Linear tension of two-dimensional drops on planar adsorbent faces

The size dependence of the linear tension of round two-dimensional equilibrium drops in the vapor phase on a homogeneous surface of an adsorbent is studied at the pressure of saturated two-dimensional vapor. The calculations are based on the lattice gas model in a quasi-chemical approximation with allowance for the correlation effects of the nearest interacting molecules. Methods for calculating linear tension using the equimolecular reference line are considered. Temperature dependences of the linear tension are studied for metastable and equilibrium drops. It is found that the differences between the thermodynamic properties of two types of drops are slight over a wide range of variation in drop radii.     

Metastable extension of the liquid-vapor phase equilibrium curve and surface tension

The method of molecular dynamics has been used to calculate the parameters of liquid-vapor phase equilibrium and the surface tension in a two-phase system of 4096 Lennard-Jones particles. Calculations have been made in a range from the triple point to near-critical temperature and also at temperatures below the triple point corresponding to the metastable equilibrium of a supercooled liquid and supersaturated vapor. To determine the surface tension, along with a mechanical approach a thermodynamic one has been used as well. The latter was based on calculation of the excess internal energy of an interfacial layer. It has been shown that in accuracy the thermodynamic approach is as good as the more sophisticated mechanical one. Low-temperature asymptotics of the phase-equilibrium curve and also of liquid and vapor spinodals have been considered in the Lennard-Jones and the van der Waals models. The behavior of the surface tension and the excess internal energy of an interfacial layer at T-->0 is discussed.     

The synthesis of metastable phases in plastic deformation of alloys

Intense plastic deformation caused by intragrain edge dislocation slip can contribute to the decomposition of equilibrium and formation of metastable phases in the volume of grains. The effect is caused by local changes in the thermodynamic properties of alloys and acceleration of diffusion in the region of a dislocation core. As a consequence, mechanical dislocation slip energy transforms into internal alloy energy, and the nonequilibrium state of the resulting alloy is “frozen.”     

A theory of a curved vapor-liquid separation boundary: The lattice gas model

Molecular theory of curved vapor-liquid interphase boundaries was considered in terms of the lattice gas model. The theory uses the quasi-thermodynamic concept of curved layers of a separation boundary with a large radius. The transition from a rectangular lattice to such layers is performed by the introduction of a variable number of the nearest neighbors. The problems (1) of the transition from distributed molecular models to layer models reflecting macroscopic symmetry of the interphase boundary and (2) of a minimum linear size of the surface region to which thermodynamic approaches are applicable were considered. Equations for the quasi-equilibrium distribution of molecules at the vapor-liquid boundary in a metastable system were constructed in the quasi-chemical approximation taking into account direct correlations between the nearest interacting molecules. A metastable state is maintained by a pressure jump described by the macro-scopic Laplace equation on a separation surface inside the interphase region. Equations for local mean pressure values and normal and tangential pressure tensor components inside the interphase region were constructed. These equations were used to obtain microscopic difference mechanical equilibrium equations for curved boundaries of spherical and cylindrical drops in the metastable state. The relation between the micro-scopic difference mechanical equilibrium equations and similar differential equations and the macroscopic Laplace equation, which described pressure jump in a metastable system, was considered. Various definitions of surface tension are discussed.     

Nonequilibrium surface tension for mixed adsorption kinetics

Experimental nonequilibrium surface tension measurements of 1–9 nonanediol solutions obtained by the oscillating-jet method have been interpreted in terms of our theoretical predictions derived for a mixed-controlled adsorption kinetics of the surfactant. The surface tension values have been calculated from the Szyszkowski equation using the Langmuir model of surfactant adsorption. Our theoretical results, obtained by a numerical solution of the adsorption equations, agree well with experimental data giving a value of the kinetics Szyszkowski constant very similar to the thermodynamic equilibrium value determined from experimental measurements of the static surface tension of 1–9 nonanediol solutions of various concentration. The approximate kinetic equation derived by P. Joos, G. Bleys, and G. Petre (J. Chim. Phys.79, 387 (1982)) for purely barrier-controlled adsorption proved to be less accurate.     

Shear thinning and shear dilatancy of liquid n-hexadecane via equilibrium and nonequilibrium molecular dynamics simulations: Temperature, pressure, and density effects

Equilibrium and nonequilibrium molecular dynamics (MD) simulations have been performed in both isochoric-isothermal (NVT) and isobaric-isothermal (NPT) ensemble systems. Under steady state shearing conditions, thermodynamic states and rheological properties of liquid n-hexadecane molecules have been studied. Between equilibrium and nonequilibrium states, it is important to understand how shear rates (gamma) affect the thermodynamic state variables of temperature, pressure, and density. At lower shear rates of gamma<1 x 10(11) s(-1), the relationships between the thermodynamic variables at nonequilibrium states closely approximate those at equilibrium states, namely, the liquid is very near its Newtonian fluid regime. Conversely, at extreme shear rates of gamma>1 x 10(11) s(-1), specific behavior of shear dilatancy is observed in the variations of nonequilibrium thermodynamic states. Significantly, by analyzing the effects of changes in temperature, pressure, and density on shear flow system, we report a variety of rheological properties including the shear thinning relationship between viscosity and shear rate, zero-shear-rate viscosity, rotational relaxation time, and critical shear rate. In addition, the flow activation energy and the pressure-viscosity coefficient determined through Arrhenius and Barus equations acceptably agree with the related experimental and MD simulation results.     

