Thermodynamic State Variables Research Articles

“Catalyzed” nucleation: A critical review of proposed theories

In industrial-scale crystallization, secondary nucleation is the most important type of nucleation. In most cases, this phenomenon can be adequately explained as the result of mechanical forces that break existing crystallites apart, the strength of the effect being a smooth function of supersaturation and stirring vigor. However, in some special cases, crystallites of other polymorphs appear and/or no nucleation occurs except at a catastrophic rate above a supersaturation threshold, mimicking primary nucleation. In this paper, we review published theories for this latter type of secondary nucleation, for which we find contradicting explanations in the literature. We divide these explanations into two broad classes, depending on whether the secondary nucleation is mediated through local deviations of the bulk thermodynamic state variables (indirect effects) or directly through the interaction energy of the surface and growth units (direct effects). We argue that theoretical explanations of the second type are insufficient and while we can find no conclusive and theoretically consistent explanation for this well-established experimental phenomenon, it is hoped that this review will stimulate further research into this puzzle.

Thermodynamics and dynamic stability: extended theories of heat conduction

Abstract The stability of homogeneous thermodynamic equilibrium is analyzed in heat conduction theories in the framework of nonequilibrium thermodynamics, where the internal energy, the heat flux and a second order tensor are thermodynamic state variables. It is shown, that the thermodynamic conditions of concave entropy and nonnegative entropy production can ensure the linear stability. Various special heat conduction theories, including Extended Thermodynamics, are compared in the general framework.

Molecular dynamics study of the sonic horizon of microscopic Laval nozzles.

A Laval nozzle can accelerate expanding gas above supersonic velocities, while cooling the gas in the process. This work investigates this process for microscopic Laval nozzles by means of nonequilibrium molecular dynamics simulations of stationary flow, using grand-canonical Monte Carlo particle reservoirs. We study the steady-state expansion of a simple fluid, a monoatomic gas interacting via a Lennard-Jones potential, through an idealized nozzle with atomically smooth walls. We obtain the thermodynamic state variables pressure, density, and temperature but also the Knudsen number, speed of sound, velocity, and the corresponding Mach number of the expanding gas for nozzles of different sizes. We find that the temperature is well defined in the sense that the each velocity components of the particles obey the Maxwell-Boltzmann distribution, but it is anisotropic, especially for small nozzles. The velocity autocorrelation function reveals a tendency towards condensation of the cooled supersonic gas, although the nozzles are too small for the formation of clusters. Overall we find that microscopic nozzles act qualitatively like macroscopic nozzles in that the particles are accelerated to supersonic speeds while their thermal motion relative to the stationary flow is cooled. We find that, like macroscopic Laval nozzles, microscopic nozzles also exhibit a sonic horizon, which is well defined on a microscopic scale. The sonic horizon is positioned only slightly further downstream compared to isentropic expansion through macroscopic nozzles, where it is situated in the most narrow part. We analyze the sonic horizon by studying space-time density correlations, i.e., how thermal fluctuations at two positions of the gas density are correlated in time and find that after the sonic horizon there are indeed no upstream correlations on a microscopic scale.

Assessing energy fluxes and carbon use in soil as controlled by microbial activity - A thermodynamic perspective A perspective paper

