| Dynamics of dilute heteropolymer solution, thermodynamic stability of quasicrystal phases of diblock copolymer melt, and phase separation of a critically quenched binary fluid/surfactant system are studied.; For the dynamics of dilute heteropolymer chain, using functional-integral representation, a mean-field equation of motion is obtained, from which the slowest relaxation mode is derived. In addition to the usual excluded-volume and hydrodynamic contributions, it is found that heterogeneity of the chain also renormalizes the mode. However, the breaking of fluctuation-dissipation relation responsible for the freezing transition in spin-glass systems is found to have no effect to the renormalization due to heterogeneity. This implies that when using spin-glass analogy to study heteropolymers, popularized by protein folding problem, care should be taken when dynamic issues are addressed.; For the stability study of diblock copolymer melt, motivated by the fact that there are two complementary approaches (packing of Penrose tiles and density-wave mean filed theory) in the theoretical study of icosahedral quasicrystals while there exists only one approach (Caspar-Klug packing theory) to understanding the icosahedral morphology of virus shells, the icosahedral phases are examined using Landau free energy expansion (Leibler's theory) with multiple harmonics. Treating the packing units (proteins) like amphiphilic copolymers, the free energies of icosahedral phases are calculated at different compositions. Compared to those of stable conventional phases, the icosahedral phases are found always less stable.; For the phase separation of a binary fluid/surfactant system, hydrodynamic effect in a Hele-Shaw cell is studied numerically using a recently proposed model. When the quench is deep, so that thermal fluctuations are ineffective, it is found that surfactants tend to be trapped in domains of binary fluid. The trapping of surfactant clusters, however, does not occur when hydrodynamic effect is absent. Dynamic scaling found in previous studies is not observed in this model. Furthermore, it is found that, in contrary to the usual expectation, the domain grows with time algebraically (more binary-fluid-like) at higher average surfactant concentrations and logarithmically (less binary-fluid-like) at lower surfactant concentrations. A simple scaling argument is given to explain this unexpected result. |
