Hydrophobicity effects in the condensation of water films on quartz

Hydrophobicity Effects in the Condensation of Water Films on Quartz M I C H E L L E L. GEE, 1 T H O M A S W. H E A L Y , AND LEE R. W H I T E 2 Department of Physical Chemistry and Department of Mathematics, University of Melbourne, Parkville, 3052, Victoria, Australia Received December 13, 1989; accepted March 28, 1990 The surface forces of thin water films condensed onto crystalline quartz plates have been investigated by ellipsometric measurements of film thickness as a function of disjoining pressure. Quartz substrates ranging from fully hydroxylated (contact angle = 0 ° ) to completely dehydroxylated(contact angle = 45 o) were used and the results obtained related to the theoretically predicted van der Waals and electrostatic forces present in the system. Water films on fully hydroxylated quartz are much thicker than expected, whereas films on fully dehydroxylated quartz are close to the Lifschitz prediction of dispersion forces. As the extent of debydroxylation decreases, the adsorption isotherm approaches that obtained on fully hydroxylated quartz. INTRODUCTION II A thin film f o r m e d by condensation o f a liquid from undersaturated vapor onto a flat solid, is, at equilibrium, subject to a force which acts perpendicular to the plane of the film. This force is t e r m e d the "disjoining pressure," H ( d ) , and is the change in free-energy o f the system with fihn thickness ( 1 ). M e a s u r e m e n t o f the disjoining pressure in thin film systems as a function of film thickness allows a means o f investigation o f the forces in these thin film systems. T h e study of these forces, expecially in thin liquid films o f water, is o f f u n d a m e n t a l and practical importance to surface science. A t h o r o u g h understanding o f the surface forces which govern the properties o f water in thin films will lead to a better understanding o f m a n y industrially pertinent problems such as colloid stability, adhesion, wetting, lubrication, and floatation. The disjoining pressure is c o m m o n l y defined in terms o f the properties o f the chemical potential o f the molecules which form the thin film and the free-energy o f the film (2), viz., 1Present address: Department of Chemical and Nuclear Engineering, University of California, Santa Barbara, CA 93106. 2 To whom all correspondence should be addressed.

-

In

Vm

=

-

[1]

~

T~

where P is the vapor pressure in equilibrium with the thin film, P0 is the saturated vapor pressure o f the liquid at temperature T, k is Boltzmann's constant, and Vm is the molecular volume o f the liquid. The specific excess freeenergy o f the film, E, is due to the action o f surface forces. The interactions between the three phases in the s u b s t r a t e / f i l m / v a p o r system, which are usually van der Waals forces and electrostatic forces, are the governing factors in the determination o f film thickness. The contributions to the total disjoining pressure o f the various surface forces present in the film are generally considered additive (3, 4), i.e., I I ( d ) = HvDw(d) q- HEL(d),

[2]

where I I ( d ) is the total disjoining pressure and consists o f a c o m p o n e n t IIvDw(d), due to van der Waals interactions, and a c o m p o n e n t IIEc(d), which arises from electrostatic interactions. Investigation o f the properties o f water in thin layers has yielded, at times, controversial results (5, 6). Belouschek et al. (7) have m o n -

450 0021-9797/90 $3.00 Copyright © 1990 by Academic Press, Inc. All rights of reproduction in any form reserved.

Journal of Colloid and lnlerface Science, Vol. 140, No. 2, December 1990

WATER FILMS ON QUARTZ itored a weak but long-range decrease in the thermal diffusivity of water films between two plates as the plate separation is decreased. This effect has been ascribed to an increased hydrogen-bond strength in the film. This hypothesis is supported by the N M R relaxation studies performed on thin water layers on silica (8) which indicate reduced rotation of the water molecules in these layers as compared to bulk water. The slightly higher viscosities of water films on solid substrates over bulk water also point to an enhancement of the structuring of the water in these thin layers (9). However, there is also evidence to the contrary (10-12) which has made this topic a contentious issue. Thermodynamic properties of thin water films have also displayed certain peculiarities. Water films adjacent to solid surfaces ranging from zeolites, silica gel, activated carbon, and porous glass to protein lysozyme ( 13 ) have all exhibited heat capacities which, when measured at room temperature, are close to the value for ice. For each system the heat capacity was observed to increase with temperature, finally reaching the value for free water at temperatures between 100 and 179°C. Water in fine pores possesses a thermal expansion which varies significantly from that of bulk water when measured at ambient temperatures ( 14, 15 ) but, as the temperature of the thin film system is raised to 70°C, its thermal expansion approaches that of bulk water. It is on the basis of reports such as those mentioned above, that many researchers concluded that water in thin layers is somehow structured differently than bulk water. Such water has often been referred to as structured or "vicinal" water ( 16, 17). Nonetheless, many dismissed the findings as a result of the peculiarities of silica. It was not until the pioneering work of Israelachvili, Pashley, and co-workers ( 18, 19) that it became truly apparent that water in thin films does indeed possess characteristics different to those of bulk water. The experiments performed by Israelachvili et al. involve direct measurement of the forces between two

451

molecularly smooth mica plates immersed in an aqueous solution as they are brought closer together. It was concluded from these measurements that there exists a short-range repulsive force between the mica plates at separations less that 30 A, in addition to the van der Waals and the electrostatic interactions. This force decays exponentially with distance and has a decay length of 5-10 A. Such behavior has been ascribed (20) to the hydration of ions at the mica/water interface by the water molecules. Hence, this extra force has been termed the "hydration" force and is simply another manifestation of the enhanced structure of water in thin films. Prior to the work of Israelachvili el al., the majority of experiments dealing with the properties of thin water films were performed on quartz or silica surfaces, and so the anomalous results obtained from these investigations were often atributed to the presence of a gel-layer on the solid surface formed by dissolution of the silica, and also to the inherent rugosity of the surface. However, the experiments on mica negate this notion since such a layer does not exist on the surface of mica in aqueous solution. Hydration forces of the type described above for the interaction of two mica plates have also been observed in similar studies where the forces were between fused silica discs (21 ). The disjoining pressure measured as a function of film thickness of water films adsorbed from the vapor phase onto quartz and silica (22, 23) and onto mica (24) is not free of anomalies. The total disjoining pressure for these systems cannot be accounted for on the basis of van der Waals interactions and electrostatic interactions alone. Therefore, in these cases, it has been proposed that the disjoining pressure be expressed as the sum of the van der Waals and the elctrostatic components as in Eq. [2], plus an extra structural term (22) IIs(d), so that

n ( d ) = nvDw(d) + nEL(d) + ns(d).

