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.     

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.     

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.     

Spectral Extinction of Colloidal Gold and Its Biospecific Conjugates

We have prepared gold sols with mean particle diametersd_min the range 4 to 50 nm and measured their extinction spectra and size dependences of the extinction peak position λ_maxand valueE_max. The measured increasing function λ_max(d_m) displays a pronounced bend near the particle diameterd_m∼ 10 nm, where the value of λ_maxsharply decreases with reduction in the particle size. To explain these findings, the extinction spectra of sols with the particle size and axial ratio polydispersity are calculated using Mie's theory, the T-matrix method, and various experimental sets of the bulk gold optical constants modified with regard to size-limiting effects. It is shown that the measured λ_max(d_m) andE_max(d_m) dependences are inconsistent with calculations based on Mie's theory and the bulk gold optical constants. The most generalized model including the size dependence of the imaginary part of the dielectric permeability and the size and shape polydispersity gives good agreement with experimental extinction spectra for 5-, 10-, 24-, and 40-nm sols, as well as with the measured functions λ_max(d_m) andE_max(d_m). Based on electron-microscopic and spectral data, calibration curves are obtained for efficient spectrophotometric control over the particle size and for estimation of the amount of restorer essential for the preparation of particles of a given size. A simplest two-layer spherical model is employed to elucidate the basic changes in sol spectra after conjugation with specific biomacromolecules and to draw some conclusions about the conjugate shell structure.     

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.     

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.     

Crazing of polystyrene containing two rubber balls: A model for ABS plastics

In order to study the crazing behavior in rubber-toughened glassy polymers, polystyrene samples containing two rubber balls of the same diameter with varying separations have been prepared. They were subjected to simple tension, and their crazing behavior was observed. When the two balls are close together, the craze-initiation stress is considerably lower than that of single-ball samples. With increase in the distance between the two balls the craze-initiation stress increases at first almost linearly and levels off when l/d reaches about 1.45, where l and d are the center-to-center distance and the diameter of the balls, respectively. When l is sufficiently small, the crazes are seen to develop extensively at the inner surfaces of the balls and finally bridge with each other. The crazes bridged between the balls expand largely in the plane perpendicular to the applied load.     

Luminescent nitro derivatives of benzotriazolo[2,1a]benzotriazole

Fluorescence was enhanced and laser activity introduced by substitution in 5,11-dehydro-5H,11H-benzotriazolo[2,1-a]benzotriazole 6 to give 2-nitro, 2,8-dinitro, 2,4,8-trinitro, and 2,4,8,10-tetranitro derivatives 9a–d . Luminescence for compounds 6 and 9a–d and the 2,8-dinitro-3,9-dimethyl and 2,3,8,9-tetramethyl-4,10-dinitro derivatives 11a,b was erratically solvent dependent when examined in ethyl acetate, acetonitrile, and acetone and was most efficient in the 2,8-dinitro derivative 9b [λ_f 479 nm (ethyl acetate) Φ 0.98, λ_f 501 nm (acetonitrile) Φ 0.58, and λ_f 494 nm (acetone) Φ 0.61] and in the tetranitro derivative 9d [λ_f 509 nm (acetonitrile) Φ 0.81 and λ_f 511 nm (acetone) Φ 0.66]. With laser activity at 560–590 nm (acetonitrile) the dye 9b was 30% as efficient as rhodamine 6G (ethanol) in power output. Luminescence was quenched by the reduction of nitro groups to give 2-amino and 2,8-diamino derivatives 9e,f and by the conversion of the tetranitro compound 9d to an unassigned diazido dinitro derivative 9g . Luminescence was not detected in 2,5-dimethyl-3,6-dinitro-1,3a-4,6a-tetraazapentalene 14 and ethyl 2,5-dimethyl-1,3a,4,6a-tetraazapentalene-3,6-dicarboxylate 15 . Azidoazobenzenes were obtained from 4-methyl- and 4,5-dimethyl-1,2-phenylene diamines via oxidation with lead dioxide to aminoazobenzene derivatives followed by treatment of the diazotized amines with sodium azide and thermolysis of azido intermediates to give 3,9-dimethyl and 2,3,8,9-tetramethyl derivatives 10a,b of the triazolotriazole 6 . Nitration converted the triazole 6 to the 2,4,8-trinitro derivative 9c and the alkyltriazoles to their dinitro derivatives 11a,b .     

Optically active copolyamides by melt and solution condensation polymerization

The melt and solution condensation copolymerization of nylon salts which were prepared from d-camphoric acid and adipic acid with hexamethylenediamine were carried out, and optically active copolyamides were obtained. The copolyamides obtained had a positive specific rotation. The specific rotations for the copolyamides increased with increasing content of d-camphoryl units in the copolymers. The optical rotatory dispersion of the copolyamides had positive curves and were found to fit the simple Drude equation. The λ_c values of the polymers obtained by the melt and solution condensation polymerization were 241 mμ and 245 mμ, respectively.     

