Equilibrium Thermodynamic Theory Research Articles

Prigogine-Defay ratio and its change with fictive temperature approaching the ideal glass transition

According to equilibrium thermodynamic theory, a liquid of zero configurational entropy would undergo an Ehrenfest type second order transition to another disordered structure at a temperature T2 known as the ideal glass transition temperature, but glass formation prevents one from observing it. The heat capacityCp, isothermal compressibility, κT, and isobaric thermal expansion coefficient, αp, change by an amount Δ at the Ehrenfest temperature, TEH=T2, and also at the glass transition temperature Tg. The Ehrenfest ratio RE at TEHorT2, ΔCp,EHΔκT,EHTEHVEH(Δαp,EH)2≡1. In contrast, experimentally determined Prigogine-Defay ratio, ∏P−D at Tg, ΔCpΔκTTV(Δαp)2>1, where V is the volume at the respective temperatures. Angell and Sichina [Ann. N. Y. Acad. Sci. 279 (1976) 53-67] discussed how ∏P−D would change to RE if a liquid could be cooled slowly enough to reach T2. After critically reviewing the basic aspects of RE and of experimental and theoretical values of ∏P−D, we use generic variations of ΔCp, ΔκT, ΔαP and V with the fictive temperature, Tf, and the extrapolated values of these quantities for o-terphenyl at T=T2, and calculate RE and ∏P−D. We find that RE<∏P−D, thus contributing to Angell-Sichina's discussion of the unique structure of the low temperature disordered phase. We then consider how ∏P−D would change if the entropy of a liquid were extrapolated such that it did not violate the third law of thermodynamics and there was no need for the conjecture of an Ehrenfest transition.

Thermodynamics predicts a stable microdroplet phase in polymer-gel mixtures undergoing elastic phase separation.

We study the thermodynamics of binary mixtures with the volume fraction of the minority component less than the amount required to form a flat interface and show that the surface tension dominated equilibrium phase of the mixture forms a single macroscopic droplet. Elastic interactions in gel-polymer mixtures stabilize a phase with multiple droplets. Using a mean-field free energy we compute the droplet size as a function of the interfacial tension, Flory parameter, and elastic moduli of the gel. Our results illustrate the role of elastic interactions in dictating the phase behavior of biopolymers undergoing liquid-liquid phase separation.

Thermodynamic characterization of RBCs highlights correlations between different hemoglobin types and Band 3 interactions

Erythrocytes during their life in the bloodstream are subjected to continuous alterations also related to age, which alter their structure and some functional properties. Some types of erythrocytes such as fetal and sickle possesses particular characteristics both functional and structural that characterize their life. In this paper a thermodynamic characterization of fetal and sickle erythrocytes comparing to normal adults is performed. After an introduction of the Kluitenberg's non equilibrium thermodynamic theory with internal variables, the state and phenomenological coefficients are determined. The interpretation of these physical parameters and the entropy production measure highlighted interesting differences between the erythrocytes tested. This characterization accompanied by biochemical investigations on the functionality of the anion exchange led to focus to hemoglobin as the main promoter of structural and functional variations affecting the deformability of the erythrocytes. In details, fetal and sickle erythrocytes showed lower deformability and greater fragility compared to normal cells. These biophysical-thermodynamic investigations open up new perspectives for the study of blood and its characteristics that can be exploited to improve blood conservation methods through careful monitoring of blood quality control.

Interfacial width and phase equilibrium in polymer-fullerene thin-films

Domain composition and interfacial structure are critical factors in organic photovoltaic performance. Here, we report neutron reflectivity, grazing-incidence X-ray diffraction and atomic force microscopy measurements of polymer/fullerene thin-films to test a hypothesis that these partially miscible blends rapidly develop composition profiles consisting of co-existing phases in liquid-liquid equilibrium. We study a range of polymer molecular weights between 2 and 300 kg mol−1, annealing temperatures between 120 and 170 oC, and timescales up to 10 min, yielding over 50 distinct measurement conditions. Model bilayers of fullerene-derivatives and polystyrene enable a rigorous examination of theoretical predictions of the effect of polymer mass and interaction parameter on the compositions, ϕ, and interfacial width, w, of the coexistent phases. We independently measure ϕ and w and find that both Flory-Huggins mean-field-theory and key aspects of self-consistent-field-theory are remarkably consistent with experiment. Our findings pave the way for predictive composition and interface design in organic photovoltaics based on simple experimental measurements and equilibrium thermodynamic theory.

