Densities of hydrocarbons in their saturated vapor and liquid states

The Sum and differences of the saturated vapor and liquid densities of 23 hydrocarbons were used to develop the following reduced density relationships for these saturated states The hydrocarbons considered included n-parafins, olefins, diolefins, naphthenes, and aromatics. Constants β, γ, and δ, and exponent n were found to be dependent on,. Equation (a) can reproduce liquid densities with an overall average deviation of 1.1 % over the entire temperature range, while Equation (b) was found to apply only in the interval 0.900 ≤ T_R ≤ 1.00 with an average deviation of 2.2%. For temperatures of T_k < 0.90, the saturated vapor density was found to depend on temperature as follows where k and m were also found to be Z_c dependent. Values calculated using Equation (c), when compared with 81 available experimental densities for 12 hydrocarbons, produced an average deviation of 3.0%.     

On the derivation and application of a new vapor pressure equation

Starting from the Clapeyron equation and making use of the equivalent expression for the reference state for latent heat of vaporization of pure liquids, namely at 0°K., a new vapor pressure equation is derived as follows: _χ(T_r) has been tabulated for T_r values in the range 0.50 < T_r <0.99 after programming on an IBM 1620 computer. The new vapor pressure equation has been tested with a variety of liquids both polar and non-polar, and found to predict vapor pressure data in the orthobaric range with an average error of ± 1.90% and maximum error of ± 3.20%. A significant outcome of this investigation is the identification of Riedel's factor α_o and Pitzer's acentric factor ω These have been shown to be functions of critical properties and reduced boiling point.     

A generalized vapor pressure equation for hydrocarbons

A reduced vapor pressure relationship of the following form has been developed: The optimum value of n was established to be 8.00 from vapor pressure data for n-heptane. A method was developed for the determination of the constants A, B, C and D from one reliable vapor pressure point. By this procedure vapor pressures were calculated for 33 hydrocarbons, including saturated and unsaturated paraffins, naphthenes, and aromatics, and were compared with corresponding experimental values. For these substances the overall average deviation between calculated and actual vapor pressure was 0.38% (1879 points). This relationship was also applied to seven additional hydrocarbons not included in its development, and for these substances the resulting average deviation was 0.36% (99 points).     

Permeation of organic vapors through polymer in the condensation region

Permeability coefficients have been measured for normal butane, isobutane, isobutylene, and butene-1 in Zendel Copolymer-I at temperatures between 30° and 70°C and at penetrant pressures p₁ up to 5.5 atm. The permeability coefficients of these organic vapors show behavior analogous to that observed for C₃ and C₂ hydrocarbons as detailed in our earlier work; i.e., near the condensation point of the penetrant, P increases as the temperature is decreased. Isothermal plots of log P versus p₁ in that region are generally linear and can be represented by empirical relations of the form where P₀ is a constant. The slope a is a function of temperature: where a₀ is a constant and b has the same value for the four hydrocarbons investigated.     

Thermal conductivity of simple gases at normal pressures

Thermal conductivity measurements available in the literature for simple gases at normal pressures (approximately 1 atmosphere) were used to obtain the product k^*λ, where the parameter, λ =M^1/2T_c^1/6/P_c^2/3. Separate relationships between k^*λ and T_R resulted for monatomic, diatomic and triatomic gases. The relationships for monatomic gases can be expressed as follows For the diatomic and triatomic gases, linear relationships resulted, when at the same reduced temperatures, their k^*λ values were plotted against (k^*λ)_m on log-log coordinates. These relationships can be expressed in equation form as follows and Thermal conductivities calculated with these relationships have been compared with experimental values and produce an average deviation of 2.8% for the monatomic gases (219 points), 4.3% for the diatomic gases (282 points) and 4.6% for the triatomic gases (242 points). In this treatment, helium and hydrogen do not follow the general pattern and consequently these substances have been treated separately.     

Predicting elastic moduli of heterogeneous polymer compositions

A new method for predicting elastic moduli M of heterogeneous polymer compositions is proposed. It is based on a phenomenological adjustment between parallel and series models for upper and lower bound moduli M_U and M_L. Thus, where ?_H is the volume fraction of hard phase, ?_S is the volume fraction of soft phase, and n is the only adjustable parameter since the upper and lower bound moduli are given by and where M_H and M_S are the moduli of the pure hard and soft phases, respectively. Predicted values of M are in agreement with measured values in a number of systems which include polyblends and composite materials of fixed morphology. The significance of n is discussed relative to concentrations in the area of a phase transition for the polyblends or relative to phase morphology in the case of fixed morphology compositions. Interestingly, the relationship, by analogy, is in agreement with measured values of polyblend melt viscosities.     

