## Doctoral Dissertations

#### Title

Determination of the MWD from the viscosity data of polymer melts

January 1996

#### Keywords

Chemistry, Polymer|Engineering, Chemical

Ph.D.

#### Abstract

Based on the model of Bersted and Slee, and later Malkin and Teishev, which assumes a truncated power-law viscosity function and a nonlinear mixing rule with a constant exponent of 3.4, Gordon and Shaw developed a differential method to determine the molecular weight distribution (MWD) from the viscosity data of polymer melts. However, the model is based on simplified assumptions and the differential process is sensitive to the quality of viscosity data. The purposes of this work were to derive the guidelines for the collection of viscosity data to ensure adequate performance of the differential process and to develop a new algorithm to increase the accuracy and the reliability of the MWD calculation from the viscosity data.^ For the differential transformation of viscosity to MWD, a minimum point density and range is required to resolve bimodality. For given point density and range, the higher the superposition between the viscosity data and the "knee" in the viscosity function produced by each mode, the better the resolution. Testing time can be reduced and resolution can still be preserved by placing more points in the key region of the viscosity curve and by skipping the unnecessary points at low shear rates.^ The nonlinear mixing rule was examined both experimentally by using real polymers and analytically. According to the theory-based quadratic mixing rule, the exponent $\alpha$ depends on the MWD of blends. For the middle range of the MWD, the nonlinear mixing rule, which assumes a constant $\alpha$ of 3.4 for all shear rates and MWDs, is almost equivalent to the quadratic mixing rule. Thus the mixing-rule assumption of Bersted and Slee should be valid for practical applications.^ Combining the self-consistent differential and integral approaches, we are able to resolve details of a MWD and quantify reasonably broad MWDs from many limited sets of viscosity data. The overemphasis of the high-molecular-weight end is due to the excitation of Rouse modes during the rheological measurements at high frequencies which hides the contribution of the low-molecular-weight components. A possible correction for this problem is to introduce a molecular-weight-independent Rouse dispersion at high frequencies in the simplified model. ^

COinS