Thermodynamic State Functions Research Articles

On the derivation of the Gibbs–Helmholtz equation

Based on a real event in the classroom during the physical chemistry course for undergraduate students, a new derivation is presented for the proof of the Gibbs–Helmholtz equation. Tried in subsequent years, it received positive reflection from chemistry BSc students proving that this straightforward derivation, which leads from the definition of G to the final expression in five steps, is more easily comprehensible. At the same time it helps the instructor to shed light—based on their temperature dependence—on the relationship between thermodynamic state functions.

Adsorption of aqueous rare earth elements using carbon black derived from recycled tires

The adsorption of an aqueous mixture of light rare earth elements (Y, La, Ce, Nd, and Sm) by carbon black derived from pyrolyzed end-of-life tires was investigated. The recycled tire carbon black (RTCB) was compared with other commercial carbon and functionalized carbon sorbent materials. The RTCB demonstrated improved adsorption for all the rare earth elements in this investigation over other carbon sorbent materials under a variety of conditions. The adsorption isotherms were observed to follow the Freundlich model with pseudo-second order kinetics. Analysis of thermodynamic state functions suggests the adsorption to be endothermic, energetically favorable under the conditions of study, and a dissociative adsorption mechanism. The use of RTCB as a sorbent material for extraction of aqueous REEs is attractive due to its inexpensive cost and utilization of a recycled material stream.

Thermodynamics of Gas–Liquid Criticality: Rigidity Symmetry on Gibbs Density Surface

The thermodynamic state function rigidity, defined simply as $$(\mathrm{d}p/\mathrm{d}\rho )_{T}$$ , where p is the pressure, $$\rho $$ is the density and T is the temperature, is the work required to reversibly increase the density of a fluid. Along any isotherm, rigidity $$(\omega )$$ decreases with density for a gas phase and increases with density for a liquid. Thermodynamics, therefore, can define a distinction between gas and liquid. For any one-phase system, rigidity is everywhere positive, in any two-phase region $$\omega =0$$ . For temperatures above critical coexistence, the rigidity has a constant value in the mesophase that separates the percolation loci, which bound the limits of existence of liquid and gas phases in the supercritical region. The law of rectilinear diameters extends in the supercritical region as a defining line of the colloid-like inversion between gas-in-liquid and liquid-in-gas. Every equilibrium state of gas phase has a corresponding isothermal state on the liquid phase with the same rigidity. We illustrate this symmetry between gas and liquid empirically using literature $$\rho (p,T)$$ equations-of-state for some real fluids, notably carbon dioxide, water and steam, and argon. At the molecular level, the symmetry can be explained by a correspondence between statistical properties of available holes in a liquid and sites of molecular clusters in the gas with equivalent number density fluctuations for complementary states of gas and liquid.

THERMODYNAMIC AFFINITY FOR SOLVENT AS A CRITERIUM OF CRITICAL SOLUTION TEMPERATURES OF PROTEIN MACROMOLECULES

Phase transitions of protein solutions which are of interest for biotechnological and biomedical purposes should be analyzed from the point of view of their interrelation with phase transitions of the structure of protein molecules on the basis of the state thermodynamic functions. This is suggested by the coupling of intra- and intermolecular interactions in protein systems. Temperature trends of the standard thermodynamic functions of native (N) and denatured (D) protein in solution have been considered within the framework of the concept of excessive melting functions that determine the thermodynamic affinity of protein molecules for solvent. Thermodynamic solution functions of protein in native (N) and denatured (D) states have been built on the basis of microcalorimetry data. The nature of enthalpy, entropy and free energy temperature changes has been shown to suggest a theoretical possibility of both higher and lower critical solution temperatures. Previously there were only experimental indications for some proteins under certain conditions (solvent composition, pH etc.), but thermodynamical interpretation was lacking. Furthermore, there appears a supercritical zone between higher and lower critical solution temperatures on the phase diagram. The zone is of open (two-phase) or closed (one-phase) type depending on the protein conformation – D or N, respectively. This applies to the range next to physiological temperatures and makes the description of supramolecular organization of protein solution possible under such conditions. Significance of the supercritical zone of protein phase states is determined by its probable contribution into self-regulation of the system in response to the changes in environmental conditions (temperature, salinity, acidity etc.).

