Characterization of polyvinyl chloride part II. The unperturbed end to end distance values obtained from a new GPC method and viscometry

A new gel permeation chromatography (GPC) method is proposed for determining the unperturbed end-to-end distance, \documentclass{article}\pagestyle{empty}\begin{document}$ \left({\frac{{r_0 ^2 }}{M}} \right)^{0.5} $\end{document}, of polymers of known molecular weights, Mn and Mw. This method requires the value of \documentclass{article}\pagestyle{empty}\begin{document}$ \left({\frac{{r_0 ^2 }}{M}} \right)^{0.5} _{{\rm ps}} $\end{document} of polystyrene which was determined through viscometry to be 0.735 \documentclass{article}\pagestyle{empty}\begin{document}$ \left({\frac{{{\rm {\AA}}^2-{\rm mole}}}{{gm}}} \right)^{0.5} $\end{document} Polyvinyl chloride (PVC) was chosen to illustrate the method and \documentclass{article}\pagestyle{empty}\begin{document}$ \left({\frac{{r_0 ^2}}{M}} \right)^{0.5} _{pvc} $\end{document} was found to be 0.99 from GPC data which is in agreement with the result obtained from viscometry, \documentclass{article}\pagestyle{empty}\begin{document}$ \left({\frac{{r_0 ^2}}{M}} \right)^{0.5} _{pvc} $\end{document} = 1.01. All \documentclass{article}\pagestyle{empty}\begin{document}$ \left({\frac{{r_0 ^2 }}{M}} \right)^{0.5} $\end{document} values were determined at 30°C. The advantage to this method lies in its speed and economy of materials.     

Dropwise condensation of different steam-air mixtures on various substrate materials

Dropwise condensation of different steam-air mixtures on three substrate materials (copper, aluminium and nickel) is studied. For each steam-air mixture, the heat flux, the heat transfer coefficient and the surface temperature are observed to be highest on copper and lowest on nickel substrates for the same identical test conditions. The above heat transfer variables are related to the bulk properties of the substrate. It is concluded that the presence of non-condensable gases is an inhibiting influence on the heat transfer performance in the condensation of steam. The normalized variables \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{h_i \left(\eta \right)}}{{h_i \left(o \right)}} $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{T_{si} \left(\eta \right)}}{{T_{si} \left(o \right)}} $\end{document} are found to be functions of the air concentration only.     

The Radiation Chemistry of Cytochrome c

The literature on the reaction of cytochrome c with the radiolytically generated radicals \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm e}_{{\rm eq}}^ -,^. {\rm OH,}^{\rm .} {\rm H,CO}_2^ -,{\rm O}_{\rm 2}^ -,{\rm Br}_{\rm 2}^ - $\end{document} and various organic radicals is reviewed. It would appear that negatively charged radicals, aided by the electric field of cytochrome c, react at the exposed haem edge. Uncharged organic radicals also react at this site. \documentclass{article}\pagestyle{empty}\begin{document}$ ^. {\rm H} $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ ^. {\rm OH} $\end{document} are likely to reduce the prosthetic group indirectly by a tunnelling mechanism.     

Simulation and optimal design of seeded continuous emulsion polymerization process

Simulation and optimal design of the reactor for the seeded continous emulsion polymerization process have been done in this work. An internal mixer (Toray Hi-Mixer) as seeder connected with a stirred tank is designed to correlate conversion, molecular weight, and MWD with the model simulation proposed. An optimal mean residence time of seeder \documentclass{article}\pagestyle{empty}\begin{document}$(\bar \theta _s)_c$\end{document} is found to lie between \documentclass{article}\pagestyle{empty}\begin{document}$(\bar \theta _1)$\end{document} and t_in, where \documentclass{article}\pagestyle{empty}\begin{document}$(\bar \theta _1)_{{\rm opt}} = (3aS_0 /2r\eta N_a \alpha)^{3/5}$\end{document} and t_in = 1.57(aS₀/r_iηN_A)^3.5. The optimal design of the process is performed according to the above relations under several polymerization conditions. In general, the increase in number of stages inside the seeder can reduced the volume of CSTR for a required production. Molecular weight of products is increased by increasing the number of stages inside the seeder, by decrasing the concentration of the initiator, and by increasing the concentration of the emulsifier under the optimal conditons.     

