Statistical Thermodynamic Approach Research Articles

Sorption Hysteresis: A Statistical Thermodynamic Fluctuation Theory.

Hysteresis is observed commonly in sorption isotherms of porous materials. Still, there has so far been no unified approach that can both model hysteresis and assess its underlying energetics. Standard approaches, such as capillary condensation and isotherms based on interfacial equations of state, have not proved to be up to the task. Here, we show that a statistical thermodynamic approach can achieve the following needs simultaneously: (i) showing why adsorption and desorption transitions may be sharp yet continuous; (ii) providing a simple (analytic) isotherm equation for hysteresis branches; (iii) clarifying the energetics underlying sorption hysteresis; and (iv) providing macroscopic and nanoscopic perspectives to understanding hysteresis. This approach identifies the two pairs of parameters (determinable by fitting experimental data) that are required to describe the hysteresis: the free energy per molecule within the pore clusters and the cluster size in the pores. The present paper focuses on providing mechanistic insights to IUPAC hysteresis types H1, H2(a), and H2(b) and can also be applied to the isotherm types IV and V.

Gaussian and Non-Gaussian Solvent Density Fluctuations within Solute Cavities in a Water-like Solvent.

We report a Monte Carlo simulation study of length-scale-dependent density fluctuations in cavities in the coarse-grained mW representation of water at ambient conditions. Specifically, we use a combination of test particle insertion and umbrella sampling techniques to examine the full range of water occupation states in spherical cavities up to 6.3 Å radius in water. As has previously been observed, water density fluctuations are found to be effectively Gaussian in nature for atomic-scale cavities, but as the cavities get larger, they exhibit a non-Gaussian "fat-tail" distribution for lower occupancy states. We introduce a new statistical thermodynamic approach to analyze non-Gaussian fluctuations based on the radial distribution of waters about cavities with varying numbers of waters within its boundaries. It is shown that the onset of these non-Gaussian fluctuations is a result of the formation of a bubble within the cavity as it is emptied, which is accompanied by the adsorption of waters onto its interior surface. We revisit a theoretical framework we previously introduced to describe Gaussian fluctuations within cavities to incorporate bubble formation by including surface tension contributions. This modified theory accurately describes density fluctuations within both atomic and meso-scale cavities. Moreover, the theory predicts the transition from Gaussian to non-Gaussian fluctuations at a specific cavity occupancy, in excellent agreement with simulation observations.

Cooperative Sorption on Heterogeneous Surfaces.

Heterogeneous adsorbents, those composed of multiple surface and pore types, can result in stepwise isotherms that have been difficult to model. The complexity of these systems has often led to appealing to empirical equations without physical insights, unrealistic assumptions with many parameters, or applicability limited to a particular class of isotherms. Here, we present a statistical thermodynamic approach to model stepwise isotherms, those consisting of either an initial rise followed by a sigmoid or multiple sigmoidal steps, founded on the rigorous statistical thermodynamic theory of sorption. Our only postulates are (i) the finite ranged nature of the interface and (ii) the existence of several different types of microscopic interfacial subsystems that act independently in sorption. These two postulates have led to the superposition scheme of simple surface (i.e., Langmuir type) and cooperative isotherms. Our approach has successfully modeled the adsorption on micro-mesoporous carbons, gate-opening adsorbents, and hydrogen-bonded organic frameworks. In contrast to the previous models that start with a priori assumptions on sorption mechanisms, the advantages of our approach are that it can be applied universally under the above two postulates and that all of the fitting parameters can be interpreted with statistical thermodynamics, leading to clear insights on sorption mechanisms.

Statistical thermodynamics approach for the available work transported by particle fluxes

The theory covers cases when the exergy concept is not fully relevant. An indicator called work content factor is used to quantify the proportion of available work in a given amount of energy. General expressions have been obtained for the flux of available work transported by particles, the rate of work deficiency and the work content factor. More specific results have been obtained for the work content factor of the low-speed and ultra-relativistic particle fluxes, respectively, by using several assumptions concerning the number of energy states, the mean occupation number of the energy states, the entropy and the module and direction of the particles speed. The theory includes extraction of work from particle fluxes governed by classical kinetic theory and heat as particular cases and has been applied to fluxes of fermions (electrons) and bosons (Helium-4) in both the low-speed and ultra-relativistic case. It has been shown that the emission of thermal photons is several orders of magnitude lower than the stimulated particle emission by the primary work extractor. As a result, a unique expression of the work content factor of the ultra-relativistic particle fluxes has been obtained for both fermions and bosons while another expression has been derived for low-speed fermions and bosons. Generally, the work content factor decreases by increasing the temperature Tc of the primary work extractor. In some cases, at large values of Tc and small values of the average directional factor of the source of particle, work cannot be extracted from the energy of the particle flux.

