Statistical Thermodynamic Theory Research Articles

Fluctuation adsorption theory: quantifying adsorbate-adsorbate interaction and interfacial phase transition from an isotherm.

How adsorbate-adsorbate interaction determines the functional shape of an adsorption isotherm is an important and challenging question. Many models for the adsorption isotherm have been proposed to answer this question. However, a successful fitting of an isotherm on its own is insufficient to prove the correctness of the model assumptions. Instead, starting from the principles of statistical thermodynamics, we propose how adsorbate-adsorbate interactions can be quantified from an isotherm. This was made possible by extending the key tools of solution statistical thermodynamics to adsorbates at the interface, namely, the Kirkwood-Buff and McMillan-Mayer theories, as well as their relationship to the thermodynamic phase stability condition. When capillary condensation and interfacial phase transition are absent, adsorbate-adsorbate interactions can be quantified from an isotherm using the Kirkwood-Buff integrals, and virial coefficients can yield multiple-body interaction between adsorbates. Such quantities can be obtained directly from the fitting parameters for the well-known isotherm models (e.g., Langmuir, BET). The size of the adsorbate cluster involved in capillary condensation and interfacial phase transition can also be evaluated from the isotherm, which was demonstrated for the adsorption isotherm of water on activated carbons of varying pore sizes from the literature. Signatures of isotherm classifications by IUPAC have been characterized in terms of multiple-body interactions between adsorbates.

Reality in a Few Thermodynamic Reference Frames: Statistical Thermodynamics From Boltzmann via Gibbs to Einstein

The success of a few theories in statistical thermodynamics can be correlated with their selectivity to reality. These are the theories of Boltzmann, Gibbs, and Einstein. The starting point is Carnot’s theory, which defines implicitly the general selection of reality relevant to thermodynamics. The three other theories share this selection, but specify it further in detail. Each of them separates a few main aspects within the scope of the implicit thermodynamic reality. Their success grounds on that selection. Those aspects can be represented by corresponding oppositions. These are: macroscopic – microscopic; elements – states; relational – non-relational; and observable – theoretical. They can be interpreted as axes of independent qualities constituting a common qualitative reference frame shared by those theories. Each of them can be situated in this reference frame occupying a different place. This reference frame can be interpreted as an additional selection of reality within Carnot’s initial selection describable as macroscopic and both observable and theoretical. The deduced reference frame refers implicitly to many scientific theories independent of their subject therefore defining a general and common space or subspace for scientific theories (not for all). The immediate conclusion is: The examples of a few statistical thermodynamic theories demonstrate that the concept of “reality” is changed or generalized, or even exemplified (i.e. “de-generalized”) from a theory to another. Still a few more general suggestions referring the scientific realism debate can be added: One can admit that reality in scientific theories is some partially shared common qualitative space or subspace describable by relevant oppositions and rather independent of their subject quite different in general. Many or maybe all theories can be situated in that space of reality, which should develop adding new dimensions in it for still newer and newer theories. Its division of independent subspaces can represent the many-realities conception. The subject of a theory determines some relevant subspace of reality. This represents a selection within reality, relevant to the theory in question. The success of that theory correlates essentially with the selection within reality, relevant to its subject.

Theoretical investigation of nitrogen gas hydrates outside of stability zone

Using a combination of Quasiharmonic Lattice Dynamic and Molecular Dynamic Simulation methods in conjunction with well developed statistical thermodynamics theory the thermodynamic properties of nitrogen gas hydrates has been calculated, with the main focus on the thermal expansion coefficient. It is shown that nitrogen gas hydrate displays larger value of the thermal expansion coefficient in comparison with hexagonal ice Ih and empty gas hydrate lattice, moreover this value is very close to one of the carbon dioxide and to other hydrates that have self-preservation effect. Exactly because of this difference in the thermal expansion coefficient it is possible to confirm existence of the self-preservation effect. The self-preservation effect can be used for creation of low-cost technology of hydrates storage and transportation technology applicable for many gas types.

Theoretical study of stability zones of mixed H2 + CO2 gas hydrates CS-I and CS-II

Using the original approach that utilizes statistical thermodynamic theory that has been developed in our group the phase p-T diagram and hydrate phase composition have been calculated for “CO2 + H2 + H2O”. Depending on the CO2 content in the gas phase two hydrates types can be formed: CS-I and CS-II. It has been found that increasing CO2 content in the gas phase drastically reduces hydrate formation pressure and in the same time reduces hydrogen uptake by the hydrate. While pure H2 hydrates have CS-II structure, addition of more than 2 mol.% of CO2 into the gas phase makes CS-I hydrate structure more stable, that displays worse maximum hydrogen content. These results could be helpful for practical use of hydrates for efficient CO2 utilization and H2 transportation.

