Intramolecular relaxation of flexible dendrimers with excluded volume

The mechanical and dielectric relaxation moduli of dendrimers with the excluded volume interactions are theoretically investigated within the framework of Rouse-Zimm theory. The excluded volume interactions in dendrimers are expressed in terms of the effective co-volume between nearest non-bonded monomers, modeled through the delta function pseudopotential. These short range interactions play a decisive role in determining the mechanical moduli of dendrimers. The characteristic feature of excluded volume effect in the mechanical moduli is typically revealed in the intermediate frequency regime, where dendrimers with varied strengths of excluded volume interactions display power-law scaling relations with frequency. The value of the power-law scaling exponents for the mechanical moduli exactly matches with the earlier results for dendrimers in good solvent conditions. The mechanical moduli are dominated by the smaller eigenvalues in the low frequency region corresponding to the collective modes with smaller relaxation rates, which increase with the corresponding increase of the excluded volume interactions. The local modes are practically independent of excluded volume. A cross-over between the loss and storage moduli is observed at the intermediate frequency regime. The position of this cross-over shifts towards the low frequency region with the decrease in the strength of the excluded volume, which resembles the behavior of dendrimers with the variation of temperature as reported in an earlier experimental work. The structure of dendrimers show a conspicuous change as a function of the effective co-volume between the nearest non-bonded monomers. The real part of dielectric relaxation moduli remains unchanged by varying excluded volume parameters, while its imaginary part varies with the change in strength of excluded volumes for the entire range of frequency except in the high frequency regime. A comparison with the model semiflexible dendrimers show that in such densely packed molecules the mechanical relaxation moduli are strongly affected by the short-ranged excluded volume interactions between the nearest non-bonded monomers.