GPU-Accelerated Molecular Dynamics Simulation to Study Liquid Crystal Phase Transition Using Coarse-Grained Gay-Berne Anisotropic Potential

Abstract

Gay-Berne (GB) potential is regarded as an accurate model in the simulation of anisotropic particles, especially for liquid crystal (LC) mesogens. However, its computational complexity leads to an extremely time-consuming process for large systems. Here, we developed a GPU-accelerated molecular dynamics (MD) simulation with coarse-grained GB potential implemented in GALAMOST package to investigate the LC phase transitions for mesogens in small molecules, main-chain or side-chain polymers. For identical mesogens in three different molecules, on cooling from fully isotropic melts, the small molecules form a single-domain smectic-B phase, while the main-chain LC polymers prefer a single-domain nematic phase as a result of connective restraints in neighboring mesogens. The phase transition of side-chain LC polymers undergoes a two-step process: nucleation of nematic islands and formation of multi-domain nematic texture. The particular behavior originates in the fact that the rotational orientation of the mesogenes is hindered by the polymer backbones. Both the global distribution and the local orientation of mesogens are critical for the phase transition of anisotropic particles. Furthermore, compared with the MD simulation in LAMMPS, our GPU-accelerated code is about 4 times faster than the GPU version of LAMMPS and at least 200 times faster than the CPU version of LAMMPS. This study clearly shows that GPU-accelerated MD simulation with GB potential in GALAMOST can efficiently handle systems with anisotropic particles and interactions, and accurately explore phase differences originated from molecular structures.

Fig 1. The vectors and parameters of two interacted ellipsoids (left), the interaction profile of GB potential (solid lines) and its modified form (MGB, dotted lines).

Interaction profiles in four orientations including side-by-side, cross, T-shape and end-to-end from left to right are presented.

Fig 2. Schematics of LC molecules (A) in small molecular LC (SMALL, B), main-chain polymers (MCLCP, C) and side-chain polymers (SCLCP, D).

Ellipsoids are mesogens, spheres are backbone connectors in SCLCP and the springs demonstrate harmonic interactions. θ is the angle between the major axis of the two adjacent GB mesogens (u_i, u_j) for MCLCP (C), while it is the angle between the major axis of the GB mesogen (u_i) and the vector from the center of the GB mesogens to the adjacent LJ beads on backbone (r_ij) for SCLCP (D). The site-site vector S_ij connects the two adjacent GB/GB sites or GB/LJ sites placed in terminal position for MCLCP and SCLCP, respectively.

Fig 3. The average simulation cost per step of GALAMOST (GALA) and LAMMPS (LAMM) with the GB (+GB) or the MGB (+MGB) interaction as a function of the number of particles in simulation systems.

Fig 4. The average simulation cost per step of GALAMOST and LAMMPS for pair force, neighbor list and integration, the three major time consuming functions in MD simulation.

Fig 5. Equilibrium configurations of typical phases with the GB interaction at various temperatures T* = 0.6 and T* = 0.8 obtained by GALAMOST with GB (left), LAMMPS with GB (middle), and GALAMOST with MGB (right).

Fig 6. Orientational order parameter S of mesogens in small molecules as a function of temperature and simulation approaches.

Fig 7. The phase diagram of mesogens in small molecular LC obtained by GPU-accelerated simulation equipped with coarse grained GB potential.

Solid circles mark our simulation results and lines are plotted for guide only. The X-axis is converted to number density for the comparison with de Miguel’s report.

Fig 8. Snapshots of typical phases for mesogens in small molecules (up), MCLCP (middle) and SCLCP (bottom) with temperature increasing from left to right.

Fig 9. The orientational order parameter S, the probability of the local orientation P (a, b), and the second virial coefficient A₂ (c, d) as a function of temperature for mesogens in small molecular, SCLCP and MCLCP systems.

Insert in (c) illustrated the multi-domain nematic phase for SCLCP system.

Fig 10. The radial distribution function g(r) and the orientational correlation functions g₂(r) at various temperatures for small molecular, MCLCP and SCLCP systems.

The three vertical dash lines label the location of the side-by-side and cross, the 2^nd nearest side-by-side and T-shape, and the end-to-end packing of mesogens from left to right.

Fig 11. The average end-to-end distance (R_f) of backbone for MCLCP and SCLCP.