Critical aggregation number

In Fig. 4-3, Q is the critical aggregation number, AGj is the surface excess free energy (between the surface and the bulk of the particle), AG is the excess free energy between a particle at r = oo and the solute in solution, "yi2 is the surface tension, and m is the molecular volume. 

Several different experimental techniques, such as fluorescence decay, electron spin resonance (ESR) spectroscopy, Raman spectroscopy, nuclear magnetic resonance (NMR) spectroscopy, neutron reflectome-try, calorimetry, Fourier-transform infrared (FT-IR) adsorption spectroscopy, small-angle neutron scattering (SANS), ellipsometry and surface force measurements, have been used to study self-assembled surfactant structures at the solid-liquid interface (11). These measurements, although providing insight into the hemimicellization process, critical aggregation numbers... 

In marked contrast, the transfer of Aerosol OT from the aqueous to the aqueous/oil interface appears to be instantaneous and cannot be completely captured in the time scale of the spinning drop measurements. This fast adsorption time-scale is anticipated for surfactants solved in the aqueous phase and partition to a significant extent into the oil phase below the critical aggregation number. A small amount of desorption of material from the interface is suggested by the slight increase in tension with time (Figure 6). 

The Critical Aggregation Number (CAN) corresponds to the cationic concentrations at which lipid particles aggregate. The result amounts to the cations expressed as monovalent cations and should not exceed 600 mmol/L. 

Figure 20 shows the plot of the surface tension vs. the logarithm of the concentration (or-lg c-isotherms) of sodium alkanesulfonates C,0-C15 at 45°C. In accordance with the general behavior of surfactants, the interfacial activity increases with growing chain length. The critical micelle concentration (cM) is shifted to lower concentration values. The typical surface tension at cM is between 38 and 33 mN/m. The ammonium alkanesulfonates show similar behavior, though their solubility is much better. The impact of the counterions is twofold First, a more polarizable counterion lowers the cM value (Fig. 21), while the aggregation number of the micelles rises. Second, polarizable and hydrophobic counterions, such as n-propyl- or isopropylammonium and n-butylammonium ions, enhance the interfacial activity as well (Fig. 22). Hydrophilic counterions such as 2-hydroxyethylammonium have the opposite effect. Table 14 summarizes some data for the dodecane 1-sulfonates.

Rupture of fractal (flocculated) aggregates of polystyrene latices in simple shear flow and converging flow was studied by Sonntag and Russel (1986, 1987b). For simple shear flow and low electrolyte concentrations, the critical fragmentation number decreases sharply with agglomerate radius (R) as... 

Figure 10.11 As the aggregate number n increases, so the fraction of the added surfactant that goes into the micelle (as y ) varies more steeply with total concentration of surfactant monomer (as V). The critical micelle concentration (CMC) is the midpoint of the region over which the concentration of the micelle changes (Reproduced by permission of Wiley Interscience, from The Colloidal Domain by D. Fennell Evans and Hakan Wennerstrom)...

Surfactant solutions critical micelle concentration distribution of reactants among particles surfactant aggregation numbers interface properties and polarity dynamics of surfactant solutions partition coefficients phase transitions influence of additives... 

Critical Micelle Concentration (cmc) is the surfactant concentration below which the formation of reverse micelles does not occur, while the number of surfactant molecules per micelle is referred to as the aggregation number, n. The cmc is obtained through physical measurements, and varies from 0.1-1.0 mmol dm in water or the nonpolar solvents. 

Monostearate of Critical micelle cone, (g/dl) Micellar molecular weight Aggregation number... 

Surfactant Solution Critical micelle concentration (mole liter-1) Aggregation number n Ratio of charge to aggregation number, z/n... 

Surfactants dissolved in liquid hydrogen fluoride form micelles if their concentration reaches the critical micelle concentration (CMC).3 5 However, the aggregation process is less favorable than in water. Consequently, the CMC values are higher and lower aggregation numbers are... 

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