Variable connectivity methods for the atomistic Monte Carlo simulation of inhomogeneous and/or anisotropic polymer systems of precisely defined chain length distribution: Tuning the spectrum of chain relative chemical potentials

Application of variable connectivity Monte Carlo (MC) methods to the simulation of atomistically detailed polymer melts leads to deviations from monodispersity. To control the chain length distribution, a spectrum mu* of chain relative chemical potentials needs to be applied. The spectrum mu* that produces the most common limiting molecular weight (MW) distributions has been obtained in the past only for polymers in the bulk, for which mu* is solely determined by combinatorial considerations. In this work, the methodology is extended to more complex systems, such as inhomogeneous and/or anisotropic polymer melts, by presenting a novel numerical scheme for deriving the relationship between mu* and desired chain length distribution, where the energetics of the system is also taken into account. We illustrate the new approach in the case of polymer melts grafted on a solid substrate (both for single and bulk chains), for which the relationship between mu* and actual chain length distribution proposed so far in the literature for free melts breaks down. In contrast, the new method correctly accounts for the effect of grafting on system polydispersity. This is verified in end-bridging Monte Carlo (EBMC) simulations of two polydisperse polyethylene (PE) melt systems, C-78 and C-156, grafted on a noninteracting, hard surface at various grafting densities sigma, for the case where the chain length distribution is constrained to be uniform or for the case where mu* = 0. The new method allows extending and consistently applying newly developed chain connectivity-altering MC algorithms to the atomistic simulation of a variety of polymer melts where polydispersity should be precisely known.