Empirical correlation of flow properties of poly(vinyl chloride)

Empirical correlations of flow properties of poly(vinyl chloride) were made using data reported by a number of investigators. Correlation was made by plotting the reduced variable viscosity η/η₀ versus \documentclass{article}\pagestyle{empty}\begin{document}$ (\eta _0 \dot \gamma \bar M_w )/(_\rho RT) $\end{document} or \documentclass{article}\pagestyle{empty}\begin{document}$ (\eta _0 \dot \gamma \bar M_w ^{0.5} )/(_\rho RT) $\end{document} for unplasticized PVC and versus \documentclass{article}\pagestyle{empty}\begin{document}$ (\eta _0 \dot \gamma \bar M_w ^{0.5} )/(_\rho RTW_2 ^a ) $\end{document} with polymer concentration, W₂, for PVC containing plasticizer.     

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.     

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.     

Elongational behavior of short glass fiber reinforced polypropylene melts

The Rheometrics Elongational Rheometer was employed to study the uniaxial extensional flow of glass fiber filled polypropylene melts, in which the fiber concentration, c, varied between zero and 40 weight percent. The constant strain rate mode was used for strain rates, \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \varepsilon \limits^. $\end{document}, between 0.003 and 0.6 s⁻¹. Steady state elongational viscosities were observed in most cases for fiber filled polypropylene melts, even at rates at which the stress continued to increase for unfilled polypropylene. The rate of relative stress growth increased with \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \varepsilon \limits^. $\end{document} and was affected by the addition of fibers. The steady elongational viscosity of the fiber reinforced melts was found to decrease with increasing \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \varepsilon \limits^. $\end{document} and to increase with increasing c. Yield stresses were observed in elongational flow at high concentrations, although there was no clear evidence of yield in steady shear.     

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.     

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.     

Total concentration of main components in solutions for metal electroplating as a criterion for classifying and choosing resource-saving compositions of solutions

A comparative analysis is performed of the variations in the total concentration of the main components $\left( {\sum\limits_i {c_i } } \right)$ , in the solutions proposed and used in different years for electroplating individual metals (Cr, Cu, Ni, Zn, Sn, Cd, Pb, and Fe). A quantitative concentration criterion is determined for classifying solutions into resource-saving ( $\left( {\sum\limits_i {c_i \leqslant 2.32} } \right)$ mol-equiv/L) and resourceintensive ( $\left( {\sum\limits_i {c_i \geqslant 2.78} } \right)$ mol-equiv/L) compositions. In addition to scientific interest, this material can be useful for developing studies aimed at reducing the negative environmental impact of electroplating shops or sections.     

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.     

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.     

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.     

Electrical conductivity and counterion association of cationic polyacrylamide derivatives in aqueous solution

Equivalent electrical conductivity (Λ) is reported for three series of cationic quaternary ammonium polyacrylamide derivatives with $\hbox{MeSO}_{4}ˆ{‐}$ , Cl⁻, Br⁻ and I⁻ as counterions at 25 °C, the polyion equivalent concentration C ranging from 5.3 × 10⁻⁴ to 6.4 × 10⁻³ N and from 1.0 × 10⁻³ to 1.4 × 10⁻² N. Equivalent electrical conductivity increases with decreasing polyion equivalent concentration, and the sequence of equivalent electrical conductivity Λ of polyelectrolytes for the same series with different counterions in the range of concentration investigated is: $\hbox{MeSO}_{4}ˆ{‐} > \hbox{Cl}ˆ{‐} > \hbox{Br}ˆ{‐} > \hbox{I}ˆ{‐}$ . The plots of the counterion–polyion interaction parameter f and degree of dissociation α of polyelectrolyte versus the polyion equivalent concentration C show that the order of counterion associating or binding to polyions for the same polyelectrolyte series in the range of concentration studied is $\hbox{MeSO}_{4}ˆ{‐} < \hbox{Cl}ˆ{‐} < \hbox{Br}ˆ{‐} < \hbox{I}ˆ{‐}$ . The chemical structures of the polyion have much influence on the Λ, f and α values of the polyelectrolytes. © 1999 Society of Chemical Industry     

