Power law relaxation and glassy dynamics in Lebwohl-Lasher model near isotropic-nematic phase transition

TL;DR

This study investigates the critical dynamics near the isotropic-nematic transition in a liquid crystal model, revealing power law relaxation, subdiffusive behavior, and dynamical heterogeneity linked to large-scale fluctuations.

Contribution

It provides new insights into the glassy and power law relaxation dynamics in the Lebwohl-Lasher model near the I-N transition, highlighting the role of free energy landscape and density fluctuations.

Findings

Power law decay of orientational correlation functions near transition

Emergence of subdiffusive and superdiffusive regimes in angular displacement

Pronounced non-Gaussian behavior indicating dynamical heterogeneity

Abstract

Orientational dynamics in a liquid crystalline system near the isotropic-nematic (I-N) phase transition is studied using Molecular Dynamics simulations of the well-known Lebwohl-Lasher (LL) model. As the I-N transition temperature is approached from the isotropic side, we find that the decay of the orientational time correlation functions (OTCF) slows down noticeably, giving rise to a power law decay at intermediate timescales. The angular velocity time correlation function also exhibits a rather pronounced power law decay near the I-N boundary. In the mean squared angular displacement at comparable timescales, we observe the emergence of a \emph{subdiffusive regime} which is followed by a \emph{superdiffusive regime} before the onset of the long-time diffusive behavior. We observe signature of dynamical heterogeneity through \emph{pronounced non-Gaussian behavior in orientational motion} particularly at lower temperatures. This behavior closely resembles what is usually observed in supercooled liquids. We obtain the free energy as a function of orientational order parameter by the use of transition matrix Monte Carlo method. The free energy surface is flat for the system considered here and the barrier between isotropic and nematic phases is vanishingly small for this weakly first-order phase transition, hence allowing large scale, collective and correlated orientational density fluctuations. This might be responsible for the observed power law decay of the OTCFs.