The forces determining the stability of thin wetting films of solutions with nonpolar solvent

Aduaraces in Co&id and Merface Science, 37 (1992) 177-193 Elsevier Science Publishers B.V., Amsterdam

177

THE FORCES DETERMINING THE STABILITY OF THIN WJZTTING FILMS OF SOLUTIONS WITH NONPOLAR SOLVENT L.B. BOINOVICH

institute of Phy~~~u~~he~~t~y of the USSR A~~~~y prospect 34117915 Moseo w, USSR

ofSciences, ~eni~~y

CONTENTS Abstract ......................................... 1. Introduction ..................................... 2. The Lifshitz Theory of the Molecular Component and its Experimental Confirmation. .................................... ... 3. Theories of the Adsorption Component and Comparison with Experiment 4. “Structural” Component - Experimental Results ................. 5. The Steric Component ................................ 6. Deviations from Theoretical Predictions as a Result of the Non-ideality of the System under Investigation ............................. 7. Conclusions ..................................... References ........................................

177 177 178 181 185 187 189 192 192

ABSTRACT This paper discusses the conditions of stability of thin wetting films of solutions with nonpolar solvent and forces acting in these films. Since in the solutions with a nonpolar solvent the basic contributions are made by the molecular, the adsorption, the structural, and the steric com~nen~ of disjoining pressure, only these components are considered in detail. The results of recent experimental works, which examined the deviations from the theoretical predictions as a result of the non-ideality of the system, are represented.

1. INTRODUCTION

The wetting films of solutions containing a nonpolar solvent are of interest for practical applications and for the investigation of the nature of long-range surface forces. Fundamental research in this field was initiated by Derjaguin R-61 who showed that the overlapping of transition zones between an interlayer and phases, which arises as a result of the isothermal approach of the volumes of two phases, causes a change 0001~868~92/$15.00

0 1992 - Ekevier Science Publishers B.V. All rights reserved.

178

in the Gibbs free energy. In the case where the overlapping occurs in a plane-parallel interlayer, the interaction is unambiguously characterized by a change in the pressure within the interlayer with the pressure in the bulk phase of which the interlayer forms a part. That excess pressure is called the disjoining pressure [l-61. Its value, which depends on the extent of overlapping, is a thermodynamic characteristic of this liquid interlayer:

n0

(1)

= -W/W

where G is the Gibbs energy per unit area of the film. The partial derivative is calculated such that all other parameters (except the thickness H) determining the free energy of the film remain constant. The known condition of stability of the wetting films follows from Eqn (1) [4] dWdH
(2)

Hence, in order to analyze the stability of wetting films of a certain composition requires that the components of disjoining pressure, their values, and the character of change with the film thickness are analyzed. At present six components of disjoining pressure are identified in scientific literature: molecular, electrostatic, structural, adsorption, steric, and electronic 161. Since in the solutions with a nonpolar solvent the basic contributions are made by the molecular, the adsorption, the structural, and the steric components, only these components will be considered in detail. 2. THE LIFSHITZ EXPERIMENTAL

THEORY

OF THE MOLECULAR

COMPONENT

AND ITS

CONFIRMATION

The molecular component of disjoining pressure is determined by the dispersion interaction forces between bodies. A general macroscopic theory of the molecular component of disjoining pressure was initially developed by Lifshitz and co-workers [7,81, and was applied to the investigation of the properties of liquid films in various works [9,101. The formula for the disjoining pressure of a liquid absorbing interlayer 3 between solids 1 and 2, as deduced in Refs [9,101, has the following form:

179 (S, + PE&W2

+ PE&

61

- Py&)

- Pq/~gw~

exp[@j%+l~jp%p

(3)

where h is Plan&s constant, c is the velocity of light in a vacuum, Sj = K&j/Es) - 1 + p2P2, and sj (j = 1,2,3) is the dielectric permittivity of the medium as a function of the imaginary frequency w = ic. Analysis of this expression shows that for the wetting films the value of II, may be positive or negative, and is determined by the relationship between ej (&) where (j = 1,2,3) in the entire frequency range. In other words, the molecular component of disjoining pressure in such a film can either enhance the stability or cause the film to rupture. The practical application of Eqn (3) is difficult because of the lack of knowledge of the total frequency spectra of dielectric permittivity and the necessity for infinite summation. Therefore, a great deal of simplifications of that formula exist. Here we note only two simplifications that are most used in practice. When the thickness His smaller than the characteristic wavelengths, h, of the absorption spectra of interacting bodies (H < < h/2x) the molecular component of disjoining pressure may be written in the following form

