Surface tension Gibbs adsorption isotherm

The deviations from the Szyszkowski-Langmuir adsorption theory have led to the proposal of a munber of models for the equihbrium adsorption of surfactants at the gas-Uquid interface. The aim of this paper is to critically analyze the theories and assess their applicabihty to the adsorption of both ionic and nonionic surfactants at the gas-hquid interface. The thermodynamic approach of Butler [14] and the Lucassen-Reynders dividing surface [15] will be used to describe the adsorption layer state and adsorption isotherm as a function of partial molecular area for adsorbed nonionic surfactants. The traditional approach with the Gibbs dividing surface and Gibbs adsorption isotherm, and the Gouy-Chapman electrical double layer electrostatics will be used to describe the adsorption of ionic surfactants and ionic-nonionic surfactant mixtures. The fimdamental modeling of the adsorption processes and the molecular interactions in the adsorption layers will be developed to predict the parameters of the proposed models and improve the adsorption models for ionic surfactants. Finally, experimental data for surface tension will be used to validate the proposed adsorption models. 

Downer et al. [29] attempted to remove divalent metal ions by an addition of EDTA in amounts sufficient to chelate the contaminants, but below the concentration at which EDTA affects the surface tension. However, adsorption isotherms derived from surface tension with a Gibbs prefactor of 2 did not agree with those obtained from neutron reflection data. A better agreement was found when using a prefactor of 1.7, consistent with about 30% dissociation of counterions. 

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 problem has been treated theoretically by the use of the Gibbs adsorption isotherm, which has been used with success in treating the interfaces between liquids and gases (30). One of the most easily measurable properties of a liquid is its surface tension, and changes in this quantity can be determined with great accuracy. The surface tension of a liquid is numerically equal to its surface energy, as also are changes in these quantities. 

The surface tension data given in Figure 3.5 was obtained for aqueous solutions of a trivalent cationic surfactant (C0RCI3) in both water and in 150 mM NaCl solution. Use the data and the Gibbs adsorption isotherm to obtain estimates of the minimum surface area per molecule adsorbed at the air/water interface. 

Beside the theoretically derived Gibbs adsorption isotherm, a large number of models have been developed that empirically describe a relationship between the interfacial coverage, the surface tension, and the surfactant concentration in the bulk phase. These adsorption isotherms are known under the names of the authors that first described them—i.e., the Fangmuir, Frumkin, or Volmer isotherms. A complete mathematical description of these isotherms is beyond the scope of this unit and the reader is encouraged to consult the appropriate literature instead (e.g., Dukhin et al., 1995). 

Using Gibbs adsorption isotherm, an expression for the time-dependent decrease of the surface tension is obtained ... 

It is well known that the surface tension of water decreases when a detergent is added. Detergents are strongly enriched at the surface, which lowers the surface tension. This change of surface tension upon adsorption of substances to the interface, is described by the Gibbs adsorption isotherm. 

The Gibbs adsorption isotherm is a relationship between the surface tension and the excess interfacial concentrations. To derive it we start with Eqs. (3.27) and (3.28). Differentiation of... 

For solutions the Gibbs dividing plane is conveniently positioned so that the surface excess of the solvent is zero. Then the Gibbs adsorption isotherm (Eq. 3.52) relates the surface tension to the amount of solute adsorbed at the interface ... 

The interfacial tension decreases with increasing amount of surface potential. The reason is the increased interfacial excess of counterions in the electric double layer. In accordance with the Gibbs adsorption isotherms, the interfacial tension must decrease with increasing interfacial excess. At charged interfaces ions have an effect similarly to surfactants at liquid surfaces. 

For ionic surfactants another effect often dominates and usually salt tends to stabilize emulsions. Reason without salt the distance between surfactants in the interface is large because the molecules electrostatically repel each other. This prevents a high surface excess. The addition of salt reduces this lateral repulsion and more surfactant molecules can adsorb at the interface. Then, according to the Gibbs adsorption isotherm Eq. (3.52), the surface tension is reduced and the emulsion is stabilized. 

If there is still a significant proportion of the amphiphile dissolved in the liquid we talk about Gibbs monolayers. Solubility in water is increased by using molecules with short alkyl chain or a high polarity of the headgroup. In this case T is determined from the reduction of the surface tension according to the Gibbs adsorption isotherm (Eq. 3.52). 

If we compress a surfactant film on water we observe that the surface tension decreases and the surface pressure increases. What is the reason for this decrease in surface tension We can explain it by use of the Gibbs adsorption isotherm (Eq. (3.52)). On compression, the surface excess increases and hence the surface tension has to decrease. This, however, is relatively abstract. A more illustrative explanation is that the surface tension decreases because the highly polar water surface (high surface tension) is more and more converted into a nonpolar hydrocarbon surface (low surface tension). 

With surfactant the surface tension is reduced according to the Gibbs adsorption isotherm Eq. (3.52). To apply Eq. (3.52) we need to know the surface excess ... 

