On physical adsorption XVII. Experimental verification of the two-dimensional van der Waals equation of state above and below the critical temperature

1962 ◽  
Vol 265 (1323) ◽  
pp. 455-462 ◽  
Keyword(s):  
Critical Temperature ◽  
Carbon Tetrachloride ◽  
Equation Of State ◽  
Adsorption Isotherms ◽  
Physical Adsorption ◽  
Van Der Waals ◽  
Phase Changes ◽  
Two Dimensional ◽  
Van Der Waals Equation ◽  
Surface Field

Adsorption isotherms of carbon tetrachloride, chloroform and fiuorotrichloromethane on a substrate of graphitized carbon are reported at temperatures between 200 and 300 °K. Evidence is presented that at these temperatures the residual heterogeneity of the substrate is not observed: under these conditions the true equation of state of the adsorbed film can be deduced directly from the measured adsorption isotherms. All the data reported are described by the adsorption isotherm equation corresponding to a two-dimensional van der Waals gas; this description continues to apply at temperatures where the isotherms show discontinuities characteristic of first-order phase changes. The two-dimensional critical temperature of each of the adsorbed films is rather less than the value predicted by the two dimensional van der Waals equation; this is taken as evidence for the polarization of the adsorbate molecules by an electric field present at the graphite surface. The results obtained with the isotropic carbon tetrachloride molecule indicate a surface field of 1 x 10 5 e. s. u./cm 2 ; we deduce that the anisotropic adsorbates should be oriented at the interface, with the axis of the permanent dipole alined with the surface field.

4. States of matter

2014 ◽  
pp. 51-69
Author(s):  
Peter Atkins
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Liquid Crystals ◽  
Magnetic Resonance ◽  
Equation Of State ◽  
Soft Matter ◽  
Van Der Waals ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
Van Der Waals Equation ◽  
Intermediate States

‘States of matter’ describes the three traditional states — gas, liquid, and solid — and the models used to predict and understand their behaviour. The van der Waals equation of state captures many of the properties of real gases. The classical way of studying the motion of molecules in liquids is to measure its viscosity. Techniques include neutron scattering and nuclear magnetic resonance. X-ray diffraction is used to determine the structures of solids. Intermediate states of matter — where liquid meets gas and liquid meets solid — are also considered. Examples include supercritical fluids, soft matter such as liquid crystals, and graphene, a remarkable and essentially two-dimensional material.

scholarly journals Limiting temperature of pion gas with the van der Waals equation of state

2016 ◽  
Vol 43 (9) ◽  
pp. 095105 ◽  
Author(s):  
R V Poberezhnyuk ◽  
V Vovchenko ◽  
D V Anchishkin ◽  
M I Gorenstein
Keyword(s):  
Equation Of State ◽  
Van Der Waals ◽  
Van Der Waals Equation

scholarly journals Nonlinear Processes in Safety Systems for Substances with Parameters Close to a Critical State

2021 ◽  
Vol 17 (1) ◽  
pp. 119-138
Author(s):  
M. R. Koroleva ◽  
◽  
O. V. Mishchenkova ◽  
V. A. Tenenev ◽  
T. Raeder ◽  
...  
Keyword(s):  
Equation Of State ◽  
Critical State ◽  
Stokes Equations ◽  
Safety Valve ◽  
Van Der Waals ◽  
Local Approximation ◽  
Critical Conditions ◽  
Nonlinear Processes ◽  
Real Gas ◽  
Van Der Waals Equation

The paper presents a modification of the digital method by S. K. Godunov for calculating real gas flows under conditions close to a critical state. The method is generalized to the case of the Van der Waals equation of state using the local approximation algorithm. Test calculations of flows in a shock tube have shown the validity of this approach for the mathematical description of gas-dynamic processes in real gases with shock waves and contact discontinuity both in areas with classical and nonclassical behavior patterns. The modified digital scheme by Godunov with local approximation of the Van der Waals equation by a two-term equation of state was used for simulating a spatial flow of real gas based on Navier – Stokes equations in the area of a complex shape, which is characteristic of the internal space of a safety valve. We have demonstrated that, under near-critical conditions, areas of nonclassical gas behavior may appear, which affects the nature of flows. We have studied nonlinear processes in a safety valve arising from the movement of the shut-off element, which are also determined by the device design features and the gas flow conditions.

Application of the van der Waals equation of state to polymers III. Correlation and prediction of upper critical solution temperatures for polymer solutions

1994 ◽  
Vol 100 ◽  
pp. 63-102 ◽  
Author(s):  
Vassilis I. Harismiadis ◽  
Georgios M. Kontogeorgis ◽  
Ana Saraiva ◽  
Aage Fredenslund ◽  
Dimitrios P. Tassios
Keyword(s):  
Equation Of State ◽  
Polymer Solutions ◽  
Van Der Waals ◽  
Van Der Waals Equation ◽  
Critical Solution Temperatures

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.

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