Langmuir 1995,11,259-264
259
Dielectric Behavior in the SrF2-H20 System. 1. Measurement at Room Temperature Yasushige Kuroda" and Yuzo Yoshikawa Coordination Chemistry Laboratories, Institute for Molecular Science, Myodaii, Okazaki 444,Japan
Tetsuo Morimotof 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 July 11, 1994. I n Final Form: October 19, 1994@ Dielectric properties, permittivities and losses, of the SrFZ-HzO system in which two-dimensional condensation of water occurs were investigated as a function of surface coverage at 298, 273, and 230 K and in the frequency range from 0.1 Hz to 5 MHz. In this system large dielectric dispersions were observed at 298 Knear 0.3 and 15 Hz and at coverages of 0.13 and 1.26 monolayers, respectively. Some experiments were carried out to elucidate these relaxations. It is concludedthat these relaxations are due to interfacial polarization arising from heterogeneity ofthe system, i.e.,Maxwell-Wagner type, and not to orientational polarization of the adsorbed water, namely Debye type. The former polarization is explained by a twolayer model based on the difference in conductances between the electrode-particle and the particleparticle. The conductance varies with the amounts of adsorbed water, and the mechanism of conduction in the adsorbed layer is interpreted in terms of Grotthus' mechanism. Moreover, it is found that the two-dimensionally condensed water causes a small change in the conductance. The adsorbed state of water on the SrFz surface is discussed on the basis of experimental data.
Introduction In the system of SrF2-HZ0, we found a step in the adsorption isotherm obtained at 283 K and ascribed it to the two-dimensional condensation of water on the homogeneous surface of SrF2.l We have investigated this interesting phenomenon by several method^.^-^ Many adsorption systems have been investigated by the dielectric relaxation m e t h ~ d . ~However, -~~ a serious problem
* To whom correspondence should be addressed.
t Present address: Department of Chemistry, Faculty of Science, OkayamaUniversity of Science,1-1Ridaicho,Okayama 700,Japan. Abstract published in Advance A C S Abstracts, December 15, @
1994. (1)Kuroda, Y.; Kittaka, S.;Miura, K.; Morimoto, T. Langmuir 1988, 4,210. (2)Kuroda, Y.; Morimoto, T. Langmuir 1988,4, 425. (3)Kuroda, Y.; Morimoto, T. Langmuir 1988,4,430. (4)Kuroda, Y.; Yoshikawa, Y.; Yokota, Y.; Morimoto, T. Langmuir 1990,6,1544. ( 5 ) Kuroda, Y.; Matsuda, T.; Nagao, M. J . Chem. Soc., Faraday Trans. 1993,89,2041. (6)McIntosh, R. L.Dielectric Behavior ofPhysically Adsorbed Gases; Marcel Dekker: New York, 1966. (7)Kamiyoshi, K.; Ripoche, J. J. Phys. Radium 1968,19,943. (8)Nair, N. K.; Thorp,J. M. Trans. Faraday SOC.1966,61,962,975. (9)Hall, P. G.; Williams, R. T.; Slade, R. C. T. J. Chem.Soc.,Faraday Trans. 1 1985,81,847. (10)Dransfeld, K.;Frisch, H. L.; Wood, E. A. J . Chem. Phys. 1962, 36,1574. (11)Baldwin, M. G.;Morrow, J. C. J . Chem. Phys. 1962,36,1591. (12)Kondo, S.;Muroya, M.; Fujiwara, H.; Yamauchi, N. Bull. Chem. SOC.Jpn. 1973,46,1362. (13)Nelson, S. M.; Newman, A. C. D.; Tomlinson, T. E.; Sutton, L. E. Trans. Faraday SOC.1969,55,2186. (14)Kaneko, K.;Serizawa, M.; Ishikawa, T.; Inouye, K. Bull. Chem. SOC.Jpn. 1976,48, 1764. (15)McCafTerty, E.;Pravdic, V.; Zettlemoyer, A. C. Trans. Faraday Soc. 1970,66,1720. (16)McCafTerty, E.;Zettlemoyer, A. C. Discuss. Faraday SOC.1971, 52,239.
