Interfacial Thermodynamics Research Articles

Interfacial Reactions, Thermodynamics and Kinetics in Doped Aluminosilicate Ceramics/Liquid Al-Alloy Contacting Systems

Doping of alumino-silicate crucibles with MgO, CaO, or BaO aimed for improving their performance towards Al-alloy melts in aluminium foundry industry. Depending on the particular oxide, doping considerably affects microstructure and crystalline state of resulting ceramics, as well as interfacial reactions with Al-alloys at elevated temperatures. Analysis of reaction features, in terms of reaction zone structure, mechanism and kinetics, for each particular doping oxide, indicates that reaction intensity and kinetics follow the order MgO>BaO>CaO.

Free Surface and Interface Thermodynamics of Liquid Nickel in Contact with Alumina

Sessile drop experiments of Ni and Ni(2at.%Al) were conducted under controlled working conditions, at 1500°C, P(O2) ≤ 10−9 Torr. It is shown that Al and oxygen atoms engaged in the capillary driven mass transport at the interface have a significant impact on the surface/interface thermodynamics. The surface energy of liquid Ni determined from experiments in which Ni comes into contact with Al2O3 is significantly lower than that of high purity Ni, due to the segregation of Al. The free energy of segregation of Al to the free surface of Ni (Δ G S) was found to range from −164 to −152 kJ/mol, indicating a relatively strong tendency for segregation of Al to the free surface of Ni(Al). It is proposed that an Al(O)-rich liquid layer forms adjacent to the Ni-Al2O3 interface, which improves interfacial adhesion. In the Ni(Al)-Al2O3 system, an increase in the Al content of the alloy leads to the improvement of both wetting and adhesion of the alloy on the ceramic, correlating with the improvement in the interface strength after solidification.

Analysis of high-pressure drop vaporization with flash vapor-liquid equilibrium calculation

A study of high-pressure drop vaporization is conducted with emphasis placed on equilibrium at vapor-liquid interface. General frame of previous rigorous model [1] is retained but tailored for flash equilibrium calculation of vapor-liquid interfacial thermodynamics. The interfacial equilibrium model is properly validated with experimental data and the improvement of the prediction accuracy is made. The flash equilibrium calculation method is shown to be useful in predicting high-pressure droplet vaporization in the respect of solution accuracy and economy in computational cost. Vaporization of n-pentane fuel droplet quiescent in nitrogen gas is examined. High-pressure effects on the droplet vaporization such as ambient gas solubility, properly variation, transient diffusion, and multicomponent transport on the droplet vaporization are investigated and discussed.

Aluminium-alumina interface morphology and thermodynamics from dewetting experiments

This work presents the morphology of micron-sized metallic drops (Al) equilibrated on ceramic substrates (sapphire), with emphasis on the interfacial region. The samples were made by controlled dewetting of a thin Al film on the basal surface of sapphire substrates, at temperatures above the melting point of Al. Morphological inspections showed that evaporation of the sapphire substrate atoms, which diffuse at the interface, has an important role in the evolution of the Al-sapphire interface morphology. The absolute value of the sapphire basal surface energy was extracted (1279 ± 78 mJ/m 2 at 900 °C). The values of the thermodynamic parameters determined from the interface morphology agree well with those from experiments made under identical conditions but using millimetre-sized drops. This confirms the validity of Young’s equation for large sessile drops in systems undergoing limited morphological changes (ridging) at the interface.

