In this work the interface system of the van der Waals fluid is investigated by using the density... more In this work the interface system of the van der Waals fluid is investigated by using the density gradient theory incorporated with the mean-field theory. Based on the mean-field dividing interface generated by the Maxwell construction, we propose a highly accurate density profile model for the density gradient theory, which facilitates reliable predictions of various properties for the interface region. It is found that the local intrinsic Helmholtz free energy peaks at the interface and that the maximum difference of the normal and tangential components of the pressure tensor corresponds to the maximum of the intrinsic Gibbs free energy. It is found that the entire phase space is divided into gas-like and liquid-like regions by the single line composed of the mean-field interface and the Widom line. The two-fluid feature of the supercritical fluid is hence inherited from the coexistence region. Phase diagrams extended into the coexistence region in all the temperature-pressure-volume planes are thus completed with the solutions to the vapor-liquid equilibrium problem by the van der Waals equation of state.
Industrial & Engineering Chemistry Research, 1998
The use of supercritical fluid chromatography measurements to obtain solute partial molar volumes... more The use of supercritical fluid chromatography measurements to obtain solute partial molar volumes at infinite dilution is investigated by a combination of theory, modeling, and thermodynamic connections to solubility. Though it is common to ignore contributions from solute self-interactions, theory and modeling show that these can be significant in the critical region. In particular, expressions for the first-order solute composition dependence in terms of convergent infinite-dilution quantities are used to estimate the errors introduced by ignoring solute self-interactions. These are considered in light of recent empirical work on solubilities and partial molar volumes that can be connected via thermodynamic relations. Finally, though various assumptions have been made about the solute partial molar volume in the stationary phase, none of these seem consist with solubility measurements which suggest that the stationary phase contribution should be both temperature-and density (pressure)-dependent.
The hard disc system plays a fundamental role in the study of two-dimensional matters [1-3]. High... more The hard disc system plays a fundamental role in the study of two-dimensional matters [1-3]. High-precision compressibility data from computer simulations have been reported for all the phases and phase transition regions [4-15]. In particular, Bernard and Krauth (Phys. Rev. Lett., 107, 155704, 2011) [10] presented a complete and accurate picture of the phase transitions of the hard disc system with simulation results. However, thorough descriptions of the system depend on analytical equations of state (EoS) over the entire density range. While majority of EoS's published are for the stable fluid region only [1,16], few attempted the liquid-hexact transition region (
In this work we define a mean-field crossover generated by the Maxwell construction as the dividi... more In this work we define a mean-field crossover generated by the Maxwell construction as the dividing interface for the vapor-liquid interface area. A highly accurate density-profile equation is thus derived, which is physically favorable and leads to reliable predictions of interfacial properties. By using the density gradient theory and a meanfield equation of sate for the Lennard-Jones fluid, we are able to extensively explore the interface system in terms of the Gibbs free energy, the Helmholtz free energy and heat capacity. The results show that the mean-field dividing interface is the natural extension of the Widom line into the coexistence region. Hence the entire phase space is coherently divided into liquid-like and gas-like regions in all three (temperature-pressure-volume) planes. Some unconventional behaviors are observed for the intrinsic heat capacity, being positive in low temperature region while negative in high temperature region. Finally, a complete picture of the m...
Since a transcendental equation is involved in vapor liquid equilibrium (VLE) calculations with a... more Since a transcendental equation is involved in vapor liquid equilibrium (VLE) calculations with a cubic equation of state (EoS), any exact solution has to be carried out numerically with an iterative approach [1,2]. This causes significant wastes of repetitive human efforts and computing resources. Based on a recent study [3] on the Maxwell construction [4] and the van der Waals EoS [5], here we propose a procedure for developing analytically approximate solutions to the VLE calculation with the Soave-Redlich-Kwong (SRK) EoS [6] for the entire coexistence curve. This procedure can be applied to any cubic EoS and thus opens a new area for the EoS study. For industrial applications, a simple databank can be built containing only the coefficients of a newly defined function and other thermodynamic properties will be obtained with analytical forms. For each system there is only a one-time effort, and therefore, the wastes caused by the repetitive efforts can be avoided. By the way, we also show that for exact solutions, the VLE problem with any cubic EoS can be reduced to solving a transcendental equation with one unknown, which can significantly simplify the methods currently employed [2,7].
