Langmuir 1990,6, 539-542
539
Local Composition Fluctuations and Wetting Phenomena E. Tronel-Peyroz," J. M. Douillard, M. Privat, and R. Bennes U A 330 Physico-Chimie des Syst&mesPolyphash, CNRS, Route de Mende, BP 5051, 34033 Montpellier Cedex, France Received January 4, 1989 We present a thermodynamic calculation to explain why a high-energy solid is dewetted by certain binary mixtures, even though both pure liquids will wet the same solid surface. It is shown that both local composition fluctuations and surface tension fluctuations cause the dewetting. The results are compared with the experiments. Excellent quantitative agreement is found.
I. Introduction Wetting phenomena have been recently studied in different physical systems: in the adsorption of liquids on substrate surface' and in binary liquid mixtures in contact with their vapor.* Most recent theoretical work has been focused on spreading of liquid drops3 and on critical ~ e t t i n g .In ~ the case of liquid mixtures, Law' has presented an analytical theory which clarified the conditions of wetting near the critical point. Far from the critical point, the conditions of wetting in binary liquid mixtures remain unclear. Even though there is an important degree of phenomenological knowledge,6 some wetting phenomena are still not understood. The aim of this paper is to explain why a solid of highenergy which is wettable by two pure liquids is dewetted by their mixture in a narrow range of composition. This has been observed in many aqueous system.' In section 111, we present a model which links this contact angle phenomena to local composition fluctuations and to surface tension fluctuations. In section IV, we compare the model with experimental data. 11. Experimental Section Liquid-vapor interfacial tensions have been measured
by using the Wilhelmy plate technique: a liquid exerts on a perfectly wettable plate a traction which can be measured by a balance and which corresponds to the surface tension exerted by the liquid on both sides of the plate. Other measurements were carried out by using the De Nouy method whereby one measures the traction force exerted on a platinum stirrup immersed in the liquid when the horizontal part of the stirrup rises above the liquid surface, drawing with it a meniscus. The contact angle was determined by using Guastalla's technique,6 known as the wetting balance method. This method is not the most precise way of measuring the contact angle, but it is the easiest to use when one wishes to observe the variation of the contact angle with the concentration of the liquid mixture, as was our case. In this study, we only used a so called "high-energy" solid which is perfectly wettable by both pure liquid components of the mixture. Amongst these solids we chose glass, which is easy to manipulate. The plates were washed with sulfochromic acid (1)Krim, J.; Dash, J. C.; Suzanne, J. Phys. Rev. Lett. 1984,52,640. Moldover, M. R. J. Chem. Phys. 1983, 79,379. (2)Schmidt, J. W.; (3) de Gennes, P . 4 . Reu. Mod. Phys. 1985,57,827. (4)Sullivan, D. E.;Telo de Gama, M. M. Fluid Interfacial Phenomena; Croxton, C . A., Ed.; Wiley: New York, 1985. (5)Law, B. M. Phys. Reu. E 1985,32,5996. (6)Davies, J. T.; Rideal, E. K. Interfacial Phenomena, 2nd ed.; Academic Press: New York, 1963. (7)Padday, J. Proc. of the 4th International Congress on Surface Actiue Substances; Brussels, 1964;p 299.
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then with water and with ethanol and finally dried in a hot air oven. To check the results given by the wetting balance, we also used the capillary rise technique:' these later results were in perfect agreement with the former. All the measurements were made in thermostated boxes, where the temperature was fixed at 25 "C. The liquid mixtures chosen were binary mixtures: waterwater-2-butoxyethano1, and ethanol, water-2-methy1-2-propano1, water-2,g-lutidine (a binary mixture of interest for critical wetting experiments). In each case, the contact angle measured shows the same variations with respect to the mixture concentration. This type of evolution, which is ~ t a n d a r dis, ~shown in Figure 1. In the same figure, we also show the variations of the liquid-vapor surface tensions with the concentration. This reveals strikingly that the contact angle only exists in the concentration range where the liquid-vapor surface tension varies greatly.
