Towards the Quantitative Prediction of the Phase Behavior of Polymer Solutions by Computer Simulation

The phase diagram of polymer solutions (cf. e.g. alkanes dissolved in supercritical carbon dioxide) is complicated, since there are four control parameters (temperature, pressure, monomer volume fraction, chain length of the polymer) and due to the interplay of liquid-vapor transitions and fluid-fluid unmixing. As a result very intricate phase diagram topologies can result. An attempt to develop coarse-grained models that can deal with this task will be described. As usual, the polymers will be modelled as off-lattice bead-spring chains, where several chemical monomers are integrated into one effective bond, torsional degrees of freedom being disregarded. But also a coarse-grained description of the solvent is needed: we show that using a simple point particle with a quadrupole moment and suitable Lennard-Jones interaction yields a very good description of pure carbon dioxide (better than fully atomistic models with potentials from ab initio quantum chemistry calculations). The strength of the quadrupole moment is taken from experiment, and the Lennard-Jones parameters are adjusted such that the experimental critical temperature and density is correctly reproduced. This procedure works for other solvents as well, such as benzene. The pure alkane phase diagram is also reproduced by similarly chosen Lennard-Jones (LJ) potentials among the monomers, and the monomer-carbon dioxide LJ parameters are chosen from Lorentz-Berthelot mixing rules. These parameters are then used as input both for Monte Carlo calculations and approximate methods to calculate the equation of state, such as density functional and perturbation theory methods. Apart from the region close to critical points, where mean-field type methods fail, the analytical calculations agree well with the simulations. The solvent model, in which quadrupolar interactions are explicitly considered, is important in order to obtain a fair agreement with mixture experimental results.