Langmuir 1992,8, 206-212
206
Effect of the Electrostatic and Structural Surface Forces on the Contact Angles in Langmuir-Blodgett Systems of Cationic Surfactants. 2. Static Advancing and Receding Contact Angles during Deposition of Mixed Monolayers of Methyl Arachidate and Dimethyldioctadecylammonium Bromide Jordan G. Petrov,*yt Angelina Angelova,t and Dietmar Mobius$ Bulgarian Academy of Sciences, Central Laboratory of Mineral Processing, P.O. Box 32, 1126 Sofia, Bulgaria, and Max-Planck-Institut fur biophysikalische Chemie, Postfach 2841,D-3400 Gottingen, FRG Received January 16, 1991. I n Final Form: August 22, 1991 By variation of the molar ratio of the neutral and the charged monolayer components, the charge densities and electrostatic potentials of the gaslliquid and the solidlliquid interfaces have been monitored. The dependence of the static advancing and receding contact angles on the molar part of the charged component has been determined at two ionic strengths (0.001 and 0.1 M NaCl). It was found that the ionic strength does not influence the static contact angles. No change was observed also when the gas/ liquid and the solid/liquid interfaces had different (both positive) potentials. Such an independence of the advancing and receding contact angles on variations of the double layer characteristics demonstrates the negligible effect of the electrostatic surface forces in the three-phase contact zone on the static contact angles and their hysteresis. At the same time a qualitative correlation between the contact angles and the dipole contribution to the electrostatic field at the interfaces was observed. Since the latter is directly related to the interfacial water structuring, it can be concluded that the structural surface forces play a dominant role in the three-phase contact zone and that they are responsible for the observed variation of the contact angles with the molar part of the charged component. Introduction In part 1 of this paper we have studied the homogeneity and electrostatic properties of the interfaces during a Langmuir-Blodgett transfer of mixed monolayers of neutral methyl arachidate (MA) and positively charged dimethyldioctadecylammonium bromide (DOMA). In part 2 we investigate the dependence of the static advancing and receding contact angles during the deposition on the molar ratio of the monolayer components (i.e. on the interfacial charge densities and potentials), Figure 1. The ionic strength of the aqueous subsolution, determining the diffuse double layer thicknesses, was also varied. One could expect that these parameters will affect the eiectrostatic forces in the three-phase contact zone and the values of OA and OR.^ Previous studies with mercury/water/air2+ and AgI/ water/air7s8 systems, where the mercurylwater and AgII water potentials can be directly measured, support such an expectation. Maximum static contact angles (having unique values 00 on mercury substrates) were found at the points of zero charge and a decrease of 00 with increasing
* To whom
correspondence should be addressed.
t Bulgarian Academy of Sciences.
Max-Planck-Institute fiir biophysikalische Chemie. (1)Martynov, G. A.; Starov, V. M.; Churaev, N. V. Kolloid J. of the USSR (Engl. Transl.) 1977, 39, 406. (2) Frumkin, A. N.; Gorodetzkaya, A. Acta Physicochim. USSR 1938, 9, 327. (3) Smolders, C. A. Red. Trau. Chim. Pays-Bas 1961, 80,699. (4) Morcos, I. J . Colloid Interface Sci. 1971, 37, 410. (5) Nakamura, Y.;Kamada, K.; Katoh, Y.; Watanabe, A. J. Colloid Interface Sci. 1973, 44, 517. (6) Hato, M. J. Colloid Interface Sci. 1989, 130, 130. (7) Billett, D. F.; Hough, D. B.; Ottewill, R. H. J . Electroanal. Chem. Interfacial Electrochem. 1976, 74, 107. (8) Ot,bwill, R. H.; Billet, D. F.; Gonzales, G.; Hough, D. B.; Lovell, V. M. Wetting,Spreading and Adhesion; Padday, J. F., Ed.; Academic Press: London, 1978; p 183. t
0743-7463/92/2408-0206$03.00/0
1 MA
M DOMA
Figure 1. Schematic presentation of the Langmuir-Blodgett deposition of mixed monolayers of dimethyldioctadecylamonium bromide (DOMA) and methyl arachidate (MA). The counterions in the liquid and the LB bilayer are not shown. $0 was observed for both positive and negative potentials. On the polycrystalline (rough and heterogeneous) AgI surfaces a considerable contact angle hysteresis was found. After the samples were polished, a strong decrease of flA was achieved. Thisresult demonstrated that the roughness and the energetic heterogeneity are probably the main reasons for the contact angle hysteresis in these systems. At the same time it was found that the values of flR remained practically unchanged after polishing; this fact brought the authors to the conclusion that OA is more sensitive to the roughness and OR to the physicochemical properties of the interfaces. Similar correlations have been observed also for other model solid surfaces, gold, platinum: and quart~.~JO In the latter case the {potential was measured to characterize
(9) Zorin, 2. M.; Romanov, V. P.; Churaev, N. V. Colloid and Polym. Sci. 1979,257, 968. (10) Menezes, J. L.; Yan,J.; Sharma, M.M. Colloids Surf. 1989, 38, 365.
