Thermodynamic Equilibrium Theory Research Articles

Peeling Reveals Problems of Strength Standards for Brittle Materials

Peeling creates a ubiquitous crack used regularly to open plastic packaging. Such peel cracks have been utilised for centuries, especially in separating cellulose fibres, yet these peeling cracks are not usually mentioned in fracture texts [1,2]. In this paper, theories and experiments show that peel cracks have unique properties quite different from the tensile-test cracks generally used to define and standardize strength of materials. Peeling is the easiest fracture test at the lowest force with the simplest theory describing constant speed cracks that are readily observed. It differs markedly from the catastrophic tensile cracks seen in many brittle materials such as concrete and glass, that accelerate rapidly at high force. The problem is that strength in peeling is not consistent with strength in tension. There is a large size effect in peeling where strength drops for larger sample size. Therefore, standards need to be modified. This paper describes peeling observations in several crack test geometries, fitting the energy theory of thermodynamic crack equilibrium, contrary to the stress/strength criteria that dominate existing brittle-material standards, which need correction.

Useful High-Entropy Source on Spinel Oxides for Gas Detection.

This study aimed to identify a useful high-entropy source for gas detection by spinel oxides that are composed of five cations in nearly equal molar amounts and free of impurities. The sensor responses of the spinel oxides [1# (CoCrFeMnNi)3O4, 2# (CoCrFeMnZn)3O4, 3# (CoCrFeNiZn)3O4, 4# (CoCrMnNiZn)3O4, 5# (CoFeMnNiZn)3O4, and 6# (CrFeMnNiZn)3O4] were evaluated for the test gases (7 ppm NO2, 5000 ppm H2, 3 ppm NH3, and 3 ppm H2S). In response to NO2, 1# and 2# showed p-type behavior while 3–6# showed n-type semiconductor behavior. There are three p-type and one n-type AO structural compositions in AB2O4[AO·B2O3] type spinel, and 1# showed a stable AO composition because cation migration from site B to site A is unlikely. Therefore, it was assumed that 1# exhibited p-type behavior. The p-type behavior of 2# was influenced by Cr oxide ions that were present at the B site and the stable p-type behavior of zinc oxide at the A site. The spinel oxides 3# to 6# exhibited n-type behavior with the other cationic oxides rather than the dominant p-type behavior exhibited by the Zn oxide ions that are stable at the A site. In contrast, the sensor response to the reducing gases H2, NH3, and H2S showed p-type semiconductor behavior, with a particularly selective response to H2S. The sensor responses of the five-element spinel oxides in this study tended to be higher than that of the two-element Ni ferrites and three-element Ni-Zn ferrites reported previously. Additionally, the susceptibility to sulfurization was evaluated using the thermodynamic equilibrium theory for the AO and B2O3 compositions. The oxides of Cr, Fe, and Mn ions in the B2O3 composition did not respond to H2S because they were not sulfurized. The increase in the sensor response due to sulfurization was attributed to the decrease in the depletion layer owing to electron sensitization, as the top surface of the p-type semiconductors, ZnO and NiO, transformed to n-type semiconductors, ZnS and NiS, respectively. High-entropy oxides prepared using the hydrothermal method with an equimolar combination of five cations from six elements (Cr, Mn, Fe, Co, Ni, and Zn) can be used as a guideline for the design of high-sensitivity spinel-type composite oxide gas sensors.

Detection of Departure from Thermal Dynamic Equilibrium in the Solar Middle and Lower Atmosphere UsingTotal Solar Eclipse Data

