DYNAMIC MECHANICAL RESPONSE OF CRAZES IN POLYSTYRENE

Dynamic mechanical analysis was used to study the mechanical properties and microstructureof crazes in polystyrene produced in air or in methanol at different temperatures. A new loss peakwas found at about 82℃,which is assigned to glass transition peak of craze fibrils. The decreaseof glass transition temperature of polymer in craze fibrils is due to the high values of surface tovolume ratio. The glass transition temperature ratio of craze fibrils to bulk material (T_g~l /Tg) hasbeen expressed as a function of the fibrils diameter (d). From T_g~l of craze fibrils,the value of fibrildiameter can be calculated. Annealing the crazed specimen at room temperature makes the fibrilsplastically deform and cause the fibrils to thin slightly,whereas annealing the crazed specimen atthe temperature near T_g of the craze fibrils makes the fibrils bundle together.     

Dependence on strain rate of the nucleation of cracks in polystyrene at 293°K

The processes associated with the deformation and fracture of polystyrene tested in uniaxial tension have been studied over a range of strain rates from 1.4 × 10^?2 to 4.3 × 10^?7 sec^?1 and at constant stresses between 4.1 and 2.9 kg/mm². The effect of strain rate on the surface craze distribution prior to fracture, the fracture stress, the mechanism of nucleation of cracks, and the nature of fracture surfaces associated with slow and fast crack propagation have been determined. The changes in fracture surface appearance have been studied using optical and stereoscan microscopy. The observations are consistent with the model presented in a previous paper. Fracture is preceded by craze formation, cavitation in the craze, coalescence of cavities to form large planar cavities which propagate slowly until a critical stage is reached at which fast crack propagation occurs. The effect of changes of strain rate and material variables on these processes is discussed.     

Growth kinetics of solvent crazes in glassy polymers

The kinetics of craze growth from sharp cracks in polystyrene (PS) and poly(methyl methacrylate) (PMMA) in contact with liquid methanol were measured with time-lapse photography as a function of the stress intensity factor K_I. At high K_I the craze length in both systems increases as √t if the sides of the craze are protected from methanol and as t if they are not, where t is the elapsed time after loading. If such a side-protected craze is dried under load and then methanol is reintroduced to the crack tip, the methanol front advances with the same kinetics as the original craze growth. This experiment Proves that solvent crazing velocities are limited by the hydrodynamic transport of solvent through the porous craze structure under a capillary pressure driving force (which can be as high as 100 atm). An improved model of fluid flow through the craze is developed and shown to predict craze growth kinetics in good agreement with those observed. The hydraulic permeability of methanol crazes in PS was found to be independent of craze length at small craze length and to be independent of K_I except at very low K_I. Although increases in molecular weight in the range M_w = 200,000 to M_w = 670,000 do not markedly affect the crazing kinetics, they greatly increase the time to fracture of the craze.     

Crazing of isotactic polypropylene in the medium of supercritical carbon dioxide

Uniaxial tensile drawing of films based on semicrystalline isotactic PP in the medium of supercritical carbon dioxide at a pressure of 10 MPa and a temperature of 35°C is studied. The tensile drawing of PP is shown to proceed in the homogeneous mode without necking and is accompanied by intense cavitation. The maximum level of porosity is 60 vol %. The porous structure that develops owing to the tensile drawing of the polymer in supercritical CO₂ is provided by formation of a set of crazes that are primarily localized in interlamellar regions. According to small-angle X-ray scattering data, the average diameter of fibrils that bridge craze walls changes slightly with an increase in tensile strain and is ∼10 nm; the specific surface of the craze fibrils is 100–150 m²/cm³.     

Monte Carlo calculations of the mean squared force in molecular liquids

The mean squared intermolecular force (F²₁) on a molecule in a diatomic liquid has been evaluated by a Monte Carlo calculation at reduced density p^* = 0.8 and reduced temperature 7^* = 0.72. The isotropic intermolecular potential is of Lennard-Jones form; anisotropic multipolar and overlap potentials of various strengths are used. For the largest strengths studied, the anisotropic contribution to (F²₁) is about 50–60% of the isotropic one.     