The well-known Maxwell construction1 (the equal-area rule, EAR) was devised for vapor liquid equi... more The well-known Maxwell construction1 (the equal-area rule, EAR) was devised for vapor liquid equilibrium (VLE) calculation with the van der Waals (vdW) equation of state (EoS)2. The EAR generates an intermediate volume between the saturated liquid and vapor volumes. The trajectory of the intermediate volume over the coexistence region is defined here as the Maxwell crossover, denoted as the M-line, which is independent of EoS. For the vdW or any cubic3 EoS, the intermediate volume corresponds to the “unphysical” root, while other two corresponding to the saturated volumes of vapor and liquid phases, respectively. Due to it’s “unphysical” nature, the intermediate volume has always been discarded. Here we show that the M-line, which turns out to be strictly related to the diameter4 of the coexistence curve, holds the key to solving several major issues. Traditionally the coexistence curve with two branches is considered as the extension of the Widom line5,6-9. This assertion causes an...
Industrial & Engineering Chemistry Research, 1991
On the basis of our previous reviaed free-volume theory, a new model with temperature-independent... more On the basis of our previous reviaed free-volume theory, a new model with temperature-independent parameters is proposed for the calculation of viscosities for liquid mixtures. It is used to estimate and predict the viscosities for diverse binary and ternary mixtures, including aqueous and partially miscible systems. For 70 binaries (2033 data points), the grand absolute average deviation percent (AAD) is 1.60 from use of the parameters regressed from the data at a constant temperature. Moreover, for 23 ternaries (560 data points) the AAD is 2.76. A rigorous comparison with the Teja and Rice method indicates that our method is a good improvement.
The well-known Carnahan-Starling (CS) equation of state (EoS) 1 for the hard sphere (HS) fluid wa... more The well-known Carnahan-Starling (CS) equation of state (EoS) 1 for the hard sphere (HS) fluid was derived from a quadratic relation between the integer portions of the virial coefficients, , , and their orders,. Here we extend the method to the full virial coefficients for the general D-dimensional case. We assume a polynomial function of (D-1) th order for the virial coefficients starting from = 4 and EoS's are derived from it. For the hard rob (D=1) case, the exact solution is obtained. For the stable hard disk fluid (D=2), the most recent virial coefficients up to the 10 th 2 and accurate compressibility data 3,4 are employed to construct and test the EoS. For the stable hard sphere (D=3) fluid, a new CS-type EoS is constructed and tested with the most recent virial coefficients 5,2 up to the 11 th and with the highly-accurate simulation data for compressibility 6-8. The simple new EoS's turn out to be as accurate as the highest-level Padé approximations based on all available virial coefficients, and significantly improve the CS-type EoS in the hard sphere case. We also shown that as long as the virial coefficients obey a polynomial function any EoS derived from it will diverge at the non-physical packing fraction, = 1.
... ModifiedFreeVolumeModel.Freevol ume models are widely used for the description of trans port ... more ... ModifiedFreeVolumeModel.Freevol ume models are widely used for the description of trans port properties, such as viscosity and diffusivity.The so called hybrid model proposed by Macedo and Litovitz2* and later derived by Chung 29from statistical mechanical considerations ...
Industrial & Engineering Chemistry Research, 1998
ABSTRACT The effective hard sphere diameter (EHSD) method has been widely used to calculate both ... more ABSTRACT The effective hard sphere diameter (EHSD) method has been widely used to calculate both equilibrium and transport properties. Various EHSD explicit equations have been proposed in the literature according to different criteria. In this work a comparison between different expressions has been carried out and suggestions are given following the comparison. As an example of the applications, the EHSD method has been applied to the prediction of the self-diffusion coefficients of the Lennard-Jones fluid, by use of the hard sphere model proposed by Erpenbeck and Wood. It is found that the temperature-dependent Boltzmann EHSD and both temperature- and density-dependent Lado modified Weeks−Chandler−Andersen EHSD give the best results.