Structure of chlorinated poly(vinyl chloride). V. Molecular parameters of chlorinated poly(vinyl chloride)

The molecular parameters of samples of chlorinated poly(vinyl chloride) (CPVC) and chlorinated β,β-dideuterated poly(vinyl chloride) (β,β-d₂-CPVC) were determined by gel permeation chromatography (GPC), light scattering, osmometry, and viscometry. Comparison of GPC, light scattering, osmometric, and viscometric data resulted in a discussion of the possibility of degradation and the causes of changes in the solution properties in chlorination of PVC and ββ-dideuterated poly(vinyl chloride) (ββ-d₂-PVC). The results obtained are discussed in relation to the mechanism of chlorination of PVC.     

Point-group symmetry and transition metal superconductivity: Nb?Mo?Tc alloys

Using a factorization of the band density of states into point-group symmetries, it is shown that the variation of the fractional density of states of one type—Γ₁₂—correlates closely (ρ₁₂ = 0.997) with variations in λM〈ω²〉. It is also shown that the Hopfield parameter η does not correlate with N_p(0)N_d(0)/N(0), which would be true if superconductivity in d-band materials was dominated by local atomic processes. It is concluded that bonding plays an important role in superconductivity in Nb-Mo-Tc alloys.     

Transport Properties from the Equation of State by Means of Enskog Theory for d-Dimensional Hard Spheres

Abstract

In this work we have used Enskog theory to evaluate transport properties in d-dimensional hard spheres. In order to carry out this study we have made use of the relation between the compressibility factor Z and the ratio X_E/X ₀, where X_E is the Enskog value for a transport property and X ₀ is that corresponding to a dilute gas. From the available numerical data for Z in simulation experiences, we have calculated the aforementioned ratio for the diffusion coefficient D, the shear viscosity coefficient η, the bulk viscosity coefficient η and the thermal conductivity coefficient λ. This calculation has been extended to hard disks (d = 2), hard spheres (d = 3) and hard hyperspheres (d = 4,5) in the maximum allowable range of densities. We have also tested the suitability of some algebraic equations of state proposed for such bodies by comparing their respective values for X_E/X ₀. Finally, we have obtained numerical values for the ratio D/D_E in the cases d = 4,5. The behavior is similar to that of hard spheres.     

Order in amorphous di‐n‐alkyl itaconate polymers,copolymers, and blends

The presence of a main‐chain correlation distance (d_II) in the poly(di‐n‐alkyl itaconate)s was confirmed with small‐angle X‐ray scattering/wide‐angle X‐ray scattering measurements taken over the temperature range of 293–478 K. Data for a series of alkyl acrylate polymers were also obtained for comparison. The intensity of the itaconate d_II peak was significant and indicated a greater level of nanophase formation than in analogous systems. In the lower members of the series, nanophase formation appeared to be further enhanced in the temperature range above the glass‐transition temperature (T_g). This was ascribed to the rapidly increasing main‐chain mobility in this region. Macroscopically phase‐separated itaconate blends displayed the individual d_II nanospacings of each homopolymer component. Copolymers, on the other hand, showed more interesting behavior. Poly(methyl‐co‐di‐n‐butyl itaconate) followed an average behavior in which the d_II spacing and T_g changed progressively with the comonomer content. In contrast, the side‐chain pairing in poly(methyl‐co‐di‐n‐octyl itaconate) generated d_II spacings characteristic of separate methyl and octyl nanodomains. The observation of the dioctyl nanodomains, along with the dioctyl side‐chain lower T_g relaxation event, confirmed the concept of independent side‐chain‐domain relaxation in these polymers. The temperature behavior of the poly(methyl‐co‐di‐n‐octyl itaconate) small‐angle X‐ray scattering profiles and scattering correlation lengths indicated that the two nanodomains were not completely structurally independent. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4000–4016, 2004     

Characterization of poly(methyl methacrylate) nanoparticles prepared by nanoprecipitation using analytical ultracentrifugation,dynamic light scattering,and scanning electron microscopy

