Surface tension Gibbs adsorption equation

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 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. 

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 [< ... 

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). 

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... 

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,... 

Hence the surface adsorption of surfactant 1 and 2, and their surface mole fractions can be obtained from the surface (interfacial) tension-concentration relationships (Fig.1 and fig.2) by applying the Gibbs adsorption equation. 

Takahashi et al.67) prepared ionene-tetrahydrofuran-ionene (ITI) triblock copolymers and investigated their surface activities. Surface tension-concentration curves for salt-free aqueous solutions of ITI showed that the critical micelle concentration (CMC) decreased with increasing mole fraction of tetrahydrofuran units in the copolymer. This behavior is due to an increase in hydrophobicity. The adsorbance and the thickness of the adsorbed layer for various ITI at the air-water interface were measured by ellipsometry. The adsorbance was also estimated from the Gibbs adsorption equation extended to aqueous polyelectrolyte solutions. The measured and calculated adsorbances were of the same order of magnitude. The thickness of the adsorbed layer was almost equal to the contour length of the ionene blocks. The intramolecular electrostatic repulsion between charged groups in the ionene blocks is probably responsible for the full extension of the... 

Surfactants are compounds that exhibit surface activity, or more generally, interfacial activity, and migrate to the interface when placed in solution. This migration results in lowering the solution surface tension (interfacial tension) as compared to the surface tension of the pure solvent. Thermodynamically, adsorption of a surfactant is deLned by the Gibbs adsorption equation ... 

The Gibbs adsorption equation enables the extent of adsorption at a liquid surface to be estimated from surface tension data. 

Adsorption can be measured by direct or indirect methods. Direct methods include surface microtome method [46], foam generation method [47] and radio-labelled surfactant adsorption method [48]. These direct methods have several disadvantages. Hence, the amount of surfactant adsorbed per unit area of interface (T) at surface saturation is mostly determined by indirect methods namely surface and interfacial tension measurements along with the application of Gibbs adsorption equations (see Section 2.2.3 and Figure 2.1). Surfactant structure, presence of electrolyte, nature of non-polar liquid and temperature significantly affect the T value. The T values and the area occupied per surfactant molecule at water-air and water-hydrocarbon interfaces for several anionic, cationic, non-ionic and amphoteric surfactants can be found in Chapter 2 of [2]. 

The image force formalism was intended primarily to relate, via the Gibbs adsorption equation, the increase of the surface tension of water to the negative adsorption of the electrolyte ions. Its effect on the double layer interactions was examined by Jonsson and Wennerstrom [4]. 

The increase of the surface tension of water by the addition of an electrolyte was traditionally related (via Gibbs adsorption equation) to the negative adsorption of ions on the interface. However, some electrolytes decrease the interfacial tension [29], hence should be positively adsorbed. Therefore, if the van der Waals interactions would repel all the ions from the interface, some additional interactions have to be included to explain the positive adsorption. 

In this case (in the absence of a surface charge) the interface is neutral. The dependence of the interfacial tension y on the uni-univalent electrolyte concentration cE can be calculated using the Gibbs adsorption equation ... 

The change in the interfacial tension due to the electrolyte ions can be calculated using the Gibbs adsorption equation (Eqs. (12)—(14)). The surface adsorptions are given by ... 

Once the additional interactions are known, the distribution of the concentration of ions near the interface can be obtained from eqs la and lb (for the appropriate boundary conditions), and consequently, the surface tension of electrolytes can be easily calculated, via the Gibbs adsorption equation. 

First let us note that experiment revealed long ago that not all ions prefer the bulk to the interface [8]. Gibbs adsorption equation predicts that the surface tension increases with the electrolyte concentration when the total surface excess of ions is negative. The conventional picture, that the ions prefer the bulk, is probably due to Langmuir, who noted that the increase in the surface tension of aqueous solutions of simple salts with increasing concentration can be explained by assuming a surface layer of pure solvent with a thickness of about 4 A [9]. However, because the aqueous solutions of some simple acids (such as HC1) possess surface tensions smaller than that of pure water [8], Gibbs adsorption equation indicates a positive total... 

The surface tension depends on the potential (the excess charge on the surface) and the composition (chemical potentials of the species) of the contacting phases. For the relation between y and the potential see - Lipp-mann equation. For the composition dependence see -> Gibbs adsorption equation. Since in these equations y is considered being independent of A, they can be used only for fluids, e.g., liquid liquid such as liquid mercury electrolyte, interfaces. By measuring the surface tension of a mercury drop in contact with an electrolyte solution as a function of potential important quantities, such as surface charge density, surface excess of ions, differential capacitance (subentry of... 

For many purposes it is conducive to start analyses with thermodynamic considerations. In this way, it is often possible to find laws of general validity and to determine the boundaries between which models can be developed. For the study of (relaxed) double layers the Gibbs adsorption equation is the starting point. Although the interfacial tension of a solid-liquid interface cannot be measured, this equation remains useful because it helps to distinguish measurable and Inoperable variables, and because it can be used to correlate surface concentrations of different species (Including the surface ions), some of which may not be analytically accessible. 

Figure 9.5. Gibbs adsorption equation. The surface excess F can be obtained (cf. equation 19) from a plot of surface tension 7 versus log activity (concentration) of adsorbate. The area occupied per molecule or ion adsorbed can be calculated.

The equations (28.28), (28.29) and (28.30) are forms of the Gibbs adsorption equation, first derived by J. Willard Gibbs (1878) it relates the surface excess of the solute to the variation of the surface tension of the solution with the concentration (or activity). If an increase in the concentration of the solute causes the surface tension of the solution to decrease, i.e., (dy/dc)T9 is negative, F2 will be positive, by equation (28.30), so that there is an actual excess of solute in the surface in other words, adsorption of the solute occurs under these conditions. If (dy/dc)T is positive, F2 is negative and there is a deficiency of the solute in the surface this phenomenon is referred to as negative adsorption. 

In these equations 6 is the adsorbate surface coverage calculated from surface pressure data by means of the Gibbs adsorption equation, x, Xg are the mole fractions of the adsorbate and solvent respectively in the bulk solution, a is the activity of the adsorbate in the bulk solution, II(= 7 — 7) is the experimental surface pressure of the adsorbed film, 7 is the surface tension of the test solution, 7° is the value of 7 of the pure solvent, R is the gas constant and T is the temperature. 

An alternative theoretical approach to the evaluation of the solid—liquid surface tension which is particularly useful at low pressure and coverage is based on an integration of the Gibbs adsorption equation (Eqn 2.60 in [7]) that can be written as... 

The comparison between Equations 5.42 and 5.43 shows that the Gibbs adsorption equation can be expressed either in terms of a, and a or in terms of o, E , and a. Note that Equations 5.42 and 5.44 are valid under equilibrium conditions, whereas Equation 5.43 can be used also for the description of dynamic surface tension (Section 5.2.2) in the case of surfactant adsorption under diffusion control, assuming local equilibrium between adsorptions E and subsurface concentrations of the respective species. 

By substimting Ci/f) for Cj in the Gibbs adsorption Equation 5.2, and integrating, we obtain the long-time asymptotics of the surface tension of a nonionic surfactant solution after a large initial perturbation ... 

---