0 1992 American Chemical Society
Effect of Surface Forces on Contact Angles
Langmuir, Vol. 8, No. 1, 1992 207
the electrostatic behavior of the solid/liquid interface and a decrease of both OA and OR, as well as of the hysteresis 6 A - OR, with 5 has been found. However, especially at high ionic strengths, this (e1ectro)kineticparameter cannot be used instead of the thermodynamic quantity $0 to calculate the electrostatic interaction in the three-phase zone. Moreover, even if the potential at the solid/liquid interface +os is known, the uncertainty and the limited amount of data for the gadliquid interfacial potential + o ~ remains ~ ~ J ~an additional problem. Only in a few of the model systems previously studied were special efforts made to distinguish between the electrostatic effects and those caused by the variation of the water structure in the three-phase contact zone. Such a discrimination is difficult, since the change of surface charge density is coupled with a change of the hydrophilicity of the interfaces. At the same time in many of the above mentioned ~ t u d i e s , 4 ~as~ Jwell ~ as in some others,13J4the values of the measured contact angles could not be explained only on the basis of the electrostatic and van der Waals surface forces. In these cases the structural surface forces had to be included in the analysis and it was found that sometimes “this component dominates all the other interactions in the calculation of the contact angles”.1° The Langmuir-Blodgett systems studied heie have the advantage that they provide direct experimental data for both +os and +oL. The parallel determination of the AV potentials of the spread monolayers enables discrimination of the Gouy-Chapman interactions between the diffuse double layers, from the dipole effects, which determine the structural surface forces. The comparison of the two effects on the static advancing and receding contact angles is the main purpose of the present investigation.
Theoretical Relationships between the Contact Angles and the Surface Forces Acting in the Three-phase Contact Zone The interactions in the three-phase contact zone have been related to the equilibrium contact angle 60 by Frumkin15 and Derjaguin16by the equation cos Bo = 1
+ l/y(IIoho+ JhIII(h)dh)
(1)
where II is the “disjoining pressure” in the three-phase zone that tends to separate the gadliquid and the solid/ liquid interfaces when being positive, h is the local distance between the two interfaces, y stands for the gadliquid surface tension, and IIoand ho are the disjoining pressure and the thickness of the equilibrium wetting film above the meniscus.17 Martynov, Starov, and Churaev’ developed similar relationships for the extremal static advancing and receding contact angles in systems with smooth, homogeneous and nondeformable solid surfaces. Considering a meniscus in a horizontal slot of thicknessH, they analyzed the changes of its curvature when additional external pressure AP has been applied either from the convex or from the concave side of the gadliquid interface. Ne(11)Scheludko, A.;Exerowa, D. Kolloid-2. 1959,165,148;1960,168, 24. (12)Usui, S.;Sasaki, H. J. Colloid Interface Sci. 1978,65, 36. (13)Lowe, A. C.; Riddiford, A. C. Can. J . Chem. 1970,48,865. (14)Derjaguin, B.V.;Churaev, N. V. Wetting Films;Nauka: Moscow, 1984;p 89. (15)Frumkin, A. N. Zh.Fiz. Khim. 1938,12,337. (16)Derjaguin, B. V. Zh. Fiz. Khim. 1940,14, 137. (17)II& can usually be neglected for small curvaturesKof the adjacent meniscus (no = P7 = y K ) which is the case for a vertical meniscus near a flat wall.