111. A Possible Model The problem is to explain why a high-energy solid which is perfectly wettable by two pure liquids taken separately is only partially wettable by a mixture of these two liquids. A high melting point solid such as glass has a free surface energy which is believed to range from several thousand to several hundred millinewtons per m&er. The mixtures which have tensions less than 70 mN-m-' would be expected to spread spontaneously on this solid. It is well-known that aqueous mixtures exhibit appreciable deviations from ideality. It would seem to us that the dewetting could be partly related to the local composition fluctuations which are always present in binary mixtures. I t is indeed well-known that the thermodynamic variables which characterize a phase (temperature, pressure, composition, etc.) fluctuate around their mean value. The same is true of the values which characterize the surface phase in the classical interface model proposed by Guggenheim." In this model, the surface layer constituting the interface between two bulk phases may be thermodynamically analyzed as a phase which is characterized by the absolute temperature, the pressure, the composition, and either the area or the surface tension of the interface. In a previous study, we applied Landau's theory to obtain the explicit expression of the surface composition fluctuations in the adsorbed layer of a binary mixture in equilibrium with its vapor." We also obtain an expression for the tension fluctuation. Tension fluctuations are due to all the thermodynamic fields (pressure, temperature, concentration, ...). (8)Neurnann, A. W.Adu. Colloid Interface Sci. 1974,4,105. (9)(a) TbnBbre, L.Mem. Seru. Chim. Etat: Paris 1955,40,77. (b) Ruch, R. J.; Bartell, L. S. J.Phys. Chem. 1960, 64,513. (10)Guggenheim, E. A.; Adam, N. K. Proc. R. SOC.London, Ser. A 1933, 139, 218. (11)Bennes, R.; Douillard, J. M.; Privat, M.; Tronel-Peyroz, E. J. Colloid Interface Sci. 1987,117,574.
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540 Langmuir, Vol. 6, No, 3, 1990
Tronel-Peyroz et al.
t
introducing (3) in (1) and taking into account (21, one has
e(0'
cos 8 = [l + (6yly)I-l (4) with 87," = 8y and yLv y to simplify the notation. The measured contact angle, Om, is the mean value of all the instantaneous values of 8, so
20
cos 8, = (cos 8 ) = [1+ ( @ y ) / y p (5) We now find an expression for (67). Let us assume for the moment that the local surface tension variations are only related to local concentration variations of the liquid-vapor transition layer (see section IV for a discussion on the contribution of capillary waves). However, in thermodynamical equilibrium the chemical potential of the solute in the bulk phase (p2*) is equal to the chemical potential of the solute in the superficial phase (11'"). It therefore follows that the composition of the transition layer is related to the bulk composition x Z a , and we may write
C
40
li_..
40
30 20
10
0.0 7
0.01
0.4 0.5
Taking the mean value of the two terms of the above relation and noting that12 ( ( a x 2 " ) ) = 0, we obtain (by introducing the value found for (67)in (5))
1
x;
The mean square deviation of the bulk composition by
( ( 6 ~ ~ ~is) given ' )
6i"1 PO
d 30
where a2* is the activity of species 2 in solution and N" the number of molecules of solute and solvent in the fluctuation, which is in a first approximation equal to l/x," (see Appendix).
10
10
Figure 1. Variations of both the liquid-vapor surface tension ( 0 )and
the contact angle solid-vapor-binary liquid mixture
(o),with respect to the bulk composition xza: (a) water-2-bu-
toxyethanol; (b) water-ethanol; ( c ) water-2-methyl-2propanol; (d) water-2,6-lutidine. As we study mixture effects, we will now restrain the reasoning to the concentration effects. We can therefore imagine that along a triple line of contact the local concentration fluctuates. For each concentration value, there corresponds a value of the surface tension and a value of the contact angle verifying Young's equation: YLV cos 8 = Ysv - YSL (1) This approach leads us to think that the contact angle should be zero if there were no concentration fluctuations in the liquid mixture. One can therefore write
YL" = rsv
- YSL
(2)
When concentration fluctuations are present, they cause tension fluctuations, and one can write that
+ 6ykI
(3) with kl = Lv, sv, SIJ Firstly, if we discount the effects due to the solid, we have the following approximation: 67," 6y,, 0. By ykl = ?/kl
IV. Discussion Qualitatively, it is very clear that ( 7 )takes into account the fact that the contact angle is only different from zero when the liquid-vapor surface tension varies greatly with the concentration as seen in Figure 1. For dilute solutions, the tension varies with the concentration in such a way that (a2y/ax2**)tends to a limit value different from zero, while in this same region ((Sx,")') tends to zero. It follows that cos 8, 1 and ern 0. For more concentrated solutions, where the surface tension varies linearly with the composition, a2y/axZa2= 0, and here again 8, 0 in agreement with the observed facts. For each system, we have calculated the contact angle using ( 7 ) , the measured values of the liquid-vapor surface tension, and the composition fluctuation term
-
-
-
The variation in calculated values (8,) is shown in Figure 2. In each case, we have evaluated the degree of uncertainty both in the calculation and in the measurement of 8, the combination of which have been represented by squares in Figure 2. We observe that all these points lie approximately on (12) Reif, F. Statistical Thermal Physics; McGraw-Hill: New York, 1965; p 12.
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Composition Fluctuations and Wetting Phenomena
The surface area is given by the general relation A =
CiNi"Ai"in which Ni" is the number of moles of the species i in the transition layer 0 and Ai"their partial molar area. One can immediately deduce that
/
For very dilute solutions, the partial molar areas A," and A," are in an almost constant ratio with the composition; it follows therefore that
-('A) - (r,+ kr2)(6A,") with k = A,"/A," = A2"O/A1"0 A
(12) 10
30
50
e,?)