Soil organic matter (SOM) plays a central role for both the C cycle and soil functions. Plants provide the input and heterotrophic (micro)organisms are essential for the turnover. Microbial metabolism links matter and energy fluxes and generates the highest energy turnover dynamics in SOM because the organisms need both energy and matter for maintenance and growth. In this perspectives paper, we evaluate the knowledge on thermodynamic approaches potentially applicable to study the turnover of organic matter in the soil system. Thermodynamics is essential for understanding organic matter turnover in soil as turnover and storage are controlled by the energy supply to, and consumption by, microbes. Instead of just comparing the heat of combustion of compounds without considering microbial anabolism, we need to apply conventional thermodynamic state variables that can be either estimated using established thermodynamic equations, or measured empirically in soil. In particular, we can follow and quantify overall changes of enthalpies by calorimetry. Here, we suggest to apply a thermodynamic concept with the related experimental approaches of calo(respiro)metry and turnover mass balances including biomass formation. This enables us to better interpret and understand the highly variable carbon use efficiency (CUE) in a multi-substrate system such as soil and to relate this to energy use efficiency (EUE). Combining the experimental measurements of the thermodynamic state variables with mass turnover data allow prediction of whether compounds can be metabolized with energy delivery to microorganisms, or be thermodynamically stabilized under the respective redox and electron acceptor conditions. Energy balancing shows how much energy is actually used and retained in the soil, how much is emitted as heat, and how much may be stabilized due to endergonic turnover reactions. Thermodynamic stabilization should therefore be considered as basic stabilization process for organic compounds in soil.

Learning thermodynamically constrained equations of state with uncertainty

Numerical simulations of high energy-density experiments require equation of state (EOS) models that relate a material’s thermodynamic state variables—specifically pressure, volume/density, energy, and temperature. EOS models are typically constructed using a semi-empirical parametric methodology, which assumes a physics-informed functional form with many tunable parameters calibrated using experimental/simulation data. Since there are inherent uncertainties in the calibration data (parametric uncertainty) and the assumed functional EOS form (model uncertainty), it is essential to perform uncertainty quantification (UQ) to improve confidence in EOS predictions. Model uncertainty is challenging for UQ studies since it requires exploring the space of all possible physically consistent functional forms. Thus, it is often neglected in favor of parametric uncertainty, which is easier to quantify without violating thermodynamic laws. This work presents a data-driven machine learning approach to constructing EOS models that naturally captures model uncertainty while satisfying the necessary thermodynamic consistency and stability constraints. We propose a novel framework based on physics-informed Gaussian process regression (GPR) that automatically captures total uncertainty in the EOS and can be jointly trained on both simulation and experimental data sources. A GPR model for the shock Hugoniot is derived, and its uncertainties are quantified using the proposed framework. We apply the proposed model to learn the EOS for the diamond solid state of carbon using both density functional theory data and experimental shock Hugoniot data to train the model and show that the prediction uncertainty is reduced by considering thermodynamic constraints.

Comparison of two enthalpic models for the thermodynamic characterization of the soil organic matter in beech and oak forests

The thermodynamic characterization of the soil organic matter could be achieved by different enthalpic models little explored for soil. This paper compares two of them for calculating the enthalpy change, the Gibbs energy change and the entropy change of the soil organic matter combustion reaction, by simultaneous differential scanning calorimetry and thermogravimetry. Soil samples were collected in beech and oak forests from different geographical areas, and at different depths to represent the L/F horizon and the mineral soil, at each sampling site. The thermodynamic state variables were calculated using two different enthalpic models, to examine how they differed in relation to different types of SOM and different forest ecosystems. Both models yielded thermodynamic variables, which although closely and significantly correlated, were statistically significantly different. All the thermodynamic variables depended on the different forest types and the different nature of the soil organic matter under study. Results allowed to discern which of the models applied better to the SOM combustion reaction designed.

Developing a thermodynamic model for the circulating air using an opaque system

AbstractThe paper focuses on energy modelling that involves a concatenated structure of a linear time‐invariant system. A block‐structured (BS) technique was adopted for a nonlinear system identification. Using the superimposition principle, the model mapped the thermodynamic state variables as an indirect function of time to the output function. The available energy and degradation of solar radiation are determined through a black box model. For testing and validation purposes, a solar collector with recirculating air was considered. The basic principle is to establish a relation between state variables and the performance parameters, without invoking the conventional thermodynamic relationship between them. The output of the model was compared with the validation data to ensure whether or not there was any affinity between them. The sigmoidal, wavenet, and polynomial forms of nonlinearity provided a good fit to the experimental dataset. The mean absolute percentage error encountered while estimating the collector efficiency was noticed to vary from −4.85 × 10−03% to 1.22 × 10−03%. Similarly, it falls in the domain of −4.73 × 10−04% to 7.78 × 10−02% for the second law efficiency. The maximum heat loss rate (BS model) obtained across the first and second passages of the solar air collector was 235.41 and 218.19 W at the air mass flow rate of 8.10 g/s, which is congruent to the validation dataset.