Nanoprecipitation represents an effective method for the production of polymeric nanoparticles. This technique was used to prepare nanoparticles from solutions of poly(methyl methacrylate) and its copolymers. Since the regulation of main parameters like particle size, particle size distribution, and molar particle mass is very important for future applications, the stable nanoparticle dispersions were examined by scanning electron microscopy, velocity sedimentation, and dynamic light scattering, whereby advantages and disadvantages of each characterization techniques are discussed. Polydispersities of particle size distributions are determined by the ratio of d_w/d_n, where d_w and d_n are weight‐ and number‐average diameters, respectively. The particle characteristics strongly depend on the chemical structure of the polymers and the way of preparation and, therefore, vary in the studied cases in the range of 6 < d_w < 680 nm, whereas the polydispersity index d_w/d_n changes in the range of 1.02 to 1.40. It is shown that nanoparticles in a desirable size range can be prepared by solvent–nonsolvent methods (dialysis technique or dropping technique). © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 3924–3931, 2010     

Deuterium labelled liquid crystalline compounds

Abstract

The synthesis of 4-(2′-methylbutyl)phenyl4′n-heptylbiphenyl-4-carboxylate-d ₁₈(7BEF5-d ₁₈) is presented. The compound is intended to be used as a means of studying the collective modes of liquid crystals by the coherent inelastic neutron scattering technique. The 4′-n-heptylbiphenyl-4-carboxylic acid-d ₁₂, a liquid crystalline intermediate was prepared as well; its acid chloride was coupled with 4-(2′-methylbutyl)phenol-d ₆ to obtain the final product. The intermediates and final products were investigated by spectroscopic methods.     

Specific features of the formation of poly(vinylchloride)-dye composites based on solvent-crazed nanostructured polymer matrices

Healing and migration of dye molecules in porous nanostructured amorphous-polymer-dye systems prepared by solvent crazing are studied by the method of spectroscopy in the visible spectral region. The conversion of the above processes is controlled by the temperature in the temperature interval above T _g of the bulk polymer. Both processes proceed simultaneously and are independent. After the removal of AALE from the composite and shrinkage of the polymer sample at room temperature, crazes preserve their fibrillar structure, which can be identified by light scattering at 400–600 nm. The main contribution to healing from the fibrillar material of crazes is provided by the reptational mobility of macromolecules, a conclusion that is confirmed by the power dependence of light scattering of the sample on the duration of its thermal treatment with an exponent of 1/4 as well as by the activation energy of this process, which is ∼400 kJ/mol. The kinetic dependences of the intensity of absorption bands of monomer forms of a dye on annealing time have an exponent of 1/2 and show two linear regions. This behavior can be explained by the migration of dye molecules in their monomer form from their absorbed state on the surface of the fibrillar crazed material first into the volume of fibrils and then into the volume of bulk-polymer regions. All the above phenomena are provided by the unique structure of the solvent-crazed polymer material (alternation of the closely spaced regions containing fibrillar material and bulk-polymer regions).     

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.     

UV‐Dissipation Mechanisms in the Eumelanin Building Block DHICA

The UV‐dissipative mechanisms of the eumelanin building block 5,6‐dihydroxyindole‐2‐carboxylic acid (DHICA) and the 4,7‐dideutero derivative (DHICA‐d₂) in buffered H₂O or D₂O have been characterized by using ultrafast time‐resolved fluorescence spectroscopy. Excitation of the carboxylate anion form, the dominating state at neutral pH, leads to dual fluorescence. The band peaking at λ=378 nm is caused by emission from the excited initial geometry. The second band around λ=450 nm is owed to a complex formed between the mono‐anion and specific buffer components. In the absence of complex formation, the mono‐anion solely decays non‐radiatively or by emission with a lifetime of about 2.1 ns. Excitation of the neutral carboxylic acid state, which dominates at acidic pH, leads to a weak emission around λ=427 nm with a short lifetime of 240 ps. This emission originates from the zwitterionic state, formed upon excitation of the neutral state by sub‐ps excited‐state intramolecular proton transfer (ESIPT) between the carboxylic acid group and the indole nitrogen. Future studies will unravel whether this also occurs in larger building blocks and ESIPT is a built‐in photoprotective mechanism in epidermal eumelanin.     

Optically active copolyamides by interfacial condensation polymerization

The polymerization of d-camphoryl dichloride with polymethylenediamines (n = 2, 3, 5, 6, 7, 9) and copolymerization of hexamethylenediamine with d-camphoryl dichloride and adipyl dichloride were carried out by the interfacial condensation method, and optically active copolyamides were obtained. The specific rotation of poly(hexamethylene camphoramide) obtained increased markedly with increasing intrinsic viscosity over the range of 0.05–0.10. The specific rotation for the copoyamides increased linearly with increasing content of d-camphoryl units in the polymers. The optical rotatory dispersion of the polyamides and copolyamides had a negative curve which fit the simple Drude equation. The λ_c values of the polyamides and the copolymers obtained were 265 and 273–285 mμ, respectively. In order to investigate the conformation of the polyamides, the effects of solvent on the specific rotation of the polymers were studied.