Surface tension of equilibrium spherical drops in the vapor phase

The properties of metastable and equilibrium drops that occur in the vapor phase and differ in the size and position of the dividing surface are compared. Using an equimolecular dividing surface, it was found that the total free energy and the total mass of the substance in drops of the same size over a broad temperature range differ by not more than 0.3%. A similar comparison for a dividing surface chosen from the equality condition of the moments of forces gives rather similar results. Using the surface where the maximum surface tension is attained as the dividing surface is impossible at low temperatures, because under these conditions, the notion of surface tension has no physical meaning. At high temperatures, the difference between the total mass of the substance for metastable and equilibrium drops does not exceed 0.6%. The calculations were carried out over a broad temperature range on the basis of the lattice-gas model in the quasichemical approximation.     

Molecular analysis of small drops in a metastable vapor

The molecular theory of curved vapor-liquid interfaces within the lattice gas model is applied to analyze supersaturated vapor states in dependence on the new phase size and system temperature. The molecular interaction is considered in the quasi-chemical approximation which describes effects of direct correlations of the nearest molecules. Two methods for determining the surface tension are discussed: equimolecular and according to the surface tension minimum in the intermediate region, i.e., on the tension surface. It is shown that a tension surface exists for metastable drops in supersaturated vapor over the temperature range, but its use leads to multivaluedness of solutions for its position; the minimum range of the existence of metastable drops is close to the previously determined lower limit for equilibrium.     

Energy Aspects of Thermal Molecular Switching: Molecular Thermal Hysteresis of Helicene Oligomers

Molecular switching is a phenomenon by which a molecule reversibly changes its structure and state in response to external stimuli or energy. Herein, molecular switching is discussed from thermodynamic and kinetic aspects in terms of energy supply with an emphasis on the thermal switching exhibited by helicene oligomers. It includes the inversion of relative thermodynamic stability induced by temperature changes and molecular thermal hysteresis in a closed system. The thermal phenomenon associated with the oligomers involves population/concentration changes between metastable states under nonequilibrium thermodynamic control.     

The condition of the phase equilibrium of a soluble nanoparticle

The condition of the phase equilibrium of an amorphous nanoparticle and a nanocrystal is derived with allowance for a possible presence of movable components in a solid body and the dependence of thermodynamic surface tension on the surface curvature. With the use of dispersion forces as an example, it is demonstrated by direct calculation that a correction to the Gibbs formula for the variations of surface tension can be substantial for nanoparticles that approach molecular sizes.     

Thermodynamics, the structure of integral membrane proteins, and transport

Membranes are structures whose lipid and protein components are at, or close to, equilibrium in the plane of the membrane, but are not at equilibrium across the membrane. The thermodynamic tendency of ionic and highly polar molecules to be in contact with water rather than with nonpolar media (hydrophilic interactions) is important in determining these equilibrium and nonequilibrium states. In this paper, we speculate about the structures and orientations of integral proteins in a membrane, and about how the equilibrium and nonequilibrium features of such structures and orientations might be influenced by the special mechanisms of biosynthesis, processing, and membrane insertion of these proteins. The relevance of these speculations to the mechanisms of the translocation event in membrane transport is discussed, and specific protein models of transport that have been proposed are analyzed.     

On the definition of a Monte Carlo model for binary crystal growth

We show that consistency of the transition probabilities in a lattice Monte Carlo (MC) model for binary crystal growth with the thermodynamic properties of a system does not guarantee the MC simulations near equilibrium to be in agreement with the thermodynamic equilibrium phase diagram for that system. The deviations remain small for systems with small bond energies, but they can increase significantly for systems with large melting entropy, typical for molecular systems. These deviations are attributed to the surface kinetics, which is responsible for a metastable zone below the liquidus line where no growth occurs, even in the absence of a 2D nucleation barrier. Here we propose an extension of the MC model that introduces a freedom of choice in the transition probabilities while staying within the thermodynamic constraints. This freedom can be used to eliminate the discrepancy between the MC simulations and the thermodynamic equilibrium phase diagram. Agreement is achieved for that choice of the transition probabilities yielding the fastest decrease of the free energy (i.e., largest growth rate) of the system at a temperature slightly below the equilibrium temperature. An analytical model is developed, which reproduces quite well the MC results, enabling a straightforward determination of the optimal set of transition probabilities. Application of both the MC and analytical model to conditions well away from equilibrium, giving rise to kinetic phase diagrams, shows that the effect of kinetics on segregation is even stronger than that predicted by previous models.     