Figure 2. Typical disjoiningpressure isotherm n(h)for a threephase system with nonzero contact angles (quartz/l X 10-9 M KCl9.
glecting the evaporation-condensation and the hydrodynamic transport of material between the deformed meniscus and the wetting film, they defined the static meniscus instability conditions 1 cp and cp I0
(2)
= cp(h,P)= P ( H - h) - JhmII(h)dh
(2a)
y
where cp
From their equations one can obtain for OR and OA COS OR
= 1+ l / y JhyII(h)dh
COS OA
= l/y
JhmII(h)dh
(3) (4)
Physically the condition cp = y corresponds to an appearance of a horizontal portion of the gas/liquid interface a t h = hl and beginning of the receding motion of the meniscus. The condition cp = 0 means an appearance of vertical portion at a particular height h = hz, leading to an instability of the deformed static advancing meniscus and to beginning of its rolling over the preceding film (see parts a and b of Figure 3 in ref 1). For systems with not very small contact angles, where contact angle hysteresis is often observed, the film preceding the meniscus is a very thin structured liquid phase.l* For such systems the disjoining pressure isotherm n(h)has a deep minimum in the negative region and resembles the exemplary onelg shown in Figure 2. In this case the critical thicknesses hl and hz have rather different values; the value of hl is close to the film thickness h,, and hz is significantly greater than h,. Assuming additivity the disjoining pressure isotherm II(h)can be presented as a superposition of van der Waals IIw(h),electrostatic n ~ ( handstructural ), IIs(h)isotherms
n(h)= nvw(h) + nE(h) + ns(h) (5) For thicknesses up to 300 A the van der Waals component can be presented by the expressionZoa n,,(h)
= A(h)/67rh3
(6)
where A is the Hamaker constant (18)Derjaguin, B.V.;Churaev, N. V. Dokl. Acad. Sci. SSSR 1972,207, 572. (19) Churaev, N. V. Rev. Phys. Appl. 1988,23,975. (20)Derjaguin, B. V.;Churaev, N. V.; Muller, V. M. Surface Forces; Nauka: Moscow, 1985;(Plenum Press: New York,London 1987): (a) p 118,(b) p 200,(c) p 204.
Petrov et al.
208 Langmuir, Vol. 8,No. 1, 1992 A(h) = Ao[ 1 -
1
(6a)
(12)
A0 is the Hamaker constant at h 4 0 , c is the light velocity, and b and d are constants specific for the system. The isotherm of the electrostatic disjoining pressure II&) for constant potential boundary conditions is related to the interfacial potentials and the ionic strength by the equation20b
does not contain the ionic strength I and has an opposite sign, predicting repulsion instead of attraction. This uncertainty and the consideration of systems with small contact angles and different interfacial potentials only, restricts the application of eq 11. Equations 1-11 show that one could expect a dependence of the equilibrium 00 and hysteresis contact angles 6 A and BR on +os and +oL and on the electrolyte concentration CObecause of the dependence of the electrostatic disjoining pressure IIE on these parameters. However, the mean interfacial dipole moment p I also changes when the molar ratio of the monolayer components, $os and $oL, are varied. According to eqs 9 and 10this variation should cause a change of the structural component IIs too. For discrimination of these two effects,a use of the independent measurements of +O and p L (part 1)was made in this study.
