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.     

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.     

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.     

Diffusion of nonionic azo dyes in nylon-6

Diffusion of 2,4-dinitroaniline and three nonionic azo dyes in Nylon-6 film was studied by analysis of the concentration-distance curves (profiles) of penetrants in the polymer. Actual diffusivities D_(c) of penetrants in polymer, diffusion coefficients as a function of the concentration C_f of penetrant in polymer, were calculated from the profile. It was found that D_(c) is almost constant or decreases gradually with decreasing C_f in the range of high-medium C_f but decreases appreciably with decreasing C_f at low C_f. The change in D_(c) with C_f was explained in terms of the dual-mode sorption-diffusion model. The penetrants diffuse in the polymer as two distinct species, i.e., a dissolved species and an adsorbed species. The former is the penetrant taken up by the polymer by a partition mechanism (dissolved species) and the latter is that taken up by Langmuir sorption (adsorbed species). The actual diffusivity D_P(c) of the dissolved species decreases with decreasing C_f. While the actual diffusivity D_L(c) of the adsorbed species normally increases gradually with decreasing C_f. D_P(c) is usually larger than D_L(c). © 1993 John Wiley & Sons, Inc.     

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.     

Decohesion of a rigid punch from an elastic layer: Transition from “flaw sensitive” to “flaw insensitive” regime

A cohesive zone model is used to study the pull‐off of a rigid flat cylindrical punch of radius c from an elastic layer of thickness h. The adhesion between the punch and the elastic layer is assumed to be sufficiently weak so that pull‐off occurs by the growth of a crack from the edge of contact. Our result shows that the pull‐off stress, when normalized by the interfacial strength σ_o, depends on a single dimensionless parameter χ_f = σc(1?v²) g(ξ)/2πEW_ad, where E and v are the Young's modulus and Poisson's ratio of the elastic layer, respectively, W_ad is the work of adhesion, and g(ξ) is a known dimensionless function of ξ ≡ c/h. χ_f can be viewed as a generalized Tabor parameter. It characterizes the transition from a “brittle” or flaw sensitive failure regime to a “ductile” or flaw insensitive regime. The result in this work is used to generalize Maugis' theory of adhesive contact to the case where the elastic substrate is of finite thickness. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3628–3637, 2005     

Gauge parameters for extrapolation of oscillator strengths ofE1 transitions along the boron isoelectronic sequence

The oscillator strengthsf forE1 transitions along an isoelectronic sequence can be written asf=aK ²+bK+c whereK is a gauge parameter representing the gauge condition of the electromagnetic field. The coefficientsa,b, andc are functions of length (f _l) and velocity (f _v) values of the oscillator strengths at the Hartree-Fock level. We have shown by making a perturbation expansion of oscillator strengthsf,f _l andf _v that the gauge parameterK is independent of the nuclear charge. This property has been exploited to extrapolatef values along the isoelectronic sequence of Boron for some representativeE1 transitions within then=2 complex. We obtain good agreement between the extrapolated results with the configuration interaction results.     

Fractionated Crystallization Kinetics and Polymorphic Homocrystalline Structure of Poly(L-lactic acid)/Poly(D-lactic acid) Blends: Effect of Blend Ratio

Stereocomplex (SC) crystallization has been an effective way to improve the physical performances of stereoregular polymers. However, the competition between homo and SC crystallizations can lead to more complicated crystallization kinetics and polymorphic crystalline structure in stereocomplexable polymers, which influences the physical properties of obtained materials. Herein, we select the medium-molecular-weight (MMW) poly(_L-lactic acid)/poly(_D-lactic acid) (PLLA/PDLA) asymmetric blends with different PDLA fractions (f_D=0.01–0.5) as the model system and investigate the effects of f_D and crystallization temperature (T_c) on the crystallization kinetics and polymorphic crystalline structure. We observe the fractionated (i.e., multistep) crystallization kinetics and the formation of peculiar β-form homocrystals (HCs) in the asymmetric blends under quiescent conditions, which are strongly influenced by both f_D and T_c. Precisely, crystallization of β-form HCs is favorable in the MMW PLLA/PDLA blends with high f_D (≥0.2) at a low T_c (80–100 °C). It is proposed that the formation of metastable β-form HCs is attributed to the conformational matching between β-form HCs and SCs, and the stronger constrain effects of precedingly-formed SCs in the early stage of crystallization. Such effects can also cause the multistep crystallization kinetics of MMW PLLA/PDLA asymmetric blends in the heating process.

     

The stability of silver iodide sols in the presence of polyacrylic acids of various molecular weights

Summary The effect of a series of polyacrylic acids, ranging in molecular weight from 1.67×10⁴ to 2.36×10⁶, on the stability of positively charged silver iodide particles has been examined. Flocculation of the sol occurred at a well defined concentration of polyacrylic acid,c _f , and a further increase in concentration of the polyelectrolyte caused restabilization of the sol. Over the range examinedc _f appeared to be related to the viscosity average molecular weight of the acid,M _v , by an equation of the form,c _f =a ·M _v ^{– b} wherea andb are constants.     

