Thermodynamic Equilibrium Distribution Research Articles

Reply to "Comment on 'Validity of path thermodynamic description of reactive systems: Microscopic simulations'".

The Comment's author argues that a correct description of reactive systems should incorporate an explicit interaction with reservoirs, leading to a unified system-reservoir entity. However, this proposition has two major flaws. First, as we will emphasize, this entity inherently follows a thermodynamic equilibrium distribution. In the Comment, no indication is provided on how to maintain such a system-reservoir entity in a nonequilibrium state. Second, contrary to the author's claim, the inclusion of a system-reservoir interaction in the traditional stochastic modeling of reactive systems does not automatically alter the limited applicability of path thermodynamics to problematic reactive systems. We will provide a simple demonstration to illustrate that certain elementary reactions may not involve any changes in reservoir components, which seem to have been overlooked by the author.

Operation of Rh/Ce0.75Zr0.25O2-δ-ƞ-Al2O3/FeCrAl wire mesh honeycomb catalytic modules in diesel steam and autothermal reforming

The Rh/Ce0·75Zr0·25O2–δ-ƞ-Al2O3/FeCrAl structured catalytic blocks of length 10, 20, and 60 mm were prepared and tested in the reactions of steam and autothermal reforming of n-hexadecane. It was found in a series of experiments on hexadecane steam reforming with the catalyst heating solely through the reactor wall that the complete conversion of hexadecane at a furnace temperature below 750 °C was not achieved even at GHSV = 10,000 h−1. Under these conditions, the formation of carbon on the catalyst surface was observed. At the reactor wall temperature of 800 °C, the complete conversion of hexadecane was achieved even in the 10 mm long catalytic block (GHSV = 60,000 h−1), accompanied by the formation of various intermediate light hydrocarbons. To achieve complete conversion of these intermediate compounds (mainly 1-alkenes), it is necessary to carry out the steam reforming reaction at GHSV = 10,000 h−1. At hexadecane autothermal reforming, heat is supplied to the reaction zone by exothermic oxidation reaction, which makes this process more efficient. In experiments with the use of additional external heat supply through the reactor wall, complete conversion of hexadecane occurred at GHSV = 120,000 h−1. To convert all by-products (mainly 1-alkenes) and achieve a nearly thermodynamic equilibrium distribution of the main reaction products (H2, CO, CO2), the reaction should be carried out at GHSV = 20,000 h−1. Without external heat supply, hexadecane conversion decreased, while the content of light hydrocarbons in the reaction products increased. An increase in the inlet amount of oxygen helps to compensate the heat losses in the reactor and to increase the efficiency of hexadecane autothermal reforming. The performed experiments allow better understanding of the processes which occur during the steam and autothermal reforming of diesel.

Thermal Field Simulation of Ag Nanoparticles Induced by Femtosecond Laser

The thermal field distribution of Ag nanoparticles induced by femtosecond laser is calculated by using two-temperature equation in this paper, and its characteristics of Ag nanoparticles with single layered and multi-layered were compared and analyzed. It is found that there will be a local “hot spot” in the electromagnetic coupling region of adjacent particles, because of the electron tunneling effect and the plasma model for electron transfer, the temperature gradient in this region shows a trend of increasing at the beginning and then decreasing. The influence of the thermal field mainly comes from two aspects, one is the electromagnetic coupling of the plasmon mode, the other is the “cumulative effect” of temperature, and with the increase of irradiation time, the influence of the laser energy accumulation becomes more and more obvious on the thermal field distribution. At the same time, the results show that the smaller Ag nanoparticles will have higher temperature and temperature gradient with the same laser energy. It is also found that the electron and lattice temperature of Ag nanoparticles will reach the thermodynamic equilibrium distribution in 20 to 30 picoseconds.

