Scattering function of semiflexible polymer chains under good solvent conditions

Abstract

Using the pruned-enriched Rosenbluth Monte Carlo algorithm, the scattering functions of semiflexible macromolecules in dilute solution under good solvent conditions are estimated both in d = 2 and d = 3 dimensions, considering also the effect of stretching forces. Using self-avoiding walks of up to N = 25,600 steps on the square and simple cubic lattices, variable chain stiffness is modeled by introducing an energy penalty ε(b) for chain bending; varying q(b) = exp (-ε(b)∕k(B)T) from q(b) = 1 (completely flexible chains) to q(b) = 0.005, the persistence length can be varied over two orders of magnitude. For unstretched semiflexible chains, we test the applicability of the Kratky-Porod worm-like chain model to describe the scattering function and discuss methods for extracting persistence length estimates from scattering. While in d = 2 the direct crossover from rod-like chains to self-avoiding walks invalidates the Kratky-Porod description, it holds in d = 3 for stiff chains if the number of Kuhn segments n(K) does not exceed a limiting value n(K)(*) (which depends on the persistence length). For stretched chains, the Pincus blob size enters as a further characteristic length scale. The anisotropy of the scattering is well described by the modified Debye function, if the actual observed chain extension <X> (end-to-end distance in the direction of the force) as well as the corresponding longitudinal and transverse linear dimensions <X(2)> - <X>(2), <R(g,⊥)(2)> are used.

Monte Carlo simulations of lattice models for single polymer systems

“…are also shown for comparison [62]. Near the peak the discrepancy of our data from the theoretically predicted formulas increases as the bending energy ε b decreases showing that the excluded volume effect sets in.…”

Is DNA a Good Model Polymer?

“…To circumvent the problem, properties such as the radius of gyration and diffusion coefficient were coded to iteratively update with each growth step, which kept the algorithm O( n 2 ) as desired. With additional scrutiny and a neighbor list, many property evaluations could be reduced to O( n ) time (such as the radius of gyration and the form factor, 18 see supporting information online), which subsequently allowed for greater reductions in the required computational time.…”

The study of the structure factor of a wormlike chain in an orientational external field

“…The oscillation is also easily developed for more flexible chains such as L/a = 5 and 10 provided that the strength of the nematic field is enhanced further, notwithstanding the corresponding pictures are not shown currently. Pierleoni et al 75 and Hsu et al 76 found the periodically oscillatory decays in the study of the structure factor of a linear flexible chain under stretch at both ends. Recently, Gemünden and Daoulas also observed the oscillatory behavior in their Monte Carlo study of uniaxial nematic polymer melts based on a discrete wormlike chain model combined with soft, anisotropic non-bonded potentials.…”