Dynamic stress intensity factors during viscoelastic crack propagation at various strain rates

Dynamic stress intensity factors K_D were measured by the caustic method and crack propagation velocity ? by the velocity gauge techniques for PMMA [poly(methyl methacrylate)] during dynamic crack propagation at various strain rates \documentclass{article}\pagestyle{empty}\begin{document}$ \rm \dot \varepsilon $\end{document} . No definite applied strain rate effects on the dynamic stress intensity factor were observed for applied strain rates ranging from 8.33 × 10^?4 to 30/sec; however, the test results do show crack propagation velocity dependency in K_D ～ ? relations. The high local strain rate region may be realized at the running crack tip even under the quasi-static loading case of \documentclass{article}\pagestyle{empty}\begin{document}$ \rm \dot \varepsilon $\end{document} = 8.33 × 10^?4/sec, since all the crack propagation velocities obtained were greater than 50 m/sec even up to 450 m/sec.     

Viscoelastic relaxations in polyepoxide joints related to the strength of bonded structures at impact rate shear loading

The aim of this paper is to show the excellent impact behavior of a modified epoxy joint on consideration of the viscoelastic relaxation processes of an adhesive. The investigation of the epoxy joint properties, over a range of strain rates ($ \mathop \gamma \limits^ \cdot $ = 10 ^?2 to 10⁴ S^?1) and temperatures (?30, 24, 60, 80°C), shows that there is a good correlation between high impact resistance and the presence of a secondary transition. We successfully applied the Bauwens approach to explain the strain rate sensitivity of the yield stress in terms of a difference in relaxation times at low and high strain rates (α and β). Our purpose is to confirm these results by applying the Escaig model, which reviews thermoset behavior in terms of a thermally activated dislocation propagation mechanism. The Bauwens approach and the Escaig model lead to the same conclusion: They indicate that there is a critical strain rate $ \mathop \gamma \limits^ \cdot $_β (T), correlated to a critical temperature T_β ($ \mathop \gamma \limits^ \cdot $), that corresponds to the limits between the two modes of deformation required to free the different kind of molecular motions implied in the deformation process, the α mode to the α + β mode. But at low temperature (?30°C), these models are no longer valid, which means that there is a heterogeneous deformation process, characterized by local molecular motions, which involve a decrease of the polymer entropy and a permanent evolution of molecular structure.     

The effect of temperature on limiting current density and mass transfer in electrodialysis

This study focuses on a high-temperature operation in electrodialysis of salt solutions and studies the effect of temperature on limiting current density and mass transfer. Experiments were conducted under various conditions of temperature (T), varying from 15 to 90°C; of dialysate concentration (C_d), varying from 5 × 10^?3 to 3 × 10^?2M ; and of dialysate velocity (u_d), varying from 0.206 to 2.44 cm s^?1. A least squares fitting of the experimental data on limiting current density (I_lim) yields an Arrhenius equation as follows: The molar flux N? (mol cm^?2 s^?1), initial concentration (C₀; M ) and temperature (T; °C) were found to have the following relationship: N?/C₀ is slightly increased with increasing temperature ranging from 25 to 70°C.     