Quantifying the effect of solvent on the morphology of organic crystals using a statistical thermodynamics approach

A method for predicting the effect of solvent on the morphology of organic crystals is presented, providing an efficient screening tool for identifying ideal crystallization solvents. The solvent effect is estimated by the computation of chemical potentials and activity coefficients of crystal surfaces using a first principles-based statistical thermodynamics approach. Density functional theory and COSMO-RS are utilized to determine the activity coefficients of the crystal growth faces of a selection of active pharmaceutical ingredients (APIs) in solvents across a broad range of polarities. The ability of COSMO-RS to predict and quantify the effects of solvent on crystal growth and morphology is assessed using hierarchical clustering to classify the solvents according to their overall interaction strength with the crystal faces. The COSMO-RS approach allows for a physical interpretation of the predictions in terms of surface polarity and is confirmed by comparison to published experimental data. Herein a methodology is reported for automated computation of the activity coefficients of all solvent-surface pairs directly from the drug crystal structure. The procedure goes beyond the traditional trial-and-error solvent selection process and has the potential to be used as a rapid computational screening tool in pharmaceutical drug development.

Thermodynamic properties of temozolomide in crystalline and gaseous aggregate states

Temozolomide (4-methyl-5-oxo-2,3,4,6,8-pentazabicyclo[4,3,0]nona-2,7,9-triene-9-carboxamide) is an active component of antitumor immunosuppressive alkylating drugs, and it used largely for the treatment of various types of malignant tumors, including malignant gliomas that are difficult to treat by surgery (glioblastoma multiforme and anaplastic astrocytoma). Wide field of temozolomide application dictates the need for its comprehensive thermodynamic study. In this work temperature dependance of the temozolomide heat capacity was obtained using the adiabatic calorimetry method and the standard thermodynamic functions of crystalline temozolomide were calculated in the temperature range 80–370 K. Standard thermodynamic functions of the temozolomide in the ideal gas state were calculated using the statistical thermodynamics approach in the temperature range 0–1000 K. To obtain the standard internal energy and enthalpies of combustion and formation of crystalline temozolomide at T = 298.15 K the combustion bomb calorimetry was used. Standard enthalpy of formation of the gaseous temozolomide was calculated in the framework of the isodesmic reactions method using quantum chemical computing. To calculate standard sublimation enthalpy of temozolomide the electrostatic potential model was applied. The results obtained can find application in solving problems of optimisation of temozolomide production processes and to validate experimentally obtained values of thermodynamic properties of the temozolomide.

Entropy characteristics in an electric double layer with off-centre charge ions. A statistical thermodynamics approach

Statistical thermodynamics methods are utilised to characterise aspects of the entropy of formation of a planar electric double layer. The model system consists of a primitive model electrolyte but with off-centre charge cations and centro-symmetric anions, next to a planar, uniformly charged electrode. An expression is developed for the entropy of off-centre charge ions. The theoretically predicted results of this entropy as a function of the electrode surface charge are compared with those from the corresponding Monte Carlo simulations. The entropy change with respect to the absolute value of the surface charge density is seen to be negative (or normal) if the displacement of the cation charge centre is zero or is independent of temperature. However, if the displacement is temperature dependent, the entropy can be positive (or anomalous). In each situation, the simulation data are well reproduced by the predicted results.

The role of entropy in the success of nonstoichiometric oxides for two-step thermochemical water and CO2 splitting

Owing to their high theoretical efficiency, two-step solar thermochemical water and CO2 splitting cycles, using a metal oxide intermediate, provide a promising pathway to store solar energy in a stable chemical bond. To date, the most successful demonstrations have utilized nonstoichiometric oxides, a class of materials capable of continuously transitioning from an oxidized to reduced state via formation of oxygen vacancies. The success of nonstoichiometric oxides is typically attributed to their ability to maintain their crystallographic phase, allowing them to be cycled many times without destabilizing–a tremendous practical advantage. In this work, we utilize a combined empirical and statistical thermodynamics approach to present an alternative explanation of the success of nonstoichiometric oxides from an entropy perspective. We first illuminate the importance of the entropy change of the reduction reaction as a key material parameter. We then develop a methodology for plotting nonstoichiometric oxides on the Ellingham diagram, enabling a direct comparison to stoichiometric materials. This analysis reveals the unique ability of nonstoichiometric oxides to achieve a significant solid-state entropy contribution, which results from the disorder generated via oxygen vacancy formation. To quantify the solid-state entropy, we develop a simple configurational entropy model applicable to any oxygen-deficient nonstoichiometric oxide. We compare model predictions to existing data for two important nonstoichiometric oxides, CeO2−δ and La0.6Ca0.4Mn0.6Al0.4O3−δ, to reveal the main trends in entropy vs δ and material composition and discuss the causes and implications of deviations from the theory.