Enhanced Thermochemical Heat Capacity of Liquids: Molecular to Macroscale Modeling

ABSTRACTThermal fluids have many applications in the storage and transfer of thermal energy, playing a key role in heating, cooling, refrigeration, and power generation. However, the specific heat capacity of conventional thermal fluids, which is directly linked to energy density, has remained relatively low. To tackle this challenge, we explore a thermochemical energy storage mechanism that can greatly enhance the heat capacity of base fluids (by up to threefold based on simulation) by creating a solution with reactive species that can absorb and release additional thermal energy. Based on the classical theory of equilibrium thermodynamics, we developed a macroscale theoretical model that connects fundamental properties of the underlying reaction to the thermophysical properties of the liquids. This framework allows us to employ state-of-the-art molecular scale computational tools such as density functional theory calculations to identify and refine the most suitable molecular systems for subsequent experimental studies. Our approach opens up a new avenue for developing next-generation heat transfer fluids that may break traditional barriers to achieve high specific heat and energy storage capacity.

Experiment and Simulation Study on the Special Phase Behavior of Huachang Near-Critical Condensate Gas Reservoir Fluid

Due to the special phase behavior of near-critical fluid, the development approaches of near-critical condensate gas and near-critical volatile oil reservoirs differ from conventional oil and gas reservoirs. In the near-critical region, slightly reduced pressure may result in considerable change in gas and liquid composition since a large amount of gas or retrograde condensate liquid is generated. It is of significance to gain insight into the composition variation of near-critical reservoir during the depletion development. In our study, we performed a series ofPVTexperiments on a real near-critical gas condensate reservoir fluid. In addition to the experimental studies, a commercial simulator combined with the PREOS model was utilized to study retrograde condensate characteristics and reevaporation mechanism of condensate oil with CO2injection based on vapor-liquid phase equilibrium thermodynamic theory. The research shows that when reservoir pressure drops below a certain pressure, the variation of retrograde condensate liquid saturation of the residual reservoir fluid exhibits the phase behavior of volatile oil.

Simulation Study on Influencing Factors of Rapid Steam-Charging Process in Steam Accumulator

In this paper, the mathematical model for the rapid steam-charging process of the steam accumulator was given based on the theory of equilibrium thermodynamics. The dynamic process has been simulated according to the model, and the effects of different factors on the steam-charging process were analyzed. The results showed that the initial coefficients of filling water had great influence on the time of steam-charging, and the influence of the considered metal’s mass was limited for the steam-charging process.

Mathematical conception of “Phenomenological” equilibrium thermodynamics

In the paper, the principal aspects of the mathematical theory of equilibrium thermodynamics are distinguished. It is proved that the points of degeneration of a Bose gas of fractal dimension in the momentum space coincide with critical points or real gases, whereas the jumps of critical indices and the Maxwell rule are related to the tunnel generalization of thermodynamics. Semiclassical methods are considered for the tunnel generalization of thermodynamics and also for the second and ultrasecond quantization (operators of creation and annihilation of pairs). To every pure gas there corresponds a new critical point of the limit negative pressure below which the liquid passes to a dispersed state (a foam). Relations for critical points of a homogeneous mixture of pure gases are given in dependence on the concentration of gases.

Relativistic Statistical Mechanics vs. Relativistic Thermodynamics

Based on a covariant theory of equilibrium Thermodynamics, a Statistical Relativistic Mechanics is developed for the non-interacting case. Relativistic Thermodynamics and Jüttner Relativistic Distribution Function in a moving frame are obtained by using this covariant theory. A proposal for a Relativistic Statistical Mechanics is exposed for the interacting case.

Main axiom of thermodynamics and entropy of number theory: Tunnel and ultrasecond quantization

We single out the main features of the mathematical theory of equilibrium thermodynamics. The theory of Bose condensate is expressed as a problem in number theory and its relation to various evolutionary processes is studied. It is proved that the points of degeneracy of the Bose gas fractal dimension in momentum space coincide with the critical points of imperfect gases, while the jumps of the critical indices and the Maxwell rule are related to tunnel quantization in thermodynamics. We consider semiclassical methods for tunnel quantization in thermodynamics as well as those for second and third quantization.

Theory of fluidity of liquids, glass transition, and melting

This is a presentation of a rigorous theory of fluidity of liquids, glass transition and melting of solids in the frame of an asymmetric double well potential model. Potential wells are doubled time to time by the local density fluctuations caused by the thermal longitudinal waves. The average frequency of doubling of potential wells is equal to the frequency of the most energetic waves which obey a law similar to Wein’s displacement law in black body radiation. Based on the equilibrium thermodynamic theory of fluctuations and the displacement law, a law of linear pre-diffusion mean-square displacement of particles in a solid is derived: the mean-square displacement of molecules within their potential wells increases linearly with temperature. It is shown that when this is broken-down (where the mean-square displacement at a certain temperature rapidly changes its slope as a function of temperature) glass devitrifies and crystal melts, and all possible solid–liquid transitions of a substance occur at the same critical mean-square displacement: any solid ( not only crystals) transforms into liquid when the mean-square displacement, as a fraction of the average intermolecular distance, acquires a certain universal critical value – the same for different substances. It is proved that molecules in a liquid perform specific Brownian motion. The average jump distance is a function of temperature and it is much smaller than the nearest intermolecular distances. At a certain temperature, shown to be the Kauzmann temperature, the average jump distance of Brownian motion becomes equal to zero: the super-cooled liquid undergoes glass transition. The transition was proven to be a phase transition of the fourth order: the free energy of the system and its first, second and third derivatives are all continuous functions, but its fourth derivative with respect to temperature is discontinuous. Molecular mobility, diffusion and viscosity are obtained as functions of temperature.