Relation between kneading behavior and flow instability of a high molecular weight high density polyethylene,applications to extrusion

Non-monotonic continuous curves of torque as a function of shaft speed, M(N), have been obtained for a high molecular weight high density polyethylene (HDPE) from measurements obtained with a torque rheometer (Haake Rheocord). Previous papers have given theoretical demonstration of the non-monotonic character of the shear stress-shear rate function, s(\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma } $\end{document}), which makes it possible to explain the extrusion behavior of a high molecular weight HDPE. In capillary rheometry, it is not possible to obtain the values of s(\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma } $\end{document}) into the “well zone” of this function because the compressibility of the polymer creates a phenomenon of oscillation in the barrel affecting the die output flow rate and the pressure loss. The M(N) function measured by the Haake Rheocord is a complete representation of the s(\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma } $\end{document}) function, although the capillary rheometer only gives a partial representation of this function. The transformation of the M(N)function into s(\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma } $\end{document}) is quite difficult because of the complex geometry of the Haake Rheocord measuring head. The “critical points” of the s(\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma } $\end{document}) function in the capillary rheometer (appearance of oscillations), can be correlated to the maximum points of the M(N) function in the Haake Rheocord at constant temperature. The non-monotonic aspect of the s(\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma } $\end{document}) function provides an important technological application: extrusion of a high molecular weight HDPE at an increased flow rate at low temperatures.     

The stress-strain behavior of materials exhibiting andrade creep

The stress-strain behavior of a material exhibiting Andrade creep (for which the creep compliance is linear in the cube-root of time) has been calculated for loading at constant strain rate \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm \varepsilon}\limits^{\rm .} $\end{document} and at constant stress rate \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \sigma \limits^. $\end{document} for the limiting case of linear viscoelastic behavior and at constant \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \sigma \limits^. $\end{document} for one type of nonlinear viscoelastic response. The recoverable strain after the stress has been removed has also been calculated for these three cases. The results of the calculations are compared with experiment.     

Zur kinetik der acrylnitril-polymerisation

The heterogeneous bulk polymerization of acrylonitrile initiated by AIBN has been studied by means of an improved dilatometric technique and a new method of analysis, where the initial reaction rate (v_w)₀ results from the intercept of a straight line in a \documentclass{article}\pagestyle{empty}\begin{document}$ \frac {\ln \left( 1 \hbox{---} {\rm U} \right)} {{\rm e}^{{- 0,5} {\rm k}_{\rm s}{\rm t} \hbox{---} 1}}$\end{document} versus t plot. It has been found that the initial reaction rate is proportional to the square root of the initial catalyst concentration S₀. The ratio of the rate coefficients of propagation and termination\documentclass{article}\pagestyle{empty}\begin{document}$\frac { {\rm k}_{\rm a} } { {\rm k}_{ {\rm w}^{2} } } $\end{document} could be calculated from the slope of a straight line passing through the origin in a plot of (v_w)₀ versus \documentclass{article}\pagestyle{empty}\begin{document}$\sqrt { {\rm S}_{0} }$\end{document} and yielded a value of 280 mol 1^?1.     

Polymer melt elongation—methods,results, and recent developments

For film blowing of polyethylene it has been shown previously that melt elongation is very powerful for polymer characterization. With two types of rheometers, simple (also called “uniaxial”) elongational tests as well as creep tests can be performed homogeneously. In simple elongation, the melts of branched polyethylene show a remarkable strain hardening. With respect to their advantages and disadvantages, these rheometers complement each other. For multiaxial elongations the various modes of deformation can be performed by means of the rotary clamp technique. With the strain rate components ordered such that \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon $\end{document}₁₁ ? \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon $\end{document}₂₂ ≥ \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon $\end{document}₃₃, the ratio m = \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon $\end{document}₂₂/\documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon $\end{document}₁₁ characterizes the test mode. The Stephenson definition of the elongational viscosities makes use of the linear viscoelastic material equation and proves to be very efficient because the linear shear viscosity (t) (“stressing” viscosity) can act as the reference for the nonlinear behavior in elongation. Results are given for polyisobutylene measured not only in simple, equibiaxial, and planar elongations, but also in new test modes with a change of m during the deformation. This allows one to investigate the consequences of a deformation-induced anisotropy of the rheological behavior.     