Study on Li ion diffusion in LixV2O5 using first principle calculations and kinetic Monte Carlo simulations

We study the Li diffusion in Li x V2O5 ()—a potential cathode material for Lithium ion batteries. Different diffusion pathways in this material with dependence on the Li ion concentration are investigated by applying first-principles calculations. The results are used to obtain the corresponding diffusion coefficients by employing two complementary methodologies: Kinetic Monte Carlo (KMC) simulations and a statistical thermodynamics approach. The KMC simulations for two different crystal planes give new evidence that the diffusion occurs mainly along the [010] direction, while the corresponding diffusion coefficients show a temperature dependence obeying Arrhenius’ Law. The necessity of the consideration of concentration-dependent barrier heights in the KMC simulations are demonstrated by looking at the significant changes of the concentration-dependence of the diffusion coefficients. The simulated diffusion coefficients of the combined approach show a good quantitative agreement with experimental data reported previously.

Anharmonic Effects on the Thermodynamic Properties of Quartz from First Principles Calculations.

The simple chemistry and structure of quartz together with its abundance in nature and its piezoelectric properties make convenient its employment for several applications, from engineering to Earth sciences. For these purposes, the quartz equations of state, thermoelastic and thermodynamic properties have been studied since decades. Alpha quartz is stable up to 2.5 GPa at room temperature where it converts to coesite, and at ambient pressure up to 847 K where it transforms to the beta phase. In particular, the displacive phase transition at 847 K at ambient pressure is driven by intrinsic anharmonicity effects (soft-mode phase transition) and its precise mechanism is difficult to be investigated experimentally. Therefore, we studied these anharmonic effects by means of ab initio calculations in the framework of the statistical thermodynamics approach. We determined the principal thermodynamic quantities accounting for the intrinsic anharmonicity and compared them against experimental data. Our results up to 700 K show a very good agreement with experiments. The same procedures and algorithms illustrated here can also be applied to determine the thermodynamic properties of other crystalline phases possibly affected by intrinsic anharmonic effects, that could partially invalidate the standard quasi-harmonic approach.

Cooperative Sorption on Porous Materials.

The functional shape of a sorption isotherm is determined by underlying molecular interactions. However, doubts have been raised on whether the sorption mechanism can be understood in principle from analyzing sorption curves via a range of competing models. We have shown recently that it is possible to translate a sorption isotherm to the underlying molecular interactions via rigorous statistical thermodynamics. The aim of this paper is to fill the gap between the statistical thermodynamic theory and analyzing experimental sorption isotherms, especially of microporous and mesoporous materials. Based on a statistical thermodynamic approach to interfaces, we have derived a cooperative isotherm, as a generalization of the Hill isotherm and our cooperative solubilization model, without the need for assumptions on adsorption sites, layers, and pore geometry. Instead, the statistical characterization of sorbates, such as the sorbate-interface distribution function and the sorbate number distribution, as well as the existence of statistically independent units of the interface, underlies the cooperative sorption isotherm. Our isotherm can be applied directly to literature data to reveal a few key system attributes that control the isotherm: the cooperative number of sorbates and the free energy of transferring sorbates from the saturated vapor to the interface. The sorbate–sorbate interaction is quantified also via the Kirkwood–Buff integral and the excess numbers.