Mg2+‐Dependent High Mechanical Anisotropy of Three‐Way‐Junction pRNA as Revealed by Single‐Molecule Force Spectroscopy

Mechanical anisotropy is ubiquitous in biological tissues but is hard to reproduce in synthetic biomaterials. Developing molecular building blocks with anisotropic mechanical response is the key towards engineering anisotropic biomaterials. The three‐way‐junction (3WJ) pRNA, derived from ϕ 29 DNA packaging motor, shows strong mechanical anisotropy upon Mg²⁺ binding. In the absence of Mg²⁺, 3WJ‐pRNA is mechanically weak without noticeable mechanical anisotropy. In the presence of Mg²⁺, the unfolding forces can differ by more than 4‐fold along different pulling directions, ranging from about 47 pN to about 219 pN. Mechanical anisotropy of 3WJ‐pRNA stems from pulling direction dependent cooperativity for the rupture of two Mg²⁺ binding sites, which is a novel mechanism for the mechanical anisotropy of biomacromolecules. It is anticipated that 3WJ‐pRNA can be used as a key element for the construction of biomaterials with controllable mechanical anisotropy.     

Low-angle electron diffraction from high temperature polystyrene crazes

Low-angle electron diffraction (LAED) was used to study the microstructure of crazes produced at different temperatures T and strain rates in thin films of monodisperse polystyrene (PS). At a slow strain rate of 4.1 × 10^?6 s^?1 both the fibril diameter D and the fibril spacing D₀ of crazes in 1800k molecular weight PS remained constant with temperature up to T ≈ 70°C and then sharply increased as T approaches T_g. At a higher strain rate of ～ 10^?2 s^?1, both D and D₀ increase only slightly with T. The values of D and D₀ over a range of temperature are in very good agreement with those values obtained in bulk samples using small-angle x-ray scattering. The crazing stress was measured as a function of temperature in the thin films of the 1800k molecular weight PS strained at the same slow strain rate used for the LAED measurements. These measurements were analyzed using a simple model of craze growth to reveal the temperature and strain rate dependence of the craze surface energy Γ. At room temperature Γ ≈ 0.076 J/m² (versus Γ ≈ 0.087 J/m² predicted) and was observed to remain constant up to T ≈ 70°C and then decrease by approximately a factor of two at T = 90°C. This decrease in Γ is believed to result from chain disentanglement to form fibril surfaces at sufficiently high temperatures and occurs in the same temperature range in which the craze fibril extension ratio λ was observed to increase.     

Effects of humidity on environmental stress cracking behavior in poly(methyl methacrylate)

Environmental stress cracking (ESC) in poly(methyl methacrylate) under different humidity conditions has been investigated. Constant stress‐intensity factor (K) ring‐type specimens were prepared, and all specimens were equilibrated at five different humidity conditions for about two years. ESC tests were carried out under the same humidity as specimens had been stored. Acoustic emission (AE) signals during ESC tests were also measured to examine the crack‐growth behavior. The threshold K value (K_th) tended to increase with increasing humidity. At a relative humidity (RH) of 11%, crack growth occurred gradually until 40 ks under a K value of 0.70 MPam^1/2, and then the crack‐growth rate began to increase and AE events were observed. A laser microscopic observation indicated that the crack extended by the coalescence between a main crack and a microcrack ahead of the main crack tip. AE signals generated are considered to be associated with the coalescence. At 98% RH, an incubation period where no crack growth was observed existed under a K value of 0.94 MPam^1/2, but the crack began to grow suddenly after that incubation period. This suggests that the craze at the crack tip may become weaker with increasing loading time under high humidity. Although the crack‐growth rate at 98% RH was higher than that at 11% RH, no AE events were observed. This suggests that the crack extended stably in the craze at a crack tip, and sorbed water may make the craze growth easy. All the results suggest that two different ESC mechanisms are activated depending on sorbed water that are varied by humidity. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 40: 1–9, 2002     

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.     