Figure 2. Correlation between the calculated contact angle 0, (evaluated with eq 7) and the measured contact angle Om for different water-nonelectrolyte mixtures: (0)ethanol; (a) 2-
methyl-2-propanol; ( 0 )2,6-lutidine; (A)2-butoxyethanol. The change of 6 for the dilute water-ethanol mixture, which is due to the capiflary waves component, is represented by an arrow pointed toward the new value.
a straight line with a unit slope showing that the correlation is correct. We can therefore conclude that this new approach (which relates the contact angle to local liquid-vapor surface tension fluctuations and therefore also to the bulk concentration fluctuations) shows encouraging results. However, such correlations need to be studied more deeply. To do this, two different effects must be taken into account in future studies: the influence of the solid and the influence of capillary waves. The influence of the solid is certainly the most difficult one to evaluate since, as was shown by M ~ h i l n e r , ' ~ the interfacial tensions solid-liquid and solid-vapor must be replaced in Young's equation by parameters which involve both elastic and plastic contributions: the generalized intensive surface parameter ys is related to and to e, the elastic surface stress, by the following equation (when the total surface strain is infinitesimal):
where de, = d Q / Qis the differential of the total surface strain, dep the plastic contribution, and de, the elastic contribution to the total surface strain. However, it is difficult to estimate the variation of these different variables with respect to the composition xiu. Since the studies of Buff, Lovett, and Stillinger,'* it is admitted that at the surface of liquids the molecules move vertically under the effect of the Brownian motion, thus giving rise to capillary waves. The variation in the surface area thus caused must be taken into account when calculating the contribution of the capillary waves to the fluctuations of the tension: ( 6 ~ ) ~Equation . 5 should thus be written
The calculation of ( 6 ~ is) not ~ a simple matter, but in the case of very dilute solutions a first attempt can be made as follows. (13) Mohilner, D.M.; Beck, T. R. J. Phys. Chem. 1979,83, 1160. (14) Buff, F. P.;Lovett, R. A.; Stillinger, F. H., Jr. Phys. Reu. Lett. 1966, 15, 621.
Furthermore, Gibb's equation gives 6y = -r216p2u. Expanding 6p," in terms of 6Al" and 6A2" and using the interfacial thermodynamical equations, one obtains (67) = 21'21yk(6A1"). If we then eliminate (6Al") between this latter relation and (12) and express rZlin terms of volumic (xi*) and superficial (xi") compositions, one has
The capillary waves theory enables us to calculate (&A)/ A in the case of a pure substance.15 In the case of very dilute solutions, one can assume that (6A) / A for a mixture is not very different from (6A)/A for pure water (i.e., = 0.447). This makes it possible, using (13), to calculate easily the new values of 8 for the water-ethanol mixture and to observe that these points lie more satisfactorily in a straight line of slope 1, thus improving the correlation 8, = dm (Figure 2). Nevertheless, such an evaluation can only serve to indicate a trend, since it makes use of the capillary waves theory, which is not yet well established. On the other hand, the approximation N* = l/x," made in section I11 requires that the bulk fluctuations hold only one molecule of the species 2; this condition is only satisfied for a water-ethanol mixture" in the extremely dilute region: x Z a < 0.06. For these two reasons, we have only taken into account the influence of the capillary waves in the case of a single binary mixture and within a narrow concentration range.
Appendix If one assumes that in the dilute concentration range there is only one solute molecule in the fluctuation, one obtains the relation N" = l/x2*. This assumption can be justified as follows: if each fluctuation only contains one solute molecule, then N F ,the number of fluctuations by volume units, is equal to N,, the number of solute molecules by volume units. Hence
NF N xPN/u' (AI) where u* is the molar volume of the binary mixture and N the Avogadro number. One can also calculate N F using light scattering and Rayleigh ratio (RF) measurements. One then obtains the relation" (15) Evans, R.Adu. Phys. 1979,28, 143. (16) Onori, G.Il Nuouo Cimento. 1986,8,465. (17) Tanford, C. Physical Chemistry of Macromolecules;Wiley: New York, 1966; p 275.