Effect of matrix's type on the dynamic properties for short fiber-elastomer composite

The dynamic moduli, E′ and E″, and tan δ for PET–CR, PET–EPDM, and PET–UR composites with unidirectional short fibers were studied as a function of temperature by using a Rheovibron. The temperature dependence of tan δ showed three peaks for PET–elastomer composites. The peaks at the low temperature corresponded to the main dispersion of the respective matrixes and the peak at about 140°C to the α-dispersion of PET fiber. A small and broad peak observed at a temperature between 60 and 120°C may be caused by the relaxation of the interface region between fibers and matrix. The longitudinal storage modulus for the composite E was given by the parallel model as \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm E'}_\parallel = V_f \cdot E'_f + V_m \cdot E'_m $\end{document}, where E and E are the storage moduli for fiber and matrix and V_f and V_m are the volume fraction of fiber and matrix, respectively. In the transverse direction of fibers, the composite modulus E was expressed by the logarithmic law of mixing as follows: \documentclass{article}\pagestyle{empty}\begin{document}$ \log E'_ \bot = V_f \cdot \log E'_f + V_m \cdot \log E'_m $\end{document}. The peak values of tan δ from the main dispersion of the respective matrixes were given by the equation, (tan δ_⊥max)_c/(tan δ_max)_m 1 ? β · V_f, where (tan δ_⊥max)_c and (tan δ_max)_m are the maximum values of the loss tangent for the composite and matrix, respectively, and β is coefficient depending on matrix's type. The β value of PET–CR composite is the largest one among those of the composites.     

Hydrolysis of 1,4-cyclohexanedimethanol-based copolyester

The solid state hydrolysis of a copolyester based on a mixture of 1,4-cyclohexanedimethanol and ethylene glycol condensed with terephthalic acid was studied at 100°C and 57 to 96 kPa water vapor partial pressure (55% to 95% relative humidity). The equilibrium water sorption in weight percent (C_∞) was found to be where P is the water vapor partial pressure in kPa. For specimens 0.32-cm thick, it took about 24 h to reach 0.9C_∞. The intrinsic viscosity (IV) was measured and used to calculate the relative change in molecular weight (M?_w) from the relationship IV ∝? (M?_w)^0.7. The decrease in molecular weight was linear with time, and the rate of decrease was found to be proportional to C_∞; the empirical correlation is where the rate constant, k, is in day^?1. A decrease of 50% in M?_w was observed after 22 days at 95% relative humidity.     

The apparent rate constant model for kinetics of radical chain copolymerization: Chemical-controlled process

In this article the kinetics of chemical-controlled radical-chain copolymerization have been reduced to pseudohomopolymerization kinetics by introducing the apparent rate constants, The methods for the determinations of the values of the apparent rate constants, mode of termination, and the methods for the calculation of molecular weights and distributions are proposed. The data required for these determinations and calculations are simply obtained by the usual steady-state method. According to the traditional kinetics along with the definitions of the apparent rate constants, these apparent rate constants as functions of traditional rate constants, monomer compositions, and copolymer compositions are derived. Further utilizing the theoretical expressions obtained, we show that the apparent rate constants are the general rate constants for both radical chain homo- and copolymerizations. The bulk radical copolymerizations of methyl methacrylate and styrene at various monomer feed compositions at 60°C are used to test the proposed model. The empirical apparent rate constants obtained are described well, by the following expressions, and and the mode of termination on the combination termination is where K and K denote the apparent rate constants of propagation and termination, respectively. The term f₁(= 1 ? f₂) stands for the mole fraction of styrene in the monomer solution fed. F₁ is the copolymer composition produced at f₁. β is the mode of termination.     