The shape of a fluid drop approaching an interface

The shape of a fluid drop approaching an interface does not change appreciably with time and is very close to the equilibrium dimensions, in spite of the large pressure gradient which is present in the draining film. This is because the net vertical force due to the excess pressure in the draining film above that in the drop is identical with that for an equilibrium film being zero for a plane interface and —2Rσ sin² ? for a deformable interface. Employing this result in a force balance around the drop which is independent of the bulk interface shows that the area A of the draining film between a fluid drop of volume V and a deformable fluid-liquid interface is given by where σ is the interfacial tension and Δρ the density difference between the drop and surrounding fluid, 1/b is the curvature at the top of the drop and h is the distance between this point and the edge of the draining film which is inclined to the horizontal at an angle ?. When the interface is a rigid plane the overall curvature 1/R of the draining film and the volume v enclosed by it, together with the angle ? are all zero. The limiting cases of the expression for very small and very large drops agree with those previously established for both deformable and rigid interfaces. An approximate expression which applies when cV^2/3 (where c = Δρg/σ) is between 0.6 and 13.5 and which gives A to within ± e% is where for a rigid plane interface and for a deformable interface When the densities of the drop and bulk heavy fluids are equal, but their respective interfacial tensions σ₁₂ and σ₂₃ with the light fluids are different, the expression becomes which estimates A/V^2/3 to within about ± 25% for σ₁₂/σ₂₃ in the range 0.11 to 9.0 and cV^2/3 (where c = Δρg/σ₁₂) between 0.6 and 13.5.     

Kinetics and mechanism of the thermal decomposition of potassium persulphate ions in aqueous solutions at 50°C in the presence of nitrogen gas and methacrylonitrile monomer

The initial rate of persulphate (I) decomposition at 50°C in the presence of nitrogen and methacrylonitrile (MAN) in an unbuffered aqueous solution (pH 4–7) may be written as: in the concentration ranges of persulphate (I) (0.25–2.50) × 10^?2 (m/dm³) and of (MAN) 0.18–0.36 (m/dm³). During the reaction, a white substance (polymethacrylonitrile) separates out in the colloidal state or in the precipitate form from the medium depending on the ionic strength of the medium. The pH of the medium was found to decrease rapidly and continuously with time in the absence of methacrylonitrile, but it decreased slowly and continuously with time in the presence of the monomer, MAN. If an additional quantity of MAN is injected late in a run, the rate of persulphate decomposition is further accelerated in a given run. However, the rate of persulphate decomposition is found to decrease continuously in the presence of MAN with time, i.e., as the monomer is converted to polymer. It is suggested that MAN accelerates the decomposition of persulphate ions, due to the following reactions in the aqueous phase: and where (M_j^˙)w is a-water soluble oligomeric or polymeric (j = 1–10) free radical. The estimated values of k₅ and k₁₀ are 1.05 × 10^?5 and 1.14 × 10³ (in dm³/m/s), respectively.     

Kinetics of the vapour phase oxidation of ethyl alcohol on vanadium pentoxide catalyst

The kinetics of V₂O₅-catalysed vapour phase oxidation of ethyl alcohol were studied with the help of a differential fixed-bed flow reactor. The partial pressures of alcohol, oxygen and water were varied in the ranges: 6–10 × 10^–3 atm, 1–10 % × 10^–1 atm, and 0–169 × 10^–3 atm respectively in the temperature range 228–264 °C. The rate equation: deduced by the assumptions of the steady-state redox mechanism, was found to conform to the experimental results. The energies of activation for the partial reactions, namely reduction and oxidation of the catalyst, were found to be 18.9 and 11.8 kcal/mol. The influence of different products was also studied in detail.     

Limitations of the Zero‐Length Column Technique to Measure Diffusional Time Constants in Microporous Adsorbents

The zero‐length column (ZLC) technique has been developed to measure the intracrystalline diffusivity of strongly adsorbed species in large zeolite crystals above 50 μm in the Henry's law range of sorption equilibrium. The ZLC is a macroscopic technique, and there is a need of large crystallites or pellets to measure the intracrystalline diffusivity D_c of fast diffusion species or the macropore diffusivity D_P of weakly adsorbed species, respectively. Another limitation is that ZLC desorption curves produce similar concentration profiles (linear isotherms) in bidisperse adsorbents (pellets) under macropore or micropore diffusion control. Moreover, the forms of the response curves are very similar in both diffusion‐ and nonlinear equilibrium‐controlled processes, leading to some misinterpretations of ZLC experiments. In this work, two criteria are developed showing that, in order to macroscopically measure the micropore diffusion time constant  or the macropore diffusion time constant , the time of the ZLC experiments t should be higher than 7.0 × 10^?2 or 7.0 × 10^?2 , respectively. The interpretation of the ZLC response curve data is also checked in two completely different regimes, showing that a single ZLC response curve is not enough to conclude if a system is under a kinetic or an equilibrium regime.     

