Gibbs interface

The second limit is named the cognition limit and arises from the less controlled assumptions concerning the complicated and ill acquainted phenomena involved in the process. Considering the interface as an equilibrium Gibbs interface and introducing the turbulent flow from the turbulent diffusion coefficient are two famous examples which illustrate this class of cognition limits. 

Figure 1 shows the GSE model for equilibrium adsorption from a bulk multicomponent gas mixture of i components (/ = 1,2. .., N) characterized by P. T, and y,. The adsorption system contains a unit amount of an inert adsorbent whose total helium void volume is u (cm /g). It is assumed that all pores of the adsorbent are accessible to the nonadsorbing helium gas. The dotted line in Fig. 1 represents the Gibbs interface separating the Gibbsian adsorbed phase and the bulk gas phase. It is arbitrarily located inside the actual bulk gas phase. The adsorbed phase has a... 

Schematic of the surface excess distribution of a surface active species across an interface between two immiscible liquids, (a) Ideal distribution showing ideal shape interface, (b) Distribution across interface. The Gibbs interface is an arbitrary line which in the first case represents the solubility in the two phases a and P and the second (b) is constrained so that the areas are equal. ...

An approach developed by Guggenheim [106] avoids the somewhat artificial concept of the Gibbs dividing surface by treating the surface region as a bulk phase whose upper and lower limits lie somewhere in the bulk phases not far from the interface. 

As an example, Tajima and co-workers [108] used labeling to obtain the adsorption of sodium dodecyl sulfate at the solution-air interface. The results, illustrated in Fig. Ill-12, agreed very well with the Gibbs equation in the form... 

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... 

The succeeding material is broadly organized according to the types of experimental quantities measured because much of the literature is so grouped. In the next chapter spread monolayers are discussed, and in later chapters the topics of adsorption from solution and of gas adsorption are considered. Irrespective of the experimental compartmentation, the conclusions as to the nature of mobile adsorbed films, that is, their structure and equations of state, will tend to be of a general validity. Thus, only a limited discussion of Gibbs monolayers has been given here, and none of such related aspects as the contact potentials of solutions or of adsorption at liquid-liquid interfaces, as it is more efficient to treat these topics later. 

The preceding evidence for orientation at the interface plus the considerations given in Section III-3 make it clear that the polar end is directed toward the water and the hydrocarbon tails toward the air. On the other hand, the evidence from the study of the Gibbs monolayers (Section III-7) was that the smaller molecules tended to lie flat on the surface. It will be seen that the orientation... 

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. 

The non-consen>ed variable (.t,0 is a broken symmetry variable, it is the instantaneous position of the Gibbs surface, and it is the translational synnnetry in z direction that is broken by the inlioinogeneity due to the liquid-vapour interface. In a more microscopic statistical mechanical approach 121, it is related to the number density fluctuation 3p(x,z,t) as... 

Equation (A3.3.73) is referred to as the Gibbs-Thomson boundary condition, equation (A3.3.74) detemiines p on the interfaces in temis of the curvature, and between the interfaces p satisfies Laplace s equation, equation (A3.3.71). Now, since ] = -Vp, an mterface moves due to the imbalance between the current flowing into and out of it. The interface velocity is therefore given by... 

Donohue M D and Aranovloh G L 1998 Classifioatlon of Gibbs adsorption Isotherms Adv. Colloid Interface Sci. 76/77 137-52... 

As in the qualitative discussion above, let 7 be the Gibbs free energy per unit area of the interface between the crystal and the surrounding hquid. This is undoubtedly different for the edges of the plate than for its faces, but we... 

The excess energy associated with an interface is formally defined in terms of a surface energy. This may be expressed in terms either of Gibbs, G, or Helmholtz, A, free energies. In order to circumvent difficulties associated with the unavoidably arbitrary position of the surface plane, the surface energy is defined as the surface excess [7,8], i.e the excess (per unit area) of the property concerned consequent upon the presence of the surface. Thus Gibbs surface free energy is defined by... 

The physics underlying Eqs. (74-76) is quite simple. A solidifying front releases latent heat which diffuses away as expressed by Eq. (74) the need for heat conservation at the interface gives Eq. (75) Eq. (76) is the local equilibrium condition at the interface which takes into account the Gibbs-Thomson correction (see Eq. (54)) K is the two-dimensional curvature and d Q) is the so-called anisotropic capillary length with an assumed fourfold symmetry. 

Ebox = total calculated energy inside the box drawn around the interface. This should be the Gibbs free energy. An approximation to it would be the internal energy atT=OK. 

The above provides a means of showing how the total excess charge on the solution side of the interface q the excess charge due to cations F+ and the excess charge due to anions F, vary with potential in a solution of fixed concentration of electrolyte. On the basis of this approach to the electrocapillary curves it has been shown that the Gibbs surface excess for cations is due solely to electrostatic forces (long-range coulombic), and this is reflected in the fact that the electrocapillary curves for different cations and... 

On account of the very great difficulty of measuring the extremely small amounts of adsorbed substance at a liquid/gas or liquid/liquid interface, very few experiments are available for testing Gibbs s equation. Zawidski(13) (1900) pointed out that the concentration of the foam of a solution should be different from that of the latter in bulk, and Miss Benson (14> (1903) by the analysis of a solution of amyl alcohol in water found... 

The Gibbs equation allows the amount of surfactant adsorbed at the interface to be calculated from the interfacial tension values measured with different concentrations of surfactant, but at constant counterion concentration. The amount adsorbed can be converted to the area of a surfactant molecule. The co-areas at the air-water interface are in the range of 4.4-5.9 nm2/molecule [56,57]. A comparison of these values with those from molecular models indicates that all four surfactants are oriented normally to the interface with the carbon chain outstretched and closely packed. The co-areas at the oil-water interface are greater (heptane-water, 4.9-6.6 nm2/molecule benzene-water, 5.9-7.5 nm2/molecule). This relatively small increase of about 10% for the heptane-water and about 30% for the benzene-water interface means that the orientation at the oil-water interface is the same as at the air-water interface, but the a-sulfo fatty acid ester films are more expanded [56]. 

At constant p and T, the Gibbs adsorption equation for an electrode interface leads to the well-known Lippmann equation12 ... 

The mapping (7) introduces the unknown interface shape explicitly into the equation set and fixes the boundary shapes. The shape function h(x,t) is viewed as an auxiliary function determined by an added condition at the melt/crystal interface. The Gibbs-Thomson condition is distinguished as this condition. This approach is similar to methods used for liquid/fluid interface problems that include interfacial tension (30) and preserves the inherent accuracy of the finite element approximation to the field equation (27)... 

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