Contact Angles for Liquid Drops at a Model Heterogeneous Surface Consisting of Alternating and Parallel Hydrophobic/Hydrophilic Strips Jaroslaw Drelich,* ,† James L. Wilbur, ‡ Jan D. Miller, † and George M. Whitesides ‡ Department of Metallurgical Engineering, University of Utah, Salt Lake City, Utah 84112, and Department of Chemistry, Harvard University, Cambridge, Massachusetts 02138 Received July 7, 1995. In Final Form: January 2, 1996 X Model heterogeneous surfaces consisting of alternating and parallel 2.55 μm hydrophobic and 2.45 μm hydrophilic strips were prepared on a gold film by patterning self-assembled monolayers of hexadecanethiol and mercaptohexadecanoic acid using an elastomer stamp. The advancing and receding contact angles were measured for liquid drops (distilled water, buffer solutions with pH ) 8.0, 10.0, and 11.0, ethylene glycol, glycerol, and formamide) placed on this specially prepared surface. Contortion of the three-phase contact line is a significant property of these systems. Both contact angles, advancing and receding, were 2-10° lower when measured with the strips normal to the three-phase contact line than those measured with the strips tangential to the three-phase contact line. For most of the systems examined, experimental contact angles, when measured for the liquid drop edge situated along the strips of the model heterogeneous surface (noncontorted three-phase contact line), were in an agreement with theoretical values calculated from the Cassie equation. Also, for most of the systems examined, there was an agreement of experimental contact angles, as measured for the liquid drop edge located normal to the strips (i.e., when the three-phase contact line was contorted), with theory calculated from the modified Cassie equation, including the line- tension term. Only in selected cases could the theory as expressed by the Cassie equation or the modified Cassie equation not predict the experimental contact angles. These were the systems in which the liquid phase interacted strongly with COOH groups of the self-assembled monolayer and completely spread over this hydrophilic portion of the surface. Introduction Over forty years ago, Cassie 1 proposed that the contact angle (θ C ) for a liquid at a composite solid surface can be predicted theoretically from a simple equation incorpo- rating the composition of a solid surface and its wetting characteristics. For a two-component surface this equa- tion is 1 where f i is the fractional area of the surface with a contact angle of θ i and the superscript C designates the contact angle for the heterogeneous surface as proposed by Cassie. Recent theoretical analysis 2-4 of the free energy for the three-phase system with a heterogeneous solid surface pointed out the limitation of Cassie’s approach and indicated that the Cassie equation (eq 1) is not universal but, rather, requires a correction that incorporates the excess free energy associated with the three-phase contact line. This correction is especially recommended for systems with micron-size (a few microns in diameter or less) heterogeneities. On this basis, a new theoretical relationship describing the equilibrium contact angle (θ MC ) for a liquid at a heterogeneous surface was derived and proposed. 2-4 For example, if a solid surface is composed of two components, uniformly distributed, the equation describing the contact angle is as follows: 4 where γ LV is the surface tension for the liquid; r i is the radius of the three-phase contact line at the i-component of the surface; γ SLVi ) (δF i /δL i ) T,V,Aij,ni is the line tension; F is the free energy of the system; T, V, A, and L are the temperature, volume, interfacial area, and length of the three-phase contact line, respectively; and the superscript MC designates the modified Cassie contact angle. The contact angles, θ C and θ MC , for the model hetero- geneous solid surface are distinguished by the drawing presented in Figure 1. In this particular case, the solid surface is composed of alternating and parallel strips differing in surface properties (surface/interfacial tension), for simplicity called hydrophobic and hydrophilic strips. A pure liquid at each surface strip forms an intrinsic contact angle (θ 1 and θ 2 where 0° < θ 1 < 180°, 0° < θ 2 < 180°, and θ 1 > θ 2 ) which satisfies the modified Young’s equation 5 where γ SV and γ SL are the interfacial tensions for the solid/ vapor and solid/liquid interfaces, respectively. Two extremely different positions of the three-phase contact line at the model heterogeneous surface are illustrated in Figure 1, for the surface strips parallel and normal to the three-phase contact line. For the first position, the wetting line is smooth because it is situated along a strip. Assuming that the dimensions of the strips are very smallsmicron-size or lesssthe * To whom correspondence should be addressed. E-mail: jdrelich@mines.utah.edu. Phone: (801)581-6814. Fax: (801)581- 4937. † University of Utah. ‡ Harvard University. X Abstract published in Advance ACS Abstracts, March 15, 1996. (1) Cassie, A. B. D. Discuss. Faraday Soc. 1948, 3, 11. (2) Drelich, J.; Miller, J. D. Part. Sci. Technol. 1992, 10, 1. (3) Drelich, J. Ph.D. Dissertation, University of Utah, 1993. (4) Drelich, J.; Miller, J. D. Langmuir 1993, 9, 619. (5) Boruvka, L.; Neumann, A. W. J. Chem. Phys. 1977, 66, 5464. cos θ MC ) f 1 cos θ 1 + f 2 cos θ 2 - ( 1 γ LV 29( f 1 γ SLV 1 r 1 - f 2 γ SLV 2 r 2 29 (2) γ SV i - γ SL i ) γ LV cos θ i + γ SLV i r i (3) cos θ C ) f 1 cos θ 1 + f 2 cos θ 2 (1) 1913 Langmuir 1996, 12, 1913-1922 0743-7463/96/2412-1913$12 00/0 © 1996 American Chemical Society + +