Interferometric Measurements of Isotherms of Sulfur Hexafluoride in the Critical Region

1972 ◽  
Vol 50 (18) ◽  
pp. 2194-2197 ◽  
Author(s):  
David A. Balzarini
Keyword(s):  
Critical Temperature ◽  
Interference Pattern ◽  
Critical Region ◽  
Sulfur Hexafluoride ◽  
Chemical Potential ◽  
Image Plane ◽  
Zehnder Interferometer ◽  
Fluid Density ◽  
Thin Sample ◽  
Pure Fluid

Isotherms of sulfur hexafluoride in the critical region have been determined by interferometric measurements. A thin sample of pure fluid, compressed under its own weight, is placed in one arm of a Mach–Zehnder interferometer. The resulting interference pattern produced in the image plane of a lens yields horizontal fringes which relate fluid density to height in the sample. Isotherms giving density versus chemical potential or pressure are obtained from analysis of the interference patterns. Six sulfur hexafluoride isotherms for temperatures between 0.0018 K and 0.0281 K above the critical temperature are plotted.

scholarly journals Using the Linear Sigma Model with quarks to describe the QCD phase diagram and to locate the critical end point

2018 ◽  
Vol 172 ◽  
pp. 08002
Author(s):  
Alejandro Ayala ◽  
Jorge David Castaño-Yepes ◽  
José Antonio Flores ◽  
Saúl Hernández ◽  
Luis Hernández
Keyword(s):  
Phase Diagram ◽  
Critical Temperature ◽  
Sigma Model ◽  
Chemical Potential ◽  
Linear Sigma Model ◽  
Transition Line ◽  
Baryon Chemical Potential ◽  
First Order ◽  
Qcd Phase Diagram ◽  
Crossover Transition

We study the QCD phase diagram using the linear sigma model coupled to quarks. We compute the effective potential at finite temperature and quark chemical potential up to ring diagrams contribution. We show that, provided the values for the pseudo-critical temperature Tc = 155 MeV and critical baryon chemical potential μBc ≃ 1 GeV, together with the vacuum sigma and pion masses. The model couplings can be fixed and that these in turn help to locate the region where the crossover transition line becomes first order.

scholarly journals Holographic s-wave superconductors with Horndeski correction

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
Jun-Wang Lu ◽  
Ya-Bo Wu ◽  
Li-Gong Mi ◽  
Hao Liao ◽  
Bao-Ping Dong
Keyword(s):  
Phase Transition ◽  
Black Holes ◽  
Critical Temperature ◽  
Chemical Potential ◽  
Low Frequency ◽  
S Wave ◽  
Quasiparticle Excitation ◽  
Numerical Result ◽  
Ads Black Holes ◽  
Numerical And Analytical Methods

Abstract Via both numerical and analytical methods, we build the holographic s-wave insulator/superconductor model in the five-dimensional AdS soliton with the Horndeski correction in the probe limit and study the effects of Horndeski parameter k on the superconductor model. For the fixed mass squared of the scalar field ($$m^2$$m2), the critical chemical potential $$\mu _c$$μc increases with the larger Horndeski parameter k, which means that the increasing Horndeski correction hinders the superconductor phase transition. Meanwhile, above the critical chemical potential, the obvious pole arises in the low frequency of the imaginal part of conductivity, which signs the appearance of superconducting state. What is more, the energy of quasiparticle excitation decreases with the larger Horndeski correction. Furthermore, the critical exponent of the condensate (charge density) is $$\frac{1}{2}$$12 (1), which is independent of the Horndeski correction. In addition, the analytical results agree well with the numerical results. Subsequently, the conductor/superconductor model with Horndeski correction is analytically realized in the four- and five-dimensional AdS black holes. It is observed that the increasing Horndeski correction decreases the critical temperature and thus hinders the superconductor phase transition, which agrees with the numerical result in the previous works.

scholarly journals Construction of a Universal Gel Model with Volume Phase Transition

Gels ◽  
2020 ◽  
Vol 6 (1) ◽  
pp. 7
Author(s):  
Gerald S. Manning
Keyword(s):  
Phase Transition ◽  
Critical Temperature ◽  
Equation Of State ◽  
Chemical Potential ◽  
Van Der Waals ◽  
Density Fluctuations ◽  
Volume Phase Transition ◽  
Restoring Force ◽  
Intrinsic Volume ◽  
Volume Phase