Theoretical investigation of thermodynamic properties of tetrabutylammonium bromide ionic clathrate hydrate

In the framework of the lattice dynamics method, the densities of the phonon states of tetrabutylammonium bromide ionic clathrate hydrate have been found. The dynamic stability of the hydrate is shown for a number of temperatures. Using the developed statistical-thermodynamic theory, the free energy curves have been constructed for a wide range of temperatures at different unit cell volumes and, based on the calculated data, the lines of thermal expansion of the hydrate have been constructed.

Features of Thermodynamic Description of Properties of Gd2O3-Y2O3-HfO2 Based Ceramics

Data on the thermodynamic description of Gd2O3-Y2O3-HfO2 system determined by high-temperature mass spectrometry at 2500 K were discussed using the Barker-Guggenheim statistical thermodynamic theory and the Redlich-Kister empirical approach to consider the accuracy and the possibility of further interpretation of the values found. A comparison was made of the results obtained on the basis of the indicated approaches with the aim of the most reliable optimization of the values of the excess Gibbs energy found in the system under consideration.

Self-preservation effect modelling in hydrate systems using Lattice Dynamic methods

The thermodynamic properties of the carbon dioxide clathrate hydrate as well as hexagonal ice Ih have been calculated using Quasiharmonic Lattice Dynamic framework in connection with Molecular Dynamic methods in order to show the existence of the self-preservation effect in the carbon dioxide hydrates. The statistical thermodynamics theory has been applied to calculate the thermal expansion coefficients for hydrate and ice systems. The calculations clearly show that because the thermal expansion of the hydrate phase is limited by the thermal expansion of ice it is possible to keep the hydrate in a stable region within the phase diagram. The differences in thermal expansion should lead to the self-preservation effect with the application of additional pressure on the hydrate phase. This effect allows using the self-preservation effect for the storage and transportation of gas in the hydrate form.

Thermodynamic analysis of the Livermore molecular-dynamics simulations of dislocation-mediated plasticity.

Results of recent large-scale molecular dynamics simulations of dislocation-mediated solid plasticity are compared with predictions of the statistical thermodynamic theory of these phenomena. These computational and theoretical analyses are in substantial agreement with each other in both their descriptions of strain-rate-dependent steady plastic flows and of transient stress peaks associated with initially small densities of dislocations. The comparisons between the numerical simulations and basic theory reveal inconsistencies in some conventional phenomenological descriptions of solid plasticity.

Molecular conformational effects in H + n-heptane reaction rate calculations

Accurate fuel combustion modelling is a matter of immense importance to design clean combustors and reduce greenhouse gas emissions and pollutants. In this Brief Communication, we present the effects of internal dynamics of one n-heptane molecule which are controlling chemical kinetics of hydrogen abstraction reactions through multi-pathway reaction dynamics. It is established that the slope of Arrhenius plots dramatically changes in comparison with the harmonic single static pathway approach in the temperature range of 200–3000 K. We apply a combination of the multiple conformation statistical thermodynamic approach and variational transition-state theory (VTST) to obtain dynamic multi-path rate coefficients (kMP-T-VTST and kMP-LH-VTST). Compared with single-path VTST (kSP-H-VTST) results, the thermal reaction rate coefficients obtained from our MP-VTST calculations differ considerably due to the fact that tunnelling and cross-conformational effects in the reactions, and the anharmonic and quasi-harmonic contributions in multiple conformer molecules cannot be ignored or simplified.

First-principles study of phase stability and solubility in Al-(Cu, Zr) alloys

ABSTRACTThe solubility limit of elements plays a crucial role in alloy designing, as well as in the understanding of kinetic processes in alloys. Using first-principles calculations, we calculated the ground states of Al-Cu and Al-Zr compounds, and predicted the stable and metastable structures of these two binaries. The results indicate that the stable structures for Al-Cu compounds are Al2Cu(cF12), AlCu(mC20), Al4Cu9(cP52) and AlCu3(tI8), and those for Al-Zr binary are Al3Zr(tI16), Al2Zr(hP12), Al3Zr4(hP7) and AlZr3(cP4). Based on the statistical-thermodynamic theory of dilute lattice gas, we presented a systematic series of calculations of the solubility limits of Cu and Zr in Al as a function of temperature. It is found that the solubility of Cu is much higher than Zr over the whole investigated temperature range.

Generalized Dynamic Equations Related to Condensation and Freezing Processes

AbstractThe generalized thermodynamic equation related to condensation and freezing processes was derived by introducing the condensation and freezing probability function into the dynamic framework based on the statistical thermodynamic fluctuation theory. As a result, the physical mechanism of some weather phenomena covered by using δ(0,1) can in turn be studied and uncovered. From the generalized dynamic equations, the tendency equation of the generalized potential vorticity (GPV) is derived. From the discussion of tendency equation of GPV, in some very thin transitional areas, GPV is found nonconserved because of the introduction of the condensation and freezing probability function, even in frictionless and moist adiabatic air motion.

