Second virial coefficients of polar gases — a correlation with stockmayer potential function

The parameters of the Stockmayer potential function were calculated by a least-squares analysis of the second virial coefficient data for 66 polar substances. By using these parameters, the second virial coefficient of these tabulated materials can be calculated with a mean standard deviation of 20.2 cm³ mole^?1 or 3.2%. The possibility of extrapolating second virial coefficients from high to low temperatures is also demonstrated.     

A Simple Modification of the Pitzer Method to Predict Second Virial Coefficients

A simple modification of the Pitzer relation to calculate second virial coefficients of polar compounds is proposed. The proposed modification is based on the use of a new parameter, β, which embodies both the contributions of acentricity and polarity to second virial coefficient values. The analytical form of the Pitzer relation is preserved and its performances are improved. Rules are given to calculate β for several classes of compounds which require only the knowledge of a few well known properties of pure compounds. A comparison between the new method and the Pitzer-Tsonopoulos relation is made on the basis of the experimental B_i data of nearly 50 compounds.     

Second virial coefficients of polar gases for a four-parameter model

The second virial coefficients of polar gases have been studied for a potential function consisting of the Kihara spherical core potential combined with a preaveraged dipole-dipole interaction term. The molecular parameters ?/κ, ρ_o, a*, and y of this potential function were determined for ten substances by a nonlinear least squares analysis of experimental second virial coefficients. These molecular parameters were related to the critical constants, acentric factors, and fourth parameters of the substances. The resulting equations reproduced the second virial coefficients to within the accuracy of the data. Comparisons with experimental data for substances not included in the development of the relationships indicated that good agreement can be obtained for polar fluids by the method of this study.     

A FOUR PARAMETER PITZER-CURL TYPE CORRELATION OF SECOND VIRIAL COEFFICIENTS

The Pitzer-Curl ( 1957) correlation of second virial coefficients is slightly modified to accommodate high temperature data ( TT₄ 4.0) of He and H₂ and extended successfully to “ nonstandard” fluids as defined by Tarakad and Danner (1977), by introducing a fourth parameter per compound. The new version improves results at the high temperature limit while it gives comparable results with the previous versions presented by Pitzer and Curl ( 1957) and Tsonopoulos ( 1974) at lower temperatures. The present approach enhances the applicability of the method for polar and associating compounds by introducing a correcting term for 129 such fluids. The extension of the correlation to mixtures requires an additional parameter per binary. Successful results were obtained for thirty nine binary systems investigated in this work     

第二维里系数与温度的关联及Lennard-Jones和Stockmayer位能参数的推算

对第二维里系数与温度的经验关联式作了评选,推荐B=B_0+B_1/t+B_2/t~2+B_3/t~3+B_4/t~4,t=T/1000,和lg(-B)=E_0+E_1(100/T)+E_2lg(T/100),对166种纯物质作了关联.利用上述物质的第二维里系数数据推算其Lennard-Jones位能参数值和41种极性物质的Stockmayer位能参数值.     

EVALUATION OF SECOND VIRIAL COEFFICIENTS FROM SATURATION DATA

A data reduction technique is introduced for the evaluation of second virial coefficients of gases at subcritical temperatures. The method makes use of the vapor-liquid equilibrium data, i.e., temperature, saturation pressure, liquid and vapor molar volumes and can be used to obtain second virial coefficients of a wide variety of fluids including polar, associating and quantum gases. The calculated second virial coefficients are in good agreement with their counterparts from literature, which are obtained from gas compressibility data by traditional data reduction methods.     

EVALUATION OF SECOND VIRIAL COEFFICIENTS FROM SATURATION DATA

A data reduction technique is introduced for the evaluation of second virial coefficients of gases at subcritical temperatures. The method makes use of the vapor-liquid equilibrium data, i.e., temperature, saturation pressure, liquid and vapor molar volumes and can be used to obtain second virial coefficients of a wide variety of fluids including polar, associating and quantum gases. The calculated second virial coefficients are in good agreement with their counterparts from literature, which are obtained from gas compressibility data by traditional data reduction methods.     

Virial coefficients of normal fluids

The force constants of the square-well potential for normal fluids were correlated in terms of the critical properties P_c, T_c, and the acentric factor ω, by means of a non-linear regression technique. The second virial coefficients, a total fo 100 points chosen uniformly with respect to P_r and ω from the compilation of Dymond, together with the compressibility factors, taken from the generalized tables of Pitzer. were employed in the correlation. The valid ranges of the correlation are 0.5 ?T_r ? 2·0 and 0 ? ρ_r ? 1·0. The calculated results for the second virial coefficients compare favourably with the generalized correlation of Pitzer and Curl. The calculated third virial and cross third virial coefficients, and the compressibility factors also agree well with the literature values.     