[31

The decay lengths of the structural force in these systems lie in the range 30-140 A. The Journal of Colloid and Interface Science, Vol. 140, No. 2, December 1990

452

GEE, HEALY, AND WHITE

large variation of the decay length from one system to another implies an inconsistency in the surface forces in these thin films of water. This incongruity is very clearly illustrated when comparing the results for the adsorption of water onto hydrophilic silica obtained by Derjaguin et al. (22) to the data of Pashley (23) for water adsorption on hydrophilic crystalline quartz. The inexplicable discordancy in the results obtained by these independent workers for systems of the type substrate/water/vapor, which normally would be expected to possess similar surface interactions, necessitates further investigations into this area. It was for the reason of, hopefully, elucidating the action of the surface forces inherent in condensed water films on quartz that the present study was begun. Here, the equilibrium film thickness of water adsorbed onto quartz has been measured ellipsometrically as a function of disjoining pressure and the results related to the theoretically predicted van der Waals forces and electrostatic forces. Experiments were performed on fully hydroxylated quartz and also on quartz samples which were thermally treated to yield surfaces of varying degrees of hydrophobicity. Thereby the electrostatic contribution to the disjoining pressure was modulated and the effects of this on the equilibrium film thickness observed. EXPERIMENTAL SECTION Materials Water. Water was fed from a Milli-Q system (i.e., Millipore Continental Water System) into the first stage of an all-pyrex still, as recommended (25). It was digested with basic permanganate for several hours in order to oxidize organic impurities and distilled directly into the second stage of the still, where it underwent a further distillation ready for immediate use. The whole system was continually purged with purified nitrogen for the entire process. See Ref. (26) for more details. Water thus prepared had a conductivity of Journal of Colloid and Interface Science, Vol. 140, No. 2, December 1990

7.2 × 10 6 ~ - 1 m - l , a p H of 5.4 _+ 0.1 when under N2, and a surface tension of 72.6 _+ 2 m N m -1 at 20°C (as measured by capillary rise). A final test of water purity was its effect on the wetting properties on clean, fully hydroxylated quartz after prolonged contact (27). A quartz plate was stored in a Teflon-sealed vial and the spreading of water on its surface was monitored for 3 days. The water was observed to completely wet the quartz after this time. Therefore, it was concluded that the amount of surfactant material still possibly remaining in the water after purification was not sufficient to affect the wetting properties of quartz, and so the water was suitable for use in the present set of experiments. Quartz. The natural crystalline quartz used in the present study was supplied by H. A. Groiss Ltd. and was cut into flat plates from the same crystal so as to ensure uniformity of the surface from one experiment to another. The plates were z-cut, i.e., cut with the optic axis perpendicular to the reflecting surface. This was necessary since the ultra-violet relaxation frequencies used in the Lifshitz calculations of van der Waals dispersion forces are for z-cut quartz. All quartz plates were polished to an optical smoothness by H. A. Groiss Ltd. who used a series of Carborundum powders for the rough grinding. This was followed by polishing with finer and finer cerium oxide based powders. Generally, after polishing and prior to cleaning, the quartz plates were mildly etched in a 1.5% w / v NH4HF2 solution for 2 h at ambient temperature. Mild etching is required to remove any amorphous material produced by polishing (29), yet the process in itself does not create any surface roughness (27). Treatment of the plates with the mixutre ammonical hydrogen peroxide was used in this work for the preparation of clean quartz surfaces, as recommended (27). Scanning electron microscopy (SEM) gave an RMS surface roughness of the quartz plates thus treated of 10 A. This is at the limits of resolution for SEM studies. Nonetheless, the refractive index

WATER

453

FILMS ON QUARTZ

of the quartz determined ellipsometrically was well within + 1% of the literature value and, furthermore, the complex component was negligible (<.001 ). Based on this and the SEM studies, surface roughness is not a crucial factor for the accurate ellipsometric measurements of film thickness conducted in the present study (26, 27). For more details of the quartz preparation procedure see Ref. (26). Dehydration o f quartz. Clean quartz plates were dehydroxylated by placing them in a quartz tube and slowly heating (i.e., ~ 0 . 5 ° C per minute) to approximately 1050°C in an electric furnace in air. The samples were held at this temperature for 2 days before gradual cooling to room temperature, thereby ensuring maximum reduction of surface hydroxyl groups and thus minimumization of surface ionization. Quartz plates thus treated have an estimated 0.4 O H groups per 100 A (2), so minimizing surface ionization, as compared to 4.6 OH groups per 100 A for fully hydroxylated quartz (28). Such dehydroxylated plates were found to have an average contact-angle (i.e., the average of the advancing and receding contact-angles) of 43 o with only 2 o hysteresis, as measured by the sessile-drop technique, and are in excellent agreement with previous measurements of this type (30). This contact-angle remained unchanged over a period of 5 days exposure to water vapor. Ellipsornetry. The adsorption isotherms were determined by the ellipsometric measurement of the equilibrium film thickness of the liquid on the quartz as a function of relative vapor pressure and all experiments were performed at 21 °. The ellipsometer used for these measurements is a standard PCSA null ellipsometer (31 ) and was constructed in the Department of Physical Chemistry, University of Melbourne. The light source was a 20 m W H e / N e laser (Spectra Physics model 120) and was set for reflection offthe substrate to a 60 ° angle of incidence. The polarizer and analyzer were identical Glan Thompson calcite prisms mounted in rotatable polarimeter heads (Bellingham and Stanley, Ltd.). The azimuths of the polarizer heads could be read to 0.005 ° .

The mica quarter wave plate was similarly mounted and set at 45 o to the plane of incidence. In ellipsometry, one measures two angles, A and ~, which express the change in polarization of a m o n o c h r o m a t i c light beam upon reflection from a planar surface. The ellipsometric angles A and • are related to the complex amplitude reflection coefficients rp and rs for p and s polarized light, respectively, via the equation (30) tan ~ e i~ = rp rs

[4]

For a clean, bare substrate, A and q are functions of the refractive index of the reflecting material, the angle of incidence, and the wavelength of the impingent light. When a thin, transparent film coats the substrate, either the refractive index or the film thickness may be calculated. Generally, the refractive index of the bulk liquid is taken to represent that of the film and so the film thickness is obtained. The computational method used in the present work to find the film thickness from the measured ellipsometric parameters dx and • is as described by McCrackin et al. (32). Vapor pressure control. Before each experiment, the sample chamber was outgassed down to approximately 10 -3 N m -z (i.e., 10 -5 m m Hg). A small amount of the water vapor was then admitted to the chamber via a tap which connected the chamber to the liquid reservoir. The vapor pressure inside the chamber was monitored by means of a pressure transducer. At equilibrium, the film thickness was measured. The process (26) of vapor admission and film thickness determination was repeated until saturation was aprroaehed. RESULTS

