Semi-Analytical Calculation of the Rouse Dynamics of Randomly Branched Polymers

We present a semi-analytical approach to the determination of the dynamic properties of randomly branched polymers under the Rouse approximation. The principle procedure is based on examining a spectrum of eigenvalues which represents the average dynamic behavior of various structures. The calculated spectra show that the eigenvalue distribution is random even within a single structure which in turn produces a continuous spectrum of values for the entire class. The auto-correlation functions for the radius of gyration squared were calculated based on these spectra, which confirms that the dynamics is non-exponential as earlier reported. A universal stretched exponent is also found in this study.