Heat capacity, enthalpy fluctuations, and configurational entropy in broken ergodic systems

A common assumption in the glass science community is that the entropy of a glass can be calculated by integration of measured heat capacity curves through the glass transition. Such integration assumes that glass is an equilibrium material and that the glass transition is a reversible process. However, as a nonequilibrium and nonergodic material, the equations from equilibrium thermodynamics are not directly applicable to the glassy state. Here we investigate the connection between heat capacity and configurational entropy in broken ergodic systems such as glass. We show that it is not possible, in general, to calculate the entropy of a glass from heat capacity curves alone, since additional information must be known related to the details of microscopic fluctuations. Our analysis demonstrates that a time-average formalism is essential to account correctly for the experimentally observed dependence of thermodynamic properties on observation time, e.g., in specific heat spectroscopy. This result serves as experimental and theoretical proof for the nonexistence of residual glass entropy at absolute zero temperature. Example measurements are shown for Corning code 7059 glass.     

Numerical approaches to determine the interface tension of curved interfaces from free energy calculations

A recently proposed method to obtain the surface free energy σ(R) of spherical droplets and bubbles of fluids, using a thermodynamic analysis of two-phase coexistence in finite boxes at fixed total density, is reconsidered and extended. Building on a comprehensive review of the basic thermodynamic theory, it is shown that from this analysis one can extract both the equimolar radius R(e) as well as the radius R(s) of the surface of tension. Hence the free energy barrier that needs to be overcome in nucleation events where critical droplets and bubbles are formed can be reliably estimated for the range of radii that is of physical interest. It is found that the conventional theory of nucleation, where the interface tension of planar liquid-vapor interfaces is used to predict nucleation barriers, leads to a significant overestimation, and this failure is particularly large for bubbles. Furthermore, different routes to estimate the effective radius-dependent Tolman length δ(R(s)) from simulations in the canonical ensemble are discussed. Thus we obtain an instructive exemplification of the basic quantities and relations of the thermodynamic theory of metastable droplets/bubbles using simulations. However, the simulation results for δ(R(s)) employing a truncated Lennard-Jones system suffer to some extent from unexplained finite size effects, while no such finite size effects are found in corresponding density functional calculations. The numerical results are compatible with the expectation that δ(R(s) → ∞) is slightly negative and of the order of one tenth of a Lennard-Jones diameter, but much larger systems need to be simulated to allow more precise estimates of δ(R(s) → ∞).     

Small Systems and Limitations on the Use of Chemical Thermodynamics

Limitations on using chemical thermodynamics to describe small systems are formulated. These limitations follow from statistical mechanics for equilibrium and nonequilibrium processes and reflect (1) differences between characteristic relaxation times in momentum, energy, and mass transfer in different aggregate states of investigated systems; (2) achievements of statistical mechanics that allow us to determine criteria for the size of smallest region in which thermodynamics can be applied and the scale of the emergence of a new phase, along with criteria for the conditions of violating a local equilibrium. Based on this analysis, the main thermodynamic results are clarified: the phase rule for distorted interfaces, the sense and area of applicability of Gibbs’s concept of passive forces, and the artificiality of Kelvin’s equation as a result of limitations on the thermodynamic approach to considering small bodies. The wrongness of introducing molecular parameters into thermodynamic derivations, and the activity coefficient for an activated complex into the expression for a reaction rate constant, is demonstrated.     

Nanoparticle adsorption at liquid-vapor surfaces: influence of nanoparticle thermodynamics, wettability, and line tension

We developed a statistical mechanical theory that describes the adsorption of nanoparticles (NPs) at liquid-vapor surfaces. This theory accounts for the surface to bulk NP thermodynamic equilibrium, as well as the NP mechanical equilibrium, wettability, and line tension at liquid-vapor surfaces. The theory is tested by examining the adsorption of 5 nm diameter dodecanethiol-ligated gold NPs at the liquid-vapor surface of a homologous series of n-alkane solvents, from n-nonane to n-octadecane, where the NP wettability decreases with an increasing n-alkane chain length.     

Temperature dependence of the surface tension of indium

Original data on the temperature dependence of the surface tension of indium, obtained using two independent approaches (a large sessile drop and the maximum pressure in a drop) are presented. The focus is on analyzing possible methodological shortcomings of experimental studies in which the surface tension values of a number of pure metals are obtained that are considerably higher than the results from measuring surface tension by traditional means. It is found that cleaning the investigated metal surfaces through bombardment with heavy ions of inert gases can lead to violations of the thermodynamic equilibrium conditions of a surface with its own saturated vapor, and to the ensuing consequences.