Die Wahl des optimalen Verfahrens für die Bestimmung des Primärradikalabbruchs aus Geschwindigkeitsdaten

The various plots for estimating the ratio of rate constants characteristic for primary radical termination, k₅/k₁k₂, have been examined systematically. Apart from the special case d ≡ k₃k₆/k₅² = 1 there is no exact linear relationship between the general quantity \documentclass{article}\pagestyle{empty}\begin{document}${\rm Y \equiv (\sqrt {c_S} c_{M}/v_{Br})^{n}}$\end{document} and the general variable \documentclass{article}\pagestyle{empty}\begin{document}${\rm X \equiv (\sqrt {c_S} /c_M)^{s} (v_{Br}/c_M^{2} )^{1 - s}}$\end{document}. In any case, however, Y can he expressed as a power series of X. Therefore the best way to obtain the most favourable linear representation of Y as a function of X is to choose s and n according to the condition that the coefficient of the term quadratic in X has to disappear (n ? 2 s + d = 0) and the coefficient of the X³-term also equals 0 or is at least close to 0. Under these conditions even those data can be represented in an almost perfect linear form which show variations of the quantity \documentclass{article}\pagestyle{empty}\begin{document}$({\rm \sqrt{c_{s}}c_{M}/v_{Br})}$\end{document} by a factor of \documentclass{article}\pagestyle{empty}\begin{document}$\sqrt{2}$\end{document} or more for different initiator concentrations c_s. If additionally allowance is made for the consumption of monomer by the initiation process the desired ratio of rate constants, k_s/k₁k₂, is obtained from the plot of Y vs. X according to the equation The application of this method is illustrated using an example from literature.     

A simplified theory for generalizing results from a radiant panel rate of flame spread apparatus

Experimental results on the rate of lateral flame spread and time for piloted ignition under an externally imposed radiant flux were analyzed with a simple theroretical model. The data were developed from a radiant panel apparatus that considers a wall mounted sample with a flux distribution \documentclass{article}\pagestyle{empty}\begin{document}$ (\dot q_{\rm e} ^{\prime \prime } ) $\end{document} of 5 W cm^?2 at the ignited end to 0.2 W cm^?2 at the other end. It is shown that after an appropriate preheating time (flux exposure time before sample is ignited) the rate of flame spread (V_f) results can be correlated by \documentclass{article}\pagestyle{empty}\begin{document}$ V_{\rm f} - {\textstyle{1 \over 2}} = C\left( {\dot q''_{{\rm o,ig}} - \dot q_{\rm e} ^{\prime \prime } } \right) $\end{document} where C is a material ‘constant’ and \documentclass{article}\pagestyle{empty}\begin{document}$ \dot q''{\rm }_{{\rm o,ig}} $\end{document} is minimum flux for piloted ignition—also a material (and configuration) constant. An extension of this model demonstrates that V_f can also be expressed in terms of an ‘ignition temperature’ and the surface temperature of the material. Both correlations are derivable from a single flame spread experiment. Results are presented for a number of typical wood and plastic materials.     

Influence of electrolytes on the absorption of nitrogen oxide components N2O4 and N2O3 in aqueous absorbents