New equipment for the determination of virial coefficients of pure substances and binary mixtures

A new equipment for the measurement of virial coefficients of pure substances and binary mixtures is described. It consists of an improved modification of the set-up proposed by Eucken and Meyer in 1929. The development is based on a critical review of the existing methods particularly with respect to adsorption effects. In order to reduce the influence of adsorption on the accuracy of virial coefficients, an optimum range for gas density is recommended. The accuracy of the virial coefficients is better than 20 cm³ mol^?1. The set-up was employed for the measurement of virial coefficients of acetone and hexane in the range from 352.95 to 393.85 K. The results are in excellent agreement with data published in literature. Furthermore, cross-virial coefficients of the binary system acetone/hexane were measured and interpreted.     

The new simple extended corresponding-states principle: vapor pressure and second virial coefficient

A new simple extended corresponding-states principle has been developed to represent and predict the thermophysical properties of fluids. The extended corresponding-states principle only requires the substance-dependent critical parameters and acentric factor which enhances the corresponding-states principle of Pitzer et al. to include the behavior of substances whose force fields deviate strongly from spherical symmetry. The additional corresponding-states parameter defined in terms of the deviation of the critical compression factor of a real molecule from that of spherical molecules is independent of experimental data for any specific property. The new simple extended corresponding-states principle presented here remarkably improves the representation of the vapor pressure from the triple point to the critical point and the second virial coefficient from the triple point to the highest temperatures over which experimental data exist. Accurate results for these two well-understood properties are given for simple, normal, polar, hydro-bonding and associating compounds. The results also show that the new simple extended corresponding-states principle is more reliable and accurately predicts the vapor pressure and second virial coefficient of a strongly nonspherical fluid than any other existing methods.     

An extension of the group contribution method for estimating thermodynamic and transport properties. Part III. Noble gases

Earlier work on the group contribution method applied to the Kihara potential is extended to noble gases for the estimation of second virial coefficients, dilute gas viscosities and diffusivities with a single set of gas group parameters. Group parameters are determined when second virial coefficient and viscosity data of pure gases are satisfactorily fitted within the experimental uncertainties. Parameters for gas groups (He, Ne, Ar, Kr and Xe) are found to provide good predictions of mixture properties: second virial cross coefficients, mixture viscosities, and binary diffusion coefficients. Application of the model shows that second virial coefficient data are represented with good results comparable to the values by means of the corresponding states correlation. The reliability of the present model in viscosity predictions is proved by comparison with the Lucas method. Prediction results of diffusivity are in excellent agreement with literature data and compare well with values obtained by means of the Fuller method.     

CORRELATION FOR THE THIRD VIRIAL COEFFICIENT USING Tc, PC, DIPOLAR POLARIZABILITY AND MEAN RADIUS OF GYRATION AS PARAMETERS

A new semi-empirical correlation for third virial coefficients of pure non-polar gases and their mixtures has been developed. It has been formulated as a sum of three contributions: two for pair additivity and non-additivity to the simple fluids and one for size and shape effects of the molecules. These contributions have been correlated with theoretically calculated data for argon, krypton and xenon and with an important set of emperimental data on third virial coefficients for 12 non-polar gases, The final correlation has been applied to 21 pure non-polar gases, 3 quantum fluids and 12 binary mixtures of classical and quantum gases. The results have been compared with other available methods. The overall comparison shows that this new method is equivalent or better than those, and that its major advantage is its predictive capability and its better theoretical representation thai should allow, in principle, its extension to more complex fluids.     

Equation of state for gaseous ethane determined from isotropic model potentials

A four-term virial equation of state was combined with isotropic model potentials to predict accurate volumetric and caloric thermodynamic properties of ethane in the gas phase. The parameters of the model potentials were determined from a fit to speed-of-sound data alone; no other data were used. The approximation used for the fourth virial coefficient included all interactions that contain up to two triplet potentials. Predicted ordinary second and third virial coefficients are in agreement with the data of Funke et al. [8]; we believe that predicted fourth virial coefficients are reliable and accurate. In the subcritical temperature region, the equation of state predicted compressibility factors that deviate by less than 0.04 percent at densities of up to 2.7 mol/dm³ (≈ 0.4ρ _c ). At supercritical temperatures, compressibility factors deviate by less than 0.02 percent at densities of up to 2.6 mol/dm³; also, in this region predicted isobaric heat capacity agrees with available data to within uncertainties of 0.4 percent at densities above 3 mol/dm³. We demonstrated that the four-term virial equation is more accurate than the three-term analogue.     

Extension of Tao-Mason Equation of State to Heavy n-Alkanes

In our previous paper we extended the Tao and Mason equation of state (TM EOS) to refrigerant fluids, using the speed of sound data. This is a continuation for evaluating TM EOS in predicting PVT prope...     

