Dynamical properties of dilute flexible polymer solutions

Abstract

We analyse the dynamical properties of dilute Polymer solutions by using scaling arguments. To this end, we generalize the scaling analysis proposed for the static properties of these solutions by introducing a dynamical exponent z. This exponent has two slightly different values for theta and good solvents. In order to compare our results with experiments, we suppose that z has its Zimm value (z = 3) in theta solutions, and another value (z = 2.9) which we pick from recent experimental results, for solutions in good solvents. We calculate the temperature, molecular weight, and scattering vector dependences of different observable quantities such as the diffusion constant, the characteristic times and frequencies, the viscosity, etc. Our results are in good agreement with experiments. They show how these dependences deviate from the classical patterns of behaviour as we change from z to z. In particular, it is found that the diffusion coefficient in a good solvent does not obey Einstein's law. The analysis is then extended to some time dependent properties, such as the dynamic viscosity and the real part of the complex modulus. It is shown that these properties exhibit cross-overs. Universal coordinates are proposed for their study. Finally, a criticism of the so called reduced variables coordinates is given. Another set of variables is given, which is valid for both low and high frequencies, whereas the usual method failed for high frequencies