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Soft matter is ubiquitous in our daily lives in the form of polymers, gels, cosmetics to even biological tissue. The unique viscoelastic properties of such materials are a consequence of their molecular structure and are studied in this thesis using Computational Rheology. By probing the stress relaxations of various soft materials like network forming telechelic star polymers, worm-like micelles and other supramolecular systems, the rheological properties of this interesting class of matter which will form the building blocks of emerging nano-material science have been explored using Brownian Dynamics Simulations and polymer theory. In chapter 2, we have studied the rheology of telechelic star polymers with functionality 13 using Brownian Dynamics. We determined the network crosslink percentage and the gelation threshold. The Rouse Model of polymer dynamics was also generalized to account for arbitrary friction and/or spring distributions, thereby contributing significantly to basic polymer theory. In chapter 3 we have studied the Boltzmann Superposition principle as applied to Orthogonal Superposition Rheology (OSR) and have provided an expression for the vertical shift in moduli that can be reproduced in simulations. Chapter 4 contains an application of OSR simulations to a concentrated worm-like micellar system where non-ordinary stress relaxations were attributed to lane formation as visible in our simulations. Additional non-monotonic stress relaxations were studied in Chapter 5 where our model helps explain the experimentally observed phenomenon of stress overshoot after stoppage of steady shear in three different supramolecular systems. The last chapter 6 has a derivation of the normal modes of a symmetric star polymer by an analytical factorization of its Rouse matrix.

Complex stress relaxations in soft matter studied by computational rheology