Order parameter modelling and atomistic simulations of liquid crystalline phases

Abstract

This thesis contains two separate research projects connected with the simulation of liquid crystals. One is connected to a novel, mesoscale simulation methodology, related to order parameter modelling while the other involves atomistic molecular dynamics simulations. In our first project, we introduce a method using local density-dependent potential, extending their use from isotropic fluids to nematic liquid crystals. As a proof of principle, we perform Monte Carlo simulations using this methodology, both in bulk and also in the presence of an external field and surface interactions. In the mean-field limit, when the local densities are calculated over a large length scale, the simulation results converge to the analytical Maier-Saupe limit. In addition, we analyze a rather simple density functional theory for this model and use this to calculate the elastic constants of the nematic phase. These theoretical results also compare favorably with the values obtained from Monte Carlo simulation in the mean-field limit. In summary, we have shown that the use of local density dependent potentials is a well-grounded and feasible way to perform order parameter modelling. In addition, however, we believe that this methodology is easy to apply, requiring only standard Monte Carlo or Molecular Dynamic simulation techniques. In our second project, all-atom Molecular Dynamics simulation is employed to reproduce nematic, twist bend nematic, smectic and twist bend smectic phases. The force field was optimized using Lennard-Jones parameters and dihedral torsional parameters. Subsequently, molecular dynamics simulations were performed using Gromacs, ultimately yielding the nematic (N), twist bend nematic (NTB), smectic A (SmA) and twist bend smectic C (SmCTB) phase. Order parameter calculations confirmed that the simulation results are in very close agreement with experimental data. Meanwhile, the calculations of the bend angle and conical tilt angle for different phases indicate that helical structures are more readily formed at lower temperatures. Analysis of the helical structures provided pitch values: approximately 11 nm for the NTB phase and around 12.5 nm for the SmCTB phase. In addition, calculations of the radius of gyration show that at lower temperatures, the terminal alkyl chains of the molecules become more elongated, and extending the terminal carbon chains facilitates the formation of the smectic phase.

Date of Award	20 May 2025
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Andrew Masters (Main Supervisor) & Paola Carbone (Co Supervisor)