Effect of excluded volume on the rheology and transport dynamics of randomly hyperbranched polymers

The rheology and transport dynamics of the randomly hyperbranched polymers with excluded volume interactions are investigated within the tenets of the Rouse-Zimm theory. The excluded volume interactions typically account for an effective co-volume between the nearest non-bonded monomers, modeled through a delta function pseudopotential, while the strength of such interactions is evaluated from the possible geometric orientations of the bonds. The mechanical moduli are primarily determined by the smaller eigenvalues corresponding to the collective modes. These modes with smaller relaxation rates increase with the decrease in the strength of excluded volume interaction parameter, while the local modes with higher relaxation rates remain unaffected. The internal structure of the randomly hyperbranched polymer is reflected in the intermediate frequency regime of the mechanical relaxation moduli, where the characteristic power-law behavior implies the fractal nature of the randomly hyperbranched polymers. The length of this power-law region increases either with the decrease in the strength of excluded volume interactions or with the increase in the number of shells of the randomly hyperbranched polymer, while the numerical values of the power-law exponents are strongly affected by the strength of excluded volume interactions. Intrinsic viscosity increases linearly for lower values of the excluded volume interaction parameters, while depicting a non-linear trend at higher strengths of excluded volume interactions. The randomly hyperbranched polymers are relatively more compact compared to the star polymer but less compact than that of dendrimers with the same number of monomers and same strength of excluded volume interactions. The values of the scaling exponents of the diffusion coefficient increase with decreasing the strength of excluded volume interactions. The scaling exponents of the diffusion coefficient of randomly hyperbranched polymers calculated with excluded volume exactly match with the earlier experimental results for hyperbranched polyglycidols in poly(vinyl alcohol) solutions.