Temperature distributions inside overdriven steady-plane shock wave fronts in iron

Temperature distributions inside overdriven steady-plane shock wave fronts in Fe for shocks up to 230 GPa are evaluated by applying temperature-dependent constant-volume specific heat to the equilibrium thermodynamic theory. Equilibrium thermodynamics can be applied to these shocks and the assumption of heat transport is valid. Thus, the inside temperature distributions are evaluated fairly correctly. Overestimations of the temperature distributions inside an inviscid solid Fe mean that the viscous pressure influences greatly on the distributions. The underestimation of the constant-volume specific heat in a higher pressure region causes the overestimation of the inside temperature distributions.

Equilibrium thermodynamic theory explicitly including heat transport for evaluation of temperature distributions in steady plane-wave fronts

Previous theories that implicitly included heat transport predicted that temperatures were reduced in proportion to the viscous stresses in the whole region of an overdriven steady wave front in 2024 Al shocked at 80 GPa. Although there was a decrease in temperature caused by the shear stress, the decrease was very slight. A more justifiable theory that includes a heat transport term, the coefficient of which depends on the form and thickness of the effective part of a specific volume wave in the steady wave front, was then developed. The range of appropriate thicknesses of the effective part of the linear and sine forms for shocks up to 80 GPa in 2024 Al were determined. In these ranges, strain increments were sufficiently small and effective temperature rise-times were sufficiently long on the electron–phonon relaxation time scale to justify using equilibrium thermodynamics. In addition, the efficacy of the inside temperature method [Sano and Abe, J. Appl. Phys. 89, 105 (2001)] was illustrated by evaluating heat transport. The inside temperature distribution can be specified if the thickness is measured because the distribution is not influenced to a great extent by the wave form.

Equilibrium thermodynamic theory for the evaluation of temperature distributions in overdriven steady-plane wave fronts

Temperature distributions in overdriven steady wave fronts in solid 2024 Al shocked up to 80 GPa, in which no melting occurred in the wave fronts, were evaluated using the equilibrium thermodynamic theory. The effective strain increments were sufficiently small and the effective temperature rise times were sufficiently long with respect to electron–phonon relaxation times to justify using equilibrium thermodynamics. In addition, the sufficiently large viscous-stress components supported the efficacy of the thermodynamic theory. The same is true of shocks up to 250 GPa in solid Pt and 230 GPa in solid Fe. Furthermore, the influence of viscous stress was examined by evaluating the temperature distributions for inviscid 2024 Al, Pt, and Fe solids using the equations for temperature derived from the Mie–Grüneisen equation. Finally, we demonstrate that there might be a solid–liquid–solid Hugoniot between the solid and liquid–solid Hugoniots for Fe and estimate the solid–liquid–solid and liquid–solid Hugoniots.

Influence of Vapor Condensation on the Adhesion and Friction of Carbon−Carbon Nanocontacts

The adhesion and friction between two orthogonally arranged carbon fibers has been measured in undersaturated vapor pressures of decane, n-propanol, and water. An analysis, which is described, of the frictional data allowed the normal adhesive force under sliding conditions to be deduced. Contact angle measurements and adsorption studies showed that both decane and n-propanol wetted the fibers and also their vapors exhibited typical BET adsorption isotherms. It was also found that water did not wet these fibers and that the adsorption isotherm could not be described by the BET equation. Equilibrium thermodynamic theory predicts that the two wetting fluids should significantly attenuate the autoadhesion. The converse was observed and is ascribed to the actions of a combination of two factors. First, it is argued that the high contact pressures (ca.109 Pa) at the carbon interface, which were developed even under the adhesive loads alone, resulted in the adsorbates being excluded or displaced from the contac...