Capillary Thermodynamics of Nematic Polymer Interfaces

The Cahn-Hoffman capillarity vector thermodynamics formalism for curved anisotropic interfaces is adapted to soft liquid crystalline polymer-isotropic fluid interfaces. The Cahn-Hoffman formalism in conjunction with the interfacial Landau-de Gennes model is used to derive compact expressions for the capillary pressure, tangential Marangoni force, and interfacial torque. It is shown that the interfacial thermodynamics of nematic polymers can be analyzed in terms of three distinct modes: (i) area size change, (ii) area rotation, and (iii) tensor order parameter curvature. The formalism allows to clearly identify the nature and magnitude of these three contributions. Characteristic cases biaxial and uniaxial nematic ordering states are analyzed. Anisotropic liquid crystal surfaces display a number of novel interfacial effects: (a) capillary pressure even for flat surfaces, (b) tensor order parameter-dependent renormalization of the tension coefficients due to anchoring energy, (c) tensor order parameter-driven transitions between classical Laplace pressure and non-classical behavior, (d) Laplace-like capillary pressure due solely to orientation curvature, (e) generation of Marangoni forces through interfacial order and/or orientation gradients, and (f) surface torques generation. Schematic of the geometry considered in this article.

Fracture properties of interfacially doped Nb-Al 2O 3 bicrystals: II, relation of interfacial bonding, chemistry and local plasticity

As described in part I, Nb and α-Al 2O 3 single crystals were diffusion bonded in UHV for several different orientations of the two constituents. These were doped to give defined levels of interface coverage of Ag, Ti, Y or S. The influence of these dopants on the fracture behaviour of the several metal–ceramic interfaces was studied. Submonolayer doping causes large changes in fracture energy J c: a strong reduction with Ag, and especially S; possibly, a small decrease with Y; and, in contrast, enhancement with Ti. Auger electron spectroscopy data indicated that the interfaces have excess oxygen and provided information on the bonding states and the local crack path. The influences of plasticity of the metal part and of interface chemistry on the bicrystal bond strength are evaluated. The change in the work of attraction, W at, is derived by means of interface thermodynamics using measured surface and interface coverages of dopant atoms. An empirical relationship is then developed between the interfacial J c and W at, which directly demonstrates increasing toughness and associated crack-tip plasticity with increasing interface bonding. The toughness spans two orders of magnitude while W at varies by 2.5 times. At a critical level of W at, a transition causes a virtual jump in interfacial J c; this is interpreted as an incipient blunting transition that is frustrated by the rate sensitive plasticity in the Nb.

Interfacial Composition and Thermodynamics of Formation of Water/Isopropyl Myristate Water-in-Oil Microemulsions Stabilized by Butan-1-ol and Surfactants Like Cetyl Pyridinium Chloride, Cetyl Trimethyl Ammonium Bromide, and Sodium Dodecyl Sulfate

The stabilization and destabilization of water-in-oil (w/o) microemulsion under varied amounts of surfactant and water and varied temperature by mixing with butan-1-ol and isopropyl myristate have been studied in detail. The surfactants used were sodium dodecyl sulfate, cetyl trimethyl ammonium bromide, and cetyl pyridinium chloride. The distribution of cosurfactant (butan-1-ol) between the interface and the oil at the threshold level of stability has been examined, and the thermodynamics of the transfer process of the cosurfactant from the oil to the interface have been evaluated. The structural parameters (dimension, population density, and water pool radius) of the dispersed water droplets in the oil phase have been also evaluated along with the examination of the interfacial population of surfactant and cosurfactant. A rational analysis of the results has been attempted.

Measurement of the Gibbsian interfacial excess of solute at an interface of arbitrary geometry using three-dimensional atom probe microscopy

We show how the Gibbsian interfacial excess of solute can be calculated from three-dimensional atom probe data, even in the case of irregularly shaped interfaces. Standard treatments of interfacial thermodynamics implicitly define a one-dimensional geometry for an interface by assuming a planar interface. Of course, many real systems exhibit non-planar interfaces, and these treatments are difficult to apply. We show how our treatment derives from Gibbs’ original approach and how it is used to derive real thermodynamic quantities. The technique can be applied to any interfacial excess quantity.

