Basis Of Statistical Thermodynamics Research Articles

(Invited) Applications of the Hakoniwa Method to Impurity Atoms Wandering Inside Si Wafers

In this presentation, we review applications for Si-related materials by utilizing the Hakoniwa method, an approach that predicts material properties on the basis of statistical thermodynamics and ab initio calculations. This method describes the behavior of Cu/Fe atoms in B-doped Si crystals. The target material (inside Si wafers) is not uniform and therefore needed to be described in a local circumstance around wandering impurity atoms inside the wafers in order to estimate compatible values with the experiments. Further descriptions are also discussed to estimate Cu/O solubility. These all approaches are spatial-averaged from the viewpoint of statistical thermodynamic treatments. Expanding the Hakoniwa method to a time-averaged approach for the SiO2/Si interface can provide a novel description of oxidizing reactions in the SiO2/Si interface and enable estimation of the interface state density.

(Invited) Applications of the Hakoniwa Method to Impurity Atoms Wandering Inside Si Wafers

In this presentation, we review applications for Si-related materials by utilizing the Hakoniwa method, an approach that predicts material properties on the basis of statistical thermodynamics and ab initio calculations. This method describes the behavior of Cu/Fe atoms in B-doped Si crystals. The target material (inside Si wafers) is not uniform and therefore needed to be described in a local circumstance around wandering impurity atoms inside the wafers in order to estimate compatible values with the experiments. Further descriptions are also discussed to estimate Cu/O solubility. These all approaches are spatial-averaged from the viewpoint of statistical thermodynamic treatments. Expanding the Hakoniwa method to a time-averaged approach for the SiO2/Si interface can provide a novel description of oxidizing reactions in the SiO2/Si interface and enable estimation of the interface state density.

Sixty Years of the van der Waals and Platteeuw Model for Clathrate Hydrates-A Critical Review from Its Statistical Thermodynamic Basis to Its Extensions and Applications.

In light of the 60-year anniversary of the publishing of "Clathrate Solutions" by van der Waals and Platteeuw in 2019, we present a critical review of the famed solid solution model first disclosed in 1959. First, we lay out the groundwork in the 1950s aimed at the development of a phenomenological approach to clathrate modeling. Then we review the statistical thermodynamics fundamentals of the model, considering van der Waals and Platteeuw's earlier works, to obtain a consistent interpretation of the model. We turn our focus to clathrate hydrates and discuss the major contributions that led to the current state-of-the-art of gas hydrate thermodynamic modeling. Finally, we present some of the areas in clathrate thermodynamics that we foresee as the new frontiers in this subject. We expect this review to help newcomers to clathrate science in elucidating some subtle aspects of the model and to intrigue clathrate experts with a fresh look on this well-established solid solution model.

Quantifying Protein Disorder through Measures of Excess Conformational Entropy.

Intrinsically disordered proteins (IDPs) and proteins with a large degree of disorder are abundant in the proteomes of eukaryotes and viruses, and play a vital role in cellular homeostasis and disease. One fundamental question that has been raised on IDPs is the process by which they offset the entropic penalty involved in transitioning from a heterogeneous ensemble of conformations to a much smaller collection of binding-competent states. However, this has been a difficult problem to address, as the effective entropic cost of fixing residues in a folded-like conformation from disordered amino acid neighborhoods is itself not known. Moreover, there are several examples where the sequence complexity of disordered regions is as high as well-folded regions. Disorder in such cases therefore arises from excess conformational entropy determined entirely by correlated sequence effects, an entropic code that is yet to be identified. Here, we explore these issues by exploiting the order-disorder transitions of a helix in Pbx-Homeodomain together with a dual entropy statistical mechanical model to estimate the magnitude and sign of the excess conformational entropy of residues in disordered regions. We find that a mere 2.1-fold increase in the number of allowed conformations per residue (∼0.7kBT favoring the unfolded state) relative to a well-folded sequence, or ∼2(N) additional conformations for a N-residue sequence, is sufficient to promote disorder under physiological conditions. We show that this estimate is quite robust and helps in rationalizing the thermodynamic signatures of disordered regions in important regulatory proteins, modeling the conformational folding-binding landscapes of IDPs, quantifying the stability effects characteristic of disordered protein loops and their subtle roles in determining the partitioning of folding flux in ordered domains. In effect, the dual entropy model we propose provides a statistical thermodynamic basis for the relative conformational propensities of amino acids in folded and disordered environments in proteins. Our work thus lays the foundation for understanding and quantifying protein disorder through measures of excess conformational entropy.