d-NMR-Untersuchung der behinderten Rotation am -Bindungsinkrement. X. N-substituierte Thiocarbamidsäure-O-phenyl- und S-äthylester

d-N.M.R.-Investigation of the Restricted Rotation at the -Bonding Increment. X. N-Substituted Thiocarbamic acid-O-Phenyl- and S-Ethylesters The free enthalpies of activation of the restricted rotation at the partial -double bond in thiocarbamic acid esters have been determined for (R¹ = methallyl; R² = me, et, iso-pr, cycl. hex; X  S and Y  O C₆H₅ respectively X  O and Y  S C₂H₅). The results have been compared with values, earlier observed for other mono- and dithiocarbamic acid esters, substituted at nitrogen analogously.     

Thermal reactions between MII sulphates and acid orthophosphates in the solid state

Two general types of high temperature reactions between M^II sulphates and acid orthophosphates have been found and a survey of some representative examples has been made. The reactions are typified by two examples using Ca²⁺ salts: and . Similar reactions have been found for other alkaline earth sulphates and phosphates and for corresponding mixed alkaline earth systems. The products have been found to be largely determined by the phase relationships in the respective M^IIO–P₂O₅ systems.     

Stepwise Stability Constants of Trivalent La,Ce, Pr,and Sm Complexes of Isopropylmercaptan

The complexation of La³⁺, Ce³⁺, Pr³⁺ and Sm³⁺ ions with isopropylmercaptan has been studied by potentiometric and conductometric titration techniques in aqueous – 10% ethanolic (V/V) medium . Title metal ions form 1:1, 1:2 and 1:3 complexes in the pH range 6.0–8.0 with considerable overlapping. Their log K_stab. values are determined at 15°, 25° and 35°C at ionic strength μ = 0.1 M (NaClO₄) by applying Calvin and Melchior's extension of Bjerrum method. The values of thermodynamic parameters ΔG, ΔH and ΔS have been calculated at 25°C with the help of an isobar and Gibb's Helmholtz equation. The trend in the stability constant values of the metal-complexes has been found to be .     

Development of a correlation between the non-polar solubility parameter,refractive index and molecular structure. I. Aliphatic hydrocarbons

For non-polar liquids (e.g. the alkanes) the cohesion energy density (λ²) can be shown to be a function of the refractive index (nD ), molal volume (V) and molecular structure according to: where Δ is the non-polar solubility parameter and the increments g_ij are determined from molecular structure. The difference between values of Δ calculated by this formula and experimental data is <0.1% for the C₅–C₁₆ n-alkanes and <0.8% for the C₅–C₈ branched isomers. The main object of this correlation was to provide a method for estimating the London dispersion force contribution to the cohesive energy of branched polar liquids.     

Differential scanning calorimetry analysis of thermoset cure kinetics: Phenolic resole resin

The Differential Scanning Calorimetry (DSC) trace for a commercial phenolic resole resin shows two distinct peaks. Assuming that these represent two independent cure reactions results in a kinetic model of the form: with κ_i = κ_io exp(-B_i/T). The Arrhenius parameters were estimated from a plot of ln(β/T) versus 1/T_p. The parameters, p, n₁, and n₂ were obtained by writing the DSC response predicted by the equation above in terms of a function which contains temperature as the only variable. with $ \theta _i = \left({1/\beta} \right)\int_{T_0}^T {\kappa _i dT \le r_i} $ dT ? r_i and r_i = 1/(1-n_i). Fitting this equation to the DSC response measured at a scan rate of 4°C/min obtains p ≈ 0.66; n₁ ≈ 0.55; n₂ ≈ 2.2; B₁ ≈ 8285; B₂ ≈ 7480; κ₁ ≈ 1. 12 × 10⁸ s^?1; κ₂ ≈ 0.99 × 10⁶ S^?1.     

