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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

An asymptotic approach for the statistical thermodynamics of certain model systems

In classical statistical thermodynamics, calculating the configuration integral is both vital and elusive. Analytic relations for configuration integrals are desirable for modeling purposes, but it is typically impossible to obtain them. Certain systems become analytically tractable after replacing steep potential energies with harmonic potentials or athermal rigid constraints, but these approximations are often inadequate, especially when modeling the stretching of molecules. It is therefore necessary to develop a systematic approach to improve upon the approximations provided by these reference systems. Here, a general asymptotic approach is introduced, where the configuration integral for the full system is obtained in terms of that of the reference system and several corrections. This asymptotic approach is first demonstrated using the simple example of a classical three-dimensional oscillator. Next, the approach is applied to modeling the stretching of single polymer chains and to modeling thermally assisted crack growth, where results are verified with respect to numerical calculations. Overall, this asymptotic approach is a valid and effective tool for statistical thermodynamics in general.

Buche, Michael Robert↗
DOE OSTI2022

Nonequilibrium statistical thermodynamics of multicomponent interfaces

Nonequilibrium interfacial thermodynamics has important implications for crucial biological, physical, and industrial-scale transport processes. Here, we discuss a theory of local equilibrium for multiphase multicomponent interfaces that builds upon the “sharp” interface concept first introduced by Gibbs, allowing for a description of nonequilibrium interfacial processes such as those arising in evaporation, condensation, adsorption, etc. By requiring that the thermodynamics be insensitive to the precise location of the dividing surface, one can identify conditions for local equilibrium and develop methods for measuring the values of intensive variables at the interface. We then use extensive, high-precision nonequilibrium molecular dynamics (NEMD) simulations to verify the theory and establish the validity of the local equilibrium hypothesis. In particular, we demonstrate that equilibrium equations of state are also valid out of equilibrium, and can be used to determine interfacial temperature and chemical potential(s) that are consistent with nonequilibrium generalizations of the Clapeyron and Gibbs adsorption equations. We also show, for example, that, far from equilibrium, temperature or chemical potential differences need not be uniform across an interface and may instead exhibit pronounced discontinuities. However, even in these circumstances, we demonstrate that the local equilibrium hypothesis and its implications remain valid. These results provide a thermodynamic foundation and computational tools for studying or revisiting a wide variety of interfacial transport phenomena.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Modeling single-molecule stretching experiments using statistical thermodynamics

Single-molecule stretching experiments are widely utilized within the fields of physics and chemistry to characterize the mechanics of individual bonds or molecules, as well as chemical reactions. Analytic relations describing these experiments are valuable, and these relations can be obtained through the statistical thermodynamics of idealized model systems representing the experiments. Since the specific thermodynamic ensembles manifested by the experiments affect the outcome, primarily for small molecules, the stretching device must be included in the idealized model system. Though the model for the stretched molecule might be exactly solvable, including the device in the model often prevents analytic solutions. In the limit of large or small device stiffness, the isometric or isotensional ensembles can provide effective approximations, but the device effects are missing. Here a dual set of asymptotically correct statistical thermodynamic theories are applied to develop accurate approximations for the full model system that includes both the molecule and the device. In conclusion, the asymptotic theories are first demonstrated to be accurate using the freely jointed chain model and then using molecular dynamics calculations of a single polyethylene chain.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

An integrated statistical-thermodynamic model for fission gas release and swelling in nuclear fuels

Here, we propose a new model for burst fission gas release induced by microcracking in ceramic nuclear fuels such as uranium dioxide. The model stipulates that the densities of defects in the fuel material, such as microcracks and fission gas bubbles on grain boundaries, evolve in accordance with the second law of thermodynamics. Central to the model is the notion of an effective temperature, conjugate to the configurational entropy of the fuel material, and directly linked to the burnup. The model predicts that microcracking, driven by the internal stress state of the fuel material, reduces the bubble storage capacity of grain boundaries, and accounts for burst fission gas release during rapid temperature transients that simulate power transients, reactor startup, and loss-of-coolant accident conditions.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Circuit complexity and functionality: A statistical thermodynamics perspective