2bd [1 ++(bc/h)13
For constant interfacial charge density &(h) is given by the relationshipzoc
where
Methods and Materials = 8.ne2Co/&T
(8a) Equations 7 and 8 serve as a good approximation if +os and +oL are less than 50-60 mV.zl The structural disjoining pressure isotherm can be presented by an exponential relationshipzz K'
ns(h)= KOexp(-hllo) (9) where KO> 0 relates to hydrophilic repulsion and KO< 0 to hydrophobic attraction and lo is the corresponding correlation length. Recent development of the theory23 gave a more detailed expression for KOin the case of hydrophilic repulsion
KO= 87qpL2/til:
(10) Here q is an order parameter (for neutral interfaces in pure water q = 0.61, p I is the normal component of the dipole moment of 1 cmz of the interface, and ti is the dielectric constant staying in the theory of the nonlocal electrostatics (having a value of about 523). Neogi2*has considered the effects of van der Waals and electrostatic interactions on the profile of a wedgelike film at the end of a static meniscus. An approximate solution is obtained for different values of +os and +oL and small 00, showing that the electrical double layer effects have no influence when the gadliquid interface has a constant charge density. At constant potential boundary condition the wedge profile h(x)can be obtained from the equation
where is the contact angle in the absence of electrical forces. This expression gives a good qualitative illustration of the fact that an increase of the potential difference +os - +oL leads to displacement of.the two interfaces to larger contact angles. However, the second term in eq 11,being very similar to the expression for IIg obtained later25for small separations between two different plates (21) Usui, S.;Hachisu, S.In Electrical Phenomena at Interfaces; Kitahara, A., Watanabe, A., Eds.; Marcel Dekker: New York and Basel, 1984; p 70. (22) Derjaguin, B. V.; Churaev, N. V. Colloids Surf. 1989, 41, 223. (23) Belaja, M. L.; Feigel'man, M. V.; Levadny, V. G. Langmuir 1987, 3, 648. (24) Neogi, P. J. Colloid Interface Sci. 1984, 98, 425. (25) Adamczyk, Z.; Belouschek, P.;Lorenz,D. Ber. Bunsen-Ges. Phys. Chem. 1990, 94, 1483.
The contact angles were measured goniometrically from photographsof the meridian cross section of the meniscus around a vertical cylinder at about6-fold magnification. Since the angles were ratherbig (50-80°),this technique gave satisfactoryaccuracy of * 2 O . Hydrophobized via dip-coating with polystyrene glass tubes (see part 1) with diameter of 1.6cm were used as solid substrates. The latter were dipped and withdrawn through the monolayer at constant velocities of 0.200 and 0.020 cm/s, respectively. Dipping at a higher velocity facilitated the monolayer transfer giving bigger dipping deposition ratios a,. The withdrawal velocitywas chosen to be less but near to the maximumdeposition velocity above which a liquid film was entrained during the deposition.26 After the dipping or withdrawal of the substrate through the monolayerwas stopped, the relaxation of the dynamicadvancing and receding angles was followed up to obtain the corresponding constant (static) values of eA and OR. The monolayermixtures were spread as 1 X M chloroform solutions, compressed up to 30 dyn/cm, and allowed to stay 2 min for evaporation of the solvent. LB depositions on three separate solid samples were used to determine the angles at given conditions, and their mean was taken as a representative value. All chemical substances, water, and other materials were the same as those described in part 1.
Results Determination of the Static Contact Angle Hysteresis. Usually the static contact angles have arbitrary values between two well-definedlimita-the critical angles at which the wetting perimeter starts to move forward or backward under the action of an external force. These extrema values determining the static contact angle hysteresis can be obtained if the velocity dependence of the dynamic receding and advancing contact angles is extrapolated to zero contact line velocity.*' Figure 3 illustrates two typical relaxation dependences of the dynamic contact angles during the transfer of the first and second monolayer onto the hydrophobic solid substrate. In this example, as well as in all systems studied in this paper, the static OA and OR values (corresponding to the plateaus where V = 0) have been reached after rather different time intervals. The relaxation of the advancing angle ceased almost immediately, while the receding one changed within a much longer time interval-during the first 5-10 min after stopping the substrate motion. The (26) Petrov, J. G.; Kuhn, H.; MBbius, D. J. Colloid Interface Sci. 1980, 73, 66.
(27) Petrov, P. G.; Petrov, J. G. Colloids Surf., in press.
Effect of Surface Forces on Contact Angles
Langmuir, Vol. 8, No, 1, 1992 209 Table I. Static Contact Angles BA and OR in Asymmetrical Model Systems with Different $os and $oL Potentials: Aqueous Phase, 0.001 M NaCl $os, mV
202 202 12 51
$oL, mV BA, deg OR, deg
I
I
10
0
20
30
Figure 3. Relaxation dependencesof the advancing and receding contact angles during the transfer of the first and second monolayer onto the hydrophobic solid substrate.