Study on Process Economics of Natural Resource Utilization

Finite supply of non-regenerative resources triggers a competition between economic entities or between areas, which requires the ways regarding their utilization with higher levels in science and the standards regarding their use with higher efficiency in economics. To solve a problem of process evaluation in science and of driving force in economics during a process design or a process run for natural resources utilization, a process evaluation parameter originated from natural gas hydrate preparation from a small scale to industrialization scale and the equation of the criterion dependent are introduced to evaluate a variety of processes of natural resources utilization. The analyses indicate that the parameter is relevant to internal undeveloped resources amount change with a stable mass composition in a virtual black box model and external variable market with an implication of process efficiency in economy or of process efficiency of resource utilization and that the parameter has similar features of the thermodynamic state functions. Moreover, the equation of the criterion provided is a difference between the value of the process evaluation parameter at the final state and the value of the process evaluation parameter at the initial state in an actual process, which can be used to determine the direction of development and to judge the size of the driving force in an actual process or an economical run. The provided examples and correlative mathematical description can guide how an identification for the undeveloped resources and a real-time adjustment of dynamic production for the developing resource are done and how decisions regarding resource exploitation, the venture forecasting of capital utilization and updating technology are made. The parameter used itself and the equation of the derived criterion can help by playing a predictive role for selecting the optimal use processes and for designing new process of the natural resource utilization or capital use, and by playing a practical role for adjusting factual production status and for improving the actual process of the utilization of resource or capital in an economic society. Finally, those closed resource systems having accumulation or depletion of the resources or a variable mass such as a decomposition system, a fission system and a biological reproduction system will become possible future research objectives under the guide of this work.

A thermodynamic assessment of micellization for a mixture of sodium dodecyl benzene sulfonate and Tween 80 surfactants for ultralow interfacial tension

Mixing of a non-ionic surfactant Tween 80 and an anionic surfactant sodium dodecyl benzene sulfonate (DBSNa) has been studied to observe their synergism. Induced by its application in IFT reduction with crude oil for a potential enhanced oil recovery, its characterisation has been done to understand the insight of micellization. The CMC for blend of Tween 80 and DBSNa was found to be 0.020±0.0059 mM. Interfacially adsorbed excess concentration Γexcess and surface tension σ reduction has been studied from the tensiometry analysis. Conductivity study has shown relevance to the CMC obtained from tensiometry and provides the binding parameters. Thermodynamic interpretation has been done to quantify the experimental observations through the analysis of regular solution theory. Thermodynamic coefficients and constants have quantified the physical phenomena and ΔH, ΔS, ΔG featured spontaneity of micellization. Cyclic voltammetry study contributes the concepts of electrochemistry and redox potential for mixture. Physical delineation of the micelle has been done by DLS interpretation. Thermodynamic state functions, viz. free energy of micellization (ΔGmicelle) and adsorption (ΔGads) have been calculated to find out the packing parameter P, which indicates a probable spherical or globular micelle of the mixed surfactant.

ChemInform Abstract: Kinetic and Thermodynamic Processes of Organic Species at the Solution—Solid Interface: The View Through an STM

AbstractReview: 67 refs.

The Thermodynamics of Time Travel

The concept of time travel captures the imagination of scientists and nonscientists alike. Though theoretical mathematical treatment of the issue in the realm of physics has offered potential means, albeit, wormholes requiring some rather strange conditions such as negative energy, what does thermodynamics suggest for the potential of time travel? Examination of the thermodynamic state functions of enthalpy and entropy from the Gibbs free energy relationship suggest that the final enthalpy after travel will be greater than the initial enthalpy before travel. The final entropy after travel will be greater than the initial entropy before travel. Transfer of mass from one multiverse to another would seem to violate various mass energy conservation laws, as well as strictures on the Second Law of Thermodynamics for the originating and a target multiverse.