Protein adsorption on ion exchange resins and monoclonal antibody charge variant modulation

A novel multicomponent adsorption equilibrium model for proteins on ion-exchange resins is developed on a statistical thermodynamic basis including surface coverage effects and protein-resin and protein–protein interactions. The resulting model exhibits a general competitive Langmuirian behavior and was applied to the study and optimization of the separation of monoclonal antibody charge variants on two strong cation exchangers. The model accounts explicitly for the effect of both pH and salt concentration, and its parameters can be determined in diluted conditions, that is, through physically sound assumptions, all model parameters can be obtained using solely experiments in diluted conditions, and be used to make predictions in overloaded conditions.The parameterization of the model and optimization of the separation is based on a two-step approach. First, gradient experiments in diluted conditions are undertaken in order to determine the model parameters. Based on these experiments and on information about the proteins of interest and the stationary phase used, all the model parameters can be estimated. Second, using the parameterized model, an initial Pareto optimization is undertaken where overloaded operating conditions are investigated. Experiments from this Pareto set are then used to refine the estimation of the model parameters. A second Pareto optimization can then be undertaken, this time with the refined parameters. This can be repeated until a satisfactory set of model parameters is found.This iterative approach is shown to be extremely efficient and to provide large amounts of knowledge based on only a few experiments. It is shown that due to the strong physical foundation of the model and the very low number of adjustable parameters, the number of iterations is expected to be at most two or three. Furthermore, the model based tool is improved as more experimental knowledge is provided, allowing for better estimations of the chromatographic processes considered at each iteration. This makes it a very suitable tool for the design and the development of preparative and industrial purification processes, including the determination of both the optimal operating conditions, as well as the allowable process operating space.

Local pressure components and interfacial tension at a liquid-solid interface obtained by the perturbative method in the Lennard-Jones system.

A classical molecular dynamics simulation was conducted for a system composed of fluid molecules between two planar solid surfaces, and whose interactions are described by the 12-6 Lennard-Jones form. This paper presents a general description of the pressure components and interfacial tension at a fluid-solid interface obtained by the perturbative method on the basis of statistical thermodynamics, proposes a method to consider the pressure components tangential to an interface which are affected by interactions with solid atoms, and applies this method to the calculation system. The description of the perturbative method is extended to subsystems, and the local pressure components and interfacial tension at a liquid-solid interface are obtained and examined in one- and two-dimensions. The results are compared with those obtained by two alternative methods: (a) an evaluation of the intermolecular force acting on a plane, and (b) the conventional method based on the virial expression. The accuracy of the numerical results is examined through the comparison of the results obtained by each method. The calculated local pressure components and interfacial tension of the fluid at a liquid-solid interface agreed well with the results of the two alternative methods at each local position in one dimension. In two dimensions, the results showed a characteristic profile of the tangential pressure component which depended on the direction tangential to the liquid-solid interface, which agreed with that obtained by the evaluation of the intermolecular force acting on a plane in the present study. Such good agreement suggests that the perturbative method on the basis of statistical thermodynamics used in this study is valid to obtain the local pressure components and interfacial tension at a liquid-solid interface.

Statistical Thermodynamic Analysis for Isothermal Hydrogenation Performances of Mg<SUB>2-</SUB><SUB>y</SUB>Pr<SUB>y</SUB>Ni<SUB>4</SUB>Intermetallics (<i>y</i> = 0.6, 0.8, 1.0)

