Nematic Ordering Problem As Polymer Excluded Volume One

TL;DR

This paper extends mean-field approximation methods to estimate parameters of the isotropic-nematic transition in polymer systems, linking polymer excluded volume effects with experimental data and critical exponents.

Contribution

It introduces a new approach to analyze the nematic ordering problem considering polymer excluded volume, providing estimates for critical exponents and entanglement concentrations.

Findings

Transition of polymer coil to ideal as chain length increases

Entanglement concentration aligns with experimental data

Number of monomers between entanglements matches theoretical ratio

Abstract

The new method of the mean-field approximation is extended. An approach which enables to estimate some parameters of the transition from the isotropic state of hard sticks to the nematic ordering phase is suggested. An technique of the investigation of the model jointed to the so-called polymer excluded volume problem is proposed. The critical exponents are estimated. The transition of a swelling polymer coil to ideal is revealed as the polymerization degree of the chain increases. The entanglement concentration obtained is in accordance with experimental data for polymers with flexible chains. The number of monomers between neighbor entanglements assumes to be the ratio of the stick length to its diameter. The comparison of the theory with experimental data is made.