# Effect of magnetic nanoparticles on the nematic-smectic-A phase transition

## TL;DR

This paper develops a phenomenological mean-field model to analyze how ferromagnetic nanoparticles influence the nematic-smectic-A phase transition in liquid crystals, revealing a critical impurity concentration that alters transition order.

## Contribution

It introduces a new mean-field model combining Flory-Huggins and Landau-de Gennes theories to quantify nanoparticle effects on phase transitions in liquid crystal mixtures.

## Key findings

- Identification of a critical nanoparticle concentration causing a transition from second to first order.
- Model predictions align well with experimental observations.
- Analysis of phase diagram topologies under varying impurity levels.

## Abstract

Recent experiments on mixed liquid crystals have highlighted the hugely significant role of ferromagnetic nanoparticle impurities in defining the nematic-smectic-A phase transition point. Structured around a Flory-Huggins free energy of isotropic mixing and Landau-de Gennes free energy, this article presents a phenomenological mean-field model that quantifies the role of such impurities in analyzing thermodynamic phases, in a mixture of thermotropic smectic liquid crystal and ferromagnetic nanoparticles. First we discuss the impact of ferromagnetic nanoparticles on the isotropic-ferronematic and ferronematic-ferrosmectic phase transitions and their transition temperatures. This is followed by analysis of various topologies in the phase diagrams. Our model results indicate that there exists a critical concentration of nanoparticle impurities for which the second order N-SmA transition becomes first order at a tricritical point. Calculations based on this model show remarkable agreement with experiment.