Circuit complexity, defined as the minimum circuit size required for implementing a particular Boolean computation, is a foundational concept in computer science. Determining circuit complexity is believed to be a hard computational problem. Recently, in the context of black holes, circuit complexity has been promoted to a physical property, wherein the growth of complexity is reflected in the time evolution of the Einstein-Rosen bridge (“wormhole”) connecting the two sides of an anti-de Sitter “eternal” black hole. Here, we are motivated by an independent set of considerations and explore links between complexity and thermodynamics for functionally equivalent circuits, making the physics-inspired approach relevant to real computational problems, for which functionality is the key element of interest. In particular, our thermodynamic framework provides an alternative perspective on the obfuscation of programs of arbitrary length—an important problem in cryptography—as thermalization through recursive mixing of neighboring sections of a circuit, which can be viewed as the mixing of two containers with “gases of gates.” This recursive process equilibrates the average complexity and leads to the saturation of the circuit entropy, while preserving functionality of the overall circuit. The thermodynamic arguments hinge on ergodicity in the space of circuits which we conjecture is limited to disconnected ergodic sectors due to fragmentation. The notion of fragmentation has important implications for the problem of circuit obfuscation as it implies that there are circuits of same size and functionality that cannot be connected via a polynomial number of local moves. Furthermore, we argue that fragmentation is unavoidable unless the complexity classes NP and coNP coincide, a statement that implies the collapse of the polynomial hierarchy of computational complexity theory to its first level.

Science & Technology - Other Topics↗
DOE OSTI2026

Thermodynamics and its prediction and CALPHAD modeling: Review, state of the art, and perspectives

Thermodynamics is a science concerning the state of a system, whether it is stable, metastable, or unstable, when interacting with its surroundings. The combined law of thermodynamics derived by Gibbs about 150 years ago laid the foundation of thermodynamics. In Gibbs combined law, the entropy production due to internal processes was not included, and the 2nd law was thus practically removed from the Gibbs combined law, so it is only applicable to systems under equilibrium, thus commonly termed as equilibrium or Gibbs thermodynamics. Gibbs further derived the classical statistical thermodynamics in terms of the probability of configurations in a system in the later 1800's and early 1900's. With the quantum mechanics (QM) developed in 1920's, the QM-based statistical thermodynamics was established and connected to classical statistical thermodynamics at the classical limit as shown by Landau in the 1940's. In 1960's the development of density functional theory (DFT) by Kohn and co-workers enabled the QM prediction of properties of the ground state of a system. On the other hand, the entropy production due to internal processes in non-equilibrium systems was studied separately by Onsager in 1930's and Prigogine and co-workers in the 1950's. In 1960's to 1970's the digitization of thermodynamics was developed by Kaufman in the framework of the CALculation of PHAse Diagrams (CALPHAD) modeling of individual phases with internal degrees of freedom. CALPHAD modeling of thermodynamics and atomic transport properties has enabled computational design of complex materials in the last 50 years. Our recently termed zentropy theory integrates DFT and statistical mechanics through the replacement of the internal energy of each individual configuration by its DFT-predicted free energy. The zentropy theory is capable of accurately predicting the free energy of individual phases, transition temperatures and properties of magnetic and ferroelectric materials with free energies of individual configurations solely from DFT-based calculations and without fitting parameters, and is being tested for other phenomena including superconductivity, quantum criticality, and black holes. Those predictions include the singularity at critical points with divergence of physical properties, negative thermal expansion, and the strongly correlated physics. Furthermore, those individual configurations may thus be considered as the genomic building blocks of individual phases in the spirit of the materials genome®. This has the potential to shift the paradigm of CALPHAD modeling from being heavily dependent on experimental inputs to becoming fully predictive with inputs solely from DFT-based calculations and machine learning models built on those calculations and existing experimental data through newly developed and future open-source tools. Furthermore, through the combined law of thermodynamics including the internal entropy production, it is shown that the kinetic coefficient matrix of independent internal processes is diagonal with respect to the conjugate potentials in the combined law, and the cross phenomena that the phenomenological Onsager flux and reciprocal relationships are due to the dependence of the conjugate potential of a molar quantity on nonconjugate molar quantities and other potentials, which can be predicted by the zentropy theory and CALPHAD modeling.

