Coarse-grained modeling of macromolecular solutions using a configuration-based approach

Abstract

An accurate, configuration-based, coarse-grained model for dilute macromolecular solutions is presented. The basic approach relies on exploring the macromolecular configurational diversity present in the flow of dilute polymeric solutions and identifying and partitioning the most frequently observed configurations, e.g., folds, half dumbbells, kinks, dumbbells, coils, and stretched states. The probability of finding any one of these configurations is calculated using a master configuration map that dictates the conditional probability of finding a configuration with a given chain extension. Each configuration class is modeled using a dumbbell description with a suitably modified drag coefficient. The configuration-based model is implemented using a Brownian dynamics simulation and the predictions are compared with the corresponding beadspring model and finitely extensible nonlinear elastic dumbbell in homogeneous steady shear and uniaxial extension. Finally, prospects for model improvement are discussed.

Individual chain dynamics of a polyethylene melt undergoing steady shear flow

“…The primary conclusion drawn from these prior results is that chain ends undergo quasiperiodic fluctuations into the flow-vorticity plane during which they can begin to experience anisotropic diffusion down the axis of "tubes" formed by the surrounding, highly oriented chains. It is worth noting that an analogous type of periodic rotational and diffusional motion has been observed in simulations before [Aust et al (1999); Aust et al (2002); Doyle et al (1997); Venkataramani et al (2008)]; these simulations have all invoked mesoscopic models of bead-spring or bead-rod chains suspended at dilute concentrations in low molecular-weight solvents where the model chains were free to maintain Jeffreys'-type tumbling orbits and stretch-recoil cycles without experiencing interference from surrounding chains. Edberg et al (1987) also found evidence of molecular rotation and stretching in NEMD simulations of small chain liquids (n-butane and n-decane); however, the simulations of an analogous periodic behavior in the dense melts on relatively large n-alkane chains, as described above, were quite unexpected.…”

“…Nonequilibrium molecular dynamics is a common technique used to study flows of chain molecules comprised of atomistically detailed particles or coarse-grained models, such as bead-spring chains where each bead represents a center of drag resistance to the surrounding flow and the spring represents a statistical segment of the atomistic chain. Most NEMD flow simulations to date have focused on the determination of bulk rheological and structural properties, whether performed for either atomistic [Mavrantzas and Theodorou (1998); Moore et al (2000); Mavrantzas and € Ottinger (2002); Baig et al (2006); Kim et al (2008a); Baig and Mavrantzas (2009)] or coarse-grained [Kr€ oger et al (1993); € Ottinger (1996); Doyle et al (1997); Kr€ oger and Hess (2000); Schieber et al (2007); Venkataramani et al (2008); Dambal et al (2009); Kushwaha and Shaqfeh (2011)] liquids. Although much new insight concerning the relationships between flow kinematics, material properties, and microstructure has been gained from these studies, this focus on bulk behavior at macroscopic length and time scales has resulted in overlooking key microscopic information concerning the molecular-scale origin of the bulk rheological and structural properties [Kim et al (2009[Kim et al ( , 2010; Kim et al (2011)], as described below.…”

Review on the Brownian Dynamics Simulation of Bead-Rod-Spring Models Encountered in Computational Rheology

“…9, at a reciprocal frequency equal to 10 1 , a diminution of the relative error from 16% to 0.7% is appreciated when the time step is reduced from λ H /100 to λ H /10…”

“…Brownian dynamics simulations have been used intensively to study the physics of different kind of macromolecules and soft matter systems [4], as for example, the rheological behaviour of polymer [5,6,7,8,9,10], the dynamics of proteins and DNA [11,12,13,14], the flow behaviour of colloids [15,16,17,18,19,20,21], the structural dynamics of liquid-crystals [22,23] and the dynamics of carbon nanotubes [24,25,26,27]. …”

“…H, ζ and ck B T are fixed to 1 in a consistent system of units. A population of 10 3 dumbbells has been employed. Relative error is defined as follows: log G BD (ω R ) − log G th (ω R ) / log Θ , where Θ = G th (ω R = 10…”