On the characterization of fluxes in nonlinear irreversible thermodynamics

The linear Onsager theory of irreversible thermodynamics is extended to include nonlinear phenomenological relations by means of Onsager fluxes. Such fluxes satisfy a full system of reciprocity relations, vanish in thermodynamic equilibrium, and give a non-negative production of entropy. A complete characterization of Onsager fluxes is obtained in terms of non-negative scalar valued functions which vanish in thermodynamic equilibrium. These same functions are also shown to characterize all C² fluxes which satisfy the second law of thermodynamics. Each system of Onsager fluxes is shown to derive from a dissipation function which attains its absolute minimum in thermodynamic equilibrium. The reaction rates given by reaction kinetics are shown to be Onsager fluxes and their dissipation functions are explicitly calculated.     

Asymptotic stability,Onsager fluxes and reaction kinetics

This paper constitutes a first step in the derivation of thermodynamics directly from the dynamics of physical systems. The existence of an asymptotically stable equilibrium point is used to construct a family of admissible entropy functions. These functions have nonnegative entropy production and assume an absolute maximum at the equilibrium point. A nonlinear generalization of the Onsager theory is then used to obtain a one-to-one correspondence between entropy production functions and the governing system of autonomous rate equations. The theory is applied to well stirred chemically reacting systems with constant temperature and pressure. This allows the derivation of chemical potentials, Gibbs' potentials and enthalpy for such systems. The rate equations for reaction kinetics and for classical thermodynamic reaction theory are obtained. Classic thermodynamic reaction theory is shown to give maximum entropy for constant enthalpy at the equilibrium point, while reaction kinetics gives this result only to within quadratic terms in the departure from equilibrium.     

Under Diffusion Control: from Structuring Matter to Directional Motion

Self‐organization in synthetic chemical systems is quickly developing into a powerful strategy for designing new functional materials. As self‐organization requires the system to exist far from thermodynamic equilibrium, chemists have begun to go beyond the classical equilibrium self‐assembly that is often applied in bottom‐up supramolecular synthesis, and to learn about the surprising and unpredicted emergent properties of chemical systems that are characterized by a higher level of complexity and extended reactivity networks. The present review focuses on self‐organization in reaction‐diffusion systems. Selected examples show how the emergence of complex morphogenesis is feasible in synthetic systems leading to hierarchically and nanostructured matter. Starting from well‐investigated oscillating reactions, recent developments extend diffusion‐limited reactivity to supramolecular systems. The concept of dynamic instability is introduced and illustrated as an additional tool for the design of smart materials and actuators, with emphasis on the realization of motion even at the macroscopic scale. The formation of spatio‐temporal patterns along diffusive chemical gradients is exploited as the main channel to realize symmetry breaking and therefore anisotropic and directional mechanical transformations. Finally, the interaction between external perturbations and chemical gradients is explored to give mechanistic insights in the design of materials responsive to external stimuli.     

Phase equilibria and metastable states

Agreement is remarked between the theory of homogeneous seed-formation and tests on the kinetics of the boiling and crystallization of fluids. The continuation of the two-phase equilibrium line into the domain where both phases are metastable is discussed. The application of thermodynamic similarity to describe the melting of substances is shown.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 53, No. 5, pp. 820–826, November, 1987.     

How does the Earth system generate and maintain thermodynamic disequilibrium and what does it imply for the future of the planet?

