Experimental and Theoretical Studies of the Molecular Motions in Polymer Crazing. 1. Tube Model

Abstract

A theoretical model has been developed to calculate the craze surface energy for monodisperse linear polymers based on the "tube model" of polymer melts. This model, which is a refinement of models previously proposed, assumes that the essential molecular processes of chain scission and disentanglement occur in the "active zone"sa region of thickness greater than or equal to the chain radius of gyration, situated at the interface between craze and bulk polymer. At high temperatures, greater than a critical temperature, T > Ttr, craze growth occurs by stress-assisted chain disentanglement; below a second critical temperature, Tcr, craze growth occurs by chain scission. Between these critical temperatures, which are molecular weight and strain-rate dependent, craze growth involves both scission and disentanglement. New experimental data on craze growth in monodisperse, linear polystyrene over a range of temperatures at two strain rates are presented, which are well described by the new theory. The theory describes all features of the data with only one fitting parameter, including small peaks observed in the crazing strain/temperature graphs in the mixed-mode region. Similar features have been reported recently in craze data from poly(methyl methacrylate) without explanation.

The Roles of Blending and of Molecular Weight Distribution on Craze Initiation

“…11 The different crazing regimes suggested by Kramer could clearly be observed in polymers of different molar mass, and a simple model based on stress-accelerated disentanglement was able to account for the dependence of crazing stress on molar mass in the disentanglement regime consistently with other studies. 24 These developments provide a valuable starting point when addressing the issue of dispersity.…”

“…Synthesis of small quantities of narrow molar mass distributions ( M̅ w / M̅ n ≤ 1.12) and miniaturization of solid-state tests enabled De Focatiis et al to study craze initiation in PS over a wide range of molar mass, between 68 and 967 kDa . The different crazing regimes suggested by Kramer could clearly be observed in polymers of different molar mass, and a simple model based on stress-accelerated disentanglement was able to account for the dependence of crazing stress on molar mass in the disentanglement regime consistently with other studies . These developments provide a valuable starting point when addressing the issue of dispersity.…”

Entanglements in Glassy Polymer Crazing: Cross-Links or Tubes?

“…Note that chain pullout may be important close to the glass transition where Λ often rises . This effect has been included in tube-models of disentanglement during crazing. , …”

“…4 This effect has been included in tube-models of disentanglement during crazing. 50,60 Macromolecules Our simulations have used a very simple bead−spring model but show strikingly universal behavior over a range of chain stiffnesses that change the entanglement density by a factor of 3. This suggests that the results may apply to a range of experimental systems.…”

Modeling of crazing using a cohesive surface methodology

“…The numerical simulation of crazing has been undertaken at various length scales. At the mo-lecular level, Han et al (1998) developed a model to describe the strain rate eect on the surface energy and crazing mechanisms in fairly low molecular weight polymers. On a somewhat larger scale of observation, Sha et al (1997) used a spring network model to explicitly model the ®brils in the craze.…”