Abstract

Recent progress is reviewed in the understanding, and computation, of self-assembly in block copolymers and in biological lipids, both neutral and charged. Key words: self-assembly, lyotropic phases, block copolymers, lipids PACS: 61.25.Hq, 87.30.Hq Block copolymers Block copolymers self assemble into a great array of stable, ordered, phases in which components of different blocks are separated. The basic reason for this is clear. The monomers comprising the different blocks prefer energetically to be surrounded by monomers of the same kind and to avoid contact with monomers of other species. At sufficiently low temperatures, therefore, the polymers will arrange themselves so as to minimize contact between the different species of monomer. Were the blocks not chemically bonded to one another, they would undergo phase separation. Because they are so bonded, they cannot separate but must arrange themselves in an ordered manner which minimizes these contacts subject to various constraints. One of these constraints is that the system be incompressible, or at least nearly so. The simplest ordered phase is lamellar, in which the lamellae are composed of a majority of one monomer or the other. In the case of diblock copolymers consisting of blocks of A and blocks of B monomers, there is a lamellae composed of a majority of A followed by one of a majority of B, then A again and so forth. At very low temperatures in which the monomers are well separated, called the strong segregation limit, the interfaces between the different lamellae are quite narrow, much narrower than the width of the lamellae themselves. Most of the energy of the system arises from the contact between monomers at these internal interfaces between lamellae. Because simplicity is introduced by the assumption of very low temperatures, much theoretical progress has been made in this limit At sufficiently high temperatures, of course, the system is disordered due to the dominance of entropy considerations, but will order when the temperature is reduced