There are abundant emission and absorption lines superimposed on the continuum spectra of the different solar atmospheric layers. The chemical composition and physical state of the solar atmosphere can be probed by the inversion of the profiles of these spectral lines. Due to the low density and large temperature difference in the chromosphere and transition region of the Sun, it is hard to establish the thermal dynamic equilibrium. It is necessary to adopt the theory of Non-Local Thermodynamic Equilibrium (N-LTE) to construct the corresponding atmospheric model. In this paper, the departure from the Local Thermodynamic Equilibrium (LTE) in the middle and lower atmosphere of the sun is investigated with the well-defined relative departure factor and the relevant calculations. We first make an inversion of the spectral lines formed at the different heights in the chromosphere and transition region during a total solar eclipse, to obtain the parameters of the observed spectral lines, such as the continuum source function, line source function, Doppler width, and thus the equivalent kinetic temperature. According to these line parameters obtained by the inversion, we calculate the quantitative results about the departure from the LTE at each space sampling point in the 2D field of view. Secondly, we reconstruct the 2D distributions of the radiation intensity, equivalent kinetic temperature, and relative departure factor according to the alignment of the optical fiber array in the integrated field unit (IFU) used by the telescope. The results show that there is a stronger correlation in the distributions of the temperature and relative departure factor existed in local small regions, but without evident correlation with the distribution of radiation intensity. There is an obvious difference between the distributions of the equivalent temperature and relative departure factor derived from two spectral lines, which shows a strong structurization and complexity existed in some local small regions of the solar atmosphere, and provides a new perspective for us to further understand the physics of the middle and lower atmosphere of the Sun.

Thermodynamic equilibrium theory revealing increased hysteresis in ferroelectric field-effect transistors with free charge accumulation

At the core of the theoretical framework of the ferroelectric field-effect transistor (FeFET) is the thermodynamic principle that one can determine the equilibrium behavior of ferroelectric (FERRO) systems using the appropriate thermodynamic potential. In literature, it is often implicitly assumed, without formal justification, that the Gibbs free energy is the appropriate potential and that the impact of free charge accumulation can be neglected. In this Article, we first formally demonstrate that the Grand Potential is the appropriate thermodynamic potential to analyze the equilibrium behavior of perfectly coherent and uniform FERRO-systems. We demonstrate that the Grand Potential only reduces to the Gibbs free energy for perfectly non-conductive FERRO-systems. Consequently, the Grand Potential is always required for free charge-conducting FERRO-systems. We demonstrate that free charge accumulation at the FERRO interface increases the hysteretic device characteristics. Lastly, a theoretical best-case upper limit for the interface defect density DFI is identified.

Study of the Comprehensive Kinetic Model of Natural Gas Hydrate Formation in a Water-in-Oil Emulsion Flow System.

Hydrate growth is influenced by many factors, including thermodynamics, kinetics, mass and heat transfer, and so on. There is thus a practical significance in establishing a model that comprehensively considers these influencing factors for hydrate crystal growth in multiphase transportation pipelines. On this basis, this paper presents a more practical and comprehensive bidirectional growth model of hydrate shells for an actual pipeline system. Thermodynamic phase equilibrium theory and water molecule penetration theory are applied in this model to develop a method for calculating the concentration change of hydrate-forming guest molecules and the permeation rate of water molecules. The temperatures on both sides of the hydrate shell are predicted by the heat transfer model. Simultaneously, decreasing the mass transfer coefficient with continuous hydrate growth is used to describe the problem in which the mass transfer efficiency decreases with a thickened hydrate shell. Then, the hydrate growth kinetic parameters of the pipeline system are optimized according to hydrate growth experiments conducted in a high-pressure flow loop and the microscopic characteristics of the particles were provided using the PVM and FBRM probes. The improved hydrate growth model can improve the prediction accuracy of hydrate formation in slurry systems.

Quantitative Relationship Between Expiratory Airflow Limitation and Dynamic Hyperinflation: A Thermo-statistical Model

Clinical assessment of expiratory flow limitation (EFL) is important for diagnosing chronic pulmonary disease (COPD). Either EFL or dynamic hyperinflation (DH) in COPD has been understood based on wave speed theory, which is widely accepted as the standard concept. However, a theoretical perspective on the relationship between EFL and DH may require another approach. This article proposed another explanation for EFL with the introduction of pulmonary entropy with thermo-statistical considerations on choke state of the pulmonary system. According to Gibbs' thermodynamic equilibrium theory, the choke state of the pulmonary system was characterized by a critical pressure (Pc) emergence in the pulmonary parenchyma, which was proportional to the elastic recoil pressure (Pel) and the slope of maximal flow-volume curve (σ). Thermodynamic balance between energies (supplied from the body as heat, stored as the entropy of lungs, and dissipated in the respiratory system) explained the work of breathing (WOB), by which it was explained that an intrinsic PEEP (PEEPi) was emerging as a difference between sufficient and insufficient WOB for energy demands of the body. It was concluded that EFL would limit the WOB into less than demanded during exercise, and that the difference between demand and performance would induce a product of PEEPi and DH in volume.