The Earth's chemical composition far from chemical equilibrium is unique in our Solar System, and this uniqueness has been attributed to the presence of widespread life on the planet. Here, I show how this notion can be quantified using non-equilibrium thermodynamics. Generating and maintaining disequilibrium in a thermodynamic variable requires the extraction of power from another thermodynamic gradient, and the second law of thermodynamics imposes fundamental limits on how much power can be extracted. With this approach and associated limits, I show that the ability of abiotic processes to generate geochemical free energy that can be used to transform the surface-atmosphere environment is strongly limited to less than 1?TW. Photosynthetic life generates more than 200?TW by performing photochemistry, thereby substantiating the notion that a geochemical composition far from equilibrium can be a sign for strong biotic activity. Present-day free energy consumption by human activity in the form of industrial activity and human appropriated net primary productivity is of the order of 50?TW and therefore constitutes a considerable term in the free energy budget of the planet. When aiming to predict the future of the planet, we first note that since global changes are closely related to this consumption of free energy, and the demands for free energy by human activity are anticipated to increase substantially in the future, the central question in the context of predicting future global change is then how human free energy demands can increase sustainably without negatively impacting the ability of the Earth system to generate free energy. This question could be evaluated with climate models, and the potential deficiencies in these models to adequately represent the thermodynamics of the Earth system are discussed. Then, I illustrate the implications of this thermodynamic perspective by discussing the forms of renewable energy and planetary engineering that would enhance the overall free energy generation and, thereby 'empower' the future of the planet.     

Three-temperature method as an origin of molecular beam epitaxy

Molecular beam epitaxy (MBE) is a highly sophisticated method of obtaining thin semiconducting compound films of high quality. This technique is now very helpful not only in the preparation of many new devices but also in solid state science and the development of entirely new materials.One of the main features of MBE today is the method of depositing stoichiometric compound films from molecular beams of the constituents impinging on a suitably heated substrate; this was developed in the 1950s and is known as the three-temperature method. The fundamental ideas of this co-evaporation method, its first applications and the extension of the method for the evaporation of ternary compounds are described.Further developments within the last decade have been in two directions: th first, the so-called hot-wall technique, is connected with deposition at close to thermodynamic equilibrium conditions and allows relatively high growth rates under a high vacuum environment; the second, a more sophisticated and universal process, is MBE which is an ultrahigh vacuum and cold-wall technique which is carried out at far from thermodynamic equilibrium.     

Deformation and thermodynamic response for a crack dislocation model of brittle fracture

Concepts from dislocation and microcrack models are used to define idealized attributes describing the tip region of a crack. The attributes characterize both geometry and deformation; and this identifies a material defect species called a crack dislocation. With the attributes as variables, a scalar density function for each crack dislocation species can be defined.The crack dislocation is different from the common edge or screw species because it creates a new surface area as well as a displacement discontinuity as it propagates through a crystalline lattice. To model the discontinuities, a relative deformation functional is developed which depends on the crack dislocation density function. Since the crack dislocations are the only material defects assumed to contribute deformation discontinuities, the model is for brittle fracture only.The thermodynamic response uses primarily the methodology established by Gibbs. The existence of an internal energy functional is assumed. The methodology results in a definition for a thermodynamic potential for crack dislocation kinetics, a generalization of the Griffith crack propagation concept, and a local measure for the surface strain energy density changes on the crack dislocation line. The equilibrium thermodynamic potential for crack dislocation kinetics introduces a thermodynamic concept to demarcate crack dislocation density transitions from stationary to non-stationary; hence, it provides an incipient fracture criterion that has a thermodynamic basis. For nonequilibrium thermodynamics, the Onsager formalism is used to model the rates and fluxes of the thermodynamic functions.     

A kinetic study of mass transfer in reversed-phase liquid chromatography on a C18-silica gel

The characteristic features of mass-transfer kinetics in a reversed-phase (RP) column packed with a C18-silica were studied. The relevant information on phase equilibrium thermodynamics and mass-transfer kinetics was obtained by frontal analysis and the pulse method, respectively. The equilibrium isotherm was accounted for by the simple Langmuir model. The ratio of the axial dispersion coefficient to the mobile-phase flow velocity increased almost linearly with increasing solute concentration. Similarly, the mass-transfer rate coefficient (km) showed a linear dependence on the solute concentration. The positive concentration dependence of km resulted from that of the surface diffusion coefficient, which was interpreted with the chemical potential driving force model. The contribution of axial dispersion to band broadening was predominant in the RP column packed with the medium-size packing material used (particle diameter, 12 microns) whereas that of the kinetics of adsorption/desorption was negligibly small. The results of this study demonstrate how an analysis of the dependence of the mass-transfer kinetics on the flow velocity and the solute concentration allows a better understanding of this kinetics.     

