Critical adsorption concentration

When a polymer is added in a surfactant system, there are two critical concentrations CAC and CMC2. CAC is the critical adsorption concentration at which surfactant starts to adsorb on the polymer chains it is lower than the critical micelle concentration (CMC). CMC2 is the surfactant concentration at which micelles are formed when polymer is present it is higher than CMC (Li et al 2002). Both CAC and CMC2 are on the order of magnitude of CMC. 

The first term on the right-hand side of Eq. (5) is based on the strength of the static and hydrophobic interactions and is independent of the degree of adsorption p. The second term is a step function of the degree of adsorption Its slope becomes steep as AF[, increases. Accordingly, the adsorption isotherm curves of linear polymers can be characterized by the critical adsorption concentration in the first term (initiation process) and cooperativity of adsorption in the second term. The critical adsorption concentration depends not only on static interaction but also on the strength of the hydrophobic interaction. In contrast, the cooperativity of adsorption depends only on hydrophobic interaction. If die cooperative interaction of the surfactant and polyelectrol)de is expressed by the inverse slope of the adsorption isotherm curve at = 0.5, die following relationship is obtained for a linear polymer,... 

Kekicheff P, Christenson FI K and Ninham B W 1989 Adsorption of cetyltrimethylammonium bromide to mica surface below the critical micellar concentration Colloid Surf. 40 31-41... 

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] ... 

Surfactants greatly improve the performance of trans-cinnamaldehyde as a corrosion inhibitor for steel in HCl [741,1590,1591]. They act by enhancing the adsorption at the surface. Increased solubility or dispersibility of the inhibitor is an incidental effect. N-dodecylpyridinium bromide is effective in this aspect far below its critical micelle concentration, probably as a result of electrostatic adsorption of the monomeric form of N-dodecylpyridinium bromide. This leads to the formation of a hydrophobic monolayer, which attracts the inhibitor. On the other hand, an ethoxylated nonylphenol, a nonionic surfactant, acts by incorporating the inhibitor into micelles, which themselves adsorb on the steel surface and facilitate the adsorption of trans-cinnamaldehyde. 

Admicelle formation and associated CAC (Critical admicelle concentration) as proposed by Scamehom (10) and Harwell (1 1) were not introduced here for a practical reason a feasible and fast method of CAC measurement does not seem to exist at the moment. The difficulties related to such delicate determinations appear well from observation of the detailed adsorption isotherms of pure sulfates mixtures published by Roberts et alii (10). 

The critical micellar concentrations of anionic/nonionic surfactant mixtures examined are low in a saline medium, so that, at the concentrations injected in practice, the chromatographic effects resulting from the respective adsorption of monomers are masked. Such surfactants propagate simultaneously in the medium in the form of mixed micelles. 

When p approaches infinity, Equation 7 reveals that equals zero, which corresponds to infinitely fast sorption kinetics and to an equilibrium surfactant distribution. In this case Equation 6 becomes that of Bretherton for a constant-tension bubble. Equation 6 also reduces to Bretherton s case when a approaches zero. However, a - 0 means that the surface tension does not change its value with changes in surfactant adsorption, which is not highly likely. Typical values for a with aqueous surfactants near the critical micelle concentration are around unity (2JL) ... 

We investigate theoretically how the adsorption of the polymer varies with the displacer concentration. A simple analytical expression for the critical displacer concentration is derived, which is found to agree very well with numerical results from recent polymer adsorption theory. One of the applications of this expression is the determination of segmental adsorption energies from experimental desorption conditions and the adsorption energy of the displacer. Illustrative experiments and other applications are briefly discussed. 

An adsorption-desorption transition is illustrated schematically in Figure 1, where we plot a displacement isotherm, i.e. the adsorbed amount of a polymer as a function of the composition of a mixture of solvent and displacer. At the left in Figure 1, where the concentration of displacer is low, the polymer surface excess is positive. As we increase the proportion of displacer in the mixture, we observe a decrease in the adsorbed amount. At a certain composition the adsorbed amount of polymer becomes zero. The concentration at which the polymer surface excess just vanishes will be denoted as the critical displacer concentration cr. Beyond 4>cr, the surface excess of the polymer is negative (and very small if the polymer concentration is low). 

