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

This work is concerned with the study of the solubility of small alkanes an d ethylene oligomers in polyethylene melts of prescribed molecular weight d istribution. The infinite dilution case is examined first, using Widom test particle insertion method. Simulation estimates of Henry's constant for al kanes from C-4 to C-8 in a melt with average chain length C-78 at T=450 K a nd P=1 atm are compared to older simulation results and to experimental dat a and are found to be adequately accurate. Cases where the oligomer is diss olved in the melt at finite concentrations are of greater practical interes t. To address these cases, two different methods are implemented. The first one employs Monte Carlo (MC) simulations in the [f(1)N(p)nPT mu (*)] stati stical ensemble, in which conventional insertion and deletion moves are use d to equilibrate the concentration of the small molecules in the PE melt. I t is observed that this technique leads to satisfactory results only for sh ort alkanes, of length up to C-10. Configurationally-biased insertions and deletions of alkane molecules in dense polymer phases become extremely diff icult and time-consuming as the length of the inserted molecule is increase d, rendering equilibration within reasonable CPU time practically impossibl e. To study the solubility of longer alkanes and oligomers in a polyethylen e melt two novel MC moves are introduced: scission of a polymer chain to cr eate 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 mo ves, a new statistical ensemble, the [f (')(1)N(p)n(0)PT mu (*)], is formul ated. The new moves lead to extremely fast equilibration of the concentrati on of alkane molecules in the polymer melt and allow studying the solubilit y of long oligomers in the polymer matrix at high pressures. Their advantag e lies exactly in the fact that they generate alkane molecules from already existing polymer chains, thereby eliminating the need for insertion and de letion moves. Results are presented from both MC methods for the sorption i sotherms of C-5, C-10, and C-20 in molten linear polyethylene and their dep endence on the average chain length of the polymer matrix. The structure of the polymer-alkane mixtures and the volume changes (swelling) of the polye thylene matrix upon sorption are also examined. Predictions obtained from t he atomistic simulations are compared extensively to available experimental data and to calculations based on the Flory-Huggins theory and the SAFT eq uation of state (EoS). The agreement between simulation and experiment is s een to be very good, demonstrating the value of the new simulation scheme d esigned and implemented in the course of this work. (C) 2001 American Insti tute of Physics.