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Langmuir 1990, 6, 542-547
i ~ ~ ( a t / ~ ~ ~ ) ~ ~ ethanol ~ ~ ~mixtures, ~ ~ aone~observes that the values of NF cal(A21 culated from (A2) are in good agreement with those cal2~~~~(aa,~/ax,') culated from (Al). Therefore, one can conclude that the approximation where h is the wavelength used and aZathe activity of N" = 1/x2* used in our evaluation of 0 is correct in the the solute. dilute concentration range. Using the values of R, given by Wood" for waterRegistry No. 2-Butoxyethanol, 111-76-2; ethanol, 64-17-5; (18)Parfitt, G. D.;Wood, J. A. Trans. Faraday SOC.1968,64,2081. tert-butanol, 75-65-0; 2,6-lutidine, 108-48-5. NF
=
Determination of Microviscosity and Micropolarity of Lyomesophases Utilizing a Fluorescent Probe R. Parthasarathy and M. M. Labes* Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122 Received April 21, 1989
The excimer to monomer emission intensity ratio (E/M) of an intramolecular excimer-formingprobe, 1,3-bis(l-pyrenyl)propane(DPyP), has been studied in dilute solutions as well as lyomesophases of potassium laurate (KL), sodium decyl sulfate (SDecS), and myristyltrimethylammonium bromide (MTAB). E/Ms in the mesophases are much lower than in dilute solution due to the combined effects of viscosity, orientational order, and specific host-guest interactions. The phase transitions from the disk-like N4 phase to the rod-like N, phase to the isotropic phase are each accompanied by increases in this ratio. Microviscosities of MTAB, SDecS, and KL are approximately 120, 70, and 60 cP, respectively. The extent of vibrational structure in the monomer emission of DPyP is sensitive to polarity, so DPyP provides a simultaneous measure of both micropolarity and microviscosity.
Introduction Microviscosity is a somewhat vague concept used to describe the short-range spatial constraints that limit molecular rearrangement over short time scales (C1ms). Estimations of microviscosity, in principle, are particularly helpful as a means of characterizing micellar domains that are expected to be important solubilization sites. Since Zachariasse' demonstrated about a decade ago that the ratio of excimer to monomer emission intensities in an intramolecular excimer-forming probe, 1,3-bis(lpyreny1)propane (DPyP), was sensitive to microviscosity, there have been many investigations utilizing this p r ~ b e and ~ - ~its chemical analogues (such as the diarylpro pane^'.^ and higher alkyl homologues' of DPyP). The technique requires a simple measurement of the intensities of excimer and monomer emission; their ratio is translated into an estimate of microviscosity by comparison with values obtained in calibrant mixtures of known macroscopic viscosity. Alternative approaches (such as fluorescence depolarization measurements) are more com(1)Zachariasse, K. Chem. Phys. Lett. 1978,57, 429. (2)Lianos, P.;Lang, J.; Strazielle, C.; Zana, R. J. Phys. Chem. 1982, 86,1019. (3)Viriot, M. L.; Bouchy, M.; Donner, M.; Andre, J. C. Photobiochem. Photobiophys. 1983,5 , 293. (4)Melnick, R. L.;Haspei, H. C.; Goldenberg, M.; Greenbaum, L. M.; Weinstein, S.Biophys. J. 1981,34,499. (5) Lianos, P.; Viriot, M. L.; Zana, R. J.Phys. Chem. 1984,'88,1098. (6) Turro, N. J.; Okubo, T. J. Am. Chem. SOC.1981,103,7224. (7)Turro, N.J.; Aikawa, M.; Yekta, A. J. Am. Chem. SOC.1979,101, 772. (8)Anderson, V. C.; Weiss, R. G. J . Am. Chem. SOC.1984,106,6628.
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plicated, accounting for the popularity of excimer spectral studies. The main assumptions underlying the use of excimerforming guests to estimate host microviscosities are as follows: (i) the rate of molecular rearrangement required for excimer formation is dictated by solvent viscosity; (ii) the solvent does not affect any other photophysical properties of the probe. Both assumptions have been questioned?,lo but little doubt remains that the excimer/ monomer emission intensity ratio of DPyP in a given sample does reflect changes in matrix cohesion at least as a function of external variable^.^^^^ The ratio, E/M, of the intensities of excimer (E) and monomer (M) emission in the fluorescencespectra of DPyP has been investigated in simple micellar systems (anionic as well as c a t i o n i ~ ) ~and ' ~ ~emulsions2 *~~ to examine the effect of additives on their organization. Phase transitions in membranes, synthetic surfactant vesicles, and thermotropic liquid crystals have been detected by changes in E/M.394 It is known that E / M decreases monotonically (linearly at viscosities greater than 10 cP) as viscosity increases, but chemical considerations often influence the precise form of this equation, even among homo(9) Henderson, C. N.; Selinger, B. K.; Watkins, A. R. J. Photochem. 1981,16,215. (IO) Snare, M. J.; Thistlethwaite, P. J.; Ghiggino, K. P. J.Am. Chem. SOC.1983,105,3328. (11)Zachariasse, K.A.; Duveneck, G.; Busse, R. J. A m . Chem. SOC. 1984,106,1045. (12) Lianos, P.; Zana, R. J. Colloid Interface Sci. 1982,88,594. (13)Lianos, P.; Lang, J.; Zana, R. J. Colloid Interface Sci. 1983,91,
276.
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