Exploring Long-Range Order in Diblock Copolymers through Cell Dynamic Simulations

Abstract

Soft materials have played an important role in the development of nanotechnology over the past decade. Diblock copolymer systems in these soft materials have opened up new avenues of research, introducing discoveries in experimental and theoretical research in the bulk and melt states. To this end, computer programming has advanced the simulation of soft materials through mathematical models that have enabled the prediction of novel ordered structures and morphologies from simulations on long-range order. Using this approach proved to be cost-effective and time-efficient. There are many mathematical models for predicting novel morphologies in diblock copolymer systems by computer simulation. Still, cell dynamic simulation (CDS) stands out for its efficiency and robustness in achieving long-range order. This paper presents a cell dynamic simulation model for predicting simulation results by examining flow, deformation and phase transitions within diblock copolymer systems in curvilinear coordinate systems. The paper insight into the interpretation, understanding, scope, and application of the partial differential equations involved in the model by presenting a block diagram of the CDS model with a modified algorithm. A numerically consistent CDS numerical scheme is developed. Laplacian is involved in the CDS model based on curvilinear geometries to solve regular and irregular system boundaries. Also, self-assembly, phase separation mechanism, predicted results and applications in diblock copolymer systems are highlighted. Finally, the results of the CDS model are also presented for comparison with other models.