Surface tension entropy

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. 

An overview of some basic mathematical techniques for data correlation is to be found herein together with background on several types of physical property correlating techniques and a road map for the use of selected methods. Methods are presented for the correlation of observed experimental data to physical properties such as critical properties, normal boiling point, molar volume, vapor pressure, heats of vaporization and fusion, heat capacity, surface tension, viscosity, thermal conductivity, acentric factor, flammability limits, enthalpy of formation, Gibbs energy, entropy, activity coefficients, Henry s constant, octanol—water partition coefficients, diffusion coefficients, virial coefficients, chemical reactivity, and toxicological parameters. 

Generalized charts are appHcable to a wide range of industrially important chemicals. Properties for which charts are available include all thermodynamic properties, eg, enthalpy, entropy, Gibbs energy and PVT data, compressibiUty factors, Hquid densities, fugacity coefficients, surface tensions, diffusivities, transport properties, and rate constants for chemical reactions. Charts and tables of compressibiHty factors vs reduced pressure and reduced temperature have been produced. Data is available in both tabular and graphical form (61—72). 

Values for many properties can be determined using reference substances, including density, surface tension, viscosity, partition coefficient, solubihty, diffusion coefficient, vapor pressure, latent heat, critical properties, entropies of vaporization, heats of solution, coUigative properties, and activity coefficients. Table 1 Hsts the equations needed for determining these properties. 

FIG. 1 The calculated surface tension of an argon fluid represented as a Lennard-Jones fluid is shown as a function of temperature. The GvdW(HS-B2)-functional is used in all cases. The filled squares correspond to step function profile and local entropy, the filled circles to tanh profile with local entropy, and the open circles to tanh profile with nonlocal entropy. The latter data are in good agreement with experiment. 

There is a discussion in the literature about the effect of undulation entropy on the equilibrium membrane tension [14,15], Formally, undulations are included in the surface tension, and thus we need not worry about this. However, if in some model the two are artificially decoupled, one may allow for a very small (positive) surface tension as the equilibrium structure. In other words, the entropy (per unit area) from undulations should compensate for the tension (excess free energy per unit area). 

Thus, Ss is the surface entropy per square centimeter of surface. This shows that, to change the surface area of a liquid (or solid, as described in later text), there exists a surface energy (y surface tension) that needs to be considered. 

The surface entropy of liquids is given by (-d y/dT). This means that the entropy is positive at higher temperatures. The rate of decrease of surface tension with temperature is found to be different for different liquids (Appendix A), which supports the foregoing description of liquids. This observation explains the molecular description of surface tension. 

Before turning to the surface enthalpy we would like to derive an important relationship between the surface entropy and the temperature dependence of the surface tension. The Helmholtz interfacial free energy is a state function. Therefore we can use the Maxwell relations and obtain directly an important equation for the surface entropy ... 

For pure liquids the description becomes much simpler. We start by asking, how is the surface tension related to the surface excess quantities, in particular to the internal surface energy and the surface entropy ... 

The surface entropy per unit area is given by the change in the surface tension with temperature. In order to determine the surface entropy one needs to measure how the surface tension changes with temperature. 

For the majority of liquids, the surface tension decreases with increasing temperature. This behaviour was already observed by Eotvos, Ramsay Shields at the end of the last century [43,44], The entropy on the surface is thus increased, which implies that the molecules at the surface are less ordered than in the bulk liquid phase. 

This is the heat per unit area absorbed by the system during an isothermal increase in the surface. Since d y/dT is mostly negative the system usually takes up heat when the surface area is increased. Table 3.1 lists the surface tension, surface entropy, surface enthalpy, and internal surface energy of some liquids at 25°C. 

Table 3.1 Surface tension, surface entropy, surface enthalpy, and internal surface energy of some liquids at 25°C.

The quantity y is usually called the surface tension for liquid-gas interfaces and the interfacial tension for liquid-liquid interfaces. We see from Equation (13.2) that y da is the differential quantity of work that must be done reversibly on the system to increase the area of the system by the differential amount da at constant entropy, volume, and mole numbers. 

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