A one-point intrinsic viscosity method for polyethylene and polypropylene

A statistical analysis of dilute solution viscosity data for a wide range of polyethylene and polypropylene samples in Decalin at 135°C has shown that the Martin equation fits the experimental data better than the Huggins equation at higher values of [η]c. A grand average k of 0.139 is applicable to both polymers. Based upon this, tables have been calculated permitting the ready determination of [η] from a single relative viscosity measurement at a known concentration. The Martin equation has been put into a universal form, permitting [η] to be calculated from a measured η_sp if k and c are known. Graphs relating η_sp to [η] are included for use of the Martin equation over wide ranges of both k and c. It was found that the Solomon and Ciuta equation fits the experimental polyethylene and polypropylene data, and the reasons for this are discussed.     

Effect of substance-dependent Ωac on vapor-liquid equilibrium calculations

The role of the dimensionless quantity Ω_a (= aP_c/R²T) at the critical points of pure substances, Ω_ac, on the representation of binary vapor—liquid equilibrium values was investigated using a two-parameter cubic equation of state together with conventional mixing rules. A two-Ω_ac method was proposed to improve the representation of the equilibrium values in the critical region by considering the value of Ω_ac substance dependent. The limitations of the proposed method was also presented.     

A modified correlation to predict the minimum velocity required to elutriate solids from a liquid-fluidized bed

The consideration of sphericity of solids for the prediction of u_me gives rise to some improvement of the correlation proposed earlier by the author. In the absence of wall-effect, the following correlation is obtained: which gives a standard deviation of ± 16.3% for 138 different experiments as against ± 21.6% for 134 runs by the correlation reported earlier. The ranges of the various groups are      

Catalytic oxidation of benzene to maleic anhydride in a continuous stirred tank reactor

The kinetics of the vapor phase oxidation of benzene has been studied over an industrial catalyst in a continuous stirred tank reactor in the temperature range from 280 to 430°C and at atmospheric pressure. The products obtained are maleic anhydride, carbon oxides and water. The rate of the overall reaction (disappearance of benzene) is represented by the following expression based upon a steady state adsorption model The rate of formation of maleic anhydride is correlated by the equation which allows for a homogeneous depletion of maleic anhydride. The rate constants k_B, k_O, k_2(g) were found to follow Arrhenius behavior.      

Kinetics of o-Xylene oxidation over sintered vanadium pentoxide in a spinning catalyst basket reactor

Kinetics of vapor phase oxidation of o-xylene has been studied over sintered and compacted vanadium pentoxide in a continuous stirred tank catalytic reactor in the temperature range of 450–517°C at atmospheric pressure. The major product obtained is phthalic anhydride. The other products are maleic anhydride and carbon dioxide. The reaction rate data are well represented (with average absolute deviation less than 6%) by the following expression derived by applying the steady-state oxidation-reduction model of Mars and van Krevelen to a parallel reaction scheme and assuming first order with respect to both o-xylene and oxygen: Significantly, the activation energies for all three postulated reactions with rate constants k₁, k₂, and k₃ turn out to be identical having a value of 14.8 kcal/mole, which may be taken to imply that there is only one rate-influencing reaction step for all the products and not three as assumed in deriving this equation.     

Investigation on Proton Conductivity of La2Ce2O7 in Wet Atmosphere: Dependence on Water Vapor Partial Pressure

The AC conductivity of fluorite‐structured La₂Ce₂O₇ ceramic was measured under air and argon with different humidity between 250 and 550 °C. It was observed that the total conductivity in wet air and argon was higher than that under dry atmospheres. The effect of water vapor partial pressure ( ) on the conductivity of La₂Ce₂O₇ in air was investigated in detail. The total conductivity increased remarkably with the water vapor partial pressure, and this phenomenon became more notable at lower temperatures. The enhancement of the conductivity was attributed to the proton conduction behavior of La₂Ce₂O₇ in wet atmospheres, and the proton conductivity reached 6.68 × 10^–5 S cm^–1 in wet air (3% H₂O) at 550 °C. The relationship between the proton conductivity (σ_H) and in wet air could be fitted to . The estimated proton transport number increased with increasing water vapor partial pressure and decreasing temperature, and varied between 0.05 and 0.89 in this study.     

