Thermodynamics liquid-solid interfaces

Adsorption at the Liquid-Solid Interface Thermodynamics and Methodology... 

In this chapter, our aim is to give an introductory account of the methodology and underlying thermodynamic principles of adsorption at the liquid-solid interface. We are mainly, but not exclusively, concerned with the characterization of the liquid-solid interface. In this context, there are two relevant topics ... 

Thermoporometry. Thermoporometry is the calorimetric study of the liquid-solid transformation of a capillary condensate that saturates a porous material such as a membrane. The basic principle involved is the freezing (or melting) point depression as a result of the strong curvature of the liquid-solid interface present in small pores. The thermodynamic basis of this phenomenon has been described by Brun et al. [1973] who introduced thermoporometry as a new pore structure analysis technique. It is capable of characterizing the pore size and shape. Unlike many other methods, this technique gives the actual size of the cavities instead of the size of the openings [Eyraud. 1984]. 

Understanding chemical reactivity at liquid interfaces is important because in many systems the interesting and relevant chemistry occurs at the interface between two immiscible liquids, at the liquid/solid interface and at the free liquid (liquid/vapor) interface. Examples are reactions of atmospheric pollutants at the surface of water droplets[6], phase transfer catalysis[7] at the organic liquid/water interface, electrochemical electron and ion transfer reactions at liquidAiquid interfaces[8] and liquid/metal and liquid/semiconductor Interfaces. Interfacial chemical reactions give rise to changes in the concentration of surface species, but so do adsorption and desorption. Thus, understanding the dynamics and thermodynamics of adsorption and desorption is an important subject as well. 

Surface phase capacity, i.e., the total amount of substances in the adsorbed phase is the second factor determining the sorption properties of the solid sorbents. This quantity is useful for calculating thermodynamic functions which characterize competitive adsorption at the liquid - solid interface and for determining the specific surface area of the sorbents. 

Relevant previous publications on adsorption energetics include, besides the classical text by Gregg and Sing [2], a more recent book by Rouquerol et al. [3] on adsorption by powders and porous solids. This book covers thermodynamic aspects of adsorption at the gas—sohd and liquid—solid interfaces, and an entire chapter is devoted to adsorption on activated carbons. In addition, two books by Bansal et al. [4, 5] review in commendable detail the fiterature on adsorption by activated carbons. 

In a situation compatible with the lubrication approximation, perturbations due to the proximity of a solid surface are weak. In this case, the translational invariance of an unbounded two-phase system is weakly broken, and both the shift of the equilibrium chemical potential due to interactions with the solid surface and the deviation from the zero-order density profile are small. Since molecular interactions have a power decay with a nanoscopic characteristic length, this should be certainly true in layers exceeding several molecular diameters. A necessary condition for the perturbation to remain weak even as the liquid-vapor and liquid-solid interfaces are drawn together still closer, as it should happen in the vicinity of a contact line, is smallness of the dimensionless Hamaker constant % = asps/p — 1- Even under these conditions, the perturbation, however, ceases to be weak when the density in the layer adjacent to the solid deviates considerably from p+. This means that low densities near the solid surface are strongly discouraged thermodynamically, and a... 

A schematic diagram of the unit cell for a vapor-Uquid-porous catalyst system is shown in Fig. 9.9. Each cell is modeled essentially using the NEQ model for heterogeneous systems described above. The bulk fluid phases are assumed to be completely mixed. Mass-transfer resistances are located in films near the vapor-liquid and liquid-solid interfaces, and the Maxwell-Stefan equations are used for calculation of the mass-transfer rates through each film. Thermodynamic equilibrium is assumed only at the vapor-liquid interface. Mass transfer inside the porous catalyst may be described with the dusty fluid model described above. 

Molecular modeling is another attractive approach that can provide necessary insight to the phenomena near surfaces. In this chapter, we illustrate methods that are commonly used for the study of wettability on solid surfaces. We begin with the thermodynamics of liquid-solid interface in the next section followed by simulation techniques and some illustrative examples. 

Adsorption at the liquid/solid interface is responsible for the decrease in solute concentration which occurs when a powder or porous solid is immersed in a suitable solution (e.g. of a dyestuff or surface active agent). A rigorous thermodynamic treatment of the experimental data is not straightforward because solvent is also adsorbed at the interface (to an unknown extent) and because the boundary of the adsorbed layer is difficult to locate exactly Fortunately, a simple interpretation is acceptable for many purposes provided that the solution is dilute and the adsorption of solute much greater than that of the solvent. 