DICE: A Monte Carlo Code for Molecular Simulation Including the Configurational Bias Monte Carlo Method

Solute-solvent systems are an important topic of study, as the effects of the solvent on the solute can drastically change its properties. Theoretical studies of these systems are done with ab initio methods, molecular simulations, or a combination of both. The simulations of molecular systems are usually performed with either molecular dynamics (MD) or Monte Carlo (MC) methods. Classical MD has evolved much in the last decades, both in algorithms and implementations, having several stable and efficient codes developed and available. Similarly, MC methods have also evolved, focusing mainly in creating and improving methods and implementations in available codes. In this paper, we provide some enhancements to a configurational bias Monte Carlo (CBMC) methodology to simulate flexible molecules using the molecular fragments concept. In our implementation the acceptance criterion of the CBMC method was simplified and a generalization was proposed to allow the simulation of molecules with any kind of fragments. We also introduce the new version of DICE, an MC code for molecular simulation (available at https://portal.if.usp.br/dice). This code was mainly developed to simulate solute-solvent systems in liquid and gas phases and in interfaces (gas-liquid and solid-liquid) that has been mostly used to generate configurations for a sequential quantum mechanics/molecular mechanics method (S-QM/MM). This new version introduces several improvements over the previous ones, with the ability of simulating flexible molecules with CBMC as one of them. Simulations of well-known molecules, such as n-octane and 1,2-dichloroethane in vacuum and in solution, are presented to validate the new implementations compared with MD simulations, experimental data, and other theoretical results. The efficiency of the conformational sampling was analyzed using the acceptance rates of different alkanes: n-octane, neopentane, and 4-ethylheptane. Furthermore, a very complex molecule, boron subphtalocyanine, was simulated in vacuum and in aqueous solution showing the versatility of the new implementation. We show that the CBMC is a very good method to perform conformation sampling of complex moderately sized molecules (up to 150 atoms) in solution following the Boltzmann thermodynamic equilibrium distribution.

Thermodynamic Equilibrium Analysis of Product Distribution in the Fischer–Tropsch Process Under Different Operating Conditions

Thermodynamic equilibrium analysis is necessary to provide a fundamental understanding of the distribution of the products formed in the Fischer–Tropsch process. The thermodynamic equilibrium distribution of the products formed at constant temperature and pressure was studied based on the minimization of the total Gibbs free energy of the system. The effects of temperature, pressure, and feed ratio on the product distribution were investigated under typical operating conditions. The distribution of the total products obtained from the reactions of added ethylene or ethanol was also studied. The results indicated that the products formed in a state of thermodynamic equilibrium follow Anderson–Schulz–Flory’s general polymerization distribution at carbon numbers greater than about three. Both olefins and paraffins are primary products and there are essentially no alcohol and water at high degrees of conversion when the conditions for thermodynamic equilibrium are satisfied. The olefins formed in the Fischer–Tropsch process consist essentially of propylene. The product distribution is very sensitive to feed composition, and to temperature and pressure to a lesser extent. The product spectrum can be described broadly by the probability of chain growth relative to chain termination. This parameter decreases with increasing temperature, the feed ratio of hydrogen to carbon monoxide, and after the addition of ethanol to the feed, but increases with increasing pressure and after the addition of ethylene to the feed. An increase in reaction temperature results in a shift in selectivity towards low carbon number hydrocarbons and more hydrogenated products.

Search for H3+ isotopologues toward CRL 2136 IRS 1

Context. Deuterated interstellar molecules frequently have abundances relative to their main isotopologues much higher than the overall elemental D-to-H ratio in the cold dense interstellar medium. H3+ and its isotopologues play a key role in the deuterium fractionation; however, the abundances of these isotopologues have not been measured empirically with respect to H3+ to date. Aims. Our aim was to constrain the relative abundances of H2D+ and D3+ in the cold outer envelope of the hot core CRL 2136 IRS 1. Methods. We carried out three observations targeting H3+ and its isotopologues using the spectrographs CRIRES at the VLT, iSHELL at IRTF, and EXES on board SOFIA. In addition, the CO overtone band at 2.3 μm was observed by iSHELL to characterize the gas on the line of sight. Results. The H3+ ion was detected toward CRL 2136 IRS 1 as in previous observations. Spectroscopy of lines of H2D+ and D3+ resulted in non-detections. The 3σ upper limits of N(H2D+)/N(H3+) and N(D3+)/N(H3+) are 0.24 and 0.13, respectively. The population diagram for CO is reproduced by two components of warm gas with the temperatures 58 and 530 K, assuming a local thermodynamic equilibrium (LTE) distribution of the rotational levels. Cold gas (<20 K) makes only a minor contribution to the CO molecular column toward CRL 2136 IRS 1. Conclusions. The critical conditions for deuterium fractionation in a dense cloud are low temperature and CO depletion. Given the revised cloud properties, it is no surprise that H3+ isotopologues are not detected toward CRL 2136 IRS 1. The result is consistent with our current understanding of how deuterium fractionation proceeds.