is often present in the assignment of the observed relaxation mechanism. For example, McCafYerty et al.15J6 studied the dielectric behavior of the a-Fez03-Hz0 system at room temperature as a function of the adsorbed (physisorbed) water and observed a relaxation at some 10 Hz. They assigned it to the Debye-type relaxation caused by the orientational polarization of the physisorbed water. On the other hand, our group observed similar relaxations at 298 K i n Ti0z-,20 Zn0,22and a-FezO3-HzOZ4systems and assigned them to the interfacial polarization arising from the heterogeneity of the system. Thus, a question as to the assignment of the observed relaxation is raised. In the present work, we investigate the dielectric properties of the SrFz-Hz0 system between 230 and 298 K i n the frequency range from 0.1 Hz to 5 MHz, with the purposes of identifying the type of observed relaxation and of characterizing the two-dimensionally condensed water.
Experimental Section The SrFz sample used in this study was prepared by the same way as described in the previous paper,' being obtained through the precipitation by mixing two aqueous solutions of Sr(NO3)z and NHJ?. The precipitatewas washed sufficientlywith distilled water. Redistilledwater (HzO)was further purified by repetition (17)Morris, B. J . Phys. Chem. Solids 1969,30,103. (18)Hoekstara, P.; Doyle, W. T. J . Colloid Interface Sci. 1971,36, 513. (19)Ozeki, S.; Masuda, Y.; Sano, H. J . Phys. Chem. 1989,93,7226. (20) Morimoto, T.; Iwaki, T. J . Chem. SOC., Faraday Trans. 1 1987, 83,943. (21)Iwaki, T.; Morimoto, T. J . Chem. Soc., Faraday Trans. 1 1987, 83,957. (22)Iwaki, T.; Morimoto, T. Langmuir 1987,3,282. (23)Iwaki, T.; Morimoto, T. Langmuir 1987,3,287. (24)Kuwabara, R.; Iwaki, T.; Morimoto, T. Langmuir 1987,3,1059.
0743-746319512411-0259$09.00100 1995 American Chemical Society
260 Langmuir, Vol. 11, No. 1, 1995
Kuroda et al.
L 02 0.3 0.4 0.5 0.6 0.8 0.9
0 '
0.7
0.1
Relative
1.0
Pressure
Figure 1. Adsorption isotherm of water on SrF2 at 298 K. V, indicates the monolayer capacity for water.
0.1 1
10 100 l k 10k lOOk 1M 1OM Frequency/Hz
of a freeze-pump-thaw cycle and was used as an adsorbate. DzO supplied from Nacalai Tesque Inc.was purified in the same
manner as the HzO. The adsorption measurement was carried out by using a conventional volumetric adsorption apparatus. The equilibrium pressure of water vapor was determined by an oil manometer: and the pressure of dinitrogen gas was measured by a capacitance pressure sensor of MKS Baratron 220 B. The adsorption isotherm was obtained at 298 K for the sample evacuated at 298 K for 4 h under a reduced pressure of 1 mPa. The specific surface area of the sample was determined by applying the BET equation to the dinitrogen adsorption data obtained at 77 K and was found to be 25.6 m2g-l, assuming the cross sectional area of a dinitrogen molecule to be 0.162 nm2. The sample cell for dielectric measurementwas composed of two concentric stainless-steel cylinders of 80 nm in length and 19 and 15 mm in outer and inner diameters, respectively. The electrodes were coated with a poly(tetrafluoroethy1ene) film of about 30 pm thickness and the capacitanceofthe film was about 1600 pF. The capacitance of the dielectriccell with nonblocking electrodes was measured at 298 K using cyclohexane, dichloroethane, and nitrobenzeneas the standard substances and was found to be 14.3 pF; the stray capacitance was 3.5 pF. The sample was packed into the dielectriccell with a packing density of 45%and was evacuated at 298 K under a pressure of 1 mPa until no further change in the dielectric permittivity occurs. Dielectricpermittivities and losses ofwater adsorbedon the SrFz surface at 298, 273, and 230 K were measured by means of impedance bridges of type TR-1OC and TR-4 manufactured by Ando Electric Co. For measurementof IR spectra, a self-supportingsampledisk was set in the in situ cell equipped with KRSd (TlBr and TlI) window^.^ The sample was evacuated at 773 Kfor 2 h, followed by rehydration by exposing to saturated water vapor for 12 h at room temperature, and then was evacuated again at 298 K to remove physisorbed water. The sample thus pretreated was equilibratedwith water vapor at various pressures. IR spectra were recorded at room temperature by using a Nicolet FTIR-710 spectrophotometer.
