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PubMed2002

Non-equilibrium thermodynamics and kinetic theory of gas mixtures in the presence of interfaces.

A broad range of the boundary value problems of the kinetic theory of gases and gas mixtures is considered based on kinetic theory and non-equilibrium thermodynamics. The interrelation of the kinetic theory and non-equilibrium thermodynamics is discussed. The balance equations at the interface are obtained for the case of the boundary layers with peculiar properties. Procedures for deriving the boundary conditions for slightly rarefied gas mixtures are outlined. The problems of calculating slip coefficients are discussed. The specificity of the kinetic effects in the boundary conditions is shown. A set of general relations related to gas mixture flows in capillaries is deduced. The possibility of non-equilibrium kinetic effects in the form of a paradoxical distribution of non-equilibrium temperature is shown. Methods of non-equilibrium thermodynamics are used to obtain the phenomenological equations describing the thermophoresis and diffusiophoresis of particles and cross phenomena. The growth and evaporation of droplets is considered based on kinetic theory and non-equilibrium thermodynamics.

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PubMed2004

Interaction of the protein transduction domain of HIV-1 TAT with heparan sulfate: binding mechanism and thermodynamic parameters.

The positively charged protein transduction domain of the HIV-1 TAT protein (TAT-PTD; residues 47-57 of TAT) rapidly translocates across the plasma membrane of living cells. This property is exploited for the delivery of proteins, drugs, and genes into cells. The mechanism of this translocation is, however, not yet understood. Recent theories for translocation suggest binding of the protein transduction domain (PTD) to extracellular glycosaminoglycans as a possible mechanism. We have studied the binding equilibrium between TAT-PTD and three different glycosaminoglycans with high sensitivity isothermal titration calorimetry and provide the first quantitative thermodynamic description. The polysulfonated macromolecules were found to exhibit multiple identical binding sites for TAT-PTD with only small differences between the three species as far as the thermodynamic parameters are concerned. Heparan sulfate (HS, molecular weight, 14.2 +/- 2 kDa) has 6.3 +/- 1.0 independent binding sites for TAT-PTD which are characterized by a binding constant K0 = (6.0 +/- 0.6) x 10(5) M(-1) and a reaction enthalpy deltaHpep0 = -4.6 +/- 1.0 kcal/mol at 28 degrees C. The binding affinity, deltaGpep0, is determined to equal extent by enthalpic and entropic contributions. The HS-TAT-PTD complex formation entails a positive heat capacity change of deltaCp0 = +135 cal/mol peptide, which is characteristic of a charge neutralization reaction. This is in contrast to hydrophobic binding reactions which display a large negative heat capacity change. The stoichiometry of 6-7 TAT-PTD molecules per HS corresponds to an electric charge neutralization. Light scattering data demonstrate a maximum scattering intensity at this stoichiometric ratio, the intensity of which depends on the order of mixing of the two components. The data suggest cross-linking and/or aggregation of HS-TAT-PTD complexes. Two other glycosaminoglycans, namely heparin and chondroitin sulfate B, were also studied with isothermal titration calorimetry. The thermodynamic parameters are K0 = (6.0 +/- 0.8) x 10(5) M(-1) and kcal/mol for heparin and K0 = (2.5 +/- 0.5) x 10(5) M(-1) and kcal/mol for chondroitin sulfate B at 28 degrees C. The close thermodynamic similarity of the three binding molecules also implies a close structural relationship. The ubiquitous occurrence of glycosaminoglycans on the cell surface together with their tight and rapid interaction with the TAT protein transduction domain makes complex formation a strong candidate as the primary step of protein translocation.

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PubMed2001

Surface activity at the planar interface in relation to the thermodynamics of intermolecular interactions in the ternary system: maltodextrin-small-molecule surfactant-legumin.

