A generalized method to calculate diffusion rates in polydisperse systems. Application to miscible polymer pairs in the concentrated regime

A generalized method for calculating diffusion rates in polydisperse systems, valid in the concentrated regime, is outlined. In the formulation of the method the discrete variable that describes the molecular size, is replaced by a continuous variable in the same range. This replacement diminishes the number of degrees of freedom but keeping the essential physics of the original statement. The effects of monomeric friction coefficient, Flory-Huggins thermodynamic interaction parameter, individual species molecular weights, local molecular weights distribution and local T_g are consistently included in the model.

The method is used to calculate concentration distribution profiles generated by diffusion of polydisperse polymers blends, and experimentally tested. For this purpose polystyrene with discrete (bimodal and tetramodal) molecular weight distributions and polystyrene with wide and continuous molecular weight distributions were used to simulate polydisperse systems. They are allowed to diffuse in a blend of polyphenylene oxide and polystyrene.

The simulated concentration profiles are compared with results obtained by using two experimental techniques based on independent physical properties, which give complementary information: Raman spectroscopy and DMA. The total PS concentration profiles calculated using the proposed method agree well with Raman spectroscopy results. Simulated DMA results—which are sensitive to the PS species molecular weight distribution—obtained using the concentration profiles calculated for each PS molecular weight species, agree well with the experimental DMA results. Calculations based on average molecular weights on the other hand, give incorrect results.