Results and Discussion The adsorption isotherm of water on SrFz at 298 K is depicted in Figure 1. The distinct feature of this adsorption isotherm is an appearance of the steep rise (step) in the relative pressure range of 0.03-0.04. This step can be attributed to the two-dimensional condensation of water arising from the lateral interaction of water molecules adsorbed on the homogeneous (100)surface of SrF2.l The monolayer volume of water (V,) was obtained by applying the "point B" methodz5 to the adsorption isotherm and was found to be 0.40 cm3 m-2, i.e., 10.8 HzO molecules nm-2. This value for the surface density of adsorbed water is higher than that for other systems involving such metal (25) Ross, S.; Olivier, J. P.On Physical Adsorption; Interscience: New York, 1964.
H
Frequency/Hz
Figure 2. Dependence of dielectric permittivity,
E', and dielectric loss, E" on frequency for various coverages (e) of adsorbed water on SrF2 at 298 K. The 0 values are 0 (O), 0.13 (O),0.56 (a),0.74 (a),0.99 (e), 1.26 (e), 1.75 (O), and 3.0 (e).
oxides as Zn0,26Cr203,27and Sn02,28all of which have been shown to give an adsorption anomaly due to the twodimensional condensation of water. Figure 2 shows the frequency dependence of dielectric permittivity, E', and dielectric loss, E", for the SrFz-HzO system at 298 K and at various coverages of water. It is seen from these figures that a large dielectric dispersion appears in the frequency region examined. The value of E' for the surface coverage zero ( 6 = 0)increases monotonously with decreasing frequency and reaches 50 at 0.1 Hz. The E" value for the same coverage ( 6 = 0) also increases with a decrease in the frequency. However, no maximum appears in the measured frequency region for this sample, though many water molecules are remaining on the sample after evacuation at 298 K (15HzO molecules nm-2).5 The shape of the curves of E' and cf' as a function of frequency is well known and the variations of E' and df ~~~
~
(26) Morimoto,T.;Nagao, M.;Tokuda,F. Bull. Chem.SOC. Jpn. 1968, 48. 1533. (27) Kittaka, S.; Nishiyama, J.; Morishige, IC;Morimoto,T. Colloids Sud. 1981. 3. 51.
(28)Kittaka, S.;Kanemoto, S.; Morimoto, T. J . Chem. SOC.,Faraday Trans. 1 1978, 74, 676.
Dielectric Behavior in the SrFZ-H20 System
Langmuir, Vol. 11,No.1, 1995 261
lOOOk
-0 /
' / 0
1
2 Coverage
3
h
4
Figure 3. Coverage dependence of dielectric permittivity at 298 K and at various frequencies: (a) 0.1 Hz;(b) 1 Hz;(c) 10 Hz;(d) 30 Hz;(e) 110 Hz;(0 1 kHz; (g) 10 kHz;(h)100 kHz.
