On the Free Energy of a Mixture of Ions: An Extension of Kramers' Theory

Berlin, T. H.; Montroll, Elliott W.

doi:10.1063/1.1700200

Cited by 47 publications

(13 citation statements)

References 2 publications

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“…[48]) in order to evaluate the two-particle density n("(rlr2) = (na(r1) * nb(r2)) = na(r1) nb(r2) . gab(rlr2) (25) which is the starting point for the calculation of thermodynamical properties.…”

Section: Nf(r1)mentioning

confidence: 99%

“…Similar as for the OCP, the static properties of the semiclassical TCP are also only weakly mass-dependent. The semi-classical region, above the temperature of degeneracy (T > T F ) and below the ionization temperature T < TI = R y / k~ forms a triangle in the density-temperature plane ( In a foregoing work [23] we studied this region on the basis of the semi-quantitative high-density asymptotics developed by Unsold [24], Berlin and Montroll [25] and Ecker and Kroll [26]. The present work.continues these investigations and uses in addition a more general ansatz for the high-density asymptotics due to Rosenfeld [lo] and extensive numerical studies of the semi-classical strongly coupled plasma by means of HNC-calculations.…”

Section: Introductionmentioning

confidence: 99%

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Quasiclassical Statistical Thermodynamics and New Padé Approximations for the Free Charges in Strongly‐Coupled Plasma

Ébeling

Stolzmann

Förster

et al. 1999

Contrib. Plasma Phys.

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HNC equations in combination with effective quasi-classical potentials are used to calculate correlation functions and the thermodynamic properties of the free charges in semi-classical non-degenerate quant.um plasmas. The interactions of the free particles are taken into account via effective potentials obtained from the Slater sum method. Analytical formulae reproducing the known limits and the HNC-results are constructed. Finally quantum effects are included as corrections by using known analytical results. This method is used to develope new Pad6 approximations for the subsystem of the free charges in mass-symmetrical as well as for' mass-unsymmetrical hydrogen-like plasmas. The most essential result of our investigations is, that in the classical limit the scaling properties correspond to the OCP, e.g. the thermodynamic functions follow for large coupling strength r a Berlin-MontrollRosenfeld asymptotics via a r + br" + c In I? + d. Including quantum effects, the coefficients depend on the temperature, e.g. the slope a(T) increases with decreasing T converging to the classical limit. The new formulae are compared with earlier variants.

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Section: Nf(r1)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quasiclassical Statistical Thermodynamics and New Padé Approximations for the Free Charges in Strongly‐Coupled Plasma

Ébeling

Stolzmann

Förster

et al. 1999

Contrib. Plasma Phys.

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“…11,12 It follows from Eq. ͑7͒ that the excess free energy of an IPL liquid is given as follows in terms of a function of density to the power n / 3 over temperature T , ͑ n/3 / T͒ ͑Klein's theorem 11,12 ͒:…”

Section: A Ipl Potentialsmentioning

confidence: 99%

“…[11][12][13][14][15][16][17][18] Such potentials have a number of simple properties. IPL potentials have, however, been considered unrealistic because their predicted equation of state is quite unrealistic and because they have no stable low-pressure liquid phase and no van der Waals loop, problems that derive from the fact that IPL potentials are purely repulsive.…”

Section: A Ipl Potentialsmentioning

confidence: 99%

Pressure-energy correlations in liquids. III. Statistical mechanics and thermodynamics of liquids with hidden scale invariance

Schrøder

Bailey

Pedersen

et al. 2009

The Journal of Chemical Physics

131

150

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In this third paper of the series, which started with Bailey et al. ͓J. Chem. Phys. 129, 184507 ͑2008͒; ibid. 129, 184508 ͑2008͔͒, we continue the development of the theoretical understanding of strongly correlating liquids-those whose instantaneous potential energy and virial are more than 90% correlated in their thermal equilibrium fluctuations at constant volume. The existence of such liquids was detailed in previous work, which identified them, based on computer simulations, as a large class of liquids, including van der Waals liquids but not, e.g., hydrogen-bonded liquids. We here discuss the following: ͑1͒ the scaling properties of inverse power-law and extended inverse power-law potentials ͑the latter includes a linear term that "hides" the approximate scale invariance͒; ͑2͒ results from computer simulations of molecular models concerning out-of-equilibrium conditions; ͑3͒ ensemble dependence of the virial/potential-energy correlation coefficient; ͑4͒ connection to the Grüneisen parameter; and ͑5͒ interpretation of strong correlations in terms of the energy-bond formalism.

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“…The latter may be a good approximation of interactions that take place in liquid PC, since this potential is quite typical of molecular systems. Thermodynamic properties of the soft-sphere model can be derived using the Klein theorem [16][17][18] , but the solution for the kinetic properties will be more complicated. Taking into account a direct analogy 10,19 sometimes supported by deeper theoretical consideration 17,18,20,21 , one may write a scaling relationship for the characteristic time of the structural relaxation (also known as α-relaxation) τ in the form:…”

Section: Introductionmentioning

confidence: 99%

Dielectric spectroscopy and ultrasonic study of propylene carbonate under ultra-high pressures

Kondrin

Gromnitskaya²,

Pronin³

et al. 2012

The Journal of Chemical Physics

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We present the high pressure dielectric spectroscopy (up to 4.2 GPa) and ultrasonic study (up to 1.7 GPa) of liquid and glassy propylene carbonate (PC). Both of the methods provide complementary pictures of the glass transition in PC under pressure. No other relaxation processes except α-relaxation have been found in the studied pressure interval. The propylene carbonate liquid is a glassformer where simple relaxation and the absence of β-relaxation are registered in the record-breaking ranges of pressures and densities. The equation of state of liquid PC was extended up to 1 GPa from ultrasonic measurements of bulk modulus and is in good accordance with the previous equations developed from volumetric data. We measured the bulk and shear moduli and Poisson's ratio of glassy PC up to 1.7 GPa. Many relaxation and elastic properties of PC can be qualitatively described by the soft-sphere or Lennard-Jones model. However, for the quantitative description of entire set of the experimental data, these models are insufficient. Moreover, the Poisson coefficient value for glassy PC indicates a significant contribution of non-central forces to the intermolecular potential. The well-known correlation between Poisson's ratio and fragility index (obtained from dielectric relaxation) is confirmed for PC at ambient pressure, but it is violated with pressure increase. This indicates that different features of the potential energy landscape are responsible for the evolution of dielectric response and elasticity with pressure increase.

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On the Free Energy of a Mixture of Ions: An Extension of Kramers' Theory

Cited by 47 publications

References 2 publications

Quasiclassical Statistical Thermodynamics and New Padé Approximations for the Free Charges in Strongly‐Coupled Plasma

Quasiclassical Statistical Thermodynamics and New Padé Approximations for the Free Charges in Strongly‐Coupled Plasma

Pressure-energy correlations in liquids. III. Statistical mechanics and thermodynamics of liquids with hidden scale invariance

Dielectric spectroscopy and ultrasonic study of propylene carbonate under ultra-high pressures

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