Two-chamber lattice model for thermodiffusion in polymer solutions

When a temperature gradient is applied to a polymer solution, the polymertypically migrates to the colder regions of the fluid as a result of thermaldiffusion (Soret effect). However, in recent thermodiffusion experiments onpoly(ethylene-oxide) (PEO) in a mixed ethanol/water solvent it is observed thatfor some solvent compositions the polymer migrates to the cold side, while forother compositions it migrates to the warm side. In order to understand thisbehavior, we have developed a two-chamber lattice model approach to investigatethermodiffusion in dilute polymer solutions. For a short polymer chain in anincompressible, one-component solvent we obtain exact results for thepartitioning of the polymer between a warm and a cold chamber. In order todescribe mixtures of PEO, ethanol, and water, we have extended this simplemodel to account for compressibility and hydrogen bonding between PEO and watermolecules. For this complex system, we obtain approximate results for thecomposition in the warmer and cooler chambers that allow us to calculate Soretcoefficients for given temperature, pressure, and solvent composition. The signof the Soret coefficient is found to change from negative (polymer enriched inwarmer region) to positive (polymer enriched in cooler region) as the watercontent of the solution is increased, in agreement with experimental data. Wealso investigate the temperature dependence of the Soret effect and find that achange in temperature can induce a change in the sign of the Soret coefficient.We note a close relationship between the solvent quality and the partitioningof the polymer between the two chambers, which may explain why negative Soretcoefficients for polymers are so rarely observed.Comment: 12 pages, 8 figure