Industrial & Engineering Chemistry Research, 1995
Infinite dilution partial molar volumes (PMV) of solutes in supercritical fluids (SCF) are very i... more Infinite dilution partial molar volumes (PMV) of solutes in supercritical fluids (SCF) are very important thermodynamic properties of SCF mixtures. But until recently very few works have been dedicated to the measurements and the prediction or correlation of these properties. In this paper we present a systematic study on various models for the representation of PMV. First, we tried to predict the PMV using model parameters regressed from solubility data. Four models have been tested, and it is found that all these models can only be used qualitatively, not quantitatively. After that, we used 11 models for the correlations with temperaturedependent parameters. It is found that the model based on Wang and Tavlarides's (WT) dilute solution expression and a three-parameter empirical equation derived in this work give the best results. Some simple correlations also give acceptable results. It is surprising that some theoretical models, e.g., Wheeler's decorated lattice gas model and the models based on the fluctuation theory do not work as well as expected. Moreover, we have used six models for correlations with temperature-independent parameters. We conclude that the model proposed in this work with three parameters based on the WT dilute solution expression gives the best results. The modified Peng-Robinson equation of state (EoS) and a n empirical correlation proposed by O'Connell give acceptable results. The main conclusion of this work is that it is possible to correlate the PMV by using a simple model, although no available model is recommended for quantitative predictions.
We define a mean-field crossover generated by the Maxwell construction as the dividing interface ... more We define a mean-field crossover generated by the Maxwell construction as the dividing interface for the vaporliquid interface area and a highly accurate density-profile equation is thus derived. By using a mean-field equation of sate for the Lennard-Jones fluid incorporated with the density gradient theory, we show that the intrinsic free energy peaks and the isobaric heat capacity exhibits local maxima at the interface. We demonstrate that the meanfield interface is the natural extension of the Widom line into the coexistence region, hence the entire space is coherently divided into liquid-like and gas-like regions in all three (temperature-pressure-volume) planes. Finally, the mean-field theory is found holding all the information for composing the phase diagrams over the entire phase space.
This paper presents a study on the relationship between transport properties and geometric free v... more This paper presents a study on the relationship between transport properties and geometric free volume for hard sphere (HS) system in dense fluid region. Firstly, a generic free volume distribution function is proposed based on recent simulation results for the HS geometric free volume by Maiti et al. 1,2 Combining the new distribution function with a local particle transportation model, we obtain a power law for the HS transport properties. Then a relation between the geometric free volume and thermodynamic free volume is established, which makes it possible to use well-developed equations of state (EoS) for the expressions of the geometric free volume. The new power law models are tested with molecular dynamic (MD) simulation results for HS viscosity, diffusivity and thermal conductivity, respectively and the results are very satisfactory. Using the power law we are able to reproduce several equations obtained from different approaches, such as the entropy scaling laws 3 , mode coupling theory 4 or empirical correlations 5. In particular, A long-standing controversy regarding the well known Cohen-Turnbull-Doolittle free volume model 6,7 is resolved by using the power law combined with an EoS.
The hard sphere system plays a basic role in condensed matter physics and related fields, and equ... more The hard sphere system plays a basic role in condensed matter physics and related fields, and equation of state (EoS) is the ultimate solution to its thermodynamic properties (1-3). Dozens of EoSs have been proposed since van der Waals historic work and many reliable EoSs are available for the stable fluid region (3). For the metstable region, all available EoSs are not accurate enough for various applications. It has been considered impossible to develop an analytical EoS for the entire stable and metstable region 4. By virtue of a potential energy landscape analysis combined with the Woodcock type EoS (2,5), here we show that a fairly simple analytical equation can be obtained to reproduce the compressibility of the entire region with high accuracy. Therefore, all four amorphous states of matter, gas, liquid, supercooled liquid and glass, can be represented with a single EoS. Examples are given to show that highly accurate EoS is necessary for applications in thermodynamic propert...
