A combined statistical mechanics and molecular dynamics approach for the evaluation of the miscibility of polymers in good, poor and non-solvents

Abstract A newly proposed method based on combining statistical mechanics and molecular dynamics techniques was developed to evaluate the miscibility of polymers in various solvents. The focus in this article is the miscibility of poly(ethylene imine), PEI, in different solvents for its crucial significance in all its industrial applications. The statistical mechanics techniques were used to derive an expression for the deformational entropy of the polymeric chains suitable enough for evaluation during a molecular dynamics run. Molecular dynamics methods were then used to evaluate the enthalpy of mixing, entropy of mixing, the loss in entropy due to the deformation of the polymeric chains and the total free energy change of mixing. The enthalpy of mixing of PEI with water was shown to have a higher negative value than that of PEI with ethanol. This was attributed to the strong attractive interactions between PEI and water molecules due to the formation of strong hydrogen bonding between the molecules. PEI and n -dodecane had, however, a positive value for the enthalpy of mixing, thus indicating repulsive interactions between the polymer and the solvent. Evaluation of the loss in entropy due to the deformation of the polymer chain showed that in both cases, the coiling of the chains in case of a non-solvent or the swelling of the chain in case of a good solvent, the entropy loss will be of a positive value thus lowering the overall entropy change. Nevertheless, the loss will be more pronounced in case of the former than the latter. Overall evaluation of the free energy change has accurately predicted a strong miscibility for PEI with water, a moderate miscibility for PEI with ethanol and immiscibility for PEI in n -dodecane and thus affirming the validity of the developed approach in evaluating the miscibility behavior of PEI in various solvents. An account of the solubility parameters and the polymer–solvent interaction parameter ( χ ) was also discussed.