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.     

Effect of molecular entanglements on craze microstructure in glassy polymers

Thin films of ten glassy polymers are bonded to copper grids and strained in tension to produce crazes, which are then examined in the transmission electron microscope. The average craze fibril extension ratio λ for each polymer is determined from microdensitometer measurements of the mass thickness contrast of the crazes. The extension ratio λ is found to increase approximately linearly with the chain contour length l_e between entanglements, as determined from melt elasticity measurements of the entanglement molecular weight of these polymers. These results are analyzed by comparing them with λ_max, the maximum extension ratio of an entanglement network in which polymer chains neither break nor reptate (i.e., permanent entanglement crosslinks are assumed). The values of λ_max are given by l_e/d where d, the entanglement mesh spacing in the unoriented glass, is computed from d = k(M_e)^1/2 with k determined either from small-angle neutron scattering results on isolated chains in the glass or from coil size measurements in dilute solutions of a θ solvent. The craze extension ratios fall somewhat below λ_max at low λ but increase to well above λ_max for polymers with high l_e. This comparison suggests a significant contribution due to chain breakage (or reptation) in the higher-λ crazes of large-l_e polymers, which may arise from the higher true stresses in the craze fibrils (which for a given applied stress increase proportionally to λ). The results also imply that a useful way to increase the “brittle” fracture stress and decrease the ductile-to-brittle transition temperature of a glassy polymer is to decrease its entanglement contour length l_e.     

Kinetics of craze initiation in polystyrene in N-alcohols

The kinetics of craze initiation has been investigated for unmodified and rubber-modified polystyrenes in n-alcohols. The dependence on time and temperature of the critical strain at which crazes could be detected visually was determined with a Bergen elliptical strain device. Sorption studies were also conducted at room temperature on films exposed to the saturated vapor of n-alcohol. The analysis of crazing data in terms of the Eyring model gave activation energies from 9.4 to 17.4 kcal/mole, increasing with increasing chain length of n-alcohol and increasing rubber content. The activation volume multiplied by a stress concentration factor decreased with increasing rubber content and was nearly independent of the chain length of the n-alcohol. The larger the diffusion coefficient, which we measured by sorption experiments, the smaller was the activation energy for craze initiation. The values of diffusion coefficients, estimated from the experimental data on craze initiation, were found to be comparable with those from the sorption experiments. It was concluded that the rate of craze initiation on exposure to liquids is controlled by the diffusion of the molecules of liquid into polymer.     

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     

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.     

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.     

Ar atom emission as a probe of craze formation and craze growth in polystyrene

A report of measurements of Ar emission during the loading of polystyrene and high impact polystyrene in vacuum is presented. Argon was introduced into the material prior to the experiment by storing the samples in an Ar atmosphere. The development of crazes during loading was monitored by videotaped visual observations and scattered light measurements. Increased Ar emission is observed at the onset of crazing, provided that the crazes intersect the surface. The strength of the Ar signal depends upon the extent of crazing; especially intense signals are observed from samples which display significant crazing prior to fracture. High-impact polystyrene shows intense emissions at yield which soon decay due to the depletion of Ar from the near surface material. The emission intensity rises again prior to fracture, when surface crazes become connected to crazes in the bulk. Thus the emission of volatile species during deformation reflects the growth of crazes intersecting the surface, as well as changes in the “connectivity” of the craze network. © 1993 John Wiley & Sons, Inc.     

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.     

Diffusion in glassy polymers. I

Synopsis The diffusion of six solvents in three crosslinked, glassy epoxy polymers is studied. Case II swelling and Fickian sorption are observed as two simple limiting cases. The mechanism of diffusion changes from one limit to another as the nature of the solvent or the crosslink density of the polymer is altered. With mixed solvents, properly chosen, a superposition of Fickian diffusion and case II swelling is observed.     

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.     

Diffusion in glassy polymers. II

The Fickian diffusion coefficient of methylene chloride in a glassy epoxy polymer is calculated with the use of Crank's model of discontinuous change of D with concentration C. The diffusion constant is obtained as 1.93 × 10^?6 cm²/sec. The swollen layer behind the advancing solvent front is essentially in the rubbery state of the same polymer. The case II swelling by benzene is discussed in terms of a convective transport arising from the partial stress (internal) tensor of the penetrant. The superposition of Fickian and case II diffusion found with mixtures of methylene chloride and benzene is also discussed briefly.     

Solvent diffusion in amorphous glassy polymers

In this article, a mathematical model is proposed for predicting solvent self‐diffusion coefficients in amorphous glassy polymers based on free volume theory. The basis of this new model involves consideration of the plasticization effects induced by small molecular solvents to correctly estimate the hole‐free volume variation above and below the glass‐transition temperature. Solvent mutual‐diffusion coefficients are calculated using free volume parameters determined as in the original theory. Only one parameter, which can be predicted by thermodynamic theory, is introduced to express the plasticization effect. Thus, this model permits the prediction of diffusion coefficients without adjustable parameters. Comparison of the values calculated by this new model with the present experimental data, including benzene, toluene, ethyl benzene, methyl acetate, and methyl ethyl ketone (MEK) in polystyrene (PS) and poly(methyl methacrylate) (PMMA), has been performed, and the results show good agreement between the predicted and measured values. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 846–856, 2000     

Anomalous transport of penetrants in glassy polymers

Solutions are presented for the Fickian and non-Fickian equations describing the case of penetrant transport in a glassy polymer. Due to associated macromolecular relaxation, a sharp penetrant front is observed which separates the glassy core from the rubbery (gel-like) layer at the surface. Concentration profiles are compared and general comments about Fickian versus non-Fickian transport in polymers are made.     

Discussion of craze formation and growth in amorphous polymers in terms of the multiplicity of glass transition at low temperatures

A craze, the typical deformation zone in an amorphous polymer, can be divided into a precraze and a proper craze. A better understanding of the two corresponding formation processes is possible in terms of glass transition multiplicity.The precraze is associated with the molecular mobility in the confined flow zone, which is part of the main transition. The proper craze corresponds to the mobility in the flow transition zone (terminal zone for shear). A negative pressure generated by nonuniaxial stress is considered to be important for the maintainance of the molecular mobility in these zones belowT _g . The behavior of the zones at negative pressure and low temperatures Tg is considered using a pressure-temperature diagram. The fibril structure of crazes is discussed by a defect diffusion model for the proper glass transition; it is correlated with the sequential physical aging of the corresponding frozen structural defects. Typical mode lengths of the molecular mobilities in the different zones are compared with typical craze parameters. The structure of the craze material is considered to result from confined flow processes which cannot percolate because in the main transition the flow is confined by entanglements, and in the flow transition zone the flow is stopped by releasing the negative pressure due to crack propagation.