The adsorption isotherm of film thickness versus relative vapor pressure for water on fully hydroxylated quartz is shown in Fig. 1. Clearly, Journal of Colloid and Interface Science, Vol. 140, No. 2, December 1990

454

GEE, HEALY, AND WHITE I

I

I

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I

m

i

120

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z

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a O 0 0 ~ m .$

| .6

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m .7

|

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RELATIVE VAPOUR PRESSURE

FIG. 1. Adsorption isotherm of water on fully hydroxylated quartz.

the form of the adsorption curve is characteristic of a wetting film. The level of adsorption shows only a very gradual build-up with vapor pressure in the low vapor pressure regime. It is not until the system nears saturation that the equilibrium film thickness undergoes a sharp increase which is indicative of the formation of multilayers of water on the quartz surface. Indeed, the adsorption isotherm never intersects the ordinate axis and so it can be stated confidently that a completely wetting film is formed by the adsorption of water onto fully hydroxylated quartz. Further confirmation of this was the inability to measure a contact-angle of water on quartz due to the immediate spreading of the water over the surface. This signifies a zero contact-angle for the water/quartz system; a point which is further illustrated by the observation of uniform, colored fringes during the steam test (26). As already stated, quartz heated to temperatures above 1000 ° result in a m i n i m u m number of surface hydroxyl groups. Knrzinger has summarized data from more than 20 independent publications which deal with heattreated silicas. It can be estimated from this data that condensation of silanol groups begins at about 170°C. Approximately half the silanol groups are removed at 500°C, but, in this case, Journal of Colloid and Interface Science, Vol. 140, No. 2, December 1990

most of the remaining hydroxyls are still in the neighborhood of another hydroxyl group, i.e., they are not isolated. Therefore, hydrogenbonding of a water molecule to the surface is still a possibility. Beyond 750°C, only isolated silanol groups remain (34), the n u m b e r of which continues to diminish as the temperature increases, until, at 1000°C, only an estimated 0.4 O H groups/100 A2 remain on the quartz surface. The adsorption isotherm of water on a heattreated quartz plate with an average contactangle of 43 ° was measured and is shown in Fig. 2. The most obvious differences between this isotherm and that of water on fully hydroxylated quartz (on Fig. 1 ) is that the magnitude of the equilibrium film thickness is m u c h lower for the heat-treated quartz case and the appearance of some structure in the adsorption isotherm of water on dehydroxylated quartz in the form of a step in the isotherm. Secondly, although the form of the two isotherms are m u c h the same in that film thickness increases gradually with vapor pressure and then shows a marked increase at saturation, the adsorption isotherm of water on dehydroxylated quartz does not asymptotically approach the ordinate axis, indicating that the film in nonwetting. This was assumed because of the measured finite contact-angle and was corroborated by measurement of a finite equi-

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RELATIVE VAPOUR PRESSURE

FlG. 2. Adsorption isotherm of water on heat-dehydroxylated quartz. Contact angle = 43 °.

WATER FILMS ON QUARTZ librium film thickness at saturation. Clearly the ability of a surface to ionize greatly enhances the formation of thick wetting water films, and once this ability is removed such films are no longer able to condense. Another feature of the adsorption of water on dehydroxylated quartz is that the film thickness does not increase monotonically with vapor pressure (as it does on fully hydroxylated quartz) but, at low vapor pressures, seems to fluctuate randomly and displays a distinct step at a relative vapor pressure of approximately 0.8. These fluctuations could be due simply to a lack of resolution of the experiment at these low film thicknesses. However, the same behavior was not observed in similar alkane adsorption experiments (35, 26) which possess equilibrium film thicknesses of about the same magnitude as those for water on dehydroxylated quartz. Therefore, the fluctuations cannot be solely a question of accuracy. This will be addressed more fully in the Discussion section. It should be noted that, after the adsorption experiment, the contact-angle of water on the quartz substrate had decreased by only 1° with no increase in hysteresis. This indicates that only a small amount of rehydroxylation, if any at all, had occurred during the course of the experiment. The same quartz plate used in the aforementioned experiment was stored in high purity water for 10 days and then cleaned in the manner described in the Experimental section. After this time, the average contact-angle of water on quartz was found to have dropped by only 3 to 37 ° with no measurable increase in hysteresis. The quartz plate was then boiled continually in clean water for 10 h in order to catalyze rehydroxylation. The contact-angle of water on the plate after this treatment was measured to 30 ° . The adsorption isotherm of water on this piece of quartz was then determined and is shown in Fig. 3. The characteristics of the curve are m u c h the same as those of water on the almost fully dehydroxylated surface, except that here the step in the adsorption isotherm is not as sharp.

455

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s

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0 .5

f

I

.6

I

,7

I

I

.8

I

f

I

.9

RELATIVE VAPOUR PRESSURE

FIG. 3. Adsorption isotherm of water on heat-dehydroxylated quartz. Contact angle = 30°.

However, at relative vapor pressures below where the step occurs, the isotherms are very similar. The larger film thicknesses obtained in this particular experiment are not surprising because of the presence of a greater n u m b e r of surface hydroxyl groups on the quartz plate as compared to the n u m b e r available for ionization in the previous experiment where the contact-angle is larger. The same quartz plate was stored in water for a further 14 days and then boiled in water for 10 h. This treatment resulted in a contactangle of water on quartz of 22 ° . The adsorption isotherm of water on this sample is plotted in Fig. 4. Again, the isotherm is characterisitc of a nonwetting film. However, the shape of the curve is smoother and the film thicknesses greater than obtained for water on quartz in the two previous experiments. It appears that the greater number of hydroxyl groups permits formation of a thicker water layer at low vapor pressures and that this layer is thick enough for the progressive build-up of water to be virtually insensitive to the chemical inhomogeneity of the underlying surface. Nonetheless, the low relative vapor pressure end of the adsorption isotherm shows what m a y be the top of the step, implying that stable films are first formed at a vapor pressure below the minim u m pressure attained in the present work. It was attempted to further reduce the conJournal of Colloid and Interface Science, Vol. 140, No. 2, December 1990

456

GEE, HEALY, A N D W H I T E i

l

I

I .6

i

i

i

|

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I .9

terials 1, 3, and 2 of the system, i.e., in the present case, quartz/water/vapor, respectively, e(i() for quartz was constructed as described by Hough and White (38), whereas the construction of e(i() for water was based on the method of Parsegian (37) employing the same spectroscopic data. The disjoining pressure II132(d) of the thin film system is easily obtained from the interaction energy since (39)

' i

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0 .5

l

I .7

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I,

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I

IIl32(d) =

-(OE~d(d))r.