Industrial & Engineering Chemistry Research, 1997
ABSTRACT A predictive equation for the infinitely dilute diffusion coefficients of various solute... more ABSTRACT A predictive equation for the infinitely dilute diffusion coefficients of various solutes in gaseous and liquid phases is proposed. The expressions proposed previously for the tracer diffusion in binary hard sphere fluids are examined critically and a new expression, based on the molecular dynamics simulations of Alder et al. (1974), obtained. The obtained expression is extended first to a Lennard−Jones fluid and then, by introducing a coupling factor, to a real fluid. The molecular diameter and energy parameters used in the equation are calculated with generalized correlations and simple combining rules. The coupling factor is correlated with the acentric factor. The derived equation is tested against a large number of experimental data: 1443 points for 120 systems, including the diffusions of various solutes in gases, supercritical fluids, and liquids. Excellent predictions were obtained: the total absolute average deviation is only 8.42%. For most systems, the predicted errors are comparable to the experimental uncertainties.
Industrial & Engineering Chemistry Research, 1997
A systematic study of the self-diffusion coefficient in hard-sphere fluids, Lennard-Jones fluids,... more A systematic study of the self-diffusion coefficient in hard-sphere fluids, Lennard-Jones fluids, and real compounds over the entire range of gaseous and liquid states is presented. First an equation is proposed for the self-diffusion coefficient in a hard-sphere fluid based on the molecular dynamics simulations of Alder et al. (J. Chem. Phys. 1970, 53, 3813) and Erpenbeck and Wood (Phys. Rev. A 1991, 43, 4254). That expression, extended to the Lennard-Jones fluids through the effective hard-sphere diameter method, represents accurately the self-diffusion coefficients obtained in the literature by molecular dynamics simulations, as well as those determined experimentally for argon, methane, and carbon dioxide. A rough Lennard-Jones expression, which contains besides the diameter σ LJ and energy LJ the translational-rotational factor, A D (which could be correlated with the acentric factor), is adopted to describe the self-diffusion in nonspherical fluids. The energy parameter is estimated using a correlation obtained from viscosity data, and the molecular diameter is obtained from the diffusion data themselves. The equation represents the self-diffusion coefficients with an average absolute deviation of 7.33%, for 26 compounds (1822 data points) over wide ranges of temperature and pressure.
In this work the interface system of the van der Waals fluid is investigated by using the density... more In this work the interface system of the van der Waals fluid is investigated by using the density gradient theory incorporated with the mean-field theory. Based on the mean-field dividing interface generated by the Maxwell construction, we propose a highly accurate density profile model for the density gradient theory, which facilitates reliable predictions of various properties for the interface region. It is found that the local intrinsic Helmholtz free energy peaks at the interface and that the maximum difference of the normal and tangential components of the pressure tensor corresponds to the maximum of the intrinsic Gibbs free energy. It is found that the entire phase space is divided into gas-like and liquid-like regions by the single line composed of the mean-field interface and the Widom line. The two-fluid feature of the supercritical fluid is hence inherited from the coexistence region. Phase diagrams extended into the coexistence region in all the temperature-pressure-volume planes are thus completed with the solutions to the vapor-liquid equilibrium problem by the van der Waals equation of state.
Industrial & Engineering Chemistry Research, 1998
The use of supercritical fluid chromatography measurements to obtain solute partial molar volumes... more The use of supercritical fluid chromatography measurements to obtain solute partial molar volumes at infinite dilution is investigated by a combination of theory, modeling, and thermodynamic connections to solubility. Though it is common to ignore contributions from solute self-interactions, theory and modeling show that these can be significant in the critical region. In particular, expressions for the first-order solute composition dependence in terms of convergent infinite-dilution quantities are used to estimate the errors introduced by ignoring solute self-interactions. These are considered in light of recent empirical work on solubilities and partial molar volumes that can be connected via thermodynamic relations. Finally, though various assumptions have been made about the solute partial molar volume in the stationary phase, none of these seem consist with solubility measurements which suggest that the stationary phase contribution should be both temperature-and density (pressure)-dependent.
