Applied & Industrial Mathematics

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Modelling of Polymer Adsorption and Looping
(2024-03-16) Koumarianos, Sperydon; Madras, Neal; Bergevin, Ozzy
Understanding the physical adsorption behavior of polymers on surfaces is crucial for advancing materials science and developing smart coatings to enhance the bio-compatibility of implanted devices. Applications, ranging from heart stents to brain-integrated microchips,have been experimentally explored to study the adsorption properties of charged polymers onto diverse surfaces. While experimental observations have indicated the presence of loops in adsorbed polymer chains, there remains a need for a comprehensive theoretical model to consistently predict these phenomena. The proposed self-avoiding walk model aims to elucidate the conformations of polymer chains on a surface lattice, emphasizing the entropic competition between flat adsorption and dangly loops during the adsorption process. Focusing on loops formed by adsorbed polymers, the study aims to determine entropically preferred looping structures. These looping structures are relevant to the biocompatibility of materials. The modeling approach involves relating entropy to partition values generated by different macro-states, with a focus on enumerating micro-states to identify the most entropically preferred behavior of adsorbed polymers.