An Off-Lattice Flory-Huggins Approach of the Partitioning of Bulky Solutes between Polymers and Interacting Liquids

Abstract

The desorption of additives and polymer residues from materials (P) is of significant concern for a wide range of applications, including polymer ageing, off-odors, and the safety of materials in contact with food or water. With diffusion coefficients, partition coefficients between P and hydrogen-bonding liquids (L), denoted Ki,L/P for a solute i, are fundamental quantities to assess the loss of plastics constituents. For a polymer with a crystallinity c, they are defined as ln(Ki,L/P) - ln(1-c) =(uexi,P- uexi,L)/(kBT), where {uexi,k}k=L,P are the excess chemical potentials and where kB is the Boltzmann constant. Our ambition was to relate calculations of {uexi,k}k=L,P at an atomistic scale to measurable partition coefficients obtained for bulky solutes with different stiffness and shape, such as hindered phenolic antioxidants, n-alkanes and n-alcohols. For large solutes in dense and cohesive phases (P or L), promising computation techniques involve free energy perturbation and non-equilibrium methods, thermodynamic integration, and extended ensembles (Gibbs or osmotic ensembles). Because the free energy landscape of the coupled i+k system contains several minima and highly heterogeneous barriers, a low convergence is generally achieved. To overcome such complications, we calculated {uexi,,k}k=L,P at atomistic scale in the framework of the Flory-Huggins approximation. The main advantage is that the mixing energy for a wide range of conformers was derived from pairwise interactions and a continuous approximation of the packing of molecules without representing explicitly large molecular systems. The translational entropy in L was inferred from a mesoscopic representation of the liquid medium matching the radial distributions calculated by isothermal and isobaric molecular dynamics simulations. The corresponding predictions were satisfactory compared with 38 experimental Ki,L/P values between polyethylenes, polystyrene and different alcohols (isopropanol, ethanol).