Upward extrapolation of saturated liquid densities

The design of new energy conversion processes requires equations of state for the working fluids. For their construction saturated liquid densities are needed which are not available for some potential working fluids at higher temperatures. Hence, we investigate how Rackett-type equations behave in extrapolations from saturated liquid densities in the temperature range 0.5 ≤ T/T_c ≤ 0.75 up to the critical temperature T_c. Extrapolation methods with different inputs from the critical point are used: (a) no critical point data, (b) critical temperature, (c) critical temperature and pressure, and (d) critical temperature and compression factor. It is found that upward extrapolations of the saturated liquid densities without using critical point data can be done with some care and that the additional use of the critical temperature improves the quality of the predictions substantially.     

EFFECT OF TACTICITY OF PMMA ON CRYSTALLINE STRUCTURE OF POLY VINYLIDENE FLUORIDE

Fourier transform infrared spectroscopy (FTIR) has been used to study the effect of tacticityof PMMA on β phase formation of poly vinylidene fluoride (PVF_2) during quenching process.For pure PVF_2, quenching at lower temperature results in the formation of β phase crystallites.The critical quenching temperature for β phase formation is about 30℃. Adding a given amountof PMMA (30%) results in the increase of the critical quenching temperature. For the blends ofPVF_2 with atactic PMMA (a-PMMA), the critical quenching temperature is about 45℃, whilefor the blends with syndiotactic PMMA (s-PMMA), attains to about 70℃.     

Approximate critical conditions in thermal explosion theory for a two-step kinetic model

Approximate critical conditions for a thermal explosion problem is developed for a two-step reactions based on theories of Semenov and Frank-Kamenetskii. The aim is to examine the contributions of the radical termination step and the temperature dependent pre-exponential factor on the critical parameters within the framework of classical stationary and non-stationary theories. In the non-stationary case, a more general expression for the critical Semenov parameter (Ψ _cr ) and critical temperature (θ _cr ) were obtained by asymptotic procedure. In the stationary case, numerical estimates for the critical Frank-Kamenetskii parameter (δ _cr ) and the critical temperature (θ _cr ) were obtained by variational method technique. It was observed that the Semenov and Frank-Kamenetskii parameters are greatly influenced by the termination step and the variable pre-exponential factor. Apart from elucidating hitherto unknown features in the theory of thermal explosion, the results are more general as some known results are easily recovered.     

Three-dimensional dilute Bose liquid at finite temperature: a Renormalization Group approach

We consider the influence of temperature on the critical behavior of a weakly interacting three dimensional Bose system. Using the flow equations of the Renormalization Group and a Φ⁴ model with dynamical critical exponent z?=?2, we calculated the critical exponent ν, and the thermodynamical parameters near the critical temperature, taking in consideration the quantum effects. The quantum effects considered using this method gives for ν the value 0.75, which is close to the value 0.73 obtained by the polynomial method. The critical temperature shift ΔT _c was obtained, in the lowest-order approximation, and turns out to be proportional to the scattering length.     

Influences of nonsolvent and temperature on critical viscoelastic behaviors of ternary polyacrylonitrile solutions around the sol-gel threshold

Viscoelastic experiments were performed to study the influence of nonsolvent and temperature on critical viscoelastic behaviors of ternary polyacrylonitrile (PAN) solutions around the sol-gel threshold. The dynamic critical parameters around the sol-gel threshold were determined using dynamic rheometer. The sol-gel transition takes place at a critical gel temperature at which the scaling law of G′(ω) ∼ G″(ω) ∝ ωⁿ holds, allowing an accurate determination of the critical gel temperature by means of the frequency independence of the loss tangent. Although the gel points of PAN solutions increase with increasing H₂O content, the results show that the scaling exponent n at the gel point is found to be universal for all ternary PAN solutions, which is independent of temperature and H₂O content, indicating the similarity of the fractal structure in the critical PAN gels. The gelation of ternary PAN solutions induced by adding a nonsolvent and by decreasing the temperature is demonstrated to be a thermoreversible process, which implies that the PAN gels are physical gels. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2637–2643, 2008     

A STUDY ON THE YIELD STRENGTH OF SBR RAW RUBBER

the relationship between intrinsic viscosity[η] and yield strength [σ?] of SBR-1500 raw rubberwas studied. It was found that the critical molecular weight for yielding varied with temperature.The critical yield temperature of SBR--1500 is 18℃, which is equivalent to transition temperature T'_(ll)as determined by linear expansion. The transition temperature T'_(ll) of SBR increased with styrenecontent in the sample.     