Curvature Effects in the Analysis of Pendant Bubble Data: Comparison of Numerical Solutions, Asymptotic Arguments, and Data

The pendant bubble method is commonly used to measure the evolution of the surface tension of surfactant solutions. Initially, the bubble interface is free of adsorbed surfactant. As time progresses, surfactant diffuses to the interface, adsorbs, and reduces the surface tension. The surface tension is assumed to be in equilibrium with the instantaneous surface concentration. Therefore, surface tension data are analyzed in terms of interfacial thermodynamics and mass transfer models in order to infer the mechanisms which determine the surfactant transport. Diffusion from the bulk solution to the bubble can be approximated as diffusion to a spherical interface. Approximating this process as diffusion to a plane introduces significant errors into the data analysis. Mass transfer to a sphere differs from that to a plane; the equilibration of the spherical interface is more rapid simply because of geometry. The failure to account for this effect in the interpretation of pendant bubble data can lead to serious errors in the transport coefficients for the surfactants. In the diffusion-controlled limit, surfactant diffuses to the sublayer immediately adjacent to the interface and adsorbs in local equilibrium according to the adsorption isotherm. There is a closed-form solution for Fick's law describing adsorption to a sphere in an infinite solution which reduces to the Ward and Tordai solution when the bubble radius is large. This equation, along with the adsorption isotherm relating the surface concentration and the sublayer concentration, must be solved numerically in order to solve for the time evolution of the surface concentration. At early times, the adsorption isotherm can be expanded about the clean interface state. At long times, small departures from the equilibrium state can be assumed. In these limits, asymptotic expansions can be obtained. The short- and long-time expansions are found in this study for adsorption to a sphere and compared to those obtained previously for adsorption to a planar interface. In particular, the long-time asymptote for adsorption to a sphere is proportional to t−3/2; this asymptote differs significantly from that for adsorption to a plane, which goes as t−1/2. The full solution for adsorption to a sphere is compared to the Ward and Tordai solution for adsorption to a planar interface. From a comparison of the full solutions, it is established that curvature cannot be neglected unless the ratio of the adsorption depth to the bubble radius is negligible. This ratio can be calculated a priori from equilibrium isotherm parameters. Using constants which describe the surfactant C12E8, for which curvature plays a strong role in the surfactant adsorption dynamics, the short- and long-time solutions for adsorption to the interface are compared to the full solutions and to dynamic surface tension data to infer the range of validity of the approximations.

Gaussian random fields with two level-cuts—Model for asymmetric microemulsions with nonzero spontaneous curvature?

The microstructure of a microemulsion is dominated by the thermodynamics of the surfactant interface between the oil and water domains. As the spontaneous curvature of this surfactant interface is strongly temperature dependent the microstructure of microemulsions also becomes temperature dependent. In the present work we have assumed that the thermodynamics of the interface is determined by the Helfrich Hamiltonian and that the interface can be described by two appropriately chosen level-cuts of a Gaussian random field. It is then possible to express the free energy density of the interface as a functional of the spectral distribution of the Gaussian random field so that the microstructure which minimizes the free energy can be determined by performing a functional minimization of the free energy with respect to the spectral distribution of the Gaussian random field. The two level-cuts are an important feature of the model since they allow us to model microemulsions with nonzero spontaneous curvature and with unequal volume fractions of water and oil. This again makes it possible to simulate the temperature driven phase inversion of the microemulsions described above. The model furthermore allows us to predict the microstructure of the microemulsion for a given composition of water, oil and surfactant and input parameters H0, κ and κ̄ as well as to predict direct space structures and scattering structure factors. Microemulsions with bicontinuous structures, droplet structures or swollen sponge-like structures are predicted dependent on the input parameters and represented in direct and inverse space. Dilution plots for scattering peak positions are in good agreement with experimental results.

Active metal brazing of zirconia

Active metal brazing is a well-established technique for the joining of ceramics to themselves and to metals. Extensive studies have been reported in the literature which examine the interfacial reactions and thermodynamics occurring between the braze alloy and ceramic.In this work, the interactions between Ag–Cu–Ti based braze alloys and partially stabilised zirconia have been examined. During brazing, the active element (titanium) reacts with the zirconia, depleting the surface region of oxygen. This manifests itself as a discolouration — darkening the zirconia. This phenomenon and how it affects the properties of zirconia forms the basis of this work.