PHASE DIAGRAM CALCULATION OF DIAMONDGROWTH FROM LOW PRESSURE GASES

The phase diagrams of diamond growth from CH4/H2, CO/H2 gases and oxyacetylene flames are calculated by non-equilibrium thermodynamic coupling model in the paper. These phase diagrams are different from those derived from classical equilibrium thermodynamic theory. A diamond growth region, which is the thermodynamic basis of diamond synthesis, exists in each calculated phase diagram. The diamond growth region reflects the roles of those activated particles such as super equilibrium atomic hydrogen during diamond deposition. The calculated phase diagrams are agreement with many reported experimental results, and they will be of favor of theoretical and experimental studies of diamond growth from gas mixtures.

Thermodynamics of tapered styrene-butadiene block copolymers

Abstract A modified version of the Leary-Henderson-Williams equilibrium thermodynamic theory is used to predict microstructural properties for tapered poly(styrene-butadiene) diblock copolymers containing a random copolymer between the blocks. The interphase thickness, interphase volume fraction, and repeat distance are all predicted to increase as the volume fraction of the added random copolymer increases, whereas the microphase-separation temperature is shown to decrease. Comparison of model results with experimental data for tapered poly(styrene-isoprene) diblock copolymers reveals good agreement for small amounts of the additional random copolymer (up to about 20 vol%). Trends indicate that, at large fractions of random copolymer, the tapered block copolymer may be in a homogeneous state when the nontapered block copolymer would be phase separated under the same conditions.

Interphase composition profile in SB/SBS block copolymers, measured with electron microscopy, and microstructural implications

The behavior of microphase-separated block copolymers has major contributions from the mixed interphase existing between the two homogeneous phases. However, relatively little has been known about the interphase itself and, in particular, its composition profile has never been measured directly. Here, we have used quantitative transmission electron microscopy to acquire the shape of the volume-fraction composition profile across this interphase. Measurements were made on four styrene (S)/butadiene (B) block copolymers having structure SBS (three) and SB (one), with molecular weights 1.0-2.3 X lo5 g/mol and overall volume compositions of 0.24-0.38 styrene. Results, averaged over the four samples, depict an asymmetric interphase profile, being rich in styrene (54 vol %) in agreement with new differential scanning calorimetry data and with dynamic mechanical testing studies of others. This profile is then used in an equilibrium thermodynamic theory (which extends earlier work by adding an enthalpic Debye term that accounts for molecular interactions beyond nearest neighbors) to predict various microstructural and thermal properties of the bulk polymer. Excellent agreement with reported data is obtained for the predicted interphase thickness and interphase volume fraction and for predictions of the repeat distance for lamellar SB copolymers.

Canonical formalism in equilibrium thermodynamics. II. Homogeneity, stability, and generalized Maxwell relations

The classical theory of equilibrium thermodynamics is formulated in a canonical context which has been recently proposed by us. It is shown that the equations of state correspond to what in analytical mechanics is called an involution system. The classical conditions of thermodynamic stability are deduced from a variational principle for the entropy function.

Relativistic heavy-ion collisions: An approach based on non-equilibrium thermodynamics

A new theory of particle production in high energy collisions is proposed which is based on non-equilibrium thermodynamics. The non-equilibrium model is a major extension of the equilibrium thermodynamic model of relativistic heavy-ion collisions developed earlier. While the equilibrium thermodynamic theory is appropriate for the formation of light nuclei and for pions, the non-equilibrium theory applies to the creation of particles heavier than the pion, which include such particles as the strange mesons, strange baryons and the anti-nucleons. Using an approach based on the degree of the reaction of kinetic theory, the time evolution of the composition of hadronic systems in incomplete equilibrium is investigated. Densities of produced particles are related to space-time quantities and to the production cross sections of the underlying dynamic processes. An application of the non-equilibrium approach to the production of strange matter is given. The importance of secondary processes, following pion production, in the formation of strange matter is shown. In fact, the secondary production process for kaons is as important as the direct production process arising from initial nucleon-nucleon (NN) collision of a first collision picture. Thus, kaons can be produced in a late stage of the collision of two nuclei and they do not necessarily reflect the early stages of the collision as first thought. Using the experimental number of kaons, the time of reaction is also estimated. No evidence for a long-lived state of the nuclear system is found. Expressions for particle production ratios are developed. The results of an equilibrium theory and a non-equilibrium theory are found to be similar for such ratios. The chemical equilibrium constant is shown to be present in the non-equilibrium theory; the Boltzmann factor in the production threshold energy appears in the equilibrium theory. The K −/ K + ratio is estimated. Surprisingly, reasonable agreement with experiment is found in the K −/ K + ratio using the equilibrium theory, even though the production processes for K +'s and K −'s treated individually, are not ones for which the equilibrium theory applies. It is shown that a fundamental difference between the equilibrium and non-equilibrium theory is lost when particle ratios for non-equilibrium particles are taken. Expressions for the production of complex composite structures made of strange particles are developed. The non-equilibrium model with some modifications may be useful for high energy NN and pion-nucleon collisions.