Langmuir 2004, 20, 1317-1320
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Adhesion and Wetting in an Aqueous Environment: Theoretical Assessment of Sensitivity to the Solid Surface Energy Abraham Marmur* Department of Chemical Engineering, Technion - Israel Institute of Technology, 32000 Haifa, Israel Received October 13, 2003. In Final Form: December 3, 2003 The sensitivity of contact angles in an aqueous environment to the surface energy of the solid is discussed. It is demonstrated that this sensitivity is much higher in an aqueous than in a vapor environment. The Girifalco-Good equation, in combination with the Owens-Wendt equation, is used for the approximate demonstrations. It is shown that the transition from complete wetting to complete dewetting by the aqueous phase in a solid-liquid-liquid system occurs over a much narrower range of the surface energy of the solid than in a solid-liquid-vapor system. It is also demonstrated that the contact angle may be extremely sensitive to small variations in the relationship between surface tensions and the corresponding interfacial tension.
Introduction Adhesion in an aqueous environment is of utmost importance in medicine, biology, and industry (e.g., refs 1-9). Adhesion of blood cells to various tissues or to artificial surfaces is the key to both life-saving and lifethreatening processes; suture replacement by tissue adhesives is an important medical need; adhesion of algae to underwater surfaces is essential for their existence, but algae adhesion to ship surfaces is a major financial burden; and adhesives for structural materials that function in an aqueous environment are important in many industries. In many cases, an adhesive must be in a liquid state at the beginning of the adhesion process, to form intimate contact with the solid surface (in the following the term “adhesive” implies an adhesive in its liquid or “soft” state). Therefore, wetting is usually the first stage in adhesion. Wetting affects adhesion in at least two ways: (a) it determines the actual contact area between the adhesive and the solid, thus affecting the adhesion strength; and (b) it determines the energetics of detachment of the adhesive from the solid. Therefore, understanding wetting is a prerequisite for understanding adhesion. A wetting system consists of a solid, a liquid, and a fluid (i.e., vapor or another, less dense, immiscible liquid). For studying adhesion in air (or in a vapor environment in general), the adhesive is simulated by the liquid, while the fluid is a gas. For the case of adhesion in an aqueous environment, the liquid represents the aqueous solution while the fluid simulates the adhesive. Thus, the following discussion refers to either solid-adhesive-vapor or to solidadhesive-liquid systems. * Fax: 972-4-829-3088. E-mail:
[email protected]. (1) Finlay, J. A.; Callow, M. E.; Ista, L. K.; Lopez, G. P.; Callow, J. A. Integr. Comp. Biol. 2002, 42, 1116. (2) Fant, C.; Elwing, H.; Hook, F. Biomacromolecules 2002, 3, 732. (3) Sackmann, E.; Bruinsma, R. F. ChemPhysChem 2002, 3, 262. (4) Dunne, W. M. Clin. Microbiol. Rev. 2002, 15, 155. (5) Clint, J. H.; Wicks, A. C. Int. J. Adhes. Adhes. 2001, 21, 267. (6) Clear, S. C.; Nealey, P. F. J. Colloid Interface Sci. 1999, 213, 238. (7) Gotoh, K.; Tao, J.; Tagawa, M. J. Adhes. Sci. Technol. 1999, 13, 1307. (8) Reid, G. Curr. Opin. Colloid Interface Sci. 1997, 2, 513. (9) Young, A. G.; Crisp, D. J. In Adhesion, Vol. 6; Allen, K. W., Ed.; Applied Sciences: London, 1982; pp 19-39.
Wetting systems are characterized by the actual contact angle that the liquid makes with a solid surface in the presence of a fluid. Thus, in a solid-adhesive-vapor system, it is the contact angle between the adhesive and the solid; in a solid-adhesive-liquid system it is the angle between the liquid (aqueous phase) and the solid. This contact angle is very well approximated by the Young contact angle, θY,10 that is given by
cos θY )
σsf - σsl σlf
(1)
In this equation σsf, σsl, and σlf are the interfacial tensions of the solid-fluid, solid-liquid, and liquid-fluid interfaces, respectively. The Young contact angle differs from the actual contact angle only if line tension is meaningful.10,11 For most practical situations of drops that are above a few micrometers in size, in solid-liquid-vapor systems, the effect of line tension is negligible.12,13 Therefore, it will be assumed below that line tension is also negligible in solid-liquid-liquid systems, when the drops are in this size range. The intrinsic property that characterizes the surface of a solid is its surface energy per unit area, σs (although “surface energy per unit area” is the preferred term for a solid surface, the term “surface tension” will also be used below when necessary for brevity and clarity). However, as is well known, eq 1 shows that the contact angle explicitly depends on the solid-liquid and solidfluid interfacial tensions and not on σs. Moreover, the interfacial tensions of the sl and sf interfaces cannot be directly measured. Thus, a fundamental need with regard to interpretation of contact angle measurements is a relationship between the surface energy per unit area of the solid and its interfacial tensions. To answer this need, semiempirical equations for interfacial tensions in terms of surface tensions have been used.14-21 Their usage for (10) Boruvka, L.; Neumann, A. W. J. Chem. Phys. 1977, 66, 5464. (11) Wolansky, G.; Marmur, A. Langmuir 1998, 14, 5292. (12) Marmur, A. J. Colloid Interface Sci. 1997, 186, 462. (13) Marmur, A.; Krasovitsi, B. Langmuir 2002, 18, 8919. (14) Ward, C. A.; Neumann, A. W. J. Colloid Interface Sci. 1974, 49, 286.
10.1021/la0359124 CCC: $27.50 © 2004 American Chemical Society Published on Web 01/24/2004
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Marmur
exact calculations is questionable;22 however, they may be utilized for estimation purposes. Because of its simplicity, and for demonstration purposes only, the pioneering Girifalco-Good equation23 will be used in the following:
σab ) σa + σb - 2φabxσaσb
(2)
In this equation, the subscripts a and b stand, in general, for phases a and b. The inaccuracies associated with this equation are covered by the empirical correction coefficient φab. To estimate the values of these correction coefficients, the Owens and Wendt equation24 will be used, as described below. Controlling the surface energy of the solid is essential for many adhesion applications. In some, notably blood cell or algae adhesion, the objective is to minimize adhesion by choosing the right solid surface. In others, maximum adhesion strength is desired. In many cases, the solid is described semiquantitatively as hydrophobic or hydrophilic, and general conclusions are drawn regarding the role of hydrophobicity (hydrophilicity) of the solid surface in adhesion. Such a semiquantitative approach may lead to uncertainties and misunderstandings. Therefore, the objective of this paper is to quantitatively discuss the sensitivity of wetting to the surface energy of the solid. Emphasis is put on the case of wetting by a liquid in an aqueous environment. As will be theoretically shown below, there may exist a vast difference between solidliquid-vapor (solid-adhesive-vapor) and solid-fluidliquid (solid-adhesive-liquid) systems. Theory Introducing eq 2 into eq 1, one gets
[
cos θY ) -
σl - σf - 2xσs(φslxσl - φsfxσf) σl + σf - 2φlfxσlσf
]
(3)
Since interest is focused here on the effect of the surface energy of the solid, the surface tension of the liquid will be considered constant throughout the following discussion. Therefore, it is useful to normalize this equation with respect to the surface tension of the liquid. Thus,
[
cos θY ) -
]
1 - Rf - 2xRs(φsl - φsfxRf) 1 + Rf - 2φlfxRf
(4)
where
Rf ≡
σf σl
(5)
is the normalized surface tension of the fluid (which is
