The thermodynamics of cluster formation in nucleation theory

We have derived a precise thermodynamic definition of the standard free energy to form a cluster which is used in nucleation theory. The results [Eq. (9)] have a form differing slightly from the form usually used in nucleation theory and show that the Lothe-Pound correction factor is based on a misconception concerning the standard states involved.     

Growth of clusters in a first-order phase transition

The results of computer simulations of phase separation kinetics in a binary alloy quenched from a high temperature are analyzed in detail, using the ideas of Lifshitz and Slyozov. The alloy was modeled by a three-dimensional Ising model with Kawasaki dynamics. The temperature after quenching was 0.59T _c, whereT _c is the critical temperature, and the concentration of minority atoms was=0.075, which is about five times their largest possible single-phase equilibrium concentration at that temperature. The time interval covered by our analysis goes from about 1000 to 6000 attempted interchanges per site. The size distribution of small clusters of minority atoms is fitted approximately byc ₁(1-)³ w(t),c ₁ (1–)⁴ Q _l w(t)^l(2l10); wherec _l is the concentration of clusters of sizel;Q ₂,...,Q ₁₀ are known constants, the cluster partition functions;t is the time; andw(t)=0.015(1+7.17t ^–1/3). The distribution of large clusters (l20) is fitted approximately by the type of distribution proposed by Lifshitz and Slyozov,c _l ,(t)=–(d/dl) [lnt+p (l/t)], where is a function given by those authors and is defined by(x)=C _o e–x-C ₁ e ^–4x/3-C ₂ e ^–5x/3;C ₀,C ₁,C ₂ are constants determined by considering how the total number of particles in large clusters changes with time.Supported by the U.S. Air Force Office of Scientific Research under Grant No. 78-3522 and by the U.S. Department of Energy under Contract No. EY-76-C-02-3077*000.     

Statistical thermodynamics of the formation of an infinite cluster of thermally reversible chemical bonds

A systematic “mean-field” treatment of the thermodynamic equilibrium formation of an infinite cluster of bonds in a system of identical monomers capable of forming from n=0 to n>2 reversible chemical bonds with one another is proposed within the Cayley-tree approximation. For this purpose the difference between the symmetry of the monomers appearing in “point-to-point” and closed bond paths, respectively, is taken into account on the basis of an analysis of the structure of the infinite cluster. Minimization with respect to the distribution of such monomers yields a nontrivial solution corresponding to a lower free energy than the classical solution, which does not allow for the symmetry difference indicated. In addition, it is shown that the classical solution corresponds to the free-energy maximum when the infinite cluster is formed and that the formation of the infinite cluster is a first-order phase transition. The possible form of the phase diagrams of the systems considered is analyzed. Zh. éksp. Teor. Fiz. 115, 979–990 (March 1999)     

Statistical thermodynamics of the liquid surface

The current theoretical situation regarding the structure of the liquid-vapour transition zone and the associated thermodynamic surface properties of simple liquids is reviewed. The thermodynamic and statistical mechanical treatments of the surface structure are assessed, and it is concluded that the former approach has limiting validity only as T→T _crit. Liquid metal systems are discussed, together with the recent experimental evidence supporting the existence of stable density oscillations at the surfaces of certain liquid metals. The liquid inert gas systems, argon in particular, are considered in some detail, and a discussion of the statistical thermodynamics of the liquid ⁴He surface is given.     

Criterion of homogeneous boiling-up of superheated liquids

It is difficult to eliminate the effect of vessel walls and impurities in practical studies of boiling-up of strongly superheated liquids. Therefore, some doubts are always cast upon validity of experiments and their agreement with the classical theory of homogeneous stationary nucleation, impairing the verification of theoretical considerations. This paper reports main results of the theory of homogeneous nucleation and presents formulas for calculating the work of formation of a critical nucleus by an incline of the accessible superheating boundary on isobars and isotherms. Matching of experimental and theoretical values of the work of formation was considered as the homogeneous boiling-up criterion. Calculations by isobars and isotherms were made for some liquids. The theoretical values of the work of formation of a critical nucleus were 1.23–4.5 times higher than the corresponding empirical values for all the liquids, i.e., they were much higher than the calculation error. Thus, boiling-up of the studied liquids was not homogeneous and, hence, it did not correspond to the classical theory of nucleation. The work was financially supported by the President of the Russian Federation (No. NSh-4429.2006.8) and the Russian Foundation for Basic Research (Grant No. 07-08-00575-a).     

Statistical thermodynamics of soft surfaces

We review the continuum, statistical thermodynamics of surfaces and interfaces in soft matter where both the energy and entropy of the surface are comparable. These systems include complex fluids that are dominated by either surface tension or the interfacial curvature, such as: fluid and solid interfaces, colloidal dispersions, macromolecular solutions, membranes, and other self-assembling aggregates such as micelles, vesicles, and microemulsions. The primary focus is on the theoretical concepts, their universality, and the role of fluctuations and inhomogeneities with connections to relevant experimental systems.     

The boiling up model for highly superheated liquid with formation of evaporation front

Boiling up of metastable liquid on the surface of a cylindrical heater is studied at high superheating, when the evaporation front is formed. Boiling up begins with formation of a spherical bubble on the heater wall. Evaporation fronts propagating along the heater with the constant velocity are formed due to development of interfacial instability. The mathematical model describing the growth of a spherical bubble and vapor cavity behind the evaporation front is developed. Results of numerical simulation agree with available experimental data.     

