Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “statistical thermodynamics”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4

First Principles Simulations of Electrified Interfaces in Electrochemistry

This chapter discusses some of the recent advances made in the first principles modeling of electrochemical catalysts. It also discusses the key development, namely the ability to explicitly treat the effects of surface electrification due to electrochemical processes and applied voltages in a computationally efficient manner. The chapter introduces the thermodynamics and statistical mechanics of electrified metal-solution interfaces. It then discusses the structure of the electrode-electrolyte interface and the effects of applied voltages, followed by an overview of the first-principles model and a motivating example. The chapter also provides a brief summary of classical thermodynamics and describes the basics of thermodynamic detour. It considers the thermodynamics of macroscopic systems and introduces several useful fundamental relations. Here, the chapter also considers a system to exist in a certain macrostate, which is a particular thermodynamic state specified by a set of fixed properties such as constant particle number, constant volume, and constant temperature.

36 MATERIALS SCIENCE↗

Treating random sequential addition via the replica method

While many physical processes are non-equilibrium in nature, the theory and modeling of such phenomena lag behind theoretical treatments of equilibrium systems. The diversity of powerful theoretical tools available to describe equilibrium systems has inspired strategies that map non-equilibrium systems onto equivalent equilibrium analogs so that interrogation with standard statistical mechanical approaches is possible. In this work, we revisit the mapping from the non-equilibrium random sequential addition process onto an equilibrium multi-component mixture via the replica method, allowing for theoretical predictions of non-equilibrium structural quantities. We validate the above approach by comparing the theoretical predictions to numerical simulations of random sequential addition.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Phase equilibrium of liquid water and hexagonal ice from enhanced sampling molecular dynamics simulations

We study the phase equilibrium between liquid water and ice Ih modeled by the TIP4P/Ice interatomic potential using enhanced sampling molecular dynamics simulations. Our approach is based on the calculation of ice Ih-liquid free energy differences from simulations that visit reversibly both phases. The reversible interconversion is achieved by introducing a static bias potential as a function of an order parameter. The order parameter was tailored to crystallize the hexagonal diamond structure of oxygen in ice Ih. Furthermore, we analyze the effect of the system size on the ice Ih-liquid free energy differences, and we obtain a melting temperature of 270 K in the thermodynamic limit. This result is in agreement with estimates from thermodynamic integration (272 K) and coexistence simulations (270 K). Since the order parameter does not include information about the coordinates of the protons, the spontaneously formed solid configurations contain proton disorder as expected for ice Ih.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Impact of thermodynamic fluctuations and pattern size on the nucleation behavior during area selective deposition

In this work, the authors explore the impact that thermodynamic fluctuations have on the spontaneous appearance of defects during area selective deposition on patterned surfaces that are fully covered by adsorbates under local thermodynamic equilibrium, such as self-assembled monolayers. By using a simple lattice gas model for the adsorbed monolayer, the authors were able to track the spontaneous formation of defects in the monolayer as a function of the pattern width. The results indicate that, for pattern widths of the order of tens of nanometers, roughening effects at the pattern edge can be the leading source for the spontaneous appearance of nucleation defects. This leads to an enhancement of the density of defects that can be up to three orders of magnitude higher than those expected in uniform (not patterned) surfaces. The model also predicts a density of defects that is inversely proportional to the pattern width. Finally, if the dynamic nucleation of defects during area selective deposition is driven by thermodynamic fluctuations, the model predicts that the nucleation rate should be proportional to the total precursor fluency and independent of purge times. Moreover, a tight confinement of the monolayer through a high quality smooth interface in the patterned substrate and strong cohesive interactions between adsorbates should each contribute to a reduction of the overall defect density.

36 MATERIALS SCIENCE↗

Accurate and efficient parameterization of an atomic cluster expansion (ACE) potential for ammonia under extreme conditions

We present a machine learning interatomic potential for ammonia designed to capture its complex multiphase behavior, including both molecular and superionic phases. The potential is based on the atomic cluster expansion (ACE) formulation and has been parameterized to facilitate high-fidelity molecular dynamics simulations of ammonia under extreme conditions, for pressures up to 100 GPa and for temperatures above 500 K and up to 6000 K. A diverse range of configurations was generated through high-quality ab initio molecular dynamics simulations, covering insulating and superionic ice phases, liquid ammonia, molecular nitrogen (N 2 ) and hydrogen (H 2 ), and metastable compounds that form upon dissociation, including $NH^{+}_{4}$, $H^{+}_{3}$, N 2 H 4 , and N 3 H. We demonstrate that the ammonia ACE potential accurately reproduces experimental and density functional theory predicted isotherms and Hugoniots. Crucially, the potential is able to capture the intricate phase behavior of ammonia, including the transition from insulating molecular fluid to the superionic phase. This work provides a robust interatomic potential that can be used for large-scale, accurate simulations of ammonia under extreme thermodynamic conditions, offering a powerful tool for investigating its behavior in various phases and applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quadrupole-mediated dielectric response and the charge-asymmetric solvation of ions in water

