Translational diffusion of polymer chains with excluded volume and hydrodynamic interactions by Brownian dynamics simulation

Abstract

Within Kirkwood theory, we study the translational diffusion coefficient of a single polymer chain in dilute solution, and focus on the small difference between the short-time Kirkwood value D (K) and the asymptotic long-time value D. We calculate this correction term by highly accurate largescale Brownian Dynamics simulations, and show that it is in perfect agreement with the rigorous variational result D < D (K) , and with Fixman's Green-Kubo formula, which is re-derived. This resolves the puzzle posed by earlier numerical results (Rey et al., Macromolecules 24, 4666 (1991)), which rather seemed to indicate D > D (K) ; the older data are shown to have insufficient statistical accuracy to resolve this question. We then discuss the Green-Kubo integrand in some detail. This function behaves very differently for pre-averaged vs. fluctuating hydrodynamics, as shown for the initial value by analytical considerations corroborated by numerical results. We also present further numerical data on the chain's statics and dynamics.

Evaluation of the Kirkwood approximation for the diffusivity of channel-confined DNA chains in the de Gennes regime

“…(2). For example, simulations in free solution 24 suggested that very long simulations, at least 100s in duration, are required to reach the asymptotic limit. As we will show later, such long simulations are infeasible for channel-confined DNA due to the cost of incorporating bead-wall hydrodynamic interactions.…”

“…(2) and hereafter, we interpret the square of a vector as R 2 ¼ R Á R, not as a dyadic product RR. The difference between D (K) and D L has been addressed for flexible and semiflexible polymer chains in free solution, [18][19][20][21][22][23][24][25][26] with errors in the range of 1% to 25% for different approaches and different polymer models. For example, the error increases by increasing the chain size, 24 or by increasing the flexibility of the chain 26 or by reducing the solvent quality.…”

“…The difference between D (K) and D L has been addressed for flexible and semiflexible polymer chains in free solution, [18][19][20][21][22][23][24][25][26] with errors in the range of 1% to 25% for different approaches and different polymer models. For example, the error increases by increasing the chain size, 24 or by increasing the flexibility of the chain 26 or by reducing the solvent quality. 23,25 Our goal here is to evaluate the ability of the Kirkwood approximation to model experimental data for DNA confinement, for example, the relaxation time data from Reisner et al 27 The total duration of these experiments is long compared to the autocorrelation time of the mean span of the chain, but is rarely longer than the time s for center-of-mass diffusion over the size of the chain.…”

Fluctuating lattice-Boltzmann model for complex fluids

“…(A1) of the form D 0 = k B T /(ξ N ), where ξ is a friction parameter. To see this term, Liu and Dünweg 72 have shown that one is to work strictly within the assumptions of Kirkwood theory so that the model exhibits clear time scale separation and, consequently, D 0 is visible at short times, but not in the long-time limit. For the sake of completeness, we performed a regression analysis for the data in Fig.…”

“…The lack of a clearly separated intermediate time scale means there is no theoretical argument that we should observe D 0 , 72 which is also the argument that Liu and Dünweg give for D 0 not being observed in MD simulations. 72 We have compared the SRD fluid parameters in Ref. 64 (such as density and viscosity) and they can be mapped to values in a similar range to ours.…”