[61: II = -A/6KH3

(4)

In this case, the interaction force proves to be proportional to the cube of the distance between bodies which is in agreement with the interaction law derived by Hamaker 1111 by the additive summation of London interaction forces. The constant A depends on the nature of interacting bodies through the frequency dependence of their dielectric permittivities. In the opposite case, i.e. large distances where H > > h/2x, Eqn (3) can be transformed into the following expression:

II = -BIH4

(5)

Now the interaction constant B is dependent only on the static values of the dielectric permittivities. We note that the films of one-component nonpolar liquids provide a convenient model for studying the molecular forces, and are repeatedly investigated in experiments. Thus, good agreement with the law II = 1/H3, within the range of thicknesses in which retardation is insignificant, was obtained for the films of liquid helium on the atomically smooth cleavage

180

faces of crystals [121,for tetradecane films on the surface of freshly-drawn quartz capillaries and on mica (Fig. 1)113-151, for alkanes on the surface of glass (Fig. 21 and quartz [l&303, of mica and steel I173 and on the surface of water fl.81. In this case, the order of magnitude (1W20 N ml of the obtained values of Hamaker constants agree with those predicted theoretically.

Fig. 1. Isotherms ofthe disjoining pressure af wetting filmsof tetradecane 0.1 and hexane (2) vn mica UT1_The Hamaker constant for films of tetradecane on mica, determined from these data, isA = -5 * 1K2’ N rn.

Investigation of thick h~d~~carbo~ films has demonstrated that the isotherms of disjoining pressure satisfactorily obey the law, corresponding to the retardation forces B/?$ for tetradecane films on steel: glass, sapphire and mica V$> 20 nm) f171, for n-heptane and cyclohexane films on steel about 40 to 80 nm thick and for n-octane and n-decane films on aluminium about 30 to 80 nm thick [19,201. Figure 3 represents some of the experimental results, The obtained values ofB are in good agreement with the theoretically calculated values and are of the order of 1W2s N m2_ The molecular component of the disjoining pressure in solution films can be calculated using the same relationships (Eqns (l-3)). The calculation, however, involves using the absorption spectra of solutions It must be noted that calculation with Eqn (11 implies uniform distribut,ion of the solution components throughout the film thickness. It is obvious that the nonuniform distribu-

181

a.7

as

a.3

Fig. 2. Isotherms of the disjoining pressure of wetting films of heptane on glass film-substrate. For the equation l-I = -A/6& experimentally determined values are: n = 3 2 0.04; A = -1.75 * 10m2’ N m.

tion of components throughout the film thickness might result from differences in the interaction energies of the different kinds of molecules with the surfaces confining the film. 3. THEORIESOF THE ADSORPTIONCOMPONENTAND COMPARISON WITH EXPERIMENT Firstly, we consider a simpler case where the solution components are nonpolar. This case was theoretically investigated by many researchers from different standpoints. Ash, Everett and Radke [Zll, and Derjaguin, Churaev and Starov ~2%241 applied a thermodynamic approach. Derja-

182

Fig. 3. Isotherms of disjoining pressure of wetting films of tetradecane [171;heptane (3) and cyclohexane (4) on steel [191.

on steel (1 and 2)

guin and Churaev have developed a theory of the adsorption component of disjoining pressure of ideal solutions. The theory allows the influence of the second component to be predicted using only the macroscopic characteristics of the components. The theory does not permit the calculation of the adsorption component of disjoining pressure only, but affords a possibility to obtain an expression for the total disjoining pressure in the film: A2 hTx3

A3 +

kT(Eht~)~

(6)

where A is the Hamaker constant for a pure solvent, A, and A3 are the interaction constants of the solute molecules with the film interfaces, Co is the solute concentration in the bulk phase, Vis the molecular volume of the solvent, k is the Boltzmann constant; and T is the temperature. Equation (6) enables the disjoining pressure in an interlayer of an ideal solution with all the energies of interaction of the solute molecules with interfaces to be determined, while neglecting the adsorption of the solute in a monolayer having thickness 6 and the influence of that monolayer on the interaction of molecules with the surfaces confining the interlayer. In the case of low interaction energies, when UtH) < < kT, and thicker films~ > > 6 (where the electromagnetic retardation effect can be ignored) Eqn (6) can be rewritten as:

