Flory theory for polymers

Flory theory for polymers.

We review various simple analytical theories for homopolymers within a unified framework. The common guideline of our approach is the Flory theory, and its various avatars, with the attempt at being reasonably self-contained. We expect this review to be useful as an introduction to the topic at the graduate student level.

FLORY THEORY REVISITED by

The Flory theory for a single polymer chain is derived as the lowest order of a cumulant expansion. In this approach, the full original Flory free energy (including the logarithmic term), is recovered. The prefactors of the elastic and repulsive energy are calculated from the microscopic parameters. The method can be applied to other types of monomer-monomer interactions, and the case of a sing...

Flory-Huggins theory for athermal mixtures of hard spheres and larger flexible polymers.

A simple analytic theory for mixtures of hard spheres and larger polymers with excluded volume interactions is developed. The mixture is shown to exhibit extensive immiscibility. For large polymers with strong excluded volume interactions, the density of monomers at the critical point for demixing decreases as one over the square root of the length of the polymer, while the density of spheres t...

Flory approximation for directed branched polymers and directed percolation

Flory theory for conductivity of random resistor networks

2014 We develop a Flory theory for the problem of conductivity in a d-dimensional random resistor network. We find that the conductivity exponent t is related to the fractal dimensionality df according to the Alexander-Orbach conjecture t = d 2 + df/2, where consistently with Flory theory df = (d + 2)/2 for percolation and df = 2(d + 2)/5 for lattice animals. The results are in excellent agreem...