A new Monte Carlo simulation approach for the prediction of sorption equilibria of oligomers in polymer melts: Solubility of long alkanes in linear polyethylene

Abstract

This work is concerned with the study of the solubility of small alkanes and ethylene oligomers in polyethylene melts of prescribed molecular weight distribution. The infinite dilution case is examined first, using Widom test particle insertion method. Simulation estimates of Henry’s constant for alkanes from C4 to C8 in a melt with average chain length C78 at T=450 K and P=1 atm are compared to older simulation results and to experimental data and are found to be adequately accurate. Cases where the oligomer is dissolved in the melt at finite concentrations are of greater practical interest. To address these cases, two different methods are implemented. The first one employs Monte Carlo (MC) simulations in the [f1NpnPTμ*] statistical ensemble, in which conventional insertion and deletion moves are used to equilibrate the concentration of the small molecules in the PE melt. It is observed that this technique leads to satisfactory results only for short alkanes, of length up to C10. Configurationally-biased insertions and deletions of alkane molecules in dense polymer phases become extremely difficult and time-consuming as the length of the inserted molecule is increased, rendering equilibration within reasonable CPU time practically impossible. To study the solubility of longer alkanes and oligomers in a polyethylene melt two novel MC moves are introduced: scission of a polymer chain to create an alkane molecule and a shorter chain, and fusion of a polymer chain and an alkane to create a longer polymer. For implementing these two new moves, a new statistical ensemble, the [f 1′Npn0PTμ*], is formulated. The new moves lead to extremely fast equilibration of the concentration of alkane molecules in the polymer melt and allow studying the solubility of long oligomers in the polymer matrix at high pressures. Their advantage lies exactly in the fact that they generate alkane molecules from already existing polymer chains, thereby eliminating the need for insertion and deletion moves. Results are presented from both MC methods for the sorption isotherms of C5, C10, and C20 in molten linear polyethylene and their dependence on the average chain length of the polymer matrix. The structure of the polymer–alkane mixtures and the volume changes (swelling) of the polyethylene matrix upon sorption are also examined. Predictions obtained from the atomistic simulations are compared extensively to available experimental data and to calculations based on the Flory–Huggins theory and the SAFT equation of state (EoS). The agreement between simulation and experiment is seen to be very good, demonstrating the value of the new simulation scheme designed and implemented in the course of this work.