For pure nonionic EO adducts, increase in the number of oxyethylene groups in the molecule results in a decrease in the tendency to form micelles and an increase in the surface tension of the solution at the critical micelle concentration (1 ) (l. ) This change in surface activity is due to the greater surface area of the molecules in the adsorption layer and at the micellar surface as a result of the presence there of the highly hydrated polyoxyethylene chain. The reduction in the tendency to form micelles is due to the increase in the free energy of micelle formation as a result of partial dehydration of the polyoxyethylene chain during incorporation into the micelle ( 1 6) (17). 

Washing and Cleaning Action. The properties of alkyl ether sulfates, due to the good solubility and the special hydrophilic/hydrophobic properties of the molecule, are of particular practical interest. From the investigations described in sections 2 and 3, it can be concluded that, in addition to the decrease in the Krafft Point, favorable properties for practical applications can be expected as a result of the inclusion of the oxyethylene groups into the hydrophobic part of the molecule. As is true for other anionic surfactants, the electrical double layer will be compressed by the addition of multivalent cations. By this means, the adsorption at the interface is increased, the surface activity is raised, and, furthermore, the critical micelle concentration decreased. In the case of the alkyl ether sulfates, however these effects can be obtained without encountering undesirable salting out effects. 

The critical micelle concentration (c.m.c.) of the material increases with decrease in pH of the solution below 5, as is to be expected as the ratio of to B- increases. The increase in the c.m.c. is somewhat greater than the increase in the C20 value with pH decrease as shown by the cmc/C2o ratio, indicating somewhat greater inhibition of micellization than of adsorption at the aqueous solution/air interface as the BHVB- ratio increases. This may reflect some steric inhibition of micellization resulting from the increased size of the protonated hydrophilic head. 

Panayiotopoulos KP, Barbayiannis N, Papatolios K (2004) Influence of electrolyte concentration, sodium adsorption ratio, and mechanical disturbance on dispersed clay particle size and critical flocculation concentration in alfisols. Comm Soil Sci Plant Anal 35 1415-1434... 

The adsorption isotherms obtained for various detergents showed a characteristic feature that an equilibrium value was obtained when the concentration of detergent was over critical micelle concentration (CMC). The adsorption was higher at 40°C than at 20°C. However, the shapes of the adsorption curves was the same (Birdi, 2002). 

It has been found that the 1,3-dioxolane ring corresponds to approximately two oxyethylene units with regard to effect on the critical micelle concentration and adsorption characteristics [42]. Thus, surfactant type I in Fig. 14 should resemble ether sulfates of the general formula R-(0CH2CH2)20S03Na. This is interesting since the commercial alkyl ether sulfates contain two to three oxyethylene units. 

Surface aggregates formed by ionic surfactant adsorption on oppositely charge surfaces have been shown to be bi layered structures (1.) and are called admicelles<2) in this paper, though they are sometimes referred to as hemimicelles. The concentration at which admicelles first form on the most energetic surface patch is called the Critical Admicellar Concentration (CAC) in analogy to the Critical Micelle Concentration (CMC), where micelles are first formed. Again, in much of the literature, the CAC is referred to as the Hemimicellar Concentration (HMC). 

Adsorption, Electrokinetic, and Flotation Properties of Minerals above the Critical Micelle Concentration... 

Adsorption of a Single Surfactant. We denote a quantity valid for surfactant i at its critical micelle concentration (cmc) in a solution of only surfactant i in water by the superscript c(i). Thus, the chemical potential of the surfactant at the cmc in the equilibrium solution or in the surface phase at the onset of micellization in the solution is given by... 

Critical Micelle Concentration. In order to demonstrate the analogy between our treatment of mixed adsorption and earlier treatments of mixed micellization, we will briefly review the thermodynamics of mixed micelles. The thermodynamics of formation of ideal mixed micelles by two surfactants has been treated by Lange and Beck (9 ) and Cling (10). Rubingh ( ) extended the treatment to account for interactions between the surfactants, essentially by writing the cmc in the mixed surfactant solution as. 

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