Craze fibril structure and coalescence by low-angle electron diffraction

Brown has shown that low-angle electron diffraction (LAED) may be used to determine fibril diameters D and spacings D₀ of crazes in thin polymer films. He found, however, that the D and D₀ determined for air crazes in polystyrene (PS) thin films were larger by about a factor of 3 than those in PS bulk crazes determined by using small-angle x-ray scattering (SAXS). We have repeated Brown's LAED experiments and find that the discrepancy may be caused by an aging effect. Our fresh crazes have D and D₀ values from LAED that are comparable to those of bulk PS crazes determined by SAXS. As the craze ages, however, fibrils retract and coalesce in wide regions of the craze, leading eventually to an observable “skin.” Aged crazes thus have much larger D and D₀ values than do fresh crazes. The large molecular mobility of the PS molecules in the fibrils necessary for this aging to occur at room temperature has important implications for fibril failure.     

Development of crazes in polycarbonate,investigated by ultra small angle X-ray scattering of synchrotron radiation

The development of crazes in polycarbonate is investigated with the method of ultra small angle X-ray scattering of synchrotron radiation. Measurements at T = 130°C are discussed. The two-dimensional scattering patterns are analysed by means of a simple fibrillar model of the crazes. The geometrical parameters of the crazes as a function of the macroscopic draw ratio λ_d are determined using a curve-fitting procedure. The craze fibril volume fraction ν_f shows a complex dependence on λ_d.     

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.     

Studies of craze fibril deformation during fatigue in polystyrene

Small-angle scattering of synchrotron x-ray radiation has been used to study the effects of fatigue on craze fibril microstructure. The results obtained during unloading and reloading during a single cycle have been compared with those predicted by a model of sinusoidally bent fibrils. In addition the total displacement of the craze boundaries was found from the change in the invariant on unloading. The mean fibril diameter D was measured at the maximum tensile strain in each cycle. Over 250 cycles, D increased by at least a factor of 2 from an initial value of 6.5 nm, with most of this change happening in the first few cycles. The increase in D must occur by fibril coalescence, a mechanism that requires that the material in craze fibrils have considerable molecular mobility, even at room temperature, 70°C below the glass transition temperature.     

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.     

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.     

Crazing and fracture in crystalline,isotactic polypropylene and the effect of morphology,gaseous environments,and temperature

Stress crazing is studied in three forms of crystalline, isotactic polypropylene (PP): (1) smectic/nonspherulitic, (2) monoclinic/nonspherulitic, and (3) monoclinic/spherulitic PP. Optical and scanning electron microscopy as well as stress—strain measurements are used to characterize crazing behavior in these three forms as a function of temperature (?210 to 60°C) and of the gaseous environment (vacuum, He, N₂, Ar, O₂, and CO₂). Forms 1 and 2 are found to craze much like an amorphous, glassy polymer in the temperature range between ?210 and ?20°C, irrespective of environment. The plastic crazing strain is large close to the glass-transition range (ca. ?20°C) of amorphous PP and in the neighborhood of the condensation temperature of the environmental gas. Near condensation, the gas acts as a crazing agent inasmuch as the stress necessary to promote crazing is lower in its presence than in vacuum. A gas is the more efficient as a crazing agent, the greater is its thermodynamic activity. Spherulitic PP (form 3) crazes in an entirely different manner from an amorphous, glassy polymer, showing that the presence of spherulites influences crazing behavior much more profoundly than the mere presence of a smectic or monoclinic crystal lattice. Below room temperature, crazes are generally restricted in length to a single spherulite, emanating from the center and going along radii perpendicular, within about 15°, to the direction of stress. They never go along spherulite boundaries. Gases near their condensation temperature act as crazing agents much as in nonspherulitic PP. Above room temperature the crazes are no longer related to the spherulite structure, being extremely long and perfectly perpendicular to the stress direction. Apparently the crystals are softened enough by thermally activated segmental motion to permit easy propagation of the craze. The morphology of the fracture surfaces and its dependence on temperature and environment is described and discussed. Concerning the action of gases as crazing agents it is argued that the gas is strongly absorbed at the craze tip, where stress concentration increases both the equilibrium gas solubility and the diffusion constant. Hence, a plasticized zone is formed having a decreased yield stress for plastic flow. This is considered to be the main mechanism by which the gas acts as a crazing agent. In addition, reduction of the surface energy of the polymer by the adsorbed gas eases the hole formation involved in crazing.     

