Two-dimensional aggregates

This expression can be generalized to two-dimensional aggregates (disclike micelles) and to spherical micelles, where... 

Abstract. Propagation of capillary waves along the surface of water covered by a homogeneous insoluble film has been a subject of numerous experimental and theoretical studies. However, it has been shown only recently that real surface films contain two-dimensional aggregates, which influence the characteristics of surface waves. The problem of multiple scattering of surface waves by two dimensional viscoelastic particles is considered briefly below. The results can be compared with the experimental data for condensed films with two-dimensional bubbles of gaseous phase. 

The heat and entropy of adsorption calculated in the manner outlined above for do-decyl sulfonate adsorption on alumina show marked changes at particular concentrations and are in agreement with the hypothesis of lateral interaction of surfactants to form two-dimensional aggregates (Fig. 4.15). Most interestingly, the association was found to produce a net increase in entropy of the system, suggesting a decrease upon aggregation... 

Fig. VII-13. Structure of particle aggregate obtained by computer modeling of two-dimensional aggregation...

The adsorption kinetics of a surfactant to a freshly formed surface as well as the viscoelastic behaviour of surface layers have strong impact on foam formation, emulsification, detergency, painting, and other practical applications. The key factor that controls the adsorption kinetics is the diffusion transport of surfactant molecules from the bulk to the surface [184] whereas relaxation or repulsive interactions contribute particularly in the case of adsorption of proteins, ionic surfactants and surfactant mixtures [185-188], At liquid/liquid interface the adsorption kinetics is affected by surfactant transfer across the interface if the surfactant, such as dodecyl dimethyl phosphine oxide [189], is comparably soluble in both liquids. In addition, two-dimensional aggregation in an adsorption layer can happen when the molecular interaction between the adsorbed molecules is sufficiently large. This particular behaviour is intrinsic for synergistic mixtures, such as SDS and dodecanol (cf the theoretical treatment of this system in Chapters 2 and 3). The huge variety of models developed to describe the adsorption kinetics of surfactants and their mixtures, of relaxation processes induced by various types of perturbations, and a number of representative experimental examples is the subject of Chapter 4. 

These estimates oversimplify both the enthalpic effects of interaction and the entropic effects of size differences. First, interactions between adsorbed molecules as described by Frumkin type models do not allow for the formation of dimers or larger aggregates in the surface layer which can occur in practice. Equations of state for monolayers showing such two-dimensional aggregation have been proposed for various models [32-42]. Second, proteins differ from surfactants in more than just the size. For proteins, surface denaturation can take place, leading to their unfolding at the surface, at least at low surface pressures. The partial molar surface area for proteins, in contrast to surfactants, is large and variable. The interrelation between the... 

This interpretation of the experimental data is erroneous. Indeed, a two-dimensional aggregation (or condensation) in an adsorption layer or a spread insoluble monolayer should be regarded to as the formation of another type of adsorbed particles, namely two-dimensional aggregates (n-mers) or domains. It is important to note that the surface concentration of the... 

For the ideal mixture (both in the bulk and at the surface) of two surfactants with similar molar areas, where only component 1 is able to form large two-dimensional aggregates in the adsorption layer, the following equations were derived in [95]... 

The analysis of the adsorption kinetics shows that also the dodecanol adsorbs diffusion-controlled, however, the corresponding adsorption isotherm has to be used which allows to cissume a two-dimensional aggregation at the surface (cf paragraph 2.7). 

Polymeric association of different molecules through multiple hydrogen bonding has been used for the formation of non-liquid-crystalline bulk solids [12], fibrous solids for gelation in solvents [119], and as monolayers [120], Simpler H-bonding such as the interaction between carboxylic acid and pyridine has also been shown to be useful for one- or two-dimensional aggregates in solid states [121-124], For example, a one-dimensional polymeric complex from an A-B type monomer is formed in crystalline solids [121],... 

The relationship between adsorption and interfacial properties such as contact angle, zeta-potential and flotation recovery is illustrated in Figure 39.2 for cationic surfactant dodecylammonium acetate/quartz system (5). The increase in adsorption due to association of surfactants adsorbed at the solid-liquid interface into two dimensional aggregates called solloids (surface colloids) or hemi-micelles occurs at about 10 M DA A. This marked increase in adsorption density is accompanied by concomitant sharp changes in contact angle, zeta-potential and flotation recovery. Thus these interfacial phenomena depend primarily on the adsorption of the surfactant at the solid-liquid interface. The surface phenomena that reflect the conditions at the solid-liquid interface (adsorption density and zeta-potential) can in many cases be correlated directly with the phenomena that reflect the... 

Richetti, P Prost, J. Barois, P. Two-dimensional aggregation and crystallization of colloidal suspension of latex spheres. J. Phys. Lett. (Paris), 1984, 45(23), L1137-L1143. 

The fact that many surfactant systems cannot be adequately described by the Frumkin mode was the reason that other models have been derived. A comprehensive overview of such models was given recently elsewhere (Fainerman et al. 1998). We want to discuss two of the most recent models considering changes in orientation of adsorbed molecules and formation of two-dimensional aggregates (Fainerman et al. 2002). These new models are suitable to describe quite a number of surfactant adsorption layers much better than classical models do. 

Surfactant adsorption layers with two-dimensional aggregation... 

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