Diblock copolymer ordering induced by patterned surfaces

– We use a Ginzburg-Landau free energy functional to investigate diblock copolymer morphologies when the copolymer melt interacts with one surface or is confined between two chemically patterned surfaces. For temperatures above the order-disorder transition a complete linear response description of the copolymer melt is given, in terms of an arbitrary two-dimensional surface pattern. The appearance of order in the direction parallel to the surface is found as a result of the order in the perpendicular direction. Below the order-disorder transition and in a thin-film geometry, our procedure enables an analytic calculation of distorted perpendicular and tilted lamellar phases in the presence of uniform or striped surface fields. Block copolymers (BCP) are macromolecules made up of two or more chemically distinct subunits, or blocks, covalently bonded together. The usual (macro-) phase separation occurring for two immiscible species is not possible for BCP because of the covalent bond between the blocks. The most studied BCP are the diblocks, for which the phase diagram is quite well understood [1–6], and was found to consist of disordered, lamellar, hexagonal and cubic micro-phases with characteristic length scale usually in the range of dozens of nanometers. The prevailing morphologies depend on three parameters: the Flory parameter χ, characterizing the incompatibility between the two blocks, the polymerization degree of the chain N , and the fraction f = NA/N of the A block in a chain of N = NA + NB monomers. For high enough temperatures the system is found in its disordered state. For symmetric melts (f = 1/2) lowering the temperature (or equivalently, raising χ) results in a phase transition to the lamellar phase through the order-disorder transition (ODT) point. For asymmetric melts (f 6= 1/2) the ordered phases can have, in addition, hexagonal (cylindrical) or cubic symmetries [1–6]. The technological importance of copolymer thin-film is prominent in diverse fields, such as in fabrication of nanolithographic templates [7], waveguides, anti-reflection coating for optical surfaces [8] and dielectric mirrors [9]. Therefore, it is highly desired to acquire a better understanding of the copolymer behavior in the presence of chemically patterned surfaces. Theoretical [10–20] and experimental [21–25] studies have been carried out in order to explore how the BCP film thickness, the range and strength of the uniform surface interactions, as well