# Roughness as a measurement of random disorder

## TL;DR

This study investigates how aerosil dispersion creates quenched random disorder in liquid crystal surfaces, linking surface roughness to disorder levels and demonstrating roughness as a measurable indicator of random disorder.

## Contribution

It introduces surface roughness as a novel quantitative measure for characterizing quenched random disorder in aerosil-dispersed liquid crystal gels.

## Key findings

- Surface roughness increases with aerosil concentration.
- Fractal aerosil surfaces correlate with disorder levels.
- Roughness measurements align with x-ray diffraction results.

## Abstract

We have studied the quenched random disorder (QRD) effects created by aerosil dispersion in octylcyanobiphenyl (8CB) liquid crystal (LC) using Atomic Force Microscopy (AFM) technique. Gelation process in the 8CB+aerosil gels yields a QRD network which also changes the surface topography. By increasing the aerosil concentration, the original smooth pattern of LC sample surfaces is suppressed by creating a fractal aerosil surface effect, these surfaces become more porous, rougher with more and bigger crevices. The dispersed aerosil also serves as pinning centers for the liquid crystal molecules. It has been observed that via the diffusion-limited-aggregation process, aerosil nano-particles yield a fractal like surface pattern for the less disordered samples. As the aerosil dispersion increases, the surface can be described by more aggregated regions which also introduce more roughness. Using this fact, we have shown that there is a net correlation between the short-ranged x-ray peak widths (-the results of previous x-ray diffraction experiments-) and the calculated surface roughness. In other words, we have shown that these QRD gels can also be characterized by their surface roughness values.