Surfactants Gibbs monolayers

Kj / y, where K is the surface dilationcil modulus, defined in 13.6.19). An alter-native Marangoni number was introduced by Edwards et al., who considered creep flow around an emulsion droplet. Their definition is Ma s K° /kar/, where a is the radius of the droplet, rj the bulk viscosity and fc (in s ) a rate constant, characteristic of the rate of supply of surfactants to the interface by transport from the bulk. The second definition rather applies to Gibbs monolayers it is a measure of the extent to which surface tension gradients can develop against the counteracting replenishment of the surface. 

E.H. Lucassen-Reynders, Surface Elasticity and Viscosity in Compression/ Dilation, in Anionic Surfactants Physical Chemistry and Surfactant Action E.H. Lucassen-Reynders, Ed., Marcel Dekker (1981). (Review of dllatlonal rheology mode, emphasis on Gibbs monolayers includes discussion on 2D equations of state.)... 

Gibbs monolayers are widespread. The simplest system is that of the surface of a fully miscible binary liquid. More complex ones are monolayers of uncharged molecules adsorbed from dilute solutions (example aliphatic alcohols from aqueous solution) electrolytes surfactants (non-ionic or ionic) polymers and polyelectrolytes and yet more. On the other hand, the methods for characterizing... 

Besides these specific methods, the general arsenal of techniques described in sec. 3.7 remains available. So, optical and Volta potential measurements cure often invoked to obtain structural information on the monolayers. These techniques do not basically differ from the corresponding ones for Langmuir monolayers. However, surface rheology differs drastically because for Gibbs monolayers transport to and from the bulk is possible. Differences start to appear if the molecules are not very small and therefore diffuse with time scales comparable (or shorter) than those of the measurements. Therefore this theme will be devloped separately before surfactant monolayers are discussed, see sec. 4.5. 

Perhaps it is fair to state that surfactant monolayers are the most abundant representatives of Gibbs monolayers. Scientific literature abounds with entries on their measurements, theory and applications. Given the scope of FIGS, a selection has to be made in which fundamental aspects are emphasized. To that end, we shall mostly adhere to the following scheme ... 

Ionic Gibbs monolayers have also been studied rheologically. An illustration is given in fig. 4.38 taken from a study by Monroy et al.These results were obtained by a longitudinal wave technique, described in an earlier paper. This surfactant very well demonstrates the maximum as a function of c at given ft), as predicted. 

Aut. Div. Much information on surfactants can be found in Marcel Dekker s Surfactant Series. (Various editors some emphasize Gibbs monolayers.)... 

An important thermodynamic property of a surfactant adsorption monolayer is its Gibbs (surface) elasticity ... 

For the first type, the Gibbs monolayers are often described as two-dimensional gaseous (or gas-like) monolayers formed on the surface of dilute solutions, having a low surface excess, and the surface pressure, n, is regarded as the two-dimensional osmotic pressure of this solution. When a two-dimensional gaseous monolayer is present on a dilute solution, the surface tension decreases linearly with the increase in concentration of the added surfactant, at constant temperature... 

As mentioned in the Sec. 1, an important thermo-dynamic parameter of a surfactant adsorption monolayer is its Gibbs (surface) elasticity. The physical concept of surface elasticity is the most transparent for monolayers of insoluble surfactants, for which it was initially introduced by Gibbs (18, 19). The increments A a and AT in the definition of Gibbs elasticity ... 

The Gibbs elasticity characterizes the lateral fluidity of the surfactant adsorption monolayer. For high values of the Gibbs elasticity the adsorption monolayer at a fluid interface behaves as tangentially immobile. Then, if two oil drops approach each other, the hydro-dynamic flow pattern, and the hydrodynamic interaction as well, is the same as if the drops were solid particles, with the only differenee that under some conditions they could deform in the zone of contact. For lower values of the Gibbs elastieity the... 

The HT voltammetry with gold electrodes was also recently used to measure the surface partitioning constant of a soluble, redox-active surfactant at the air/water interface [25]. Malec and coworkers modified the surface of gold electrodes by self-assembly of short alkane chain thiols in order to mimic the thermodynamic properties of the air/water interface. They relied on the fact that the surface tensions of the air/water interface and of the liquid alkane/water interface are similar [8]. Indeed, the HT measurements of the Gibbs monolayer formation constant were in agreement with their surface tensiometry and Brewster angle microscopic measurements [25]. 

Gibbs and Insoluble Monolayers The adsorption of surfactant molecules at the surface of a liquid can be so strong that a monomolecular film (Gibbs monolayer) of unidirectionally ordered surfactants is formed (Fig. 5). Since the decrease in surface tension is directly related to the surface excess adsorption of the surfactant by the Gibbs adsorption equation (Eq. 6), the formation of the Gibbs mono-layer can be monitored by decrease of the surface tension. The maximum number of molecules filling a given area depends upon the area occupied by each molecule. 

A schematic comparison of the two situations of the film balance is illustrated in Fig. 6. The trough is filled with pure water and the left and right side of the surface is separated. At the beginning, the surface of the subphase is completely clean and the surface tension of each side is that of pure water (yo)- In case (a), a soluble surfactant is placed on one side of the trough. A Gibbs monolayer will be immediately formed by adsorption of the surfactant molecules to the surface on this side, while the residual molecules will be dissolved in the subphase. The surfactant molecule in the aqueous phase can diffuse to the opposite side of the barrier therefore, after the system reaches equilibrium, the formation of the saturated film accompanying the same decrease of the surface tension will be achieved on both the sides. 

The spreading procedure allows exact control of the number N° of surfactant molecules to be placed in the interface. This makes quantitative interpretation of monolayer studies possible. In such studies, it is usual to first deposit au amount of surfactant that is far less than the amount that can be accommodated in a close-packed monolayer and, thereafter, to compress the interfacial area to reach close packing of surfactant molecules. Thus, in contrast to Gibbs monolayers (in which the interfacial pressure is not affected by the available interfacial area), Langmuir s monolayers are eminently suitable to determine pressure-area isotherms. These are described and discussed in Section 7.4. 

When a surfactant is injected into the liquid beneath an insoluble monolayer, surfactant molecules may adsorb at the surface, penetrating between the monolayer molecules. However it is difficult to determine the extent of this penetration. In principle, equilibrium penetration is described by the Gibbs equation, but the practical application of this equation is complicated by the need to evaluate the dependence of the activity of monolayer substance on surface pressure. There have been several approaches to this problem. In this paper, previously published surface pressure-area Isotherms for cholesterol monolayers on solutions of hexadecy1-trimethyl-ammonium bromide have been analysed by three different methods and the results compared. For this system there is no significant difference between the adsorption calculated by the equation of Pethica and that from the procedure of Alexander and Barnes, but analysis by the method of Motomura, et al. gives results which differ considerably. These differences indicate that an independent experimental measurement of the adsorption should be capable of discriminating between the Motomura method and the other two. 

In principle, the penetration or adsorption of surfactant, Tg is given by the Gibbs equation. For a non-ionic monolayer and an ionised surfactant (as in the system examined), this equation is ... 

Another dynamic factor affecting the rate of diffusion transfer, mentioned long ago by Gibbs [9], is the elasticity of the surfactant monolayers which decreases the capillary pressure in small bubbles during their compression and increases it in large bubbles during their expansion. This effect is most pronounced in bubbles whose adsorption layers contain insoluble surfactants. Analysis of the influence of this factor on diffusion transfer has been reported in [486], However, no experimental verification has been performed so far. 

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