Mean-square radius of gyration and the hydrodynamic radius for topological polymers expressed with graphs evaluated by the method of quaternions revisited

Abstract

We revisit the numerical quaternionic study on the mean-square radius of gyration and the hydrodynamic radius for topological or graph-shaped polymers. We show that it is consistent with other approaches although we apply a nontrivial modification of the quaternionic method [51] for generating random polygons. In the modified method we generate random walks that connect two given points by rescaling the bond length and assign them some weight. We evaluate by it the mean-square radius of gyration and the hydrodynamic radius for several topological polymers. We correct the plots of Ref. [46] for the hydrodynamic radius versus the segment number and for the ratio of the gyration to the hydrodynamic radius versus the segment number. The estimated ratios are close to the values derived from an analytic assumption of the pair distribution function. The gyration radius of the multi-theta chain evaluated by the modified method agrees with exact Gaussian results [48]. We derive the moments of the bond vectors' coordinates distribution in random polygons generated by the quaternionic method.