Theory of contact angles

Young was the first to describe contact angle equilibrium, in 1805. The vectorial summation of forces at the three-phase intersection point (the so-called three-phase contact point) gives 

It is also possible to derive the Young s equation from thermodynamical considerations. The displacement of the contacting liquid is such that the change in area of a solid covered, AA, results in the change in surface free energy  

At equilibrium, when the interfacial area goes to zero at the limit 

The (A6IAA) term behaves as a second-order differential and drops out in taking the limit of AA — 0, so one obtains from Equation (641) 

Equation (643) is identical to Young s equation, as given by Equation (640). 

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The wetting behavior of polymers is reviewed beginning with the thermodynamic conditions for contact angle equilibrium. The critical surface tension of polymers is discussed followed by some of the current theories of wettability, notably the theory of fractional polarity and theories of contact angle hysteresis. The nonequilibrium spontaneous and forced spreading of polymer liquids is reviewed from two points of view, the surface chemical perspective and the hydrodynamic perspective. There is a wide di.sperity between these two viewpoints that needs to be resolved inorder to establish the predictive relations that govern spreading behavior. 

Good, R. J. and van Oss, C. J., The modern theory of contact angles and the hydrogen bond components of surface energies, in Modern Approaches to Wettability - Theory and Applications, Schrader, M. E. and Loeb, G. I. (Eds), Plenum Press, New York, 1992, pp. 1-27. 

The theory of Good and Girifalco is easily derived We will review the theoretical basis here, in order to introduce a contribution to the theory of contact angles which has not been published heretofore. 

The wettabiHty theory of adhesion is iaextricably related to the study of contact angles of Hquids on soHd surfaces. A force balance at the poiat of contact between the Hquid and the soHd can be written (3)... 

Given the importance of surface and interfacial energies in determining the interfacial adhesion between materials, and the unreliability of the contact angle methods to predict the surface energetics of solids, it has become necessary to develop a new class of theoretical and experimental tools to measure the surface and interfacial energetics of solids. Thia new class of methods is based on the recent developments in the theories of contact mechanics, particularly the JKR theory. 

Several theories have been formulated in order to explain the difference between the state of the adsorbate during adsorption and desorption. For example, Zsigmondy postulated that hysteresis was caused by a difference of contact angle during adsorption and desorption. 

A number of chapters have been overhauled so thoroughly that they bear only minor resemblance to their counterparts in the first edition. The thermodynamics of polymer solutions is introduced in connection with osmometry and the drainage and spatial extension of polymer coils is discussed in connection with viscosity. The treatment of contact angle is expanded so that it is presented on a more equal footing with surface tension in the presentation of liquid surfaces. Steric stabilization as a protective mechanism against flocculation is discussed along with the classical DLVO theory. 

Examination of the relevant theory indicates that the adjuvant effect of surface-active agents on herbicide action is maximized when the quantity FI = yL cos 0, or the film pressure at the liquid/solid interface, has a maximum value. Measurement of surface tension of 1.0% aqueous solutions and of contact angle on a number of substrates (Teflon, paraffin) and plant-leaf surfaces (soybean, com) as a function of hydrophile-lipophile balance show at least one maximum, and these values are in good agreement with earlier experimental data on herbicidal activity. 

Other discrepancies between the black film behaviour and DLVO-theory are related to the difference in the critical electrolyte concentration, corresponding to the transition between the two black films types (see Section 3.4.2) the existence of a second minimum in the 11(A) isotherm the sharp rise in the disjoining pressure (after the second minimum). All this is evidenced by the measurements of contact angles between the film and bulk phase. 

Current theories to explain hysteresis of contact angles are primarily based on the concepts of surface roughness, surface heterogeneity, friction, and adsorption phenomena. Unintentional adsorption, or contamination—the result of inadequate experimental technique—is, however, the most frequent explanation. As all systems involving solids are subject to the reasons indicated above for hysteresis, we chose the system mercury-benzene-water, which should be affected only by adsorption phenomena, controllable under proper experimentation. An additional advantage is the fact that all interfacial tensions involved can be measured. 