The hard disc system plays a fundamental role in the study of two-dimensional matters [1-3]. High... more The hard disc system plays a fundamental role in the study of two-dimensional matters [1-3]. High-precision compressibility data from computer simulations have been reported for all the phases and phase transition regions [4-15]. In particular, Bernard and Krauth (Phys. Rev. Lett., 107, 155704, 2011) [10] presented a complete and accurate picture of the phase transitions of the hard disc system with simulation results. However, thorough descriptions of the system depend on analytical equations of state (EoS) over the entire density range. While majority of EoS's published are for the stable fluid region only [1,16], few attempted the liquid-hexact transition region (
In this work we define a mean-field crossover generated by the Maxwell construction as the dividi... more In this work we define a mean-field crossover generated by the Maxwell construction as the dividing interface for the vapor-liquid interface area. A highly accurate density-profile equation is thus derived, which is physically favorable and leads to reliable predictions of interfacial properties. By using the density gradient theory and a meanfield equation of sate for the Lennard-Jones fluid, we are able to extensively explore the interface system in terms of the Gibbs free energy, the Helmholtz free energy and heat capacity. The results show that the mean-field dividing interface is the natural extension of the Widom line into the coexistence region. Hence the entire phase space is coherently divided into liquid-like and gas-like regions in all three (temperature-pressure-volume) planes. Some unconventional behaviors are observed for the intrinsic heat capacity, being positive in low temperature region while negative in high temperature region. Finally, a complete picture of the m...
Since a transcendental equation is involved in vapor liquid equilibrium (VLE) calculations with a... more Since a transcendental equation is involved in vapor liquid equilibrium (VLE) calculations with a cubic equation of state (EoS), any exact solution has to be carried out numerically with an iterative approach [1,2]. This causes significant wastes of repetitive human efforts and computing resources. Based on a recent study [3] on the Maxwell construction [4] and the van der Waals EoS [5], here we propose a procedure for developing analytically approximate solutions to the VLE calculation with the Soave-Redlich-Kwong (SRK) EoS [6] for the entire coexistence curve. This procedure can be applied to any cubic EoS and thus opens a new area for the EoS study. For industrial applications, a simple databank can be built containing only the coefficients of a newly defined function and other thermodynamic properties will be obtained with analytical forms. For each system there is only a one-time effort, and therefore, the wastes caused by the repetitive efforts can be avoided. By the way, we also show that for exact solutions, the VLE problem with any cubic EoS can be reduced to solving a transcendental equation with one unknown, which can significantly simplify the methods currently employed [2,7].
The well-known Maxwell construction1 (the equal-area rule, EAR) was devised for vapor liquid equi... more The well-known Maxwell construction1 (the equal-area rule, EAR) was devised for vapor liquid equilibrium (VLE) calculation with the van der Waals (vdW) equation of state (EoS)2. The EAR generates an intermediate volume between the saturated liquid and vapor volumes. The trajectory of the intermediate volume over the coexistence region is defined here as the Maxwell crossover, denoted as the M-line, which is independent of EoS. For the vdW or any cubic3 EoS, the intermediate volume corresponds to the “unphysical” root, while other two corresponding to the saturated volumes of vapor and liquid phases, respectively. Due to it’s “unphysical” nature, the intermediate volume has always been discarded. Here we show that the M-line, which turns out to be strictly related to the diameter4 of the coexistence curve, holds the key to solving several major issues. Traditionally the coexistence curve with two branches is considered as the extension of the Widom line5,6-9. This assertion causes an...
Industrial & Engineering Chemistry Research, 1991
On the basis of our previous reviaed free-volume theory, a new model with temperature-independent... more On the basis of our previous reviaed free-volume theory, a new model with temperature-independent parameters is proposed for the calculation of viscosities for liquid mixtures. It is used to estimate and predict the viscosities for diverse binary and ternary mixtures, including aqueous and partially miscible systems. For 70 binaries (2033 data points), the grand absolute average deviation percent (AAD) is 1.60 from use of the parameters regressed from the data at a constant temperature. Moreover, for 23 ternaries (560 data points) the AAD is 2.76. A rigorous comparison with the Teja and Rice method indicates that our method is a good improvement.