202 113 14 54
Table 11. Static Contact Angles @A and Bg in Asymmetrical Model Systems with Different $os and $oL Potentials: Aqueous Phase, 0.1 M NaCl $os, mV
t/min
202 179 74 52
93 93 73
GoL, mV 0A,deg OR, deg
93 67 75 51
51
93 27 74 50
80
t
1
Lo/ I
0
I
0,l
,
1
02
0.3
XD
Figure 4. Dependences of the static advancing OA and receding OR contact angles for “symmetrical” DOMA/MA LangmuirBlodgett systems (see the text) on the molar part of the charged component XD:subsolutions,0.001 M NaCl (A)and 0.1 M NaCl (0).
reasons for such a difference are a matter of wetting kinetics and they will be considered in a separate publication. Effect of the Interfacial Gouy-ChapmanPotentials and Ionic Strength. Up to a molar part of the charged monolayer component, X D= 0.23, the mixtures have been transferred onto the solid substrates at equal dipping and withdrawal deposition ratios of 0.94 for 0.001 M NaCl and 0.97 for 0.1 M NaC1, respectively. Therefore under these conditions the above systems have practically the same gaslliquid and solid/liquid interfacial charge densities and electrostatic potentials.28 The static contact angles for such “symmetric” systems are plotted versus X Din Figure 4. The data show that the receding angle OR decreases strongly up to XD = 0.10, passing through a shallow minimum a t X D = 0.17. The advancing angle 6 A remains constant up to X D = 0.17 and decreases slightly above X D = 0.23.29 Taking into account the exact values of the dipping deposition ratios, we should consider the above systems as slightly asymmetric electrostatically, i.e. with slightly different +os and +oL. We can prove the importance of such an asymmetry experimentally by transferring mixtures with different composition during the dipping and withdrawal. The results for three such systems transferred fromO.OO1 M NaCl subsolutions are illustrated in Table I. They show that a change of +oL by 90 mV at constant $8 = 202 mV and the corresponding variation of the electrostatic surface forces in the three-phase zone do not influence the static contact angles and their hysteresis. (28) Petrov, J. G.; MBbius, D. Langmuir 1990, 6, 746. (29) The decrease of OA and the increase of OR at XD > 0.23 could be due to the slightly lower dipping deposition ratios. This tendency is more clearly expressed at XD= 0.30, where a. = 0.87, a, = 0.86 (see part 1) and correspondingly Oa = 70” and OR = 55”.
I
50
,
100
I
1
200 Yo [mvl
150
,
250
Figure 5. Relationship between the measured static contact angles OA and OR and the experimentallydeterminedelectrostatic surface potential, $0: subsolution,0.001 M NaC1. Comparison of the particular values in Figure 4 obtained under the similar conditions but for different ionic strengths of the subsolutions shows that they coincide within the experimental scattering. Thus a hundred-fold increase of the ionic strength does not affect the static advancing and receding contact angles. Similar comparison of Tables I and I1 demonstrates that also at different values of +os and toL the increase of the ionic strength from 0.001 to 0.1 M does not change the contact angle values.
Discussion Our data, as other earlier investigations: show that the receding angles are more sensitive to the interfacial physicochemical properties than the advancing. This fact could be due to the different lower limits of the integrals in eqs 3 and 4. If the receding angles are large (as in our case), hl= ho, and the values of 6R are determined mainly by the large negative part of the disjoining pressure isotherm; see Figure 2. For this reason OR should be sensitive especially to the interfacial properties affecting the short range interactions as IIs and varying the position and the deepness of the II(h)minimum. Due to the larger value of h2 the integral in eq 4 is small and the advancing angles 6.4 are close to 90°, depending mainly on the long range interactions as IIvw and IIE. The 6 / x D dependences from Figure 4, together with the +o/XDdata from part 1, can be presented in the scale O/+o excluding XD. Thus a direct relationship between the measured advancing and receding contact angles and the experimental values of the electrostatic potentials of the interfaces can be obtained. This relationship, shown in Figure 5, is similar to the earlier observations for other model system^^-^ demonstrating that the contact angles decrease with the increase of the Gouy-Chapman potentials of the interfaces. On the other hand, the indepen-
Petrou et al.
