Adsorption isotherms surfactants

For small-molecule surfactants, emulsification leads to equilibrium adsorption. This means that knowledge of the adsorption isotherm, surfactant concentration, and total droplet surface area permits calculation of F . This is not possible for proteins. 

Fig. XI-13. Adsorption isotherms for SNBS (sodium p-3-nonylbenzene sulfonate) (pH 4.1) and DPC (dodecyl pyridinium chloride) (pH 8.0) on mtile at approximately the same surface potential and NaCl concentration of O.OlAf showing the four regimes of surfactant adsorption behavior, from Ref. 175. [Reprinted with permission from Luuk K. Koopal, Ellen M. Lee, and Marcel R. Bohmer, J. Colloid Interface Science, 170, 85-97 (1995). Copyright Academic Press.]...

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.). 

The conformity to laws of adsorption, in particular their thermodynamic fundamentals, is independent of whether a water-air or a water-apolar oil interface is considered, provided that the surfactant is soluble only in one phase. If the oil phase in a liquid two-phase system is apolar, this condition is valid for many surfactants. Thus, all surfactants with an adequate solubility in water are almost insoluble in the hydrocarbon phase. If this condition is not met, e.g., in the system water-amyl alcohol, the thermodynamically based adsorption isotherms are more complicated to set up [39]. 

The adsorption behavior of homologous sodium alcohol sulfates at the interface can be characterized by the adsorption isotherms. However, the adsorption parameters of these isotherms are very sensitive to impurities present in the surfactant. Wiinstneck et al. [145] determined the equilibrium values of... 

Typical adsorption isotherms are shown in Figs. 16 and 17. Despite the large experimental scatter, a steep increase in adsorption can be seen at low concentrations, followed by a plateau at concentrations exceeding the CMC. Similar behavior has been observed before with model surfactants [49-54] and has also been predicted by modem theories of adsorption [54]. According to Fig. 16, adsorption increases modestly with salinity provided that the calcium ion concentration remains low. The calcium influence, shown in Fig. 17, cannot be explained by ionic strength effects alone but may be due to calcium-kaolinite interactions. 

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]. 

Of special interest in liquid dispersions are the surface-active agents that tend to accumulate at air/ liquid, liquid/liquid, and/or solid/liquid interfaces. Surfactants can arrange themselves to form a coherent film surrounding the dispersed droplets (in emulsions) or suspended particles (in suspensions). This process is an oriented physical adsorption. Adsorption at the interface tends to increase with increasing thermodynamic activity of the surfactant in solution until a complete monolayer is formed at the interface or until the active sites are saturated with surfactant molecules. Also, a multilayer of adsorbed surfactant molecules may occur, resulting in more complex adsorption isotherms. 

For the pseudo-binary mixture (a = 0.5) of sulfonate and nonylphenol with 30 E.O., figure 2 shows how the concentration of each of their monomer calculated by the RST theory (1), varies as a function of the overall surfactant concentration. It can be expected that the asymptotic regime in which monomer concentrations are stabilized will correspond to a plateau of the adsorption isotherm for the surfactant mixtures considered. 

Experiment C is designed to yield information on the amount of the surfactant that is actually adsorbed on the rock. This experiment measures the variation of surfactant concentration at the outlet of the core, after injection of a "slug of surfactant. The surfactant concentration in the brine depends on the position along the core and on time. The experiment is dynamic because the changing, but near equilibrium level of the adsorbed surfactant at any point along the rock sample is a function of the concentration in the solution at that point. This is described by the adsorption isotherm from a plot of M, the mass of surfactant adsorbed per gram of rock vs. Concentration. 

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. 

In dilute solutions of surfactants adsorption processes are controlled by transport of the surfactant from the bulk solution towards the surface as a result of the concentration gradient formed in the diffusion layer the inherent rate of adsorption usually is rapid. For non-equilibrium adsorption the apparent (non-equilibrium) isotherm can be constructed for different time periods that are shifted with respect to the true adsorption isotherm in the direction of higher concentration (Cosovic, 1990) (see Fig. 4.10). 

The adsorption isotherm of sodium dodecyl sulfate (SDS) on alumina at pH = 6.5 in 0.1 M NaCI (Fig. 4.11a) is characteristic of anionic surfactant adsorption onto a positively charged oxide. As shown by Somasundaran and Fuerstenau (1966) and by Chandar et al. (1987), the isotherm can be divided into four regions. These authors give the following explanation for the adsorption mechanism ... 

Comparison of these adsorption isotherms with those obtained for the linear alkyl aryl sulfonates (Figure 6) reveals the behavior of the 2 ( ) HDBS to be close to that which would be expected for a 1 (t> HDBS and that of the 8 ( ) HDBS to be equivalent to that of a tridecyl benzene sulfonate. Development of a cguantitative model that can account for the effect of the position of the benzene group on the chain warrants additional data for a variety of surfactants with branched chains. 

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 Eq. 16, hi is another adsorption constant (independent of surface coverage) and is equal to the product of hi in Eq. 11 and the base of natural logarithm (= 2.718). For systems containing only one surfactant. Pi = Pu = 0, and Eqs. 15 and 16 reduce to the well-known Frumkin equation of state and adsorption isotherm described as... 

Regarding the adsorption isotherm, the Eriunkin isotherm is usually used for surfactant ions and the Stern isotherm for the coimterion adsorption in the Stern layer. For these isotherms, the following equations can be derived. 

The Frumkin adsorption isotherm for the surfactant ions gives... 

The description of a mixed adsorption layer of ionic and nonionic surfactants requires the appropriate adsorption isotherms. For example, the Frumkin isotherm gives... 

A new analysis of the adsorption layer of ionic surfactants with new adsorption isotherms and equations of states was made in [42]. The effect of mono and bivalent anions on the adsorption of cethyltrimethyl ammonium salts was recently examined in [43]. 

The standard deviation has been determined as ct = j where v is the number of degrees of freedom in the fit. The parameters for the molecular interaction /3, the maximum adsorption Too, the equilibrium constant for adsorption of surfactant ions Ki, and the equilibrium constant for adsorption of counterions K2, are thus obtained. The non-linear equations for the Frumkin adsorption isotherm have been numerically solved by the bisection method. 

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