Challenges in Multiscale Modeling of Polymer Dynamics

Abstract

The mechanical and physical properties of polymeric materials originate from the interplay of phenomena at different spatial and temporal scales. As such, it is necessary to adopt multiscale techniques when modeling polymeric materials in order to account for all important mechanisms. Over the past two decades, a number of different multiscale computational techniques have been developed that can be divided into three categories: (i) coarse-graining methods for generic polymers; (ii) systematic coarse-graining methods and (iii) multiple-scale-bridging methods. In this work, we discuss and compare eleven different multiscale computational techniques falling under these categories and assess them critically according to their ability to provide a rigorous link between polymer chemistry and rheological material properties. For each technique, the fundamental ideas and equations are introduced, and the most important results or predictions are shown and discussed. On the one hand, this review provides a comprehensive tutorial on multiscale computational techniques, which will be of interest to readers newly entering this field; on the other, it presents a critical discussion of the future opportunities and key challenges in the multiscale geometric mapping matrix between all-atomistic and coarse-grained models N number of monomers per chain N e entanglement length, which is the number of monomers between two entanglements n v number of polymer chains per unit volume n ij (n 0 (r ij )) entanglement number (at equilibrium) between particle pairs i and j p r , P R configurational probability distributions in all-atomistic and coarse-grained models, respectively R ee end-to-end distance of polymer chain R G radius of gyration of polymer chain s segment index/contour length variable along primitive chain S(q) single chain coherent dynamic scattering function Z number of entanglements per chain, defined as Z = N/N e α exponent in standard Mittag-Leffler function σ

Estimation of error in observables of coarse-grained models of atomic systems

“…where repeated indices are summed throughout their range, m αβ = m (α) δ αβ is the mass of atom α, superimposed dots indicate time derivations, r βi is the component of r β in direction i, ∂ αi = ∂/∂r αi u(r n (t)) is the total interatomic potential of the system given, e.g., by (2), and f αi (t) is the ith component of applied force on atom α at time t. We will add initial conditions,ṙ βi (0) = v βi , and r βi (0) = r 0 βi , where v βi and r 0 βi , for now, are assumed to be given.…”

“…A very large literature exists on various coarse-graining mapping schemes, and choices of the appropriate map from the AA to the CG system or vice versa are often based on heuristic methods (see e.g. [2]). Our general approach can be adapted to any such well-defined AA-to-CG or CG-to-AA map, but for definiteness, we describe one such family of mappings.…”

“…The use of coarse-grained (CG) approximations has been prevalent in molecular dynamics (MD) simulations for many decades Comprehensive reviews of a large segment of the literature on CG models was recently given by Noid [1] and Li et al [2], and an application to semiconductor nano-manufacturing is discussed in Farrell et al [3]. The issue of central importance in developing CG models is the accuracy with which they approximate key features of the atomistic system.…”

USNCTAM perspectives on mechanics in medicine

“…A realistic coarse-grained model has also been developed to correctly reproduce the conformation of PEG polymers in water [114,115], based on the inverse Boltzmann method [116][117][118]. The following results are obtained through our simulations.…”

Refinement of a coarse-grained model of poly(2,6-dimethyl-1,4-phenylene ether) and its application to blends of PPE and PS

“…Basically, CG models group clusters of atoms into super-atoms, or beads, thus reducing the total number of interaction sites in the system. With this approach in mind, many groups have developed CG models using various approaches with numerous applications appearing in the literature over the past four decades [13][14][15][16][17]. But most CG models have focused on a few classical polymer types such as polystyrene (PS) [18][19][20][21][22][23][24][25][26].…”