183

I-w=-&+

Co@,+A3) W&6)3

const =-$-

(7)

An analysis of Eqns (6) and (7) indicates that the addition of solute can either increase or decrease the stability of the solvent wetting films depending on the relationship between the dielectric permittivity values e(E’ZJ of the solvent and the substrate, and also the solvent and the solute used. The calculation made on the basis of a macroscopic approach indicates that the effect of the adsorption component may be noticeable in the range of thicknesses H < 5 nm. The microscopic approaches using the molecular statistics method were developed by Kunyi, Rusanov and Brodskaya I251, and Chan, Mitchell, Ninham and Pailthorpe [261. For the case of the potential of intermolecular forces, whichis proportional to l/r6 (where r is the distance between molecules), the results obtained in Refs 125,261give an expression of the following form for the dependence of II on the film thickness:

where the first term describes the dispersion interaction of the media confining the interlayer through a uniform solution film, while the second term takes into account the nonuniformity of the film in relation to its composition and structure. A combined macroscopic and microscopic approach was developed by Vasiliev, Toshev and Ivanov [27,281 for the case of strictly regular solutions. A few works concern the experimental investigation of the wetting films of solutions with both nonpolar components. An analysis of the available experimental data [16,29,301 does not enable one to confirm quantitatively any of the theoretical approaches used. The qualitative influence of the addition of the second component (the weak dependence of the film thickness on concentration, and the sign of a change in thickness -whether an increase or a decrease), however, is in agreement with the predictions of the theory of the adsorption component of disjoining pressure. Figure; 4 and 5 show the dependence of film thickness on solute concentration for solutions of pentane in hexane (Fig. 41, and for carbon tetrachloride in heptane ‘(Fig. 5) 1301. Solutions of polar substances in nonpolar solvents were considered in Ref. [311. The presence of a dipole moment should bring about a change in the adsorption component of disjoining pressure, because now the redist~bution of components across the film thickness is determined not only by the dispersion forces of interaction with interfaces, but also by

184

HI A 11YO-o

O

0

00

0 8

0 -*-

-

00

6 .

Fig. 4. Thicknesses of wetting films of pentane solutions in hexane on glass film-substrate versus concentration, II = 5.7. lo5 N rnm2.

Fig. 5. Thicknesses of wetting films of carbon ~trachloride solutions in hexane on glass film-substrate versus concentration under the disjoining pressure 5.1’ lo5 N mm2(&; 1.3 1lo5 N m-* CO).

the image forces. By taking into account the image forces Eqn (6) becomes:

l-w=-&+

Cop2 V(H- 6)s - 16 * T/* tzl ’

Co@, +A3)

in + U(Pl2

l

(313)

[(n + 1)H aI3

4312

-

+ P13)

QtH + Sj3 -

4l312/313@f

- 36)

(n + fJ3p

(9)

where p is a dipole moment of the solute molecule, rjii= (.si- E$/(E~+ &j> and sj are the static values of the dielectric permittivities of the interlayer and the media confining the interlayer. An analysis of Eqn (9) however, indicates that the term associated with the presence of a dipole moment of dissolved molecules, which is additional to the one in Eqn (61, will be comparable with the contribution of the molecular component only with very great values of the dipole moment p > 10 D. In the case where p is of the order of 1-2 D the ~nt~bution of that term to the total disjoining pressure is negligibly small (Fig. 6). In contrast, the available experimental data on the investigation of the wetting films of the solutions of polar components in nonpolar solvents indicate the strong influence of polar additions on the values of equilibrium film thicknesses [16,19,30,321, 4. “STRUCTURAL”