Isothermal hydrogenation performances of intermetallic Mg<SUB>2-y</SUB>Pr<SUB>y</SUB>Ni<SUB>4</SUB> alloys with <i>y</i> = 0.6, 0.8 and 1.0 reported by Terashita<i>et al</i>.were analyzed on the basis of statistical thermodynamics under a simplifying<i>a priori </i>assumption of constant nearest neighbourH-H interaction<i>E</i>(H-H) in a given phase at arbitrary <i>T</i> aiming at characterizing basic aspects of state of H atoms in the interstitial sites in H-storage alloy. To fulfill this <i>a priori</i> assumption, number θ of available interstitial sites per metal atom was chosen by preliminary search attempt at the onset of the statistical thermodynamic analysis. Primary H solution in Mg<SUB>2-y</SUB>Pr<SUB>y</SUB>Ni<SUB>4 </SUB>was analyzed by the model with θ = 0.15. The chosen  value 0.15 for the model analysis was close to be 1/6 (≈ 0.167) which was half of 1/3 (=[Mg + Pr]/[Mg + Pr + Ni])implying that about half of the (Mg + Pr)-related interstitial sites were provided as the available sites for occupation by H atoms in the primary H solution of Mg<SUB>2-y</SUB>Pr<SUB>y</SUB>Ni<SUB>4</SUB>. On the other hand, hypo-stoichiometric M<SUB>4</SUB>H<SUB>3</SUB> type hydride of Mg<SUB>2-y</SUB>Pr<SUB>y</SUB>Ni<SUB>4</SUB> was analyzed by the model with θ = 0.75 and θ' = 0.333 where ' refers to the lower limiting composition of the phase. This model yielded situation with <i>E</i>(H-H) = 0 for any Mg<SUB>2-y</SUB>Pr<SUB>y</SUB>Ni<SUB>4</SUB>examined. Chosen value of θ' = 0.333 appeared to imply that the filling of Ni-related interstitial sites by H atoms started after preferential full occupation of the (Mg + Pr)-related interstitial sites by H atoms in the two-phase equilibrium range at invariable <i>p</i>(H<SUB>2</SUB>) plateau during H-charging.

Predictions of thermodynamic properties of energetic materials using COSMO-RS

Abstract In this work, conductor-like screening for real solvents (COSMO-RS) calculations were carried out using COSMOtherm program in conjunction with Gaussian03 packages. The objective was to predict thermodynamic properties for two nitrogen-rich energetic materials which are less harmful for the environment than the conventional ones, namely 3,6-di(hydrazino)-1,2,4,5- tetrazine (DHT) and 3,3’-azo-bis(6-amino-1,2,4,5-tetrazine) (DAAT) for which no experimental data are available to our best knowledge. COSMO-RS approach is a combination of quantum chemical and statistical thermodynamic basis, which allow a physically meaningful description of molecular interactions between pure molecules and solvents in solution. Recently, this approach has been used for the prediction of an enormous number of physicochemical properties especially aqueous solubility, Henry’s law constant, vapor pressure and partition coefficient. The vapor pressure of pure compounds is one of the most important thermodynamic properties required for the chemical process design as well as for the fate assessment of pollutants in the environment. To validate the accuracy of COSMO-RS approach for the two molecules of interest, six reference energetic molecules have been studied, for which experimental data are available, such as cyclotetramethylene-tetranitramine (HMX), 2,4,6-trinitrotoluene (TNT), cyclotrimethylenetrinitramine (RDX), 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (CL-20), 1,1-diamino-2,2-dinitroethylene (FOX-7) and n-methyl-p-nitroaniline (MNA). From predicted results, a good agreement has been noted. DAAT molecule shows a lower volatility in the medium so that a low detectability compared to the DHT and other reference molecules. Both DHT and DAAT showed negative logarithmic values of Octanol-Water partition coefficients, this means that they don’t have the tendency to enhance the bioaccumulation process in soils.

Empirical Expression of Phosphorus Solubility in Molten Fe1-yCry Given as Functions of Temperature and Phosphorus Activity

Chemical activity-temperature-composition (a-T-x-y) relationships determined by Knudsen effusion technique were made available for molten Fe-Cr-P system by a group of Russian researchers. Nevertheless, they were not presented in form of solubility x in Fe1-yCryPx as explicit functions of phosphorus activity aP and temperature T for given y and thence they are not readily usable for evaluating P solubility in molten Fe1-yCry at arbitrary T under certain aP. In the present work, effort was invested to derive empirical expression for the solubility x in Fe1-yCryPx as functions of T and aP at given y from the reported aP-T-x-y relationships in discrete tabulated format. Such analytical expression of solubility x might allow us to proceed with more profound consideration for atomic interaction and atomic configuration in the molten Fe1-yCryPx on the basis of statistical thermodynamics.

