# Patterns of Nanoporous Spherical Packing Emerging under Influence of Curvature and Confinement

## DOI:

https://doi.org/10.21015/vtm.v12i1.1754## Keywords:

Spherical forming system, Diblock copolymers, Celle dynamic simulations, Confinement, Discretization, Polar grid system, Nanoporous membrane## Abstract

Nanoporous membranes are popular in nanotechnology due to biomedical and industrial applications. During the past decade, experimental, theoretical and computational research into porous membranes and soft materials has opened up new mathematical dimensions. In bulk, diblock copolymers exhibit ordered morphologies such as parallel matrices of lamellae, bicontinuous matrices of gyroids, hexagonal matrices of cylinders and body-centred cubic matrices of spheres. In melt, confinement plays an essential role in tuning the frustration of the diblock copolymer system to predict more nanostructures. These nanostructures depend on the composition of the copolymers, their confining geometries and the degree of structural frustration. An isotropic 9-point stencil for Laplacian is constructed. The discrete finite-difference technique is used in polar grids to discretize the macromolecule of the diblock copolymer system to study spherical patterns to study the effect of curvature and confinement with a well-known and efficient cell dynamic simulation model. Intel FORTRAN (IFORT) codes are generated to run the CDS model and visualisation of simulation results is observed with the help of OPENDX. A comparison of the proposed study with existing experimental and computational studies is also presented.

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*VFAST Transactions on Mathematics*,

*12*(1), 121–136. https://doi.org/10.21015/vtm.v12i1.1754

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