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Inverse method for determining general molecular weight distribution from polymer rheology
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DOI：10.1122/8.0001064.png)
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Abstract
En 中文
Determination of polymer molecular weight distribution (MWD) from rheological measurements is desirable due to the ease and low cost of rheometry compared to other methods such as gel permeation chromatography. However, relating MWD to rheology requires the inversion of rheological models, for which there is no analytic solution. Prior approaches assume a functional form for the MWD (such as a lognormal or generalized exponential distribution), minimizing the error with respect to the functional form's degrees of freedom. While this is a powerful and robust technique for determining general polymer properties, such as average MWD or polydispersity, it requires former knowledge of the shape of the MWD. This work presents a generalized approach to solving the inverse problem directly, with no former knowledge of the MWD or assumptions regarding its functional form. To close the inverse problem and establish uniqueness, Lagrange multipliers constraints on the MWD are included. The method is applied with reptation-based models to a variety of polycarbonate, polyethylene, and polystyrene polymers. For samples whose rheology are well described by reptation, the predicted MWD is shown to match experimental measurements very well. For samples that are not well-described by reptation, the predicted MWD naturally differs from experiment, highlighting the need for determining accurate forward models for understanding rheology response in a given sample. The proposed inverse method is shown to provide a good estimate for the MWD, assuming linear viscoelastic rheology, establishing it as a viable practical tool for rheology-based characterization.
Keywords:
Polymer rheology
Reptation models
Molecular weight distribution
Inverse methods
Constrained optimization
Journal
IF:
3.2
Papers:
2.5K
Citations:
7.0K
