Free surfactant concentration

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]. 

Surfactant head groups. The remarkable fact remains that this charge neutralization allows aggregation to take place at free surfactant concentrations orders of magnitude below the cmc, dependent on the polyion charge density. 

Electrophoretic Mobility (I0 5cm2s lv 1) Free Surfactant Concentration (I0 4N) pH Primary Recovery (%)... 

Additive effects Low amounts of methanol have little effect on the free surfactant concentration (Table I). Nevertheless, the adsorbed amount of surfactant is decreased by 5% v/v methanol. The decreasing is slight (8%) with ODS Hypersil and the two surfactants and with SAS Hypersil and CTAB, but it can reach 30% in the case of SDS on SAS Hypersil (Table IV). 

FIG. 3 Dependence of the amount of binding, f, in CP+-PA -H20 solutions in the plateau region of binding (at free surfactant concentration cfs = 5 X 1CT5 mol duT3) on the degree of ionization, a. 

The effect of simple salt on the surfactant binding confirms the electrostatic nature of the surfactant ion-polyion interactions (step 1, Scheme 1). Any increase in the ionic strength of solution shifts the onset of binding toward higher free surfactant concentrations (compare isotherms in water, 0.01 M, and 0.1 M NaCl, Figure 6) and decreases the amount of bound surfactant. These observations can be related to the screening influence of the simple salt, which acts to diminish the electrostatic interactions between surfactant cations and polyanions. This is also well documented in the literature for a variety of polyelectrolyte-surfactant pairs [26-29],... 

If it is assumed that for any given free surfactant concentration for an extent of binding v, corresponding to a complex PS , then... 

With a laboratory prototype of the bubble tensiometer, it has been possible to measure surface tonsions continuously to within 1-2% [27]. A commercial instrument based on these principles is marketed by Chemdyne Corporation of Mesa, Arizona. The free surfactant concentration can be determined from knowledge of the surface tonsion and a surfactant calibration curve for the system in question. 

Figure 4 Free surfactant concentration X/s as a function of total surfactant concentration Xs- The critical micellar concentration (cmc) is given by the intersection of the dashed line, which has a unit slope, and the line through the high concentration data. (From Ref 31.)...

Figure 7 Temperature dependence of the free surfactant concentration as a function of the total surfactant concentration. A line of unit slope is shown for reference (dashed line). Lines through the high concentration regions are shown to guide the eyes. The points of intersection of these lines with the dashed line give the respective erne s. Note that the temperature, w" = /( /l.v, is in dimensionless units. (From Ref. 31.)...

Figure 20.2. The binding isotherm of a surfactant to a polymer without distinct hydrophobic moieties, giving the concentration of bound surfactant as a function of the free surfactant concentration, can be interpreted as a lowering of the surfactant CMC by the polymer, or a strongly co-operative binding...

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