First-Principles Study of Phase Stability and Solubility in Fe-RE (Y, La, Ce) Alloys

The solubility limit of elements plays a crucial role in alloy designing, as well as in the understanding of kinetic processes in alloys. Using first-principles calculations, we calculated the ground states of Fe-RE compound, and predicted the stable and metastable structures of Fe-Y and Fe-Ce. The results indicate that the stable structures for Fe-Y compounds are Fe 12 Y.tI26, Fe 17 Y 2 .hP38 and Fe 2 Y.cF24, and those for Fe-Ce binary are Fe 17 Ce 2 .hP38, Fe 19 Ce 5 .hR24 and Fe 2 Ce.cF24. Based on the statistical-thermodynamic theory of dilute lattice gas, we presented a systematic series of calculations of the solubility limits of RE in α -Fe as a function of temperature. It is found that the solubilities are sorted in the following order: S La > S Ce > S Y , corresponding to the trend in the solubility formation enthalpies: H sol (La)< H sol (Ce)< H sol (Y).

The COSMO and COSMO‐RS solvation models

The conductor‐like screening model COSMO, a variant of the dielectric continuum solvation models, has become very popular due to its algorithmic simplicity, numerical stability, and its great insensitivity with respect to outlying charge errors. The advanced model COSMO‐RS, i.e., COSMO for realistic solvation, is a statistical thermodynamics theory based on COSMO polarization charge densities, which overcomes many of the limitations and theoretical shortcomings of dielectric continuum models. Due to its ability to treat mixtures at variable temperatures, it has become very popular in chemical engineering and in wide areas of physical and medicinal chemistry. COSMO‐RS may currently be considered the most accurate model for the prediction of solvation energies. This article provides a short description of the basic concepts of both models, of the differences with other solvation models, and of their application areas. Finally, Direct‐COSMO‐RS, a recent direct integration of the COSMO‐RS concept into quantum chemical calculations, is briefly described. WIREs Comput Mol Sci 2018, 8:e1338. doi: 10.1002/wcms.1338This article is categorized under: Structure and Mechanism &gt; Computational Materials Science

Mode-selective control of thermal Brownian vibration of micro-resonator (Generation of a thermal no-equilibrium state by mechanical feedback control)

Recently, there have been various attempts to dampen the vibration amplitude of the Brownian motion of a microresonator below the thermal vibration amplitude, with the goal of reaching the quantum ground vibration level. To further develop the approach of reaching the quantum ground state, it is essential to clarify whether or not coupling exists between the different vibration modes of the resonator. In this paper, the mode-selective control of thermal Brownian vibration is shown. The first and the second vibration modes of a micro-cantilever moved by a random Brownian motion are cooled selectively and independently below the thermal vibration amplitude, as determined by the statistical thermodynamic theory, using a mechanical feedback control method. This experimental result shows that the thermal no-equilibrium condition was generated by mechanical feedback control.

Theoretical research on the catalytic reaction mechanism of N2O and CO over Ni5 cluster

In this paper, the reaction mechanism for N2O with CO on the surface of Ni5 cluster was investigated by the B3LYP method of density functional theory (DFT). Ni atom of various species was calculated using B3LYP/ LANL2DZ basis set, and C, N, O atoms at B3LYP/6-31G∗ level. In the temperature range of 100–1000K, the statistical thermodynamics and Eyring transition state theory with Winger correction were used to study the kinetic characters of reaction. The calculation results indicated that the reaction of N2O with CO on Ni5 cluster had two major reacting processes: (1) O atom first dissociated from N2O on Ni5 cluster, and then reacted with CO on Ni5 and (2) on the surface of Ni5 catalyst, O atom of N2O direct interacted with C atom of CO, resulting into the dissociation of N2O and the form of CO2. The direct O extraction channel was the main channel due to its low potential energy and high rate constant.

On the surface tension of molten salts and its temperature dependence

ABSTRACTA new equation, based on Eyring statistical thermodynamic theory, has been developed to calculate the surface tension and its temperature dependence of high-temperature molten salts. The derived equation has been applied to the calculation of the temperature dependence of the surface tension of molten alkali halides. The model used here is analytical and free of interatomic potentials usually used in computer simulation. The only data needed for the calculation are the sublimation energy and the temperature dependence of the liquid density, which are readily available. The need for such a model stems from the fact that the data in the literature are scarce and the temperature range studied is limited by the experimental demand of high temperatures and clean surface environment, which is difficult to attain. The ratio of surface to bulk Madelung constant was calculated to be 0.95, which is found to be constant for all molten salts studied. This finding is interesting and is presented for the first time. The error in this estimate did not exceed 1.3%. The values calculated do commensurate with the available experimental values for many of the molten salts. The results of temperature-dependent surface tension calculations of molten LiCl (910–1150 K), NaCl (1080–1230 K) and KCl (1050–1300 K) are fitted as = 223.5 − 0.0814 (T-Tm), = 114.4 − 0.091 (T-Tm) and = 91 − 0.066 (T-Tm) (mJ m−2), respectively, where the surface tension decreases linearly with temperature and agrees well with the existing data.

