Equilibrium, Structural, and Mechanical Properties of Soft and Bio Molecular Systems: from Single Polymer to Polymeric Gels

This thesis explores the equilibrium, mechanical, thermodynamic, and non-equilibrium properties of soft materials through a connected set of problems. We explore the equilibrium morphology of a semiflexible polymer inside a soft tubule whose lateral dimension is much smaller compared to the radius of gyration of the chain. As a function of the rigidity of the tube we observe a coil to globule transition of the chain. Further, we observe a shape transition from an oblate spheroid to a toroidal coil as the chain stiffness. We characterise the confined shapes using statistical measures and obtain a minimum energy shape of the confining tubule from a variational calculation. Next, we report a computational model of a spherical microgel (cross-linked polymer networks encapsulating a solvent) with tuneable mechanical, thermodynamic, and transport properties that are dictated by the underlying network topology, using coarse-grained molecular dynamics (CGMD) simulations. We, therefore, characterise the structure of the microgel using the density, pair correlation function, the shape asphericity parameter, and the network topology including defects, nodes, loops and path distributions. We compute the viscoelastic response of the gel subject to frequency-dependent bulk compression and shear deformation to extract elastic moduli based on microscopic interaction parameters and compare the results against a neo-Hookean constitutive model. Understanding regulatory processes that arrest droplet growth in phase separating fluid mixtures is an interdisciplinary topic of much current interest with applications ranging from materials engineering to biology. We therefore describe the thermodynamics of an unstable binary mixture, having a gel component where a competition between surface tension and network elasticity stabilises a disperse microdroplet phase of many droplets. Finally, we combine our learnings to explore solvent mediated translocation of microgels through narrow channels and find the conditions for successful translocation, the shape of translocating gels, solvent flow through translocating and arrested microgels.