42 ENGINEERING↗
DOE OSTI2023

Automated reaction kinetics and network exploration (Arkane): A statistical mechanics, thermodynamics, transition state theory, and master equation software

The open-source statistical mechanics software described here, Arkane–Automated Reaction Kinetics and Network Exploration–facilitates computations of thermodynamic properties of chemical species, high-pressure limit reaction rate coefficients, and pressure-dependent rate coefficient over multi-well molecular potential energy surfaces (PES) including the effects of collisional energy transfer on phenomenological kinetics. Arkane can use estimates to fill in information for molecules or reactions where quantum chemistry information is missing. The software solves the internal energy master equation for complex unimolecular reaction systems. Inputs to the software include converged electronic structure computations performed by the user using a variety of supported software packages (Gaussian, Molpro, Orca, TeraChem, Q-Chem, Psi4). The software outputs high-pressure limit rate coefficients and pressure-dependent phenomenological rate coefficients, as well as computed thermodynamic properties (enthalpy, entropy, and constant pressure heat capacity) with added energy corrections. Some of the key features of Arkane include treatment of 1D, 2D or ND hindered internal rotation modes, treatment of free internal rotation modes, quantum tunneling effect consideration, transition state theory (TST) and Rice-Ramsperger-Kassel-Marcus (RRKM) rate coefficient computations, master equation solution with four implemented methods, inverse-Laplace transform of high-pressure limit rate coefficients into the energy domain, energy corrections based on bond-additivity or isodesmic reactions, automated and efficient PES exploration, and PES sensitivity analysis. The present work describes the design of Arkane, how it should be used, and refers to the theory that it employs. Arkane is distributed via the RMG-Py software suite (https://github.com/ReactionMechanismGenerator/RMG-Py).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Understanding solvent effects on adsorption and protonation in porous catalysts

Abstract Solvent selection is a pressing challenge in developing efficient and selective liquid phase catalytic processes, as predictive understanding of the solvent effect remains lacking. In this work, an attenuated total reflection infrared spectroscopy technique is developed to quantitatively measure adsorption isotherms on porous materials in solvent and decouple the thermodynamic contributions of van der Waals interactions within zeolite pore walls from those of pore-phase proton transfer. While both the pore diameter and the solvent identity dramatically impact the confinement (adsorption) step, the solvent identity plays a dominant role in proton-transfer. Combined computational and experimental investigations show increasingly favorable pore-phase proton transfer to pyridine in the order: water < acetonitrile < 1,4 – dioxane. Equilibrium methods unaffected by mass transfer limitations are outlined for quantitatively estimating fundamental thermodynamic values using statistical thermodynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Transport phenomena in electrolyte solutions: Nonequilibrium thermodynamics and statistical mechanics

The theory of transport phenomena in multicomponent electrolyte solutions is presented here through the integration of continuum mechanics, electromagnetism, and nonequilibrium thermodynamics. The governing equations of irreversible thermodynamics, including balance laws, Maxwell's equations, internal entropy production, and linear laws relating the thermodynamic forces and fluxes, are derived. Green–Kubo relations for the transport coefficients connecting electrochemical potential gradients and diffusive fluxes are obtained in terms of the flux–flux time correlations. Furthermore, the relationship between the derived transport coefficients and those of the Stefan–Maxwell and infinitely dilute frameworks are presented, and the connection between the transport matrix and experimentally measurable quantities is described. To exemplify the application of the derived Green–Kubo relations in molecular simulations, the matrix of transport coefficients for lithium and chloride ions in dimethyl sulfoxide is computed using classical molecular dynamics and compared with experimental measurements.

42 ENGINEERING↗
DOE OSTI2022

Freely jointed chain models with extensible links

We report analytical relations for the mechanical response of single polymer chains are valuable for modeling purposes, on both the molecular and the continuum scale. These relations can be obtained using statistical thermodynamics and an idealized single-chain model, such as the freely jointed chain model. To include bond stretching, the rigid links in the freely jointed chain model can be made extensible, but this almost always renders the model analytically intractable. Here, an asymptotically correct statistical thermodynamic theory is used to develop analytic approximations for the single-chain mechanical response of this model. The accuracy of these approximations is demonstrated using several link potential energy functions. This approach can be applied to other single-chain models, and to molecular stretching in general.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Laplace's method applied to functional integrals

In statistical thermodynamics, partition functions are required to evaluate the current state. It is typically impossible to analytically calculate the resulting configuration integrals, but it is sometimes possible to obtain approximations in the limit of steep potential energies. This approach directly leverages Laplace’s method for approximating integrals and has been quite successful in recent applications. Motivated by models with an infinite number of degrees of freedom, this approach should be extended to the statistical thermodynamics of fields. To that end, Laplace’s method is developed for functional integrals.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

New Dimension in Ab Initio Electronic Structure Theory: Temperature, Pressure, and Chemical Potential

