The entanglement network and craze micromechanics in glassy polymers

Crazes have been grown from crack tips in thin films of the following five polymers: polytertbutylstyrene (PTBS), polystyrene (PS), poly(styrene-acrylonitrile) (PSAN), poly(phenylene oxide) (PPO), and poly(styrene-methyl methacrylate) (PSMMA). These polymers represent a wide range of l_e values, where l_e is the chain contour length between entanglements. Quantitative transmission electron microscopy has been used to analyze the extension ratio λ_craze and displacement profiles for these crazes. From these measurements the craze surface stresses have been computed by using the method of distributed dislocations. This analysis also permits an accurate measure of the level of the applied stress σ_∞. These measurements show that the stress necessary for crazing increases as l_e decreases and that the higher surface stresses present at crack tips generate crazes that have higher λs than isolated crazes in the same polymers. Surface drawing is shown to be the dominant mechanism for craze thickening in all five polymers.     

On some mechanical effects in glassy polymers attributed to chain entanglements

The important role of the entanglements in the deformation of high-molecular-weight glassy polymers is demonstrated by two phenomena: the build-up of material resistance in polymethylmethacrylate after chain interpenetration and the intrinsic crazing of polycarbonate which is observed when the entanglement network reaches its limits of extension.Dedicated to Prof. Dr. F. H. Müller.     

On the formation of topological entanglements during the contact of glassy polymers

Fracture energy (G) of the symmetric amorphous polystyrene (PS)–PS interfaces that were partially healed at temperatures (T) below the glass transition temperature of the bulk ( $ T_{\text{g}}^{\text{bulk}} $ ) has been measured at ambient temperature and compared with those reported in the literature (G ₀) for the symmetric PS–PS interfaces that were fully healed at T?>? $ T_{\text{g}}^{\text{bulk}} $ . It has been shown that G developed at T?<? $ T_{\text{g}}^{\text{bulk}} $ corresponds to G ₀ for the polymers having the molecular weight larger than the entanglement molecular weight. This behaviour indicates that topological entanglements can be formed across the contact zone of the polymers with glassy bulk via the interdiffusion of the chain segments located in the viscoelastic contact layer.     

Effects of molecular entanglements during electrospray of high molecular weight polymers

Concentration-dependent bimodal size distributions (comprised of single-molecule particles and multimolecule clusters) observed by microscopic examination of particles collected during electrospray (ES) of dilute solutions of high molecular weight polymers suggest that chain entanglement can interfere with the droplet subdivisions believed to be intrinsic to the electrospray process. The feasibility of such interference is discussed in the context of the spray model of Kebarle, along with its potential impact on the ES mass spectrometry of macromolecules.     

The influence of surface phenomena on molecular mobility in glassy polymers

Literature data on molecular mobility in glassy polymers have been analyzed. It has been shown that, in the temperature range corresponding to the glassy state of a polymer, a large-scale (segmental) molecular motion is possible, with this motion being responsible for the physical (thermal) aging of the polymer. Heating of an aged polymer restores its initial state, and the aging process begins again (effect of “rejuvenation”). At the same time, aging processes may be initiated by a mechanical action on a glassy polymer. It is sufficient to subject an aged polymer to a mechanical action to transfer it to a state characteristic of a polymer heated above the glass-transition temperature. It should be noted that deformation of a glassy polymer is nonuniform over its volume and occurs in local zones (shear bands and/or crazes). It is of importance that these zones contain an oriented fibrillized polymer with fibril diameters of a few to tens of nanometers, thereby giving rise to the formation of a developed interfacial surface in the polymer. The analysis of the published data leads to a conclusion that the aging of a mechanically “rejuvenated” polymer is, as a matter of fact, the coalescence of nanosized structural elements (fibrils), which fill the shear bands and/or crazes and have a glasstransition temperature decreased by tens of degrees.     

The effect of plasticization on craze microstructure

The structure of crazes in plasticized polystyrene has been studied by means of small-angle x-ray scattering and optical interference microscopy. Addition of plasticizer causes a rapid increase in the mean fibril diameter D and a slow decrease in the craze fibril volume fraction v_f. The crazing stress σ_c was also measured and it was found that the product D σ_c is independent of plasticizer concentration. These results are shown to be consistent with the entanglement model for controlling v_f and the meniscus instability model of craze thickness growth.     

Effect of end‐tethered polymers on surface adhesion of glassy polymers

The adhesion between a glassy polymer melt and substrate is studied in the presence of end‐grafted chains chemically attached to the substrate surface. Extensive molecular dynamics simulations have been carried out to study the effect of the areal density ∑ of tethered chains and tensile pull velocity v on the adhesive failure mechanisms. The initial configurations are generated using a double‐bridging algorithm in which new bonds are formed across a pair of monomers equidistant from their respective free ends. This generates new chain configurations that are substantially different than the original two chains such that the systems can be equilibrated in a reasonable amount of cpu time. At the slowest tensile pull velocity studied, a crossover from chain scission to crazing is observed as the coverage increases, while for very large pull velocity, only chain scission is observed. As the coverage increases, the sections of the tethered chains pulled out from the interface form the fibrils of a craze that are strong enough to suppress chain scission, resulting in cohesive rather than adhesive failure. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 199–208, 2004     