We report on the effect of potato maltodextrins with variable dextrose equivalent (Paselli SA-2, SA-6 and SA-10) on the surface behavior at the air-water interface of the mixture: legumin+small-molecule surfactant. Distinct in nature small-molecule surfactants (model: sodium salt of capric acid, Na-caprate; and commercially important: a citric acid ester of monoglyceride, CITREM) have been under our consideration. The role of the structure of both of the maltodextrins and the small-molecule surfactants in the effect studied has been elucidated by measurements in a bulk aqueous medium of the enthalpy of their interaction from mixing calorimetry, value of weight average molecular weight of the maltodextrins and the thermodynamics of the pair maltodextrin-solvent and maltodextrin-protein interactions from laser static light scattering. The combined data of mixing calorimetry and light scattering suggest some complex formation between the small-molecule surfactants and the maltodextrins. Predominantly hydrophobic interactions along with hydrogen bonding form the basis of the complexes. The effect of the maltodextrins on the thermodynamics of the protein heat denaturation and thereby on the protein conformational stability in the presence of the small-molecule surfactants has been studied by differential scanning calorimetry. The interrelation between the thermodynamics of intermolecular interactions in a bulk and the surface behavior at the planar air-water interface of the ternary systems (maltodextrin+legumin+small-molecule surfactant) has been elucidated by tensiometry. The effect of the maltodextrins on the surface activity of mixtures of legumin with the small-molecule surfactants is governed by the competitive in relation to the protein interactions with the small-molecule surfactants and a subsequent change in the thermodynamic properties of the both biopolymers, which are favorable to the ternary complex formation.

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PubMed2005

Solvation thermodynamics: theory and applications.

Potential distribution and coupling parameter theories are combined to interrelate previous solvation thermodynamic results and derive several new expressions for the solvent reorganization energy at both constant volume and constant pressure. We further demonstrate that the usual decomposition of the chemical potential into noncompensating energetic and entropic contributions may be extended to obtain a Gaussian fluctuation approximation for the chemical potential plus an exact cumulant expansion for the remainder. These exact expressions are further related to approximate first-order thermodynamic perturbation theory predictions and used to obtain a coupling-parameter integral expression for the sum of all higher-order terms in the perturbation series. The results are compared with the experimental global solvation thermodynamic functions for xenon dissolved in n-hexane and water (under ambient conditions). These comparisons imply that the constant-volume solvent reorganization energy has a magnitude of at most approximately kT in both experimental solutions. The results are used to extract numerical values of the solute-solvent mean interaction energy and associated fluctuation entropy directly from experimental solvation thermodynamic measurements.

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PubMed2006

Nonequilibrium thermodynamics--A tool to describe heterogeneous catalysis.

In the study of multi-component mass transfer it is common to use the film model, in which all the resistance to mass transfer towards a catalytic surface is assumed to be localized in a diffusion layer in front of the surface. At the surface one furthermore assumes that the temperature and chemical potentials are continuous, while the coupling of a possible heat flux to the mass fluxes is assumed to be negligible. Both these assumptions are questionable. Using nonequilibrium thermodynamics we discuss how to integrate the coupling between heat and mass fluxes in the description of the film. Furthermore, following Gibbs, we introduce the surface as a separate thermodynamic system where the coupling between the vectorial heat flux and the scalar reaction rate is allowed and can be significant in heterogeneous catalysis. Non-equilibrium thermodynamic theory for surfaces allows one to find the proper rate equations. It allows for a consistent and complete description of mass and heat transfer through the film and subsequently from the film to the surface where the reaction takes place. Fast endo- or exothermic surface reactions in heterogeneous catalysis may give significant temperature gradients between a catalyst surface and the media, which will, when not accounted for, lead to an incorrect evaluation of the activity, stability and selectivity of a catalyst. Non-equilibrium thermodynamics is a useful tool for predicting the surface temperature as well as for analyzing the system. In this contribution we sketch how to systematically set up the complete description, in which the film and the surface "sum up" to one effective surface.

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PubMed2004

Thermodynamics of soft anisotropic contact lines.

Contact lines arising from the intersection of interfaces between liquids and nematic liquid crystals are representative models of soft anisotropic contact lines. This paper presents the thermodynamics of soft anisotropic contact lines and the derivation of the one dimensional (1D) Gibbs-Duhem adsorption equation. Consistency between the 1D Gibbs-Duhem equation and the classical equations of lineal nematostatics is shown. Using a phase space that takes into account thermodynamics, liquid crystalline order, and geometric variables, the generalized nematic line Gibbs-Duhem equation reveals the presence of couplings between curvature, torsion, adsorption, temperature, and average molecular orientation. Merging the thermodynamic analysis with nematostatics results in a model for contact line shape and orientation selection. The ability of an adsorbed solute to orient the director and to bend and twist the contact line is predicted. The thermodynamic origin of preferred orientation at a straight contact line is established.

