Phase diagram of a general biaxial nematic model based on density of states computation

ABSTRACT

The phase diagram of a general biquadratic Hamiltonian model of biaxial nematic liquid crystals was investigated both analytically through mean-field approximation and with computer simulations. However, their largely concurrent predictions are not borne out by experimentation, and the issue is still debated. We revisited this problem with Monte Carlo simulations based on the computation of density of states of the system through entropic sampling procedure, traversing through the relevant model parameter space (S) along representative trajectories. Our recent work indicated that the competing roles of different contributions in the Hamiltonian over significant regions of S could be the underlying entropic reason defying the earlier predictions. We find that our data differ from the reported results qualitatively, specifically as the trajectories approach the so-called partly repulsive regions of S. The complex free-energy profiles that we obtain in such cases, as a function of system order parameters, indicate entropic barriers to the development of the biaxial order to the expected degree. Significant increase in the influence of the intermolecular interactions between the uniaxial and biaxial tensors, at the expense of contributions from pure biaxial couplings, is indicated to be the inhibiting factor for the onset of the biaxial phase.

Graphical Abstract

KEYWORDS:

• Biaxial nematics
• phase diagrams
• density of states computation
• Wang–Landau algorithm
• frontier sampling
• free-energy curves
• entropic ensemble

Acknowledgements

We acknowledge the computational support from the Centre for Modelling Simulation and Design (CMSD) and the School of Computer and Information Sciences (DST PURSE II Grant) at the University of Hyderabad. BKL acknowledges financial support from Department of Science and Technology, Government of India vide grant ref No: SR/WOS-A/PM-2/2016 (WSS) to carry out this work.

Disclosure statement

No potential conflict of interest was reported by the authors.