The influence of electrolytes, which are dissolved in the aqueous absorbent and do not react with nitrogen oxides, on the absorption kinetics of both these components was investigated experimentally. In addition to demineralized water, various salt solutions of different concentrations as well as sodium hydroxide solution were used as absorbents. The term H \documentclass{article}\pagestyle{empty}\begin{document}$ H\sqrt {k_1 D} $\end{document} for N₂O₄ and N₂O₃, which is important for the design of industrial absorbers, was determined as a function of composition and concentration of the absorbents. In the case of N₂O₄, the chosen measuring and evaluation methods permitted a separate determination of the rate constant k of the pseudo first order reaction and of the solubility H. The diffusion coefficient D of the gas in the absorbent can be obtained only by calculation. Experimental results showed that \documentclass{article}\pagestyle{empty}\begin{document}$(H\sqrt {k_1 D} )\,_{{\rm N}_{\rm 2} {\rm O}_{\rm 4} } $\end{document} decreases with increasing ionic strength I, however, without a clear indication of any ion-specific effects. This decrease does not appear to be caused simply by a reduction in solubility (salting out effect), or in diffusion coefficient, but at least, to the same extent, through a decrease of the rate constant k with increasing electrolyte content in the absorbent. The measurements permitted the determination of the gas-based salting out parameter for N₂O₄. The investigations on the absorption of N₂O₃ in water and in an Na₂SO₄ solution showed no experimentally detectable influence of dissolved salts on \documentclass{article}\pagestyle{empty}\begin{document}$(H\sqrt {k_1 D} )\,_{{\rm N}_{\rm 2} {\rm O}_{\rm 3} } $\end{document}. The numerical value of \documentclass{article}\pagestyle{empty}\begin{document}$(H\sqrt {k_1 D} )\,_{{\rm N}_{\rm 2} {\rm O}_{\rm 3} } $\end{document} is six times that of \documentclass{article}\pagestyle{empty}\begin{document}$(H\sqrt {k_1 D} )\,_{{\rm N}_{\rm 2} {\rm O}_{\rm 4} } $\end{document}.     

The rheology and spin coating of polyimide solutions

The rheological properties of five types of concentrated polyamic acid and polyimide solutions are characterized by non-Newtonian shear viscosity η(\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma} $\end{document}) and primary normal stress coefficient Ψ₁(\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma} $\end{document}) measurements over a wide range of shear rates. Onset of non-Newtonian flow of the polyamic acid solutions was observed in the shear rate range 30 to 400s^?1 and of the fully imidized polyimide solution at below 3 × 10^?2s^?1. Significant viscoelastic properties exemplified by normal stresses were observed in all the solutions. The solution rheology results are discussed in the context of spin coating for the deposition of thin films. The relative magnitude of effects of non-Newtonian flow on the dynamics of spin coating is assessed with a Deborah number characteristic of the flow.     

Yield stress and flow measurements in ABA block copolymer melts

A parallel-plate constant-stress rheometer is used to measure the yield stress τ_y, and the post-yield flow curve T(\documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document}), where τ is shear stress and \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} is shear rate, for microphase-separated triblock copolymer melts. Five polymer samples, all styrene-butadiene-styrene but with differing composition ratios and molecular weights, are tested at 125°C. Specimens are prepared by casting sheets from solutions made with different solvents. The τ(\documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document}) is found usually to be sigmoidal, for the range 10^?5 < \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} < 10^?3 s^?1, representing different stages of microstructural degradation in flow. Measurements indicate that a true τ_y exists, with values in the range 100 < τ_y < 500 Pa for these melts. A general trend is detected for τ_y to decrease as the casting solvent solubility parameter increases. A scheme for correlating the dependence of τ_y, on composition and molecular weight is proposed for the various polymers. For selected samples, the effect of mechanical history (sequence of stress application) and a temperature variation that crosses T_s (110 to 150°C) are also explored.     

Fluidity and Order in the Hydrocarbon-Water Interface of Synthetic and Biological Micelles as Determined by Fluorescence Polarization

A fluorescence polarization technique which was previously described was Utilized for the evaluation of microviscosities, \documentclass{article}\pagestyle{empty}\begin{document}$$ \bar \eta $$\end{document}, transition temperatures and degrees of order in the hydrocarbon-water interface of a series of micellar systems. The systems studied were micelles of compounds with a hexadecyl chain attached to different polar heads, and liposomes of lecithin and lecithin-cholesterol (～ 2:1). 1-Dimethylamino naphthalene 5-sulfoamide (DNSA) was found to dissolve in a well-defined region of the micelles studied and was employed as the fluorescence probe. The DNSA inclusion region possesses an apparent dielectric constant in the range of 28–40, inferred from the emission maximum of the embedded DNSA, and was therefore interpreted to be the hydrocarbon-water interface. In all systems studied the value of \documentclass{article}\pagestyle{empty}\begin{document}$$ \bar \eta $$\end{document} falls in the narrow range of 17–40 centipoises at 27°C. From the change of \documentclass{article}\pagestyle{empty}\begin{document}$$ \bar \eta $$\end{document} with temperature in the range of 0–60°C, phase transitions at 37, 33, 29 and 19°C were detected for micelles of cetyltrimethylammonium bromide, tetramethylammonium palmitate, cetylbetaine and egg lecithin, respectively. No phase transition was observed for lecithin-cholesterol liposomes. Fluorescence polarization spectra of DNSA dissolved in the micelles indicated that a certain degree of order prevails in their hydrocarbon-water interface.     