with frequency are correlated with each other (KramersKronig relationship); E" has a characteristic frequency dependence, passing through a maximum value at the frequencywhere d undergoes its maximum rate of change with frequency. The frequency indicating a maximum E" corresponds to the characteristic frequency (fm) for the observed dispersion. For the sample with zero coverage, E" shows a monotonous increase with decreasing frequency and gives no maximum, which may imply the presence of relaxation in a much lower frequency region. As the physisorption of water proceeds and hence 6 increases, E' increases in the lower frequency region and gives almost constant values in the frequency region higher than 100 kHz. For the coverage of 0.13, the E' curve gives a limiting value, 200, a t the lowest frequency, passes a broad transition region extending from 1to 1000 Hz, and finally approaches another limiting value in the higher frequency region. Correspondingto these changes in E', the E" curve represents a peak centered on the inflection point (fm = 0.3 Hz) in the E' curve. This peak gradually shifts to the higher frequency as the water coverage increases and, finally,fmreaches 15 Hz a t 6 = 1.26. Based on these data in Figure 2, both curves of E' and E" seem to be typical of Debye-type dispersion in the experimental frequency range. However, the relaxation frequencies (fm) obtained for the SrF2-H20 system are distributed from 0.3 to 15 Hz, lying far below the relaxation frequencies for pure water, 16 GHz (at 293.1 K),29and for pure ice, 7.2 kHz (at 273.0 K).30 The dielectric permittivity (E') is replotted against surface coverage ( 6 )for fixed frequencies between 0.1 Hz and 100 kHz in Figure 3. It is found from this figure that in the initial stage of physisorption (8 5 0.3) E' increases more steeply for the lower frequency range than for the higher frequency range. In the middle stage (0.3 < 8 < 0.81, corresponding to the region where a step appears in the adsorption isotherm, E' gives almost constant values, independent of the frequency range. On further adsorption ofwater (6 L 0.81, dincreases to approach a constant value again. It is interesting to note that for the higher frequency range cf L 1kHz) the physisorbed water in the first layer does not affect the dielectric permittivities of (29) Lane, J. A.; Saxton, J. A. Proc. R . SOC. London,A 1962,213,400. Saxton, J. A. Proc. R . SOC.London, A 1962,213,473. Collie, C. H.; Hasted, J. B.; Ritson, D. M. Proc. Phys. SOC.1948,60, 145. (30)Auty, R.P.; Cole, R. H. J. Chem. Phys. 1952,20,1309.
loo
200 E'
300
400
Figure 4. Cole-Cole plots for various coverages of adsorbed water on SrFz at 298 K. Coverages are 0 (O), 0.13 (O),0.26 (0, 0.56 ((31, 0.74 (a),0.92 (e),and 0.99 (8).
the system but that in the second layer causes a drastic increase in c'. A similar feature of the E' curve has been observed by McCafferty et al. for the a-Fe203-HzO system.lsJ6 They attributed the observed relaxation to the orientational polarization of adsorbed water and the increase in E' with a commencement of the formation of the second layer to the increased ability of the adsorbed water molecules to respond to the ac field, and they concluded that water molecules in these multilayers must be more mobile than those in the monolayer. On the other hand, the tendency for the lower frequency range is quite different here from that described for the a-Fez03system; E' increases steeply with a slight increase in the adsorbed amounts in the lower coverage region. In the coverage between 0.3 and 0.8, the increase in cf with coverage is very small for all the frequency range. These data cannot be explained by the orientational polarization of the adsorbed water molecules as described by McCafferty et al., this discrepancy being probably because they did not obtain data at lower frequencies. Furthermore, the value of E' at lower frequencies, e.g., 30 or 110 Hz, exceeds ca. which corresponds to the value of E' for water, and it reaches several hundreds (Figures 2 and 3); the obtained values of E' are rather high to consider the observed relaxation as the orientational polarization of adsorbed water. Consequently, these facts seem to be contradicted with the assignment of the dispersion to the Debye type, i.e., the orientational rotation of water molecules. The Cole-Cole plots32for the relaxation observed a t 298 K are shown in Figure 4. The chord length of these plots equals to the value of (€0 - E,), where €0 and E , are the static permittivity and the limiting high-frequency permittivity,respectively. It is found that the chord length ofthis relaxation does not depend on the adsorbed amount in the present system. The chord length ofthe Cole-Cole plots near coverage unity seems to be longer than that for the lower coverage,which may be caused by an overlapping of another relaxation present in the lower frequencyregion (Figure 2). According to O n ~ a g e r the , ~ ~chord length of the Cole-Cole plots is expressed by the followingequation
where N is the number of molecules,,uthe dipole moment of the molecule, E the dielectric permittivity, n the refractive index, K the Boltzmann constant, and T the absolute temperature. On the basis of his model, we assume that the observed relaxation is assigned to the orientational polarization of the adsorbed water. In such case, the chord length should be proportionalt o the amount of adsorbed water (N>. However, our data cannot be well (31)Hasted, J.B.Water;Franks, F., Ed.; Plenum: New York,1972; VOl. 1. (32) Cole, K. S.; Cole, R. H. J. Chem. Phys. 1941,9 , 341. (33)Onsager, L.J.Am. Chem. SOC.1936,58,1486.
