Micellisation

As the concentration of aqueous solutions of many amphiphilic substances increases, there 

The primary reason for micelle formation is the attainment of a state of minimum free energy. At low concentration, amphiphiles 

The free energy change of a system is dependent on changes in both the entropy and enthalpy that is, AG = AH-T AS. For a micellar system at normal temperatures the entropy term is by far the most important in determining the free energy changes (T AS constitutes approximately 90-95% of the AG value). Micelle formation entails the transfer of a hydrocarbon chain from an aqueous to a nonaqueous environment (the interior of the micelle). To understand the changes in enthalpy and entropy that accompany this process, we must first consider the structure of water itself. 

The behaviour of a solution of amphipathic molecules reflects the opposing tendencies of one part of the molecule to separate out as a distinct phase while the other tends to stay in solution. The factors that have to be considered in discussing the effects of this balance therefore include (i) the interactions of hydrocarbon chains with water, (ii) the interaction of hydrocarbon chains with themselves, (iii) the solvation of the head group, and (iv) the interaction between the solvated head groups mediated in the case of ionic groups by their ionic atmospheres. The balance will clearly also be influenced by the relative sizes of the hydrophilic 

T pe and gene a f omnia R o an alkyl tail groupi Aamp Ir i 

N(C H-,iI Dodoes Ips ridimuni iodide Cetvlpyridmimii chloritle CPC1 

Merely listing the factors controlling micellisation shows that any valid theory is bound to be complicated in detail. However, some useful generalisations can he developed from first principles. 

We have already seen in Chapter 9 that the aggregation of particles can be discussed in terms of a sequence of addition reactions, shown in equation (9.7). Exactly the same arguments can he applied to the case of micellisation, but we have to discuss the problem in a little more detail since, unlike floes, micelles do not grow to a macroscopic size. In particular we have to take account of the fact that the successive equilibrium constants K(i, i + 1) [equation (9.8) depend on i. 

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Extensive discussions have focused on the conformation of the alkyl chains in the interior ". It has been has demonstrated that the alkyl chains of micellised surfactant are not fully extended. Starting from the headgroup, the first two or three carbon-carbon bonds are usually trans, whereas gauche conformations are likely to be encountered near the centre of tlie chain ". As a result, the methyl termini of the surfactant molecules can be located near the surface of the micelle, and have even been suggested to be able to protrude into the aqueous phase "". They are definitely not all gathered in the centre of tire micelle as is often suggested in pictorial representations. NMR studies have indicated that the hydrocarbon chains in a micelle are highly mobile, comparable to the mobility of a liquid alkane ... 

Herein Pa and Pb are the micelle - water partition coefficients of A and B, respectively, defined as ratios of the concentrations in the micellar and aqueous phase [S] is the concentration of surfactant V. ai,s is fhe molar volume of the micellised surfactant and k and k , are the second-order rate constants for the reaction in the micellar pseudophase and in the aqueous phase, respectively. The appearance of the molar volume of the surfactant in this equation is somewhat alarming. It is difficult to identify the volume of the micellar pseudophase that can be regarded as the potential reaction volume. Moreover, the reactants are often not homogeneously distributed throughout the micelle and... 

Herein [5.2]i is the total number of moles of 5.2 present in the reaction mixture, divided by the total reaction volume V is the observed pseudo-first-order rate constant Vmrji,s is an estimate of the molar volume of micellised surfactant S 1 and k , are the second-order rate constants in the aqueous phase and in the micellar pseudophase, respectively (see Figure 5.2) V is the volume of the aqueous phase and Psj is the partition coefficient of 5.2 over the micellar pseudophase and water, expressed as a ratio of concentrations. From the dependence of [5.2]j/lq,fe on the concentration of surfactant, Pj... 

Interestingly, at very low concentrations of micellised Qi(DS)2, the rate of the reaction of 5.1a with 5.2 was observed to be zero-order in 5.1 a and only depending on the concentration of Cu(DS)2 and 5.2. This is akin to the turn-over and saturation kinetics exhibited by enzymes. The acceleration relative to the reaction in organic media in the absence of catalyst, also approaches enzyme-like magnitudes compared to the process in acetonitrile (Chapter 2), Cu(DS)2 micelles accelerate the Diels-Alder reaction between 5.1a and 5.2 by a factor of 1.8710 . This extremely high catalytic efficiency shows how a combination of a beneficial aqueous solvent effect, Lewis-acid catalysis and micellar catalysis can lead to tremendous accelerations. 

The volume of the micellar pseudophase can be estimated from the molar volume of the micellised surfactant V-moiji ... 

Mukerjee P, Cardinal JR, Desai NR. In Mittal KL, editor. Micellisation, solubilisation and microemulsions. New York Plenum 1977. p. 241. 

ATRP is a powerful synthetic tool for the synthesis of low molecular weight (Dp < 100-200), controlled-structure hydrophilic block copolymers. Compared to other living radical polymerisation chemistries such as RAFT, ATRP offers two advantages (1) facile synthesis of a range of well-defined macro-initiators for the preparation of novel diblock copolymers (2) much more rapid polymerisations under mild conditions in the presence of water. In many cases these new copolymers have tuneable surface activity (i.e. they are stimuli-responsive) and exhibit reversible micellisation behaviour. Unique materials such as new schizo-... 