Drying transition may occur in a liquid phase upon heating along the liquid-vapor coexistence curve (see Section 2.1). This transition has drastic effect on the liquid-solid interface above the temperature Tj of a drying transition, the liquid is separated from the solid surface by a macroscopic vapor layer. However, even below Tj and out of the liquid-vapor equilibrium, distant etfect of the drying transition may noticeably affect the liquid density profile. Therefore, it is important to know the temperature of the drying transition of water and its sensitivity to the water-surface interaction. This allows description of the density profiles of liquid water near hydrophobic surfaces at various thermodynamic conditions. 

The basic thermodynamic framework for interfacial thermodynamics was developed by J. W. Gibbs in the late nineteenth century. Central to this formalism is the concept of the dividing surface, which is a mathematical surface to which all excess interfacial thermodynamic quantities are assigned. Once such a dividing surface is defined, the extensive thermodynamic quantities of the two-phase system can be written as the sum of contributions from the two bulk phases (calculated as if each bulk phase were uniform up to the dividing surface) and an excess contribution that is due to the presence of the interface. For a liquid-solid interface of a general multi-component system this procedure gives... 

There have been several liquid-solid interface simulations on the LJ system. These are reviewed in some detail in Ref. 3. Of these, by far the most extensive are those of Broughton and Gilmer. These studies of the structure and thermodynamics of fee [100], [110] and [111] LJ crystal-liquid interfaces were part of a six-part series on the bulk and surface properties of the LJ system. Like most of the earlier simulations, these were done under triple-point conditions. The numbers of particles for the [111], [100] and [110] simulations were 1790, 1598 and 1674, respectively. Analysis of diffusion profiles, various layer-dependent trajectory plots, pair correlation functions, nearest-neighbor fractions and angular correlations yield a width of about three atomic diameters for all three interfaces. The density profiles indicate an interface width that is larger... 

To date, the theories that are best suited to calculate both the detailed structure and thermodynamics of a liquid-solid interface are those based on DFT, which is a general procedure for determining the free energy associated with a given spatially dependent single-particle density, p r). That is, the... 

The thermodynamic work of adhesion, on the other hand, is the work required to pull apart a unit area of a liquid-solid interface, thus creating one solid-vapour and one liquid-vapour interface ... 

In the original Fowkes model [14], only dispersion component of the surface tension was considered, which is caused by London dispersion force. The London dispersion forces arise from the interaction of fluctuating electronic dipoles with induced dipoles in neighboring atoms or molecules [15], It exists in all type of materials and always presents as an attractive force at the liquid-solid interface. The work of adhesion from dispersion interaction has been proved thermodynamically to take the form of the geometric mean according to the Berthelot mixing rule [17, 18]. 

The purpose of this chapter is to introduce the effect of surfaces and interfaces on the thermodynamics of materials. While interface is a general term used for solid-solid, solid-liquid, liquid-liquid, solid-gas and liquid-gas boundaries, surface is the term normally used for the two latter types of phase boundary. The thermodynamic theory of interfaces between isotropic phases were first formulated by Gibbs [1], The treatment of such systems is based on the definition of an isotropic surface tension, cr, which is an excess surface stress per unit surface area. The Gibbs surface model for fluid surfaces is presented in Section 6.1 along with the derivation of the equilibrium conditions for curved interfaces, the Laplace equation. 

In the last two sections the formal theory of surface thermodynamics is used to describe material characteristics. The effect of interfaces on some important heterogeneous phase equilibria is summarized in Section 6.2. Here the focus is on the effect of the curvature of the interface. In Section 6.3 adsorption is covered. Physical and chemical adsorption and the effect of interface or surface energies on the segregation of chemical species in the interfacial region are covered. Of special importance again are solid-gas or liquid-gas interfaces and adsorption isotherms, and the thermodynamics of physically adsorbed species is here the main focus. 

Chapter 1 reviews the concepts necessary for treating the problems associated with the design of industrial reactions. These include the essentials of kinetics, thermodynamics, and basic mass, heat and momentum transfer. Ideal reactor types are treated in Chapter 2 and the most important of these are the batch reactor, the tubular reactor and the continuous stirred tank. Reactor stability is considered. Chapter 3 describes the effect of complex homogeneous kinetics on reactor performance. The special case of gas—solid reactions is discussed in Chapter 4 and Chapter 5 deals with other heterogeneous systems namely those involving gas—liquid, liquid—solid and liquid—liquid interfaces. Finally, Chapter 6 considers how real reactors may differ from the ideal reactors considered in earlier chapters. 

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