The non-slip boundary condition is discussed in an excellent paper by Huh and Scriven They take note of the fact that, previous workers seem not to have been well informed by fluid mechanics , in aUuding to the essentially surface chemical analyses of spreading dynamics. Another point they address is that except for very smooth surfaces and non-adsorbing hquids the advancing or receding of the contact line proceeds in a slip-stick and discontinuous fashion a fact which is the focus of attention in current analyses of contact angle hysteresis using the theory of random fluctuations... 

The correlation of pull-off forces with the cosine of contact angles measured with water clearly showed the applicability of this approach for various polar pol3uners (66,85). For apolar pol5miers, for example, the Lifshitz theory can be successfully applied to predict the chemical contrast. Feldman and co-workers demonstrated this powerful quantitative approach for different pol5miers probed with gold-coated and silicon oxide coated tips in perfluorodecalin (86), in which the dispersive van der Waals interactions are selectively amplified (see section Surface Forces and Energies). 

In a large part of the (current) literature the Lifshitz-van der Waals component (o, is simply termed dispersion component and the Lewis acid-base interactions (o ) are interpreted as polar interactions even though the material s dipole moments may be zero or the interactions originating from permanent dipoles are very small and can be easily associated with the dispersion part [6]. The misleading denominations go back to a historical misidentification of the acid-base interactions as polar interactions in the Owens-Wendt-Rabel-Kaelble [7-9] approach to calculate the IFT [6] (OWRK model). However, as an impact on the SFE calculation by this misinterpretation of this old theory occurs only when a monopolar base interacts with a monopolar acid, this nomenclature is still widely used. And here in this work we will also use the terms dispersion and po/ar interactions to differentiate the two major contributions to SFE, ST, and IFT. For a detailed discussion of the use of contact angles in determining SFE of solids and other methods of determining SFE, see Etzler [10]. 

Such analysis is based on the theories presented in this chapter, the concept of the contact angle and the associated Young equation discussed in Chapter 4. The analysis of solid interfaces and its application in understanding wetting and adhesion will be illustrated in Chapter 6, after the concept of contact angle is presented in Chapter 4 and surfactants in Chapter 5. Theories for interfacial tension wiU be discussed in more detail in Chapter 15. 

The second approach is particularly usefid and builds on the theories of interfacial tensions (Chapter 3) and concepts of contact angle/Young equation (Chapter 4) presented previously. When these theories are applied to solid-liquid interfaces and combined with Young s... 

The various approaches motioned previously in this chapter can be used to estimate the surface tensions, e.g. of various polymers. Thus, polymer surface tensions have been reported using interfacial theories and contact angle data, from the critical surface tension (Zisman plot) and from extrapolating melt data to room temperature. There is relatively good agreement among the various methods for many polymers, within 4—5 mN m Some typical results are shown in Table 6.5. 

Problem 6.2 Characterization of a PVC surface with the Owens-Wendt theory The contact angles of water and methylene iodide have been measured on a PVC (poly(vinyl chloride)) surface to be equal to 87° and 36°, respectively. The surface tension of water is at 25 °C equal to 72.8 with a dispersion part equal to 21.8. For methylene iodide, the surface tension is 50.8, and the dispersion part is 49.5. All surface tension values are in mN m. Assuming the validity of the Owens-W endt theory, calculate the surface tensions (total, dispersion and specific) of the sohd PVC surface and comment briefly on the results. 

Show that in the case of the Girifalco-Good theory the contact angle is related to the solid surface tension via the following equation ... 

The basic theory of wetting is reviewed, covering the concepts of contact angle and polymer surface and interfacial tensions. The necessity of taking into account the interactions between interfaces in the three -phase region is stressed. 

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