Standard Definitions of Persistence Length Do Not Describe the Local “Intrinsic” Stiffness of Real Polymer Chains

Abstract

On the basis of extensive Monte Carlo simulations of lattice models for linear chains under good and Θ solvents conditions, and for bottle-brush polymers under good solvent conditions, different methods to estimate the persistence lengths of these polymers are applied and compared to each other. While for chain molecules at the Θ point standard textbook definitions of the persistence length yield consistent results, under good solvent conditions the persistence length (according to its standard definitions) diverges when the chain length of the macromolecules tends to infinity. Accurate simulation results for chain lengths up to Nb = 6400 allow us to verify the theoretically predicted power laws for the decay of the bond orientational correlation function. For the case of bottle-brush polymers, this dependence of “the” persistence length on the backbone chain length obscures the dependence on the side chain length, that is controversially discussed in the literature. Alternative definitions of a persistence length that do not suffer from this problem, based on the total linear dimension of the chain or on the scattering function via the so-called “Holtzer plateau” are studied as well. We show that the backbone contour length of the bottle-brush needs to be very large (about 100 persistence lengths in typical cases) to reach the asymptotic limit where the bottle-brush satisfies the self-avoiding walk statistics, and where a well-defined persistence length can be extracted. An outlook to pertinent experimental work is given.