Surfactant adsorption modeling

FIGURE 12.14 Graphic representation of a pH-(iependent surfactant adsorption model. 

Ruch and Bartell [84], studying the aqueous decylamine-platinum system, combined direct estimates of the adsorption at the platinum-solution interface with contact angle data and the Young equation to determine a solid-vapor interfacial energy change of up to 40 ergs/cm due to decylamine adsorption. Healy (85) discusses an adsorption model for the contact angle in surfactant solutions and these aspects are discussed further in Ref. 86. 

These assumptions are akin to those taken in account in the mixed adsorption model of Trogus (12). The difference between the two models lies in the relationship linking CMCs of single and mixed surfactants and monomer molar fractions Trogus used the empirical equation proposed by Mysels and Otter (13) in our model, the application of RST leads to an equation of the same type. 

Calculation examples of mixed surfactant adsorption The solid chosen as the model adsorbent was made up of a natural sand (specific area =380 cm2/g) mixed with 5% clay (Charentes kaolinite with specific area = 26.8 m2/g). This material was taken as a model of clayey sandstone reservoirs. 

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. 

The orientation and Frumkin adsorption models have recently been combined to describe adsorption layer for surfactant-protein mixtures in [37] and [38]. 

Ionic surfactants are electrolytes dissociated in water, forming an electrical double layer consisting of counterions and co-ions at the interface. The Gouy-Chapman theory is used to model the double layer. In conjunction with the Gibbs adsorption equation and the equations of state, the theory allows the surfactant adsorption and the related interfacial properties to be determined [9,10] (The Gibbs adsorption model is certainly simpler than the Butler-Lucassen-Reynders model for this case.). 

Fig.l Surface tension versus solution concentration of nonionic surfactant CnEs as measured at r = 298.15 K (data points) [45], and as predicted by the Szyszkowski-Langmuir adsorption model (thin line) described by Eq. 20 and by the Frumkin adsorption model (thick line) described by Eqs. 17-18... 

Fig. 3 Comparison of the surface tension for nonionic surfactant CnEg as measured at T = 298.15 K, data points [45], with improved models considering orientational states of surfactant molecules at the surface. The data shown are obtained by regression analysis minimizing the revised chi-square The calculation with fi = 0 represents the best fit of the improved Szyszkowski-Langmuir model described by Eqs. 21 and 22. The other calculated curve with =- 3.921 shows the best fit of the improved Frumkin adsorption model described by Eqs. 23 and 24...

Fig. 4 Comparison between the experimental surface tension data for CnEs surfactant, data points [45], and the extended S-L adsorption model (line) by the aggregation of surfactant molecules at the sm-face described by Eq. 27-29. The best fit gives a>i = 557,691 m /mol, Tc = 1004.471 m /mol, and = 3.003...

The dispersion interaction between the surface active ions and the water-air interface was recently considered in the modeling of the equilibrium adsorption [62]. The molecular dynamic simulations are used in the recent years to describe the surfactant adsorption at the air-water interface [63-65],... 

This overview will outline surfactant mixture properties and behavior in selected phenomena. Because of space limitations, not all of the many physical processes involving surfactant mixtures can be considered here, but some which are important and illustrative will be discussed these are micelle formation, monolayer formation, solubilization, surfactant precipitation, surfactant adsorption on solids, and cloud point Mechanisms of surfactant interaction will be as well as mathematical models which have been be useful in describing these systems,... 

Scamehorn et. al. (19) reported the adsorption isotherms for a binary mixture of anionic surfactants. A formal adsorption model developed for single surfactant systems ( ) was extended to this binary system and shown to accurately describe the mixed adsorption isotherms (19). That theoretically based model was very complex and is probably not feasible to extend beyond two surfactant components. 

The objective in this section is to derive a mathematical model that can be used to extract the rate of adsorption from experimentally obtained dynamic surface tension data. Various investigators have speculated that the mechanism of surfactant adsorption involves two subsequent steps ... 

Xu, S., and S.A. Boyd. 1995. Alternative model for cationic surfactant adsorption by layer silicates. 

It was reported earlier (1) that surfactant adsorption at a polymer/water interface can be related to the polarity of the polymer surface. The model used in that study was tested satisfactorily by using the available literature data on polymer polarity and sodium lauryl sulfate adsorption on latex surfaces. 

The non-specific adsorption of surfactants is based on the interaction of the hydrophilic headgroup and the hydrophobic alkyl chain with the pigment and substrate surfaces as well as the solvent. For the adsorption of surfactants, different models have been developed which take into account different types of interactions. A simple model which excludes lateral interactions of the adsorbed molecules is the Langmuir equation ... 

Figure 3.2 Adsorption models for surfactants [6] (a) model of Fuerstenau, (b) model of Scame-horn, Chandar, Dobias and (c) model of Harwell etal.

On one hand it is investigated how the addition of cationic surfactants affects the pattern collapse of 193 nm photoresist lines. On the other hand, the adsorption of the surfactant on model photoresist surfaces is explored by a variety of surface chemical methods. Of special interest is how the surfactant changes the surface properties of the photoresist as surface potential and wettability. For an optimum modelling of the properties of real photoresist structures, both unexposed photoresists and photoresists that have been UV exposed, baked and developed are studied. 

The stationary phases play an important part in Liquid Chromatography using micellar mobile phases. They interact with both the surfactant and with solutes. To study the interactions with surfactants, adsorption isotherms were determined with two ionic surfactants on five stationary phases an unbonded silica and four monomeric bonded ones. It seems that the surfactant adsorption closely approaches the bonded monolayer (4.5 pmol/m2) whatever the bonded stationary phase-polarity or that of the surfactant. The interaction of the stationary phase and solutes of various polarity has been studied by using the K values of the Armstrong model. The KgW value is the partition coefficient of a solute between the... 

Wilson and co-workers developed a statistical mechanical model for single component surfactant adsorption (29-31) and expanded it to a binary system (2,3). Different adsorption curves were generated by varying the Van der Waals interaction parameters. The mixed adsorption equations that were developed were very complex and were not applied to experimental data. 

The fit of experimental data to a Langmuir (or another) adsorption isotherm does not constitute evidence that adsorption satisfies the criteria of the adsorption model. Frequently, adsorption to a surface is followed by additional interactions at the surface for example, a surfactant undergoes two-dimensional association subsequent to becoming adsorbed or charged ions tend to repel each other within the adsorbed layer. 

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