An analysis of vapour transfer in unsaturated freezing soils

The effects of vapour on water content in different unsaturated frozen soils have not been systematically analyzed in the literature. Based on the thermodynamic equilibrium theory and coupled water-heat theory, a new method for calculating unfrozen water content and ice content is obtained. A new model is then built by importing this method to the coupled heat and mass transfer theory. Unfrozen water content and ice content in this new model are only related to hydraulic parameters and temperature, which means specific physical meaning. The comparisons between simulations and test results of sandy loam validate the new model. Simulated results also show that temperature is the major factor to vapour transfer instead of suction. And vapour transfer in silt and sand cannot be neglected with freezing except clay. Initial water content, freezing temperature, freezing time and ground water table can all influence vapour transfer in freezing soils. In a word, even though the water content increment is low, the total mass of the increased amount and the average increase of the total water content in the frozen area are about 40 kg and 0.033 within the unit area in susceptible frost heaving soils such as silt, respectively. Remarkable frost heave could then occur due to vapour. Therefore, the vapour in unsaturated frozen soils must be paid more attention to in practical engineering. This paper strengthens the understanding of canopy effect and also validates that canopy effect usually occurs in covered freezing silt instead of sand or clay.

Microdroplet nucleation by dissolution of a multicomponent drop in a host liquid

Multicomponent liquid drops in a host liquid are very relevant in various technological applications. Their dissolution or growth dynamics is complex. Differences in solubility between the drop components combined with the solutal Marangoni effect and natural convection contribute to this complexity, which can be even further increased in combination with the ouzo effect, i.e. the spontaneous nucleation of microdroplets due to composition-dependent miscibilities in a ternary system. The quantitative understanding of this combined process is important for applications in industry, particularly for modern liquid–liquid microextraction processes. In this work, as a model system, we experimentally and theoretically explore water–ethanol drops dissolving in anethole oil. During the dissolution, we observed two types of microdroplet nucleation, namely water microdroplet nucleation in the surrounding oil at drop mid-height, and oil microdroplet nucleation in the aqueous drop, again at mid-height. The nucleated oil microdroplets are driven by Marangoni flows inside the aqueous drop and evolve into microdroplet rings. A one-dimensional multiphase and multicomponent diffusion model in combination with thermodynamic equilibrium theory is proposed to predict the behaviour of spontaneous emulsification, i.e. microdroplet nucleation, that is triggered by diffusion. A scale analysis together with experimental investigations of the fluid dynamics of the system reveals that both the solutal Marangoni flow inside the drop and the buoyancy-driven flow in the host liquid influence the diffusion-triggered emulsification process. Our work provides a physical understanding of the microdroplet nucleation by dissolution of a multicomponent drop in a host liquid.

Thermodynamic analysis of syngas production via tri-reforming of methane and carbon gasification using flue gas from coal-fired power plants