Determination of ceiling temperature and thermodynamic properties of low ceiling temperature polyaldehydes

Knowledge of the ceiling temperature and thermodynamic variables for low ceiling temperature polymers is critical to understanding the material's synthesis and use. Synthesis of the polymer below its ceiling temperature is the routine polymerization route. In situ ¹H NMR of the equilibrium polymerization reaction can provide critical information for determining the enthalpy and entropy of polymer formation. Three polyaldehydes were synthesized with in situ ¹H NMR, and their energies of formation were determined for the linear region of ceiling temperature. Insights into the mechanism of polymerization were also found using this method. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 221–228     

Critical Behavior of {DMA + AOT + Octane} Nonaqueous Microemulsions with Various Molar Ratios of DMA to AOT

The coexistence curves of two nonaqueous microemulsions systems of {dimethylacetamide (DMA) + sodium di(2-ethyl-1-hexyl)sulphosuccinate (AOT) + n-octane}, with the molar ratios ω=(3.06 and 3.86) of DMA to AOT, were determined by precisely measuring the refractive index at constant pressure at temperatures within about 7 K of the critical temperature T _c. The critical exponents β and critical amplitudes B have been deduced from the coexistence curves. It was found that the values of β for both systems are inconsistent with the expected 3D-Ising value but approach the Fisher-normalization value of 0.365 over a rather wide temperature range. By increasing the molar ratio ω, the critical temperature T _c increases, but the critical (volume fraction) composition φ _c decreases, which is different from the trends observed for aqueous microemulsions.     

Rheology and morphology change with temperature of SEBS/hydrocarbon oil blends

The effect of hydrocarbon oil incorporation on the rheological and phase behaviors of poly(styrene‐b‐(ethylene‐co‐butylene)‐b‐styrene) (SEBS) has been investigated. SEBS‐A1 (neat SEBS) shows a presence of very long relaxation time mode even at the highest temperature carried out here. On the other hand, G′ of SEBS‐A3 (oil concentration = 50 wt %) drastically decreases with increase of temperature at a critical temperature, which can be assigned to be order–disorder transition (ODT). The critical temperature was determined by two rheological criteria. Incorporation of hydrocarbon oil affects the ODT temperature. The rheological response is very sensitive to a few temperature increases around the ODT temperature. Above the critical temperature, G′ finally yields the terminal flow in the low frequency range. The morphological observation at various temperatures was determined using atomic force microscopy (AFM) equipped with environmental controller. This enabled in situ observation of structural change of SEBS induced by temperature and phase transition. We found that the layered texture, mostly aligned along the surface can be seen for SEBS‐A1 ranging from room temperature to 230 °C, though the image contrast reduced by an increase of temperature. SEBS‐A3 showed sphere domains at room temperature and also remains the structure at a critical temperature. The phase separated structure disappeared almost completely above ODT temperature, which was confirmed by the rheologial criteria. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 955–965, 2009     

A Study on the Adsorption Isotherms in the Vicinity of the Critical Temperature

Adsorption data of nitrogen and methane on micro-porous activated carbon and on meso-porous silica gel were measured near the critical temperature. It was found that the values of the compressibility factor (z) exerted a significant effect on the behavior of isotherms. Selection of reliable z-values is very important for the analysis of experimental results obtained near the critical temperature. The isotherms on activated carbon always show type-I features at sub- and supercritical temperatures, but those on silica gel remarkably show a change from type-II at sub-critical temperatures to type-I at supercritical temperatures. The critical temperature appears to be shifted up in some case.     

Critical behaviour of optical birefringence in the vicinity of nematic–isotropic and smectic A–isotropic phase transitions of the eight members of alkyloxy-cyanobiphenyls

We report the measurements of birefringence (Δn) as a function of the temperature of a homologous series of alkyloxy-cyanobiphenyls (nOCB) liquid crystalline compounds by means of high-resolution optical transmission method. The temperature dependence of the birefringence has been determined from the transmitted intensity data for two different wavelengths. The order parameter critical exponent β, obtained by using a four-parameter fitting procedure consistent with the mean-field theory for a weakly first order transition, is found to be in good agreement with the theoretically predicted tricritical value. A weak birefringence has been found to develop on approaching the clearing temperature, which is tentatively attributed to the formation of a small mesophase domain within the isotropic phase. This striking behaviour leads to a further quantification of the critical fluctuation close to the transition. Finally, the order character of the nematic–isotropic (N–I) and smectic A–isotropic (SmA–I) phase transitions have been assessed by using the birefringence data. The critical exponent α (usually assigned to the heat capacity) extracted from Δn data describes the critical nature of N–I and SmA–I transitions and strongly supports the tricritical nature of the same.     

Tetrasulphur Tetranitride: Phase Transition and Crystal Structure at Elevated Temperature

Rietveld X‐ray crystal structure investigations on S₄N₄ give evidence for a new orthorhombic high‐temperature phase (Pbcn, a = 883.9(1) pm, b = 875.5(1) pm, c = 725.81(9) pm) very close to the explosion temperature of the solid‐state material. The phase transition can be described using Landau's theory, yielding a critical temperature of 397 K and a critical exponent of 0.50.     

The complete closed coexistence curves for 2H,3H,6H,7H,8H-5,8-(Dimethylmethano)-5(R)-methylquinoxaline with water and with deuterium oxide

The complete closed solubility curves for 2H, 3H, 6H, 7H, 8H-5,8-(dimethylmethano)-5(R)-methylquinoxaline with water and with deuterium oxide have been determined. With water the lower critical solution temperature (LCST) was found to be 51.4°C and the critical solution temperature (CST) was found to be 215.0°C. With deuterium oxide the values were 40.4°C for the LSCT and 221.7°C for the CST. The deuterium oxide curve completely encompassed the water curve. Solution compositions at the critical temperatures were also determined.     

