Surfactant equilibrium

Surfactant equilibrium concentrations of the adsorbed-materials analysed by SEM. 

Figure 1 shows the typical topography presented by the LDH particles. A heterogeneous surface can be identified and a deeper analysis will also show the largest pores. This topography pattern was also observed in the SDS-adsorbed material when the surfactant equilibrium concentration was lower than the corresponding CMC (8.2x1 O 3 mol dm 3). No other different image patterns were observed. 

Surfactant equilibrium isotherms and sorption envelopes on kaolinite were determined in triplicate batch experiments for the appropriate solution chemistry conditions. After equilibration, the solids were separated by centrifugation at 7000 rpm for 30 min and aliquots of the supernatant were taken for analysis. Residual SDS and Tween 80 concentrations (Ssurf, mM) were determined after taking into account dilution factors and system losses,... 

In spite of these important differences, silicone surfactants share much in common with conventional surfactants. Equilibrium and dynamic surface tension vary with concentration and molecular architecture in similar ways. Silicone surfactants self-associate in solution to form micelles, vesicles and liquid crystal phases. Self-association follows similar patterns as molecular size and shape are varied and silicone surfactants containing polyoxyalkylene groups exhibit a cloud point. HLB values can be calculated for silicone surfactants, although more useful values can be obtained from calculations that take into account the differences between silicone and hydrocarbon species. 

Uddin MS and Kathiresan M. Extraction of metal ions by emulsion liquid membrane using bi-functional surfactant equilibrium and kinetic studies. Sep Purif Technol 2000 19 3-9. 

Thin liquid films in foam and emulsion systems are usually stabilised by soluble surfactants. During the formation of such films the flow-out process of liquid disturbs the surfactant equilibrium state in the bulk and film surfaces. The situation of drainage of a surfactant containing liquid film between two oil droplets is shown in Fig. 3.15. (after Ivanov Dimitrov 1988). Here j" and are the bulk fluxes in the drops and the film, respectively, j and j are the fluxes due to surface diffusion or spreading caused by the Marangoni effect, respectively. 

Datwani, S.S. and Stebe, K.J., Surface tension of an anionic surfactant equilibrium, dynamics, and analysis for Aerosol-OT, Langmuir, 17, 4287, 2001. 

THU Thum, T., Coudere, S., Sidhu, J., Bloor, D M., Penfold, J., Holzwarth, J.F., and Wyn Jones, E., Study of mixed micelles and interaction parameters for triblock copolymers of the type EOm-POn-EOm and ionic surfactants equilibrium and stmcture, Langmuir, 18, 9267,2002. 

Hydrophilic surfactants adsorb best on aqueous phases, whereas hydrophobic surfactants adsorb best on lipophilic surfaces (oils). Data on adsorption at constant temperature are usually plotted as a function of the surfactant equilibrium concentration plots for solid substrates are termed Langmuir isotherms. From such isotherms the maximum surfactant concentration at the interface (Fmax) can be derived and the maximum area occupied by the surfactant at the interface ( max) can be calculated. In addition, the Gibbs adsorption equation can be extracted. 

It was determined, for example, that the surface tension of water relaxes to its equilibrium value with a relaxation time of 0.6 msec [104]. The oscillating jet method has been useful in studying the surface tension of surfactant solutions. Figure 11-21 illustrates the usual observation that at small times the jet appears to have the surface tension of pure water. The slowness in attaining the equilibrium value may partly be due to the times required for surfactant to diffuse to the surface and partly due to chemical rate processes at the interface. See Ref. 105 for similar studies with heptanoic acid and Ref. 106 for some anomalous effects. 

A surfactant for evaporation control has an equilibrium film pressure of 15 dyn/cm. Assume a water surface and 25°C and calculate the distance traveled by the spreading film in 8 sec. 

The foregoing is an equilibrium analysis, yet some transient effects are probably important to film resilience. Rayleigh [182] noted that surface freshly formed by some insult to the film would have a greater than equilibrium surface tension (note Fig. 11-15). A recent analysis [222] of the effect of surface elasticity on foam stability relates the nonequilibrium surfactant surface coverage to the foam retention time or time for a bubble to pass through a wet foam. The adsorption process is important in a new means of obtaining a foam by supplying vapor phase surfactants [223]. 

Assume diat die chemical potential, p., of surfactant in aggregates of size N in equilibrium widi one anodier is unifonii. One may dierefore write... 

At low concentrations surfactant molecules adsorbed at the surface are in equilibrium with other molecules in solution. Above a threshold concentration, called the critical micelle concentration (cmc, for short), another equilibrium must be considered. This additional equilibrium is that between individual molecules in solution and clusters of emulsifier molecules known as micelles. 

