We consider a bistable reaction-diffusion system arising in the theory of phase transitions; it appears in several physical contexts such as thin magnetic films and the microphase separation in diblock copolymer melts. Mathematically it takes the form of an Allen-Cahn equation coupled to an elliptic equation. This system possesses a Lyapunov functional which represents the Gibbs free energy of ...

A generic field-theoretic model for the self-assembly of particles with isotropic interactions, motivated by ideas in DNA-mediated colloidal assembly, is presented. A simplest possible system of colloids in explicit solvent is examined to determine the ability of non-connected particles to form complex nanometre or micron scale equilibrium structures in the absence of confounding kinetic effect...

We perform a self-consistent-field/density-functional-theory hybrid analysis for a system of diblock copolymers mixed with polydisperse, hard, spherical particles of various chemical species. We apply this theory to study the equilibrium morphologies of two different binary sphere/diblock melts. First, we examine the case where the particles have two different sizes, but both types are preferen...

\Vc analyzc ncarly continuous transitions to pcriodic structures expanding the dcnsity of thc periodic strllcture in multiple harmonics. A thrce dimensional hexagonal structure identified as a "Lamellar-Catenoid" is the equilillrium structurc near thc transition. It consists of alternating lamellar domains connectcd by an orthogonal array of hexagonally packed cylinders. \Ve obtain the periodic...

A mean-field analysis of microphase separation and phase behavior is described for melts of linear A-B multiblock copolymers, each chain consisting of a stochastic sequence of flexible segments (each with M monomers), AM and BM, for a total of Q >> 1 segments per chain. We find a phase diagram similar to that for statistical A-B copolymers (M = 1) but with an isotropic Lifshitz point that shoul...

Hexagonally ordered spherical and cylindrical morphologies (P6/mmm and P6/mm space group symmetries) have been identified in bulk poly(styrene-b-isoprene-b-styreneb-ethylene oxide) (SISO) tetrablock terpolymers. These materials were synthesized by adding up to 32% by volume O blocks to a parent hydroxy-terminated SIS triblock copolymer containing 40% S by volume, and the resulting morphologies ...