1H magic angle rotation NMR in polymer studies

The principles of the method of NMR line narrowing by measurement with spinning of the sample about the magic axis (MAR-NMR) are introduced, with particular emphasis on the effects of internal motion upon the possibilities and limitations of the method. The applications of the method in ¹H-NMR studies of polymer structure and dynamics are then reviewed. Due to both theoretical and experimental limitations, narrowing of dipolar broadened NMR lines by MAR can be observed in ¹H NMR spectra only in those cases where internal motion is anisotropic, or in heterogeneous systems where line width is limited by differences of magnetic susceptibility. In polymers, both solid and liquid, the method makes possible differentiation between isotropic and anisotropic internal motion. In systems with anisotropic internal motion, MAR-NMR makes possible a characterization of motional codes which normally are obscured by residual dipolar interactions, as well as of geometrical restrictions upon these motions.     

Quantitative approaches to particle cavitation,shear yielding,and crazing in rubber-toughened polymers

Models for rubber particle cavitation, shear yielding, and crazing are reviewed, and their ability to predict the large-strain deformation behavior of toughened polymers is discussed. An existing model for void initiation and expansion in rubber particles correctly predicts the observed trends: cavitation resistance increases when either the shear modulus or the surface energy of the rubber is increased, or the particle size is reduced. However, further work is needed to improve quantitative modeling of the thermally- and stress-activated void nucleation step. Shear yielding, which is also a rate process, is much better understood; here, the main problems in modeling relate to the formation and evolution of porous shear bands. Craze growth and failure are also reasonably well understood, but previous attempts at modeling have been hampered by uncertainties about craze initiation. To overcome these difficulties, a new theory of crazing is proposed, which treats initiation as a fracture process, and defines a new materials property, G_nasc, the energy required to form unit area of nascent craze. Because nascent crazes are ∼20 nm thick, G_nasc is low: calculations give values <0.5 J m⁻² for polystyrene. A new criterion incorporating a plasticity factor fits the data of Sternstein and coworkers on crazing under biaxial loading. In combination with theories of particle cavitation and shear yielding, the fracture mechanics model explains why the balance between crazing and shear yielding is governed by particle size, for example in ABS. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1399–1409, 2007     

Single-crystal Anisotropic Proton Conductivity in the Clathrate of the Hydrogen-diquinuclidine Ion Inserted in a Polyanionic Thiourea–chloride Matrix

The anisotropic proton conductivity of a large-sized single crystal of the supramolecular, commensurate host–guest inclusion compound constituted by a polyanionic thiourea–chloride matrix defining channels in which the diquinuclidinium cations [Q₂H]⁺ are hosted is reported. Specimens in the millimetre scale display an anisotropy factor of about 100, with electrical conductivities along molecular channels of the order of 10^-4?S?cm^-1 at room temperature.     

Criterion for craze nucleation in polycarbonate

Plastic deformation and crazes were initiated in polycarbonate bars containing a round notch by three-point bending. Morphological observations revealed that internal crazes are nucleated by a hydrostatic stress component caused by plastic constraint ahead of the fully developed plastic deformation zone. The characteristics of the deformation bands for quenched and slowly cooled materials are in good agreement with the logarithmic spiral curves predicted from a slip-line theory. The distribution of the stress components in the plastic deformation zone was analyzed using this theory. The critical hydrostatic stress is 87 MN/m² for slowly cooled polycarbonate and 89 MN/m² for quenched material. These results are compared with those of the craze nucleation models of Gent and Argon.     

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.     

Craze growth and healing in polystyrene

The kinetics of craze growth and craze healing were studied by dark-field optical microscopy in monodisperse molecular weight polystyrene (PS) that varied in molecular weight from 88,000 to 1,334,000. The following observations were made. (1) G₁ the virgin growth rate, decreased rapidly with increasing molecular weight until M_n ～ 200,000 and then remained constant. (2) G₁ decreased with increasing craze density. (3) The growth rates of approaching craze tips decreased when the craze tips overlapped, and the effect was less for crazes whose parallel growth paths were greater than 40 μm apart. (4) Complete craze healing was observed by comparison of the nucleation times, τ₂, and growth rates, G₂, of healed individual crazes with the craze kinetics of the virgin sample. (5) The extent of healing was characterized using four cases in which τ and G were measured as a function of healing time, temperature, constant stress, and molecular weight. (6) Craze healing times were found to increase with molecular weight and were analyzed in terms of the modified molecular weight of the craze zone. (7) Significant bond rupture was determined to occur during crazing by comparison of healing times with stress relaxation and diffusion data. (8) Craze healing studies provide insight into both crack healing and fracture of glassy polymers.     