Tri-reforming of methane (TRM) and carbon gasification (CG) for syngas production were analyzed in this study using flue gas from coal-fired power plants as feedstock based on the thermodynamic equilibrium theory. The obtained results suggested that for both TRM and CG, reaction temperature should be higher than 500 °C to obtain positive carbon dioxide conversion and higher yields of hydrogen and carbon monoxide. The results also indicated that both TRM and CG are unfavorable at high pressure. Conversions of carbon dioxide, methane and carbon decreased as the reaction pressure increased. In TRM with methane added into flue gas, carbon dioxide conversion, methane conversion, and hydrogen/carbon monoxide ratio were enhanced by increasing methane/carbon dioxide ratio. For CG with carbon added into the flue gas, negative carbon dioxide conversion was found for low carbon/carbon dioxide ratios. The hydrogen/carbon monoxide ratio was found to be less than unity at high temperatures because no hydrogen source was added. From carbon dioxide equivalent analysis, it was found that the reduced carbon dioxide equivalent can be enhanced with higher conversions of carbon dioxide and methane and lower methane yield. It was also found that TRM was more competitive in reducing carbon dioxide equivalent as compared with CG. From the energy balance analysis, higher energy input was required when the methane/carbon dioxide or carbon/carbon dioxide ratio was increased. Although thermoneutral reaction could be achieved, low or negative carbon dioxide conversion was resulted. For air or water added in TRM, decreased carbon dioxide conversion was found due to more carbon dioxide production from methane oxidation or water-gas shift reaction. For air or water added in CG, carbon dioxide conversion was also found to decrease due to more carbon dioxide production from carbon oxidation or water-gas shift reaction. This study also indicated that the only way to achieve high carbon dioxide conversion is to increase the methane in TRM or carbon in CG. However, carbon formation and lower carbon conversion were possible with increased methane and carbon additions in TRM and CG, respectively.

Transport capacity of gas confined in nanoporous ultra-tight gas reservoirs with real gas effect and water storage mechanisms coupling

It is a well-established fact that mineral matter in actual ultra-tight gas reservoirs presents a strong affinity for water. However, the presence of water within nanopores has not drawn due attention and is generally overlooked by previous literature. Furthermore, the other key physics required to be captured is how to upscale the gas conductance from a single nanopore to a core scale, which greatly aggravates the complexity of the issue. To date, the comprehensive apparent permeability model considering the aforementioned features is still lacking and the intent of this research is to achieve this goal. Firstly, the Beskok’s model is utilized to characterize bulk-gas transport behavior through nanotubes. And Li’s model is employed to quantify water storage mechanisms, which are based on thermodynamic equilibrium theory between liquid and vapor. More features, such as stress dependence and real gas effect are incorporated. Thus, the apparent permeability model for a single nanopore is developed. Secondly, actual core sample is discretized to numerous little cells and the pores within each cell are assumed to possess uniform pore size, which are assigned by Monte Carlo sampling from pore size distribution (PSD). Thus, the transport capacity of each cell can be quantified by utilizing the aforementioned established model for a single nanopore. Finally, based on apparent permeability of each cell, a reliable geostatistical method is employed to calculate the effective permeability of the core sample. And the proposed apparent permeability model for actual ultra-tight gas reservoirs is successfully verified against experimental data collected from published documents. Subsequently, we identify the effect of PSD, relative humidity, real gas effect and stress dependence on the apparent permeability of actual ultra-tight gas reservoirs. Results show that the presence of heterogeneity in 2D will contribute to the increase of effective permeability and the influence of water condensation only works when the relative humidity is relatively high (>0.8). Moreover, the real gas effect has little effect on the gas transport behavior at a certain pressure and can be neglected.

Crystallization and melting behavior of i-PP: a perspective from Flory's thermodynamic equilibrium theory and DSC experiment

A novel conceptual framework that generates insightful new results about crystallization and melting behaviors of i-PP.

From Steam Engines to Chemical Reactions: Gibbs’ Contribution to the Extension of the Second Law

The present work analyzes the foundations of Gibbs’ thermodynamic equilibrium theory, with the general aim of understanding how the Second Law—as formulated by Clausius in 1865—has been embodied into Gibbs’ formal system and extended to processes involving chemical reactions. We show that Gibbs’ principle of maximal entropy (and minimal energy) is the implicit expression of Clausius’ Second Law. In addition, by making explicit some implicit passages of Gibbs logical path, we provide an original formal justification of Gibbs’ principle. Finally we provide an analysis of how Gibbs’ principle—conceived for homogeneous isolated systems with fixed chemical composition—has come to be applied to systems entailing chemical transformations.