Viscometric behavior of mesomorphic ethyl cellulose solution in chloroform

A simple modification of the viscometer used to determine the viscosity of concentrated solutions is described which permits the ready measurement of viscosity versus shear rate behavior above room temperature. Basic experimental viscometry was performed on the ethyl cellulose–chloroform system using a B-type (Brookfield-like) rotating-cylinder viscometer. Data are compared with theoretical predictions. The flow curves exhibit yield stress at low shear rate. The yield stress is dependent on concentration and temperature. The viscosity versus concentration curves show typical mesomorphic behavior. The concentration dependences of viscosity and yield stress are similar. The critical concentration increases with temperature. In the single-phase region (isotropic or anisotropic state) the viscosity decreases with temperature and the apparent activation energy (E_a) for flow is positive, but in the biphasic range the viscosity increases with temperature and E_a is negative. The experimental results for the critical concentration appear to agree with Flory's theory of rodlike molecules when the ratio of persistence length to diameter of the chain is taken as the aspect ratio.     

Evaluating the Thermal Hazard of Double-Base Propellant SQ-2 by Using Microcalorimetry Method

The thermal decomposition behavior of double‐base rocket propellant SQ‐2 was studied by a Calvet microcalorimeter at four different heating rates. The kinetic and thermodynamic parameters were obtained from the analysis of the heat flow curves. The critical temperature of thermal explosion (T_b), the self acceleration decomposition temperature (T_SADT), the adiabatic decomposition temperature rise (ΔT_ad), the time‐to‐explosion of adiabatic system (t), critical temperature of hot‐spot initiation (T_cr), critical thermal explosion ambient temperature (T_acr), safety degree (SD) and thermal explosive probability (P_TE) were presented to evaluate the thermal hazard of SQ‐2.     

Liquid–liquid phase separation in multicomponent polymer solutions. II. The critical state

Theoretical and experimental evidence is put forward to prove that the determination of the phase-volume ratio as a function of temperature and concentration is a sensitive and simple means of determining the liquid–liquid critical state. Knowledge of the critical conditions permits very accurate calculations of the interaction parameter g in the free-energy function. In experiments with polystyrene–cyclohexane, g was found to depend on the concentration. The value of g and its concentration dependence agree very well with the results of osmotic measurements by Rehage and Palmen. In experiments with polyethylene–diphenyl ether, g proved to be independent of concentration in the range of measurement. The temperature function was found to be: g = ?0.6086 + 482.2/T (at 137–148°C.). Gibbs' expressions for the critical conditions were worked out for a free-energy relation in the form of an extended Flory-Huggins function.     

Relationship between the density of supercritical CO<Subscript>2</Subscript> + ethanol binary system and its critical properties

The dependent relation between temperature and pressure of supercritical CO₂+ ethanol binary system under the pressure range from 5 to 10 MPa with the variety of densities and mole fractions of ethanol that range from 0 to 2% was investigated by the static visual method in a constant volume. The critical temperature and pressure were experimentally determined simultaneously. The PTρ figures at different ethanol contents were described based on the determined pressure and temperature data, from which pressure of supercritical CO₂ + ethanol binary system was found to increase linearly with the increasing temperature. P-T lines show certain convergent feature in a specific concentration of ethanol and the convergent points shift to the region of higher temperature and pressure with the increasing ethanol compositions. Furthermore, the effect of density and ethanol concentration on the critical point of CO₂ + ethanol binary system was discussed in details. Critical points increase linearly with the increasing mole fraction of ethanol in specific density and critical points change at different densities. The critical compressibility factors Z_c of supercritical CO₂ + ethanol binary systems at different compositions of ethanol were calculated and Z _c -ρ figure was obtained accordingly. It was found from Z _c -ρ figure that critical compressibility factors of supercritical CO₂ unitary or binary systems decline linearly with the increasing density, by which the critical point can be predicted precisely.     

Enthalpy recovery in semicrystalline polymers

Constitutive equations are derived for enthalpy recovery in glassy polymers after thermal jumps. The model is based on the theory of cooperative relaxation in a version of the trapping concept. It is demonstrated that a critical temperature T_cr and a critical degree of crystallinity f_cr exist in a semicrystalline polymer above which structural relaxation vanishes.     

The influence of shear rate, temperature and chain conformation on the critical concentration c

 When viscometry is used, a crossover phenomenon is observed separating the dilute solutions into extremely dilute solutions and dilute solutions. The critical concentration c ^**, determined from this crossover phenomenon, strongly depends on the shear rate in the solution. At very high values of shear rate the critical concentration c ^** becomes very low and depends only on the contour length of the elongated chains of different polymers. An increase of the temperature induces an increase of c ^** because the relaxation time of the chains decreases. If a polymer adopts a rodlike conformation (in a given solvent at a given temperature) the excluded volume of its chains increases and its critical concentration c ^** decreases. Received: 14 October 1996 Accepted: 3 March 1997