Ab initio electronic structure theory has transformed gas-phase molecular science with its predictive ability. In the attempt to bring such predictive ability to macroscopic systems and condensed matter, the theory must integrate quantum mechanics with statistical thermodynamics, so that thermodynamic functions such as free energy, internal energy, entropy, and chemical potentials are computed as functions of temperature in a systematically converging series of approximations. Here, a general, versatile strategy of elevating ab initio electronic structure theory to nonzero temperatures is introduced and discussed.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Computational thermodynamics and its applications

Thermodynamics is a science concerning the state of a system, whether it is stable, metastable or un- stable, when interacting with the surroundings. In this overview, fundamentals of thermodynamics are briefly reviewed through the combination of first and second laws of thermodynamics for open and nonequilibrium systems to demonstrate that the reversible equilibrium and irreversible nonequilibrium thermodynamics can be integrated to enhance the power and utilities of thermodynamics. The recent progresses in computational thermodynamics, the remaining challenges, and potential impacts in broad scientific fields are discussed here. It is shown that computational thermodynamics enables the modeling of thermodynamics of a state as a function of both external and internal variables and quantitative calculations of a broad range of properties of a multicomponent system in terms of first and second derivatives of energy, including not only equilibrium states when there are no driving forces for any internal processes and but also non-equilibrium states with driving forces for internal processes. Consequently, external constraints such as fixed strain and internal degree of freedoms such as ordering and defects can be described in a coherent framework and applied to materials design. Furthermore, two important but largely overlooked aspects in thermodynamics will be discussed, i.e. the rigorous application of statistical thermodynamics with the probability of configurations and their contributions to system properties, and the applications of second derivatives of energy with respect to either two extensive variables or two potentials or a mixture of them in terms of understanding and predicting emergent behaviors, critical phenomena, kinetic coefficients, and mechanical properties.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Modeling aqueous association constants and mineral solubilities at subcritical and supercritical temperatures

The need for sustainable power generation has increased interest in the use of hydrothermal fluids for industrial applications. New high-enthalpy geothermal systems and biowaste-to-fuel processes are two relevant examples that employ supercritical fluids which require an in-depth understanding of complex chemical reactions occurring near the supercritical temperature of water (374 °C). As these processes operate in thermodynamic regimes that are not currently covered by a standard molar Gibbs energy of formation model, only empirical fits for single reaction systems are available which limit the use of multi-component phase equilibria calculations that are standard practice for less extreme environments. Here, in this paper, we advance a standard molar Gibbs energy of formation model able to operate in these otherwise inaccessible thermodynamic states to include species needed for key mineral solubility systems and ion association reactions. This work extends a model based on molecular statistical thermodynamics (MST) into four new systems (Na 3 PO 4 -H 2 O, LiOH-H 2 O, KOH-H 2 O, and BaSO 4 -H 2 O) by extending the model to cover 10 new species. For each of these systems, model predictions were consistently within the experimental uncertainties for the new systems covered. A breakdown of MST contributions to the model revealed that electrostatic and hard sphere contributions were key to reproducing density dependencies of standard molar Gibbs energy of formation values around the critical point of water.

42 ENGINEERING↗
DOE OSTI2022

Solvation Thermodynamics of Solutes in Water and Ionic Liquids Using the Multiscale Solvation-Layer Interface Condition Continuum Model

We report molecular assembly processes are generally driven by thermodynamic properties in solutions. Atomistic modeling can be very helpful in designing and understanding complex systems, except that bulk solvent is very inefficient to treat explicitly as discrete molecules. The SLIC/CDC multiscale model combines continuum solvent electrostatics based on the solvent layer interface condition (SLIC) with statistical thermodynamic models for hydrogen bonding and nonpolar modes: cavity formation, dispersion interactions, combinatorial mixing (CDC). The SLIC/CDC model predicts Gibbs energies of solvation for a database of 500 solutes in water with average accuracy better than 1 kcal/mol both for experimental measurements and for explicit-solvent molecular dynamics simulations. The separate SLIC/CDC energy mode values agree quantitatively with those computed from explicit-solvent molecular dynamics. The SLIC/SASA multiscale model combines the SLIC continuum electrostatic model with the solvent accessible surface area (SASA) nonpolar energy mode. The SLIC/SASA model predicts Gibbs energies of solvation with better than 1.4 kcal/mol average accuracy in aqueous systems and better than 1.6 kcal/mol average accuracy in ionic liquids. Both models predict solvation entropies, and are the first implicit-solvation models capable of predicting solvation heat capacities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Methane Adsorption on Heteroatom-Modified Maquettes of Porous Carbon Surfaces