Molecular Mechanism for Gramicidin Dimerization and Dissociation in Bilayers of Different Thickness

Membrane protein functions can be altered by subtle changes in the host lipid bilayer physical properties. Gramicidin channels have emerged as a powerful system for elucidating the underlying mechanisms of membrane protein function regulation through changes in bilayer properties, which are reflected in the thermodynamic equilibrium distribution between nonconducting gramicidin monomers and conducting bilayer-spanning dimers. To improve our understanding of how subtle changes in bilayer thickness alter the gramicidin monomer and dimer distributions, we performed extensive atomistic molecular dynamics simulations and fluorescence-quenching experiments on gramicidin A (gA). The free-energy calculations predicted a nonlinear coupling between the bilayer thickness and channel formation. The energetic barrier inhibiting gA channel formation was sharply increased in the thickest bilayer (1,2-dierucoyl-sn-glycero-3-phosphocholine). This prediction was corroborated by experimental results on gramicidin channel activity in bilayers of different thickness. To further explore the mechanism of channel formation, we performed extensive unbiased molecular dynamics simulations, which allowed us to observe spontaneous gA dimer formation in lipid bilayers. The simulations revealed structural rearrangements in the gA subunits and changes in lipid packing, as well as water reorganization, that occur during the dimerization process. Together, the simulations and experiments provide new, to our knowledge, insights into the process and mechanism of gramicidin channel formation, as a prototypical example of the bilayer regulation of membrane protein function.

Relativistic kinetic theory for spin-1/2 particles: Conservation laws, thermodynamics, and linear waves.

We study a recently derived fully relativistic kinetic model for spin-1/2 particles. First, the full set of conservation laws for energy, momentum, and angular momentum are given together with an expression for the (nonsymmetric) stress-energy tensor. Next, the thermodynamic equilibrium distribution is given in different limiting cases. Furthermore, we address the analytical complexity that arises when the spin and momentum eigenfunctions are coupled in linear theory by calculating the linear dispersion relation for such a case. Finally, we discuss the model and give some context by comparing with potentially relevant phenomena that are not included, such as radiation reaction and vacuum polarization.

On the Thermodynamic Equilibrium Distribution of a Charge in a Homogeneous Chain with a Defect

Based on the semi-classical Holstein Hamiltonian we consider charge transfer along a DNA chain of sites at different thermostat temperatures. Recently, using the computer simulation, it has been shown that the charge distribution in homogeneous chains in thermodynamic equilibrium depends not only on the temperature, but also on the length of the chain. We have studied numerically the case of polyadenine fragments with a defect site in the middle of the chain. The results demonstrate qualitatively similar behavior of thermodynamic equilibrium quantities in the case of the homogeneous chain and of the chain with a defect. Insertion of a trap-site enhances the stability of polaron states.

Benzene alkylation with methanol over phosphate modified hierarchical porous ZSM-5 with tailored acidity

Abstract The acidity and acid distribution of hierarchical porous ZSM-5 were tailored via phosphate modification. The catalytic results showed that both benzene conversion and selectivity of toluene and xylene increased with the presence of appropriate amount of phosphorus. Meanwhile, side reactions such as methanol to olefins related with the formation of by-product ethylbenzene formation and isomerization of xylene to meta -xylene were suppressed efficiently. The acid strength and sites amount of Bronsted acid of the catalyst were crucial for improving benzene conversion and yield of xylene, whereas passivation of external surface acid sites played an important role in breaking thermodynamic equilibrium distribution of xylene isomers.

Thermodynamic equilibrium distribution of light olefins in catalytic pyrolysis

Catalytic pyrolysis is a promising technology to produce light olefins. Gibbs free-energy minimization method was used to study the thermodynamic equilibrium distribution of olefins in catalytic pyrolysis with Aspen Plus software. The result showed that olefin systems with different carbon numbers demonstrated a similar thermodynamic equilibrium distribution. The ethene equilibrium composition increased with increasing reaction temperature and decreased with increasing total hydrocarbon pressure. By contrast, the propene equilibrium composition reached a maximum of 40wt% at 850–950K under 0.1MPa. Ethene yield and propene yield of thermodynamic equilibrium, catalytic pyrolysis and thermal pyrolysis were compared. The use of catalyst greatly increased the yields of ethene and propene, but the yields were still lower than the equilibrium data. Catalytic pyrolysis was carried out in the interaction zone where both catalytic conversion and thermal conversion were important. Propene yield was close to ethene yield at about 950K from the thermodynamic view. Given the shape-selective effect of the catalyst on branched olefins with large carbon number, the equilibrium carbon number distribution of olefins possibly shifted from large carbon numbers to low carbon numbers, resulting in enhanced ethene and propene yields.