Momentum work and the energetic foundations of physics. IV. The essence of heat, entropy, enthalpy, and Gibbs free energy

Momentum work enables a complete shift from kinematics to dynamics. This involves changes in the very fundamentals of physics, not only in mechanics, statistical mechanics, and special relativity, as shown in Papers I–III [G. Kalies and D. D. Do, AIP Adv. 13(6), 065121 (2023); G. Kalies, D. D. Do, and S. Arnrich, AIP Adv. 13(5), 055317 (2023); and G. Kalies and D. D. Do, AIP Adv. (in press) (2023)] of this series, but also in thermodynamics. In this paper, we challenge the narrative that classical phenomenological thermodynamics is completed and show that it represents an efficient interim solution that hides essential information. The essence of heat transfer and entropy is revealed, and an answer is given to the question of why entropy had to remain abstract and elusive in the past. Furthermore, we uncover the specific forms of energy behind thermodynamic state variables, such as enthalpy, Helmholtz free energy, and Gibbs free energy, which play a central role in describing chemical reactions and phase transitions. We thereby lay the foundation for thermodynamics to evolve from a framework theory valid for macroscopic systems to vivid quantum-process thermodynamics.

Space-time variational material modeling: a new paradigm demonstrated for thermo-mechanically coupled wave propagation, visco-elasticity, elasto-plasticity with hardening, and gradient-enhanced damage

We formulate variational material modeling in a space-time context. The starting point is the description of the space-time cylinder and the definition of a thermodynamically consistent Hamilton functional which accounts for all boundary conditions on the cylinder surface. From the mechanical perspective, the Hamilton principle then yields thermo-mechanically coupled models by evaluation of the stationarity conditions for all thermodynamic state variables which are displacements, internal variables, and temperature. Exemplary, we investigate in this contribution elastic wave propagation, visco-elasticity, elasto-plasticity with hardening, and gradient-enhanced damage. Therein, one key novel aspect are initial and end time velocity conditions for the wave equation, replacing classical initial conditions for the displacements and the velocities. The motivation is intensively discussed and illustrated with the help of a prototype numerical simulation. From the mathematical perspective, the space-time formulations are formulated within suitable function spaces and convex sets. The unified presentation merges engineering and applied mathematics due to their mutual interactions. Specifically, the chosen models are of high interest in many state-of-the art developments in modeling and we show the impact of this holistic physical description on space-time Galerkin finite element discretization schemes. Finally, we study a specific discrete realization and show that the resulting system using initial and end time conditions is well-posed.

Energy saving through modifications of the parallel pump schedule at a pumping station: A case study

Diverse state-of-the-art methods can be utilized to reduce energy consumption in water supply and distribution systems, including using high-efficiency equipment, shifting energy use away from peak demand times, energy recovery and storage devices, and renewable energy. However, the benefit of using high efficiency equipment can sometimes never be completely realized, as the performance of the individual pumps within a site can be reduced from optimal owing to a variety of reasons: a lower operating rate of the water treatment plant than the design flow rate, hydraulic conditions such as pipeline resistance or determined pressure, and pump scheduling. This research focused on optimizing pump scheduling through real-time monitoring utilizing smart temperature and pressure sensors, wireless low-power data communicators, and a pump data analysis algorithm to determine the hydraulic efficiency from thermodynamic state variables with subsequent parallel pump optimization. Thermodynamic pump performance measurements provided real-time information, including flow rate, specific power, and pump efficiency, in both individual and parallel pump operations. Evaluation of the specific power under diverse parallel pump operation scenarios demonstrated a variation of 0.115–0.140 kWh/m3 in the range of 7800–10,100 m3/h. However, the deviation in specific power was more than 17 % when operating at less than 7800 m3/h and more than 10,000 m3/h. The summary of the pump combination operation suggested that energy could be saved by up to 15 % by optimum pump scheduling, that is, small capital investment, simple optimization of control through thermodynamic state variable measurement, analysis, and feedback.

