General Methodology for Estimating the Stiffness of Polymer Chains from Their Chemical Constitution: A Single Unperturbed Chain Monte Carlo Algorithm

Abstract

The spatial dimensions and the stiffness (characteristic ratio, C ∞) of polymer chains are intimately related to key macroscopic properties such as the plateau modulus and the melt viscosity. Furthermore, these molecular features are very important in the selection and design of copolymer species used in directed self-assembly lithographic processes. We have developed a general methodology for predicting the chain dimensions of any polymer chain in the unperturbed state starting from its detailed atomistic structure. The methodology is based on performing Metropolis Monte Carlo (MC) simulation, leading to equilibration of the conformational distribution of a single unperturbed polymer chain, subject only to local interactions along its backbone. To define what constitutes local interactions, the maximal topological distance of repeat units between which nonbonded forces are active is varied systematically, until a maximum in stiffness is achieved. Our methodology was validated by comparing the predicted characteristic ratios for a series of polymers against the corresponding values estimated from MC simulations of the same polymers in the melt state based on the same force field. Furthermore, we have predicted the characteristic ratios for three polymers used in directed self-assembly lithographic processes and shown that they are in good agreement with reported experimental values.

Predicting experimental results for polyethylene by computer simulation

“…In effect, to solve this problem Karayannis et al proposed a hybrid of the asymmetric UA model of Toxvaerd and the TraPPE-UA FF (KMT-UA) [53,62]. In this case, values of C  of 8.06 -8.27 can be observed for linear PE, which is considered within the range of experimental results [88]. MD simulations of CG long PE models also return slightly higher values of C  = 8.93 [97].…”

Tacticity Effect on the Conformational Properties of Polypropylene and Poly(ethylene–propylene) Copolymers

“…of single unperturbed chains of chiral homopolymers as well as block and random copolymers with various constitutions. The ensembles of single unperturbed chains whose conformational properties were calculated were created and equilibrated by applying the Metropolis Monte Carlo algorithm developed by Tzounis et al, which has been successfully applied to a variety of polymer systems with different chemical constitution.…”

Using Monte Carlo to Simulate Complex Polymer Systems: Recent Progress and Outlook

“…On the basis of single chain Metropolis Monte Carlo simulations, Tzounis et al [88] proposed a methodology for computing the unperturbed chain dimensions of any polymer chain, irrespective of its chemical or architectural complexity. The authors tested many Monte Carlo moves and the most efficient ones in terms of their capability to relax both linear and branched polymer chains were found to be the rotate strand (pivot) and rotate branch ones, as they could induce drastic changes to the conformation of long strands and branches along the polymer chain.…”

“…Monte Carlo simulations with a single-site bond fluctuation model have also been used [98] to study protein adsorption on end-grafted polymers and investigate the role of polymer [88] for six different polymers [polyethylene (PE), isotactic polypropylene (i-PP), atactic polystyrene (a-PS), poly(ethylene oxide) dimethyl ether (PEODME), poly(dimethylsiloxane) (PDMS), and atactic poly(methyl methacrylate) (a-PMMA)], and the simulation predictions for the dependence of chain characteristic ratio C n on the number of backbone bonds n at 450 K. Reprinted (adapted) with permission from Tzounis et al [88]. Copyright (2017) American Chemical Society.…”