The correct thermodynamic treatment of adsorption processes is possible only on liquid-gas and liquid-liquid interfaces, where the surface energy or the surface tension of the liquid can precisely be determined. For these systems, the Gibbs adsorption isotherm can be applied. For example on a liquid-liquid interface,... 

On a liquid-gas interface, the partial pressure of the adsorbed gas is substituted in Equation 1.59. On the solid-gas and solid-liquid interfaces, only the excess surface concentration can be measured directly, and not the surface tension. The Gibbs adsorption isotherm is suitable for the calculation of the change of surface tension. 

The surface tension of an electrode in contact with solution depends on the metal-solution potential difference. The equation describing this dependence is called the electrocapillary equation. It follows from the Gibbs adsorption isotherm, as we shall show in a moment. Before we do that, however, let us write this equation and discuss some of its consequences. 

Surfactant surface activity is most completely presented in the form of the Gibbs adsorption isotherm, the plot of solution surface tension versus the logarithm of surfactant concentration. For many pure surfactants, the critical micelle concentration (CMC) defines the limit above which surface tension does not change with concentration, because at this stage, the surface is saturated with surfactant molecules. The CMC is a measure of surfactant efficiency, and the surface tension at or above the CMC (the low-surface-tension plateau) is an index of surfactant effectiveness (Table XIII). A surfactant concentration of 1% was chosen where possible from these various dissimilar studies to ensure a surface tension value above the CMC. Surfactants with hydrophobes based on methylsiloxanes can achieve a low surface tension plateau for aqueous solutions of —21-22 mN/m. There is ample confirmation of this fact in the literature (86, 87). 

An increase in surface concentration of active substance T occurs in the following relation with surface tension y (the Gibbs adsorption isotherm) ... 

When an electrolyte is added to water, a small increase in surface tension is observed [6]. This is illustrated for several 1-1 electrolytes in fig. 8.7. The Gibbs adsorption isotherm for these systems can be written as... 

An important principle from thermodynamics is the well-known Gibbs adsorption isotherm, which provides a relationship among the bulk-phase concentration c, the interfacial concentration T, and the interfacial tension (essentially the surface free energy per unit area) ... 

Tn his classic book (I) N. K. Adam discussed the behavior of very dilute - monolayers at the air/water (A/W) interface and using measurements published ear her by Jessop and himself (2, 3, 4), he showed that surface pressure (n)-area (A) isotherms for insoluble uncharged species, when plotted on a nA vs. n basis, suggested a limit of IkT at zero II. The same limit was also suggested by Schofield and Rideal s plot (5) of Frumkin s surface tension data (6) using the Gibbs adsorption isotherm to calculate A. Adam (I) stressed that n should be measured to the second decimal place to establish this limit unequivocally Adam and Jessop (4) provide one of the few sound extrapolations to this limit with their data on the esters of some dicarboxylic acids. 

The Gibbs adsorption isotherm shows the dependence of the extent of adsorption of an adsorbent on its bulk concentration or pressure. However, we also need to know the state of the adsorbate at the surface. These are interrelated because the extent of material adsorb-tion on a surface depends on the state of the surface. The behavior of the molecules in the surface film is expressed by a surface equation of state which relates the spreading pressure, n, which is the difference between the solvent and solution surface tensions, %= % - y to the surface concentration of the adsorbent. This equation is concerned with the lateral motions and interactions of the molecules present in an adsorbed film. In general, the surface equation of state is a two-dimensional analogue of the three-dimensional equation of state of fluids, and since this is related to monomolecular films, it will be described in Sections 5.5 and 5.6. It should be remembered that on liquid surfaces, usually monolayers form, but with adsorption on solid surfaces, usually multilayers form (see Section 8.3). 

Surface tensions of the soluble alkali salt of di- and tri-hydroxy bile salts have been widely employed [5,11,12,33,70-74] to measure CMCs of bile salts (see Section VI.l). Employing Gibbs adsorption isotherm equation and the steep slope of the experimental surface tension versus bile salt concentration curve, the surface excess, i.e. concentration of bile salt molecules/cn of interface, can be calculated accurately in high bulk ionic strength [12,70], Using this value and Avogadro s number, the area per molecule at the interface can be calculated [6]. These values (Table 3b),... 

This is the Gibbs adsorption isotherm. If the surface tension of the solution decreases with... 

Plot y versus In m and determine the surface excess of acetic acid using the Gibbs adsorption isotherm. (Note We can use the molality, m, in the isotherm instead of C2, the molarity.) b) At 25 °C, the surface tensions of propionic acid solutions in water are... 

The Gibbs adsorption isotherm relates the change of the tension, y, of the substrate in contart with the dilute polymer solution with the surface excess, Ts, as... 

The MPB approximation has been used recently, in 1991, by Bhuiyan et al. [25] for the surface tension problem. The excess surface tension was determined by numerical integration of the Gibbs adsorption isotherm (the Gibbs equation), with the electrolyte activity obtained from the bulk MPB approximation. A simple model of the interface, used previously in another study [16], was adopted. In an earlier study [26], this version of the MPB equation had been reported to be... 

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