Neural-network approach to modeling liquid crystals in complex confinement.

Area of Science:

• Physics
• Materials Science
• Computational Chemistry

Background:

• Determining the structure of confined liquid crystals is challenging due to non-uniform density and order parameter profiles.
• Traditional methods like solving Euler-Lagrange equations or free energy minimization are computationally intensive and prone to convergence issues.

Purpose of the Study:

• To introduce an unsupervised multilayer perceptron (MLP) artificial neural network as an alternative method for free energy minimization in confined fluids.
• To assess the MLP algorithm's accuracy and efficiency in predicting liquid crystal structure and equilibrium free energy.

Main Methods:

• Developed an unsupervised multilayer perceptron (MLP) artificial neural network for free energy minimization.
• Applied the MLP to a fluid of hard nonspherical particles confined between planar substrates with variable penetrability.
• Compared MLP results for density-orientation profiles and free energy with Euler-Lagrange equation solutions and Monte Carlo simulations.

Main Results:

• The MLP method achieved very good agreement with established computational techniques (Euler-Lagrange and Monte Carlo simulations).
• The MLP approach demonstrated competitive speed, flexibility, and refinability compared to traditional methods.
• The algorithm proved effective in calculating density-orientation profiles and equilibrium free energy.

Conclusions:

• The unsupervised MLP artificial neural network offers a computationally efficient and accurate alternative for studying confined liquid crystals.
• The method's flexibility allows for straightforward generalization to complex patterned-substrate geometries, addressing limitations of conventional theoretical treatments.