The history of the rectilinear diameter law

Reif-Acherman, Simón

doi:10.1590/s0100-40422010000900033

Cited by 44 publications

(57 citation statements)

References 23 publications

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“…For simple liquids, whence the linear law is an accurate representation, the limiting density on the metastable coexistence line is 2y m , where y m is the density constant in the LRDs. LRD has a long history [78] in the determination of van der Waals hypothetical 'critical density', which the recent work we have discussed argues does not exist as such [79,80]. The significance of the limiting density constant, however, in its relation to an amorphous ground state with a thermodynamic status, has, until recently, been overlooked [85].…”

Section: Discussionmentioning

confidence: 99%

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Renaissance of Bernal's random close packing and hypercritical line in the theory of liquids

Finney

Woodcock

2014

J. Phys.: Condens. Matter

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We review the scientific history of random close packing (RCP) of equal spheres, advocated by J D Bernal as a more plausible alternative to the non-ideal gas or imperfect crystal as a structural model of simple liquids. After decades of neglect, computer experiments are revealing a central role for RCP in the theory of liquids. These demonstrate that the RCP amorphous state of hard spheres can be well defined, is reproducible, and has the thermodynamic status of a metastable ground state. Further evidence from simulations of square-well model liquids indicates an extended role of RCP as an amorphous ground state that terminates a supercooled liquid coexistence line, suggesting likewise for real liquids. A phase diagram involving percolation boundaries has been proposed in which there is no merging of liquid and gas phases, and no critical singularity as assumed by van der Waals. Rather, the liquid phase continuously spans all temperatures, but above a critical dividing line on the Gibbs density surface, it is bounded by a percolation transition and separated from the gas phase by a colloidal supercritical mesophase. The colloidal-like inversion in the mesophase as it changes from gas-in-liquid to liquid-in-gas can be identified with the hypercritical line of Bernal. We therefore argue that the statistical theory of simple liquids should start from the RCP reference state rather than the ideal gas. Future experimental priorities are to (i) find evidence for an amorphous ground state in real supercooled liquids, (ii) explore the microscopic structures of the supercritical mesophase, and (iii) determine how these change from gas to liquid, especially across Bernal's hypercritical line. The theoretical priority is a statistical geometrical theory of RCP. Only then might we explain the coincident values of the RCP packing fraction with Buffon's constant, and the RCP residual entropy with Boltzmann's ideal gas constant.

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Section: Discussionmentioning

confidence: 99%

“…They found that square-well liquids in the coexistence range of temperatures obey the law of rectilinear diameters (LRDs) 5 [78]. They fitted the density curves of the coexisting phases to the following equations which imply obedience to LRD:…”

Section: Liquid-vapour Coexistencementioning

confidence: 99%

Renaissance of Bernal's random close packing and hypercritical line in the theory of liquids

Finney

Woodcock

2014

J. Phys.: Condens. Matter

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“…This semi-empirical method consists in plotting the midpoints of each tie-line, defining the associated straight line with the better regression parameters, and then extrapolating this latter until its intersection with the experimental binodal curve [3]. However, this graphical method needs a fairly good symmetry between both sides of the binodal curve, which provides a good linearity of the midpoints.…”

Section: Straight Diameter Methodsmentioning

confidence: 99%

Ternary critical point determination of experimental demixion curve: calculation method, relevance and limits

Goutaudier

Bonnet²,

Tenu

et al. 2013

MATEC Web of Conferences

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Abstract. In many cases of miscibility gap in ternary systems, one critical point at least, stable or metastable, can be observed under isobaric and isothermal conditions. The experimental determination of this invariant point is difficult but its knowledge is essential. The authors propose a method for calculating the composition of the invariant solution starting from the composition of the liquid phases in equilibrium. The computing method is based on the barycentric properties of the conjugate solutions (binodal points) and an extension of the straight diameter method. A systematic study was carried out on a large number of ternary systems involving diverse constituents (230 sets ternary systems at various temperatures). Thus the results are presented and analyzed by means of consistency tests.

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“…In 150 years since Andrews' discovery of a critical temperature (T c ), however, nobody has reported a direct measurement of a liquid-gas "critical volume" [3]. Moreover, empirically parameterized cubic equations-of-state, in the spirit of van der Waals, have required ever-increasing numbers of adjustable parameters to reproduce the thermodynamic state functions with 5-6 figure numerical accuracy along critical and supercritical isotherms [3,4].…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, empirically parameterized cubic equations-of-state, in the spirit of van der Waals, have required ever-increasing numbers of adjustable parameters to reproduce the thermodynamic state functions with 5-6 figure numerical accuracy along critical and supercritical isotherms [3,4]. This progressive inadequacy of cubic equations-of-state is indicative that the hypothesis of supercritical "continuity of gas and liquid" may be suspect.…”

Section: Introductionmentioning

confidence: 99%

Percolation Transitions and Fluid State Boundaries

Leslie¹

2017

CMST

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Percolation transitions define gas-and liquid-state limits of existence. For simple model fluids percolation phenomena vary fundamentally with dimensionality (d). In 3d the accessible volume (VA) and excluded volume (VE = V −VA) percolation transitions occur at different densities, whereas in 2d they coincide. The region of overlap for 3d fluids can be identified as the origin of a supercritical mesophase. This difference between 2d and 3d systems vitiates the hypothetical concept of "universality" in the description of critical phenomena. Thermodynamic states at which VA and VE, for a spherical molecule diameter σ, percolates the whole volume of an ideal gas, together with MD computations of percolation loci for the penetrable cohesive sphere (PCS) model of gas-liquid equilibria, show a connection between the intersection of percolation loci, and the 1 st -order phase-separation transition. The results accord with previous findings for square-well and Lennard-Jones model critical and supercritical fluid equilibria. Percolation loci for real liquids, e.g. CO2 and argon, can be determined from literature thermodynamic equation-of-state data, and exhibit similar supercritical gas-and liquid-state bounds. For these real fluids the mesophase bounds extend to low density and pressures and appear to converge onto the Boyle temperature (TB) in the low-density limit.

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The history of the rectilinear diameter law

Cited by 44 publications

References 23 publications

Renaissance of Bernal's random close packing and hypercritical line in the theory of liquids

Renaissance of Bernal's random close packing and hypercritical line in the theory of liquids

Ternary critical point determination of experimental demixion curve: calculation method, relevance and limits

Percolation Transitions and Fluid State Boundaries

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