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PubMed2005

On the universal behavior of some thermodynamic properties along the whole liquid-vapor coexistence curve.

When thermodynamic properties of a pure substance are transformed to reduced form by using both critical- and triple-point values, the corresponding experimental data along the whole liquid-vapor coexistence curve can be correlated with a very simple analytical expression that interpolates between the behavior near the triple and the critical points. The leading terms of this expression contain only two parameters: the critical exponent and the slope at the triple point. For a given thermodynamic property, the critical exponent has a universal character but the slope at the triple point can vary significantly from one substance to another. However, for certain thermodynamic properties including the difference of coexisting densities, the enthalpy of vaporization, and the surface tension of the saturated liquid, one finds that the slope at the triple point also has a nearly universal value for a wide class of fluids. These thermodynamic properties thus show a corresponding apparently universal behavior along the whole coexistence curve.

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PubMed2005

Global thermodynamics of hydrophobic cavitation, dewetting, and hydration.

Pure water experimental and simulation results are combined to predict the thermodynamics of cavity formation, spanning atomic to macroscopic length scales, over the entire ambient liquid temperature range. The resulting cavity equation of state is used to quantify dewetting excess contributions to cavity formation thermodynamics and construct a thermodynamic perturbation theory of hydrophobic hydration. Predictions are compared with large cavity simulations and experimental rare-gas hydration thermodynamics data (for He, Ne, Ar, Kr, Xe, and Rn). Key findings include the strong temperature dependence of the critical length scale for hydrophobic dewetting and the evaluation of fundamental solute-solvent interaction contributions to rare-gas hydration chemical potentials.

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PubMed2002

Statistical thermodynamics of quantum Brownian motion: construction of perpetuum mobile of the second kind.

The Brownian motion of a quantum particle in a harmonic confining potential and coupled to harmonic quantum thermal bath is exactly solvable. Though this system presents at high temperatures a pedagogic example to explain the laws of thermodynamics, it is shown that at low enough temperatures the stationary state is non-Gibbsian due to an entanglement with the bath. In physical terms, this happens when the cloud of bath modes around the particle starts to play a nontrivial role, namely, when the bath temperature T is smaller than the coupling energy. Indeed, equilibrium thermodynamics of the total system, particle plus bath, does not imply standard equilibrium thermodynamics for the particle itself at low T. Various formulations of the second law are found to be invalid at low T. First, the Clausius inequality can be violated, because heat can be extracted from the zero point energy of the cloud of bath modes. Second, when the width of the confining potential is suddenly changed, there occurs a relaxation to equilibrium during which the entropy production is partly negative. In this process the energy put on the particle does not relax monotonically, but oscillates between particle and bath, even in the limit of strong damping. Third, for nonadiabatic changes of system parameters the rate of energy dissipation can be negative, and, out of equilibrium, cyclic processes are possible which extract work from the bath. Conditions are put forward under which perpetuum mobility of the second kind, having one or several work extraction cycles, enter the realm of condensed matter physics. Fourth, it follows that the equivalence between different formulations of the second law (e.g., those by Clausius and Thomson) can be violated at low temperatures. These effects are the consequence of quantum entanglement in the presence of the slightly off-equilibrium nature of the thermal bath, and become important when the characteristic quantum time scale variant Planck's over 2pi /k(B)T is larger than or comparable to other time scales of the system. They show that there is no general consensus between standard thermodynamics and quantum mechanics. The known agreements occur only due to the weak coupling limit, which does not pertain to low temperatures. Experimental setups for testing the effects are discussed.

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PubMed2004

Physical analogy between continuum thermodynamics and classical mechanics.

The main focus of this paper is the profound physical analogy between a continuum thermodynamical system, which evolves with relaxation under (possibly) nonisothermal conditions, and a classical mechanical system of a few interacting particles moving with dissipation in (possibly), time-dependent nonconservative fields. This analogy is applied to the problem of phase transitions in a one-dimensional thermodynamic system. The thermomechanical analogy stems from the validity of variational methods in mechanics and thermodynamics and allows for a different interpretation of the dynamical selection principle in the theory of pattern formation. This physical analogy is very helpful for understanding different nonlinear thermodynamic phenomena and for developing intuition in numerical simulations.