Convective drying of wood chips: Accelerating coupled DEM-CFD simulations with parametrized reduced single particle models

The simulation of industry-scale reactive bulks is challenging due to the complex interaction between fluid and particles. The particles in the bulk and their interaction with the fluid flow can be described by combined Discrete Element Method - Computational Fluid Dynamics (DEM-CFD) models. However, the computational cost of the Finite Volume (FV) methods deployed in these models can become prohibitively expensive, especially for high inner-particle resolution. Single particle Reduced Models (RMs) can be used to achieve both fast and accurate descriptions of the processes in each particle. As an example of bulk systems comprising heat and mass transfer, we compared FV and RM simulations for the drying of wood chips in a bulk reactor. A manifold-based nonlinear interpolation was applied to resolve changing boundary conditions for the RM. Our simulations showed that RMs provide accurate values for the thermodynamic state variables of the particles. Furthermore, the time required for the bulk simulation was reduced by 67% with the RMs. It is evident that simulations with high inner-particle resolution can be accelerated by RMs if manifold-based nonlinear interpolation is used to address changing boundary conditions.

Prediction of equations of state of molecular liquids by an artificial neural network.

In this work an artificial neural network (ANN) was used to determine the pressure and internal energy equations of state of noble gases and some molecular liquids by predicting thermodynamic state variables like density and temperature encoded in the radial distribution function. The ANN is trained to predict the thermodynamic state variables using only the structural data. Then, predicted values are used to compute equations of state of real liquids such as argon, neon, krypton and xenon as well as some molecular liquids like nitrogen, carbon dioxide, methane and ethylene. In order to assess the ANN predictions the relative percentage error with the exact values were determined, showing that its magnitude is less than 1%. Thus, the comparison between equations of state computed with the predicted variables and experimental results exhibits a very good agreement for most of the liquids studied here. Since our ANN implementation only requires the microscopic structure as an input, data incoming from experiments, theoretical frameworks or simulations are suitable to perform predictions of state variables and with that complement the thermodynamic characterisation of liquids through the determination of equations of state. Moreover, further improvements or extensions related with the microscopic structure database can be safely addressed without changing the neural network architecture presented here.

Learning Summary Statistics for Bayesian Inference with Autoencoders

For stochastic models with intractable likelihood functions, approximate Bayesian computation offers a way of approximating the true posterior through repeated comparisons of observations with simulated model outputs in terms of a small set of summary statistics. These statistics need to retain the information that is relevant for constraining the parameters but cancel out the noise. They can thus be seen as thermodynamic state variables, for general stochastic models. For many scientific applications, we need strictly more summary statistics than model parameters to reach a satisfactory approximation of the posterior. Therefore, we propose to use a latent representation of deep neural networks based on Autoencoders as summary statistics. To create an incentive for the encoder to encode all the parameter-related information but not the noise, we give the decoder access to explicit or implicit information on the noise that has been used to generate the training data. We validate the approach empirically on two types of stochastic models.

Thermodynamics of Soil Microbial Metabolism: Applications and Functions

The thermodynamic characterization of soils would help to study and to understand their strategies for survival, as well as defining their evolutionary state. It is still a challenging goal due to difficulties in calculating the thermodynamic state variables (enthalpy, Gibbs energy, and entropy) of the reactions taking place in, and by, soils. Advances in instrumentation and methodologies are bringing options for those calculations, boosting the interest in this subject. The thermodynamic state variables involve considering the soil microbial functions as key channels controlling the interchange of matter and energy between soil and the environment, through the concept of microbial energy use efficiency. The role of microbial diversity using the energy from the soil organic substrates, and, therefore, the who, where, with whom, and why of managing that energy is still unexplored. It could be achieved by unraveling the nature of the soil organic substrates and by monitoring the energy released by the soil microbial metabolism when decomposing and assimilating those substrates. This review shows the state of the art of these concepts and the future impact of thermodynamics on soil science and on soil ecology.