[6]

PRESURE

FIG. 4. Adsorption isotherTn of water on heat-dehydroxylated quartz. Contact angle = 22 °.

This is directly related to the relative vapor pressure of the system via Eq. [ 1]. W A T E R ON D E H Y D R O X Y L A T E D Q U A R T Z

tact-angle of water on quartz and measure the adsorption isotherms. Unfortunately, further treatment of the quartz plate resulted in a large contact-angle hysteresis ( .-~ 10 °). This indicates that the surface roughness has increased to such an extent that the wetting behavior is affected. Indeed, ellipsometric measurements on the base quartz plate at this stage of the series of experiments gave a refractive index with a complex component of ~0.01. This implies a degree of surface roughness which would significantly affect the formation of water fihns and also the interpretation of the ellipsometry data (27). DISCUSSION

kT ~,

87vd2 n=0

.

xdxln(D(x)),

D(x)

V o l . 1 4 0 , N o . 2, D e c e m b e r

~8 "-I--,

/i':.2

[5]

where k is Boltzmann's constant, and Tis the absolute temperature. The prime on the summation indicates that the n = 0 term should be divided by 2. The limit of integration rn accounts for retardation effects (37). The function is related to the dielectric response functions q(i~) of each of the maJournal of Colloid and Interface Science,

12

z

The van der Waals interaction energy per unit area E132(d) between half-spaces 1 and 2 separated by distance d is, from Lifshitz theory (36), given by (37) El32(d)-

The Lifshitz prediction of the disjoining pressure as a function of film thickness is compared to the experimental data for water adsorbed onto heat dehydroxylated quartz in Fig. 5. The Lifshitz theory adequately accounts for the overall form of the adsorption isotherm for water on quartz with a contact angle of 43 ° , but does not predict the fine structure of the isotherm. This is not surprising when one

1990

• I

,,

4 FILM

• "

8 THICKNESS

"

Q z

I

12 (ANGSTROMS)

FIG. 5. Comparison between theory and experiment for the adsorption of water on heat-treated quartz. Circles, contact-angle = 43°; squares, contact-angle = 30°; triangles, contact-angle ~ 22 °; solid line, Lifshitz prediction.

WATER

FILMS ON QUARTZ

considers that the Lifshitz theory is a continu u m model and does not take into account the molecularity of the system. It is, however, judicious to assert from the reasonable fit of the data to theory on removal of hydroxyl groups from the surface of quartz by heating to ~ 1 0 0 0 ° C that ionization and hydrogen bonding are both precluded and only van der Waals forces are operant. Once the degree of hydroxylation is increased, van der Waals forces are no longer the sole interaction. Ionization is again possible and electrostatic forces come into play. This is shown by the shift to thicker films as the extent of hydroxylation is increased, i.e., as the contact-angle is decreased. Another feature of the isotherms on heattreated quartz is, as stated above, the fluctuation in the film thicknesses (as a function of vapor pressure) at low relative vapor pressures which is not entirely due to experimental error. A possible physical reason for the fluctuating film thicknesses is the sparseness of hydroxyl groups on the quartz surface after heattreatment. It has been mentioned previously that there exists only 0.4 O H groups/100 ~2 on the surface of quartz heated to 1000°C. Consequently, water is most likely to prefer these isolated OH groups as adsorption sites (40, 41 ). An increase in vapor pressure results in the adsorption of water to the preadsorbed water molecules which, in turn, leads to the formation of water clusters. The existence of these clusters has been observed previously (42) by neutron-scattering studies. As the vapor pressure is increased, the water clusters grow. The presence of the water on dehydroxylated quartz results in the breakage of some siloxane bonds to form silanol groups, thus extending the hydrophilic regions on the surface. Consequently, the water in the clusters is now able to spread over these newly created hydrophilic areas and so the effective film thickness is less than that measured at the lower vapor pressure. The whole process is repeated until the clusters are close enough together for the water molecules to associate. The film thickness increases smoothly from this

457

point onward. An argument for the formation of water clusters has been invoked by Hertl and Hair (40) in explanation of the stepped adsorption isotherm which they obtained for water on chemically treated silica powder. An alternative yet completely analogous description of water adsorption on dehydroxylated quartz systems is to consider the films as unstable at small film thicknesses; that is, the films are metastable. This rationale was adopted by Blake and Kitchener (43) in order to interpret their results for water on methylated quartz surfaces. Films are metastable below some critical film thickness where a film coexists with bulk liquid (i.e., microdroplets) on the quartz surface. At higher vapor pressures, that is to say at lower disjoining pressures, and beyond, stable films are formed. Indeed, the fluctuations in film thickness at low relative vapor pressures can be considered the metastable regions. Above a certain critical vapor pressure there is a sudden j u m p in film thickness and stable films are formed from that point onward. It should be noted that, in the metastable region of each isotherm of water on heat-dehydroxylated quartz, the fluctuations diminish as the contact-angle decreases since the underlying surface becomes more homogeneous. Probably the most interesting aspect of water adsorption on heat-dehydroxylated quartz is the apparent step in each isotherm. In fact, the relative vapor pressure at which the step occurs appears to be dependent upon the contact-angle of water on the quartz surface. This trend is shown more clearly in Table I: the greater the hydrophobicity of the surface, the TABLEI R e l a t i o n s h i p between the C o n t a c t Angle o f W a t e r on H e a t - T r e a t e d Q u a r t z a n d the Step in the A d s o r p t i o n Isotherm

Contact angle

Onset of step (relativevapor pressure)

21 ° 30 ° 43 °

0.62 0.75 0.80

Journal of Colloid and Interface Science, Vol. 140, No. 2, December 1990

458

GEE, HEALY, AND WHITE

greater the potential barrier to stable film formation and the higher the relative vapor pressure required to overcome this barrier. If one now ignores the fluctuations in film thickness at low relative vapor pressures and draws a smoothed curve for each isotherm (Fig. 6), there exists a plateau in this region. Furthermore, the height of this plateau (i.e., the film thickness) for all three isotherms is very close to that of the diameter of a water molecule, i.e., 2.85 A (44). Additionally, the thickness by which the film increases after the step in the isotherm is again approximately equal to the dimensions of a water molecule. Clearly here, water adsorption onto hydrophobic quartz does indeed occur in a stepwise fashion. Initially, one monolayer of water is adsorbed, but an energy barrier, which is contact-angle dependent, must be overcome before adsorption of another monolayer. The thickness of the plateau and the heights of the steps are listed in Table II for all three isotherms of water on heat-treated quartz. It is interesting to note that the plateau height increases with a decrease in contactangle. This is consistent with the notion of initial monolayer adsorption as stated above. The

stepheight 4~

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RELATIVEVAPOURPRESSURE FIG. 6. Comparison of the adsorption isotherms for water on heat-treated quartz showing the relative plateau heights and step heights. (A) contact-angle = 22 °, (B) contact-angle = 30 °, (C) contact-angle = 43 °. Journal of Colloid and Interface Science,

