# softmatter:Polymer

Repeating structural unit of polystyrene

A polymer is a a high-molecular weight molecule made up of repeating segments, called monomers. A polymer made purely of one type of monomer is refered to as a homopolymer; polymers consisting of more than one type of monomor are generally classified as copolymers, where Block copolymers are one specific type of copolymer. Polymer molecules can be made of only a few repeating chains or thousands, producting a wide range of accessible molecular weights.

## Characterizing polymers

Two common methods for classifying polymers are the number-averaged, Mn, and weight-averaged, Mw molecular weights for polydisperse systems. Additional methods to classify the polymers are the end-to-end distance, radius of gyration, Rg, overlap concentration, C*, and Characteristic ratio (polymer) $C_\infty$.

## Modeling polymers

A common model for simulation polymers is the bead-spring model, whereby individual atoms or groups of atoms are represented to by a single spherical particle, connected to neighboring particles via springs, such as FENE or harmonic Springs. This creates a freely jointed polymer chain. Additional constraints can be added restricting the angle bending and bond rotation.

Phase separation of a polymer blend can be modeled by solution of a partial differential equation, called the Cahn-Hilliard equation, using FiPy. Here's an example of a phase-separating blend at three different times following a quench through the critical point from the stable to the unstable region of the phase diagram.