Determination of the number‐, weight‐, and z‐average dimensions of macromolecules by viscosity and GPC measurements

Abstract

AbstractThe molecular weight averages are calculated which have to be inserted into the Fox‐Flory relationship \documentclass{article}\pagestyle{empty}\begin{document}$ {{\left[ \eta \right] = \Phi (\overline {r_{{\rm av}}^{\rm 2} } )^{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern‐\nulldelimiterspace} 2}} } \mathord{\left/ {\vphantom {{\left[ \eta \right] = \Phi (\overline {r_{{\rm av}}^{\rm 2} } )^{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern‐\nulldelimiterspace} 2}} } {M_{{\rm av}} }}} \right. \kern‐\nulldelimiterspace} {M_{{\rm av}} }} $\end{document} if the number‐, weight‐, or z‐average dimensions are to be determined for polymolecular polymer samples. The resulting complex molecular weight averages \documentclass{article}\pagestyle{empty}\begin{document}$ M_{r_{\rm n} } \eta _{\rm w},{\rm }M_{r_{\rm w} } \eta _{\rm w} $\end{document}, and \documentclass{article}\pagestyle{empty}\begin{document}$ M_{r_{\rm z} } \eta _{\rm w} $\en{document} are compared with simple molecular weight averages and for Schulz‐Zimm and logarithmic normal distributions of the molecular weight their numerical relations to the viscosity‐(Mη), number‐ (Mn), and weight‐average molecular weight (Mw) calculated. A simple straight‐forward method is outlined for the determination of the number‐, weight‐, and z‐average dimensions of polymolecular polymers from viscosity and gel permeation chromatography measurements.