Kuroda et al.
262 Langmuir, Vol. 11, No. 1, 1995
10’0 0.1
1
10 100 l k 10k lOOk 1M 10M Frequency/ Hz
Figure 5. Plots of dielectric loss against frequency at 6 = 1.26 and at various temperatures: (a) 298 K (b) 273 K, (c) 230 K.
expressed by eq 1, and hence the observed dispersion does not seem to be due to the orientational polarization of the adsorbed water. Further support for the above view comes from a consideration of activation energy. Figure 5 shows the frequency dependence of E” for the SrFz-Hz0 system (6 = 1.26) when the temperature is varied. The activation energy was obtained by the aid of the Eyring equation from the plots of In f m against P1. The motion responsible for this relaxation is characterized by the activation energy of ca. 38.4 kJ mol-l, being what one would expect for the appreciably restricted motion. This activation energy is comparable to that for the relaxation observed a t room temperature in the system Ti0Z-HzOz0 or Zn0-Hz0.22 Furthermore, the dielectric relaxation time, rd, in the present system can also be calculated from the Cole-Cole plots. A measure of the distribution of relaxation times is given by the curvature of these plots; they are semicircular in shape when there is a single relaxation time, and they form a n arc if the relaxation times have a d i ~ t r i b u t i o n The . ~ ~ distribution of tdvalues is suggested by the deviation from a semicircle, as is observed in Figure 4. The averaged r d values are estimated to be 5.3 x lo-’ and 1.1 x s for the coverages 0.3 and 1.26,respectively. These values are much larger than those of ice (6.3 x s at 273 KI3O or liquid water (9 x 10-l2 s a t 293 KLz9 This fact suggests that the relaxation observed in the present system is not caused by the orientational polarization of adsorbed water. These considerations may preclude the relaxation mechanism in which the observed dielectric dispersion is due to the orientational polarization of the adsorbed water molecules. In such a system including electrodes, powder samples, and adsorbed water (as in the present system), there are boundaries between the individual components. In this case, interfacial polarization is expected and it is referred to as a Maxwell-Wagner type relaxation after ~ ~ , type ~ ~ of dispersion arises at the first p r ~ p o n e n t . This low frequencies and is due to the accumulation of interfacial charge and it becomes increasingly important when the dielectric constants and conductances in the (34) Cole, R. H.Prog. Dielectr. 1961,3,47. (35) Bijttcher, C. J. F. Theory of Electric Polarization; Elsevier: Amsterdam, 1973. (36)Van Beek, L. K. H. Prog. Dielectr. 1967,7,69.