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PubMed2004

Steady shear flow thermodynamics based on a canonical distribution approach.

A nonequilibrium steady-state thermodynamics to describe shear flow is developed using a canonical distribution approach. We construct a canonical distribution for shear flow based on the energy in the moving frame using the Lagrangian formalism of the classical mechanics. From this distribution, we derive the Evans-Hanley shear flow thermodynamics, which is characterized by the first law of thermodynamics dE=TdS-Qdgamma relating infinitesimal changes in energy E, entropy S, and shear rate gamma with kinetic temperature T. Our central result is that the coefficient Q is given by Helfand's moment for viscosity. This approach leads to thermodynamic stability conditions for shear flow, one of which is equivalent to the positivity of the correlation function for Q. We show the consistency of this approach with the Kawasaki distribution function for shear flow, from which a response formula for viscosity is derived in the form of a correlation function for the time-derivative of Q. We emphasize the role of the external work required to sustain the steady shear flow in this approach, and show theoretically that the ensemble average of its power W must be non-negative. A nonequilibrium entropy, increasing in time, is introduced, so that the amount of heat based on this entropy is equal to the average of W. Numerical results from nonequilibrium molecular-dynamics simulation of two-dimensional many-particle systems with soft-core interactions are presented which support our interpretation.

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PubMed2005

Topology and phase transitions: from an exactly solvable model to a relation between topology and thermodynamics.

The elsewhere surmized topological origin of phase transitions is given here important evidence through the analytic study of an exactly solvable model for which both topology of submanifolds of configuration space and thermodynamics are worked out. The model is a mean-field one with a k-body interaction. It undergoes a second-order phase transition for k=2 and a first-order one for k >2 . This opens a perspective for the understanding of the deep origin of first and second-order phase transitions, respectively. In particular, a remarkable theoretical result consists of a mathematical characterization of first-order transitions. Moreover, we show that a "reduced" configuration space can be defined in terms of collective variables, such that the correspondence between phase transitions and topology changes becomes one-to-one, for this model. Finally, an unusual relationship is worked out between the microscopic description of a classical N -body system and its macroscopic thermodynamic behavior. This consists of a functional dependence of thermodynamic entropy upon the Morse indexes of the critical points (saddles) of the constant energy hypersurfaces of the microscopic 2N-dimensional phase space. Thus phase space (and configuration space) topology is directly related to thermodynamics.

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PubMed2005

Thermodynamic equilibrium and its stability for microcanonical systems described by the Sharma-Taneja-Mittal entropy.

It is generally assumed that the thermodynamic stability of equilibrium states is reflected by the concavity of entropy. We inquire, in the microcanonical picture, about the validity of this statement for systems described by the two-parametric entropy S(kappa,r) of Sharma, Taneja, and Mittal. We analyze the "composability" rule for two statistically independent systems A and B, described by the entropy S(kappa,r) with the same set of the deformation parameters. It is shown that, in spite of the concavity of the entropy, the "composability" rule modifies the thermodynamic stability conditions of the equilibrium state. Depending on the values assumed by the deformation parameters, when the relation S(kappa,r)(A union B) > S(kappa,r)(A) + S(kappa,r)(B) holds (superadditive systems), the concavity condition does imply thermodynamics stability. Otherwise, when the relation S(kappa,r)(A union B) < S(kappa,r)(A) + S(kappa,r)(B) holds (subadditive systems), the concavity condition does not imply thermodynamical stability of the equilibrium state.

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PubMed2006

Explanation of the Gibbs paradox within the framework of quantum thermodynamics.