The well-known Carnahan-Starling (CS) equation of state (EoS) 1 for the hard sphere (HS) fluid wa... more The well-known Carnahan-Starling (CS) equation of state (EoS) 1 for the hard sphere (HS) fluid was derived from a quadratic relation between the integer portions of the virial coefficients, , , and their orders,. Here we extend the method to the full virial coefficients for the general D-dimensional case. We assume a polynomial function of (D-1) th order for the virial coefficients starting from = 4 and EoS's are derived from it. For the hard rob (D=1) case, the exact solution is obtained. For the stable hard disk fluid (D=2), the most recent virial coefficients up to the 10 th 2 and accurate compressibility data 3,4 are employed to construct and test the EoS. For the stable hard sphere (D=3) fluid, a new CS-type EoS is constructed and tested with the most recent virial coefficients 5,2 up to the 11 th and with the highly-accurate simulation data for compressibility 6-8. The simple new EoS's turn out to be as accurate as the highest-level Padé approximations based on all available virial coefficients, and significantly improve the CS-type EoS in the hard sphere case. We also shown that as long as the virial coefficients obey a polynomial function any EoS derived from it will diverge at the non-physical packing fraction, = 1.
... ModifiedFreeVolumeModel.Freevol ume models are widely used for the description of trans port ... more ... ModifiedFreeVolumeModel.Freevol ume models are widely used for the description of trans port properties, such as viscosity and diffusivity.The so called hybrid model proposed by Macedo and Litovitz2* and later derived by Chung 29from statistical mechanical considerations ...
Industrial & Engineering Chemistry Research, 1998
ABSTRACT The effective hard sphere diameter (EHSD) method has been widely used to calculate both ... more ABSTRACT The effective hard sphere diameter (EHSD) method has been widely used to calculate both equilibrium and transport properties. Various EHSD explicit equations have been proposed in the literature according to different criteria. In this work a comparison between different expressions has been carried out and suggestions are given following the comparison. As an example of the applications, the EHSD method has been applied to the prediction of the self-diffusion coefficients of the Lennard-Jones fluid, by use of the hard sphere model proposed by Erpenbeck and Wood. It is found that the temperature-dependent Boltzmann EHSD and both temperature- and density-dependent Lado modified Weeks−Chandler−Andersen EHSD give the best results.
Industrial & Engineering Chemistry Research, 1995
Infinite dilution partial molar volumes (PMV) of solutes in supercritical fluids (SCF) are very i... more Infinite dilution partial molar volumes (PMV) of solutes in supercritical fluids (SCF) are very important thermodynamic properties of SCF mixtures. But until recently very few works have been dedicated to the measurements and the prediction or correlation of these properties. In this paper we present a systematic study on various models for the representation of PMV. First, we tried to predict the PMV using model parameters regressed from solubility data. Four models have been tested, and it is found that all these models can only be used qualitatively, not quantitatively. After that, we used 11 models for the correlations with temperaturedependent parameters. It is found that the model based on Wang and Tavlarides's (WT) dilute solution expression and a three-parameter empirical equation derived in this work give the best results. Some simple correlations also give acceptable results. It is surprising that some theoretical models, e.g., Wheeler's decorated lattice gas model and the models based on the fluctuation theory do not work as well as expected. Moreover, we have used six models for correlations with temperature-independent parameters. We conclude that the model proposed in this work with three parameters based on the WT dilute solution expression gives the best results. The modified Peng-Robinson equation of state (EoS) and a n empirical correlation proposed by O'Connell give acceptable results. The main conclusion of this work is that it is possible to correlate the PMV by using a simple model, although no available model is recommended for quantitative predictions.
We define a mean-field crossover generated by the Maxwell construction as the dividing interface ... more We define a mean-field crossover generated by the Maxwell construction as the dividing interface for the vaporliquid interface area and a highly accurate density-profile equation is thus derived. By using a mean-field equation of sate for the Lennard-Jones fluid incorporated with the density gradient theory, we show that the intrinsic free energy peaks and the isobaric heat capacity exhibits local maxima at the interface. We demonstrate that the meanfield interface is the natural extension of the Widom line into the coexistence region, hence the entire space is coherently divided into liquid-like and gas-like regions in all three (temperature-pressure-volume) planes. Finally, the mean-field theory is found holding all the information for composing the phase diagrams over the entire phase space.