Treating water as a linearly responding dielectric continuum on molecular length scales allows very simple estimates of the solvation structure and thermodynamics for charged and polar solutes. While this approach can successfully account for basic length and energy scales of ion solvation, computer simulations indicate not only its quantitative inaccuracies but also its inability to capture some basic and important aspects of microscopic polarization response. Here, we consider one such shortcoming, a failure to distinguish the solvation thermodynamics of cations from that of otherwise-identical anions, and we pursue a simple, physically inspired modification of the dielectric continuum model to address it. The adaptation is motivated by analyzing the orientational response of an isolated water molecule whose dipole is rigidly constrained. Its free energy suggests a Hamiltonian for dipole fluctuations that accounts implicitly for the influence of higher-order multipole moments while respecting constraints of molecular geometry. Finally, we propose a field theory with the suggested form, whose nonlinear response breaks the charge symmetry of ion solvation. An approximate variational solution of this theory, with a single adjustable parameter, yields solvation free energies that agree closely with simulation results over a considerable range of solute size and charge.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Heterogeneous and Framework-Bound Copper Species Contribute to Catalytic Partial Methane Oxidation in Cu–Chabazite Zeolites

The relationship between continuous partial methane oxidation (PMO) rates and Cu site speciation in Cu-CHA zeolite catalysts is explored through differential rate measurements across a series of samples of varying compositions combined with density functional theory, first-principles thermodynamics, and statistical models that characterize Cu speciation. Under continuous PMO conditions (573 K, 0.07 kPa O 2 , 3 kPa H 2 O), Cu ions are shown to anchor to the CHA framework in both monomeric (Z 2 Cu and Z 2 CuH 2 O) and dimeric (O- and OH-bridged Cu) forms that are sensitive to the identity of the local framework anchoring site. Consequently, across the studied compositional range, Cu-CHA catalysts are predicted to contain a mixture of monomeric and dimeric Cu sites. Cu-normalized CH 3 OH formation rates extrapolated to zero conversion reflect contributions from multiple site types. Predicted CH 3 OH formation rates indicate that the Cu site reactivity toward CH 4 is influenced by zeolite composition and is likely limited by the reduction half-cycle.

03 NATURAL GAS↗

Finite-temperature many-body perturbation theory for electrons: Algebraic recursive definitions, second-quantized derivation, linked-diagram theorem, general-order algorithms, and grand canonical and canonical ensembles

A comprehensive and detailed account is presented for the finite-temperature many-body perturbation theory for electrons that expands in power series all thermodynamic functions on an equal footing. Algebraic recursions in the style of the Rayleigh–Schrödinger perturbation theory are derived for the grand potential, chemical potential, internal energy, and entropy in the grand canonical ensemble and for the Helmholtz energy, internal energy, and entropy in the canonical ensemble, leading to their sum-over-states analytical formulas at any arbitrary order. For the grand canonical ensemble, these sum-over-states formulas are systematically transformed to sum-over-orbitals reduced analytical formulas by the quantum-field-theoretical techniques of normal-ordered second quantization and Feynman diagrams extended to finite temperature. It is found that the perturbation corrections to energies entering the recursions have to be treated as a nondiagonal matrix, whose off-diagonal elements are generally nonzero within a subspace spanned by degenerate Slater determinants. They give rise to a unique set of linked diagrams—renormalization diagrams—whose resolvent lines are displaced upward, which are distinct from the well-known anomalous diagrams of which one or more resolvent lines are erased. A linked-diagram theorem is introduced that proves the size-consistency of the finite-temperature many-body perturbation theory at any order. General-order algorithms implementing the recursions establish the convergence of the perturbation series toward the finite-temperature full-configuration-interaction limit unless the series diverges. As a result, the normal-ordered Hamiltonian at finite temperature sheds light on the relationship between the finite-temperature Hartree–Fock and first-order many-body perturbation theories.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

The role of rotation-vibration coupling in symmetric and asymmetric isotopomers of ozone