210 Langmuir, Vol. 8, No. 1, 1992
r
Figure 6. Preexponential constant of the structural disjoining pressure KC, versus the molar part of the charged component XD: A, 0.001 M NaCl; 0 , O . l M NaCl subsolutions.
dence of OR and 6A on the ionic strength (Figure 4) and their insensitivity to changes of +oL, keeping +os constant (Tables I and 11), manifest the negligible contribution of the electrostatic disjoining pressure. These experimental results show evidence that the above correlation between 8~ and $0 is only apparent and cannot be considered as a proof of the effect of the electrostatic surface forces on the static contact angles and their hysteresis. According to ref 30 the van der Waals disjoining pressure is negative for similar Langmuir-Blodgett systems. The Hamaker constant is practically independent on the nature of the hydrophilic head groups of the deposited monol a y e r ~and ~ ~coincides within the scattering of the data with the values for hydrocarbons interacting through a water layer.31 Therefore the change of OR and AB = e A 8R with X D ,illustrated in Figure 4, is not due to IIvw(h) because the variation of XDaffects mainly the molar ratio of MA and DOMA hydrophilic heads, changing the density of the hydrocarbon tails only slightly. Thus the dependence of 8R on X Dcould be related only to changes of the structural disjoining pressure component IIs(h). Since the hydration force weakly depends on ionic strength,z3such an explanation correlates with our observation that OR and 6 A do not depend on the salt concentration of the subsolution. Using eq 10 and assuming lo to be 2.5A as for lipid bilayersz3and to remain constant with x13,~' we have proved this effect on the preexponential constant KOin eq 9. The mean normal dipole moment of the interfaces p I was estimated from the measurements of AV and $0 (part 1) according the formula32
pl,m is the mean normal molecular dipole moment in mD and F30 is the mean area per monolayer molecule at 30 dyn/cm in A2/molecule. AV and +O were taken in mV. The result presented in Figure 6 shows that the values ofKO for 0.001 and 0.1 M NaCl do not differ. The variation of KO with X D is due to the change of the mean dipole moments of the interfaces (all other quantities of eq 10 are kept constant) which do not depend on the ionic strength. The estimated KOvalues have the same order of magnitude as those obtained experimentally in many (30) Schulze, H.J.; Birzer, J. 0. Colloids Surf. 1987, 24, 209. (31) Israelachvili,J. N.Intermolecular and Surface Forces; Academic Press: London and New York 1985. (32) Schulman, J. H.; Hughes, A. H. Proc.R. SOC.London, A 1932,138, 430. (33) Kornyshev, A. A.; Leikin, S.Phys. Reu. A. 1989, 40, 6431.
other investigations of the hydration forces acting between lipid bilayer^.^^-^^ However, the values of the contact angles measured in this work are too large to expect such a determining role of the hydration force. As Derjaguin and Churaev statezz the hydrophilic repulsion is an important component of the force balance if 6.4 < 15'; when the advancing contact angle eA 1 64', the hydrophobic attraction plays a predominant role. We can check the contributions of the disjoiningpressure components quantitatively evaluating Bo on the basis of the eqs 1 and 6-10 and having in mind that OR I Bo I 6A. Unfortunately similar estimation df these contributions directly for the critical advancing and receding contact angles (eqs 3 and 4) is impossible because of the steepness of the nonequilibrium transition zone between the deformed meniscus and the wetting film' and the absence of any specification of the lower limits of integration hl and h2. As a consequence of eq 1 and eqs 6-10 it follows that
(+Os2 + +?')(cth
~ h -, 1) + Koloexp(-hollo) (12)
and
COS Bou - 1) = Ad127rh;
+ 8r sh Kho