Statistical thermodynamic approach to austenitic Fe1-yNbyNx system

Available equilibrium P-T-C (pressure-temperature-composition) relationships reported for fcc (face centred cubic) Fe1-yNbyNx alloys with Nb content y up to 0.00561 were analysed on the basis of statistical thermodynamics. The reported P-T-C relationships showed a trend of rising N level x with increasing Nb content y under comparable conditions of temperature T and nitrogen partial pressure p(N2). Statistical models assuming several types of atom clustering modes were compared. A model in which interstitial N atoms were preferentially consumed first to form Nb-N dipoles in the Fe1-yNby lattice, and then the remaining N atoms were distributed over O sites (octahedral interstitial sites) surrounded by six Fe atoms without Nb, was concluded to be the most realistic one.

Structure and dynamics of water: from ambient to supercritical

Our recent works on supercritical water are reviewed. In order to elucidate the hydrogen bonding state of supercritical water, the proton chemical shift of the water proton is measured at temperatures up to 400 °C and densities of 0.19, 0.29, 0.41, 0.49, and 0.60 g/cm3. The magnetic susceptibility correction is made in order to express the chemical shift relative to an isolated water molecule in dilute gas. The chemical shift is then related to the average number of hydrogen bonds in which a water molecule is involved. It is found that the hydrogen bonding persists at supercritical temperatures and that the average number of hydrogen bonds is at least one for a water molecule at the densities larger than the critical. The density dependence of the chemical shift at supercritical temperatures is analyzed on the basis of statistical thermodynamics. It is shown that the hydrogen bonding is spatially more inhomogeneous at lower densities. The dipole moment of water at supercritical states is also estimated from the number of hydrogen bonds. The dynamical counterpart of our structural study of supercritical water has been performed by NMR relaxation measurements. Using D2O, we measured the spin-lattice relaxation time and determined the reorientational relaxation time as a function of the water density and temperature. It is then found that while the reorientational relaxation time decreases rapidly with the temperature in the subcritical condition, it is a weak function of the density in the supercritical conditions.

Statistical modeling of equilibrium adsorption of non-ideal mixtures on zeolites

A new model for equilibrium adsorption of a binary mixture on zeolites that takes into account the energy nonuniformity of the adsorption field in the zeolite cavities was developed on the basis of statistical thermodynamics. The nonuniformity of the adsorption field produces rearrangement of molecules in the cavity volume, decreasing the entropy, internal energy, and Helmholz free energy. A procedure for calculation of the thermodynamic functions from the data on the adsorption of pure components was proposed. The limiting cases of maximum ordering of the molecules in the cavity and their random distribution were considered. The approach proposed was exemplified by the substantially non-ideal system nitrogen--argon--zeolite NaX at 160 K. The proposed model describes the behavior of this mixture much better than that of the ideal adsorbed solution theory.

Ionic description of intercalation in Li xMn 2O 4 system

The influence of intercalation on the lattice energy and configuration entropy of a Li x Mn 2O 4 crystal is discussed in the paper. Conclusions have been drawn which permit the ionic description of intercalation. On the basis of statistical thermodynamics and the Born–Haber cycle the change of the Gibbs free energy has been calculated. The OC voltage of the Li/Li +/Li x Mn 2O 4 cell has been estimated as well.

Equilibrium adsorption of binary mixtures of gases by zeolites and the state of the adsorption phase

A method for analyzing the state of the adsorption phase was developed on the basis of statistical thermodynamics for the case of equilibrium adsorption of binary gaseous mixtures. The procedure for treating experimental data to determine the Helmholtz energy and other thermodynamic functions of a mixture of molecules occluded within zeolite cavities was proposed. A measure of ideal behavior of a mixture of a small number of molecules in the micropore was formulated; in the asymptotic limit such a behavior leads to the Raoult law and to assumption of the validity of the Raoult law when moving along the line of constant value of the Gibbs integral in the ideal adsorption solution theory.

Experimental tests of the Peyrard-Bishop model applied to the melting of very short DNA chains

The melting curves of short heterogeneous DNA chains in solution are calculated on the basis of statistical thermodynamics, and compared to experiments. The computation of the partition function is based on the Peyrard-Bishop Hamiltonian, which has already been adopted in a theoretical description of the melting of long DNA chains. In the case of short chains it is necessary to consider not only the breaking of the hydrogen bonds between single base pairs, but also the complete dissociation of the two strands forming the double helix.

NMR Study of Water Structure in Supercritical Conditions.