Vol. 140,No. 2, December1990

TABLE II Comparison between the Plateau Heights and the Step Heights in the Adsorption Isotherms of Water on HeatTreated Quartz of Different Degrees of Hydrophobicity Contact-angle

Plateau height(~)

Step height(A)

22 ° 30 ° 43 °

3.20 2.89 2.30

2.95 2.89 2.89

fact that the plateau height at a contact-angle of 43 ° is slightly less than the diameter of a water molecule suggests that the water molecules are sitting flatter on the quartz surface than when the contact-angle is smaller. Since at a contact-angle of 43 ° there exists only a sparse n u m b e r of surface hydroxyl groups, the interaction is almost completely dominated by van der Waals forces and so hydrogen bonding is very restricted. As the contact-angle decreases, i.e., the surface becomes more hydrophilic, the water molecules tend to sit up on the surface in a more oriented manner due to the increased hydrogen-bonding capacity of' the quartz. This tendency increases with decreasing contact-angle, as observed from the results shown in Table II. However, it is dearly displayed that the second and subsequent layers of water molecules are not influenced in this way by the underlying surface since, in all three cases, the step heights are within error of each other and the water molecule diameter. After one monolayer is formed, the quartz surface no longer exerts the same influence it had on the adsorption behavior of water. Nonetheless, the state of the bare quartz surface is what governs the characteristics of water adsorption, as evidenced by the fact that the isotherms of water on hydrophobic quartz do not at all approach the isotherm of water on fully hydroxylated quartz even after a monolayer of water has adsorbed. WATER ON FULLY HYDROXYLATED QUARTZ

It was stated above that the total disjoining pressure in the water/fully hydroxylated

WATER FILMS ON QUARTZ

459

quartz system can be considered as the sum of two contributions: the van der Waals dispersion forces, IIvDw(d), and the electrostatic forces arising from dissociation of the surface hydroxyl groups of quartz, IIzL(d). In classical DLVO theory (45), the 17EL(d) is obtained from the equation

measured (27) value o f ~ s o f - 1 5 0 mV at pH 7 for values of no which correspond to electrolyte concentrations of 10 -3 to 10-6M. The IIEL(d) thus obtained was added to the van der Waals component of the disjoining pressure IIvDw ( d ) to give the total predicted disjoining pressure II(d). Figure 7 gives a comparison between the H E y = 2 k T n o cosh ~ - 1 , [7] predicted II(d) and that obtained experimentally for water on fully hydroxylated quartz. where k is Boltzmann's constant, T is the ab- It should be noted that the theoretical curves solute temperature, e is the electronic charge, are indistinguishable on this scale. Clearly, no is the bulk electrolyte number density, and there is a marked difference between experi~d is the potential at the air/water interface. ment and theory. The theoretical II(d) is sigThe surface potential of the substrate, ~I,~, nificantly less than the experimental 17(d) for is usually assumed to be the measured ~'-po- all values o f d and does not possess the plateau tential, in calculation of ~I'd by means of the region so prominent in the experimental resuits. Poisson-Boltzmann equation (46) It is unlikely that any possible misconcepd2y tions in the Lifshitz calculations of the van der d X 2 - sinh(y), [8] Waals forces are the reason behind the difference between experiment and theory since this where has been shown quite clearly above to reasonably account for the adsorption of water on X --~ KX 1 [91 heat dehydroxylated quartz. However, the ef y = --£--~ DLVO theory does possess two fundamental shortcomings in its physical assumptions when applied to thin films on a solid substrate from are the scaled distance and potential respectively, and K is given by 4 i..... = [ 87re2n0 ]1/2 [ ,kT J '

[10]

where ~ is the dielectric constant of the liquid film. To solve Eq. [ 8 ] a constant surface potential ~s at the quartz/water interface is usually assumed. The differential equation is then solved from X = Kd, where d is the film thickness, y = Ya, and d y / d x = 0, to X = 0 at the quartz/ water interface. The boundary conditions that Y = Ys (i.e., • = ~s) at this interface must be satisfied. Once the chosen parameters satisfy the above boundary conditions, the solution, i.e., qa, is used in Eq. [7] to give IIEL for a particular d. The above calculations were performed for the q u a r t z / w a t e r / v a p o r system using the

%

z

0

'" 0

10

20

30

FILM T H I C K N E S S

40

50

60

(ANGSTROMS)

FIG. 7. Comparison between theory and experiment for the adsorption of water on fully hydroxylated quartz. The theoretical curve is the total disjoining pressure, i.e., IIvow(d) + IIEL(d), as calculated from the DLVO theory.

JournalofColloidandInterfaceScience,Vol.

140, N o . 2, D e c e m b e r 1990

460

GEE, HEALY, A N D W H I T E

the vapor phase. First, it is assumed that the potential at the quartz/water interface is fixed and is not affected by variation of film thickness. A second and more serious inadequacy is the use of the no parameter. The quartz/ water/vapor system is not in equilibrium with any bulk electrolyte of number density no. Rather, equilibrium is achieved through the vapor phase. There should be no univalent electrolyte anywhere in the system. Consequently, a more appropriate expression for IIEL(d) was derived (26) in order to make the comparison between theory and experiment physically meaningful. This theory accounts for the absence of an infinite reservoir of bulk electrolyte and also allows for mass action in the system with particular attention to the amphoteric nature of the quartz surface (46). The statistical mechanical derivation of mass action in thin films (26) is similar to that derived for dissociation of a surface in equilibrium with bulk H + ions (47). Unfortunately, the results of this analysis are not significantly different from the classical DLVO predictions. Hence, the discrepancy between theory and experiment of the disjoining pressure as a function of film thickness for the q u a r t z / w a t e r / v a p o r system is not explained by the incorrect assumptions made in the DLVO theory. The above mentioned analysis of electrostatics in thin film systems was further elaborated (26) to allow for a layer of oriented water molecules at the quartz/water interface and also at the air-water interface. The air/ water interface has a measured (48) surface potential, X0 o f - 2 5 _+ 10 mV relative to bulk water, so such an idea is completely plausible. It is important here to distinguish between the electrostatic and entropic contributions to the disjoining pressure of these oriented water molecules. Given a dipole distribution, assumed constant as the film thickness changes, the electrostatic effect can be computed as detailed in Ref. (26). Calculation of the entropic structural effect is a difficult problem in statistical mechanics and was not attempted in the present work. Journal of Colloid and Interface Science, Vol. 140, No. 2, December 1990

Although the inclusion of interfacial dipole layers did result in the prediction of larger film thicknesses than expected from DLVO theory (26), it still does not reconcile experiment and theory. It appears that some other force or some peculiarity of the experimental system is responsible for the thick water films obtained on fully hydroxylated quartz. The film thickness of water on fully hydroxylated quartz as a function of disjoining pressure is again shown in Fig. 8 together with the data of previous workers, (i.e., the results of Pashley (23) on crystalline quartz, the data of Hall (49) on vitreous silica, and the data of Busscher et al. (50) on glass). No two sets of data are the same, which is surprising since quartz, silica, and glass possess similar surface properties and so would be expected to display c o m m o n wetting characteristics. It should be noted that the form of the adsorption isotherms of Hall and of Busscher are similar to that obtained for water on hydrophobic glass since the curves tend toward a finite thickness at saturation. It is possible that insufficient care was taken in the cleaning of the silica and the glass surfaces in these two studies, resulting in

i

J

u

i

i

s

200

i

160

~120

~.