Factors influencing the kinetics of electrochemical reactions in milling

Input of mechanical energy at a high rate can drive a system and induce phase transformations and chemical reactions away from equilibrium. The evolution of such a change depends on both thermodynamic as well as kinetic factors. Besides the microstructural changes like attainment of nanostructure, which alters the overall free energy, the high rate of mechanical energy input also changes the kinetics by influencing the mass transport and related processes. In order to understand these factors, we have recently started a programme of looking at the influence of mechanical energy on driving simple chemical reactions in solid state. In this presentation we shall present and discuss the results of two kinds of situation that we have studied. The first one is simple electrochemical replacement reactions between metals and metal sulphates in solid state. We show that the mechanical milling alters the kinetics of these reactions, which can be rationalized by considering the phenomena taking place at the microscopic level. For example we will show that the crystal structure of the sulphate and the nature of the reaction product at the interface influence the mechanochemistry significantly. It is even possible in some special cases to alter the direction of the chemical reaction. In the second set of results we shall present the effect of mechanical milling on the site occupancy in ferrites, which can lead to a significant change in magnetic behaviour.     

Kinetic,thermodynamic, and isosteric heat of dibutyl and diethyl phthalate removal onto activated carbon from Albizzia julibrissin pods

The adsorption performance of diethyl and dibutyl phthalates on a new activated carbon prepared from an abundant biomass “Albizzia julibrissin Pods,” treated chemically by H₃PO₄ is investigated through the equilibrium and kinetic study. The effect of different parameters like contact time, initial phthalate concentrations, and temperature on the adsorption capacities was studied in batch mode to evaluate the optimal conditions. Adsorption isotherms for both phthalates were fit at different temperatures using the Langmuir and Freundlich nonlinear regression. Adsorption kinetics were adjusted to various linear models, such as pseudo-first-order, pseudo-second-order, liquid film diffusion, intraparticle diffusion, and Boyd. The thermodynamic analysis indicated that the adsorption was spontaneous and exothermic in nature. The adsorption isosteric heat revealed a heterogeneous surface with different adsorption sites activities.     

Bromide ion removal from contaminated water by calcined and uncalcined MgAl-CO3 layered double hydroxides

A fundamental investigation on the uptake of bromide ion from contaminated water by calcined and uncalcined MgAl-CO3 layered double hydroxides (LDHs) were conducted in batch mode. The uptake capacity of calcined LDHs (CLDH) is higher than that of uncalcined LDHs, due to their different mechanisms which are confirmed by powder X-ray diffraction, FT-IR spectroscopy and TG-MS measurements. The former mechanism is based on the reconstruction of CLDH to Br-LDHs, whilst the latter is related to the surface adsorption. It has been found that the LDHs calcined at 500 degrees C with Mg/Al molar ratio of 4 represents the highest capacity to remove bromide ion from aqueous solution. The equilibrium isotherms of uptake of bromide by CLDH were well fitted by the Langmuir equation, and thermodynamic parameters such as Delta G0, Delta H0 and Delta S0 were calculated from Langmuir constants. The negative value of Delta H0 confirms the exothermic nature of adsorption. Three kinetics models were used to fit the kinetics experimental data, and it was found that the pseudo-second order kinetics model could be used to describe the uptake process appropriately. The value of Ea was calculated to be 79.9 kJ/mol, which suggests that the process of uptake bromide is controlled by the reaction rate of bromide with the CLDH rather than diffusion.     

Modelling precipitation sequences in power plant steels Part 1 – Kinetic theory

Abstract

The ability of steels to resist creep deformation depends on the presence in the microstructure of carbides and intermetallic compounds which precipitate during tempering or during elevated temperature service. The precipitation occurs in a sequence which leads towards thermodynamic equilibrium. The present paper deals with an extension of the Johnson-Mehl-Avrami theory for overall transformation kinetics. The modification permits the treatment of more than one precipitation reaction occurring simultaneously, afeature which isfound to be essential for representing the reactions observed experimentally in a wide range of secondary hardening steels.