Alite-C<sub>3</sub>A-Gypsum系の水和反応における相互作用機構の解明

For understanding the cement hydration composed of high C₃A content, pure clinker phases such as Alite, Tricalcium aluminate (C₃A) were synthesized and five different compositions of mixtures were prepared. The hydration of samples were followed by calorimetry. Quantitation of the crystalline and amorphous products were conducted by X-ray diffraction and Rietveld analysis. It was found that the hydration between C₃A and Gypsum was accelerated by hydration of Alite. It was implied that amorphous materials produced from the hydration between C₃A and Gypsum as well as the hydration of Alite. Rise of pH due to precipitation of portlandite from Alite hydration accelerated the hydration between C₃A and Gypsum. It could be explained on the basis of thermodynamic equilibrium theory that AFm phase with low sulfate content precipitated in the vicinity of C₃A particle. In the bulk solution far from the surface of C₃A, AFt with high sulfate content precipitated. Subsequently, because of low sulfate content in AFm, mass transfer into C₃A particle kept proceeding and hydrating C₃A continuously progressed. That is why hydration reaction of C₃A proceeds when added Alite in contrast to the hydration without Alite.C₃A含有量の多いセメントの水和反応について理解することを目的とし、その主たる反応を司るAlite、C₃A、Gypsumを混合したモデルセメントの水和実験を行った。発熱量測定、XRD・リートベルト解析、TG-DTA測定の結果、Aliteの水和反応がC₃A-Gypsum系の水和反応を促進させることを確認した。さらに、その要因はAliteの水和反応からPortlanditeが生成することによるpH上昇であり、その際C₃A粒子付近に析出するAFm相に含まれるSO₄²⁻量が少ないため、未水和C₃Aへの物質の透過が継続するからであることが示唆された。

Thermodynamic equilibrium diagram of CaCl2-Ca(OH)2-H2O system

The lg c-pH diagram of the CaCl2-Ca(OH)2-H2O system and its two subsystems at 298.15 K are constructed according to the theory of thermodynamic equilibrium. The interaction characteristics between the solubility of CaCl2 and Ca(OH)2 can be found out from the diagrams. CaCl2·6H2O (s), Ca(OH)2(s) and solution coexist when the pH value of solution is about 10.8. CaCl2 with the minimum solubility of 1 682.4 g/L is in equilibrium with solution when the pH value is lower than 9.4, and Ca(OH)2 with the minimum solubility of 2.749 g/L is in equilibrium with solution at the pH value over 12.1, which provides a theoretical basis for the treatment and reuse of calcium chloride mother liquor for collocating lime cream which is the precipitant in the process of synthesizing magnesium hydroxide.

Analyses and development of a hierarchy of frozen soil models for cold region study

Numerous frozen soil models currently in use differ in the complexity of their governing equations or/and in the processes being considered. It is important to comprehensively examine and categorize these on the basis of physical principles, assumptions, and relationship to each other. In this paper frozen soil models are classified into different levels according to the complexity of the governing equations. On the basis of scale analysis, models with different levels of complexity were derived from the most complicated frozen soil model. Rationales for the simplification of models at different levels are discussed. To overcome the difficulties in achieving numerical solutions, a new method of substituting soil enthalpy and total water mass for soil temperature and volumetric liquid water content in governing equations is introduced for each level of the frozen soil models. Models with different complexity levels are assessed with observational data. The preliminary monthly and seasonal evaluation shows that the results from the models with different complexity are generally similar but with substantial differences at the Tibetan D66 site during the melting and freezing period. The model including the contribution of vapor flux due to the matric potential gradient to the water balance performs the best at the D66 site. Compared to the corresponding original models, the frozen soil model versions with enthalpy and total water mass for governing equations appear to produce consistently better performance. Furthermore, the rationale of different methods for the freezing‐melting process in frozen soil is discussed. It has been noted that the model derived from the freezing point depression equation and the soil matric potential equation is supported by both thermodynamic equilibrium theory and the simulation results.