80

,o

- ,

0 .5

.6

.7

.8

.9

1

R~LATIVE VAPOURPRESSURE FIG. 8. A comparison of data obtained from various workers for the adsorption of water on different types of silica surfaces. Solid circles, water on quartz (this work); open squares, water on quartz Ref. (23); open circles, water on glass Ref. (50); open triangles, water on amorphous silica Ref. (49).

461

WATER FILMS ON QUARTZ

wetting behavior which resembles that expected for surfaces with a small contact-angle. It was, in fact, found in the present work that the equilibrium film thicknesses were dependent upon the preparation of the quartz. Thick wetting films on quartz were obtained if, immediately after cleaning, the wetted quartz plate was placed in the sample chamber and the excess water desorbed under vacuum, hence preventing adsorption of atmospheric surface contaminants. If, instead, the quartz plate was blown dry with clean nitrogen and then mounted in place, decidedly thinner films were observed. Indeed, such treatment of the quartz resulted in comparable film thicknesses to those obtained by Hall and by Busscher et al. Additionally, all of the above three sets of data tend toward a similar point of intersection with the ordinate axis. The discrepancy between the present data and the work of Pashley cannot be explained in terms of nonwetting behavior. Pashley was able to achieve much thicker wetting films than predicted by the sum of the electrostatic and the van der Waals disjoining pressures, as is the situation for this work; yet the films obtained here are markedly thinner than those measured by Pashley. Guidelines set down by Pashley (27) for the preparation and handling of quartz samples were followed in this work. Therefore, it is unlikely that the disagreement is due to differing levels of surface contamination. One major difference does, however, remain between the two studies. Here, the vapor pressure was controlled by variation of the amount of vapor admitted to the cell from a reservoir of pure water, while Pashley adjusted the vapor pressure by doping the water with known molarities of salt. The merits of these two methods are discussed fully in Ref. (26). Let it be stressed here that both techniques are valid. Nonetheless, perhaps it is this difference in experimental procedure which has led to the disagreement in the data. Therefore, it was deemed necessary to repeat the water adsorption experiment but, this time to adjust the vapor pressure by doping the water.

Lithium chloride (LiC1) was used here as the dopant because of its ability to suppress the vapor pressure of water to very low values (51) (i.e., P/Po ~ 0.12 at saturation of LiC1 at 25°). The lithium chloride was purified by repeated recrystallization from pure water. The results obtained are plotted in Fig. 9 and compared with the previously determined adsorption isotherm. Clearly, the two sets of results are in complete accordance with each other. This validates the vapor pressure control method adopted in this work and ascertains that this method is not the cause behind the discrepancy between these results and those of Pashley. It also emphasizes the reliability and accuracy of the present data for the adsorption of water on hydrophilic quartz. It has been stated by Pashley (52), that a simple BET model of multilayer adsorption applies near saturation and for thick adsorption layers. The BET equation is (53) V

V~n

cx

(1 - x ) [ 1 + ( c -

[11]

1)x]'

where V/Vm equals the number of adsorbed monolayers, x = P/Po, Vm is the molar volume of water, and

120

~

lO0

e~

~

so

~ z

6O

~"

40

2o

I

•3

I

I

.5

I

I

,

.7

,

I

.9

RELATIVE VAPOUR PRESSURE

FIG. 9. Adsorption isotherm of water on quartz obtained from two separate experiments using different methods of controlling the vapor pressure. Circles, controlled admission of vapor (see text); crossed circles, doping of bulk liquid (see text). Journal of Colloid and Interface Science, Vol. i40, No. 2, December 1990

462

GEE, HEALY, AND WHITE

where Q~ and QL are the heats of adsorption in the first and subsequent layers respectively and R is the gas constant. For c >> 1, as is the case for water on quartz (5 3 ), Eq. [ 11 ] approximates to Vm 3 V d

~

P P0'

1---

[13]

since the molecular diameter of water is approximately 3 A where d (the film thickness) is measured in angstroms. Now, from Eq. [ 1] it follows that

Pashley (52) found that Eq. [14] correctly predicts the adsorption isotherm of water on quartz over a wide range of vapor pressures. This prediction is plotted in Fig. 10 together with the experimental data of the present study. It is interesting to note that the experimental curve approaches the predicted isotherm at very large relative pressures. Another observation is that at relative vapor pressures below 0.8, the predicted film thicknesses are

close to the measured thicknesses. However, this area of coincidence of the two curves occurs only because the predicted isotherm crosses the experimental isotherm in this region. It cannot be concluded that behavior of water adsorption on quartz is predicted by a BET model in the present work since the actual form of the two curves are evidently different. It has been postulated (52) that another possible reason for the anomalous thick films observed in the adsorption of water on quartz is the presence of a monolayer of low molecular-weight salt. If it is assumed that the quantity of this impurity is fixed, then, as the vapor pressure is increased, the film thickness must also increase in order to dilute the impurity sufficiently to give the same vapor pressure. In this instance, P --=X-

Po

K1 d

KId+K2'

[15]

where X is the mole fraction of water in the film, K1 d is the number of water molecules in the film, and K2 is the number of solute species in the film. Equation [ 15 ] may be written as

P0 p where K =

K 1+ d

[16]