0.1
1
10 100 l k 10k lOOk 1M 1( H Frequency/Hz
Figure 6. Dependence of conductance, G, on frequency for various coverages of adsorbed water on SrF2 at 298 K. The 6 values are 0 (a),0.13 (b),0.56 (c),0.74 (d), 0.99 (e),1.26 (0,and 1.75 (g).
two phases (particle-electrode and particle-particle) differ appreciably; the mechanism of this dielectric dispersion is due to the conductance variations in each component in the heterogeneous systems. The conductance, G, in the SrFZ-HzO system for the various coverages is plotted against the frequency in Figure 6. G value increases with increasing frequency. It should be noted that a steep rise in the conductance occurs and it shifts to the higher frequencies with increasing coverage. E“ is correlated with the measured conductance G by the following equation
where C is the capacitance of the sample, o the angular frequency, and f the frequency. Thus the frequency region where the steep rise in the G-f curve appears corresponds to the region showing a maximum in the 6”-f curve. Actually, a straight line (asdenoted by dotted line in Figure 6) is obtained by connecting the points where G undergoes its maximum rate of change with frequency in each coverage. The point of intersection of this line and G-f curve corresponds to the frequency a t which E” is a maximum. The frequency showing a steep rise in the G-f curve shifts to the higher frequencies as the surface coverage of physisorbed water increases. If we assume the Maxwell-Wagner type relaxation based on the increase in the conductance and heterogeneity of the system, the observed relaxation can be described by the two-layer model which has been applied to the adsorption system of Ti02-Hz0.20 According to this model, the following equation holds when the electrode is covered with a blocking film
, I
d $l+G, -1
fm=G do
(3)
where E,. is the permittivity in the vacuum, €1 and € 2 are the dielectric permittivities in the two layers, particleelectrode and particle-particle, respectively, GI and Gz
Dielectric Behavior in the SrFZ-HzO System
Langmuir, Vol. 11, No.1, 1995 263
are the electrical conductivities in both layers, and dl and d2 are the thicknesses ofthe two layers, respectively. When
-
10-b
we use the electrodes blocked with a n insulating thin film, GIis much smaller than Gz. Under such condition, eq 3 can be simplified as follows:
d C
t a
(4)
Equation 4 indicates that the f m value shifts to higher frequency with increasing G2 value, which is consistent with the present experimental result. Thus the observed phenomenon seems to be well explained by the two-layer model and it is concluded that the increase in G due to the adsorption of water causes the dielectric dispersion observed a t room temperature in the present SrF2-H20 system. This system is well expressed by the following equation proposed by Jonschel.3'
gt
oc gn-l
C 10-7 0
E
:
109 E
10-'0-,
0.1
,1111~
,,,,,u, 10 100 lk 10k lOOk 1M 1(
1
Frequency/ Hz
(5)
where n = 0.45a t 8 = 0 in the present case. This behavior is explained by rotation of giant dipoles which consist of grains making near-point-contacts with each other.38 In our system, the rotation of giant dipoles would result from proton transfers among adsorbed water molecules. The conductivity varies with humidity by several orders of magnitude, as is seen from Figure 6. Since the adsorbed water plays a n important role in the conduction process, the electrical conduction takes place through the Grotthus chain reactiod9 in which a proton is transferred progressively from one water molecule to the next in the physisorbed layer on the solid surface, as in the case of liquid water. In such a case the conductance depends on the properties of water; in other words, deuteration of the solid surface and adsorption of deuterium oxide instead of HzO may alter the electroconductance. The proton conduction (conductance)decreases when DzO is used and its ratio of H2O to DzO is expected to be about 1.4as in the case ofliquid water.40 In order to prove this hypothesis, we measured the conductance of the DzO system in almost the same surface coverage as in the case of the water (HzO) system (Figure 7). It is evident from Figure 7 that for the same coverage the conductance of the water (H2O) system is larger than that of the DzO system. The observed values at 1kHz are shown in Table 1. The ratios (~1.4) of conductance of the hydrogen to deuterium ions in water are in fair agreement with the values for liquid water40 or silica-water system.41 Such & isotope effect confirms the assumption that the transport of charge occurs through a proton-hopping mechanism. These results lead us to conclude that this dispersion is due to the interfacial polarization, which is caused by the increase in conductance, and is well explained by the two-layer model. From the above discussion, the observed relaxation is ascribed to the proton hopping of adsorbed water; the adsorption of water is followed by dissociation into oxonium and hydroxide ions. The protonic conductance, Gpr,is defined as
(37)Jonscher, A. K. Nature 1977,267, 673. (38)Jonscher, A. K Philos. Mag. 1978,38, 587. (39)Hertz, H.G.;Braun, B. M.; Muller, K. J.; Maurer, R. J . Chem. Educ. 1987, 64, 777. (40)Conway, B.E.;Bocklis, J. O'M.; Linton, H. J . Chem.Phys. 1956, 24, 834. (41)Anderson, J. H.; Parks, G. A. J.Phys. Chem. 1968, 72, 3662.
