scholarly journals Prototype equation of state for phase transition of confined fluids based on the generalized van der Waals partition function

2021 ◽  
Vol 154 (11) ◽  
pp. 111104
Author(s):  
Hertanto Adidharma ◽  
Sugata P. Tan
Keyword(s):  
Phase Transition ◽  
Equation Of State ◽  
Partition Function ◽  
Van Der Waals ◽  
Confined Fluids

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.

THERMODYNAMICS OF q-MODIFIED BOSONS

1996 ◽  
Vol 10 (06) ◽  
pp. 683-699 ◽  
Author(s):  
P. NARAYANA SWAMY
Keyword(s):  
Mechanical Properties ◽  
Phase Transition ◽  
Equation Of State ◽  
Partition Function ◽  
Statistical Mechanics ◽  
Specific Heat ◽  
Thermodynamic Functions ◽  
Bose Condensation ◽  
Grand Partition Function ◽  
Statistical Mechanical

Based on a recent study of the statistical mechanical properties of the q-modified boson oscillators, we develop the statistical mechanics of the q-modified boson gas, in particular the Grand Partition Function. We derive the various thermodynamic functions for the q-boson gas including the entropy, pressure and specific heat. We demonstrate that the gas exhibits a phase transition analogous to ordinary bose condensation. We derive the equation of state and develop the virial expansion for the equation of state. Several interesting properties of the q-boson gas are derived and compared with those of the ordinary boson which may point to the physical relevance of such systems.

Critical behavior of pure confined fluids from an extension of the van der Waals equation of state

2010 ◽  
Vol 55 (2) ◽  
pp. 455-461 ◽  
Author(s):  
Leonardo Travalloni ◽  
Marcelo Castier ◽  
Frederico W. Tavares ◽  
Stanley I. Sandler
Keyword(s):  
Equation Of State ◽  
Critical Behavior ◽  
Van Der Waals ◽  
Confined Fluids ◽  
Van Der Waals Equation

scholarly journals COLLECTIVE MOTION OF MICRO-ORGANISMS FROM FIELD THEORETICAL VIEWPOINT

1996 ◽  
Vol 11 (11) ◽  
pp. 915-920
Author(s):  
SHIN’ICHI NOJIRI ◽  
MASAKO KAWAMURA ◽  
AKIO SUGAMOTO
Keyword(s):  
Phase Transition ◽  
Equation Of State ◽  
Collective Motion ◽  
Red Tide ◽  
Van Der Waals ◽  
Type Equation ◽  
Velocity Fields ◽  
Micro Organisms

We analyze the collective motion of micro-organisms in the fluid and consider the problem of the red tide. The red tide is produced by the condensation of the micro-organisms, which might be similar to that of the strings. We propose a model of the generation of the red tide. By considering the interaction between the micro-organisms mediated by the velocity fields in the fluid, we derive the Van der Waals type equation of state, where the generation of the red tide can be regarded as a phase transition from the gas of micro-organisms to the liquid.

Equation of State and Phase Transition of the Spherical Lattice Gas

1960 ◽  
Vol 120 (1) ◽  
pp. 22-32 ◽  
Author(s):  
Walter Pressman ◽  
Joseph B. Keller
Keyword(s):  
Phase Transition ◽  
Equation Of State ◽  
Lattice Gas

Equation of state and phase transition of antigorite under high pressure and high temperature

2014 ◽  
Vol 228 ◽  
pp. 56-62 ◽  
Author(s):  
Cuiping Yang ◽  
Toru Inoue ◽  
Akihiro Yamada ◽  
Takumi Kikegawa ◽  
Jun-ichi Ando
Keyword(s):  
Phase Transition ◽  
High Pressure ◽  
High Temperature ◽  
Equation Of State
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