K2/K1, and so

100

I 71 8O

z < ~

60

~ 4o ,.,I 2O

I

0 .5

I

.6

I

T

.7

f

I

,8

I

I

I

,9

RELATIVE VAPOUR PRESSURE

FIG. 10. Comparison between the experimental data for water adsorption on fully-hydroxylated quartz and the predicted isotherms which assumes that adsorption follows a BET type of behavior. Journal of Colloid and Interface Science, VoI. 140, No. 2, December 1990

which is analogous to Eq. [ 14 ]. K corresponds to the thickness of one monolayer which is, in this case, the impurity layer. Obviously, K = 3 A will yield the same prediction as Eq. [14] at large d. Values of K e q u a l to 2 A, 5 A, and 7 A were taken to see whether the fit of Eq. [14] could be improved. The results are given in Fig. 11 together with the experimental data for comparison. Clearly, the analysis of Eq. [ 17 ] does not yield a better fit than that of Eq. [14], nor is it expected to since the two predicted curves are virtually the same. However, the curve for D = 2 A, i.e., the curve predicted by Eq. [ 17 ], is closest to the exper-

WATER •

•

|

|

•

•

•

i

FILMS ON QUARTZ

•

100

~o c

13

e :

20

•

•

i

|

|

l

i

i

I

.6 ,7 .8 .9 R£LATIVR VAPOUR PR£SSUI~J~

FIG. 11. Comparison between the experimental data for water adsorption on fully hydroxylated quartz and the predicted isotherms which assume the presence of a watersoluble impurity of a particular thickness K. Curve A, K = 2 ~.; curve B, K = 5 A; curve C, K = 7 ~,.

imental data. All that may be concluded is that neither the BET model nor the hypothesis of a water-soluble impurity layer adequately accounts for the behavior of water adsorption on quartz as measured in the present work. It is documented (54) that certain types of silica possess a gel layer caused by the dissolution of the silica when in contact with water (28). This was mentioned by Pashley (52) as a possible answer to the thick film anomaly but was discounted because there was no experimental evidence for the formation of this layer on the surface of crystalline quartz. Ellipsometry is a technique which has been successfully used for the characterization of vitreous silica (55) and so may also be used to monitor the crystalline quartz surface. Values of 2x and • are able to be measured for the bare quartz surface if the literature value of refractive index of the quartz substrate (i.e., 1.54) is taken to be representative of the experimental surface. A and • can then be related to the thickness of a surface layer. The possible gel layer consists of amorphous quartz with a density less than that of the hard, crystalline material and so should have a refractive index less than 1.54.

463

It is well known (31 ) that, in ellipsometry, the greater the difference between the refractive index of the film and the substrate, the larger the variation of 2x and • with film thickness. Unfortunately, the refractive index of the film cannot be determined accurately due to the very small variation of • with film thickness for film refractive indices close to that of the substrate. Unless the refractive index of the film is known, it is impossible to estimate a film thickness with any certainty. For instance, if • is 4.73, the film thickness could lie anywhere between 80 and 190 A over the range of probable refractive indices 1.521.33 for the present system. The difficulty is even more pronounced for lower film thicknesses. Additionally, these measurements do not allow for surface roughness. Surface heterogeneities manifest themselves as a small perturbation of the measured A and • values from those expected for an atomically smooth surface. Consequently, unless the exact nature of the surface roughness is known, it is virtually impossible to say whether or not the ellipsometric angles measured on the bare substrate are due to a gel layer or to surface roughness. The above argument does not negate the possible existence of a gel layer but asserts that if such a layer is present, it could not be detected with any degree of certainty by the experimental means available here. Crystalline quartz is soluble in water (28), albeit to a lesser extent than vitreous silica. Therefore, there is no reason why a gel layer could not form on the crystalline surface. A gel layer can account for the discrepancy between this work and that of Pashley simply if one assumes that the layer was thicker on the quartz surfaces used by Pashley. Indeed, after cleaning, Pashley stored the plates in distilled water until ready for use. The plates used in this work were used immediately after cleaning and did not spend any time whatsoever in storage. It is clear that there was less time available in the present work for dissolution of the quartz and so the gel layer would not be expected to be as thick. One may ask the question why, if the gel is Journal of Colloid and Interface Science, Vol. 140, No. 2, December 1990

464

GEE, HEALY, A N D W H I T E

formed by dissolution of the quartz, does its thickness cease to increase; i.e., equilibrium is reached after something approaching a monolayer is dissolved. Obviously, there is an equilibrium between the dissolution of the surface and the n u m b e r of ions released into the adsorbed film on dissolution. This would result in a reduction in the rate of dissolution and finally in complete cessation, since only a finite volume of water, i.e., the film, is available for participation in the reaction. One would, however, expect this equilibrium concentration to be fixed at the solubility of quartz and not to be a function of film thickness. CONCLUSIONS

The existence of different amounts of solute on various silica or quartz surfaces, or that certain silica samples dissolve to varying extents, appears to be the most obvious explanation for the thick wetting films of water observed on fully hydroxylated quartz. Indeed, certain workers (56, 57) have reported films even thicker than those measured here or by Pashley (21), whereas others (58, 59) have results in reasonable agreement with those of Pashley. Another possible explanation for the large n u m b e r of discordant results obtained in this field is that the adsorption of water on quartz depends critically on the arrangement of the surface hydroxyl groups which can either enhance or destroy the hydrogen-bonding network of the water (33) on the surface. The results obtained here for water adsorption on dehydr0xylated quartz certainly exemplify the importance of the quartz substrate in stable film formation. These arguments are consistent with the observation that the thicknesses of organic liquid films are in good agreement with the Lifshitz prediction (35), since the postulated involatile solute would be insoluble in an organic liquid film. Additionally, it is possible that the result of heat treatment of the quartz surface prevents dissolution of the quartz thereby obliterating the solute effect. However, it would be expected that eventually, as the Journal of Colloid and Interface Science, Vol. 140, No. 2, December 1990

quartz becomes more hydrophilic, dissolution would once again commence. This is not at all indicated by the present results. It does seem apparent that the surface structure of the substrate plays an important role in the wetting of quartz by water. Nonetheless, it should be remembered that the Lifschitz theory is, like most wave-mechanical theories, based on m a n y approximations and assumptions, both physical and mathematical. For example, indices of refraction and absorption coefficients are, in general, isotropic. Consequently, any molecular orientation should change the numbers appropriate to the Lifschitz calculations. Some molecular alignment, as dealt with from an electrostatics viewpoint (26), is undoubtedly present in thin water films on quartz and other substrates. It might be that if this was considered along with the electrostatics, the results could be explained. Perhaps one or some combination of the above possibilities is the answer to the problem of water adsorption on quartz. The only certainty is that a great deal more experimental and theoretical work is necessary before the mystery of this and similar systems is finally unravelled. REFERENCES

1. Derjaguin, B. V., and Obuchov, E., Colloid Z 1, 385 (1935). 2. Derjaguin, B. V., and Shcherbakov, Ya. I., Kolloidn. Zh. 31, 47, (1969). 3. Kitchener, J. A., "Wetting," S.C.I. Monograph No. 25. Soc. Chem. Ind., London, 1967. 4. Sheludko,A., Adv. Colloidlnterface Sci. 1, 391 ( 1967). 5. Clifford,J., in "Water--A ComprehensiveTreatise" (F. Franks Ed.), Vol. 5. Plenum, New York, 1975. 6. Derjaguin, B. V., and Churaev, N. V., Prog. Surf. Memb. Sci. 14, 69 (1981). 7. Belouschek,P., and Suppa, M., Z. Phys. Chem. 146, 77 (1985). 8. Rennie,G. K., and Clifford,J., J. Chem. Soc. Faraday" Trans. •73, 680 (1977). 9. Peschel,G., and Adlfinger, K. H., J. Colloidlnterface Sci. 34, 505 (1970). 10. Roberts,A. D., and Tabor, D., Spec. Discuss. Faraday Soc. 1,243 (1970). 11. Roberts, A. D., and Tabor, D., Proc. R. Soc. A 235, 323 ( 1971 ).

