Gibbs surface tension equation

The change in a, is caused by the change in bulk solute concentration. This is the Gibbs surface tension equation. Basically, these equations describe the fact that increasing the chemical potential of the adsorbing species reduces the energy required to produce new surface (i.e. y). This, of course, is the principal action of surfactants, which will be discussed in more detail in a later section. 

There is, of course, also a generalized form of the ordinary Gibbs surface tension equation, which is broadly consistent with the Helfrich expression (Eq. (3)) above, albeit of an entirely different model-independent nature. At constant temperature, it reads [20] ... 

For constant electrolyte composition and Galvani potential difference, the surface concentration of the adsorbed porphyrins can be evaluated from the Gibbs surface tension expression described by Equation (11.14) , ... 

Gibbs equation of surface concentration This equation relates the surface tension (y) of a solution and the amount (T) of the solute adsorbed at unit area of the surface. For a single non-ionic solute in dilute solution the equation approximates to... 

These surface active agents have weaker intermoiecular attractive forces than the solvent, and therefore tend to concentrate in the surface at the expense of the water molecules. The accumulation of adsorbed surface active agent is related to the change in surface tension according to the Gibbs adsorption equation... 

The type of behavior shown by the ethanol-water system reaches an extreme in the case of higher-molecular-weight solutes of the polar-nonpolar type, such as, soaps and detergents [91]. As illustrated in Fig. Ul-9e, the decrease in surface tension now takes place at very low concentrations sometimes showing a point of abrupt change in slope in a y/C plot [92]. The surface tension becomes essentially constant beyond a certain concentration identified with micelle formation (see Section XIII-5). The lines in Fig. III-9e are fits to Eq. III-57. The authors combined this analysis with the Gibbs equation (Section III-SB) to obtain the surface excess of surfactant and an alcohol cosurfactant. 

Smith [113] studied the adsorption of n-pentane on mercury, determining both the surface tension change and the ellipsometric film thickness as a function of the equilibrium pentane pressure. F could then be calculated from the Gibbs equation in the form of Eq. ni-106, and from t. The agreement was excellent. Ellipsometry has also been used to determine the surface compositions of solutions [114,115], as well polymer adsorption at the solution-air interface [116]. 

If the surface tension of a liquid is lowered by the addition of a solute, then, by the Gibbs equation, the solute must be adsorbed at the interface. This adsorption may amount to enough to correspond to a monomolecular layer of solute on the surface. For example, the limiting value of in Fig. Ill-12 gives an area per molecule of 52.0 A, which is about that expected for a close-packed... 

Fig. Ill-IS. Surface tension data for aqueous alcohol illustration of the use of the Gibbs equation. (1) -butyl (2) -amyl (3) -hexyl (4) -heptyl (5) -octyl. (Data from Ref. 126).

Adsorption may occur from the vapor phase rather than from the solution phase. Thus Fig. Ill-16 shows the surface tension lowering when water was exposed for various hydrocarbon vapors is the saturation pressure, that is, the vapor pressure of the pure liquid hydrocarbon. The activity of the hydrocarbon is given by its vapor pressure, and the Gibbs equation takes the form... 

Thus, adding surfactants to minimize the oil-water and solid-water interfacial tensions causes removal to become spontaneous. On the other hand, a mere decrease in the surface tension of the water-air interface, as evidenced, say, by foam formation, is not a direct indication that the surfactant will function well as a detergent. The decrease in yow or ysw implies, through the Gibb s equation (see Section III-5) adsorption of detergent. 

Equation 9 states that the surface excess of solute, F, is proportional to the concentration of solute, C, multipHed by the rate of change of surface tension, with respect to solute concentration, d /dC. The concentration of a surfactant ia a G—L iaterface can be calculated from the linear segment of a plot of surface tension versus concentration and similarly for the concentration ia an L—L iaterface from a plot of iaterfacial teasioa. la typical appHcatioas, the approximate form of the Gibbs equatioa was employed to calculate the area occupied by a series of sulfosucciaic ester molecules at the air—water iaterface (8) and the energies of adsorption at the air-water iaterface for a series of commercial aonionic surfactants (9). 

The stabihty of a single foam film can be explained by the Gibbs elasticity E which results from the reduction ia equiUbrium surface concentration of adsorbed surfactant molecules when the film is extended (15). This produces an iacrease ia equiUbrium surface tension that acts as a restoring force. The Gibbs elasticity is given by equation 1 where O is surface tension and is surface area of the film. 

Such nonequilihrium surface tension effects ate best described ia terms of dilatational moduh thanks to developments ia the theory and measurement of surface dilatational behavior. The complex dilatational modulus of a single surface is defined ia the same way as the Gibbs elasticity as ia equation 2 (the factor 2 is halved as only one surface is considered). 