The physical principle underlying the familiar condensation transition from vapor to liquid is the competition between the energetic tendency to condense owing to attractive forces among molecules of the fluid and the entropic tendency to disperse toward the maximum volume available as limited only by the walls of the container. Van der Waals incorporated this principle into his equation of state and was thus able to explain the discontinuous nature of condensation as the result of instability of intermediate states. The volume phase transition of gels, also discontinuous in its sharpest manifestation, can be understood similarly, as a competition between net free energy attraction of polymer segments and purely entropic dissolution into a maximum allowed volume. Viewed in this way, the gel phase transition would require nothing more to describe it than van der Waals’ original equation of state (with osmotic pressure Π replacing pressure P). But the polymer segments in a gel are networked by cross-links, and a consequent restoring force prevents complete dissolution. Like a solid material, and unlike a van der Waals fluid, a fully swollen gel possesses an intrinsic volume of its own. Although all thermodynamic descriptions of gel behavior contain an elastic component, frequently in the form of Flory-style rubber theory, the resulting isotherms usually have the same general appearance as van der Waals isotherms for fluids, so it is not clear whether the solid-like aspect of gels, that is, their intrinsic volume and shape, adds any fundamental physics to the volume phase transition of gels beyond what van der Waals already knew. To address this question, we have constructed a universal chemical potential for gels that captures the volume transition while containing no quantities specific to any particular gel. In this sense, it is analogous to the van der Waals theory of fluids in its universal form, but although it incorporates the van der Waals universal equation of state, it also contains a network elasticity component, not based on Flory theory but instead on a nonlinear Langevin model, that restricts the radius of a fully swollen spherical gel to a solid-like finite universal value of unity, transitioning to a value less than unity when the gel collapses. A new family of isotherms arises, not present in a preponderately van der Waals analysis, namely, profiles of gel density as a function of location in the gel. There is an abrupt onset of large amplitude density fluctuations in the gel at a critical temperature. Then, at a second critical temperature, the entire swollen gel collapses to a high-density phase.

ON THE LIQUID–VAPOR COEXISTENCE CURVE OF XENON IN THE REGION OF THE CRITICAL TEMPERATURE

1952 ◽  
Vol 30 (5) ◽  
pp. 422-437 ◽  
Author(s):  
M. A. Weinberger ◽  
W. G. Schneider
Keyword(s):  
Critical Temperature ◽  
Critical Region ◽  
Van Der Waals ◽  
Coexistence Curve ◽  
Packing Materials ◽  
Critical Data ◽  
Van Der Waals Theory ◽  
Liquid Vapor

The liquid–vapor coexistence curves of very pure xenon have been determined in bombs of vertical lengths 1.2 cm. and 19 cm. The longer bomb yielded a flat-topped coexistence curve, the shorter a more rounded curve. The classical van der Waals theory is capable of explaining a large portion of the flat top if effects of gravity are taken into account. Details of the theoretical variation of the width of the flat top with vertical bomb lengths are given. The critical data obtained for xenon are ρc = 1.105 gm./cc., Tc = 16.590 ±.001 °C. The danger of contamination of gases in the critical region on contact with gasket or packing materials is stressed.

THE VISCOSITY OF CARBON DIOXIDE IN THE CRITICAL REGION

1940 ◽  
Vol 18b (10) ◽  
pp. 322-332 ◽  
Author(s):  
S. N. Naldrett ◽  
O. Maass
Keyword(s):  
Carbon Dioxide ◽  
Critical Temperature ◽  
Lower Limit ◽  
Critical Region ◽  
Liquid State ◽  
Condensation Temperature ◽  
Constant Density ◽  
Time Lags ◽  
Great Precision ◽  
Temperature Time

Measurements of the viscosity of carbon dioxide in the critical region have been made with great precision by means of an oscillating disc viscosimeter. The variation of viscosity with temperature at constant density has been determined for 14 different densities. Isothermals have been evaluated from a plot of the isochores. One isothermal was determined directly and is in agreement with those determined indirectly.The form of the viscosity-temperature isochores is not the same as that found by Mason and Maass (12) for ethylene, in that there is no minimum at the critical temperature nor even up to 7 °C. above. For the region just above the condensation temperature, the viscosity is more dependent on density than on temperature; the isochores are almost flat and are well separated. However, the isothermals are spread between an upper and a lower limit of density, showing that viscosity is not entirely independent of temperature. Time lags were observed in the present investigation in the opposite direction to those observed by Geddes and Maass (9); this would appear to decrease the strength of their claims that the time lags that they observed are due to the formation of a structure in the liquid state.