Adsorbate-adsorbate interactions on microporous materials

Simple isotherm models can fit microporous adsorption yet the molecular interactions underlying the successful fitting have often remained obscure. Here we demonstrate how semi-empirical isotherm model data can be mined to reveal the reality of adsorbate-adsorbate molecular interactions. This was made possible by the fluctuation adsorption theory, a rigorous theory based only on the principles of statistical thermodynamics. For microporous carbons, adsorbate-adsorbate interactions quantified from the Dubinin-Radishkevich (DR) and Dubinin-Astakhov (DA) models successfully capture the primary micropore filling mechanism and the subsequent layer adsorption, leading to a liquid-like behaviour of the adsorbates. The microscopic meanings of the DR and DA parameters and the adsorption potential have also been clarified via statistical thermodynamics. • A novel statistical thermodynamic approach to adsorption has been developed. • Adsorbate-adsorbate interaction can be quantified from semi-empirical isotherm models. • Molecular basis of Dubinin-Radishkevich and Dubinin-Astakhov models clarified. • Adsorbate-adsorbate interactions support the proposed adsorption mechanisms. • Physical meaning of the “adsorption potential” was clarified.

Two-temperature balance equations implementation, numerical validation and application to H2O–He microwave induced plasmas

Global Models are widely used to study reaction kinetics in low-temperature plasma discharges. The governing conservative equations are simplified into a system of ordinary differential equations in order to provide computationally feasible conditions to study complex chemistries with hundreds of species and thousands of reactions. This paper presents a detailed two-temperature global model for a H2O–He mixture. The model developed in this work uses a statistical thermodynamics approach to solve the heavy particles energy equation self-consistently together with the electron energy and particles balance equations in order to improve the description of reactive plasma environments. Three analytical test cases are presented to validate and demonstrate the capability of this newly developed functionality embedded in PLASIMO software’s [] global model module. The developed H2O–He models are compared with the reported results for a radio-frequency plasma [] and then with experimental measured electron densities and gas temperature for a microwave induced plasma. In addition, conversion and energy efficiencies of hydrogen and hydrogen peroxide productions are compared with experimental values (only for hydrogen) for a pure H2O microwave induced plasma and with available literature results. This comparison underlines the challenges toward finding an optimal plasma configuration and conditions for production of hydrogen from water. The three analytical test cases for validation of the gas-temperature balance implementation in the PLASIMO global model and the detailed developed H2O–He model can be used as benchmarks for other global plasma models. The PLASIMO input files for the presented H2O–He model are available as supplementary materials (https://stacks.iop.org/PSST/30/075007/mmedia); for any future update, please consult the PLASIMO website, https://plasimo.phys.tue.nl.

Mechanism of dye solubilization and de-aggregation by urea

Urea is an effective solubilizer for dyes with low aqueous solubility. To establish, at a molecular level, the reason behind the action of urea as an effective solubilizer, we employ a rigorous statistical thermodynamics approach based on the Kirkwood-Buff theory of solutions. We show that (i) contrary to the classical hypothesis on “water structure breaking”, the effect of urea on dye hydration makes a minor contribution to solubilization; (ii) the driving force of solubilization is the accumulation of urea around hydrophobic dye molecules.

Theoretical Insights into Y2C2@C82: Vibrational Frequency Influencing the Thermodynamic Stability

AbstractY2C2@C82 series (as well as Y2@C84 series) and the parent C82 cages were investigated by density functional theory in conjunction with statistical thermodynamic analyses. C2(39717)‐C82 is the most stable isomer of pristine C82 cages, and Y2@D2d(51591)‐C84 is the most low‐lying isomer of Y2C84 series. At the temperature range of fullerene formation, C2(39712)‐C82, Cs(39713)‐C82, and C3v(39717)‐C82 are the three most abundant C82 isomers, and Y2C2@Cs(39715)‐C82, Y2C2@C3v(39717)‐C82, and Y2C2@C2v(39718)‐C82 are the three only abundant Y2C84 isomers. However, mole fraction of Y2@D2d(51591)‐C84 turns to be very low at the high temperature range. Further statistical thermodynamic analyses revealed that vibrational frequencies are the underlying reason for high abundances of Y2C2@Cs(39715)‐C82, Y2C2@C3v(39717)‐C82, and Y2C2@C2v(39718)‐C82 and low abundance of Y2@D2d(51591)‐C82 at high temperature range. The statistical thermodynamic analysis approach to separately consider energy, rotation and vibration partition functions can be used to investigate other endohedral metallofullerenes.

Personalized therapy design for systemic lupus erythematosus based on the analysis of protein-protein interaction networks.

We analyzed protein expression data for Lupus patients, which have been obtained from publicly available databases. A combination of systems biology and statistical thermodynamics approaches was used to extract topological properties of the associated protein-protein interaction networks for each of the 291 patients whose samples were used to provide the molecular data. We have concluded that among the many proteins that appear to play critical roles in this pathology, most of them are either ribosomal proteins, ubiquitination pathway proteins or heat shock proteins. We propose some of the proteins identified in this study to be considered for drug targeting.

