THERMAL-CONDUCTIVITY OF DILUTE-SOLUTIONS OF CHAIN-LIKE POLYMERS

The Curtiss-Bird phase-space kinetic theory of polymers is used to der ive an expression for the thermal conductivity of a dilute polymer sol ution, with the polymers represented as arbitrary bead-spring models. Then the general expression is specialized to Rouse bead-spring chains (with Hookean springs). The resulting expression contains several mom entum-space averages as well as the configuration-space distribution f unction for the polymer chains. Use is made of the authors' previous w ork on the solution of the Fokker-Planck equation for arbitrary bead-s pring models to evaluate the momentum-space averages. Then two special cases are considered: (a) the Hookean dumbbell model, in a fluid with velocity,gradients, and (b) the Rouse chain model, with the fluid at rest. For the latter, the authors' previous study of the properties of tensor Hermite polynomials is helpful for solving the partial differe ntial equation for the configurational distribution function for a pol ymer molecule in a fluid with a constant imposed temperature gradient. It is shown how the Gaussian distribution function is distorted in a nonisothermal system, but this distortion contributes only about 5% to the final value of the thermal conductivity. The results for the Rous e chain are compared with those previously obtained for several dumbbe ll models. (C) 1997 American Institute of Physics.