Critical micelle concentration pure surfactant solution

In recent studies, Friberg and co-workers (J, 2) showed that the 21 carbon dicarboxylic acid 5(6)-carboxyl-4-hexyl-2-cyclohexene-1-yl octanoic acid (C21-DA, see Figure 1) exhibited hydrotropic or solubilizing properties in the multicomponent system(s) sodium octanoate (decanoate)/n-octanol/C2i-DA aqueous disodium salt solutions. Hydrotropic action was observed in dilute solutions even at concentrations below the critical micelle concentration (CMC) of the alkanoate. Such action was also observed in concentrates containing pure nonionic and anionic surfactants and C21-DA salt. The function of the hydrotrope was to retard formation of a more ordered structure or mesophase (liquid crystalline phase). 

The formation of mixed micelles in surfactant solutions which contain two or more surfactant components can be significantly affected by the structures of the surfactants involved. The observed critical micelle concentration (cmc) is often significantly lower than would be expected based on the erne s of the pure surfactants. This clearly demonstrates that interactions between different surfactant components in the mixed micelles are taking place. 

Above the critical micelle concentration (C ) in a pure surfactant solution the chemical potential of the monomer is given by... 

Surfactant surface activity is most completely presented in the form of the Gibbs adsorption isotherm, the plot of solution surface tension versus the logarithm of surfactant concentration. For many pure surfactants, the critical micelle concentration (CMC) defines the limit above which surface tension does not change with concentration, because at this stage, the surface is saturated with surfactant molecules. The CMC is a measure of surfactant efficiency, and the surface tension at or above the CMC (the low-surface-tension plateau) is an index of surfactant effectiveness (Table XIII). A surfactant concentration of 1% was chosen where possible from these various dissimilar studies to ensure a surface tension value above the CMC. Surfactants with hydrophobes based on methylsiloxanes can achieve a low surface tension plateau for aqueous solutions of —21-22 mN/m. There is ample confirmation of this fact in the literature (86, 87). 

The surface tension of a solution of a surfactant is lower than that of the pure solvent. Surface tension is roughly a linear function of ln(surfactant concentration) up to the critical micelle concentration (CMC) (Figure 3). Above the CMC the thermodynamic activity of the surfactant does not increase with the addition of more surfactant, and the surface tension remains constant. Interfacial tension also decreases with the concentration of an emulsifier dissolved in one of the phases. In Figure 4 the decrease in y does not level off, because the emulsifier (PGMS) does not form micelles in the organic solvent phase (heptane). The changes in the slope of the plot are attributed to changes in orientation of emulsifier molecules at the interface (7). 

The nature and limits of applicability of specific methods for determining critical micelle concentrations vary widely. Most methods have been developed for a relatively small set of pure surfactants involving very dilute electrolyte solutions and only ambient temperature and pressure. The determination of cmc at elevated temperature and pressure is experimentally much more difficult than for ambient conditions and comparatively little work has been done in this area. Most high temperature cmc studies have been by conductivity measurements and have therefore been limited to ionic surfactants. For example, erne s at up to 166 °C have been reported by Evans and Wightman [50]. Some work has been reported using calorimetry, up to 200 °C by Noll [5J ], and using F... 

Critical Micelle Concentrations.—Lipophilic crown-ether derivatives promise many interesting applications. Surface-tension measurements on the annelides (la), (lb), and (2) demonstrate that micelles are formed in dilute aqueous solution no protonation of (la) occurs in neutral solution above the c.m.c. In the latter two cases the metal ion is completely bound to the macrocycle and evaluation of the tensiometric data demonstrates that the surface area of annelides increases on metal-ion complexation. The optically active surfactant (3) exhibits increased circular dichroism above its c.m.c., and the c.m.c. of racemic (4) is higher than that of its pure enantiomers. ... 

Figure 13.5 shows the variations of surface tension versus surfactant concentration for pure surfactant system and the mixture of polymer/surfactant where the polymer concentration is constant. In the case of pure surfactant solution, a sharp decrease in the surface tension occurs with the increase in surfactant concentration up to the critical micelle concentration (CMC). For surfactant concentrations higher than the CMC, the surface tension remains constant. In the mixture of polymer and surfactant, the surface tension plot shows two break points. The first point is the CAC point where the interaction between the polymer and the surfactant begins. The second point is the PSP point where the polymer chains become saturated with the surfactant. When the interaction between the polymer and surfactant is weak, CAC and PSP values are close to the CMC of pure surfactant (Mohsenipour 2011). 

Differences in bulk composition are possible in a thin foam film as a result of stretching of the film. If the film is sufficiently thin, then any stretching causes a depletion of the bulk phase surfactant solution between the air-liquid surfaces of the foam film as more surfactant adsorbs on those surfaces. Distances perpendicular to the film are small so that, provided the stretching occurs reasonably slowly, the equilibrium inside the film element may be always maintained. Depletion of bulk phase the surfactant concentration will therefore necessarily mean an increase of the surface tension of the film as it is stretched. This will, however, only occur if reduction of the surfactant concentration causes a concomitant increase in surface tension. In the case of a pure surfactant at concentrations above the critical micelle concentration (CMC), this may not always happen. 

In order to learn about the effect of substituents close to the ester bond of surface-active esters on the kinetics of the hydrolysis, a series of well-defined PEG esters of fatty acids were synthesized and their hydrolysis rates were investigated both below and above the critical micelle concentration (CMC) [1]. The ester surfactants studied are shown in Fig. 1. They were synthesized in pure form by reacting the acid chloride with a large excess of tetra(ethylene glycol) using pyridine as nonnucleophilic base. The desired product, i.e., the PEG monoester, was removed from the excess tetra(ethylene glycol) by extraction into ethyl acetate from a saturated sodium chloride solution (so-called Weibull extraction). The degradation profile at various pH values was... 

If the surfactant solution is too dilute, the surface tension of the solution will not differ sufficiently from that of pure solvent for the restoring force to counteract the effects of casual thermal and mechanical agitation. This will lead to a very transient foam. Experimental data have shown that the optimal concentration to use is usually within a factor of two of the critical micelle concentration. 

Dialysis and electrodialysis are techniques which are applicable to the separation of smaller ions and molecules, including ionic surfactants, from larger species. These methods have been used to separate sodium dodecylsulfate from biochemical media (106). Such separations must normally be run at surfactant concentrations below the critical micelle concentration, since the micelles are too large to pass through the dialysis membrane. A general difficulty in application to trace analysis is the loss of surfactant due to adsorption on the surface of the apparatus. Most often, the object of the experiment is the purification of a protein solution, rather than isolation of a pure solution of the surfactant. Dialysis has been used for the removal of hydrocarbon oil solvent from lubricating oil surfactants in micellar form. In this case, n-heptane was used as solvent at reflux temperature (107). 

Measurements of supercritical ethane density versus the AOT concentration shown in Figure 4 (T = 37 C, P = 250 bar) indicate that the properties of the supercritical continuous phase resemble those of the pure fluid. The dispersed micelle phase does not appear to increase the critical temperature or critical pressure of the binary solution to the point of inducing a phase change in the system. There is a small increase in density as surfactant is added to the system which confirms the visual observation that a second liquid phase of much higher density is not formed. 

An example where these characteristic changes are easily observable, are titration experiments with micellar solutions of surfactants which are titrated into the vessel filled with pure water. Initially, dilution of the micellar solution leads to complete demicellization. When the concentration of monomers in the cell approaches the critical micellar concentration cmc the heat effect connected with the transfer of surfactants from the micelle to the aqueous solution disappears and the heat of reaction approaches zero [118-123]. 

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