A model of environmental craze growth in polymers

A model of environmental craze growth has been developed based on the customary meniscus (or Rayleigh-Taylor) instability model of craze propagation but allowing for the possibility that environmental plasticization may cause the active layer of material adjacent to the craze to be of significant thickness with respect to the fibril spacing. Initially, as the active layer thickness increases, the fibril growth rate increases at constant fibril spacing, but eventually the fibril spacing comes to be controlled only by the active layer thickness and not by the surface tension and stress. This model of craze growth has been coupled to a model of stress-enhanced case II diffusion that is itself based on the Thomas-Windle model. Two main regimes of craze thickness growth are distinguished. In one the craze growth rate is controlled by the velocity of the diffusion front, the meniscus instability growth rate is assumed to be relatively slow, so that a significant plasticized active layer exists whose thickness assures that the meniscus instability front travels at the same speed as the diffusion front. In the other regime the propagation of the craze front is sufficiently fast that it also forms the diffusion front, so the growth rate is controlled by a combination of the two processes: diffusion and meniscus instability.     

Diffusion in glassy polymers

Two versions of the free‐volume theory of diffusion are compared by considering differences in the predictions for the activation energy for the diffusion process. A number of data‐theory comparisons for free‐volume theory are discussed and evaluated. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 785–788, 2003     

Effect of microheterogeneities on the diffusion of gases through glassy polymers

The diffusion of gases through glassy polymers is studied and the effective diffusion coefficient D^eff is represented as the result of the superposition of two fundamental mechanisms, namely slipping and hopping. D^eff is calculated by a two-point correlation method. Comparisons are made with experimental data of Meares for diffusion coefficients of Kr, O₂, He, and A in poly(vinyl acetate) in the glassy state. Good fits are obtained and yield significant parameters.     

Adhesion through molecular entanglements in polymer interfaces

This paper examines the role of polymer interdiffusion or interpenetration along and across a boundary of two compatible but dissimilar polymers in controlling interfacial adhesion in the interface region (interphase). The effect of interphase adhesion on the mechanical properties as well as the deformation and fracture behavior of sandwich laminates of poly(methylmethacrylate) (PMMA) and poly(vinylidene) fluoride (PVF₂) have been studied. The interphase has been characterized using microscopy (optical, transmission, and scanning electron), dynamic mechanical spectroscopy, and x-ray microanalysis. Conditions of multiple crazing/fracture in the brittle phase (PMMA) and shear yielding in the ductile phase (PVF₂) are discussed. Scanning electron micrographs confirm these deformation modes in PMMA-PVF₂ sandwich composite laminates.     

Dynamic heterogeneities in glassy polymers

The photoinduced isomerization of molecules incorporated in a glassy polymer matrix exhibits a wide spectrum of quantum yields. The source of the spectrum is matrix heterogeneities. The kinetics of the photoisomerization of 1-naphthyl-p-azomethoxybenzene in poly(ethyl methacrylate) and poly(n-butyl methacrylate) films is first used to study the rearrangement of the environments of photochromic molecules. The nonequilibrium distribution of cis molecules over the spectrum is obtained via conversion of trans molecules with the highest quantum yield into the cis form with the use of 405-nm light. The kinetics of attainment of the photostationary ratio for concentrations of cis and trans isomers under the action of light with a wavelength of 546 nm is studied through variation in the pause between the conversion of molecules into the cis form and the beginning of the studied process. It is shown that reversible changes in the structure of polymer matrices occur at a high rate at temperatures much lower than the glasstransition temperature.     

Strain-induced fibrillation of glassy polymers

Literature data on structural rearrangements taking place in amorphous glassy polymers upon their plastic deformation are analyzed. This deformation is shown to be primarily accompanied by polymer self-dispersion into fibrillar aggregates composed of oriented macromolecules with a diameter of 1—10 nm. The above structural rearrangements proceed independently of the deformation mode of polymers (cold drawing, crazing, or shear banding of polymers under the conditions of uniaxial drawing or uniaxial compression). Principal characteristics of the formed fibrils and the conditions providing their development are considered. Information on the properties of the fibrillated glassy polymers is presented, and the pathways of their possible practical application are highlighted.     

Diffusion in glassy polymers. III

The diffusion studies of several solvents in epoxy polymer reported by Kewi and Zupko in Part I of this series are explained with the solution obtained from the generalized diffusion equation which includes the internal stress contribution. The rate of permeation of a penetrant through a polymer film and the time lag needed to reach steady state are also given for the generalized diffusion equation.     

The thermoelastic effect in glassy polymers

The thermoelastic effect has been measured in compression on four glassy polymers; namely, polystyrene, poly(methyl methacrylate), polycarbonate, and epoxy resin. Quantitative results have been obtained for the first time on three of these polymers. It has been shown that by paying attention to specimen geometry and instrumentation results can be obtained to a high degree of accuracy (better than ±1.5% on a given set of measurements). The polymers are shown to obey the classical Thompson equation for thermoelasticity in solids over the temperature range studied (ca. 220–350°K). By inference such materials can be expected to behave classically in general. The results have been used, as first suggested by Trainor and Haward, to obtain values for the linear thermal expansion coefficient and the values so obtained are shown to be in excellent agreement, in general, with literature values obtained by more conventional methods. Results are given for a range of stress from 5 MN m^?2 to between 25 and 50 MN m^?2 according to ambient temperature. The method affords a measurement of parameters, in particular, linear thermal expansion coefficient. Values of specific heat for the four plastics have been measured by differential scanning calorimetry and the results compared with published data.