The proton chemical shift of water is measured at temperatures up to 400°C and densities of 0. 19, 0. 29, 0. 41, 0. 49, and 0. 60 g/cm3. The magnetic susceptibility correction is made in order to express the chemical shift relative to an isolated water molecule in dilute gas . The chemical shift is related to the average number of hydrogen bonds in which a water molecule is involved. It is found that the hydrogen bonding persists at supercritical temperatures and that the average number of hydrogen bonds is at least one for a water molecule in the supercritical densities . The density dependence of the chemical shift at supercritical temperatures is analyzed on the basis of statistical thermodynamics. It is shown that the hydrogen bonding is spatially more inhomogeneous at lower densities. The dipole moment of water at supercritical states is estimated from the number of hydrogen bonds. we perform the proton chemical shift measurements for a water molecule as a function of the density. than that in the gas phase, and this enhancement of supercritical water by fitting the experimentally determined number of hydrogen bonds.

Carbon solubility in face centred cubic Co 1− yNi y alloy lattice analysed by statistical thermodynamics

Carbon solubility in face centred cubic (fcc) Co 1− y Ni y alloy lattice was analysed on the basis of statistical thermodynamics under the a priori assumption of negligible C-C interaction in the fcc Co 1− y Ni y lattice. The minimum C solubility observed around the composition y between 0.6 and 0.8 was concluded to be ascribable to the minimised number of available interstitial sites for occupation by C atoms in the fcc Co 1− y Ni y lattice. The observed patterns of variations for the C solubility and the extent of stabilisation of the C atom in the fcc Co 1− y Ni y lattice with respect to the composition y appeared to be comparable to those observed for fcc Fe 1− y Ni y C x when compared in terms of the average number of 3 d electrons per metal atom.

Structural study of supercritical water. I. Nuclear magnetic resonance spectroscopy

The proton chemical shift of water is measured at temperatures up to 400°C and densities of 0.19, 0.29, 0.41, 0.49, and 0.60g/cm3. The magnetic susceptibility correction is made in order to express the chemical shift relative to an isolated water molecule in dilute gas. The chemical shift is related to the average number of hydrogen bonds in which a water molecule is involved. It is found that the hydrogen bonding persists at supercritical temperatures and that the average number of hydrogen bonds is more than one for a water molecule in the supercritical densities. The density and temperature dependence of the chemical shift at supercritical temperatures are analyzed on the basis of statistical thermodynamics. It is shown that the hydrogen bonding is spatially more inhomogeneous at lower densities.

A theory of suppressed nitrogen solubility in Fe–Z–N ternary alloy systems in the relatively high range of concentration of Z (Z=Si or C)

It was shown in earlier work that, for the FeZ z N x in the relatively low range of z, the solubility pattern of N as a function of temperature T and nitrogen partial pressure p(N 2) can be interpreted in terms of decreased number θ of available interstitial sites for occupation by N atoms per Fe atom in the Fe lattice in proportion to increased z under the assumption of negligible interaction between two interstitial constituents, N and Z (Z=Si or C). In the present work, solubility reduction of N in ternary FeZ z N x with increasing z in the relatively high range of z were analysed on the basis of statistical thermodynamics. The present analysis for molten FeSi z N x in the relatively high range of z showed that a correction to the θ versus z relation for the relatively high range of z was desirable taking into account overlapping of blocked interstitial sites for occupation of N atoms in order to reproduce the observed equilibrium pressure–temperature–composition (PTC) relation for this system while the interaction between N and Si remains negligible. On the other hand, for the simulation of equilibrium PTC relation for austenitic FeC z N x alloy over the entire range of z analysed, significant N–C interaction was important in addition to the blockage effect for the available interstitial sites for occupation of N atoms.

Statistical thermodynamic approach to carbon solubility in face centred cubic Fe1-yNiyalloy lattice

Carbon solubility in a face centred cubic (fcc) Fe1-yNiy alloy lattice was analysed on the basis of statistical thermodynamics assuming negligible C—C interaction in the fcc Fe1-yNiy lattice. The minimum carbon solubility was observed for values of y of ~ 0·6–0·7 and appeared to be ascribable to the minimum number of available interstitial sites for occupation by carbon atoms in the fcc Fe1-yNiy lattice around this composition. Accordingly, the extent of stabilisation for carbon atoms in the fcc Fe1-yNiy was estimated to be a minimum around this composition. The observed variation for the carbon solubility and the extent of stabilisation of the carbon atoms in the fcc Fe1-yNiy lattice with respect to the composition y appeared to be related to the stability of the ferromagnetic phase.MST/3251