Viscosity and compliance from molar mass distributions using double reptation models

Various empirical correlations between linear viscoelastic properties and molar mass distribution of linear polymers have been proposed. Many of these summarize the distribution in terms of the first few moments. This is sufficient when studying samples of limited variability. In parallel, various fundamental models that enable calculation of these rheological characteristics from the full distribution have been proposed. The advantage of the modeling approach is the ease of creating distributions, thus enabling independent control of moments up to any desired order. It is the goal of this contribution to explore this advantage and compare the findings of the single exponential (DRSE) and modified time-dependent diffusion (DRmTDD) double reptation models with the empirical relations. The models predict that η ₀ is primarily a function of the weight-average molar mass M _w, with subtle dependence on polydispersity. Furthermore, the model \(J^{0}_{{\text{e}}}\) depends mainly on a combination of the second (M _z/M _w) and third (M _z+1/M _z) polydispersity index. The DRmTDD model shows that conventional moment-based fit equations are only valid for limited distribution parameter ranges. General fit equations are proposed based on genetic programming. The details of the predictions are sensitive to the precise physical model formulation and need to be validated from experiments.