The above equations represent the sum of the components of the specific free energy of interaction G, between the solid/liquid and the gadliquid interfaces in the three phase contact zone. The first term on the right-hand side stands for the van der Waals component Gvw,the second terms are the electrostatic components at boundary conditions of constant potential G& (eq 12) and constant charge Gi (eq 131, and the third term relates to the contribution of the repulsive (hydration) structural interactions. The obtained values of Gi are shown in Table I11 at three arbitrary (small) values of h0.39 They confirm qualitatively our experimental observations: for ho = 5 and 10 A, GE is about an order of magnitude smaller than GVWand 1.5-2 orders of magnitude smaller than Gs and its variation with the ionic strength and +oL (at constant +os) does not affect the total value of G and the contact angles. On the other side the quantitative comparison of cos Both with the value of cos ORexP = 0.515, corresponding to the experimental conditions of Table 111, manifests a strong disagreement between theory and experiment. Different reasons for such a discrepancy could be considered: (1) The steep character of the transition zone and inapplicability of eqs 1 and 6-10. Previous publication^,^^^^ have applied the FrumkinDerjaguin theory for angles up to 50' without any (34) Simon, S. A.; McIntosh, Th. J.; Magid, A. D. J.Colloid Interface Sci. 1988, 126, 74. (35) Dzhavakhidze, P. G.;Kornyshev, A. A.; Levadny, V. G.Nuouo Cimento SOC.Ital. Fis, D 1988, lOD,627. (36) Parsegian, V. A. Ado. Colloid Interface Sci. 1982, 16, 49. (37) Lis, L. J.; McAlister, M.; Fuller, N.; Rand, R. P.; Parsegian, V. A. Biophys. J. 1982, 37, 657. (38) Rand, R. P.; Das, S.;Parsegian, V. A. Chem. Scr. 1986, 25, 15. (39) According to the experimental results of Okahata (Okahata, Y.; Agira, K. J. Chem. Soc., Chem. Commun. 1987,1535.) about the residual water in multilayers of cadmium arachidate, ho = 7 A for this system. (40) Churaev, N. V. Physical Chemistry of the Mass-transport Phenomena in Porous Media; Khimia: Moscow, 1990, p 227 (in Russian).
Effect of Surface Forces on Contact Angles
Langmuir, Vol. 8, No. 1, 1992 211
Table 111. Components of the Specific Gibbs Energies of Interaction in the Three-phase Contact Zone and the Calculated Values of Bo for a Mixed Monolayer of XD = 0.023: 7 = 42.5 dyn/cm, A0 = 6 X 10-14dyn cm, KO= 1.6 X 109 dyn/cm, 10 = 2.5 A, CO = 0.1 M NaCl, $os = $oL = 27 mV, ~ - 1= 9.5 A
cos 00th cos 00th boundary Gvw, GE, Gs, (VW+ (VW+ ho,A condition dyn/cm dyn/cm dyn/cm EL+S) EL) 5 $0 = const -0.637 0.032 5.413 1.113 0.986 a0 = const -0.637 0.125 5.413 1.115 0.988 10
20
a0
= const = const
-0.159 -0.159
0.022 0.047
0.733 0.733
1.014 1.015
0.997 0.997
$0 a0
= const = const
-0.040 -0.040
0.009 0.012
0.013 0.013
1.OOO
0.999 0.999
$0
1.OOO
comments of the requirement of the theory for a shallow meniscus-film transition zone which is fulfilled only for small contact angles. Unfortunately the rigor of this restriction cannot be discussednow because of the absence of a more general theoretical solution. (2) Overestimation of the positive IIs due to incorrect calculation of KOor improper value of lo. If one takes into account only the head group dipole moments,4l a lower value of KO = 3.12 X lo7 dyn/cm2 is evaluated from eq 10 for the LB system considered in Table 111. This gives cos eoth = 0.99, which is also far away from the experimental value of cos ORexp = 0.515. The effect of the repulsive hydration force is directly demonstrated by the last column of Table 111,where the estimation of cos eoth only on the basis of GW and GE is presented. Such an estimation shows that the theoretical values obtained are also much higher than cos 6Rexp. The above analysis proves that in the framework of the Frumkin-Derjaguin model used, realistic values of cos eoth could be obtained only if the attractive force is much greater. Sincethe constants b, c, and d in eq 6a are positive, the value of GVWin Table I11 (obtained with A0 but not with A(h))may be overestimated and the real van der Waals contribution may be still lower. Therefore another non van der Waals and nonelectrostatic attractive force should be responsible for the observed difference. The hydrophobic attraction between the methyl groups of the hydrophilic heads of MA and DOMA (Figure 7), that has been neglected in the disjoining pressure analysis, could be the lacking factor. It is well-known that such negative structural disjoining pressure is much stronger than the positive At the same time its inclusion as a fourth term in the force balance in eq 5 is impossible because the hydration and the hydrophobic forces are not a d d i t i ~ e . ~For ~ ?this ~ ~ reason the complete quantitative solution of the problem requires further development of the theory for a steep transition zone as well as better description of the structural interactions of interfaces containing both hydrophilic and hydrophobic functional groups.