A theoretical framework and a computer code (SpectrumSDT) are developed for accurate calculations of coupled rotational–vibrational states in triatomic molecules using hyper-spherical coordinates and taking into account the Coriolis coupling effect. Concise final formulas are derived for the construction of the Hamiltonian matrix using an efficient combination of the variational basis representation and discrete variable representation methods with locally optimized basis sets and grids. First, the new code is tested by comparing its results with those of the APH3D program of Kendrick et al. [Kendrick, Pack, Walker, and Hayes, J. Chem. Phys. 110, 6673 (1999)]. Then, accurate calculations of the rovibrational spectra are carried out for doubly substituted symmetric ( 18 O 16 O 18 O) and asymmetric ( 18 O 18 O 16 O) ozone isotopomers for the total angular momentum up to J = 5. Together with similar data recently reported for the singly substituted symmetric ( 16 O 18 O 16 O) and asymmetric ( 16 O 16 O 18 O) ozone isotopomers, these calculations quantify the role of the Coriolis coupling effect in the large mass-independent isotopic enrichment of ozone, observed in both laboratory experiments and the atmosphere of the Earth. It is found that the Coriolis effect in ozone is relatively small, as evidenced by deviations of its rotational constants from the symmetric-top-rotor behavior, magnitudes of parity splittings (Λ-doubling), and ratios of rovibrational partition functions for asymmetric vs symmetric ozone molecules. It is concluded that all of these characteristics are influenced by the isotopic masses as much as they are influenced by the overall symmetry of the molecule. It is therefore unlikely that the Coriolis coupling effect could be responsible for symmetry-driven mass-independent fractionation of oxygen isotopes in ozone.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Controlling the dopant profile for SRH suppression at low current densities in λ ≈ 1330 nm GaInAsP light-emitting diodes

The quantum efficiency of double hetero-junction light-emitting diodes (LEDs) can be significantly enhanced at low current density by tailoring the spatial profile of dopants to suppress Shockley–Read–Hall recombination. To demonstrate this effect, we model, design, grow, fabricate, and test a GaInAsP LED (λ≈ 1330 nm) with an unconventional dopant profile. Compared against that of our control design, which is a conventional n + -n - p + double hetero-junction LED, the dopant profile near the n - p + hetero-structure of the design displaces the built-in electric field in such a way that the J 02 space charge recombination current is suppressed. The design principle generalizes to other material systems and could be applicable to efforts to observe and exploit electro-luminescent refrigeration at practical power densities.

42 ENGINEERING↗

Efficient Langevin dynamics for “noisy” forces

Efficient Boltzmann-sampling using first-principles methods is challenging for extended systems due to the steep scaling of electronic structure methods with the system size. Additionally, stochastic approaches provide a gentler system-size dependency at the cost of introducing “noisy” forces, which could limit the efficiency of the sampling. When the forces are deterministic, the first-order Langevin dynamics (FOLD) offers efficient sampling by combining a well-chosen preconditioning matrix S with a time-step-bias-mitigating propagator [G. Mazzola and S. Sorella, Phys. Rev. Lett. 118, 015703 (2017)]. However, when forces are noisy, S is set equal to the force-covariance matrix, a procedure that severely limits the efficiency and the stability of the sampling. Here, we develop a new, general, optimal, and stable sampling approach for FOLD under noisy forces. We apply it for silicon nanocrystals treated with stochastic density functional theory and show efficiency improvements by an order-of-magnitude.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The concept of spin ice graphs and a field theory for their charges

Originally detected in rare earth pyrochlores, spin ice physics is now being artificially extended to a variety of geometries that control collective behavior and exotic properties, making graph theory their proper framework. We relate spin ice notions, such as ice rule, ice manifold, Coulomb phases, charges, and monopoles, to graph-theoretical notions, such as balance, in/out-degrees, and Euler paths. We then propose a field-theoretical treatment in which topological charges and monopoles are the degrees of freedom, while the binary spins are subsumed in an entropic interaction among charges. We show that for a spin ice on a graph in a Gaussian approximation, the kernel of the entropic interaction is the inverse of the graph Laplacian, and we compute screening functions from the graph spectra as Green operators for the screened Poisson problem on a graph. We then apply the treatment to star graphs, tournaments, cycles, and regular spin ice in different dimensions. Our aim is twofold: to set spin ice physics in a proper graph setting, where only topological rather than geometrical notions hold, and to invite graph theorists to contribute their powerful tools to the field of spin ice.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Machine learning prediction of self-diffusion in Lennard-Jones fluids

In this work, different machine learning (ML) methods were explored for the prediction of self-diffusion in Lennard-Jones (LJ) fluids. Using a database of diffusion constants obtained from the molecular dynamics simulation literature, multiple Random Forest (RF) and Artificial Neural Net (ANN) regression models were developed and characterized. The role and improved performance of feature engineering coupled to the RF model development was also addressed. The performance of these different ML models was evaluated by comparing the prediction error to an existing empirical relationship used to describe LJ fluid diffusion. It was found that the ANN regression models provided superior prediction of diffusion in comparison to the existing empirical relationships.