This paper presents a study on the relationship between transport properties and geometric free v... more This paper presents a study on the relationship between transport properties and geometric free volume for hard sphere (HS) system in dense fluid region. Firstly, a generic free volume distribution function is proposed based on recent simulation results for the HS geometric free volume by Maiti et al. 1,2 Combining the new distribution function with a local particle transportation model, we obtain a power law for the HS transport properties. Then a relation between the geometric free volume and thermodynamic free volume is established, which makes it possible to use well-developed equations of state (EoS) for the expressions of the geometric free volume. The new power law models are tested with molecular dynamic (MD) simulation results for HS viscosity, diffusivity and thermal conductivity, respectively and the results are very satisfactory. Using the power law we are able to reproduce several equations obtained from different approaches, such as the entropy scaling laws 3 , mode coupling theory 4 or empirical correlations 5. In particular, A long-standing controversy regarding the well known Cohen-Turnbull-Doolittle free volume model 6,7 is resolved by using the power law combined with an EoS.
The hard sphere system plays a basic role in condensed matter physics and related fields, and equ... more The hard sphere system plays a basic role in condensed matter physics and related fields, and equation of state (EoS) is the ultimate solution to its thermodynamic properties (1-3). Dozens of EoSs have been proposed since van der Waals historic work and many reliable EoSs are available for the stable fluid region (3). For the metstable region, all available EoSs are not accurate enough for various applications. It has been considered impossible to develop an analytical EoS for the entire stable and metstable region 4. By virtue of a potential energy landscape analysis combined with the Woodcock type EoS (2,5), here we show that a fairly simple analytical equation can be obtained to reproduce the compressibility of the entire region with high accuracy. Therefore, all four amorphous states of matter, gas, liquid, supercooled liquid and glass, can be represented with a single EoS. Examples are given to show that highly accurate EoS is necessary for applications in thermodynamic propert...
Industrial & Engineering Chemistry Research, 1997
ABSTRACT A predictive equation for the infinitely dilute diffusion coefficients of various solute... more ABSTRACT A predictive equation for the infinitely dilute diffusion coefficients of various solutes in gaseous and liquid phases is proposed. The expressions proposed previously for the tracer diffusion in binary hard sphere fluids are examined critically and a new expression, based on the molecular dynamics simulations of Alder et al. (1974), obtained. The obtained expression is extended first to a Lennard−Jones fluid and then, by introducing a coupling factor, to a real fluid. The molecular diameter and energy parameters used in the equation are calculated with generalized correlations and simple combining rules. The coupling factor is correlated with the acentric factor. The derived equation is tested against a large number of experimental data: 1443 points for 120 systems, including the diffusions of various solutes in gases, supercritical fluids, and liquids. Excellent predictions were obtained: the total absolute average deviation is only 8.42%. For most systems, the predicted errors are comparable to the experimental uncertainties.
Industrial & Engineering Chemistry Research, 1997
A systematic study of the self-diffusion coefficient in hard-sphere fluids, Lennard-Jones fluids,... more A systematic study of the self-diffusion coefficient in hard-sphere fluids, Lennard-Jones fluids, and real compounds over the entire range of gaseous and liquid states is presented. First an equation is proposed for the self-diffusion coefficient in a hard-sphere fluid based on the molecular dynamics simulations of Alder et al. (J. Chem. Phys. 1970, 53, 3813) and Erpenbeck and Wood (Phys. Rev. A 1991, 43, 4254). That expression, extended to the Lennard-Jones fluids through the effective hard-sphere diameter method, represents accurately the self-diffusion coefficients obtained in the literature by molecular dynamics simulations, as well as those determined experimentally for argon, methane, and carbon dioxide. A rough Lennard-Jones expression, which contains besides the diameter σ LJ and energy LJ the translational-rotational factor, A D (which could be correlated with the acentric factor), is adopted to describe the self-diffusion in nonspherical fluids. The energy parameter is estimated using a correlation obtained from viscosity data, and the molecular diameter is obtained from the diffusion data themselves. The equation represents the self-diffusion coefficients with an average absolute deviation of 7.33%, for 26 compounds (1822 data points) over wide ranges of temperature and pressure.
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