Onset of self-assembly

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 ξ∼(c-c*)-γ, where c* is the minimum concentration below which self-assembly is impossible, c is the current concentration, and γ was found numerically to be fairly close to 2/3. The renormalized diffusion constant vanishes as the critical concentration is approached, indicating the occurrence of critical slowing down, while the correlation function remains finite at the transition point. copyright 1998 The American Physical Society