Experimental and theoretical studies disagree on the energetics of methane adsorption on carbon materials. However, this information is critical for the rational design and optimization of the structure and composition of adsorbents for natural gas storage. The delicate nature of dispersion interactions, polarization of both the adsorbent and the adsorbate, interplay between H-bonding and tetrel bonding, and induced dipole/Coulomb interactions inherent to methane physisorption require computational treatment at the highest possible level of theory. In this study, we employed the smallest reasonable computational model, a maquette of porous carbon surfaces with a central site for substitution and methane binding. The most accurate predictions of methane adsorption energetics were achieved by electron-correlated molecular orbital theory CCSD(T) and hybrid density functional theory MN15 calculations employing a saturated, all-electron basis set. Here, the characteristic geometry of methane adsorption on a carbon surface (“lander approach”) arises due to bonding interactions of the adsorbent π-system with the proximal H–C bonds of methane, in addition to tetrel bonding between the antibonding orbital of the distal C–H bond and the central atom of the maquette (C, B, or N). The polarization of the electron density, structural deformations, and the comprehensive energetic analysis clearly indicate a ∼3 kJ mol –1 preference for methane binding on the N-substituted maquette. The B-substituted maquette showed a comparable or lower binding energy than the unsubstituted, pure C model, depending on the level of theory employed. The calculated thermodynamic results indicate a strategy for incorporating electron-enriched substitutions (e.g., N) into carbon materials as a way to increase methane storage capacity over electron-deficient (e.g., B) modifications. The thermochemical analysis was revised for establishing a conceptual agreement between the experimental isosteric heat of adsorption and the binding enthalpies from statistical thermodynamics principles.

03 NATURAL GAS↗
DOE OSTI2024

Statistical mechanical model for crack growth

Analytic relations that describe crack growth are vital for modeling experiments and building a theoretical understanding of fracture. Upon constructing an idealized model system for the crack and applying the principles of statistical thermodynamics, it is possible to formulate the rate of thermally activated crack growth as a function of load, but the result is analytically intractable. In this report an asymptotically correct theory is used to obtain analytic approximations of the crack growth rate from the fundamental theoretical formulation. These crack growth rate relations are compared to those that exist in the literature and are validated with respect to Monte Carlo calculations and experiments. The success of this approach is encouraging for future modeling endeavors that might consider more complicated fracture mechanisms, such as inhomogeneity or a reactive environment.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Ensemble Effects on Hydroxide Bond Dissociation Free Energies in Polyoxovanadate Clusters

Understanding structure-property relationships is foundational to numerous modern chemistries, such as proton-coupled electron transfer (PCET). However, an experimentally measured property is the result of the behavior from an ensemble of molecules. Neglecting ensemble effects, especially under complex chemical environments, may obfuscate these relationships and lead to discrepancies between theory and experiment. In this work, we demonstrate the impact of configurational entropy and local chemical environments on hydroxide bond dissociation free energies [BDFE- (O−H)] for a set of polyoxovanadate nanoclusters, at ambient conditions. The O−H bond strengths are investigated via density functional theory (DFT) coupled with statistical thermodynamic analysis and bilinear modeling, and compared with previous experimental results on the same systems, namely electrochemical solutions of: [V 6 O 13−x (OH) x (TRIOL R ) 2 ] −2 (x = 2, 4, 6; R = NO 2 , Me) and [V 6 O 11−x (OMe) 2 (OH) x (TRIOL NO 2 ) 2 ] −2 (x = 2, 4). Interestingly, we find that ensemble effects, even at room temperature, can account for a significant portion of the BDFE(O−H) trend with the degree of reduction via H atom binding, which cannot be fully captured by single-structure, static DFT calculations. Moreover, we find that the ensemble effects may be replicated statistically, requiring only enumeration of energetically accessible H-binding sites. With the ensemble effects resolved, we present a simple bilinear model to reconcile remaining biases between experiment and ensemble-informed theory, which corelate with clusterspecific electronic environment differences. The bilinear model achieves outstanding accuracy vs experiments with a root-mean squared error of 0.4 kcal/mol. Finally, based on the physicochemical characteristics of hydrogen interaction with polyoxometalates, we present a simple methodology that captures the BDFE(O−H) trend while dramatically reducing required DFT calculations by 98% and achieving accuracy within 1 kcal/mol. Overall, this work elucidates the roles and structural origins of configurational entropy and chemical effects on polyoxometalate hydroxide bond energies, with potential applicability to various atomically precise metal oxide systems. Importantly, it introduces models for rapid and highly accurate property calculations in connection with experiments.

Cluster chemistry↗