Distribution functions and dynamical properties of stiff macromolecules

Abstract

SUMMARYAn analytically tractable model for chain molecules with bending stiffness is presented and the dynamical properties of such chains are investigated. The partition function is derived via the maximum entropy principle taking into account the chain connectivity as well as the bending restrictions in form of constraints. We demonstrate that second moments agree exactly with those known from the Kratky-Porod wormlike chain. Moreover, various distribution functions are calculated. In particular, the static structure factor is shown to be proportional to l / q at large scattering vectors q. The equations of motion for a chain in a melt as well as in dilute solution are presented. In the latter case the hydrodynamic interaction is taken into account via the Rotne-Prager tensor. The dynamical equations are solved by a normal mode analysis. In the limit of a flexible chain the model reproduces the well-known Rouse and Zimm dynamics, respectively, on large length scales, whereas in the rod limit the eigenfunctions correspond to bending motion only. In addition, the coherent and incoherent dynamic structure factor is discussed. For melts we show that at large scattering vectors the incoherent dynamic structure factor is a universal function of only the combination q8/3p'/3, where 1/(2p) is the persistence length of the macromolecules. The comparison of the theoretical results with quasielastic neutron and light scattering experiments of various polymers in solution and melt exhibits good agreement. Our investigations show that local stiffness strongly influences the dynamics of macromolecules on small length scales even for long and flexible chains.

Fluctuating lattice-Boltzmann model for complex fluids

“…Figure 13(a) suggests that z = 2.43 is quite optimal for a 32-bead chain in the range k ∈ [1.0, 2.4] σ −1 . Corresponding data for the 64-bead chain collapse best for z = 2.54 ± 0.02 in the laboratory frame of reference thus approaching the 8/3 found by Winkler et al 73 We note that the scaling does not break down in Fig. 13(a) for length scales longer than R g such as 2π/(1.0 σ −1 ) ≈ 6.3 nm in the laboratory frame even though R g = 3.92 nm.…”

“…The collapse is plotted as a function of (k z t) 2/3 as it has been shown theoretically that log F(x) ∼ x 2/3 for k 3 k B T t/(6πη) 1. 73 Mussawisade et al 64 have confirmed by simulation a theoretic argument 73 stating that the dynamic scaling exponent should, in fact, assume the value of 8/3 similar to a semiflexible polymer in the laboratory frame for k R g 1. Figure 13(a) suggests that z = 2.43 is quite optimal for a 32-bead chain in the range k ∈ [1.0, 2.4] σ −1 .…”

Nonlinear elasticity and friction of liquid-crystalline polymer monolayers

“…Obviously, the orientation of two successive segments, n, nЈ, is not independent, but connected by the transition probability g(n͉nЈ), 16 which can be obtained from the expression for the elastic energy of the continuum model of the persistent chain 17,18 …”

Multi-Particle Collision Dynamics: A Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids

“…To extract the scaling relation for the intramolecular dynamics, which corresponds to the prediction (91), we resort to the following considerations. As is well known, the dynamic structure factor for a Gaussian distribution of the differences r i (t)−r j (0) and a linear equation of motion is given by [70,121] S(q, t) = S(q, 0)e…”