DOI 10.1140/epje/i2001-10060-4 Eur. Phys. J. E 8, 103–110 (2002) T HE EUROPEAN P HYSICAL JOURNAL E c  EDP Sciences Societ`a Italiana di Fisica Springer-Verlag 2002 Influence of surface ordering on the wetting of structured liquids R. Limary, P.F. Green a , and K.R. Shull 1 Graduate Program in Materials Science and Engineering, Department of Chemical Engineering and Texas Materials Institute, The University of Texas at Austin, Austin TX 78712, USA 2 Department of Materials Science and Engineering, Northwestern University, Evanston, IL 60208-3108, USA Received 3 August 2001 and Received in final form 1 November 2001 Abstract. The substrate is shown to induce substantial ordering in diblock copolymer thin films above the bulk order-disorder transition (ODT) where, thermodynamically, a phase mixed state is favored. Initially, uniform films reorganize to form a hierarchy of transient surface patterns and stable film thicknesses that depend on the initial film thickness and on the substrate. Self-consistent field calculations of the free energy of the system for different situations, depending on the relative tendency for the different block components to be attracted to the substrate and/or free surface, provide an explanation of the formation of the stable film thicknesses. A continuum picture proposed earlier by Brochard et al. provides an explanation of the wetting characteristics of this system. In some cases the ordering destabilizes the film so that dewetting occurs (wetting autophobicity), whereas in other cases the surface ordering results in a kinetic stabilization of a film that would otherwise dewet. PACS. 68.15.+e Liquid thin films – 61.30.Hn Surface phenomena: alignment, anchoring, anchoring tran- sitions, surface-induced layering, surface-induced ordering, wetting, prewetting transitions, and wetting transitions 1 Introduction It is well known that the interfacial properties of molecular liquids are determined to a large extent by the detailed chemical structure of the liquid in question. Amphiphilic surfactants, where the same molecule has regions of both hydrophilic and hydrophobic character, are no exceptions. The interfacial behavior of these surfactant molecules is determined by very specific molecular interactions that are difficult to model in detail. Block copolymers are examples of amphiphilic struc- tured liquids. Because interactions between unlike seg- ments that comprise the chain are spread out over larger distances, many of the detailed intermolecular interac- tions can be characterized by a single thermodynamic, phenomenological, parameter [1–5]. For an A-B diblock copolymer, the relevant thermodynamic parameter is the Flory-Huggins interaction parameter, χ, which can be de- termined from experiment [2,3]. For a flexible diblock copolymer consisting of an A block with degree of poly- merization N A in conjunction with a B block with de- gree of polymerization N B , the bulk phase behavior is determined by three parameters, the Flory-Huggins in- teraction parameter, χ, the total degree of polymerization N = N A + N B , and by the symmetry parameter f = N A /N . Block copolymers exhibit an order-disorder tran- a e-mail: green@che.utexas.edu sition (ODT) dictated by the condition χN > (χN ) ODT , where χ is inversely proportional to temperature T . For symmetric diblock copolymers (f ∼ 1/2) alternating A- rich and B-rich phases, lamellae, characterize the struc- ture below the ODT, where the ODT is specified by the condition (χN ) ODT ≈ 10.5 [1]. The ordered state, χN > 10.5, is characterized by three segregation regimes, weak, intermediate and strong, depending on the value of χN [2–5]. The chains in the A-rich and B-rich phases must stretch beyond their un- perturbed dimensions, subject to a constant segmental density constraint, in order to minimize the number of un- favorable, A/B, contacts. In the strong segregation regime χN ≫ 10.5, the chains assume an extended conformation, and the scaling of the domain dimensions with N is given by [2–5] L/a = 2(8/3π 4 ) 1/6 χ 1/6 N 2/3 , (1) where a is a segmental length, assumed here to be the same for both copolymer blocks. In this limit, the in- teractions between the components are localized within a narrow interfacial region with dimensions that scale as aχ −1/2 . In thin films below the bulk ODT (χN > 10.5), in- teractions of the chains with the boundaries, the free sur- face and the polymer/substrate interface, determine the local segmental concentration profile [6–9]. In this regime, where ordering is thermodynamically favored, the self-