Interfacial stability of an indium tin oxide thin film deposited on Si and Si0.85Ge0.15

The stability of the interface formed by depositing indium tin oxide (ITO) thin films on Si and Si0.85Ge0.15 substrates was investigated. Cross-sectional transmission electron microscopy combined with Fourier-transform infrared spectroscopy, energy dispersive x-ray analysis, x-ray diffraction, and capacitance–voltage measurements were used to characterize the interface immediately after rf magnetron sputter deposition as a function of annealing time in ultrahigh purity (UHP) N2 at 785 °C for 10–80 min. The In–Si–O2 ternary phase equilibrium diagram was calculated to predict the possible product layer sequences. A 2-nm-thick interfacial amorphous silicon oxide, associated with ion implantation intermixing, is present in the ITO/Si as-deposited sample, while a 3–7-nm-thick amorphous oxide interlayer is observed in the ITO/Si0.85Ge0.15 sample. During annealing in UHP N2, the interlayer oxide growth rate follows the initial stage of conventional oxidation. In the ITO/Si system, experimental observations revealed a preference for the displacement reaction limited by the diffusivity of Si through the SiO2 layer, i.e., Si/SiO2/In/In2O3. This solid-state oxidation process has the potential for in situ fabrication of ITO metallized SiO2 gates in Si thin film transistor applications. On the other hand, the more complicated quaternary In–Si–Ge–O2 system reveals two distinct reaction layer morphologies, suggesting that the presence of Ge strongly influences the stability of the interfacial thermodynamics and kinetics.

Humidification of air with warm water at elevated pressure in wetted-wall column

A comprehensive analysis of pressurized air humidification in wetted-wall column has been carried out. A developed mathematical model consists of mean flow conservation equations with a full account of variable properties and gas-liquid interfacial thermodynamics, in which a low-Reynolds number к − ε turbulence model in conjunction with combined heat and mass transfer analysis. The influence of various high-pressure phenomena (including property variation, thermodynamic non-ideality etc.) on gas-liquid heat and mass transfer is numerically examined in detail. Results are presented for air-water under different conditions. Particular attention is paid to investigating the variation of the local Nusselt and Sherwood number of gas. The results show that buoyancy force caused by properties variation will reduce the local heat and mass transfer coefficients, and that the extent of reduction in local heat and mass transfer coefficients increases with operate pressure and inlet temperature difference between gas and liquid.

Statistical mechanics of vacancy and interstitial strings in hexagonal columnar crystals

Columnar crystals contain defects in the form of vacancy-interstitial loops or strings of vacancies and interstitials bounded by column "heads" and "tails." These defect strings are oriented by the columnar lattice and can change size and shape by movement of the ends and by forming kinks along the length. Hence an analysis in terms of directed living polymers [S. A. Safran, Statistical Thermodynamics of Surfaces, Interfaces, and Membranes (Addison-Wesley, Reading, MA, 1994), Sec. 8] is appropriate to study their size and shape distribution, volume fraction, etc. If the entropy of transverse fluctuations overcomes the string line tension in the crystalline phase, a string proliferation transition occurs, leading to a supersolid phase [E. Frey, D. R. Nelson, and D. S. Fisher, Phys. Rev. B 49, 9723 (1994); see also J. Prost, Liq. Cryst. 8, 123 (1990)]. We estimate the wandering entropy and examine the behavior in the transition regime. We also calculate numerically the line tension of various species of vacancies and interstitials in a triangular lattice for power-law potentials as well as for a modified Bessel function interaction between columns such as occurs in the case of flux lines in type-II superconductors or long polyelectrolytes in an ionic solution. We find that the centered interstitial is the lowest-energy defect for a very wide range of interactions; the symmetric vacancy is preferred only for extremely short interaction ranges.

