DETERMINATION OF THE CUMULANT EXPANSION FOR AUTOCORRELATION OF POLYMER COILING
ABSTRACT
This study provides a theoretical tool to determine the validity of the Rouse bead-and-spring polymer model for an experimental polymer-solvent system. The cumulant expansion that can be used to calculate the internal motion autocorrelation for a polymer in solution is determined. Combined with the existing expression for the diffusional autocorrelation, the overall theoretical autocorrelation can be calculated. Agreement of this theoretical autocorrelation with the experimental autocorrelation found from dynamic light scattering verifies the application of the Rouse model. The analytical determination of the first cumulant is reviewed, and an expression for all higher order cumulants is determined through numerical analysis. It is discovered that for conditions where the internal contribution to the autocorrelation is significant that all higher order cumulants are functions only of the first cumulant. Therefore, the theoretical autocorrelation can be calculated solely from the existing analytical expression for the first cumulant.