Statistical thermodynamics of the Fröhlich-Bose-Einstein condensation of magnons out of equilibrium.

This work presents a nonequilibrium statistical-thermodynamic approach to the study of a Fröhlich-Bose-Einstein condensation of magnons under radio-frequency radiation pumping. Fröhlich-Bose-Einstein condensates display a complex behavior consisting in steady-state conditions to the emergence of a synergetic dissipative structure resembling the Bose-Einstein condensation of systems in equilibrium. Then a kind of "two-fluid model" arises: the "normal" nonequilibrium structure and the Fröhlich condensate, which is shown to be an attractor to the system. In this study we analyze some aspects of the irreversible thermodynamics of this dissipative complex system. We obtained the expression for the informational entropy of the two-fluid condensate and introduced an order parameter to characterize the role of the Fröhlich interaction in ordering the system. The analysis highlights the order increase due to the Fröhlich interaction. We also study the informational entropy production of the system, considering its internal and external parts. Finally, the Glansdorff-Prigogine criteria for evolution and (in)stability are verified.

Thermodynamic model of gene regulation for the Or59b olfactory receptor in Drosophila.

Complex eukaryotic promoters normally contain multiple cis-regulatory sequences for different transcription factors (TFs). The binding patterns of the TFs to these sites, as well as the way the TFs interact with each other and with the RNA polymerase (RNAp), lead to combinatorial problems rarely understood in detail, especially under varying epigenetic conditions. The aim of this paper is to build a model describing how the main regulatory cluster of the olfactory receptor Or59b drives transcription of this gene in Drosophila. The cluster-driven expression of this gene is represented as the equilibrium probability of RNAp being bound to the promoter region, using a statistical thermodynamic approach. The RNAp equilibrium probability is computed in terms of the occupancy probabilities of the single TFs of the cluster to the corresponding binding sites, and of the interaction rules among TFs and RNAp, using experimental data of Or59b expression to tune the model parameters. The model reproduces correctly the changes in RNAp binding probability induced by various mutation of specific sites and epigenetic modifications. Some of its predictions have also been validated in novel experiments.

Poisson–Boltzmann Equation for Microfluidic Transport Phenomena with Statistical Thermodynamics Approach

With the advent of microfluidics and lab-on-chip systems, DNA and protein separation technologies are being developed for biology, diagnostics, and health purposes. Fully realizing these applications requires developing numerical models for sample transport. In this paper, a thorough investigation of electrokinetics and microfluidics transport phenomena reviews the background of the Poisson–Boltzmann equation. A detailed derivation of the equation is presented, which is not available in the microfluidic literature at one place, with the view of providing a more consolidated and comprehensive understanding of it. This equation is then applied to find the electric potential and charge density distributions in the electric double layer (EDL). The present study provides a detailed derivation of the Boltzmann distribution, and principles of probability are used to identify the most-probable ion distribution. This distribution is subject to constraints of constant number of particles and total energy of the system; Lagrangian multipliers are used to solve the resulting constrained optimization problem. Classical thermodynamics is shown to be consistent with the distribution of ions: the Boltzmann distribution. Then, based on Coulomb’s law, the derivation of Poisson’s equation, and its special form of Laplace’s equation, the electric potential distribution in the EDL and in the bulk flow is derived and presented. By applying classical thermodynamics and integrating the Boltzmann distribution and Poisson equation together, the Poisson–Boltzmann equation is achieved.

Effect of mixed partial occupation of metal sites on the phase stability of \u03b3-Cr23\u2212xFexC6 (x\u2009=\u20090\u20133) carbides

The effect of mixed partial occupation of metal sites on the phase stability of the γ-Cr23−xFexC6 (x = 0–3) carbides is explored as function of composition and temperature. Ab initio calculations combined with statistical thermodynamics approaches reveal that the site occupation of the carbides may be incorrectly predicted when only the commonly used approach of full sublattice occupation is considered. We found that the γ-M23C6 structure can be understood as a familiar sodium chloride structure with positively charged rhombic dodecahedron (M(4a) M12(48h)) and negatively charged cubo-octahedron (M8(32f) C6(24e)) super-ion clusters, together with interstitial metal atoms at the 8c sites. The stability of the partially occupied phase can be easily rationalized on the basis of a super-ion analysis of the carbide phase. This new understanding of γ-M23C6 carbides may facilitate further development of high-chromium heat-resistant steels.