Diffusion of a solute in dilute solution in a supercritical fluid

1991 ◽  
Vol 433 (1887) ◽  
pp. 63-79 ◽  
Keyword(s):  
Diffusion Coefficient ◽  
Critical Temperature ◽  
Equation Of State ◽  
Supercritical Fluid ◽  
Critical Region ◽  
Critical Density ◽  
Partial Molar Volumes ◽  
Dilute Solution ◽  
Binary Diffusion Coefficient ◽  
Binary Diffusion

The experimental evidence for the behaviour of the binary diffusion coefficient for a solute in dilute solution in a supercritical fluid (a fluid above its critical temperature and pressure) is reviewed. Measurements at very low dilution, particularly by the Taylor dispersion technique, indicate that, at constant temperature a few degrees above the critical temperature, the product of density and the diffusion coefficient exhibits a small, continuous and undramatic variation from zero density to well above the critical density. However, some measurements made at higher, but still very low concentrations (e.g. with mole fractions around 10 -3 ), show a lowering of the coefficient in the critical region. The equations, based on non-equilibrium thermodynamics, are put into a form in which the behaviour of the binary diffusion coefficient in the critical region, but not very close to the critical point, may be examined using an equation of state. Calculations for naphthalene in solution in carbon dioxide are carried out using the van der Waals equation of state for mixtures to indicate the form and order of magnitude of the ‘anomalous’ lowering of the coefficient, and especially its dependence on concentration. These indicate a substantial effect even at naphthalene mole fractions of 4.0 x 10 -4 or less and a temperatures 1, 3 and 9 K above the critical temperature of the pure solvent. In addition the flux of a solute in a supercritical fluid in the critical region with respect to space or cell-fixed coordinates is discussed. Because of the large and negative partial molar volumes of solutes like naphthalene in this region, the frames of reference, according to which the diffusion coefficients are defined, can be caused to move rapidly, commonly towards the source of concentration. Thus fluxes of solute with respect to space-fixed coordinates are further substantially reduced in the critical region. The combination of the lowering of the diffusion coefficient and barycentric motion can therefore cause a very significant reduction of solute mass transfer in the critical region and may be the explanation of the sometimes very large diffusion anomalies observed experimentally.

COEXISTENCE PHENOMENA IN THE CRITICAL REGION: III. COMPRESSIBILITY OF ETHYLENE AND XENON FROM LIGHT SCATTERING

1955 ◽  
Vol 33 (9) ◽  
pp. 1399-1407 ◽  
Author(s):  
F. E. Murray ◽  
S. G. Mason
Keyword(s):  
Critical Temperature ◽  
Light Scattering ◽  
Critical Region ◽  
Variable Function

Turbidity measurements in the region immediately above the critical temperature are used to calculate values of (∂p/∂ν)T These results show that (∂p/∂ν)T is a continuously variable function of the density to within 0.02 °C. above the critical temperature. The experiments indicate that there exists no region above Tc throughout which (∂p/∂ν)T = 0 in ethylene or xenon.

scholarly journals Wilhelm Wien’s Photons Creating the BohEmian Pilot Wave for the Guiding of the Individual Huygens - de Broglie Particles on the Helical Path Governed by the Newton - Bohm Evolute (the Bohmian Pilot Wave) through the Young - Feynman Double - Slit Barrier.

2019 ◽  
Vol 11 (5) ◽  
pp. 10
Author(s):  
Jiri Stavek
Keyword(s):  
Interference Pattern ◽  
Beam Splitter ◽  
Zehnder Interferometer ◽  
Pilot Wave ◽  
System Temperature ◽  
Experimental Possibility ◽  
Diffraction Patterns ◽  
The Individual ◽  
Double Slit ◽  
Mach Zehnder Interferometer