Modelling phase equilibria of pure ionic liquids from a new equation of state

A perturbed hard-trimer (PHT) equation of state (EOS) has been employed to model densities and some derived thermodynamic properties of 39 ionic liquids (ILs) considering a trimer expression obtained from the statistical associating fluid theory as the reference physical model. The van der Waals dispersion forces were applied as perturbation term. The proposed model was tested using ILs containing imidazolium, pyrrolidinium, pyridinium, phosphonium and piperidinium cations. Two parameters appeared in the PHT EOS which are temperature-dependent, reflecting the dispersive energy parameters among trimers, ε and the hard-core diameter, σ, were determined based on the molecular scaling parameters. The performance of the proposed PHT EOS has been evaluated by predicting the volumetric and first and second derivatives thermodynamic properties in the pressure and temperature ranges within 0.1–200 MPa and 273–472.6 K, respectively. From 6331 data points examined, the average absolute deviation (AAD) of the correlated (at 0.1 MPa) and predicted (at high pressures) densities from the experimental ones was found to be 0.18 %. Furthermore, the isothermal compressibilities and thermal expansion coefficients as well as the heat capacities were estimated through the PHT EOS with uncertainties of the order of ±11.09, ±11.76 and ±3.34 %, respectively. Further, the vapour pressures of ILs are also predicted by the proposed model. The trend of the predicted vapour pressure is in accord with those reported in literature.

     

Statistical thermodynamics of an anharmonic oscillator

In the present study we investigate the statistical thermodynamics of the anharmonic oscillator, whose energies are characterized by the potential 1/2x ²+x ⁴. Employing the energies recently obtained by Hioe and Montroll, we compute the partition function and the thermodynamic quantities for the anharmonic and quartic oscillators. Low- and high-temperature formulas are presented for the thermodynamic quantities of the oscillators.     

Effect of the heating-surface material on the boiling curve of liquids

The curve of saturated pool boiling of water at atmospheric pressure is experimentally studied for various heating surface materials. The heat-generating elements are made of copper (65, 100 μm in diameter), tungsten (90 μm in diameter), and nichrome (100 and 150 μm in diameter) wires. The time to burnout of a heating element is not always correspondent to the boiling crisis. At a controlled heat load, the quantity of heat transferred from a metallic surface to boiling water increases with the heat load.     

On the entropy contribution to thermodynamics of melted flux liquids

The lattice models of thermally disordered flux line system are studied by the random walk method. We formulate rigorously the 2D model having an exact solution. In three dimensions the method leads to the generalized Bethe approximation. The critical behavior of both thermodynamic and correlation functions nearH _c1 is considered. An examination of a possible transition between entangled and disentangled phases is done.     

Statistical thermodynamics of isolated rigid rod-like molecules near a surface

The configurational behaviour and thermodynamic properties of a dilute gas of rigid rod-like molecules in the vicinity of a macroscopic planar adsorption surface are investigated using statistical mechanics. The interaction energy between the surface and a rod-like molecule is determined as a function of both its molecular centre of mass separation R and its orientation relative to the surface. In calculating this interaction energy, each rod segment and molecule comprising the surface is assumed to interact through a Lennard-Jones pair potential. The average molecular order parameter is then determined as a function of R. We find that an isolated rod-like molecule tends to align nearly parallel to the surface for small separations. However, as R increases the order parameter first passes through a maximum then decays to zero as R ^-5 for large R. The configurational behaviour of an isolated rod-like molecule located between two parallel adsorption surfaces is also considered briefly. The surface spreading pressure, excess surface energy and entropy are also obtained for a dilute gas of rod-like molecules near a surface. We find that the extent of surface binding increases nearly exponentially with molecular length at constant temperature and surface density, and that the excess surface energy and entropy are essentially proportional to the molecular length.     

Statistical thermodynamics of the stability of multivalent ligand-receptor complexes

Multivalent ligands can form ligand-receptor complexes that are orders of magnitude more stable than their monovalent counterparts. A theory of this "enhancement effect" based on fundamental principles of statistical thermodynamics is presented. A key finding is a simple analytical expression that provides clear and direct insight into the mechanism by which the enhanced stability of the multivalent ligand-receptor complex can be achieved. The theory explains experimental data on the activation of ion channels in the membranes of cells by polymer-linked divalent ligands.     

低温液体核态流动沸腾传热的机理模型

对核态沸腾表面上的各种传热机理进行了分析和量化,建立了低温液体核态流动沸腾传热的机理模型,并将该模型纳入双流体模型实现了数值求解,数值预测的结果详细地反映出了壁面上各参数随流动的变化情况。该机理模型的计算结果表明,气泡挣脱后液体与过热壁面间的激冷效应是导致壁面上各参数在OSV处突变的根本原因。     

On a new foundation of equilibrium thermodynamics

This paper presents a new foundation of equilibrium thermodynamics based on certain ideas of T. Ehrenfest. The main result is the proof for the existence of entropy as a consequence of the conservation of energy for conservative thermal systems.