Thermodynamic equilibrium of CaSO 4-Ca(OH) 2-H 2O system

The p c—pH diagrams of the CaSO 4-Ca(OH) 2-H 2O system and its two subsystems at 298.15 K were constructed according to the theory of thermodynamic equilibrium. The interaction characteristics between the solubility of CaSO 4(s) and Ca(OH) 2(s) can be found out from the diagrams. CaSO 4(s), Ca(OH) 2(s) and solution coexist when the pH value of solution is about 13.2. CaSO 4(s) with the minimum solubility of 0.411 g/L is in equilibrium with solution when the pH value is lower than 13.2, and Ca(OH) 2(s) with the minimum solubility of 2.749 g/L is in equilibrium with solution at the pH value over 13.2, which provides a theoretical basis for the treatment and reuse of industrial wastewater, especially for the wastewater containing sulfate which can be treated by lime-milk neutralization.

Hydrogen production from biomass coupled with carbon dioxide capture: The implications of thermodynamic equilibrium

In this work we report on the consequences of thermodynamic equilibrium for hydrogen ( H 2 ) generation via steam gasification of biomass, coupled with in situ carbon dioxide ( CO 2 ) capture. Calcium oxide (CaO) is identified as a suitable sorbent for CO 2 capture, capable of absorbing CO 2 to very low concentrations, at temperatures and pressures conducive to the gasification of biomass. The proposed process exploits the reversible nature of the CO 2 capture reaction and leads to the production of a concentrated stream of CO 2, upon regeneration of the sorbent. We develop a thermodynamic equilibrium model to investigate fundamental reaction parameters influencing the output of H 2-rich gas. These are: (i) reaction temperature, (ii) reaction pressure, (iii) steam-to-biomass ratio, and (iv) sorbent-to-biomass ratio. Based on the model, we predict a maximum H 2 concentration of 83%-mol, with a steam-to-biomass ratio of 1.5 and a Ca-to-C ratio of 0.9. Contrary to previous experimental studies, this maximum H 2 output is reported at atmospheric pressure. Model predictions are compared with an experimental investigation of the pyrolysis of pure cellulose and the reactivity of CaO through multiple CO 2 capture and release cycles using a thermogravimetric analyser, coupled with a mass spectrometer (TGA–MS). On this basis, we demonstrate the applicability of thermodynamic equilibrium theory for the identification of optimal operating conditions for maximising H 2 output and CO 2 capture.

Thermodynamic equilibrium model of pyroelectric polycrystalline thin films

This study deals with the thermodynamic equilibrium theory of pyroelectric polycrystalline thin films. The unit cell of pyroelectric polycrystalline thin films in the ferroelectric phase to be considered is assumed as a dipole and is a nondipole at its paraelectric phase. The phase transition between ferroelectric and paraelectric phases is hypothesized as an equilibrium of the dipoles and the nondipole. Based on the thermodynamic equilibrium theory, an expression formula about the spontaneous polarization and temperature is suggested. Considering the sandwich structure of pyroelectric polycrystalline thin films, an equation about the relations between pyroelectric coefficient and temperature was established.

Hamiltonian theory of stochastic acceleration

Stochastic acceleration, defined in terms of a stochastic equation of motion for the acceleration, is derived from a Hamiltonian model. A free particle is coupled bilinearly to a harmonic bath through the particle's momentum and coordinate. Under appropriate conditions, momentum coupling induces velocity diffusion which is not destroyed by the spatial coupling. Spatial-momentum coupling may induce spatial subdiffusion. The thermodynamic equilibrium theory presented in this paper does not violate the second law of thermodynamics, although the average velocity squared of the particle may increase in time without bound.

Geometrical Contribution to Yield Strength in Small Volumes

AbstractCritical thickness theory was developed to account for the ability of thin epitaxial metal and semiconductor layers to support high misfit or coherency strain. The thermodynamic equilibrium theory is correct, and is well approximated by a theory based on geometrical arguments. The latter theory is readily extended to arbitrary misfit strain profiles including linearly graded layers, for which a surface layer free of misfit dislocations. This result applies as well to linear strain gradients introduced by deformation, in which case the misfit dislocations are known as geometrically necessary dislocations. We show that a consequence of this surface layer is that the apparent yield strength of the material increases in small structures such as thin wires in torsion. Under large plastic deformation, even if the material is perfectly plastic, critical thickness theory also predicts an apparent work-hardening. The predictions of critical thickness theory are in excellent agreement with experimental data in the literature.