A thermodynamic description of the hysteresis in specific-heat curves in glass transitions

By refining the definition of thermodynamic equilibrium and state variables (thermodynamic coordinate, TC) for solids, it is determined that the state of a glass substance transforms into an equilibrium state after it is solidified. In contrast, the state of a glass substance during the glass transition is a nonequilibrium state. The specific-heat (C) versus temperature (T) curve exhibits hysteresis, which is traditionally believed to invalidate thermodynamic methods. However, the glass transition slowly occurs in a manner such that structural change is decoupled with the fast process of thermal relaxation of phonons, which enables us to describe the hysteresis by thermodynamic methods. The hysteresis is caused by the structural relaxation and the time of relaxation is determined by the energy barrier, which depends solely on the current value of TCs. Therefore, the state in hysteresis can be described by the information of the current structure alone: history-dependent response functions are unnecessary. On the basis of these conclusions, the behavior of the C-T curve with changing heating/cooling rate γ is simulated. The main features of the hysteresis, the shift of C to higher temperatures with increasing γ, the hump structure, and the memory effect are well reproduced from a structure-dependent energy barrier. In view of the structural dependence of the energy barrier, it is not surprising to observe deviations from the Arrhenius law. However, only the terms that are higher than linear in T are observed in Arrhenius plot as the deviation. An important finding of this study is that the apparent energy barrier obtained using the Arrhenius plot significantly overestimates the real value. The extraordinarily large values of the pre-exponential factor of the relaxation time can also be understood on this basis.

Determination of thermodynamic state variables of liquids from their microscopic structures using an artificial neural network.

In this work we implement a machine learning method to predict the thermodynamic state of a liquid using only its microscopic structure provided by the radial distribution function (RDF). The main goal is to determine the equation of state of the system. The goal is achieved by predicting the density, temperature or both at the same time using only the RDF. We implement and train a machine learning feed forward artificial neural network (ANN) to address the different cases of interest where single or simultaneous predictions are done. Due to its versatility, in this study the Lennard-Jones (LJ) fluid is used as the reference system. The ANN is trained in a wide range of densities and temperatures, covering the liquid-vapour coexistence, liquid phase and supercritical states. We show that the overall percentage relative error of most of the predictions in different cases of study is around 3%. As a practical case of study we use the ANN predictions to determine the pressure equation of state for different isotherms and we found a very good agreement with respect to the exact results. Our ANN implementation is a versatile and useful tool to predict thermodynamic state variables when some information is unknown and, consequently, to enhance the thermodynamic description of liquids.

Molecular insights into shock responses of amorphous polyethylene

Shock responses of amorphous polyethylene (APE) were characterized utilizing two different types of methodology, direct non-equilibrium molecular dynamics (NEMD) and multi-scale shock technique (MSST). Providing a detailed physical view of the shock front itself, pico-second time resolved evolution of plasticity behind the shock front was explored by NEMD through simulating piston driven shock compression. The induced-shock propagation and reflection were visualized according to the evolution of the particle displacement, particle velocity field and pressure field. Exponential relations between the compression rate in a shock wave and the hydrodynamic pressure, in addition, the thickness of shock front and the hydrodynamic pressure were clarified, which quantitatively indicate the shrinkage of shock front resulted from higher compression strength under larger piston velocity. On the other hand, in addition to reproducing the final compressed states, the thermo-dynamical state variables behind the leading shock front were captured by MSST with a much smaller computational cell with enough efficiency and accuracy. Hugoniot relations were obtained to predict the bulk sound speed and two material constants indicating the compressibility with reliable values compared with the existing results. Temperature-dependency was clarified as that high temperature reduces the bulk sound speed with low density and improves the compressibility of material. The temperature-sensitivity of compressibility weakens or even disappears during the transition from glassy state to rubbery state. The critical shock velocity, which equals to the bulk sound speed at a given temperature, was specified to guarantee stable shock wave instead of quasi-isentropic wave propagation in APE. Only a single plastic shock wave with a steep front travelling at a constant velocity greater than the bulk sound speed generates in APE, resulting in the over-driven in the material.