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.     

Crosslinking,filler, or transition constraint of polymer networks. I

The basic theory of modulus/swelling is developed to allow for limited extensibility, filler reinforcement or transition effects, and steric hindrance of aligned segments by extended chains or filler particles. Filler forms an effective hard fraction C_h per cubic centimeter of compound with v_c a new (compound) index of swelling. For 1/M_c + σ fix points having ratio φ to gum values 1/F₀(v_r) and with F(v_c) replacing the Flory function F(v_r): where σ denotes entanglement. Linkage reinforcement φ does not vary with sulfur crosslinking of SBR. Vacuoles invalidate φ from mass-increment F₀(v_r)/F(v_r) for inert fillers. Then, or for Graphon, with negligible φ ≈ 1: The effective C_h includes rubber stretched hard on Graphon by swelling or trapped inside hard aggregates. Only the right-hand equation fits normal blacks. In theory, C_h can always be obtained from swollen moduli G by linear slopes (1 + 1.4C_h) relating F(v_c) and (1 ? C)ρRT/G. For filler fractions C ≥ 0 cm^?3 and low strains α = 1.5?2.0 below prestretch the modulus G is given a new basic definition: Here C₂* ≈ 0.7 corresponds to Mooney-Rivlin C₂ and the effective crosslinking 1/[M_c] = (ρRT)^?1G is equal to (1 ? C)(1/M_c + σ) for unswollen prestretched rubber (v_r = 1). For higher strains a hypothesis of strain hardening is proposed. This is distinct and opposite in character to the initial prestretch softening (Mullins effect). Nonlinear effects of crosslinks are expressed by a fractional stress-upturn Ω (1/M_c + σ), effective mesh wieght (1/M_c + σ)^?1 ? Ω, and hard fraction Ω(1/M_c + σ). For μ_h characterizing strain hardening up to the prestretch (α_h ? 1) their contribution is: The sixth-power refinement has J = j(α_b ? 1)^1/2 with j ≈ 0.4. The hard phase is augmented by filler and grows with increasing strain up to the prestretch.     

Temperature and pressure dependence of the free volume in the perfluorinated polymer glass CYTOP: A positron lifetime and pressure‐volume‐temperature study

The microstructure of the free volume was studied for an amorphous perfluorinated polymer (T_g = 378 K). To this aim we employed pressure–volume–temperature experiments (PVT) and positron annihilation lifetime spectroscopy (PALS). Using the Simha‐Somcynsky equation of state the hole free volume fraction h and the specific free and occupied volumes, V_f = hV and V_occ = (1 ? h)V, were determined. Their expansivities and compressibilities were calculated from fits of the Tait equation to the volume data. It was found that in the glass V_occ has a particular high compressibility, while the compressibility of V_f is rather low, although h (300 K) = 0.108 is large. In the rubbery state the free volume dominates the total compressibility. From the PALS spectra the hole size distribution, its mean, 〈v_h〉, and mean dispersion, σ_h, were calculated. From a comparison of 〈v_h〉 with V_f a constant hole density of N_h′ = 0.25 × 10²¹ g^?1 was estimated. The volume of the smallest representative freely fluctuating subsystem, 〈V_SV〉 ∝ 1/σ_h², is unusually small. This was explained by an inherent topologic disorder of this polymer. 〈v_h〉 and σ_h show an exponential‐like decrease with increasing pressure P at 298 K. The hole density, calculated from N_h′ = V_f/〈v_h〉, seems to show an increase with P which is unexpected. This was explained by the compression of holes in the glass in two, rather than three, dimensions. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2519–2534, 2007     

Star polymer diffusion in concentrated solutions: Dependence on functionality via the coupling model

The coupling model is formulated in terms of the dynamic constraint entropy, S_c(t), and subsequently compared with measured tracer diffusion coefficients D for linear, 3-arm star, and 12arm star polystyrenes in solutions of poly (vinyl methyl ether) (PVME) /o-fluorotoluene. Inequalities between the dynamic constraint entropies, S_cf and S_cf′(t), respectively, for f-arm and f′-arm stars, enable us to explain the experimental observation that at constant arm molecular weight, the ratio D_star/D_linear decreases substantially with increasing concentration above the entanglement concentration for the PVME. This work indicates that not only the reptation model, but also the coupling model, can account for the experimental observation that in entangled solutions the mechanism for diffusion depends on diffusant architecture.     

