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 $\xi \sim (c-c^{*}{)}^{-\gamma }$, where $c^{*}$ is the minimum concentration below which self-assembly is impossible, $c$ is the current concentration, and $\gamma$ was found numerically to be 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.