Vapor liquid equilibrium data for alcohol n-Amylamine binary systems at 333.15 K. Reduction of the experimental data by a novel model-free method

Vapor liquid equilibrium measurements for the binary systems of n-amylamine with methanol, ethanol and 1-propanol at 333.15 K are reported. The measurements were made in a static equilibrium cell of the Van Ness type and the experimental data were reduced using a model-free method. This model-free method is an adaptation of the method of Mixon et al. in which a material balance is introduced to correct for the mols of the gas phase. Second virial coefficients of n-amylamine and cross second virial coefficients for the binary systems were measured in this work and parameters for the Tsonoupolos correlation are reported.     

Tao-Mason状态方程扩展用于重正烷烃(英文)

In our previous paper we extended the Tao and Mason equation of state (TM EOS) to refrigerant fluids, using the speed of sound data. This is a continuation for evaluating TM EOS in predicting PVT properties of heavy n-alkanes. Liquid density of long-chain n-alkane systems from C 9 to C 20 have been calculated using an analytical equation of state based on the statistical-mechanical perturbation theory. The second virial coefficients of these n-alkanes are scarce and there is no accurate potential energy function for their theoretical calculation. In this work the second virial coefficients are calculated using a corresponding state correlation based on surface tension and liquid density at the freezing point. The deviation of calculated densities of these alkanes is within 0.5% from experimental data. The densities of n-alkanes obtained from the TM EOS are compared with those calculated from Ihm-Song-Mason equation of state and the corresponding-states liquid densities (COSTALD). Our results are in favor of the preference of the TM EOS over other two equations of state.     

An extension of the group contribution method for estimating thermodynamic and transport properties part II. Polyatomic gases (F2, Cl2, CS2, H2S, NO and N2O)

Earlier work on the group contribution method applied to the Kihara potential is extended to polyatomic gases for the calculation of second virial coefficients, viscosities and diffusivities of dilute gases with a single set of gas group parameters. Functional group parameters are evaluated from the simultaneous regression of second virial coefficient and viscosity data of pure gases. Parameters for gas groups (F₂, Cl₂, CS₂, H₂S, NO, nd N₂O) are found to provide good predictions of second virial cross coefficients, mixture viscosities and binary diffusion coefficients of gas-gas mixtures. Application of the model shows that second virial coefficient data can be represented with good results comparable to the values by means of the corresponding states model. The reliability of the present model in viscosity predictions is proved by comparison with the Lucas method. Predictions of binary diffusion coefficients are in excellent agreement with experimental data and compare well with values obtained by means of the Fuller method.     

Calculations of Derivative of Second Virial Coefficients based on the exp-6 intermolecular potential

The quantity of the partial derivative of second virial coefficients with respect to temperature in reduced form, T^*∂B^*/∂T^* has been computed for an exp-6 intermolecular potential The results are tabulated over the reduced temperature range T^* from 0.4 to 400, and for seven values of the parameters α from 12 to 15. The outputs lead us to lay the foundation for the applications of the theoretical virial type equation of state ⁽⁶⁾ like VLW using the best form exp-6 for high pressure studies.     

Water soluble copolymers. 54: N-isopropylacrylamide-co-acrylamide copolymers in drag reduction: Synthesis,characterization, and dilute solution behavior

Copolymers of N-isopropylacrylamide (IPAM) and acrylamide (AM) have been synthesized by free radical polymerization in deionized water using potassium persulfate as the initiator. Copolymer compositions were obtained by elemental analysis and ¹³C NMR. An r₁r₂ value of 0.99 indicates ideal copolymerization with random incorporation of the comonomers in the copolymers. Weight average molecular weights, second virial coefficients, diffusion coefficients, and average diameters were obtained via classical and quasielastic low angle laser light scattering. The molecular weights for all the copolymers and the homopolymers of IPAM and AM ranged from 2.2 × 10⁶ to 5.2 × 10⁶ g/mol. The second virial coefficients in deionized water increased with increasing acrylamide content in the copolymers. The dilute solution properties of the copolymers were studied by turbidimetry, microcalorimetry and viscometry. All the copolymers, with the exception of IPAM-40 (the copolymer synthesized with 40 mole% IPAM in the feed), showed lower critical solution temperatures below 100°C. The solution studies were performed in deionized water, 0.514 M NaCl, and 1 M urea. The properties of the IPAM copolymers were influenced by both hydrophobic associations and hydrogen bonding. In 0.2% (～7mM) sodium dodecyl sulfate, the alkyl chain of the surfactant molecules associates with the IPAM moieties on the copolymer backbone, leading to high intrinsic viscosities and the elevation of the LCST above 100°C.     

Application of the Virial Equation of State in calculating interior ballistics quantities

In calculating interior ballistics quantities the virial equation state is applied as an equation of state for real gases. A method shown of calculating the second and third virial coefficients for and mixtures of gases by using potential functions. A FORTRAN program has been set up for these calculations.