COMPONENT

-

EXPERIMENTAL

RESULTS

The analysis carried out in Ref. I161indicates that none of the theories taking into account the film nonunifo~ity both with regard to its imposition and to its structure, adequately describe the experimentally observable effects. The objective laws that are identified in the course of the experimental investigation of the films of the solutions of polar substances in nonpolar media consist of: (a) the noticeable influence of very small (in the order of 0.001 iW proportion) concentrations of polar additions; (b) the influence of those additions - the influence is greater the larger the size of a molecule of solute and the smaller the initial film thickness; (c) on reaching a certain concentration, the thicknesses of solution films cease to depend noticeably on their composition. Figure 7 shows an example of such systems revealing such laws. The data represented here are obtained at a large value of II and with small film thicknesses. However, similar effects were observed in the heptaneorganic acid systems investigated by Kusakov and Titievskaya iI91 even in sufficiently thick films and under low disjoining pressures. The laws thus observed indicate the effect of a new component of disjoining pressure in addition to the molecular and adsorption component in the films of the solutions of polar substances in a nonpolar solvent. This component is probably associated with collective excitations in the film of nonpolar solvent under the effect of a solute in the presence of a wall, which can lead to static and/or dynamic structuring, and is therefore called the structural component. An analysis of the experimental data indicates that this component, IIs, depends exponentially on

186

HI A

b

Fig. 6. Components of the disjoining pressure for wetting films of solutions on dielectric substrate with a solute dipole moment (a) p = 1.5 D; (b) p = 10 D. The concentration of solute molecules is 0.01 mole proportion. (1) contribution of image forces; (2) adsorption component of disjoining pressure; (3) molecular component of disjoining pressure.

thickness: IIs = K * exp (-H/L) where the pre-exponential factor substantially depends on concentration, while the correlation length L is of the order of the size of a solute

molecule. For example, for pentanol solutions in heptane L = 0.5 nm. The above-mentioned data indicate that the stability ofthe films of the solutions of polar substances in nonpolar solvents is determined by the molecular, the adsorption, and the structural component of disjoining pressure. The contributions of different components depend both on the concentration of the solute and on the film thickness (Fig. 8). A number of theories on the structural component have been published, but all of them conemn W&W or water so&ions, taking into account the specific features ofa~ueo~s media, Hence, they cannet be applied for the description of solutions with nonpolar solvent. 5. THE STERICCOMPONENT To investigate the films of surfactants and polymers in nonpolar solvents it is necessary to take into account the steric component of disjoining pressure. The latter arises as a result of the interaction of the adsorption layers of surfactants and polymers when they overlap. The mechanism of formation of the steric component of disjoining pressure which is described in the literature may be s~mar~~ed as: (1) the elastic repukion of the adso~t~on s~rfac~~t layers owing ta their mechanical

188 ilu

80 78 68 54 49 39 29

e

‘\

‘\

‘Y. ;w__--

_...---

-5

_--

18

26

22

24

2

_____-___------*--._

26

._

__

28

----f-.-e_

3t

_.

32

34

,_*

36

Hr R

Fig. 8. Contributions of different components of disjoining pressure for wetting films of solutions C7H1s - CBHIIOH versus film thickness for the concentration of solute molecules: taf 0.65 . 10" mole proportion; (b) 2.69 . lop3mole proportion. (1) molecular component of disjoining pressure; (2) adsorption component of disjoining pressure; 43) “structural” component of disjoining pressure.

strength; (2) the effects associated with the interaction of the chains of polymeric molecules in the course of their mutual overlapping (e.g. the entropy repulsion, bulk limitations, orientation limitations). The first mechanism was formulated by Rebinder 1331 in order to explain the enhanced suitability of colloids in the course of their stabilization by surfactants. As regards the second mechanism, to calculate the steric component under conditions of the mutual interpenetration of the chains of adsorbed molecules a great number of factors must be taken into account: conformation and elastic properties of those molecules,

189

interactions of the links of molecules with one another and with interfaces, the distribution of the electron density along a chain, the kinetic effects associated with the slowness of the rebuilding of the structure of adsorbed layers during overlapping, etc. This hinders the development of the rigorous theory of the steric component of disjoining pressure. Different theories of the steric component, using a number of simplifying assumptions, were developed by Mackor and co-worker [34,351, Vold 1361, Vincent and co-workers 137,381, Hesselink 1391, Napper and co-workers [40,413, Wendel 1421, and Kurilo and Glavati 1431. A detailed review of these theories was performed by Tadros [441. Systematic investigations of the steric component in wetting films were not carried out. However, the experimental data gathered on the investigation of the steric component in symmetric interlayers [45-511 indicate that the contribution of the steric component to the total disjoining pressure in the films of the solutions of macromolecules in nonpolar solvents can be significant. In this case, as distinct from the adsorption component of disjoining pressure, the effect of the steric component can be seen at a distance of the order of hundreds of nanometers. 6. DEVIATIONS FROM THEORETICAL PREDICTIONS AS A RESULT OF THE NON-IDEALITY

