  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.