Micellization of Some Bile Salts in Binary Aqueous Solvent Mixtures

The micellization behavior of bile salts—sodium cholate and sodium deoxycholate was studied in aqueous methanol, ethanol and ethylene glycol mixtures (10–20 % v/v) over a temperature range (300–320 K) by surface tension and conductivity methods. Critical micelle concentration, extent of counter ion binding (α), interfacial property (A _min, ζ_max, π-CMC, $ \Updelta G_{\text{ad}}^{ \circ } $ ) and thermodynamic parameters ( $ \Updelta G_{\text{m}}^{ \circ } $ , $ \Updelta H_{\text{m}}^{ \circ } $ , $ \Updelta S_{\text{m}}^{ \circ } $ ) for the micellization process are reported and discussed.     

Thermodynamic Properties of Sulfobetaine-Type Surfactants

Sulfobetaine-type surfactants containing a hydroxy group were synthesized by the reaction of long chain monoalkyl dimethyl tertiary amine with 3-chloro-2-hydroxypropanesulfonic acid sodium salt. The structures were characterized by ¹H NMR and ESI-MS. Their critical micelle concentrations (CMC) in aqueous solution were determined by the plate method in the temperature rang from 298.15 to 328.15 K. The thermodynamic parameters of micellization ( $\Delta G_{\text{mic}}^{\theta}$ , $\Delta H_{\text{mic}}^{\theta}$ and $\Delta S_{\text{mic}}^{\theta}$ ) and surface adsorption ( $\Delta G_{\text{ad}}^{\theta}$ , $\Delta H_{\text{ad}}^{\theta}$ and $\Delta S_{\text{ad}}^{\theta}$ ) were calculated from CMC data. The results showed that the micellization and surface adsorption of these surfactants in aqueous solution was a spontaneous and entropy-driven process. The micellization and surface adsorption became easier when the alkyl chain length increased from 12 carbon atoms to 14. The enthalpy–entropy compensation of micellization and adsorption was investigated. The compensation temperature were found to be (311 ± 2) K for both micellization and adsorption. The $\Delta H_{\text{mic}}^{*}$ and $\Delta H_{\text{ad}}^{*}$ decreased, but the $\Delta S_{\text{mic}}^{*}$ and $\Delta S_{\text{ad}}^{*}$ increased with increasing the hydrophobic chain length from 12 to 14.     

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.     

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.     

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.     

Study of intermolecular interactions in binary mixtures of methyl acrylate with benzene and methyl substituted benzenes at different temperatures: An experimental and theoretical approach

The ultrasonic speeds, u and viscosities, η of the binary mixtures of methyl acrylate with benzene, toluene, o-xylene, m-xylene, p-xylene, and mesitylene over the whole mole fraction range were measured at six different temperatures and at atmospheric pressure. From the experimental data, the excess isentropic compressibility, K_S^E, excess ultrasonic speed, u^E, excess molar isentropic compressibility, K_s,m^E, excess specific impedance, Z^Eand deviations in viscosity, Δηhave been calculated. The partial molar isentropic compressions, K_s,m,1 and K_s,m,2, and excess partial molar isentropic compressions, ${\mathop K\limits^{ - E}}$_s,m,1 and ${\mathop K\limits^{ - E}}$_s,m,2 over the whole composition range, partial molar isentropic compressions, and , and excess partial molar isentropic compressions, $\mathop K\limits^{ - \hat E} $_s,m,1 and $\mathop K\limits^{ - \hat E} $_s,m,2 of the components at infinite dilution have also been calculated. The results specified the existence of weak interactions between unlike molecules, and these interactions follow the order: benzene > toluene > p-xylene > m-xylene > o-xylene > mesitylene. The magnitude of interactions was found to be dependent on the number and position of the methyl groups in these aromatic hydrocarbons.     

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.