Interacting chain model for poly(ethylene glycol) from first principles—stretching of a single molecule using the transfer matrix approach

Abstract

Based on ab initio quantum-mechanical calculations on short segments (up to four subunits) of poly(ethylene glycol), we construct n-state interacting chain models with n=3 or 7 with nearest-neighbor interactions that also account fully for the geometrical structure of the molecule (bond lengths, bond angles, and dihedral angles). For chains up to N=21 subunits we construct, in the three-state model, all 3N conformers exactly. For longer chains we apply the transfer matrix method in the Gibbs ensemble in the presence of an external force. The force-extension curve is calculated with high accuracy by both methods, and the results are compared with each other and with experimental data. We show that the infinite chain length limit is reached at about N=200. We analyze the effect of variation of geometrical and energy parameters in the model, as well as the effect of chain length on our final results. Chain end distribution functions, probabilities of rotational states and the persistence length are calculated. We show that additional rotational states beyond those of the potential minima used in the rotational-isomeric-state approximation must be included for an accurate description.