Oxygen, α-element and iron abundance distributions in the inner part of the Galactic thin disc★†

We derived elemental abundances in 27 Cepheids, the great majority situated within a zone of Galactocentric distances ranging from 5 to 7 kpc. One star of our sample, SU Sct, has a Galactocentric distance of about 3 kpc, and thus falls in a poorly investigated region of the inner thin disc. Our new results, combined with data on abundances in the very central part of our Galaxy taken from the literature, show that iron, magnesium, silicon, sulphur, calcium and titanium local thermodynamic equilibrium abundance radial distributions, as well as non-local thermodynamic equilibrium distribution of oxygen reveal a plateau-like structure or even positive abundance gradient in the region extending from the Galactic Centre to about 5 kpc.

Invariant solutions for the nonlinear diffusion model of turbulence

We study Leith’s model of turbulence represented by a nonlinear degenerate diffusion equation (Leith 1967 Phys. Fluids 10 1409–16, Connaughton and Nazarenko 2004 Phys. Rev. Lett. 92 044501–506). The model is constructed such that in the case of vanishing viscosity, there are two steady-state solutions: the Kolmogorov spectrum that corresponds to the cascade state and a thermodynamic equilibrium distribution. Using group analysis, we have obtained integral equations which describe allessentially different invariant solutions of the Leith equation with or without viscosity. The integral equations defining these solutions reveal new possibilities for analytical and numerical studies. In these equations, the presence of arbitrary constants allows one to solve them for different boundary conditions. We have proved existence and uniqueness for such boundary value problems.

Kinetic Description of Random Optical Waves and Anomalous Thermalization of a Nearly Integrable Wave System

This article is composed of two parts. The first part is aimed at providing an overview on the kinetic description of random nonlinear waves considering the one-dimensional nonlinear Schr¨odinger (NLS) equation as a representative model of optical wave propagation. We expose, in particular, the key problem of achieving a closure of the infinite hierarchy of moment equations for the random field. The hierarchy is closed at the first order when the statistics of the random wave is non-stationary or when the response time of the nonlinearity is non-instantaneous, which, respectively, leads to the Vlasov kinetic equation and the weak-Langmuir turbulence equation. When the amount of nonstationary statistics is comparable to the amount of non-instantaneous nonlinearity, we derive a generalized Vlasov-Langmuir equation that provides a unified formulation of the Vlasov and Langmuir approaches. On the other hand, when the statistics of the random wave is stationary and the nonlinear response instantaneous, the closure of the hierarchy of moment equations requires a second-order perturbation expansion procedure, which leads to the Hasselmann (or wave turbulence) kinetic equation. Contrarily to the Vlasov and Langmuir equations, the Hasselmann equation is irreversible, a feature which is expressed by a H-theorem of entropy growth that describes wave thermalization toward the thermodynamic equilibrium distribution, i.e. the Rayleigh-Jeans (RJ) spectrum. In the second part of the paper, we discuss a process of anomalous thermalization by considering the example of the scalar NLS equation whose integrability is broken by the presence of third-order dispersion. The anomalous thermalization is characterized by an irreversible evolution of the wave toward an equilibrium state of a fundamental different nature than the conventional RJ equilibrium state. The wave turbulence kinetic equation reveals that the anomalous thermalization is due to the existence of a local invariant in frequency space Jω, which originates in degenerate resonances of the system. In contrast to integral invariants that lead to a generalized RJ distribution, here, it is the local nature of the invariant Jω that makes the new equilibrium states fundamentally different than the usual RJ equilibrium states. We study in detail the anomalous thermalization by means of numerical simulations of the NLS equation and of the wave turbulence equation by using an improved criterion of applicability of the kinetic theory. The spectrum of the field is shown to exhibit an intriguing asymmetric deformation, which is characterized by the unexpected emergence of a constant spectral pedestal in the long-term evolution of the field. It turns out that the local invariant Jω explains all the essential properties of the anomalous thermalization of the wave.