Conformation of poly(dimethyl siloxane) and polystyrene in solution measured by polarized Raman scattering

Depolarization ratios ρ have been measured over ranges of temperature T and molecular weight M for polystyrene (PS) dissolved in cyclohexane (1002 cm^?1 Raman band) and for poly(dimethyl siloxane) (PDMS) dissolved in benzene (2907 cm^?1 Raman band). The ranges in the case of PS are 15 < T < 65°C and 2 × 10³ < M < 4 × 10⁵ and in the case of PDMS are ?3 < T < 60°C and M = 10⁴. Measurements were also made of PDMS radii of gyration using conventional light scattering. The results are interpreted in terms of a theory connecting rotational isomeric populations with polymer extension. In the case of PDMS, an experimental value of the proportionality constant for trans isomers (D₂ = ?3.9 ± 0.9) is deduced. This is closer to the theoretical value than previous estimates but there is still some discrepancy. In the case of PS the isomeric changes resulting from extension are independent of M for M > 10⁴. Deviations are observed for lower M.     

Crazing and shear deformation in crosslinked polystyrene

Thin films of polystyrene (PS) are bonded to copper grids and crosslinked with electron irradiation. When the films are strained in tension regions of local plastic deformation, either crazed or plane stress deformation zones (DZs), nucleate and grow from dust particles. the nature of the local deformation, as well as the local extension ration λ, is determined by transmission electron microscopy. The behavior of the PS glass is consistent with its being a network of molecular strands of total density v = v_E + v_X, where v_E is the entangled strand density inferred from melt elasticity measurements of uncrosslinked PS and v_X is the density of crosslinked strands determined from the ratio of the applied electron dose to the electron dose for gelation. when v is less than 4 × 10²⁵ m^?3 (<1.3v_E), only crazes are observed whose microstructure is similar to those in uncrosslinked PS. As v increases from 4 × 10²⁵ to 8 × 10²⁵ m^?3 (from 1.3v_E to 2.5v_E) shear deformation begins to compete with crazing. As v increases above 8 × 10²⁵ m^?3, only shear DZs are observed, the strain in which becomes progressively more diffuse as v increases. The λ in the crazes and DZs correlate well with λ_max, the maximum extension ratio of a strand in a network of density v computed using the Porod×Kratky model. For crazes ln(λ) ? 0.9 ln(λ_max) and for DZs ln(λ) ? 0.55 ln(λ_max). The strain at which crack nucleation is first observed increases as v increases from <5% in uncrosslinked PS with v = 3.3 × 10²⁵ m^?3 to >20% in PS with v = 33 × 10²⁵ m^?3 (v = 10v_E); crosslinking to still higher crosslink densities, e.g., v = 14v_E, results in cracks which propagate in a catastrophic manner at low applied strains. An optimum v thus exists, one not too high to suppress local shear ductility but high enough to suppress crazes which can act as crack nucleation sites. these results are compared with previous results on a variety of linear homopolymers, copolymers, and polymer blends that are characterized by a wide range of v (v = v_E). The transitions from crazing to crazing plus shear and from crazing plus shear to shear only take place at almost identical values of v. In addition the correlation between λ in the crazes and DZs and λ_max for a single network strand is the same for both classes of polymers. This agreement implies that chain scission is the major mechanism by which strands in the entanglement network are removed in forming fibril surfaces. Craze suppression, by either increasing v in the crosslinked polymer or v_E in the uncrosslinked ones, is due to the extra energy required to break more main-chain bonds to form these surfaces.     

NMR study of molecular reorientations in NH4H2AsO4

Zeeman (T_1Z) and dipolar (T_1D) spin-lattice relaxation times of protons in NH₄H₂AsO₄ were measured as a function of temperature. The existence of a slow motion (τ ≈ 10^?3 see) is established, which is most probably a low frequency hindered reorientation of H₂AsO₄ groups. This motion is slowed down below the Curie point T_c. A sharp increase of the dipolar relaxation rate above T = 314°K indicates the possibility of a new high temperature phase transition in this compound.     