74 ATOMIC AND MOLECULAR PHYSICS↗

Wave function methods for canonical ensemble thermal averages in correlated many-fermion systems

We present a wave function representation for the canonical ensemble thermal density matrix by projecting the thermofield double state against the desired number of particles. Furthermore, the resulting canonical thermal state obeys an imaginary-time evolution equation. Starting with the mean-field approximation, where the canonical thermal state becomes an antisymmetrized geminal power (AGP) wave function, we explore two different schemes to add correlation: by number-projecting a correlated grand-canonical thermal state and by adding correlation to the number-projected mean-field state. As benchmark examples, we use number-projected configuration interaction and an AGP-based perturbation theory to study the hydrogen molecule in a minimal basis and the six-site Hubbard model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Electronic structure and optical properties of quantum crystals from first principles calculations in the Born–Oppenheimer approximation

In this work, we develop a formalism to accurately account for the renormalization of the electronic structure due to quantum and thermal nuclear motions within the Born–Oppenheimer approximation. We focus on the fundamental energy gap obtained from electronic addition and removal energies from quantum Monte Carlo calculations in either the canonical or grand-canonical ensembles. The formalism applies as well to effective single electron theories such as those based on density functional theory. We show that the electronic (Bloch) crystal momentum can be restored by marginalizing the total electron–ion wave function with respect to the nuclear equilibrium distribution, and we describe an explicit procedure to establish the band structure of electronic excitations for quantum crystals within the Born–Oppenheimer approximation. Based on the Kubo–Greenwood equation, we discuss the effects of nuclear motion on optical conductivity. Our methodology applies to the low temperature regime where nuclear motion is quantized and, in general, differs from the semi-classical approximation. We apply our method to study the electronic structure of C2/c-24 crystalline hydrogen at 200 K and 250 GPa and discuss the optical absorption profile of hydrogen crystals at 200 K and carbon diamond at 297 K.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Unfolding bovine α-lactalbumin with T-jump: Characterizing disordered intermediates via time-resolved x-ray solution scattering and molecular dynamics simulations

The protein folding process often proceeds through partially folded transient states. Therefore, a structural understanding of these disordered states is crucial for developing mechanistic models of the folding process. Characterization of unfolded states remains challenging due to their disordered nature, and incorporating multiple methods is necessary. Combining the time-resolved x-ray solution scattering (TRXSS) signal with molecular dynamics (MD), we are able to characterize transient partially folded states of bovine α-lactalbumin, a model system widely used for investigation of molten globule states, during its unfolding triggered by a temperature jump. We track the unfolding process between 20 μs and 70 ms and demonstrate that it passes through three distinct kinetic states. The scattering signals associated with these transient species are then analyzed with TRXSS constrained MD simulations to produce protein structures that are compatible with the input signals. Without utilizing any experimentally extracted kinetic information, the constrained MD simulation successfully drove the protein to an intermediate molten globule state; signals for two later disordered states are refined to terminal unfolded states. From our examination of the structural characteristics of these disordered states, we discuss the implications disordered states have on the folding process, especially on the folding pathway. Finally, we discuss the potential applications and limitations of this method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Prototype equation of state for phase transition of confined fluids based on the generalized van der Waals partition function

A simple self-consistent prototype equation of state (EOS) based on the Generalized van der Waals (vdW) partition function has been demonstrated to describe the phase transition of simple fluids in nanopores with uniform size. Different from those commonly presented in the literature, the new EOS does not need an auxiliary equation that is conventionally applied to provide the capillary pressure derived from surface tension. Lastly, the encouraging performance of the EOS calls for further extension to applications with more complex fluids and porous media.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Inverse design of equilibrium cluster fluids applied to a physically informed model

Inverse design strategies have proven highly useful for the discovery of interaction potentials that prompt self-assembly of a variety of interesting structures. However, often the optimized particle interactions do not have a direct relationship to experimental systems. In this work, we show that Relative Entropy minimization is able to discover physically meaningful parameter sets for a model interaction built from depletion attraction and electrostatic repulsion that yield self-assembly of size-specific clusters. Here, we then explore the sensitivity of the optimized interaction potentials with respect to deviations in the underlying physical quantities, showing that clustering behavior is largely preserved even as the optimized parameters are perturbed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