Size and Shape of Micelles

The solubility of ionic surfactants increases gradually with increasing temperature, but at a critical temperature there is a rapid increase of solubility with further increase in temperature. This critical temperature is termed the Krafft Temperature (it increases with increasing alkyl chain length). 

Surface Activity and Adsorption at the Air/Liquid and Liquid/Liquid Interfiices 

This is dealt with in detail in Chapter 3 and only a summary is given here. Adsorption of surfactants at the air/liquid or liquid/Hquid interface lowers the surface or interfacial tension y. Just before the c.m.c., the y — log[CsAA] curve is linear and above the c.m.c. y becomes virtually constant. From the slope of the linear portion of the y — log C curve one can obtain the amount of surfactant adsorption T (mol m ), usually referred to as the surface excess using the Gibbs equation [8], where R is the gas constant and T is the absolute temperature, 

The free energy of micellisation is large and negative, indicating that micelle formation is spontaneous and that micelles are thermodynamically stable. 

The adsorption of surfactants at the solid/liquid interface may be described by the Langmuir equation [9], 

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The size and shape of micelles also are affected by fluormation Whereas hydrocarbon surfactants usually form spbencal micelles, linear fluorocarbon surfactants tend to produce larger rodhke speacs [31, 32 This is attnbuted to two inherent charac-tenshcs of the (CF2) chain (1) it adopts a hehcal rather than a linear zigzag conformation [dd 34, 35, 36], and (2) it is much suffer than the (CH2) cham [d5 37, 38] The relatively sbff, helical (CFj) chains thus prefer cylindrical to sphencal packing... 

Micelles are extremely dynamic aggregates. Ultrasonic, temperature and pressure jump techniques have been employed to study various equilibrium constants. Rates of uptake of monomers into micellar aggregates are close to diffusion-controlled306. The residence times of the individual surfactant molecules in the aggregate are typically in the order of 1-10 microseconds307, whereas the lifetime of the micellar entity is about 1-100 miliseconds307. Factors that lower the critical micelle concentration usually increase the lifetimes of the micelles as well as the residence times of the surfactant molecules in the micelle. Due to these dynamics, the size and shape of micelles are subject to appreciable structural fluctuations. 

The size and shape of micelles have been a subject of several debates. It is now generally accepted that three main shapes of micelles are present, depending on the surfactant structure and the environment in which they are dissolved, e.g., electrolyte concentration and type, pH, and presence of nonelectrolytes. The most common shape of micelles is a sphere with the following properties (i) an association unit with a radius approximately equal to the length of the hydrocarbon chain (for ionic micelles) (ii) an aggregation number of 50-100 surfactant monomers (iii) bound counterions for ionic surfactants (iv) a narrow range of concentrations at which micellization occurs and (v) a liquid interior of the micelle core. 

It is also known that additives may change the size and shape of micelles.At a certain point, as the surfactant or additive concentrations change, ionic micelles may change shape from spherical or nearly spherical to rodlike or other elongated forms. This may also affect the solubilization of the additive. It appears that alkane solubilization increases as the micelles become large, rodlike aggregates, whereas for polar additives like alcohols the solubilization decreases. ... 

The size and shape of micelles are determined by a delicate balance between various factors, such as chemical constitution, electrical repulsion of head groups, amphiphile and solute concentration, and temperature. The addition of electrolytes will in general raise aggregation numbers of ionic micelles and may even induce sphere-rod transitions. Temperature has an enormous influence on aggregation numbers of nonionic micelles, but only a little effect on those of ionic and amphoteric micelles. There is a vast literature covering the subject (24,25,36). 

As is the case for all macromolecules, the analyses of the size and shapes of micelles become of importance, when considering their colligative properties. Since the interfacial area between the macromolecule and the solvent determines the interactions between these species, it is obvious that the shape attained under given temperature and pressure will be determined by the lowest free energy of the macromolecule in solvent phase. These considerations have been the subject of analyses in various literature reports [27,311. 

In all the above methods, measurements can be made at sufficiently low concentration to avoid complications arising from particle-particle interactions. The results obtained are extrapolated to infinite dilution to obtain the desirable property such as the molecular weight and radius of gyration of a polymer coil, the size and shape of micelles, etc. 

According to the theory of amphiphilic aggregation, the size and shape of micelles is determined by the packing parameter, P = where is the head-... 

The size and shape of micelles are very important parameters. However, an introduction to their theoretical background is beyond the scope of this monograph. Those who are interested in more detailed discussion should refer to books on the subject of light scattering. ... 

Relaxation measurements yield information on the size and shape of micelles. Hoffmann et al. [77] observed that below a certain temperature, the amplitudes of the two relaxation processes decreased rapidly and amplitudes of new relaxation processes appeared. The new processes were attributed to the relaxation effects of another type of micelle, which appeared to be emulsion dropletlike giant molecules. The residence time of the surfactant molecules in the new micelle was unusually long, explained by the incorporation of ion pairs, formed by the surfactant and its counterion, in the micelle. The existence of giant micelles has been disputed by Fontell and Lindman [82]. Subsequent studies by Hoffmann et al. have indicated that the giant aggregates are probably dispersions of liquid crystalline mesophases (see Section 7.1). 

Micelles are in a dynamic state. Their characteristics, size, and shape vary with the structure of the surfactant and the solution conditions, such as the concentration, ionic strength, temperature, pressure, and the nature of additives. The aggregation number of the micelles is not independent of the method by which it is measured. The experimentally determined size and shape of micelles are therefore not unequivocally defined parameters of a surfactant solution but descriptive characteristics of micelles. 

Hoffmann et al. [55] examined the size and shape of micelles of LiPFO (lithium perfluorooctanoate) and DEAFN (diethylammonium perfluoronona-noate) by SANS. Mixtures of H2O and D2O were used as the solvent to increase the accuracy of SANS data by varying the contrast of the solvent. Spherical micelles were found in LiPFO solutions and spherical vesicles of various size in DEAFN solutions. 

Burkitt et al. [56] investigated the size and shape of micelles of ammonium salts of octanoic, decanoic, and perfluorooctanoic acids by SANS. Ammonium octanoate and ammonium decanoate formed spherical micelles having a micellar weight of 1640 and 12,576, respectively. Ammonium perfluorooctanoate formed cylindrical micelles with a mean micellar weight of 17,610. This corresponded to a mean association number of 43 at 0.12M. Burkitt at al. proposed a cylindrical micelle in which the head groups are hexagonally close-packed and the fluorocarbon chains form helical rows (Fig. 7.3). 

Burkitt et al. [228,229] used SANS to examine the size and shape of micelles in solutions containing ammonium perfluorooctanoate or mixtures of ammonium perfluorooctanoate with ammonium decanoate. The SANS measurements were made by the external contrast variation technique using mixtures of water and D2O as the solvent. By selecting appropriate H2O-D2O ratios, it is possible to view hydrocarbon and fluorocarbon micelle species independently. At a match point, the scattering length density of the H2O-D2O mixture is equal to that of the surfactant and the surfactant is at zero contrast. If the surfactants in a binary mixture form separate micelles, two match points are found. If mixed micelles are formed, scattering would occur at the contrast match points for each surfactant, but another match point is found as well. 

Micellar effects on reaction rates and equilibria are insensitive to changes in the size and shape of micelle. 

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