Determination of molecular weight distributions of linear flexible polymers from linear viscoelastic material functions

作者：David W. Mead · 发表于：Journal of Rheology · 年份：1994 · DOI：10.1122/1.550527 · 被引用次数：177 · 研究领域：Rheology and Fluid Dynamics Studies、Polymer crystallization and properties、Material Dynamics and Properties

Numerical and analytical methods are developed to invert the double reptation mixing rule to determine the molecular weight distribution (MWD). An analytic method involving Mellin transforms is developed for the case of a single exponential monodisperse relaxation function. A general analytic solution for the MWD is generated for a step-function monodisperse relaxation function. Numerical methods are developed for more general multiple time constant monodisperse relaxation functions. Both analytical and numerical methods are simple, robust, and capable of appropriately handling error-infected experimental data. The power-law relaxation modulus associated with broad MWD commercial polymer is analytically inverted to generate the corresponding molecular weight distribution. MWDs calculated from rheological data for polybutadiene and polypropylene are in close agreement with the corresponding GPC data and are very sensitive to small amounts of high molecular weight material present. The fundamental origins of this sensitivity lie in the intrinsically nonlinear nature of the dependence of rheological properties on molecular weight. The quality of the results suggest that the ‘‘double reptation’’ mixing rule captures an essential feature of the physics of entangled polydisperse polymeric systems.