Entanglement swelling in polymer glasses

A polymer system in which the chains are much longer than the entanglement molecular weight, $M_{+} \gg M_{e}$, is well entangled. When a thin, glassy polymer film is uniaxially strained, deformations which are almost visible to the naked eye called crazes may be formed. Measuring volume fractions of deformed to undeformed regions provides a method by which entanglement densities of similar systems can be compared\footnote{ACM Yang, EJ Kramer, CC Kuo, SL Phoenix, \emph{Macromolecules} \textbf{19} 2020 (1986)}. We present results of deformation experiments, probed using atomic force microscopy, in which well entangled polystyrene networks have been diluted with various weight fractions of polystyrene with molecular weight in the vicinity of $M_{e}$. Upon dilution the system assumes an effective reduction in the entanglement density. The effective entanglement density is predicted by a conceptually simple model with $M_e$ as the only free parameter.