Surface Thermodynamics of Liquid

The topic of capillarity concerns interfaces that are sufficiently mobile to assume an equilibrium shape. The most common examples are meniscuses, thin films, and drops formed by liquids in air or in another liquid. Since it deals with equilibrium configurations, capillarity occupies a place in the general framework of thermodynamics in the context of the macroscopic and statistical behavior of interfaces rather than the details of their molectdar structure. In this chapter we describe the measurement of surface tension and present some fundamental results. In Chapter III we discuss the thermodynamics of liquid surfaces. 

The precise thermodynamic relationship between the surface tension and the surface excess can be worked out and the resulting relationship is rigorous and accurate (see Section 6.5.3). The catch is, however, that the method is only suited for the interface between a liquid metal (e.g., mercury) and a solution. This is because the surface tension of liquids can be easily determined (see Section 6.5.1.1) but not the... 

Levi, G., Clarke, D.R. and Kaplan, W.D., Free surface and interface thermodynamics of liquid nickel in contact with alumina , Inter. Sci., 2004 12(1) 73-83. 

In all of these systems, certain aspects of the reactions can be uniquely related to the properties of a surface. Surface properties may include those representative of the bulk material, ones unique to the interface because of the abrupt change in density of the material, or properties arising from the two-dimensional nature of the surface. In this article, the structural, thermodynamic, electrical, optical, and dynamic properties of solid surfaces are discussed in instances where properties are different from those of the bulk material. Predominantly, this discussion focuses on metal surfaces and their interaction with gas-phase atoms and molecules. The majority of fundamental knowledge of molecular-level surface properties has been derived from such low surface area systems. The solid-gas interface of high surface area materials has received much attention in the context of separation science, however, will not be discussed in detail here. The solid-liquid interface has primarily been treated from an electrochemical perspective and is discussed elsewhere see Electrochemistry Applications in Inorganic Chemistry). The surface properties of liquids (liquid-gas interface) are largely unexplored on the molecular level experimental techniques for their study have begun only recently to be developed. The information presented here is a summary of concepts a more complete description can be found in one of several texts which discuss surface properties in more detail. ... 

The molar surface areas and surface tensions of the metastable liquid B, C, O, and N have been estimated from the experimental values available in the literature using code written for this purpose. The chemical potential of the fictitious component, pArea, is equivalent to the surface tension of liquid melt, <7, with the unit, mN m 1. In this way, surface tension of a multicomponent melt can be directly determined using commercial thermodynamic software, ChemSheet, for example. 

In a recent study, a new model of fluids was described by using the generalized van der Waals theory. Actually, van der Waals over 100 years ago suggested that the structure and thermodynamic properties of simple fluids could be interpreted in terms of neatly separate contributions from intermolecular repulsions and attractions. A simple cubic equation of state was described for the estimation of the surface tension. The fluid was characterized by the Lennard-Jones (12-6) potential. In a recent study the dependence of surface tension of liquids on the curvature of the liquid-vapor interface has been described. ... 

Pak and Chang have previously developed a partition function for liquid water applying the modified theory of significant liquid structure proposed by Chang et al. There, it is assumed that Ice-I-like, Ice-III-like, and gas-like molecules exist in liquid water and the molecules like Ice I and Ice III, both of which are oscillating torsionally, are in thermodynamic equilibrium. The equilibrium constant has been taken equal to the ratio of the partition functions of the two species. Various thermodynamic properties and the surface tension of liquid water from the partition function were successfully calculated. 

A THERMODYNAMIC ESTIMATE OF THE THICKNESS OF THE SURFACE LAYER OF LIQUIDS. 

The free energy of formation of a surface is always positive, since work is required in creating a new surface, which increases the total free energy of the system. In order to minimize their free energy solids or liquids assume shapes in equilibrium with the minimum exposed surface area as possible. For example, liquids tend to form a spherical shape and crystal faces which exhibit the closest packing of atoms tend to be the surfaces of lowest free energy of formation and thus the most stable. Surface tension is one of the most important thermodynamic parameters characterizing the condensed phase. Table II lists selected experimentally determined values of surface tensions of liquids and solids that were measured in equilibrium with their vapor. 

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. 

Thermodynamics of Liquid Surfaces (Corresponding States Theory of Liquids)... 

Ward C, Neumann A. (1974) On the surface thermodynamics of a two-component liquid-vapor-ideal solid system. J Colloid Interface Sci 49 286—290. 

A general prerequisite for the existence of a stable interface between two phases is that the free energy of formation of the interface be positive were it negative or zero, fluctuations would lead to complete dispersion of one phase in another. As implied, thermodynamics constitutes an important discipline within the general subject. It is one in which surface area joins the usual extensive quantities of mass and volume and in which surface tension and surface composition join the usual intensive quantities of pressure, temperature, and bulk composition. The thermodynamic functions of free energy, enthalpy and entropy can be defined for an interface as well as for a bulk portion of matter. Chapters II and ni are based on a rich history of thermodynamic studies of the liquid interface. The phase behavior of liquid films enters in Chapter IV, and the electrical potential and charge are added as thermodynamic variables in Chapter V. 

It was made clear in Chapter II that the surface tension is a definite and accurately measurable property of the interface between two liquid phases. Moreover, its value is very rapidly established in pure substances of ordinary viscosity dynamic methods indicate that a normal surface tension is established within a millisecond and probably sooner [1], In this chapter it is thus appropriate to discuss the thermodynamic basis for surface tension and to develop equations for the surface tension of single- and multiple-component systems. We begin with thermodynamics and structure of single-component interfaces and expand our discussion to solutions in Sections III-4 and III-5. 

Figure III-l depicts a hypothetical system consisting of some liquid that fills a box having a sliding cover the material of the cover is such that the interfacial tension between it and the liquid is zero. If the cover is slid back so as to uncover an amount of surface dJl, the work required to do so will he ydSl. This is reversible work at constant pressure and temperature and thus gives the increase in free energy of the system (see Section XVII-12 for a more detailed discussion of the thermodynamics of surfaces).

The equilibrium shape of a liquid lens floating on a liquid surface was considered by Langmuir [59], Miller [60], and Donahue and Bartell [61]. More general cases were treated by Princen and Mason [62] and the thermodynamics of a liquid lens has been treated by Rowlinson [63]. The profile of an oil lens floating on water is shown in Fig. IV-4. The three interfacial tensions may be represented by arrows forming a Newman triangle ... 

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