The issue of the Gibbs paradox is that when considering mixing of two gases within classical thermodynamics, the entropy of mixing appears to be a discontinuous function of the difference between the gases: it is finite for whatever small difference, but vanishes for identical gases. The resolution offered in the literature, with help of quantum mixing entropy, was later shown to be unsatisfactory precisely where it sought to resolve the paradox. Macroscopic thermodynamics, classical or quantum, is unsuitable for explaining the paradox, since it does not deal explicitly with the difference between the gases. The proper approach employs quantum thermodynamics, which deals with finite quantum systems coupled to a large bath and a macroscopic work source. Within quantum thermodynamics, entropy generally loses its dominant place and the target of the paradox is naturally shifted to a decrease of the maximally available work before and after mixing (mixing ergotropy). In contrast to entropy this is an unambiguous quantity. For almost identical gases the mixing ergotropy continuously goes to zero, thus resolving the paradox. In this approach the concept of "difference between the gases" gets a clear operational meaning related to the possibilities of controlling the involved quantum states. Difficulties which prevent resolutions of the paradox in its entropic formulation do not arise here. The mixing ergotropy has several counterintuitive features. It can increase when less precise operations are allowed. In the quantum situation (in contrast to the classical one) the mixing ergotropy can also increase when decreasing the degree of mixing between the gases or when decreasing their distinguishability. These points go against a direct association of physical irreversibility with lack of information.

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PubMed2006

Nonequilibrium thermodynamics of glasses.

We consider the nonequilibrium thermodynamics of glasses from various perspectives. For the commonly used equilibriumlike approach based on Gibbs' fundamental form with an additional pair of conjugate variables, we discuss possible choices of the independent out-of-equilibrium variable and we illustrate some implications by concrete results for a well-known exactly solvable lattice model. The choice of variables is further illuminated from the complementary atomistic perspective offered by the inherent-structure formalism. A general formalism of nonequilibrium thermodynamics is employed (i) to derive the standard equilibriumlike approach, (ii) to formulate two self-contained levels to describe glassy dynamics and thermodynamics, and (iii) to offer guidance for future simulations of glasses. The thermodynamic approach suggests to introduce four-point correlation functions associated with structural rearrangements after imposed deformations, which might offer a possibility to detect a growing length scale at the glass transition without employing any dynamic information.

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PubMed2002

Thermodynamic discontinuity between low-density amorphous ice and supercooled water.

A combination of reverse Monte Carlo, molecular dynamics, and lattice dynamics simulations were used to obtain structural and thermodynamic data for low-density amorphous ice. A thermodynamically discontinuous transformation to a phase with properties and a structure consistent with supercooled liquid water is found to occur at approximately 130 K. Quantum corrections have a profound effect on thermodynamic properties and the location of important thermodynamic points in the water phase diagram.

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PubMed2004

Extended irreversible thermodynamics modeling for self-heating and dissipation in piezoelectric ceramics.

Self-heating or dissipation of piezoelectric ceramic elements is observed to be severe under dynamic operations even in the linear range. In this paper, a nonequilibrium thermodynamic model is developed to delineate the coupled irreversible mechanical, electric, and thermal processes, which jointly contribute to dissipation. Specifically, additional nonequilibrium state variables, also known as thermodynamic fluxes, are brought in to describe each of these processes. The characteristic relaxation of these processes is modeled. The nonnegative rate of entropy production is found to be in quadratic form of thermodynamics fluxes. The energy balance equation, which governs the transformation between different energy forms, is obtained in the framework of extended irreversible thermodynamics. Using this model, the dissipation of a piezoceramic stack actuator under harmonic electric or mechanical loadings in linear operation range is studied. The harmonic-balance methods are utilized as solution techniques. In contrast to the existing piezoelectric dissipation models, the dissipation by the developed model is verified to nonlinearly depend on operating frequency, with a peak dissipation occurring at some operating frequency that is related to characteristic relaxation of irreversible processes. The measurements of newly introduced parameters are also discussed.

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PubMed2005

Characterization of digital waveforms using thermodynamic analogs: applications to detection of materials defects.

We describe characterization of digital signals using analogs of thermodynamic quantities: the topological entropy, Shannon entropy, thermodynamic energy, partition function, specific heat at constant volume, and an idealized version of Shannon entropy in the limit of digitizing with infinite dynamic range and sampling rate. We show that analysis based on these quantities is capable of detecting differences between digital signals that are undetectable by conventional methods of characterization based on peak-to-peak amplitude or signal energy. We report the results of applying thermodynamic quantities to a problem from nondestructive materials evaluation: detection of foreign objects (FO) embedded near the surface of thin graphite/epoxy laminates using backscattered waveforms obtained by C-scanning the laminate. The characterization problem was to distinguish waveforms acquired from the region containing the FO from those acquired outside. In all cases the thermodynamic analogs exhibit significant increases (up to 20-fold) in contrast and for certain types of FO materials permit detection when energy or amplitude methods fail altogether.

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