Influence of the interphase on block copolymer thermodynamics: Extension of the leary model

The Leary–Williams model for the microphase thermodynamics of triblock ABA copolymers has been modified to accommodate deviations from homogeneous random-coil configurations in the B-chain dimensions as well as in those of the A chains, and has also been extended to cover the case of diblock AB copolymers. Only planar morphology is considered, but qualitative conclusions reported herein are expected to hold for other morphologies as well. The focus is on interphase thickness ΔT, with predictions made also for separation temperature T_s and planar repeat distance D. Results are presented as systematic functions of copolymer composition (0 ≤ ?_A ≤ 1), total molar volume (25,000 ≤ ? ≤ 4 × 10⁶ cm³/g mol), block architecture (AB vs. ABA), temperature (298, 373 K), and for five different interphase composition profiles. In most cases, A represents a polystyrene block and B a butadiene block in these calculations. Predictions for ΔT increase with temperature and depend on architecture, profile, and ?; comparisons with data are close, in the range 15–30Å. It is shown that T_s depends strongly on profile choice and ?_A, reaching a maximum in the ?_A midrange but always with ?_A > 0.5. The major parameter influencing D (at constant ?) is architecture, with D(SB) ≈ 2D(SBS), and D(?) varies from D ∝ ?^0.75 at low ? to D ∝ ?^0.5 at high ?.     

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.     

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.     

The 1B1u ← 1A1g 0—0 transition in crystal benzene

The transition linewidth ΔE in crystal C₆H₆, C₆D₆ and sym-C₆H₃D₃ has been measured as a function of temperature T from 4.2 to 135°K, and it extrapolates to a common value of ΔE_o = 50 cm^? at O°K. In C₆H₆ ΔE = (50 + 7T^{$\text{1}\text{2}$}) cm^?1, indicative of strong exciton—phonon coupling, and there is a line shift of +40 cm^?1 per substituent deuteron. Fluorescence excitation spectral data are used to separate the ¹B_1u(= S₂) decay rate k_H = 9.4 × 10¹² sec^?1, derived from ΔE₀, into S₂S₁ internal conversion (rate ≈ 6.6 × 10¹² sec^?1) and S₂S_x (channel 3) internal conversion (rate ≈ 2.8 × 10¹² sec^?1. A similar value of k_H = 9.9 × 10¹² sec^?1 is obtained from the S₂S_o fluorescence quantum yield of liquid benzene.     

Physical aging and dye diffusion in polysulfone below the glass transition temperature

The effect of physical aging on the tracer diffusion coefficient D of camphorquinone in polysulfone is investigated. It is shown that if the sample is sufficiently annealed and physical aging is nearly complete, the temperature dependence of D will reflect the primary α-relaxation process of the host polymer. In the temperature range between T_g (=185°C) and 165°C, D is found to be a function of time, and the time dependence of D is given by D = At^?μ, with μ approximately equal to unity. © 1994 John Wiley & Sons, Inc.     

Impact of chain architecture (branching) on the thermal and mechanical behavior of polystyrene thin films

The modulus and glass transition temperature (T_g) of ultrathin films of polystyrene (PS) with different branching architectures are examined via surface wrinkling and the discontinuity in the thermal expansion as determined from spectroscopic ellipsometry, respectively. Branching of the PS is systematically varied using multifunctional monomers to create comb, centipede, and star architectures with similar molecular masses. The bulk‐like (thick film) T_g for these polymers is 103 ± 2 °C and independent of branching and all films thinner than 40 nm exhibit reductions in T_g. There are subtle differences between the architectures with reductions in T_g for linear (25 °C), centipede (40 °C), comb (9 °C), and 4 armed star (9 °C) PS for ≈ 5 nm films. Interestingly, the room temperature modulus of the thick films is dependent upon the chain architecture with the star and comb polymers being the most compliant (≈2 GPa) whereas the centipede PS is most rigid (≈4 GPa). The comb PS exhibits no thickness dependence in moduli, whereas all other PS architectures examined show a decrease in modulus as the film thickness is decreased below ～40 nm. We hypothesize that the chain conformation leads to the apparent susceptibility of the polymer to reductions in moduli in thin films. These results provide insight into potential origins for thickness dependent properties of polymer thin films. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Self-bonding in an amorphous polymer below the glass transition: A T-peel test investigation

