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DIBLOCK COPOLYMER LAMELLAE EMERGING PATTERNS WITH CELL DYNAMIC SIMULATIONS USING DIAGONAL DISCRETIZATION METHOD OF LAPLACIAN WITH 9-POINT STENCIL IN POLAR MESH SYSTEM

Muhammad Javed Iqbal1*, Inayatullah Soomro, Usama Gulzar, Muhammad Salman Javed

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ABSTRACT

The use of soft materials in nanotechnology is revolutionizing the industry. Given their special importance in soft and advanced functional materials, theoretical researchers are presenting their studies in search of new equilibrium configuration phases in diblock copolymer systems. In this regard, prospective research has predicted lamella morphologies in new nanostructures through mathematical modelling and simulations. Confinement has also been applied to enable new emerging nanostructure patterns by establishing a surface field. The choice of a fast and efficient cell dynamic simulation model to observe the role of order parameters between two incompatible blocks of a diblock copolymer system distinguishes it from other prevailing models. In this study, we present a new diagonal approximation method to discretize the macromolecule of the diblock copolymer system in polar geometries. A new diagonally discretized 9-point stencil has been numerically formulated for simulation in the CDS model after developing a FORTRAN code for a set of PDEs involved in the CDS model.  The new confined nano-particle patterns are presented by visualizing numerical data using OPENDX. Comparison of the proposed study with existing studies validates and distinguishes the research from the proposed studies.