The Computation of the Thermodynamic Properties of Real Gases and Mixtures of Real Gases.

Beattie, James A.

doi:10.1021/cr60137a010

Cited by 79 publications

(52 citation statements)

References 59 publications

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“…An equation of state of this form may be integrated using the general limit theorem [15] to give the Helmoltz free energy of the binary mixture [16] !…”

Section: A Free Energy Of Mixing For a Mixture Of Dpd Particlesmentioning

confidence: 99%

New parametrization method for dissipative particle dynamics

Travis

Bankhead

Good

et al. 2007

The Journal of Chemical Physics

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We introduce an improved method of parameterizing the Groot-Warren version of Dissipative Particle Dynamics (DPD) by exploiting a correspondence between DPD and Scatchard-Hildebrand regular solution theory. The new parameterization scheme widens the realm of applicability of DPD by first removing the restriction of equal repulsive interactions between like beads, and second, by relating all conservative interactions between beads directly to cohesive energy densities.We establish the correspondence by deriving an expression for the Helmoltz free energy of mixing obtaining a heat of mixing which is exactly the same form as that for a regular mixture (quadratic in the volume fraction) and an entropy of mixing which reduces to the ideal entropy of mixing for equal molar volumes. We equate the conservative interaction parameters in the DPD force law to the cohesive energy densities of the pure fluids providing an alternative method of calculating the self-interaction parameters as well as a route to the cross-interaction parameter.We validate the new parameterization by modelling the binary system: SnI 4 /SiCl 4 , which displays liquid-liquid coexistence below an upper critical solution temperature around 140˚C. A series of DPD simulations were conducted at a set of temperatures ranging from 0˚C to above the experimental upper critical solution temperature using conservative parameters based on extrapolated experimental data. These simulations can be regarded as being equivalent to a quench from a high temperature to a lower one at constant volume.Our simulations recover the expected phase behaviour ranging from solid-liquid coexistence to liquid-liquid co-existence and eventually leading to a homogeneous single -3-phase system. The results yield a binodal curve in close agreement with one predicted using regular solution theory, but, significantly, in closer agreement with actual solubility measurements.-4-

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“…An equation of state of this form may be integrated using the general limit theorem [15] to give the Helmoltz free energy of the binary mixture [16] !…”

Section: A Free Energy Of Mixing For a Mixture Of Dpd Particlesmentioning

confidence: 99%

New parametrization method for dissipative particle dynamics

Travis

Bankhead

Good

et al. 2007

The Journal of Chemical Physics

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“…For each compression, the number of moles of methanol was calculated using the perfect gas equation and compared to the value obtained using the virial equation discussed by Beattie (1949). A maximum deviation of 0.25% was observed and the deviations showed no trend with increasing pres sure.…”

Section: Methodsmentioning

confidence: 99%

Adsorption of methanol vapor on silver iodide

Edwards¹

1967

J. Phys. Chem.

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“…Details of the derivation of Equation (6), and Equation (11) in the following, can be found for example in Beattie (1955) or in Appendix A.…”

Section: Principlesmentioning

confidence: 99%

“…Gillespie 1925Gillespie , 1936Beattie 1930, 1949, 1955, Beattie and Stockmayer 1951. For the derivation of the general accepted forms of the fugacity the so called "general limit method" is used, which avoids basically indefinite integrals 1 if real fluids are handled using ideal gases as a reference model.…”

Section: Appendix a Derivationsmentioning

confidence: 99%

Equations of State for Complex Fluids

Gottschalk¹

2007

Reviews in Mineralogy and Geochemistry

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INTRODUCTIONCompositions of coexisting fluids at elevated pressure-temperature conditions can be calculated by applying thermodynamics as in any other chemical equilibrium. This calculation requires the evaluation of the thermodynamic properties of the phase components i at the respective pressure P, temperature T, and the individual abundances x i , i.e. composition. In comparison with solids, fluids normally have distinct PVT-behaviors. Furthermore, because of their disordered state and the relatively weak bonding between molecules, fluid species mix much more easily than solid-phase components. The evaluation of the thermodynamic properties of fluids requires, therefore, special treatment and procedures that differ significantly from those used for solids. For fluids, this treatment includes a distinct and different standard state than for solids and a special description of the volume V as a function of P, T (or P as a function of V and T) and x i , i.e. an equation of state (EOS). PRINCIPLESFor geological systems, which are usually defined by the variables P and T, the Gibbs free energy G is the function of choice to describe equilibria. At constant P and T the chemical equilibrium condition is defined by (the Table 1 lists the symbols used):The partial derivative of G with respect to P is the volume VTherefore, the pressure-dependence of G is obtained by integration of Equation (2) with boundaries from the reference pressure P r , i.e. ambient pressure of 0.1 MPa, to the required P G (P,T ) = G (P r ,T ) + VdP For solids using the standard state of a pure phase component at reference conditions P r and T r , (i.e. 0.1 MPa, 298 K) integration over P leads to,where h i o and s i o are the molar enthalpy and entropy at P r and T, v i o the molar volume as a function of P at T of the pure phase component i, and a i is its activity, which also incorporates in this case any volume effects of mixing.However, for fluids the standard state is defined differently, and Equation (5) is not used in this form. The principal thermodynamic equations are rearranged in such a way that, at the standard state, the properties of a pure fluid are taken as if this fluid would behave like an ideal gas. For fluids, the standard state is, therefore, that of a hypothetical ideal gas at P r at any required temperature T. The use of this standard state leads to the following expression,in which the asterisk denotes the hypothetical ideal gas standard state properties. Details of the derivation of Equation (6), and Equation (11) in the following, can be found for example in Beattie (1955) or in Appendix A.The integral term in Equation (6) provides the definition of the fugacity coefficientThus Equation (6) can be written asand with definition of the fugacity f i m 1 The term phase component is used as a synonym for a endmember of a solution, i.e. for fluids specific species or molecules, whereas the term component is used in the classic thermodynamical sense.2 The lower integration boundary is strictly 0 MPa and not just some low pre...

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The Computation of the Thermodynamic Properties of Real Gases and Mixtures of Real Gases.

Cited by 79 publications

References 59 publications

New parametrization method for dissipative particle dynamics

New parametrization method for dissipative particle dynamics

Adsorption of methanol vapor on silver iodide

Equations of State for Complex Fluids

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