Films of amorphous polystyrene (PS) with a weight-average molecular weight (M_w) of 225 × 10³ g/mol were bonded in a T-peel test geometry, and the fracture energy (G) of a PS/PS interface was measured at the ambient temperature as a function of the healing time (t_h) and healing temperature (T_h). G was found to develop with (t_h)^1/2 at T_h = T_g-bulk − 33 °C (where T_g-bulk is the glass-transition temperature of the bulk sample), and log G was found to develop with 1/T_h at T_g-bulk − 43 °C ≤ T_h ≤ T_g-bulk − 23 °C. The smallest measured value of G = 1.4 J/m² was at least one order of magnitude larger than the work of adhesion required to reversibly separate the PS surfaces. These three observations indicated that the development of G at the PS/PS interface in the temperature range investigated (<T_g-bulk) was controlled by the diffusion of chain segments feasible above the glass-transition temperature of the interfacial layer, in agreement with our previous findings for fracture stress development at several polymer/polymer interfaces well below T_g-bulk. Close values of G = 8–9 J/m² were measured for the symmetric interfaces of polydisperse PS [M_w = 225 × 10³, weight-average molecular weight/number-average molecular weight (M_w/M_n) = 3] and monodisperse PS (M_w = 200 × 10³, M_w/M_n = 1.04) after healing at T_h = T_g-bulk − 33 °C for 24 h. This implies that the self-bonding of high-molecular-weight PS at such relatively low temperatures is not governed by polydispersity. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1861–1867, 2004     

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.     

A consistent model for the thermal decomposition of NCN3 and the singlet– triplet relaxation of NCN

The thermal decomposition of cyanogen azide (NCN₃) and the subsequent collision‐induced intersystem crossing (CIISC) process of cyanonitrene (NCN) have been investigated by monitoring excited electronic state ¹NCN and ground state ³NCN radicals. NCN was generated by the pyrolysis of NCN₃ behind shock waves and by the photolysis of NCN₃ at room temperature. Falloff rate constants of the thermal unimolecular decomposition of NCN₃ in argon have been extracted from ¹NCN concentration–time profiles in the temperature range 617 K <T< 927 K and at two different total densities: k(ρ ≈ 3 × 10^?6 mol/cm³)/s^?1=4.9 × 10⁹ × exp (?71±14 kJ mol^?1/RT) (± 30%); k(ρ ≈ 6 × 10^?6 mol/cm³)/s^?1=7.5 × 10⁹ × exp (‐71±14 kJ mol^?1/RT) (± 30%). In addition, high‐temperature ¹NCN absorption cross sections have been determined in the temperature range 618 K <T< 1231 K and can be expressed by σ /(cm²/mol)= 1.0 × 10⁸ ?6.3 × 10⁴ K^?1 × T (± 50%). Rate constants for the CIISC process have been measured by monitoring ³NCN in the temperature range 701 K <T< 1256 K resulting in k_CIISC (ρ ≈ 1.8 ×10^?6 mol/cm³)/ s^?1=2.6 × 10⁶× exp (‐36±10 kJ mol^?1/RT) (± 20%), k_CIISC (ρ ≈ 3.5×10^?6 mol/cm³)/ s^?1 = 2.0 × 10⁶ × exp (?31±10 kJ mol^?1/RT) (± 20%), k_CIISC (ρ ≈ 7.0×10^?6 mol/cm³)/ s^?1=1.4 × 10⁶ × exp (?25±10 kJ mol^?1/RT) (± 20%). These values are in good agreement with CIISC rate constants extracted from corresponding ¹NCN measurements. The observed nonlinear pressure dependences reveal a pressure saturation effect of the CIISC process. © 2012 Wiley Periodicals, Inc. Int J Chem Kinet 45: 30–40, 2013     

Raman depolarization measurements over the entire miscible range for polystyrene–cyclohexane and polydimethylsiloxane–benzene solutions: Determination of upper theta temperatures

Raman depolarization ratio measurements (ρ) have been made for 20% polydimethylsiloxane (PDMS) solutions in benzene and 10% Polystyrene (PS) solutions in cyclohexane over the temperature range 20 > T > 200°C. The bands studied were the 2907 cm^?1 methyl stretch in PDMS and the 1002 cm^?1 ring breathing mode in PS. The measured ρ are related to rotational isomeric state populations and a qualitative picture of the polymer conformation changes over much of their miscible ranges is described. Measurements of ρ for PDMS gum over the temperature ranges 20 < T < 200°C have been obtained and the upper theta temperature has been determined to be 171 ± 3°C for PDMS/benzene. Quantitative information about the variation of the polymer solvent interaction parameter χ can in principle be obtained.