Dynamics of Rigid and Flexible Constraints for Polymers. Effect of the Fixman Potential

Models of polymers can generally be divided into two classes: (a) flexible, wherein bond lengths and valence angles are constrained to nearly constant values by strong, harmonic potentials, and (b) rigid, wherein the constrainb are geometric, Le., fixed bond lengths and angles. In general, the statistical mechanics of such systems differ. By introduction of a compensating potential based on the metric determinant of the unconstrained coordinates (the Fixman potential), the rigid model can be made to reproduce the equilibrium flexible results. It is not clear whether the corresponding dynamics are also reproduced. The purpose of the present work is to investigate the effect of the Fixman potential on dynamics. We have performed Brownian dynamics simulations of three models of a n-butane-like molecule: flexible, rigid, and rigid-plus-Fixman potential. Results show that for certain autocorrelation functions of the dihedral angle, there is a definite, though small, difference in dynamics between the rigid and flexible models in the low-friction limit. A t high friction the difference has decreased and the dynamics are essentially the same. The effect of the Fixman potential is minimal in both cases.