A one-point intrinsic viscosity method for hydroxyethylcellulose,hydroxypropylcellulose, and sodium carboxymethylcellulose

Statistical analysis of viscosity measurements on dilute solutions of hydroxyethylcellulose (HEC), hydroxypropylcellulose (HPC), and sodium carboxymethylcellulose (CMC) in the solvents water, 50/50 (v/v) water/ethanol, and 0.1M NaCl, respectively, demonstrated that the Martin equation, fits experimental data better than the Huggins equation, An average Martin k of 0.191 is applicable to a variety of HEC and HPC samples, including fractionated and unfractionated experimental and commercial preparations covering a wide range of substitution. In the case of a similar variety of CMC samples, an average k of 0.161 is characteristic. Based on these k values and using the Martin equation in the form tables were developed which permit direct reading of [η] values corresponding to single η_rel measurements at concentrations of 0.05, 0.10, 0.20, or 0.50 g/dl. Intrinsic viscosities obtained in this fashion differ from those determined by the usual dilution multipoint technique on the same samples by an average of but 2%, at an estimated time saving of 50% or more. This degree of variation is no greater than that expected in routine measurements on duplicate solutions.     

On the solubility parameter of polar polymers

The binary cluster integral, β, was computed from intrinsic viscosity data. Subtracting from β the polar contribution, β_e, calculated from YRCR theory,⁹ the nonpolar interaction parameter, β_n, was found. The calculations were performed for poly(vinylacetate) and poly(methyl methacrylate), each in 16 solvents. The correlation between β_n and the solvent solubility parameter, δ₁, was found to be similar to that reported^8,17 for solutions of natural rubber, cis-polybutadiene and for poly(vinyl chloride). This correlation can be crudely approximated by the formula where E and F are functions of the ill-defined symmetry of the solvent molecule and δ_m is the δ₁ value for the local maximum of the function. At δ₁ = constant, the more spherical is the molecule, the higher is the β_n value. It was shown that for most cases separation of the solvent into two classes (linear and nonlinear) is sufficient. This β_n behavior finds support in the Funk and Prausnitz⁶ report on aromatic–saturated hydrocarbon mixtures and in the theoretical calculations of Huggins.^21,22     

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     

Theoretical model for the elastic behavior of composites reinforced with short fibers

The two simplest models that can be put forward to account for the elasticity of composite materials are the Reuss model and the Voigt model in which the constituents undergo, respectively, the same stress or the same strain. Experimental measurements always fall between the values predicted by these models. We propose correcting the Reuss model by stating σ_f and ?_m being the average stresses undergone, respectively, by reinforcing agent and the matrix. Similarly, we shall modify the Voigt model by supposing σ_f and ?_m being the average strain undergone, respectively, by reinforcing agent and the matrix. K and L are interrelated tensors which depend on the nature of the reinforcing agent, on its possible orientation, and on the mechanical behavior of the interface and also on the moduli of the constituents. We have developed the equations for determining the tensors with regard to fiber composite, taking into account the characteristics of the fibers (length, diameter, orientation, interface). The evaluation of K and L enables us, therefore, to calculate the modulus or the compliance. Conversly, by measuring the modules or the complience, one can determine K or L and , in this way, obtain data on the machnism of load transfer from the matrix to the reingforcing agent and thus on the behavior of their interface. The theoretical values of the Young modules calculated from our model are in good agreement with the experemental values obtained by Lees.⁸     

Lewis acid–base properties of cellulose acetate phthalate‐polycaprolactonediol blend by inverse gas chromatography

The net retention volumes, V_N, of n‐alkanes and five polar probes are determined on cellulose acetate phthalate–polycaprolactonediol blend column by inverse gas chromatography in the temperature range 323.15–363.15 K. The dispersive surface energy, $\gamma _{\bf S}^{\bf d}$ , of the blend has been calculated using the V_N values of n‐alkanes and the $\gamma _{\bf S}^{\bf d}$ at 333.15 K is 12.6 mJ/m². The $\gamma _{\bf S}^{\bf d}$ values are decreasing linearly with increase of temperature. The V_N values of the five polar solutes are used to calculate the specific component of the enthalpy of adsorption, ${\Delta }{H}_{\bf a}^{\bf S}$ . The Lewis acid–base parameters, K_a and K_b, are derived using ${\bf \Delta }{H}_{\bf a}^{\bf S}$ values and are found to be 0.019 and 0.403, respectively. The K_a and K_b values indicate that the blend surface contain more basic sites and interact strongly with the acidic probes. The acid–base parameters have been used to analyze the preferential interaction of the solid surface with acidic and basic probes. POLYM. ENG. SCI., 2013. © 2013 Society of Plastics Engineers