Melt rheology and extrudability of polyethylenes

Commercial high density polyethylene (HDPE), low density polythylene (LDPE), and linear low density polyethylene (LLDPE) resins were tested at 150, 170, and 190°C in steady state, dynamic, and extensional modes. Within the low rates of deformation \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} = ω ≤ 0.3, the steady state and dynamic functions agreed: η = η′ and N₁ = 2G′; at the higher rates, the steady state parameters were larger. The elongational viscosity, η_e, was measured under a constant rate, \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon $\end{document}, or stress, σ, condition. In the first case for LLDPE, the transient η reached an equilibrium plateau value, η_e. For HDPE, η increased up to the break point. For LDPE, stress hardening was recorded. Under constant stress the η_e, could always be determined; its value, within experimental error, agreed with the maximum value of η determined in a constant \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon$ \end{document} experiment. The maximum strain at break was only ε = 1.5 for HDPE and 3, to 4 for LDPE and LLDPE. The rate of deformation dependence of the η (or η′) and η_n may be discussed in terms of the Trouton ratio, R_T = η_e/3η at \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} = ω = \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon$ \end{document}: R_T ≤ 1.2 for LLDPE, R_T ≤ 2.5 for HDPE, and R_T ≤ 15 for LDPE. The PE resins were extruded at 190°C through a laboratory extruder equipped with a slit or rod die. The rotational speed of the screw varied from 0 to 90 rpm. Extrusion pressure, output, and energy were measured and correlated with the rheological parameters of the resins.     

Light-scattering studies on solutions of high and low molecular weight polystyrene mixtures used as models of microgel-containing solutions

Diluted solutions of linear polystyrene (PS) in toluene and dioxane were studied by the light-scattering method. The solutes were mixtures of high-M?_w and low M?_w PS. The dissolved PS mixtures were regarded as polymer solutions containing microgels, the high-M?_w PS being looked upon as the microgel counterpart. The calculation method as proposed by Strazielle¹ and Burchard² was used to evaluate the microgel percentage and particle size, whereby the method could be verified against mixtures with well-known weight composition and \documentclass{article}\pagestyle{empty}\begin{document}$ \overline {\left( {r_g ^2 } \right)} ^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} $\end{document}. The \documentclass{article}\pagestyle{empty}\begin{document}$ \overline {\left( {r_g ^2 } \right)} ^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} $\end{document} values evaluated for the mixtures from the experimental data were compared with those estimated from the molecular weights of the components, their weight concentrations, and their \documentclass{article}\pagestyle{empty}\begin{document}$ \overline {\left( {r_g ^2 } \right)} ^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} $\end{document} values. The method^1,2 was found to be useful for evaluating the microgel content in a sample, but not for \documentclass{article}\pagestyle{empty}\begin{document}$ \overline {\left( {r_g ^2 } \right)} ^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} $\end{document} values as calculated by Guinier's procedure nor those calculated by Zimm's procedure; the former were low and the latter were even incongruous. A comparative analysis of the theoretical function P^?1(θ)-versus-sin² (θ/2) and experimental (Kc/R(θ))_c=0-versus-sin² (θ/2) curves allowed to discuss the effect of the course of these curves at samll angles from 0° to 30° on M?_w and \documentclass{article}\pagestyle{empty}\begin{document}$ \overline {\left( {r_g ^2 } \right)} ^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} $\end{document} as determined for the high and low molecular weight polystyrene mixtures in toluene as solvent.     

Polymerization of olefins through heterogeneous catalysis. II. Kinetics of gas phase propylene polymerization with Ziegler–Natta catalysts

Propylene was polymerized in gas phase over a \documentclass{article}\pagestyle{empty}\begin{document}${\rm TiCl}_3 \cdot \frac{1}{3}{\rm AlCl}_3$\end{document} (Stauffer Type AA) Catalyst with AlEt₂Cl cocatalyst both with and without H₂ present. The effects of polymerization temperature, monomer concentration, catalyst composition, and hydrogen were investigated. The experiments were carried out at operating conditions approaching industrial practice.     

