Langmuir adsorption isotherm ionic surfactant

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. 

In general, the adsorption of ionic surfactants follows the Langmuir isotherm, as discussed in Section 4.1. The adsorption of the surfactants onto the solid surfaces is dependent on the orientation and the packing efficiency of the solid surfaces. The onset of the adsorption plateau may occur at the critical micelle concentration (c.m.c.) of the surfactant in water, as shown in Figure 4.28. If the adsorption isotherm... 

The adsorption of ionic surfactants on hydrophobic surfaces may be represented by the Stern-Langmuir isotherm [17]. Consider a substrate containing sites... 

As this subject was covered in detail in Chapter 5, only a summary will be provided at this point. Surfactant adsorption is usually reversible, and hence thermodynamics can be applied for deriving the adsorption isotherm. Eor example, the adsorption of ionic surfactants onto hydrophobic surfaces may be represented by the Stern-Langmuir isotherm [13]. Consider a substrate containing sites (molm ) on which F molm of surfactant ions are adsorbed. The surface coverage 0 is (F/NJ and the fraction of uncovered surface is (1 — 0). The Stern-Langmuir... 

The definition of Gibbs elasticity given by Eq. (19) corresponds to an instantaneous (Aft t ) dilatation of the adsorption layer (that contributes to o ) without affecting the diffuse layer and o. The dependence of o on Ty for nonionic surfactants is the same as the dependence of o on Ty for ionic surfactants, cf Eqs (7) and (19). Equations (8) and (20) then show that the expressions for Eq in Table 2 are valid for both nonionic and ionic siufactants. The effect of the surface electric potential on the Gibbs elasticity Eq of an ionic adsorption monolayer is implicit, through the equilibrium siufactant adsorption T y which depends on the electric properties of the interface. To illustrate this let us consider the case of Langmuir adsorption isotherm for an ionic surfactant (17) ... 

To illustrate the dependence of the mobility function d>y on the concentration of surfactant in the continuous phase, in Fig. 12 we present theoretical curves, calculated in Ref 138 for the nonionic surfactant Triton X-100, for the ionic surfactant SDS ( + 0.1 M NaCl) and for the protein bovine serum albumin (BSA). The parameter values, used to calculated the curves in Fig. 12, are listed in Table 4 and K are parameters of the Langmuir adsorption isotherm used to describe the dependence of surfactant adsorption, surface tension, and Gibbs elasticity on the surfactant concentration (see Tables 1 and 2). As before, we have used the approximation Dj Dj (surface diffusivity equal to the bulk dif-fusivity). The surfactant concentration in Fig. 12 is scaled with the reference concentration cq, which is also given in Table 4 for Triton X-100 and SDS + 0.1 M NaCl, cq is chosen to coincide with the cmc. The driving force, F, was taken to be the buoyancy force for dodecane drops in water. The surface force is identified with the van der Waals attraction the Hamaker function Ajj(A) was calculated by means of Eq. (86) (see below). The mean drop radius in Fig. 12 is a = 20 /pm. As seen in the figure, for such small drops 4>y = 1 for Triton X-100 and BSA, i.e., the drop sur-... 

The result of these investigations leaves the following view of adsorption of ionic surfactants onto hydrophobic surfaces. Measured adsorption isotherms (Langmuir type) and comparisons between particle sizes as measured by soap titration and... 

Hoeft [44] also studied the cooperative and competitive adsorption of ionic surfactant mixtures onto hydrophobic surfaces. When shorter alkyl chain surfactants (sodium octyl sulfonate and sodium decyl sulfonate) are adsorbed, the decyl will displace the octyl surfactant. For mixtures of sodium dodecyi sulfonate and sodium octyl sulfonate, however, there appears to be an association between the surfactant molecules leading to enhanced adsorption of the sodium dodecyi sulfonate with no depletion of the octyl sulfonate adsorption. This is shown in Fig, 2, where the lines indicate the expected adsorption determined using a two-component Langmuir adsorption isotherm with the adsorption parameters determined analyzing the data from adsorption of each species individually. Also shown in Fig. 2 is the concentration of surface-active materials in the aqueous phase at equilibrium. In each of these experiments the total molar concentration and amount of surfactant solution added to the latex was a constant, as was the amount of latex. Thus a lower value for the bulk concentration corresponds to greater adsorption. 

Adsorption of ionic surfactants at the solid/solution interface is of vital importance in determining the stability of suspension concentrates. As discussed in Chapter 5, the adsorption of ionic surfactants on solid surfaces can be measured directly by equilibrating a known amount of solid (with known surface area) with surfactant solutions of various concentrations. After reaching equilibrium, the solid particles are removed (for example by centrifugation) and the concentration of surfactant in the supernatant liquid is determined analytically. From the difference between the initial and flnal surfactant concentrations (Ci and C2 respectively) the number of moles of surfactant adsorbed, F, per unit area of solid is determined and the results may be fitted to a Langmuir isotherm. 

Results on the adsorption of ionic surfactants on pesticides are scarce. However, Tadros [81] obtained some results on the adsorption of NaDBS and CTABr on a fungicide, namely ethirimol. For NaDBS, the shape of the isotherm was of a Langmuir type, giving an area/DBS at saturation of 0.14 nm. The adsorption of CTA showed a two-step isotherm with areas/CTA of 0.27 and 0.14 nm. These results suggest full saturation of the surface with surfactant ions that are vertically oriented. 

The binding of series of phenols, cresols and xylenols to the non-ionic surfactant cetomacrogol 1000 can be described by a Langmuir adsorption isotherm [19]... 

Equation 5.57 shows that the adsorption flux of surfactant is influenced by the subsurface concentration of counterions, C2,. At last, if there is equilibrium between surface and subsurface, we have to set g, = 0 in Equation 5.57, and thus we obtain the Langmuir isotherm for an ionic surfactant ... 

Gonzdlez-Garda et al. (2001) describe the adsorption isotherms at 20 °C of four AC of the non-ionic surfactant Triton X-100 from aqueous solution over a wide concentration range. The adsorption was explained using one or a combination of two Langmuir equations, depending on the equilibrium concentration range studied. The results indicate that there are at least two kinds of interactions, the first related to a direct interaction between the AC surface and adsorbate molecules, and the second mainly due to the interaction... 

Here, 8 is the thickness of the adsorption layer, p.o and Xo are the standard chemical potentials of a surfactant molecule on the surface and in the bulk of the solution, respectively c and B are measured in cm". In spite of the fact that Eq. (2) is originally derived for the special case of localized adsorption of noninteracting molecules, it can be successfully applied to various surfactants, including ionic ones [13—17]. The Langmuir isotherm can be generalized for multicomponent adsorption [18]. 

---