Surfactant micelles size correlation

Surfactant-based ultrafiltration (SBUF) has been investigated since the 1980s for removing dissolved organic compounds, especially hazardous wastewater, as discussed in Chapter 1. The basis of SBUF is that at concentrations above the critical micelle 

The micelle diameter can be calculated by measuring the micelle diffusion coefficient using the technique of dynamic light scattering (DLS). If one assumes that aU micelles are spherical in shape, the radius of a micelle in solution may be calculated by using the Stokes-Einstein relation  

Diffusion coefficient vs. moiecuiar weight plot for macromolecules. Diffusion coefficients for Tween 80 and RC-520 Points A and B refer to pseudomolecular weights of Tween 80 and RC-520, respectively. 

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The structure of the AOT micellar system, as well as the state of water entrapped inside swollen micelles, have been characterized using different techniques, such as photon correlation spectroscopy (25), positron annihilation (26), NMR (27, 28), fluorescence (29-32) and more recently small angle neutron scattering (33). The existence of reversed micelles has been demonstrated in the domain of concentrations explored by protein extraction experiments. Their size (proportional to the molar ratio of water to surfactant known as wo), shape and aggregation number have been determined. Furthermore, the micelle size distribution is believed to be relatively monodisperse. 

For those systems near a phase transition, the apparent hydrodynamic diameter of the droplets (or the correlation length), as calculated using the Stokes-Einstein equation, appears to decrease as pressure increases [2,4,39]. For example, the apparent hydrodynamic diameter of a microemulsion droplet (for [surfactant] = 150 mM and 5) in supercritical xenon [2] decreases from 6.5 to 4.5 nm as pressure is increased from 350 to 550 bar (10 bar = 1 MPa). This effect is due to the change in the extent of micelle clustering rather than an actual change in the micelle size. 

Figure 6.9 A correlation between the size of surfactant micelles and molecular weight of macromolecules. Source [18], Copyright 1996 from Separation Science and Technology by R. Singh. Reproduced by permission of Taylor Francis Group, LLC, http //www.taylorandfrancis.com.

Studies of micelle formation indicate that surfactant properties such as the cmc and aggregation number can be reasonably well correlated with the size and nature of the hydrophobic group. Unfortunately, comparably convenient relationships are not always so apparent in terms of surfactant structure and solubihzing power, probably because the structure of the additive can play such an important role in the overall aggregation process. Nevertheless, many of the factors discussed previously that cause an increase in micelle size might also be expected to increase the solubilizing power of the system. 

The exit rate constants of the excited anions after the photoprotolytic dissociation of l,4-dichloro-2-naphthol within decylsulfate, dedecylsulfate, and cetylsulfate micelles were measured with a fluorescence quencher hardly penetrating the micelles, - the nitrate ion [121]. The addition of nitrate into the solution quenched the fluorescence of those anions which escape from the micelles within the lifetime of the excited state only. The exit rate constant of the naphtholate anion increases with increasing length of the hydrocarbon radical in the micelle-forming surfactant. The exit rate is thus controlled by the lowering of the micelle polarity (i.e. by the free energy of the exit process) rather than by the micelle size or the distance that the anion must diffuse. Perhaps one can establish a kind of correlation between the rate constant of this process and its free energy as was done for photochemical electron transfer [126] and proton transfer [156,157]. 

Returning to the micelle size distribution, we can estimate how this distribution changes upon the addition of solute a. Suppose again that the two-component system of surfactant and water behaves as an associated ideal dilute solution for which (8.9.11) and (8.9.13) are valid. By adding the solute a we can define the new species A(k, n), i.e., an aggregate with n monomers and k solute molecules a. Since the strong correlations between a and An are within the species A k, n), the assumption of associate ideality can be retained for all the species A k, n). Hence the analogue of (8.9.11) is now... 

Above the CMC of each surfactant, linear enhancements in HCB solubility were observed, similar to trends reported for HOCs in micellar solutions (7,5,75). The corresponding WSR values for Tween 60, Tween 80 and Triton X-100, calculated using Equation 1, were 0.59 g/kg, 0.63 g/kg and 0.35 g/kg, respectively. The lower HCB solubilization capacity of TritonX-100 is consistent with solubility correlations developed by PenneU et al. (5) for a range of surfactants and HOCs. This behavior is attributed to the greater alkyl chain length, and hence larger micelle size of Tween 60 and Tween 80 relative to that of Triton X-100. 

The energetics and kinetics of film formation appear to be especially important when two or more solutes are present, since now the matter of monolayer penetration or complex formation enters the picture (see Section IV-7). Schul-man and co-workers [77, 78], in particular, noted that especially stable emulsions result when the adsorbed film of surfactant material forms strong penetration complexes with a species present in the oil phase. The stabilizing effect of such mixed films may lie in their slow desorption or elevated viscosity. The dynamic effects of surfactant transport have been investigated by Shah and coworkers [22] who show the correlation between micellar lifetime and droplet size. More stable micelles are unable to rapidly transport surfactant from the bulk to the surface, and hence they support emulsions containing larger droplets. 

Water activity can be nsed to quantify water in all non-conventional media and is used to an increasing extent. However, in microemulsions containing reversed micelles, water is still often quantified as the molar ratio of water to surfactant (abbreviated as Wq or R). This parameter is used because it is correlated with the size of the reversed micelles, which in turn is correlated with enzymatic activity. 

Since they act as surfactants, copolymers are added in only small amounts, typically from a thousandth parts to a few hundredth parts. Theoretically, Leibler [30] showed that only 2% of a diblock copolymer may thermodynamically stabilize an 80%/20% incompatible blend with an optimum morphology (submicronic droplets). However, in practice kinetic control and micelle formation interfere in this best-case scenario. To a some extent, compatibilization increases with copolymer concentration [8,31,32], Beyond a critical concentration (critical micellar concentration cmc) little or no improvement is observed (moreover, for high amounts, the copolymer can act as a plasticizer). Copolymer molecular weight influence is similar to that of the concentration effect. For example, in a PS/PDMS system [8,31,32], when the copolymer molecular weight increases, domain size decreases to a certain extent. Hu et al. [31] correlated their experimental results with theoretical prediction of the Leibler s brush theory [30]. Leibler distinguishes two regimes to characterize the behaviour of the copolymer at the interface... 

Solubilization of monomers in the micellar core of surfactants has earlier been well demonstrated (M). It was, therefore, of interest to examine the solubilization of a water-insoluble monomer such as styrene in the core of the polyester micelles. A technique by Funke was followed, in which a micellar polyester solution was titrated with styrene while its optical density recorded. For the system MD 60-styrene, 0.60 + 0.05 g of styrene is solubilized per gm polyester. Similarly the increase in micellar size, due to swelling by styrene, could be followed by photon correlation spectroscopy. This is shown in Figure 3, corresponding to the plot of ... 

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