Relaxation of shear and normal stresses in step-shear deformation of a polystyrene solution. Comparison with the predictions of the Doi–Edwards theory

The shear stress σ, two components of birefringence, and extinction angle were measured for a concentrated polystyrene solution in step-shear deformation of magnitude of shear 0.3 ≤ γ ≤ 4.0. The stress-optical coefficient did not depend on either γ or time. The first and the second normal-stress differences v₁ and v₂ were evaluated with the use of the stress-optical law. Over a certain range of long times, σ could be factored as σ = γh(γ)G(t) and the quantity h(γ) agreed with the prediction of the Doi–Edwards theory based on the de Gennes tube model of entangled polymer chains. At short times the effect of γ on σ/γ was smaller than at long times. The relaxation spectrum became approximately independent of γ at the short-time end of the rubbery plateau region. The ratios v₁/σ and v₂/v₁ were independent of time and were in quantitative agreement with those predicted by the Doi–Edwards theory: v₁/σ was equal to γ, v₂/v₁ was negative, and |v₂/v₁| decreased with increasing γ.     

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.     

Concentration-dependence of faradaic currents and conductivity in a polystyrene sulfonic latex suspension

The conductivity, κ, in a suspension of polystyrene sulfonic latex without supporting electrolyte showed a linear dependence on the volume fraction, v_f, of the latex for v_f<0.03 with a finite intercept. In contrast, this deviated upward from the linear line for v_f>0.03. These variations were qualitatively consistent with the dependence of the voltammetric reduction current of H⁺ on v_f without supporting electrolyte. The current values were only a few percent of the theoretical diffusion-controlled current that could be observed in the suspension with supporting electrolyte. This fact indicates the electrostatic immobilization of the hydrogen ions by sulfonic latex particles. A plot of the current against κ at common values of v_f showed that the current for v_f>0.07 was smaller than the value predicted from the conductivity. This can be explained in terms of a combination of the increase in electrostatically unbounded H⁺ estimated by conductance measurements and electric migration in which the electrochemical depletion of [H⁺] also causes the depletion of the latex.     

The Prenucleation Equilibrium of the Parathyroid Hormone Determines the Critical Aggregation Concentration and Amyloid Fibril Nucleation

Nucleation and growth of amyloid fibrils were found to only occur in supersaturated solutions above a critical concentration (c_crit). The biophysical meaning of c_crit remained mostly obscure, since typical low values of c_crit in the sub-μM range hamper investigations of potential oligomeric states and their structure. Here, we investigate the parathyroid hormone PTH₈₄ as an example of a functional amyloid fibril forming peptide with a comparably high c_crit of 67±21 μM. We describe a complex concentration dependent prenucleation ensemble of oligomers of different sizes and secondary structure compositions and highlight the occurrence of a trimer and tetramer at c_crit as possible precursors for primary fibril nucleation. Furthermore, the soluble state found in equilibrium with fibrils adopts to the prenucleation state present at c_crit. Our study sheds light onto early events of amyloid formation directly related to the critical concentration and underlines oligomer formation as a key feature of fibril nucleation. Our results contribute to a deeper understanding of the determinants of supersaturated peptide solutions. In the current study we present a biophysical approach to investigate c_crit of amyloid fibril formation of PTH₈₄ in terms of secondary structure, cluster size and residue resolved intermolecular interactions during oligomer formation. Throughout the investigated range of concentrations (1 μM to 500 μM) we found different states of oligomerization with varying ability to contribute to primary fibril nucleation and with a concentration dependent equilibrium. In this context, we identified the previously described c_crit of PTH₈₄ to mark a minimum concentration for the formation of homo-trimers/tetramers. These investigations allowed us to characterize molecular interactions of various oligomeric states that are further converted into elongation competent fibril nuclei during the lag phase of a functional amyloid forming peptide.     

Conformational Analysis of Biphenyl Derivatives. I. A Novel Steric Constant from the Internal Rotation Rate of 2,2′‐Bis‐(N‐Substituted Carbamoylmethyl)Biphenyl by Means of Dynamic NMR

A novel scale of steric substituent constant E_s^D is defined from the correlation of the logarithms of the internal rotation rate (k_r) at 393 K with Hancock (E_s^c) steric constant by means of dynamic NMR. In the inhibition of Pseudomona species lipase by 2,2′‐bis‐(N‐substituted carbamoylmethyl)biphenyls (1‐8), the logarithms of bimolecular rate constants are multiply correlated with both the Taft substituent constant σ* and E_s^D.     

Temperature-sensitive poly(vinyl methyl ether) hydrogel beads

Temperature-sensitive hydrogel beads were prepared by radiation crosslinking of poly(vinyl methyl ether) PVME spheres wrapped in Ca-alginate. The obtained gel beads have diameters in the sub-millimeter or millimeter range (depending on the PVME concentration). They were characterized by sol-gel analysis, swelling measurements, and differential scanning calorimetry. The gel content g increases with increasing radiation dose D. The swelling degree Q_v decreases with increasing PVME concentration c_p and increasing D. In comparison to PVME bulkgels the phase-transition temperature of the synthesized PVME gel beads is a little decreased.