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