Appendix One of the reviewers has drawn our attention to the possibility of interpreting the results of this investigation on the basis of the paper of Fokking and Ralstont3 presenting another (thermodynamic)consideration of the variations of the contact angles with changes in electrostatic properties of the solid/liquid interface. The main (41) Vogel, V.; Miibius, D. J. Colloid Interface Sci. 1988, 126,408. (42) Israelachvili,J. N.;Pashley, R. M.J. Colloid Interface Sci. 1984, 98,500. (43) Fokking, L. G.J.; Ralston, J. Colloids Surf. 1989,36,69.
Figure 7. Molecular models of the monolayer components: methyl arachidate (MA) and dimethyldioctadecylammonium bromide (DOMA).
idea is that the interfacial free energy of the charged , be presented as a sum of two terms: interface, y s ~ can the free energy of the same interface, but in a neutral state, ys~O,and the energy of the double layer formation, Wdl.
Expressing the second term on the right-hand side as
and substituting both equations in Young's equation, the authors obtain the theoretical relationship between 60and such electrostatic properties of the solid/liquid interface as a$ and $os (A.3) Here 00 and eo,,, are the contact angles for the charged and the neutral interfaces. An excellent agreement between the theory and the experimental results of Ottewill et al.7 for the system AgI/ Ag+ solution/air has been obtained, without any free parameters. The above consideration neglects the formation of a double layer at the liquid/gas interface and its influence . could be grounded for inorganicsalt solutions on y ~ v This without surfactants where y ~ = v ~ L V O even at high salt concentration. In the Langmuil-Blodgett systemsstudied, the liquid/gas interface consists of the same (or similar) monolayer hydrophilic groups and it has the same (or similar) electrostatic properties as the solid/liquid one. However, the surface pressure a and the surface tension y ~ are v kept constant during the deposition of all DOMA/
Petrov et al.
212 Langmuir, Vol. 8,No. 1, 1992 MA mixtures. Thus in our experiments y ~ was v independent of uoL and $oL; when uoL and $oL changed the automatic servodevice of the Langmuir through responded with a change of the monolayer area to maintain ~ L = V constant. The later enables the formal application of eq A.3 also to our results, making use of the experimental ao/$o data available for the system considered. Figure 8 shows the theoretical dependences of the contact angle 00 as a function of the molar part of the charged component XD.Curve 1is plotted for 0.1 M NaCl and curve 2 for 0.001M NaCl subsolution. A graphical integration of the UO/$O data from Figure 8 of part 1has been performed for their calculation and the relationship between uo and XD was taken into account. Our experimental data for OR vs XD on 0.1 and 0.001 M NaCl subsolution are also presented in Figure 8. The theoretical trend following from eq A.3 is qualitatively similar to the experimental one. The independence of OR on the ionic strength is also well explainable: The maximum difference between curves 1 and 2 is 3O, which is less than the experimental scattering of our data. However, the predicted dependence of 00 on XDis much weaker than the observed one. This discrepancy could in principle be due to neglecting the interaction between the solid/liquid and the liquid/ gas double layers in the three-phase contact zone, but such an explanation contradicts our experimental observation. Another reason which, we believe, gives greater contribution is the variation of the dipole potential together with $0. Such a variation leads to the fact that cos e,,,,, in eq 3 (being a measure of the interaction of the solid surface with water, of its hydrophobicity) is not more a constant but changes with XD,i.e. with uos and +os.
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XI, Figure 8. Theoretical dependence of the equilibrium contact angle 80 on the molar part of the charged componentXDcalculated on the basis of eq A.3: curve 1 (0.1 M NaCl) and curve 2 (0.001 M NaCl). The experimental values of OR are shown by circles and triangles for 0.1 M NaCl and 0.001 M NaCl subsolutions, respectively. As our experimental data from part 1(Figures 8 and 9) suggest, the interfacial dipole potential is about an order of magnitude higher than that of the Gouy-Chapman one. The same conclusion has been reached also by some latest theoretical consideration^.^^ This dipole field determining the water structure near the interfaces could be the major factor regulating the values of the contact angles. Registry No. Methyl arachidate,1120-28-1;dimethyldioctadecylammonium bromide, 3700-67-2.