Analyticity for Some Operator Functions from Statistical Quantum Mechanics

For rather general thermodynamic equilibrium distribution functions the density of a statistical ensemble of quantum mechanical particles depends analytically on the potential in the Schrodinger operator describing the quantum system. A key to the proof is that the resolvent to a power less than one of an elliptic operator with non-smooth coefficients, and mixed Dirichlet/Neumann boundary conditions on a bounded up to three-dimensional Lipschitz domain boundedly maps the space of square integrable functions to the space of essentially bounded functions.

Monotonicity properties of the quantum mechanical particle density: an elementary proof

The negative quantum mechanical particle density in its dependence on the potential in the Hamiltonian is a nonlinear operator. We give an explicit proof of the monotonicity of this operator for a large class of admissible thermodynamic equilibrium distribution functions. In particular the zero temperature case is included.

H-MCM-22 zeolitic catalysts modified by chemical liquid deposition for shape-selective disproportionation of toluene

Catalysts were prepared by dealumination of H-MCM-22 zeolite with oxalic acid leaching, followed by shaping and liquid phase modification with siloxane. The catalytic performance was measured with selective disproportionation of toluene in a fixed-bed reactor. The unmodified H-MCM-22 zeolite exhibited much higher initial activity than H-ZSM-5 with a thermodynamic equilibrium distribution of xylene products. The oxalic acid treatment of H-MCM-22 improved the selectivity for para-xylene by 10–18%. The modification by siloxane of the oxalic acid treated H-MCM-22 turned out to be highly selective for para-xylene, however, with the expense of the conversion. It is proposed that the high para-selectivity was closely associated with the contraction of micropore windows and the elimination of acid sites at the external surface by the deposited silica. Therefore, the modified H-MCM-22 is a potential catalyst for the selective disproportionation of toluene with a high para-selectivity.

Stability and band gaps of As‐rich and N‐rich GaAsN alloys: Density‐functional supercell calculations

AbstractTotal energies and band gap energies of cubic cells with various arrangements of Ga32As32−nNn (n = 0–8 and n = 28–32 corresponding to 0.0–25.0% N and 12.5–0.0% As) are calculated using the density‐functional supercell method. In the As‐rich limit up to an exchange of 6.2% N isolated N atoms (maximum N distance) are the most stable arrangement and provide the typical reduction of the band gap energy from about 1.5 eV (GaAs) to about 1 eV caused by reduction of the N distance. For higher N content special N distributions are the most stable arrangements. GaNm clusters (m = 2–4) and isolated N atoms are less stable. The band gap remains nearly constant at about 1 eV between 6.2 and 18.8% N. The good agreement between the experimental band gap energies and ones calculated for the most stable arrangements points out that the experimental distribution of the atoms is the thermodynamic equilibrium distribution. In the N‐rich limit, linear As chains in [110] direction or fragments of them are the most stable arrangement. At 9.4% As the band gap disappears. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Kinetic Theoretical Foundation of Lorentzian StatisticalMechanics

A new kinetic theory Boltzmann-like collision term includingcorrelations is proposed. In equilibrium it yields the one-particledistribution function in the form of a generalised-Lorentzianresembling but not being identical with the so-called κdistribution frequently found in collisionless turbulent systems likespace plasmas. We show that this distribution function satisfies ageneralised H-theorem, yields an expression for the entropythat is concave. Thus, the distribution is a“true” thermodynamic equilibriumdistribution, presumably valid for turbulent systems. In equilibriumit is possible to construct the fundamental thermodynamic quantities.This is done for an ideal gas only. The new kinetic equation can formthe basis for obtaining a set of hydrodynamic conservation laws andconstruction of a generalised transport theory for strongly correlatedstates of a system.

Model for hydrogen desorption in SiGe(100) films

A model to describe hydrogen desorption from SiGe(100) that takes into account the nature of the surface bonding is presented. It is based on the presence of three dimer types in the SiGe(100) surface (Si–Si, Ge–Ge, and Si–Ge), in which there is a thermodynamic preference of hydrogen atoms to pair up before the desorption reaction. The desorption kinetics are, therefore, assumed to be controlled by the population of paired hydrogens in the three dimer types, according to a first-order law. It is also assumed that diffusion, which tends to drive the occupancy of hydrogen atoms in the dimers towards the thermodynamic equilibrium distribution, is not instantaneous. The comparison with experimental results shows that desorption is a diffusion limited process.