Wäßrige Dispersionen anionischer Polyurethane mit Sulfonatgruppen

For dispersions of anionic polyurethanes with sulfonate groups it was found that the number of particles N formed was directly proportional to the ion concentration: a is a constant containing an ion-specific factor, [SO^?₃]₀ is considered as that amount of sulfonate groups which forms water-soluble electrolytes and polyelectrolytes not contributing to the stabilization. In addition to ionomers and water-soluble products polymer molecules without ionic groups are formed. An equation developed by Flory has been adapted to calculate the molecular weight distribution. The mean particle diameter of the resulting dispersion can be controlled not only by the amount of introduced ions but also by addition of neutral salts.     

Kinetics of carbon dioxide absorption in aqueous solutions of diisopropanolamine

A bubble column absorber was used to investigate kinetics of the reaction between carbon dioxide and aqueous solutions of diisopropanolamine (DIPA), by means of gas absorption experiments. These were conducted in the temperature range of 20 to 40°C, with DIPA concentrations from 5 to 500 mol/m³, and CO₂ partial pressures between 5 and 101 kPa. A model based on the Danckwerts' surface reneval theory was used to analyze the experimental results and to determine the rate constant. The obtained data support the assumption of a second-order overall reaction, with the rate constants being well correlated by the Arrhenius equation:      

Barus effect in nylon 6 polymer melts

The maximum diameter of broadening of nylon 6 polymer melts due to the Barus effect d_max were measured under various conditions of spinneret die dimensions and polymer temperatures. The results obtained were formulated and compared with the typical past theories on the mechanism of occurrence of the Barus effect. The Barus effect was formulated by using the relation between stress and strain in the theory of rubber elasticity: where τs is the shear stress generated inside the spinneret die, T is the absolute temperature of polymer melts, λ is the elongation ratio parallel to the polymer stream, and d₀ is the diameter of spinneret die. This formula coincides with the experimental results.     

Impact energy absorption of unidirectional glass fiber-epoxy composites

The influence of resin and fiber properties on the impact behavior of composites can be assessed in a three-point drop-weight impact test by varying the length-to-thickness ratio of the specimen. The fracture initiation energy per unit deformed volume, w_i, can be described by the expression: where τ₁₁ is the tensile stress, τ₁₂ is shear stress; E₁₁ is tensile modulus; and G₁₂ is shear modulus. A unidirectional glass fiberepoxy composite was tested at impact velocities of 2.2 m/s (5 mph) and 4.5 m/s (10 mph). The energy to initiate fracture, w_i, was in the range of 2 to 3.5 MJ/m³, apparently independent of impact velocity. The total energy absorbed by the impacted composite was also found to be independent of impact rate but very sensitive to the length to thickness ratio: about 13 and 3.5 MJ/m3 at the corresponding ratios of 4.6 and 23. It was generally observed that high fracture energy is associated with extensive specimen delamination, i.e. failure in shear.     

Interferometric study of creep deformation and some structural properties of polypropylene fiber at three different temperatures

Influence of temperature on creep deformation for polypropylene PP fiber under a constant load was studied interferometrically. The automated multiple‐beam Fizeau system in transmission was equipped with a mechanical creep device attached to a wedge interferometer. This system was used to determine the optical properties (n^∥, n^?, and Δn) of PP fiber during the creep process at constant loading with varying temperature. The creep compliance was drawn as a function of both time and temperature. An empirical formula was suggested to describe the creep compliance curves for PP fibers and the constants of this formula were determined. Two Kelvin elements combined in series were used to provide an accurate fit to the experimental compliance curves. The stress–strain curve via creep was studied to determine some mechanical parameter of PP fibers, Young's modulus E, yield stress σ_y, and yield strain ε_y. The optical orientation function f(θ), the dielectric constant d, the dielectric susceptibility χ, the surface reflectivity , and the average work per chain W′ were also calculated. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Jet penetration measurements in a venturi scrubber