The dependence of craze velocity on the pressure and temperature of the environmental gas

The craze velocity was determined for poly(chlorotrifluoroethylene) (PCTFE) in CH₄ and for PCTFE, polystyrene, and poly(methyl methacrylate) in N₂. It was found that for temperatures near the boiling point the velocity and number of crazes depended on the relative pressure given by P exp[-(Q_v/R) (T_B^?1 - T^?1)], where P is the pressure, Q_v is the heat of vaporization, and T_B is the boiling point. The craze velocity was related to the coverage of the adsorbed gas. For coverages corresponding to a few monolayers the logarithm of the velocity was proportional to the relative pressure. As the temperature increases from T_B, the creep rate decreases because gas desorbs with increasing temperature; the creep rate attains a minimum value at a temperature where the general process of thermally activated deformation becomes dominant.     

Micro and nano layered polymers

The crazing behavior of coextruded microlayer sheets consisting of alternating layers of polycarbonate (PC) and styreneacrylonitrile copolymer (SAN) was investigated as a function of PC and SAN layer thicknesses. In this study, the total sheet thickness remained essentially constant and the PC and SAN layer thicknesses were changed by varying both the total number of layers from 49 to 1857 and the PC/SAN volume ratio.^[1,2] Photographs of the deformation processes were obtained when microspecimens were deformed under an optical microscope. Three different types of crazing behavior were identified: single crazes randomly distributed in the SAN layers, doublets consisting of two aligned crazes in neighboring SAN layers, and craze arrays with many aligned crazes in neighboring SAN layers. The transition from single crazes to doublets was observed when the PC layer thickness was decreased to 6 microns. Craze array development was prevalent in composites with PC layer thickness less than 1.3 microns. It was concluded that SAN layer thickness was not a factor in formation of arrays and doublets; formation of craze doublets and craze arrays was dependent only upon PC layer thickness.     

Chain scission in polystyrene by impact fracture

The number of chain scissions n_s per unit fracture area by impact in high-molecular weight polystyrene is determined to be approximately 3.3 × 10¹⁴/cm² at room temperature. This is almost 20 times larger than would be expected if chain scissions took place only at, or very close to, fracture surfaces. This result was obtained by measuring the molecular weight decrease and the total fracture area of the impact fragments by using size exclusion chromatography and statistical particle size measurements, respectively. The large n_s strongly indicates that significant chain breakage occurs during crazing before the propagation of cracks. An average craze thickness before breakdown under impact is estimated from n_s to be around 2 μm. In a diluted polymer, n_s is found to be significantly lower than the extrapolated value, assuming a linear dilution of entangled chain crossings at the fracture surface. This low chain scission density, however, can be explained by taking into account the reduction of craze breakdown strain in the diluted polymers. Finally, the broken chain ends of polystyrene appear to be stable under ambient conditions. © 1992 John Wiley & Sons, Inc.     

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.     

Rheological properties of anisotropic poly(para-benzamide) solutions

A study has been made of the viscous properties of poly(para-benzamide) (PBA) solutions in dimethyl acetamide, which undergo a transition from an isotopic to an anisotropic (liquid-crystal) state at a definite concentration C^*. The polymer solutions behave in many respects (as regards the concentration and temperature dependence of viscosity, etc.) like solutions of low molecular weight compounds forming a liquid crystal phase, although the transitions are less pronounced in the polymer solutions owing to their polydispersity. It is shown that the viscometric method, being extremely sensitive to C^*, is convenient for determining phase diagrams of anisotropic polymer solutions. The values of C^* as related to the molecular weight of PBA have been determined, and a general criterion for transition from isotropic to anisotropic solutions established; the latter has the form (CM?)^* ≈ 1.3 × 10⁵ at 20°C. This criterion is in line with the condition for the formation of the liquid-crystal structure in a dispersion of rodlike particles as proposed by Flory. Generalized concentration dependences of viscosity have been plotted by reducing concentration to C^* and viscosity, to the maximum viscosity at the phase transition point. In investigating the flow properties of PBA solutions we revealed the existence of a yield point in the range of low shear stresses, and an intersection of the flow curves of solutions of different concentration at high shear stresses, which excludes a generalized representation of the flow curves in reduced ordinary-type coordinates.