The value of 9 can be estimated on purely theoretical grounds from estimates of the adsorption of surfactant which, in turn, can be estimated from the Gibbs adsorption equation relating adsorption to surface-tension lowering. 

The appreciation of the importance of adsorption phenomena at liquid interfaces is probably as old as human history, since it is easily recognized in many facets of everyday life. It is not surprising that liquid interfaces have been a favorite subject of scientific interest since as early as the eighteenth century [3,4], From an experimental point of view, one obvious virtue of the liquid interfaces for studying adsorption phenomena is that we can use surface tension or interfacial tension for thermodynamic analysis of the surface properties. The interfacial tension is related to the adsorbed amount of surface active substances through the Gibbs adsorption equation. 

Van der Waals, whose theory has been further developed by Hulshoff and by Bakker, went one step further than Gibbs by assuming that there exists a perfectly continuous transition from one medium to the other at the boundary. This assumption limits him to the consideration of one particular case that of a liquid in contact with its own saturated vapour, and mathematical treatment becomes possible by the further assumption that the Van der Waals equation (see Chapter II.) holds good throughout the system. The conditions of equilibrium thus become dynamical, as opposed to the statical equilibrium of Laplace s theory. Van der Waals arrives at the following principal results (i) that a surface tension exists at the boundary liquid-saturated vapour and that it is of the same order of magnitude as that found by Laplace s theory (2) that the surface tension... 

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. 

The Gibbs equation relates the extent of adsorption at an interface (reversible equilibrium) to the change in interfacial tension qualitatively, Eq. (4.3) predicts that a substance which reduces the surface (interfacial) tension [(Sy/8 In aj) < 0] will be adsorbed at the surface (interface). Electrolytes have the tendency to increase (slightly) y, but most organic molecules, especially surface active substances (long chain fatty acids, detergents, surfactants) decrease the surface tension (Fig. 4.1). Amphi-pathic molecules (which contain hydrophobic and hydrophilic groups) become oriented at the interface. 

Gibbs adsorption equation phys chem A formula for a system involving a solvent and a solute, according to which there Is an excess surface concentration of solute if the solute decreases the surface tension, and a deficient surface concentration of solute if the solute increases the surface tension. gibz ad sorp shan i.kwa-zhon Gibbs adsorption isotherm physchem An equation for the surface pressure of surface [< ... 

Fig. 5, curve 1, shows - for dodecyl ether sulfates - the areas occupied by a molecule at c as a function of the number, m,of EO groups. The values were calculated by the Gibbs equation from the surface tension measurements. For 0 - m - 2 there is an area increase with increasing m, however, considerably... 

The Gibbs adsorption equation is a relation about the solvent and a solute (or many solutes). The solute is present either as excess (if there is an excess surface concentration) if the solute decreases the y, or as a deficient solute concentration (if the surface tension is increased by the addition of the solute). 

We would anticipate from a consideration of the Gibbs equation that the addition of a solute to a solvent will cause marked changes in the composition of the surface phase if the solvent and solute possess different surface tensions. On the addition of a highly capillary active material to water the surface phase becomes rich in the solute and the surface tension of the solution will fall rapidly. 

In the previous sections we have noted that the hypothesis of a unimolecular Gibbs layer for solutions of liquids of markedly different internal pressures together with the equation of Gibbs leads to values for molecular areas and thicknesses which are not at all unreasonably different from those determined by means of X-ray measurements, or from a study of insoluble substances on the surface of water, but cannot be said to be identical within the limits of experiment. In one respect, however, such soluble films differ from the insoluble films which we shall have occasion to examine in the next chapter the surface tension of solutions which according to the Gibbs adsorption equation... 

The inorganic salts raise the surface tension of water and in accordance with the thermod3mamic considerations implied in the Gibbs equation, the surface concentration of solutions must be less than the bulk concentration. 

Warburg (Wted. Ann. XLi. 1, 1890) observed that the surface tension of the interface between mercury and dilute acid docixiascs as the amount of the corresponding mercury salt present in the solution increases. He therefore concluded that the salt is positively adsorbed in accordance with Gibbs adsorption equation. The adsorption by mercury of its salts from aqueous solution has been directly observed by McLewis jPA /s. Ghem. Lxxvil. 129,... 

Patrick (ibid. Lxxxvi. 645, 1914), Euler and Zimmerlund (ArMv Kemi, Min. Oeol. viii. 14, 1921). Only the last mentioned attempted a quantitative estimation, but made no surface tension measurements by which Gibbs equation might have bcjon toatesd. McLewis was of the opinion that Gibbs equation in the form... 

---