Cf, C y, and Cq are the concentrations of the substance in question (which may be a colligend or a surfactant) in the feed stream, bottoms stream, and foamate (collapsed foam) respectively. G, F, and Q are the volumetric flow rates of gas, feed, and foamate respectively, is the surface excess in equilibrium with C y. S is the surface-to-volume ratio for a bubble. For a spherical bubble, S = 6/d, where d is the bubble diameter. For variation in bubble sizes, d should be taken as YLnid fLnidj, where n is the number of bubbles with diameter dj in a representative region of foam. 

Beyond the CMC, surfactants which are added to the solution thus form micelles which are in equilibrium with the free surfactants. This explains why Xi and level off at that concentration. Note that even though it is called critical, the CMC is not related to a phase transition. Therefore, it is not defined unambiguously. In the simulations, some authors identify it with the concentration where more than half of the surfactants are assembled into aggregates [114] others determine the intersection point of linear fits to the low concentration and the high concentration regime, either plotting the free surfactant concentration vs the total surfactant concentration [115], or plotting the surfactant chemical potential vs ln( ) [119]. 

Tethering may be a reversible or an irreversible process. Irreversible grafting is typically accomplished by chemical bonding. The number of grafted chains is controlled by the number of grafting sites and their functionality, and then ultimately by the extent of the chemical reaction. The reaction kinetics may reflect the potential barrier confronting reactive chains which try to penetrate the tethered layer. Reversible grafting is accomplished via the self-assembly of polymeric surfactants and end-functionalized polymers [59]. In this case, the surface density and all other characteristic dimensions of the structure are controlled by thermodynamic equilibrium, albeit with possible kinetic effects. In this instance, the equilibrium condition involves the penalties due to the deformation of tethered chains. 

In highly diluted solutions the surfactants are monodispersed and are enriched by hydrophil-hydrophobe-oriented adsorption at the surface. If a certain concentration which is characteristic for each surfactant is exceeded, the surfactant molecules congregate to micelles. The inside of a micelle consists of hydrophobic groups whereas its surface consists of hydrophilic groups. Micelles are dynamic entities that are in equilibrium with their surrounded concentration. If the solution is diluted and remains under the characteristic concentration, micelles dissociate to single molecules. The concentration at which micelle formation starts is called critical micelle concentration (cmc). Its value is characteristic for each surfactant and depends on several parameters [189-191] ... 

For the solid-liquid system changes of the state of interface on formation of surfactant adsorption layers are of special importance with respect to application aspects. When a liquid is in contact with a solid and surfactant is added, the solid-liquid interface tension will be reduced by the formation of a new solid-liquid interface created by adsorption of surfactant. This influences the wetting as demonstrated by the change of the contact angle between the liquid and the solid surface. The equilibrium at the three-phase contact solid-liquid-air or oil is described by the Young equation ... 

The concepts of interface rheology are derived from the rheology of three-dimensional phases. Characteristic for the interface rheology is the coupling of the motions of an interface with the flow processes in the bulk close to the interface. Thus, in interface rheology the shear and dilatational stresses of the interface are in equilibrium with the corresponding shear stress in the bulk. An important feature is the compressibility of the adsorption layer of an interface in contrast, the flow elements of the bulk are incompressible. As a result, compression or dilatation of the adsorption layer of a soluble surfactant is associated with desorption and adsorption processes by which the interface tends to reinstate the adsorption equilibrium with the bulk phase. 

Like other surfactants, alkanesulfonates generate lyotropic liquid-crystalline phases. But the phase equilibria can only be inadequately described because of the enormous experimental difficulties in, for instance, establishing an appropriate equilibrium. Nevertheless, for simple ternary systems the modeling of surfactant-containing liquid-liquid equilibria has been successfully demonstrated [60],... 

An example for a partially known ternary phase diagram is the sodium octane 1 -sulfonate/ 1-decanol/water system [61]. Figure 34 shows the isotropic areas L, and L2 for the water-rich surfactant phase with solubilized alcohol and for the solvent-rich surfactant phase with solubilized water, respectively. Furthermore, the lamellar neat phase D and the anisotropic hexagonal middle phase E are indicated (for systematics, cf. Ref. 62). For the quaternary sodium octane 1-sulfonate (A)/l-butanol (B)/n-tetradecane (0)/water (W) system, the tricritical point which characterizes the transition of three coexisting phases into one liquid phase is at 40.1°C A, 0.042 (mass parts) B, 0.958 (A + B = 56 wt %) O, 0.54 W, 0.46 [63]. For both the binary phase equilibrium dodecane... 

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... 

C,4—C20 AOS surfactants were laboratory-prepared by Tuvell et al. [2]. Table 3 shows the CMC values of these single-carbon-cut AOS surfactants and of reference compounds, their areas per molecule at the water-air interface inferred from plots of surface tension vs. In (concentration), and the surface tension at the CMC, all at 23°C. The area of the molecule is proportional to the equilibrium adsorptivity, which in turn is taken as a comparative measure of the surface activity of the molecule. Tuvell et al. [2] argue that the greater the... 

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