| The interfacial properties of inhomogeneous systems are most simply described by square gradient theories, which write the free energy as an integral over a functional of the concentration. In this thesis, we study concentration fluctuations in semidilute polymer solutions, in which polymers are overlapping in solution, using a modified (Cahn-de Gennes) square gradient theory. The Cahn-de Gennes theory incorporates correlations from polymer elasticity and has successfully been used in the past to provide mean field descriptions of interfacial energies and concentration profiles in a variety of solvent and boundary conditions. We begin by reviewing the bulk thermodynamics of polymer solutions and correlations due to polymer connectivity to motivate the form of the modified square gradient theory. We then set up the program of calculations and investigate the fluctuations in bulk, phase-separated solutions and in the presence of adsorbing and repulsive surfaces. Fluctuations exhibit particularly interesting behavior at adsorbing surfaces in poor solvent; their divergence at the onset of complete wetting, a type of surface phase transition, is related to capillary waves that are found at the free interface of two coexisting phases in the bulk. |