The maximum centreline penetrations, l^**, of cross-current liquid jets in a Venturi scrubber were measured for orifice diameters, d, of 1.397, 2.108, 2.565 and 3.860 mm. The data are correlated by for the range of conditions, 36 ≤ gas throat velocity V_g ≤ 125 m/s; 1.2 ≤ liquid injection velocity V_j ≤ 18 m/s; 0.06 ≤ liquid to gas ratio      

The glassy state,ideal glass transition,and second‐order phase transition

According to Ehrenfest classification, the glass transition is a second‐order phase transition. Controversy, however, remains due to the discrepancy between experiment and the Ehrenfest relations and thereby their prediction of unity of the Prigogine‐Defay ratio in particular. In this article, we consider the case of ideal (equilibrium) glass and show that the glass transition may be described thermodynamically. At the transition, we obtain the following relations: and with Λ = (α_gβ_l − α_lβ_g)²/β_lβ_gΔα²; and The Prigogine‐Defay ratio is with Γ = TV(α_lβ_g − α_gβ_l)²/β_lβ_gΔβ, instead of unity as predicted by the Ehrenfest relations. Dependent on the relative value of ΔC_V and Γ, the ratio may take a number equal to, larger or smaller than unity. The incorrect assumption of perfect differentiability of entropy at the transition, leading to the second Ehrenfest relation, is rectified to resolve the long‐standing dilemma perplexing the nature of the glass transition. The relationships obtained in this work are in agreement with experimental findings. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 71: 143–150, 1999     

Use of various processes for pilot plant treatment of wastewater from a wood‐processing factory

The wastewater from a wood‐processing factory is characterized by a high COD, chlorides and nitrogen content. Various treatment processes were applied to treat this wastewater in pilot‐scale units. By applying one‐stage denitrification–activated sludge biological treatment it was not possible to remove nitrogen. Nitrification was inhibited by wastewater compounds. By applying a second stage of a nitrification biofilter it was possible to have a high degree of nitrification. The denitrification was complete. With biological methods the reduction of COD, and ‐N and ‐N concentrations to acceptable values was not achievable. Physical–Chemical methods as H₂O₂/UV, electrolysis and ozonation were used as post‐treatment of effluents from the biological system. Radical degradation, initiated by the powerful hydroxyl radicals which are generated from H₂O₂ by UV activation, is used for wastewater post‐treatment. The combination of H₂O₂/UV was not suitable for post‐treatment of this wastewater. With electrolysis, ‐N and COD removal can be complete. The total amount of ammonia and organic nitrogen converted to nitrate nitrogen for current density of 1.15 Adm^?2 and energy consumption of 71.6 kWhm^?3 was 0.35 gdm^?3. Further biological denitrification is required for ‐N removal to permitted values. Energy consumption for the elimination of 1 kg COD was 40.4 kWh and 35.8 kWh for current densities of 0.7 Adm^?2 and 1.15 Adm^?2 respectively. The energy required to reach the limit value of COD equal to 150 mgdm^?3 for current density of 1.15 Adm^?2 was 71.6 kWhm^?3. With ozonation, the COD removal can be complete. Further biological nitrification–denitrification is required to remove ‐N and ‐N to permitted values. At pH 7.0, in order to reach the limit value of COD equal to 150 mgdm^?3, specific ozone dose was 6.0 g per g of COD removed and the total amount of ammonia and organic nitrogen converted to nitrate nitrogen was 0.25 gdm^?3. The total equivalent energy required is estimated to be 75.0 kWhm^?3. © 2001 Society of Chemical Industry