FIGURE 5.7 Absorption of dietary fat-soluble substances via the lipid route affected by insufficiently emulsified and micellised lipids. 

Micellisation is, therefore, an alternative mechanism to adsorption by which the interfacial energy of a surfactant solution might decrease. 

When one considers the energetics of micellisation in terms of the hydrocarbon chains of the surfactant molecules, the following factors are among those which must be taken into account ... 

Micellisation permits strong water-water interaction (hydrogen bonding) which would otherwise be prevented if the surfactant was in solution as single molecules wedged between the solvent water molecules. This is a most important factor in micelle formation and also of course, in any adsorption process at an aqueous interface. It is often referred to as the hydrophobic effect49. 

There are two current theories relating to the abruptness with which micellisation takes place above a certain critical concentration53,155. 

The first of these theories applies the law of mass action to the equilibrium between unassociated molecules or ions and micelles, as illustrated by the following simplified calculation for the micellisation of non-ionic surfactants. If c is the stoichiometric concentration of the solution, x is the fraction of monomer units aggregated and m is the number of monomer units per micelle,... 

The alternative approach is to treat micellisation as a simple phase separation of surfactant in an associated form, with the unassociated surfactant concentration remaining practically constant above the... 

Since the equilibrium constant, 07C, in equation (4.23) and the standard free energy change, AG°, for the micellisation of 1 mole of surfactant are related by... 

In general, micellisation is an exothermic process and the c.m.c. increases with increasing temperature (see page 86). This, however, is not universally the case for example, the c.m.c, of sodium dodecyl sulphate in water shows a shallow minimum between about 20°C and 25°C. At lower temperature the enthalpy of micellisation given from equation (4.28) is positive (endothermic), and micellisation is entirely entropy-directed. 

The cause of a positive entropy of micellisation is not entirely clear. A decrease in the amount of water structure as a result of micellisation may make some contribution. A more likely contribution, however, involves the configuration of the hydrocarbon chains, which probably have considerably more freedom of movement in the interior of the micelle than when in contact with the aqueous medium. 

Micelle-forming surfactants exhibit another unusual phenomenon in that their solubilities show a rapid increase above a certain temperature, known as the Krafft point. The explanation of this behaviour arises from the fact that unassociated surfactant has a limited solubility, whereas the micelles are highly soluble. Below the Krafft temperature the solubility of the surfactant is insufficient for micellisation. As the temperature is raised, the solubility slowly increases until, at the Krafft temperature, the c.m.c. is reached. A relatively large amount of surfactant can now be dispersed in the form of micelles, so that a large increase in solubility is observed. 

This argument does not necessarily hold for processes such as adsorption from solution and micellisation, since a certain amount of destructuring (e.g. desolvation) may be involved and the net entropy change may be positive. 

Determine an enthalpy of micellisation in accord with the phase separation model. 

Fig. 29 Dependence of the degree of micellisation on the molar fraction of acrylic acid and topology (o) AA20 side chains, ( ) AA37 side chains, (A) AA85 side chains, ( ) block copolymers...

These surfactants can form micelles provided that the salt concentration is low. The cmc of 6-SLABS was readily determined by spectrophotometry at 262 nm, and the discontinuity in the plot is clearly shown in Fig. 19.2(a) from which the cmc can be obtained as 0.0014 mol dm-3. It should be noted that the cmc is found to be essentially independent of temperature over the experimentally-measured range of 15-30°C. This is generally found for micellisation involving ionic surfactants in water, so that the enthalpy change on transferring monomer from aqueous solution to the micelle is approximately zero. There is a 20% decrease in extinction coefficient of the benzene ring chromophore on transfer from an aqueous... 

In order to develop efficient techniques for the preparation and application of foams in industry, agriculture, firefighting, etc., it is necessary to know the physicochemical parameters of surfactants and their relationship with the foam stabilising ability of the surfactant solutions. Usually the criterion of the surfactant foaming ability is the adsorption of these compounds at the solution/air interface and the related to it properties, such as decrease in surface tension, adsorption work, maximum adsorption T. [13,39,43]. CMC is often used as a characteristic of a foaming agent (if micellisation is possible in the surfactant solution). Parameters related to foam stability, such as foam lifetime and foam column height, are also employed [12,13,39],... 

When cationic micelles are employed, the counter ions are often halide ions. It is found that the fluorescence lifetime of micellised aromatic hydrocarbons is reduced by bromide ions (Hautala et al., 1973 Miller et al., 1977). Whether the quenching is due to the heavy atom effect, electron transfer, or nucleophilic attack has not been determined. 

When anionic micelles are employed the counter ions can often have a profound effect upon the photophysical processes of micellised compounds. Thus if the counter ion is a heavy atom, e.g. silver, intersystem crossing can become highly efficient and make it possible for phosphorescence to be readily detected at room temperature (Kalyanasundaram et al., 1977 Humphry-Baker et al., 1978). If, on the other hand, the counter ion does not interfere with photophysical processes, high triplet yields can be observed, e.g. for N-methyl-phenothiazine (Moroi et al., 1979a), zinc(II) tetrasulphophthalo-cyanine (Darwent, 1980), because the high likelihood of single occupancy of micelles precludes triplet-triplet annihilation. 

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