Cholesterics of colloidal helices: Predicting the macroscopic pitch from the particle shape and thermodynamic state

Building a general theoretical framework to describe the microscopic origin of macroscopic chirality in (colloidal) liquid crystals is a long-standing challenge. Here, we combine classical density functional theory with Monte Carlo calculations of virial-type coefficients to obtain the equilibrium cholesteric pitch as a function of thermodynamic state and microscopic details. Applying the theory to hard helices, we observe both right- and left-handed cholesteric phases that depend on a subtle combination of particle geometry and system density. In particular, we find that entropy alone can even lead to a (double) inversion in the cholesteric sense of twist upon changing the packing fraction. We show how the competition between single-particle properties (shape) and thermodynamics (local alignment) dictates the macroscopic chiral behavior. Moreover, by expanding our free-energy functional, we are able to assess, quantitatively, Straley's theory of weak chirality, which is used in several earlier studies. Furthermore, by extending our theory to different lyotropic and thermotropic liquid-crystal models, we analyze the effect of an additional soft interaction on the chiral behavior of the helices. Finally, we provide some guidelines for the description of more complex chiral phases, like twist-bend nematics. Our results provide new insights into the role of entropy in the microscopic origin of this state of matter.

Thermodynamic properties of harmonic oscillator system in noncommutative phase space

In the last 15 years, noncommutative effects have received much attention and have been extensively studied in the fields of quantum mechanics, field theory, condensed matter physics, and astrophysics. The aim of this paper is to investigate the thermodynamic properties of a harmonic oscillator system in noncommutative phase space. For an example, the effects of noncommutativity between positions and that between momenta in the phase space on thermodynamic properties of two- and three-dimensional harmonic oscillator system are studied by a statistical method. First, in the commutative phase space, the thermodynamic state functions are obtained from the partition functions of the harmonic oscillator system which satisfies Boltzmann statistics. Then, in the noncomummutative phase space, both noncommutative positions and noncommutative momenta are represented in terms of the commutative positions and momenta of the usual quantum mechanics by linear transformation method. Meanwhile, the other physical quantities such as the volume element, the number of microstates, and partition function in the noncommutative phase space are represented in terms of commutative positions and momenta. Finally, the thermodynamic and statistical state functions for the system in the noncommutative phase space are derived from the partition function, and the thermodynamic state functions in noncummutative and commutative phase spaces are compared with each other. The results show that the noncommutative effect changes the values of microscopic functions such as the partition function and entropy with the correction terms including noncummutative parameters. As the noncommutative parameters vanishes, i.e., reaches the commutative limit, the partition and entropy functions of the system coincide with the results of usual thermodynamics and statistical physics. Moreover, the macroscopic state functions such as the internal energy and heat capacity, remain constant. The results imply that the correction terms in the partition function and entropy may result from the corrections of the number of microstates and potential energy of the system by noncommutativity of the position and momentum. In conclusion, the method used in the paper is corresponding to the classical system that satisfies Boltzmann statistics, and the results derived here can provide a starting point for further studying the quantum system that satisfies Fermi-Dirac and Bose-Einstein statistics.

Surface Absorption of a Solution at Equilibrium

Surface adsorption of a solution is still a challenging problem in the thermodynamics of surfaces. In this work, a new thermodynamic state function is defined. The equilibrium condition of surface adsorption is that the differential of this state function is equal to zero. Based on this condition, we derived a new equation to describe surface adsorption at equilibrium. No hypothetical dividing surface is needed in this derivation. The new equation is quite different from the Gibbs adsorption equation. We also performed molecular dynamic simulations of aqueous sodium chloride solutions. The simulated results are in good agreement with our theoretical predictions.

Free Energy of Damaged Solids

This paper examines the free energy potentials of damaged solids for the construction of damage mechanics constitutive models. The physical meaning of free energy in solid mechanics is analyzed in contrast with that in traditional fields of thermodynamics; 1D stress-strain curves are used to show the relationships between various thermodynamic state functions in isothermal loading processes; and the role of plastic free energy in damage evolution is discussed both macroscopically and microscopically. It is concluded that plastic free energy, which is a macroscopic representation of some additional microscopic elastic energy, cannot do work during unloading but get released when damage takes place, constituting part of the driving force for damage evolution.