Figure 7. Dependence of conductance,G, for various coverages of adsorbed H2O (0)and DzO (0)on SrFz at 298 K. The 6 values are (a)0 (HzO,DzO),(b) 0.26 (HzO,DzO),(c) 0.99 (HzO),
1.0 (DzO), and (d) 1.26 (HzO), 1.23 (DzO).
Table 1. Conductance of SrFZ-H20 and -DaO Systems at Various Coverages and at 298 K ~~
coverage ( 6 ) of the
coverage conductance (e) of the HzO system GH2dS DzO system 0 3.08 x 0 0.26 1.80x 0.26 0.99 7.04 x 1.00 1.26 1.80 x 1.23
I
lO-4
~
conductance GD,dS 2.84 x 1.17 x
hldGD2o
1.08 1.54 1.33 1.37
5.28 x 1.31 x
/-
lU9P I-
t 0
1u"
1
o 2
3
I
4
'
Coverage
Figure 8. Coverage dependence of conductance at 298 K and at various frequencies: (a) 0.1 Hz; (b) 1Hz; (c) 10 Hz;(d) 30 Hz; (e) 110 Hz; (01kHz; (g) 10 M z ; (h) 100 kHz.
where q is the charge of proton, nprthe number of proton, and pprthe mobility of protons. The variation of conductance with surface coverage is shown in Figure 8. In the absence of physisorbed water, the sample has a poor conductance. When physisorption starts to occur, the G value for the higher frequency increases remarkably with increasing coverage, followed by a slight increase, and
264 Langmuir, Vol. 11, No. 1, 1995
Wave n u mbe r/ 1O2 cm-' Figure 9. IR spectra of SrFz with different amounts of physisorbed water. The B values are 0 (a), 0.2 (b), 0.5 (c), 0.8 (d), 0.9 ( e ) , 1.0 (0, 1.2 (g), and 1.6 (h).
