Thermophoresis of linear polymer chains

The thermophoresis of a linear polymer chain in a solvent is examined theoretically and is shown to be due to the action of two forces. The first one is Waldmannʼs thermophoretic force (stemming from the departure of the molecular-velocity distribution from Maxwellʼs equilibrium distribution), which here is extrapolated to a dense medium by using scaling considerations. The second force is due to the fact that the viscous friction varies with position owing to the temperature gradient, which brings a zeroth-order correction to the Stokes law of friction. The present scaling theory is compared with recent experiments and is found to account for: (i) the existence of both signs of the thermodiffusion coefficient; (ii) the absolute magnitude of the coefficient; (iii) the fact that it is independent of the chain length in the high-polymer limit; and (iv) the dependence on solvent viscosity. The variation of the coefficient for short chains is also examined.