Molecular Dynamics Simulations Of A Single Ring Polyelectrolyte Chain In Dilute Solutions

Using molecular dynamics(MD) simulations, a comparative study of various properties of a ring polyelectrolyte(PE) chain with its linear counterpart in dilute salt-free solutions with the good solvent condition is conducted. A splitting in the plots of the scaling exponentof two kinds of PEs against the Bjerrum length at intermediate strength of Coulomb interaction is observed. Also, a difference in the degree of counter-ion condensation in the similar regime of Coulomb interaction emerges. The difference in the degree of counter-ion condensation can be explained in terms of the G-factor, which is the ratio of mean squared gyration radii of these two kinds of PE chains and reflects the topological conformation difference between them.Furthermore, it is interesting to find that the dependence of the scaling exponent on the degree of counter-ion condensation is topologically invariant for ring and linear PE chains. These properties above in more dilute solutions are also well examined using Langevin MD method.Considering electrophoresis characteristics of PEs in dilute solutions under the external electric field. The effect of hydrodynamic interaction here is omitted owing to the enough large polymerization of PEs. The same critical electric field strength for ring and linear PEs is found by Langevin MD. When the field strength exceeds the critical value, the degrees of counter-ion condensation start to sharply decrease where the ring decrease pronouncedly less than the linear. Because linear PEs in strong electric field can sufficiently stretch to nearly straight line, while ring chains stretch much less due to their own topological constraint. Thus the difference of condensation degree between two chains increases and leads the increasing difference of electrophoresis mobility. A peak value of mobility difference in various Coulomb interaction is observed and stronger electric field induces the peak value increasing and right-shift which can guide the electrophoresis separation of ring and linear PE mixtures.