Superficial stress and strain at coherent interfaces

The thermodynamics of a coherent interface separating two non-hydrostatically stressed crystals is examined using the Gibbsian paradigm of a dividing surface and associated superficial quantities. Cahn–Hilliard diffuse interface theory is used to derive equations governing the equilibrium composition, stress, and strain profiles through a planar surface of discontinuity. Expressions are then obtained for the superficial stress and strain (excess volume) assuming the isotropic elastic constants are independent of composition and the lattice parameter is a quadratic function of the composition. Materials parameters are identified for which the superficial stress becomes independent of the position of the dividing surface, and the dependence of the superficial stress on the application of a stress normal to the interface, as well as the strain components in the plane of the interface, is calculated for various compositional strains. The superficial stress is estimated to be of the order 1–10 3 dynes/cm and can be either positive or negative in sign.

Stability of droplets and channels on homogeneous and structured surfaces

Wetting of structured or imprinted surfaces which leads to a variety of different morphologies such as droplets, channels or thin films is studied theoretically using the general framework of surface or interface thermodynamics. The first variation of the interfacial free energy leads to the well-known Laplace equation and a generalized Young equation which involves spatially dependent interfacial tensions. Furthermore, we perform the second variation of the free energy for arbitrary surface patterns and arbitrary shape of the wetting morphology in order to derive a new and general stability criterion. The latter criterion is then applied to cylindrical segments or channels on homogeneous and structured surfaces.

Replica theory of the random spherical interface

We investigate the thermodynamics of a spherical interface with quenched disorder in D spatial dimensions, using the variational replica approach of M\'ezard and Parisi. While the disorder-free system exhibits a continuous phase transition analogous to Bose condensation for $D>~3,$ arbitrarily weak disorder removes this transition in three and four dimensions. For $D<~4$ there is a critical value of the mean square wandering of the interface, below which there is no breaking of replica symmetry, and above which the replica symmetry is spontaneously broken at a finite temperature. Replica symmetry breaking is discontinuous, but the one step solution is found to be unstable. We also calculate the helicity modulus of the interface and show that for any D it is equal to that of the pure system at the same temperature and chemical potential.

Pressure-dependence of the interfacial tension of a critical nucleus in the binary-ideal solution

We consider the pressure-dependence of the interfacial tension of a critical nucleus on the basis of the Gibbs interfacial thermodynamics formalism. We rewrite the Gibbs–Duhem relation for the critical nucleus in the multicomponent fluid for the general formulation. The binary-ideal-solution reduction version of the formula is shown to be in good agreement with experimental results.

What do we know that van der Waals did not know?

Reference is made to some of the areas in which van der Waals's work in the nineteenth century anticipated modern developments. This includes applications of the mean-field approximation to the study of dense liquids, of critical phenomena in pure and multicomponent fluids, and of higher-order critical points, particularly tricritical points. The main focus of this lecture, though, is on interfacial structure and thermodynamics, where the work of the present author has had its roots in van der Waals's theory of capillarity. Problems treated include those of wetting and line tension in three-phase equilibrium; pre- (or premonitory) wetting and premelting (surface melting) and the associated boundary tension in the interface between bulk phases; and fluctuations in the internal composition of interfaces and three-phase lines.

Integral equation methods in plane-strain elasticity with boundary reinforcement

In this paper, a linear theory of elastic boundary reinforcement of an elastic solid is developed for plane–strain deformations. The reinforcement consists of a thin elastic coating bonded to part of the boundary of the solid. The elastic properties of the coating incorporate both extensibility and bending rigidity. Interior and exterior mixed–boundary problems are formulated and solved using integral equation methods. The boundary value problems are reduced to systems of singular integro–differential equations to which Noether–type theorems are shown to apply. The case corresponding to a coating which has only extensibility properties and no bending rigidity is particularly interesting from a mathematical point of view and is given special attention. Finally, existence and uniqueness results are presented for both interior and exterior reinforcement problems of plane–strain.