2,293 research outputs found
Analytical Rescaling of Polymer Dynamics from Mesoscale Simulations
We present a theoretical approach to scale the artificially fast dynamics of
simulated coarse-grained polymer liquids down to its realistic value. As
coarse-graining affects entropy and dissipation, two factors enter the
rescaling: inclusion of intramolecular vibrational degrees of freedom, and
rescaling of the friction coefficient. Because our approach is analytical, it
is general and transferable. Translational and rotational diffusion of
unentangled and entangled polyethylene melts, predicted from mesoscale
simulations of coarse-grained polymer melts using our rescaling procedure, are
in quantitative agreement with united atom simulations and with experiments.Comment: 6 pages, 2 figures, 2 table
A First Principle Approach to Rescale the Dynamics of Simulated Coarse-Grained Macromolecular Liquids
We present a detailed derivation and testing of our approach to rescale the
dynamics of mesoscale simulations of coarse-grained polymer melts (I. Y.
Lyubimov et al. J. Chem. Phys. \textbf{132}, 11876, 2010). Starting from the
first-principle Liouville equation and applying the Mori-Zwanzig projection
operator technique, we derive the Generalized Langevin Equations (GLE) for the
coarse-grained representations of the liquid. The chosen slow variables in the
projection operators define the length scale of coarse graining. Each polymer
is represented at two levels of coarse-graining: monomeric as a bead-and-spring
model and molecular as a soft-colloid. In the long-time regime where the
center-of-mass follows Brownian motion and the internal dynamics is completely
relaxed, the two descriptions must be equivalent. By enforcing this formal
relation we derive from the GLEs the analytical rescaling factors to be applied
to dynamical data in the coarse-grained representation to recover the monomeric
description. Change in entropy and change in friction are the two corrections
to be accounted for to compensate the effects of coarse-graining on the polymer
dynamics. The solution of the memory functions in the coarse-grained
representations provides the dynamical rescaling of the friction coefficient.
The calculation of the internal degrees of freedom provides the correction of
the change in entropy due to coarse-graining. The resulting rescaling formalism
is a function of the coarse-grained model and thermodynamic parameters of the
system simulated. The rescaled dynamics obtained from mesoscale simulations of
polyethylene, represented as soft colloidal particles, by applying our
rescaling approach shows a good agreement with data of translational diffusion
measured experimentally and from simulations. The proposed method is used to
predict self-diffusion coefficients of new polyethylene samples.Comment: 21 pages, 6 figures, 6 tables. Submitted to Phys. Rev.
Theoretical Reconstruction of the Structure and Dynamics of Polymer Melts from Their Coarse-Grained Description
A theoretical formalism to reconstruct structural and dynamical properties of polymer liquids from their coarse-grained description is developed. This formalism relies on established earlier analytical coarse-graining of polymers derived from the first principles of liquid theory. The polymer chain is represented at a mesoscale level as a soft particle. Coarse-grained computer simulations provide input data to the reconstruction formalism and allow one to achieve the most gain in computational efficiency.
The structure of polymer systems is reconstructed by combining global information from mesoscale simulations and local information from small united-atom simulations. The obtained monomer total correlation function is tested for a number of systems including polyethylene melts of different degrees of polymerization as well as melts with different local chemical structure. The agreement with full united-atom simulations is quantitative, and the procedure remains advantageous in computational time.
The dynamics in mesoscale simulations is artificially accelerated due to the coarse-graining procedure and needs to be rescaled. The proposed formalism addresses two rescalings of the dynamics. First, the internal degrees of freedom averaged out during coarse-graining procedure are reintroduced in "a posteriori" manner, rescaling the simulation time. The second rescaling takes into account the change in friction when switching from a monomer level description to mesoscopic. Both friction coefficients for monomer and soft particle are calculated analytically and their ratio provides the rescaling factor for the diffusion coefficient. The formalism is extensively tested against the united-atom molecular dynamic simulations and experimental data. The reconstructed diffusive dynamics of the center-of-mass for polyethylene and polybutadiene melts of increasing degrees of polymerization show a quantitative agreement, supporting the foundation of the approach.
Finally, from the center-of-mass diffusion the monomer friction coefficient is obtained and used as an input into Cooperative Dynamics theory. The dynamics of polymer chains at any length scale of interest is described through a Langevin equation. In summary, the proposed formalism reconstructs the structure and dynamics of polymer melts enhancing computational efficiency of molecular dynamic simulations.
This dissertation includes previously published and unpublished co-authored material
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