Coarse-grained models for polymer solutions and colloid-polymer mixtures

Coarse-grained models are a very powerful ---and sometimes necessary--- tool in the analysis of the thermodynamic properties of macromolecular fluids. In these models, most of the original, microscopic degrees of freedom are integrated out and each macromolecule is mapped onto a set of effective sites, mutually interacting by means of appropriate intermolecular and intramolecular potentials. Depending on the number of sites n chosen, each macromolecule can be represented as a soft monoatomic molecule (n=1), or as a soft n-atomic molecule (n>1). The complexity of determining the complete set of effective interactions among the coarse-grained sites is such that an exact mapping is unfeasible in practice, hence approximations must be introduced, which always generate a lack of consistency between the original and the coarse-grained model. In this thesis, we apply coarse-graining strategies to the investigation of the universal, large scale and thermodynamic properties of polymer solutions and colloid-polymer mixtures, for two different polymer architectures: linear chains and star polymers. We begin the discussion by briefly summarizing the main concepts of statistical mechanics and polymer physics, in a general fashion. We then revise the formalism behind structure-based coarse-graining procedures, both single-site and multi-site, critically analyzing their limits of validity and the methods proposed in the literature to extend them. Thereafter, we determine the accuracy of coarse-grained, single-site mappings in reproducing the correct thermodynamic behavior of solutions of linear chains and colloid-linear chain mixtures, for different average polymer-to-colloid size ratios. In conclusion, we discuss coarse-grained models for star polymer solutions in good solvents. We introduce a new multi-site model for star polymers, whose validity should extend up to the semidilute regime, and compare its predictions for the thermodynamic properties of the system with those obtained by means of single-site models.