gives almost constant value until the coverage becomes about 0.8. After the completion of the monolayer of adsorbed water, the G value increases again, even for the low frequency region, and approaches a constant value asymptotically. This tendency can be explained by the adsorption model for water on SrF2. An IR spectroscopic study helps to account for these results. Figure 9 displays the IR spectra obtained a t various stages of physisorption ofwater. The IR spectrum for the coverage zero gives the bands a t 3683,2586,1948, 1656, and 986 cm-l and in the range 3400-3200 cm-'. The bands except for the broad band in the range 34003200 cm-l are found to be due to strongly adsorbed water in fxed state on the SrFz surface.2 For the lower coverages the IR spectra are little affected by the adsorption ofwater. An interesting feature appears when the coverage of water increases; the intensities ofthe bands at 3683,2586,1948, and 986 cm-' decrease with increasing coverage. Especially, the former three bands entirely vanish when the coverage exceeds unity, and instead of them a new band comes out a t 2927 cm-l. Furthermore, the intensity of the band at 986 cm-l becomes weak, accompanied by a shift to wavenumber 926 cm-'; on further increase in the coverage it shifts to 879 cm-'. The commencement of the second-layer adsorption gives a new shoulder a t 680 cm-', accompanying a significant increase in the intensities of the bands at 3406 and 1645 cm-l. These bands become progressively greater as the adsorption proceeds, and they can be assigned respectively to the librational, OH stretching, and bending vibrations of water molecules adsorbed on more than the second layer. Although a number of water molecules strongly adsorbed is present on the SrFz surface, 15 HzO nm-2,5these water molecules seem to be not responsible for the electrical conductivity. Accordingto the adsorption model proposed on the basis of the IR data,2 a water molecule is adsorbed to attach one of the lone pairs in its 0 atom to the surface Sr2+ion and a t the same time to unite one of the two hydrogens in water with the neighboring F- ion through hydrogen bonding, resulting in strong adsorption of water molecules. Although another hydrogen exists in
Kuroda et al. a free state, its bond is directed at right angles to the surface. Hence, these free hydrogens of adsorbed waters do not interact with each other. When physisorbed water molecules are absent, only free protons formed in the strongly adsorbed layer can migrate by hopping from site to site across the surface, and therefore the value of ,up, is expected to be small. A steep increase in G in the low coverage region (9 5 0.3) is observed for higher frequencies (Figure 8), though there is no distinct change in IR spectra in these coverages. This phenomenon can be explained on the basis of the polarization of adsorbed water molecules resulting from their relatively strong interaction with the surface. Such consideration is in harmony with the high value of adsorption heat, 75 k J mol-', at these coverage^.^ These water molecules may contribute to the conductivity. However, since there are few water molecules and nprhas a small value in eq 6, G might have a small value according to eq 6. Under these conditions, f m appears a t a lower frequency as expected from eq 4. G gives a constant value in the coverage range, 0.3 5 9 5 0.8. This range corresponds to one where a steep increase in the adsorbed amount gives rise to a step in the adsorption isotherm. In the same region, the intensities of IR bands a t 3683,2586,1948, and 986 cm-l decrease, accompanying by new bands at 2927 and 926 or 879 cm-l, which are assigned to the strongly adsorbed water molecules interacting with physisorbed water. It was found that the SrFz surface has a homogeneous nature with a n adsorption energy of about 58 k J mol-' for water, being large compared with the heat of liquefaction of water vapor.5 This implies that the water molecules physisorbed on the strongly adsorbed water are localized. Furthermore, the hydrogen-bonding energy between two-dimensionally condensed water molecules was estimated to be 7.3 k J mol-', which is smaller compared with that in the bulk water, about 12 k J mol-'. These data indicate that the adsorbed water in the first layer interacts strongly with water molecules underlying it, but the mutual interaction between adsorbed molecules is weaker compared with that for the bulk water. The state of water molecules adsorbed on the SrFz surface is constrained and hence the hydrogen bonding formed between them is distorted. The adsorbed water in the first layer tends to pack so densely, as expected from the V, value (Figure 11, that the formation ofhydrogen bondings between water molecules may be subjected to steric hindrance. Therefore, the proton hopping from one water molecule to the next may be depressed by constrained hydrogen-bonding interactions, which results in a small contribution to the conduction. I t is clear that the G value begins to increase again on further adsorption of water. When the adsorbed amount exceeds the monolayer capacity ( 6 2 11,the intensities of the IR bands at 3406 and 1645 cm-' increase drastically, accompanied by a new band a t 680 cm-l. These frequencies are intermediate between those of liquid and solid water. This indicates that the adsorbed water molecules in a higher layer than the second are held less firmly compared with those in the first layer. The former water molecules can form a hydrogen-bonded network. The adsorption onto the first water layer (i.e., the formation of the second layer) probably creates channels of protonic conduction. In this case, nprand ,up,are different from those for the first layer. When water molecules are adsorbed, they are hydrogen-bonded to the next water molecules through the proton of water and this proton is transferred to the next site, which contributes to the electrical conduction. LA940548H