OF THE SYSTEM UNDER INVESTIGATION

The theories and methods for calculation of the components of disjoining pressure described above were developed by assuming ideal interfaces and strictly determined systems. However, both in experiment and in practice we generally have to deal with systems whose investigation is complicated by factors such as roughness, transition layers, impurities, etc. which are difficult to control. It is obvious that the appearance of such factors must cause deviations between the experimentally determined values and the theoretical values which are calculated by using ideal models. Thus, for n-decane films of thickness > 2.5 nm, on the oxidized aluminium surface 1521 a deviation from the inverse cube law was detected. The films of benzene, carbon tetrachloride, n-octane, and cyclohexane on the gold-coated piezoquartz surface have been investigated [531. In this case, good agreement with the inverse cube law was obtained only for film thicknesses < 3 nm. For larger film thicknesses (3-17 nm), a dependence of the form D = K/X-P was observed where n varied from 1.94 to 2.26. Good agreement with the inverse cube law was obtained by Wade and Slutsky I541 for n-heptane films on piezoquartz, and by Boinovich 1301 for n-hexane on K-8 glass. However, the experimental values of Hamaker constant exceeded the theoreti~lly predicted value

190

by more than an order of magnitude. The authors also relate this fact to the effect of roughness. The influence of roughness on molecular forces is not striking: it was theoretically predicted by Van Bree et al. [%I, and Starov and Churaev 1561, as well as by others. In the work by Boinovich 1301and Ingram W7l attempts were made to confirm experimentally the influence of roughness on the deviation ofthe isotherms of disjoining pressure from that theoretically predicted. It has been shown 1573 that for quantitative agreement between the experimental dependence of hydrocarbon films on quartz and that predicted by the theory of molecular forces, it is necessary to assume the existence, on quartz, of a surface layer having a modified density and a bottle-shaped surface. As was shown by Boinovich I301 for n-hexane films on glass substrates, the joint action of substrate roughness and polar impurities leads to the

8.8

8.6 8.4 8.2

Fig. 9. Isotherms of disjoining ressure of wetting films of hexane on: (1) polished substrate,A = - (8.8 + 0.2) . 10 IB N m; (2) smooth film-substrate produced in damp air, A = - (2.52 0 .4).10-20 N m; (3) smooth film-substrate produced in dry nitrogen, A = (8.8 f 2 .2) . 10W2’ N m.

191

conclusion that the isotherms of disjoining pressure satisfactorily obey the law of inverse cubes (Fig. 9), but the value of the Hamaker constant decreases with decreasing surface roughness and decreasing quantity of polar impurities. Thus, for the case of a polished substrate having a roughness of about 5 + 2 nm and also traces of water, the observable Hamaker constant exceeds the theoretical value by more than one order of magnitude. At the same time, on a smooth substrate of the same composition which also has traces of water (film-substrate [161 produced in damp air) the Hamaker constant becomes lower. Finally, for the case of a smooth film-substrate produced in dry nitrogen the Hamaker constant obtained from the experiment is close to the theoretically calculated value. The roughness and surface admixtures influence not only the law of change in disjoining pressure with the film thickness at a constant concentration, but also the character of the influence of additions of the second component (nonpolar one) on the stability of films of a nonpolar solvent. This effect was observed t301 for a hexane-pentane system on

H Cnrl

7

-

6

9

5

-

4

-

3

-

Fig. 10. Isotherms of disjoining pressure of wetting films of hexane (0) and solutions of pentane in hexane, with a mole proportion of solute molecules CA) 5% and (+I 20%.

192

polished glass (having roughness up to 5 nm) in the presence of water traces (compare Fig. 10 with Fig. 3), and for a heptane+arbon tetrachloride system on the molecular-smooth substrates in the presence of acetone vapours 1301. 7. CONCLUSIONS From the previous discussion, it follows that not all the experimental laws of behaviour of the wetting films of the solutions of nonpolar components can be satisfactorily explained. The mechanism of the formation of the structural component of disjoining pressure in nonpolar media is still not fully clear. The systematic investigation of the steric component in the wetting films of the solutions of macromolecules in solvents is also of great interest. REFERENCES 1

7 8 9 10 11 12 13 14 15 16 17

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