Comparing kinetics and mechanism of adsorption and thermo-oxidative decomposition of Athabasca asphaltenes onto TiO2, ZrO2, and CeO2 nanoparticles

In this study, nC7-asphaltenes adsorption and subsequent catalytic oxidation over three transition metal oxide nanoparticles, namely TiO2, ZrO2, and CeO2 were investigated. nC7-asphaltenes studied were obtained from Athabasca vacuum residue using n-heptane. The adsorption equilibrium data of nC7-asphaltenes, dissolved in toluene, fitted very well to the Langmuir adsorption isotherm model. The adsorption behavior of nC7-asphaltenes appeared to change with the type of adsorbent used. It was found that nC7-asphaltenes adsorption at 25°C is metal oxide specific and the adsorption capacities ranked in the following order: CeO2>ZrO2>TiO2. On the other hand the adsorption affinity followed the following order: CeO2>TiO2>ZrO2. Theoretical calculations of the interaction between the Quinolin-65 (Q-65) (a compound used as a model asphaltene molecule) and some of the metal oxides surfaces were carried out to get more insight into its adsorption behavior. Adsorption energies of Q-65 on the surfaces indicated that there are different adsorption sites on each metal oxide. To confirm the catalytic activity of the selected oxide nanoparticles, the nC7-asphaltenes adsorbed onto the transition metal oxide nanoparticles were subjected to oxidation up to 700°C in a thermogravimetric analyzer. All tested nanoparticles showed high catalytic activity for post adsorption oxidation. The oxidation kinetics was studied using the Ozawa–Flyn–Wall (OFW) corrected method. The mechanism function of the nC7-asphaltenes oxidation is strongly dependent on the type of nanoparticles. The kinetic oxidation parameters and the transition state thermodynamic functions for the oxidation process of nC7-asphaltenes in the presence and absence of nanoparticles, to the best of our knowledge, are reported for the first time. Among the selected transition metal oxide nanoparticles, CeO2 appears to have the lowest values of effective activation energy and change in Gibbs free energy of activation (ΔG‡).

Vibrational and thermodynamic properties of GeSe in the quasiharmonic approximation

Finite-temperature properties such as thermodynamic state functions can be obtained for a range of crystalline materials by combining density functional theory (DFT) with lattice-dynamics approaches. Despite the usefulness of such first-principles predictions, their results must be carefully checked for accuracy, especially in cases where the DFT description of the material itself is nontrivial. Here, we investigate a prototypical layered semiconductor, namely, germanium selenide (GeSe) by dispersion-corrected DFT, lattice-dynamics computations, and a thermodynamic framework that relies on the quasiharmonic approximation (QHA). We study phonon band structures, their evolution under pressure, and finite-temperature thermodynamic state functions. Besides the layered orthorhombic structure, this analysis includes the high-temperature cubic (rocksalt-type) polymorph of GeSe, which is shown to exhibit imaginary vibrational modes but emerging dynamic stability under increasing external pressure. The effect of these imaginary vibrational modes on the QHA and hence on computed thermochemical properties is critically evaluated. First-principles thermodynamics correctly predict a high-temperature transition from the orthorhombic to the cubic structure, albeit the transition temperature is severely underestimated. This simple compound allows us to address important methodological questions regarding the QHA treatment of crystalline solids.

Applied Thermodynamics: Grain Boundary Segregation

Chemical composition of interfaces—free surfaces and grain boundaries—is generally described by the Langmuir–McLean segregation isotherm controlled by Gibbs energy of segregation. Various components of the Gibbs energy of segregation, the standard and the excess ones as well as other thermodynamic state functions—enthalpy, entropy and volume—of interfacial segregation are derived and their physical meaning is elucidated. The importance of the thermodynamic state functions of grain boundary segregation, their dependence on volume solid solubility, mutual solute–solute interaction and pressure effect in ferrous alloys is demonstrated.

Thermodynamics of largeNgauge theory from top-down holography

By considering fluxes on D7 branes and explicitly computing their back-reaction on the geometry with and without a black hole, we show how the UV divergence of Klebanov-Strassler model can be regulated. Using the form of the metric and fluxes in the extremal and non-extremal limit, we compute the on-shell gravity action including the localized sources up to linear order in perturbation parameter g_sM^2/N, g_sN_f where N,M and N_f are units of D3,D5 and D7 charges in the dual gauge theory. Using the gravitational description, we show how the gauge theory undergoes a first-order Hawking-Page like phase transition and compute the critical temperature T_c. Finally, we obtain the equation of state for the gauge theory by computing thermodynamic state functions of the black hole and exhibit how black holes in deformed cone geometry can lead to results that are qualitatively similar to lattice QCD simulations.

