The onset of self-assembly

Abstract

We have formulated a theory of self-assembly based on the notion of local gauge invariance at the mesoscale. Local gauge invariance at the mesoscale generates the required long- range entropic forces responsible for self-assembly in binary systems. Our theory was applied to study the onset of mesostructure formation above a critical temperature in estane, a diblock copolymer. We used diagrammatic methods to transcend the Gaussian approximation and obtain a correlation length zeta ~ (c-c*)^-gamma, where c* is the minimum concentration below which self-assembly is impossible, c is the current concentration, and gamma was found numerically to be close to 2/3. The renormalized diffusion constant vanishes as the c* is approached, indicating the occurrence of critical slowing down, while the correlation function remains finite at the transition point.