An analytical equation derived from a perturbation theory to calculate Henry's constants for square well mixtures

An analytic form for Henry's constant is derived and applied to several systems. The derivation is based on the use of Leonard-Henderson-Barker perturbation theory for a square well pair potential assuming the Ponce-Renon analytical solution of the square well fluid. Computed values of Henry's constants for CH4-Ar, CH4-N2, CH4-He, CH4-H2, C2H6-N2 and C2H6-CH4 mixtures are compared with experiment. The agreement is quite satisfactory, with mean relative deviations between 2.5 and 8 per cent. Heats of solutions are also computed and compared with experiment.

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Analytical equation for the Helmholtz free energy of a pure fluid, using the perturbation theory and a square well potential

The Journal of Chemical Physics ◽

10.1063/1.432254 ◽

1976 ◽

Vol 64 (2) ◽

pp. 638-640 ◽

Cited By ~ 32

Author(s):

Luis Ponce ◽

Henri Renon

Keyword(s):

Free Energy ◽

Perturbation Theory ◽

Helmholtz Free Energy ◽

Analytical Equation ◽

Pure Fluid ◽

Square Well

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Erratum: Analytical equation for the Helmholtz free energy of a pure fluid, using the perturbation theory and a square‐well potential

The Journal of Chemical Physics ◽

10.1063/1.432172 ◽

1976 ◽

Vol 64 (12) ◽

pp. 5321-5321

Author(s):

Luis Ponce ◽

Henri Renon

Keyword(s):

Free Energy ◽

Perturbation Theory ◽

Helmholtz Free Energy ◽

Analytical Equation ◽

Pure Fluid ◽

Square Well

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Zur Lösung der BETHE-GOLDSTONE-Gleichung bei nicht-verschwindendem Gesamtimpuls I

Zeitschrift für Naturforschung A ◽

10.1515/zna-1963-0415 ◽

1963 ◽

Vol 18 (4) ◽

pp. 531-538

Author(s):

Dallas T. Hayes

Keyword(s):

Approximate Solution ◽

Analytical Solution ◽

Nuclear Matter ◽

Analytical Solutions ◽

Projection Operator ◽

Center Of Mass ◽

Separable Potential ◽

Localized Solutions ◽

Non Local ◽

Square Well

Localized solutions of the BETHE—GOLDSTONE equation for two nucleons in nuclear matter are examined as a function of the center-of-mass momentum (c. m. m.) of the two nucleons. The equation depends upon the c. m. m. as parameter due to the dependence upon the c. m. m. of the projection operator appearing in the equation. An analytical solution of the equation is obtained for a non-local but separable potential, whereby a numerical solution is also obtained. An approximate solution for small c. m. m. is calculated for a square-well potential. In the range of the approximation the two analytical solutions agree exactly.

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Quantum square-well with logarithmic central spike

Modern Physics Letters A ◽

10.1142/s0217732318500098 ◽

2018 ◽

Vol 33 (02) ◽

pp. 1850009 ◽

Cited By ~ 2

Author(s):

Miloslav Znojil ◽

Iveta Semorádová

Keyword(s):

Perturbation Theory ◽

Boundary Conditions ◽

Closed Form ◽

Wave Functions ◽

Change Of Variables ◽

State Dependent ◽

Square Well ◽

Strength Formula ◽

Schrödinger Perturbation ◽

Dependent Interaction

Singular repulsive barrier [Formula: see text] inside a square-well is interpreted and studied as a linear analog of the state-dependent interaction [Formula: see text] in nonlinear Schrödinger equation. In the linearized case, Rayleigh–Schrödinger perturbation theory is shown to provide a closed-form spectrum at sufficiently small [Formula: see text] or after an amendment of the unperturbed Hamiltonian. At any spike strength [Formula: see text], the model remains solvable numerically, by the matching of wave functions. Analytically, the singularity is shown regularized via the change of variables [Formula: see text] which interchanges the roles of the asymptotic and central boundary conditions.

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Thermodynamic perturbation theory: Sticky chains and square-well chains

Physical Review E ◽

10.1103/physreve.48.3760 ◽

1993 ◽

Vol 48 (5) ◽

pp. 3760-3765 ◽

Cited By ~ 69

Author(s):

M. Banaszak ◽

Y. C. Chiew ◽

M. Radosz

Keyword(s):

Perturbation Theory ◽

Thermodynamic Perturbation Theory ◽

Square Well ◽

Thermodynamic Perturbation

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Perturbation theory of the pair correlation function in molecular fluids

Canadian Journal of Physics ◽

10.1139/p78-075 ◽

1978 ◽

Vol 56 (5) ◽

pp. 571-580 ◽

Cited By ~ 31

Author(s):

R. L. Henderson ◽

C. G. Gray

Keyword(s):

Perturbation Theory ◽

Correlation Function ◽

Pair Correlation Function ◽

Pair Correlation ◽

Mean Field ◽

Pair Potential ◽

Harmonic Series ◽

Harmonic Space ◽

Potential Symmetries ◽

Harmonic Components

We study the perturbation theory of the angular pair correlation function g(rω1ω2)in a molecular fluid. We consider an anisotropic pair potential of the form u = u0 + ua, where u0 is an isotropic 'reference' potential, and for simplicity in this paper we assume the perturbation potential ua to be 'multipole-like', i.e., to contain no l = 0 spherical harmonics. We expand g in powers of ua about g0, the radial distribution function appropriate to u0. This series is examined by expanding ha = h−h0 (where h = g−1) and its corresponding direct correlation function ca in spherical harmonic components. We consider approximate summations of the series in ua that automatically truncate the corresponding harmonic series, so that the Ornstein–Zernike (OZ) equation relating ha and ca can be solved in closed form. We first expand ca = c1 + c2 + … where cn includes all terms in ca of order (ua)n. Taking ua to be a quadrupole–quadrupole interaction, we find that a 'mean field' (MF) approximation ca = c1 gives rise to only three nonvanishing harmonic components in ha, so that OZ is solved explicitly in Fourier space. The MF solution for multipoles of general order is given in an appendix. Graphical methods are then used to identify the class of all terms in the ua series that are restricted to the harmonic space defined by MF. A portion of this class can be summed by solving OZ with the closure ca = −βg0ua + h0(ha−ca), where β = (kT)−1, h0 = g0−1 This system is designated as generalized MF (GMF), and solved by numerical iteration. Numerical results from MF and GMF are presented for quadrupolar ua, taking u0 to be a Lennard-Jones potential. Symmetries imposed by the restricted harmonic space are foreign to the full g, yet harmonics within this space are sufficient for evaluation of many macroscopic properties. The results are therefore evaluated in harmonic form by comparison with the corresponding harmonic components of the 'correct' g as evaluated by Monte Carlo simulation.

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