Thermochemical Ranking and Dynamic Stability of TeO2Polymorphs from Ab Initio Theory

The ability to predict temperature-dependent properties of solids from ab initio theories alone has marked a fundamental step forward in realistic materials modeling. Here, we use density functional theory (DFT)-based thermochemistry to investigate crystalline tellurium dioxide (TeO2). While the DFT description of its polymorphs is challenging, we demonstrate that the inclusion of suitable dispersion corrections makes a thermochemical analysis and a correct stability ranking possible. Paratellurite (α-TeO2), a technologically most important compound used in optical devices, is lowest in Gibbs free enthalpy in agreement with previous thermochemical experiments. While α-TeO2 exhibits a three-dimensional bonding network, the well-known mineral tellurite (β-TeO2) contains two-dimensional sheets; nonetheless, we demonstrate that both polymorphs are extremely similar in thermodynamic state functions and chemical bonding. The latter is analyzed with the crystal orbital Hamilton population (COHP) method and offered as a possible explanation for the small stability difference (<1 kJ mol–1). Finally, a recently synthesized polymorph (γ-TeO2) is found to be higher in energy as expected (+6 kJ mol–1 at 300 K) but nonetheless dynamically stable. These results shed new light on the TeO2 polymorphs but also provide more general insight into the capabilities of theoretical materials modeling at finite temperatures.

Gibbs Density Surface of Water and Steam: 2nd Debate on the Absence of Van Der Waals’ “Critical Point”

A revised phase diagram for water shows three distinct fluid phases. There is no continuity of liquid and gas, and no “critical point” on Gibbs’ density surface as hypothesized by van der Waals. A supercritical colloidal mesophase bounded by percolation transition loci separates supercritical liquid water and gas-phase steam. The water phase is bounded by a percolation transition (PA) of available volume, whereas steam is bounded by the loci of a percolation transition (PB) at a density whereupon a bonded molecular cluster suddenly percolates large distances. At the respective percolation densities, there is no barrier to nucleation of water to steam (PA) or steam to water (PB). Below the critical temperature, the percolation loci become the metastable spinodals in the two-phase coexistence region. A critical divide is defined by the interception of PA and PB the p-T plane. Critical parameters are obtainable from slopes and intercepts of pressure-density supercritical isotherms within the mesophase. The supercritical mesophase is a fourth equilibrium state besides ice, water and steam. A thermodynamic state function rigidity (dp/dρ)T defines a distinction between liquid and gas, and shows a remarkable symmetry due to an equivalence in number density fluctuations, arising from available volume and molecular clusters, in liquid and gas respectively. Following an earlier debate in these pages [“Fluid phases of argon: A debate on the absence of van der Waals’ critical point” Natural Science 5 (2) 194-206 (2013)], we here report further debate on a science of criticality applied to water and steam (APPENDIX 1).

Probes of universality in AdS/CFT

We discuss some universal relations that hold for conformal field theories which admit a dual classical gravitational description in anti-de Sitter space. These relations therefore apply in a suitable large N limit, and imply that various hydrodynamic transport coefficients for conserved currents and thermodynamic state functions are entirely fixed by central charges.

Theoretical interpretation of the role of the ionic liquid phase in the (R)-Ru-BINAP catalyzed hydrogenation of methylacetoacetate

Recently, the work focusing on the role of alkyl chain length in the N[R,222][Tf2N] ionic liquids and its reflection in the kinetic parameters of stereoselective hydrogenation of methylacetoacetate over (R)-[RuCl(binap)(p-cymene)]Cl complex was reported. Irregular trends in the principle parameter of enantioselectivity were observed. Here, a possible theoretical explanation of such irregular trends elucidated with the help of molecular simulations methods is presented. A stepwise approach is proposed for evaluating the energetically most stable conformers of a series of individual N[R,222][Tf2N] for the interpretation of selectivity-structure effects observed experimentally. Initially, Monte Carlo molecular mechanics was used followed by a semi-empirical PM3 method to elucidate also the characteristic thermodynamic functions of state and theoretical molecular spectra. The density functional theory was finally applied. The specific absolute entropy data revealed that due to the partition of the cation and anion twisted closer approach the ionic liquids N[8,222][Tf2N] and N[12,222][Tf2N] may stabilize the structures of the (R)-[RuCl(binap)(p-cymene)]Cl complex.