A Phenomenological Molecular Model for Yielding and Brittle-Ductile Transition of Polymer Glasses

This work formulates, at a molecular level, a phenomenological theoretical description of the brittle-ductile transition (BDT) in tensile extension, exhibited by all polymeric glasses of high molecular weight (MW). The starting point is our perception of a polymer glass (under large deformation) as a structural hybrid, consisting of a primary structure due to the van der Waals bonding and a chain network whose junctions are made of pairs of hairpins and function like chemical crosslinks due to the intermolecular uncrossability. During extension, load-bearing strands (LBSs) emerge between the junctions in the affinely strained chain network. Above the BDT, i.e., at "warmer" temperatures where the glass is less vitreous, the influence of the chain network reaches out everywhere by activating all segments populated transversely between LBSs, starting from those adjacent to LBSs. It is the chain network that drives the primary structure to undergo yielding and plastic flow. Below the BDT, the glassy state is too vitreous to yield before the chain network suffers a structural breakdown. Thus, brittle failure becomes inevitable. For any given polymer glass of high MW, there is one temperature TBD or a very narrow range of temperature where the yielding of the glass barely takes place as the chain network also reaches the point of a structural failure. This is the point of the BDT. A theoretical analysis of the available experimental data reveals that (a) chain pullout occurs at the BDT when the chain tension builds up to reach a critical value f(cp) during tensile extension; (b) the limiting value of f(cp), extrapolated to far below the glass transition temperature T(g), is of a universal magnitude around 0.2-0.3 nN, for all eight polymers examined in this work; (c) pressurization, which is known [K. Matsushige, S. V. Radcliffe, and E. Baer, J. Appl. Polym. Sci. 20, 1853 (1976)] to make brittle polystyrene (PS) and poly(methyl methacrylate) (PMMA) ductile at room temperature, can cause f(cp) to rise above its ambient value, reaching 0.6 nN at 0.8 kbar. Our theoretical description identifies the areal density ψ of LBSs in the chain network as the key structural parameter to depict the characteristics of the BDT for all polymer glasses made of flexible (Gaussian) linear chains. In particular, it explains the surprising linear correlation between the tensile stress σ(BD) at the BDT and ψ. Moreover, the theoretical picture elucidates how and why each of the following four factors can change the coordinates (σ(BD), T(BD)) of the BDT: (i) mechanical "rejuvenation" (i.e., large deformation below T(g)), (ii) physical aging, (iii) melt stretching, and (iv) pressurization. Finally, two methods are put forward to delineate the degree of vitrification among various polymer glasses. First, we plot the distance of the BDT from T(g), i.e., T(g)/T(BD) as a function of ψ to demonstrate that different classes of polymer glasses with varying degree of vitrification show different functional dependence of T(g)/T(BD) on ψ. Second, we plot the tensile yield stress σ(Y) as a function T(g)/T to show that bisphenol-A polycarbonate (bpA-PC) is less vitreous than PS and PMMA whose σ(Y) is considerably higher and shows much stronger dependence on T(g)/T than that of bpA-PC.