Re-patterning of cylindrical packing of diblock copolymers under confinement and curvature effects by using approximations of PDE’s involved in the CDS model on polar mesh system

Abstract

Soft materials, including diblock copolymers, are advancing nanotechnology due to their unique properties, applications materials include energy harvesting, water sanitation, environmental treatment, nanosensors, drug delivery and nanolithography. These materials are light, cheap, efficient, sensitive, durable and more functional, whose new morphologies have been predicted by mathematicians through simulation. This work produces and predicts the pattern of packing of nano-cylinders by using confinement to appreciate the frustration in the packing of nano-cylinders under the influence of curvature. In this contribution, the cell dynamic simulations model is used to examine the impact of circular annular pore confinement on system orientation toward cylindrical morphologies. A 9-point stencil approximates the isotropic Laplacian by finite-difference discretization on a polar grid to meet the requirement of a cell dynamic simulation model. FORTRAN codes are generated for the set of PDEs included in the CDS model. OPEN DX is used to visualise the predicted cylindrical patterns. The consistency of our results with experimental observations makes our research valid and significant.

Keywords

• mathematical modelling and simulation
• numerical solution of PDE
• laplacian
• soft matter
• confinement
• diblock copolymers