# Quenched disorder

A two-dimensional visualization of a fibrous network undergoing shear strain.

Quenched disorder occurs in a system when certain characteristics of the system have some randomness to them at all times, even at minimal temperatures and energies. Thus, one can describe the system as having disorder "frozen" or "quenched" into it at all times. Quenched disorder is often found in polymer materials. Quenched variables in a system cannot be associated with a relaxation time.

## Examples

• Atactic polymers: Molecules with chemical groups attached in a random order along the polymer chain have inherent quenched disorder. As explained in Jones, these materials form glasses at low temperatures. This type of quenched disorder amounts to randomness in the stereochemistry of the molecule. Polysaccharides exhibit these characteristics.
• Random copolymers: Random copolymers are classic examples of systems with quenched disorder. In these structures, the ordering of the various monomer species is random, and as a result these materials typically do not crystallize, but rather form glasses at low temperatures.
• Cross-linking and branching: Cross-linking in a polymer material also amounts to quenched disorder and can prevent crystallization. Similarly, polymers with branches and star-shaped polymers do not easily crystallize.

## Current research

Simulation of a two-dimensional network exhibiting quenched disorder from Wyart et al. Under shear strain, rotational deformation can be observed in different regions.

Quenched disorder has proven to be a characteristic of systems that is difficult to analyze. Wyart et al investigated the elasticity of floppy and stiff random networks in 2008 and proposed that a "relative network coordination" parameter $\delta z$ could be used to characterize fibrous networks with quenched disorder, such that the coordination is a measure of the relative number of cross-links between points in the network compared with the number of degrees of freedom of those points. They found that this coordination parameter could be used to classify materials with quenched disorder as either floppy, rigid, or isostatic, the crossover regime.