Kinetic study of the hydrolysis of cellulose acetate in the pH range of 2–10

A kinetic study of the hydrolysis of 39.8 wt.-% acetyl cellulose acetate has been made as a function of pH and temperature over the pH range of 2.2–10 and temperature range of 23–95°C. The hydrolysis reaction was carried out on highly porous membranes under quasihomogeneous conditions and the data have been treated as a pseudo-first-order reaction in acetyl concentration. The reaction can be represented by the equation \documentclass{article}\pagestyle{empty}\begin{document}$k_1 {\rm = }\;k_{\rm H ^ +} \left[ {{\rm H^+}} \right]{\rm +}k_{\rm OH^-}\left[ {{\rm OH}^ - } \right] + k_{\rm H_2O} $\end{document}, and where \documentclass{article}\pagestyle{empty}\begin{document}$k_{\rm H} ^ + {\rm = 5}{\rm .24}\;{\rm x 10}^{\rm 5} {\rm exp }\left\{ {{\rm ‐ 16}{\rm .4 x 10}^{\rm 3} /RT} \right\},{\rm }k_{{\rm OH}} ^ ‐ {\rm = 1}{\rm .55}\;{\rm x 10}^{\rm 4} {\rm exp }\left\{ {{\rm ‐ 8}{\rm .1 x 10}^{\rm 3} /RT} \right\}$\end{document}, and \documentclass{article}\pagestyle{empty}\begin{document}$k_{\rm H_2O} {= 4.25\;\times 10}^{- 2} {\rm exp }\left\{ {{- 11.5 \times 10^3 /RT}} \right\}$\end{document} (where the quantities in brackets are activities of the ions shown).     

A study of the fatigue behavior of fiber reinforced nylons

A phenomenological model combining a Weibull distribution function with a kinetic equation for flaw growth has been used to describe the static tensile strengths and fatigue lives of short graphite-fiber reinforced nylon 66 materials. A simple Weibull function of the form \documentclass{article}\pagestyle{empty}\begin{document}$ P\left( {\sigma _b } \right) = \exp - \left( {{{\sigma _b } \mathord{\left/ {\vphantom {{\sigma _b } {\hat \sigma }}} \right. \kern-\nulldelimiterspace} {\hat \sigma }}} \right)^{9.5} $\end{document} described the distribution of static strengths. The scale factor \documentclass{article}\pagestyle{empty}\begin{document}$ {\hat \sigma } $\end{document} varies with the annealing treatment and, in general, is a function of environmental variables. The cumulative distribution of breaking times in fatigue can be characterized by a translated three parameter Weibull function \documentclass{article}\pagestyle{empty}\begin{document}$ P\left( {t_B } \right) = \exp - \left\{ {\left. {\left( {\frac{{\sigma _{\max } }}{{\hat \sigma }}} \right)^{16} + \frac{{t_B }}{{\hat t}}} \right\}} \right.^{0.59} . $\end{document} The average time to break (which is related to the time scale factor \documentclass{article}\pagestyle{empty}\begin{document}$ {\hat t} $\end{document}), appears to be a function of the flaw growth rate. The distribution equation has been found to predict the number of half cycle failures and is thus a valid model for the proof testing of large populations. An electrical resistivity method was developed to measure flaw growth rates in prenotched cantilever beams. Experimental data fit the following equation: ln (Δa/Δn) = ?88.88 + (12.46 ± 5.68) ln (K_eff)_max. The correlation coefficient was 0.81. From curve fitting of fatigue data it appeared that flaw growth rate varied with the ninth power of flaw length (Δa/Δn) = Ma⁹. The direct measure of flaw growth rate using electrical resistance gave Δa/Δn = Ma^6.23±2.84 with 90 percent confidence. The two measurements overlap within the 90 percent confidence bands, but predictions of fatigue life using the flaw propagation data were not good. Scanning electron microscope studies showed that specimens with a short fatigue life have glassy, fibrillated fracture surfaces while specimens with a long fatigue life exhibit a high degree of ductility in portions of the fracture surface. These differences are traced to differences in the size and shape of flaws.     

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.