In our approach we have combined knowledge of Old Masters (working in this field before the year 1905), New Masters (working in this field after the year 1905) and Dissidents under the guidance of Louis de Broglie and David Bohm. In our model the quantum particle is represented as the Huygens-de Broglie’s particle on the helical path (full wave) guided by the Newton-Bohm entangled helical evolute (Bohmian Pilot Wave). These individual Huygens - de Broglie particles in the Young - Feynman double - slit experiment react with Wilhelm Wien’s photons that are always present inside of the apparatus (Wien’s displacement law). Wilhelm Wien’s photons form collectively the Wien filter guiding the Huygens - de Broglie particles through the double - slit barrier towards a detector (BohEmian Pilot Wave). The interplay of those events creates the observed interference pattern. In the very well-known formula describing the intensity of double-slit diffraction patterns we have newly introduced the concept curvature κ of the Huygens - de Broglie particle and thus giving a physical interpretation for the Newton - Bohm guiding wave (the Bohmian Pilot Wave): for photons κ = π/λ, for electrons κ = 2π/λ. Moreover, we have introduced into that formula the expression λmax from the Wien’s displacement law to describe geometry of the double - slit barrier. We propose to modify the value λmax by the change of the system temperature. There is a second experimental possibility - we can insert into those slits filters to remove Wien’s photons while the Huygens - de Broglie particles continue towards a detector - we should observe the particle behavior. The similar situation might occur in the Mach - Zehnder interferometer. In this case the individual Huygens - de Broglie particle reacts in the first beam splitter with the Wien photon: the Huygens - de Broglie particle goes through one path while the Wien photon goes through the second path. In the second beam splitter they interact again and create the interference pattern on one detector. We can experimentally modify the resulting interference pattern in the Mach - Zehnder interferometer - by the temperature change of the system or by inserting filters to remove Wien’s photons from one or both paths. Can it be that Nature cleverly creates those interference patterns while the Bohmian pilot wave and the BohEmian pilot wave are hidden in plain sight? We want to pass this concept into the hands of Readers of this Journal better educated in the Mathematics and Physics.

Aspects of Electronic Structure Instability in Search for New Superconductors: Superconducting Boride at Liquid Nitrogen Temperature?

2008 ◽  
Vol 73 (6-7) ◽  
pp. 795-810 ◽  
Author(s):  
Pavol Baňacký
Keyword(s):  
Electronic Structure ◽  
Critical Temperature ◽  
State Transition ◽  
Chemical Potential ◽  
Liquid Nitrogen Temperature ◽  
Temperature Dependent ◽  
Nuclear Dynamics ◽  
Electron Phonon Coupling ◽  
Superconducting Compounds ◽  
Oppenheimer Approximation

It has been shown that electron-phonon coupling in superconductors induces temperature-dependent electronic structure instability which is related to fluctuation of analytic critical point of some bands across the Fermi level. The band fluctuation results in a considerable reduction of chemical potential and to breakdown of the adiabatic Born-Oppenheimer approximation. At critical temperature Tc, superconducting system undergoes transition from the adiabatic electronic ground state into the antiadiabatic state at broken symmetry, which is stabilized due to the effect of nuclear dynamics. This effect is absent in non-superconducting compounds. In a good agreement with the experimental Tc of superconducting state transition, the critical temperature of the adiabatic ↔ antiadiabatic state transition has been calculated for three different superconductors. Two hypothetical compounds, LiB and ZnB2, are predicted to be potential superconductors with Tc about 17 and 77.5 K, respectively.

scholarly journals A NOTE ON HOLOGRAPHIC SUPERCONDUCTORS WITH WEYL CORRECTIONS

2011 ◽  
Vol 26 (38) ◽  
pp. 2889-2898 ◽  
Author(s):  
D. MOMENI ◽  
M. R. SETARE
Keyword(s):  
Critical Temperature ◽  
Critical Exponent ◽  
Linear Relation ◽  
Chemical Potential ◽  
Equations Of Motion ◽  
Chemical Potential Difference ◽  
Conformal Dimension ◽  
Holographic Superconductors ◽  
Analytical Properties ◽  
Good Agreement

We study analytical properties of the holographic superconductors with Weyl corrections. We describe the phenomena in the probe limit neglecting backreaction of the spacetime. We observe that for the conformal dimension △+ = 3, the minimum value of the critical temperature [Formula: see text] at which condensation sets, can be obtained directly from the equations of motion as [Formula: see text], which is in very good agreement with the numerical value [Formula: see text] [Phys. Lett. B697, 153 (2011)]. This value of [Formula: see text] corresponds to the value of the Weyl's coupling γ = -0.06 in Table 1 of Phys. Lett. B697, 153 (2011). We calculate the [Formula: see text] for another Weyl's coupling γ = 0.02 and the conformal dimension △- = 1. Further, we show that the critical exponent is [Formula: see text]. We observe that there is a linear relation between the charge density ρ and the chemical potential difference μ-μ c qualitatively matches the numerical curves.

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