WATER FILMS ON QUARTZ 12. Israelachvili, J. N., J. Colloid Interface Sci. 110, 263 (1986). 13. Vucelic, V., and Vucelic, D., Chem. Phys. Lett. 102, 371, (1983). 14. Derjaguin, B. V., Karasev, V. V., and Khromova, E. N., J. Colloid Interface Sci. 78, 274 (1980). 15. Derjaguin, B. V., Karasev, V. V., and Khromova, E. N., J. Colloid lnterface Sci. 2, 586 (1986). 16. Drost-Hansen, W., Z Colloid Interface Sci. 58, 251 (1977). 17. Etzler, F. M., and Drost-Hansen, W., Croat. Chem. Acta. 56, 563 (1983). 18. Israelachvili, J. N., and Adams, G. E., J. Chem. Soc. Faraday Trans. •74, 975 (1978). 19. Pashley, R. M., J. Colloid Interface Sci. 83, 531 (1981). 20. Israelachvili, J. N., Faraday Discuss. 65, 20 (1978). 21. Peschel, G., Belouschek, P., Muller, M. M., Muller, M. R., and Konig, R., Colloid Polym. Sci. 260, 444 (1982). 22. Derjaguin, B. V., and Churaev, N. V., J. Colloid Interface Sci. 49, 249 (1974). 23. Pashley, R. M., and Kitchener, J. A., J. Colloid Interface Sci. 71, 491 (1979). 24. Perevertaev, V. D., Metsik, M. S., and Golub, L. M., Kolloidn. Zh. 41, 159 (1979). 25. Smith, V. C. in "Ultrapurity" (M. Ziefand R. Speights, Eds.) Dekker, New York, 1972. 26. Gee, M. L., Ph.D. thesis, Department of Physical Chemistry, University of Melbourne, 1987. 27. Pashley, R. M., Ph.D. thesis, Department of Mineral Resources Engineering, Imperial College of Science and Technology, London, 1978. 28. Iler, R. K., "The Chemsitry of Silica." Wiley-Interscience, New York, 1979. 29. Alexanian, C., Cr. Acad. Sci. 242, 2145 (1956). 30. Lamb, R. N., and Furlong, D. N., J. Chem. Soc. Faraday Trans. L 78, 61 (1982). 31. Azzam, R. M. A., and Bashara, N. M., "Ellipsometry and Polarised Light." Elsevier/North-Holland, New York, 1977. 32. McCracldn, F. L., Passaglia, E., Stromberg, R. R., and Steinberg, H. L., J. Res. Nat. Bur. Stands. 67A, 363 (1963). 33. Kn6zinger, H., in "The Hydrogen Bond" (P. Schuster, G. Zundel, and C. Sandorfv, Eds.) Vol. 3. NorthHolland, Amsterdam, 1976. 34. Levine, S. M., and Garofalini, S. H., J. Chem. Phys. 55, 9 (1976).

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35. Gee, M. L., Healy, T. W., and White, L. R., J. Colloid Interface Sci. 131, 18 (1989). 36. Lifshitz, E. M., Soy. Phys. JETP2, 73 (1956). 37. Parsegian, V. A., in "Physical Chemistry: Enriching Topics from Colloid and Surface Science" IUPAC Comm. 1.6. (H. van Olphen and K. J. Mysels, Eds.), Theorex, CA, 1975. 38. Hough, D. B., and White, L. R., Adv. Colloidlnterface Sci. 14, 3 (1980). 39. Derjaguin, B. V., and Shcherbakov, Ya. I., KolloidZ. 31, 47 (1969). 40. Hertl, W., and Hair, M. L., Nature223, 1151 (1969). 41. Tempelhoff, K., Winde, H., and Hennig, K., Z. Chem. 12, 276 (1972). 42. Boutin, H., and Prask, H., Surf Sci. 2, 261 (1964). 43. Blake, T. D., and Kitchener, J. A., J. Chem. Soc. Faraday Trans. 168, 1435 (1972). 44. Eisenberg, D., and Kauzmann, W., "The Structure and Properties of Water." Oxford Univ. Press, London New York, 1969. 45. Verwey, E. J. W., and Overbeek, J. Th. G., "Theory of the Stability of Lyopholic Colloids." Elsevier, Amsterdam New York, 1948. 46. Yates, D. E., and Healy, T. W., J. Colloid Interface Sci. 55, 9 (1976). 47. Healy, T. W., Yates, D. E., White, L. R., and Chart, D., J. Electroanal. Chem. 80, 57 (1977). 48. Farrell, J. R., and McTigue, P., J. Electroanal. Chem. 139, 37 (1982). 49. Hall, A. G., J. Phys. Chem. 74, 2742 (1970). 50. Busscher, H. J., Kip, G. A. M., van Silfhout, A., and Arends, J., J. Colloid Interface Sci. 114, 307 (1986). 51. Pearce, J. P., and Nelson, A. F., J. Amer. Chem. Soc. 54, 3544 (1932). 52. Pashley, R. M., aL Colloid Interface Sci. 78, 246 (1980). 53. Brunauer, S., Emmett, P. H., and Teller, E., J. Amer. Chem. Soc. 60, 309 (1938). 54. Yates, D. E., Ph.D. thesis, Department of Physical Chemistry, University of Melbourne, 1975. 55. Vedam, K., and Malin, M., Mater. Res. Bull. 9, 1503 (1974). 56. Garbatski, U., and Folman, M., J. Phys. Chem. 60, 793 (1956). 57. McHaflfie,I. R., and Lehner, S., J. Chem. Soc. Faraday Trans H 1559 (1925). 58. Frazer, J. H., Phys. Rev. 33, 97 (1929). 59. Fisher, L., Nature 293, 575 ( 1981 ).

Journalof ColloidandInterfaceScience.VoL 140,No. 2, December1990