Simulational Analysis of Relaxation in Polymer Systems

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1. Relaxation rates and modes of a single polymer chain confined in a slit by repulsive walls are studied. Their behaviors for the directions parallel to the walls can be understood as those of a two-dimensional excluded volume chain of blobs, of which size is comparable to the width of the slit. The behaviors for the perpendicular direction can be understood by assuming a repulsive interaction between the perpendicular components of the displacements of neighboring blobs.2. Relaxation rates and modes of a star polymer are studied. From the dependence of the relaxation modes and rates on the number of arms and the number of segments per arm, two relaxation processes corresponding to the deformation of the overall shape and the exchange of the positions of two neighboring arms are found. Although the former has been predicted by a theory, the latter has not.3. Relaxation rates and modes of a polymer chain trapped in a tube network are studied in two and three dimensions. In two dimensio … More ns, because of the excluded volume interaction, the exponent of the power law dependence of the relaxation rates on the number of segments is larger than the theoretical value for the case of no excluded volume interaction. The behavior of the smallest relaxation rate is different form that of the other relaxation rates. In three dimensions, the excluded volume interaction has little effect.4. Relaxation rates and modes of a polymer chain in a melt are studied. The apparent exponent of the power law dependence of the inverse of the smallest relaxation rate on the number N of segments increases beyond the theoretically predicted value, three, as N increases. From the data for the largest values of N, the apparent exponent is estimated as 3.5, which is consistent with the experimental results. The exponent of the power law dependence of the p-th smallest relaxation rate on p is smaller than the theoretical value, two. The behaviors of the first and second slowest relaxation modes are consistent with the theoretical prediction.5. Relaxation rates and modes of a single polymer chain are studied, where the excluded volume interaction and the hydrodynamic interaction are taken into account. A theoretical formula which describes how the relaxation rate spectrum changes as the strength of the hydrodynamic interaction changes is proposed and is confirmed by simulations. Less