Gradient and GENERIC time evolution towards reduced dynamics.

Reduction of a mesoscopic dynamical theory to equilibrium thermodynamics brings to the latter theory the fundamental thermodynamic relation (i.e. entropy as a function of the thermodynamic state variables). The reduction is made by following the mesoscopic time evolution to its conclusion, i.e. to fixed points at which the time evolution ceases to continue. The approach to fixed points is driven by entropy, that, if evaluated at the fixed points, becomes the thermodynamic entropy. Since the fixed points are parametrized by the thermodynamic state variables (by constants of motion), the thermodynamic entropy arises as a function of the thermodynamic state variables and thus the final outcome of the reduction is the fundamental thermodynamic relation. This reduction process extends also to reductions in which the reduced theory still involves the time evolution (e.g. reduction of kinetic theory to hydrodynamics). The essence of the extension is the replacement of the mesoscopic time evolution of the state variables with the corresponding mesoscopic time evolution of the vector field (i.e. of the fluxes). The fixed point in this flux time evolution is the vector field generating the reduced mesoscopic time evolution. The flux-entropy driving the flux time evolution becomes, if evaluated at the fixed point, the flux fundamental thermodynamic relation in the reduced dynamical theory. We show that the flux-entropy is a potential related to the entropy production. This article is part of the theme issue 'Fundamental aspects of nonequilibrium thermodynamics'.

Commissioning of the Cryogenic Phase Equilibria Test Stand CryoPHAEQTS

Medium-sized cryogenic applications such as local hydrogen liquefaction or HTS power applications require temperatures below 77 K at some kW cooling power. These conditions are efficiently reached by cryogenic mixed refrigerant cycles (CMRC). The CMRC development relies on physical property data of cryogenic fluid mixtures that is not available for most binary and multi-component systems. The cryogenic phase equilibria test stand CryoPHAEQTS provides precise physical property data of cryogenic fluid mixtures at temperatures from 15 K to 300 K and at pressures up to 150 bar. It also allows flammable mixtures (e.g. containing hydrogen) or oxidizing mixtures (e.g. containing oxygen). Vapor-liquid equilibria (VLE), vapor-liquid-liquid equilibria (VLLE) and the liquidus line of solid-liquid equilibria (SLE) are obtained by direct sampling from the equilibrium cell and analysis by gas chromatography. The equilibrium cell offers optical access by 4 windows to identify the coexisting phases. The cell temperature is set by a pulse-tube cryocooler and a counter-heater. As a unique feature, the specific heat capacity of the vapor phase in equilibrium is measured by the combination of a novel thermal and a Coriolis type flow meter. Having measured both caloric and thermal properties of the mixtures, we can develop new equations of state that cover all thermodynamic state variables. In this talk, we report on the progress in the construction and commissioning of CryoPHAEQTS. Validation of the measurement accuracy is presented by comparison of pure substances measurements against literature data.

INVESTIGATION ON THERMODYNAMIC VARIABLES OF THE ENZYME DURING THE CRYOTHERAPY

In this paper, we present the thermodynamic behavior of an artificial enzyme when cells are affected by the cryotherapy. In order to illustrate the Gibbs free energy and the enthalpy of the enzyme at the extreme temperature, by using the concept of the thermodynamic laws and kinetics of the enzyme, we measure the thermodynamic variables of the ground state and the transition state of the specific artificial enzyme at the different temperatures during cryotherapy. The results can be used to explain that, cells could survive at the extreme temperature below the freezing point by changing the activation enthalpy and the enthalpy.