Statistical Thermodynamic Theory of Heat-Induced Gelation of Aqueous Methylated Polyrotaxane Solutions

Chemically modified polyrotaxanes by methylation are water-soluble and show high-temperature gelation in water. To elucidate the molecular mechanism, we developed a theoretical model incorporating the following contributions: hydration–dehydration of cyclic molecules, formation of one-dimensional aggregates composed of a various number of cyclic molecules along the polymer chain, and formation of junction structures by associating between the aggregates. We numerically calculated the sol–gel transition line, the average aggregate length, the average junction multiplicity, the heat capacity change of the solution, the hydration ratio of cyclic molecules, and the translational entropy of cyclic molecules along the chain. We compared our results with the previously reported experimental data, and we discussed the molecular mechanism of the high-temperature gelation and the formation of the junction structures based on the sliding feature of cyclic molecules.

How Entrainers Enhance Solubility in Supercritical Carbon Dioxide.

Supercritical carbon dioxide (scCO2) on its own can be a relatively poor solvent. However, the addition at relatively modest concentration of "entrainers", simple solvent molecules such as ethanol or acetone, can provide a significant boost in solubility, thereby enabling its industrial use. However, how entrainers work is still under debate; without an unambiguous explanation, it is hard to optimize entrainers for any specific solute. This paper demonstrates that a fundamental, assumption-free statistical thermodynamic theory, the Kirkwood-Buff (KB) theory, can provide an unambiguous explanation of the entrainer effect through an analysis of published experimental data. The KB theory shows that a strong solute-entrainer interaction accounts for the solubility enhancement, while CO2 density increase and/or CO2-entrainer interactions, which have been assumed widely in the literature, do not account for solubilization. This conclusion, despite the limited completeness of available data, is demonstrably robust; this can be shown by an order-of-magnitude analysis based upon the theory, and can be demonstrated directly through a public-domain "app", which has been developed to implement the theory.

Gelation of carrageenan: Effects of sugars and polyols

The gelation of κ-carrageenan, a common polysaccharide for food gelling and thickening, is enhanced by the addition of sugars and polyols. Three different hypotheses have been proposed to explain this phenomenon: (i) the enhancement of the water structure around polysaccharides, and the concurrent change in polysaccharide hydration, induced by the cosolvent; (ii) exclusion of cosolvents from polysaccharide surfaces; (iii) binding between sugars/polyols and polysaccharides in the gel phase. To examine the above hypotheses, as well as to reveal the true driving forces responsible for gelation enhancement, we applied our recent statistical thermodynamic theory of gelation, derived from the rigorous Kirkwood–Buff theory. The hydration change is shown to be negligibly small relative to cosolvent exclusion and cosolvent-biopolymer binding, which can be rationalized by considering a sol–gel equilibrium in which (1) the exclusion of sugars/polyols from κ-carrageenan's surface in the sol phase, and (2) the binding of sugars and polyols in the gel phase, shift the sol–gel equilibrium of κ-carrageenan to the gel state. This novel picture is consistent with a wealth of experimental evidence and provides a mechanistic insight into how polyol and sugar cosolvents influence the gelation of κ-carrageenan on a molecular level.

Calculation of Thermodynamic Properties in Solid-Liquid, Solid-Gas and Liquid-Gas Region

The paper features the mathematical model of analytical calculation of thermodynamic properties like viscosity, speed of sound and thermal conductivity for fluids in one and two-phase region (fluid-solid, fluid-gas) on the basis of statistical mechanics. For the calculation of thermal conductivity and viscosity for fluids will be presented Chung-Lee-Starling model Equations for the thermal conductivity are developed based on kinetic gas theories and correlated with the experimental data. The low-pressure transport properties are extended to fluids at high densities by introducing empirically correlated density dependent functions. These correlations use acentric factor, dimensionless dipole moment and an empirically determined association parameters to characterize molecular structure effect of polyatomic molecules. The calculation of thermodynamic properties for fluids was developed under the theory of statistical thermodynamics and statistical associated fluid theory. For the calculation of thermal conductivity of solids are the most important two contributions: the heat transport by electrons (el) and by phonons (ph). In our model we have made the assumption that heat transport by electrons and by phonons is independent and the thermal conductivity is than a sum of both terms.