 Kis calculated from the obtained parameters to be 3 GHz a t a coverage of 1.26. This value is comparable to that of adsorbed water on Si02 obtained through the time-domain method.41 For ice, hE* is 53 kJ mol-l in the temperature range from 207.3 to 273.0 K,37,42 and for water it is 18 kJ mol-l in the temperature range from 273.1 to 333.1 K.38,43 (37)Auty, R. P.; Cole, R. H. J . Chem. Phys. 1962,20, 1309. (38) Saxton, J. A. Proc. R. SOC.A 1952, 213, 473. (39) Dransfeld, K.; Frisch, J. L.; Wood, E. A. J . Chem. Phys. 1962, .?fi - - , -1574 - . -. (40) Kamiyoshi, K.; Ripoche, J. J . Phys. Radium 1958,19, 943. (41) Sakamoto, T.;Nakamura, H.; Uedaira, H.; Wada, A. J . Phys. Chem. 1989,93, 357. (42) Kawada, S. J . Phys. SOC.Jpn. 1978,44, 1881.
The values obtained for the adsorbed water a t the initial stage and a t monolayer coverage are closer to the value for the liquid water. The value of the activation energy for the dielectric relaxation of the two-dimensionally condensed water is intermediate between those of ice and water. One notable difference between the adsorbed system and ice or water is that the data for ice and water may be accounted for on the assumption that the observed relaxation consists of a single relaxation time, while our data require a distribution of relaxation times. The variation of heat of adsorption of water on SrFz with surface coverage is shown in Figure 8. The initial decrease in heat may be correlated with a heterogeneity in the strength of adsorption sites, and the succeeding slight increase can be ascribed to the two-dimensional condensation of water resulting from the lateral interaction of water molecules adsorbed on the homogeneous surface of SrFz in the coverage region from 0.2 to 0.8, corresponding to the step in the adsorption isotherm.25 After the completion of monolayer coverage, the heat of adsorption shows a rapid fall and finally approaches the heat of liquefaction of water vapor (HL). On the basis of the calorimetric and dielectric data, the following model can be constructed for the adsorbed water. (1) The SrFz sample (6 = 0) evacuated a t 298 K has strongly adsorbed water (15 H2O molecules nm-2). However, the relaxation due to these water was not observed. This fact indicates that these species cannot respond to the ac field, which is distinct from the behavior of chemisorbed water (surface hydroxyls) on ZnO and Ti02.30,31It supports the adsorption model that the strongly adsorbed water molecules get stuck on the SrF2 surface through the formations of hydrogen bonding with F- ion and of coordination bonding with Sr2+ (2) In the region 8 5 0.2, the interaction energy between water molecules and the SrF2 surface is 90-70 kJ mol-', being indicative of a strong interaction. On the other hand, hE* is 16 kJ mol-l, in good agreement with the hE* value for liquid water, and the relaxation time has a value of 1.7 x s at 159 K. These values indicate that the water molecules are tightly bound to the SrFz surface, (43) Luck, W. A. P. The Hydrogen Bond; Schuster, P., Zundel, G., Sandorfy, C., Eds.; Dynamics, Thermodynamics and Special System: North-Holland, Amsterdam, 1976, Vol. 3.
Kuroda et al.
2178 Langmuir, Vol. 11, No. 6, 1995 keeping their rotational freedom. This also reveals that water is adsorbed without lateral interaction on the active sites dispersed on the surface. (3) In the coverage region where two-dimensional condensation of water occurs, hE* is larger than that in the initial adsorption stage and the relaxation time is s at 159 K. The rotation of water equal to 4.8 x molecules is expected to be more hindered compared with that of bulk water, though not a s much a s in ice. This is caused by the lateral interaction between water molecules and by the interaction of adsorbed species with the underlying surface. (4)Beyond the monolayer coverage (0 2 l),hE* becomes equal to that of bulk water again and the relaxation time
is 2 x lo-' s at 159 K, which indicates a high rotational mobility of the adsorbed water. This is consistent with the result of calorimetric measurement. In general, it is said that a solid surface exerts a strong field on the adsorbed water over a considerable distance. The reason for such motional behavior of the second layer of water on SrFz cannot be given a t present.
Acknowledgment. Thanks are due to Professor Tetsuya Hanai of Kyoto University for reading the manuscript and making a number of helpful suggestions. LA940821F
