Surfactant Langmuir adsorption isotherm

In the simplest case, for which all adsorption sites are equivalent and do not interact with each other, the fraction of surface covered by adsorbate, covered related to the surfactant concentration, CSURF> the adsorption constant, in mol/m3, by the Langmuir adsorption isotherm ... 

Equations D3.5.30 and D3.5.32 are both very valuable. They state that the rate of adsorption can be obtained from plots of the interfacial tension versus either tA- (for t—>0) or lth (for the long-term solution f— >). With these two equations the tool to extract the adsorption rate from experimentally obtained surface tension-time curves is at hand. It should be noted that instead of the Gibbs model, one could use one of the previously mentioned adsorption isotherms such as the Langmuir adsorption isotherm to convert interfacial tension to interfacial coverage data. The adsorption isotherms may be obtained by fitting equilibrium surface tension data versus surfactant concentration. 

Each surfactant adsorption isotherm (that of Langmuir, Volmer, Frumkin, etc.), and the related expressions for the surface tension and surface chemical potential, can be derived from an expression for the surface free energy, F, which corresponds to a given physical model. This derivation helps us obtain (or identify) the self-consistent system of equations, referring to a given model, which is to be applied to interpret a set of experimental data. Combination of equations corresponding to different models (say, Langmuir adsorption isotherm with Frumkin surface tension isotherm) is incorrect and must be avoided. 

The Langmuir Adsorption Isotherm A type of adsorption isotherm commonly observed in adsorption from solutions of surfactants is the Langmuir-type isotherm (Langmuir, 1918), expressed by... 

The comparison of the empirical Szyszkowski equation (II. 18) with the Gibbs equation (II.5) indicates that Langmuir adsorption isotherm (11.22) is well suited also for the description of adsorption at the air - surfactant solution interface. It is interesting to point out that at the gas - solid interface, for which eq. (11.22) was originally derived various deviations from Langmuirian behavior are often observed. 

Theoretical modelling of surfactant adsorption uses as a starting point the theoretical isotherms derived from statistical and kinetic data for the gas-solid interface. The most common model is the one based on the Langmuir adsorption isotherm (see Chapter 11,2) ... 

The thermodynamics and dynamics of interfacial layers have gained large interest in interfacial research. An accurate description of the thermodynamics of adsorption layers at liquid interfaces is the vital prerequisite for a quantitative understandings of the equilibrium or any non-equilibrium processes going on at the surface of liquids or at the interface between two liquids. The thermodynamic analysis of adsorption layers at liquid/fluid interfaces can provide the equation of state which expresses the surface pressure as the function of surface layer composition, and the adsorption isotherm, which determines the dependence of the adsorption of each dissolved component on their bulk concentrations. From these equations, the surface tension (pressure) isotherm can also be calculated and compared with experimental data. The description of experimental data by the Langmuir adsorption isotherm or the corresponding von Szyszkowski surface tension equation often shows significant deviations. These equations can be derived for a surface layer model where the molecules of the surfactant and the solvent from which the molecules adsorb obey two conditions ... 

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-... 

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. 

This section will deal with the above interfacial aspects starting with the equilibrium aspects of surfactant adsorption at the air/water and oil/water interfaces. Due to the equilibrium aspects of adsorption (rate of adsorption is equal to the rate of desorption) one can apply the second law of thermodynamics as analyzed by Gibbs (see below). This is followed by a section on dynamic aspects of surfactant adsorption, particularly the concept of dynamic surface tension and the techniques that can be applied in its measurement. The adsorption of surfactants both on hydrophobic surfaces (which represent the case of most agrochemical solids) as well as on hydrophilic surfaces (such as oxides) will be analyzed using the Langmuir adsorption isotherms. The structure of surfactant layers on solid surfaces will be described. The subject of polymeric surfactant adsorption will be dealt with separately due to its complex nature, namely irreversibility of adsorption and conformation of the polymer at the solid/liquid interface. 

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]... 

Many adsorption phenomena especially of surfactants, polymers, proteins and the chemical adsorption of gases on solids can be well represented by the Langmuir adsorption isotherm. This equation can be expressed in a suitable linear form and we can obtain the two parameters of the model, of which one is the concentration or volume at maximum (full) coverage or the so-called monolayer coverage. Knowledge of this monolayer coverage and of the specific surface area of the solid can help us estimate the surface area occupied by a molecule at the interface and thus the amount needed for stabilization. The specific solid surface area can be obtained from gas adsorption measurements on the same solid. 

Ctotai is the total surfactant concentration in the emulsion, Vw is the volume of the continuous water phase, Cb the concentration of free surfactant molecules in the bulk phase. At the total interfadal area in the emulsion and Hthe adsorption (surfactant molecules per surface area). Combining Eq. (2) with the Langmuir adsorption isotherm Eq. (3) leads to Eq. (4) with b being the adsorption coefficient. 

The major surfactant in the foam may usually be considered to be present at the bubble surfaces in the form of an adsorbed monolayer with a substantially constant F, often of the order of 3 X 10" (g mol)/ cm", for a molecular weight of several hundred. On the other hand, trace materials follow the linear-adsorption isotherm Tj = KiCj if their concentration is low enough. For a wider range of concentration a Langmuir or other type of isotherm may be applicable (Davies and Rideal, loc. cit.). 

For instance, the time course of SPE demonstrates that the solvent phase surfactant concentration steadily decreases (Fig. 3) [58]. The w/o-ME solution s water content decreases at the same rate as the surfactant [58]. The protein concentration at first increases, presumably due to the occurrence of Steps 2 and 3 above, but then decreases due to the adsorption of filled w/o-MEs by the solid phase (Fig. 3) [58]. Additional evidence supporting the mechanism given above is the occurrence of a single Langmuir-type isotherm describing surfactant adsorption in the solid phase for several SPE experiments employing a given protein type (Fig. 4) [58]. Here, solid-phase protein molecules can be considered as surfactant adsorption sites. Similar adsorption isotherms occurred also for water adsorption [58]. 

The fits of experimental data to a Langmuir (or another) adsorption isotherm does not constitute evidence that adsorption is the actual mechanism that accounts for the loss of the sorbate from the solution. Very frequently adsorption to a surface is followed by additional interactions at the surface, e.g., a surfactant undergoes two-dimensional association subsequent of becoming adsorbed or charged ions tend to repel each other within the adsorbed layer. 

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