Pseudophase separation model

To this point, only models based on the pseudo—phase separation model have been discussed. Mixed micelle models utilizing the mass action model may be necessary for micelles with small aggregation numbers, as demonstrated by Kamrath and Franses ( ). However, even for large micelles, the fundamental basis for the pseudophase separation model needs to be examined. In micelles, how much solvent or how many counterions (bound or in the electrical double layer) should be included in the micellar pseudo-phase is unclear. The difficulty is normally surmounted by assuming that the pseudo—phase consists of only the surfactant components i.e., solvent or counterions are ignored. The validity of treating the micelle on a surfactant—oniy basis has not been verified. Funasaki and Hada (22) have questioned the thermodynamic consistency of such an approach. 

The pseudophase-separation model for surfactant solutions (84, 132, 135) states that a surfactant solution above its critical micelle concentration (CMC) consists of two pseudophases in equilibrium with each other singly dispersed surfactant monomer molecules and micelles. When the surfactant solution is in contact with a solid, the adsorbed phase constitutes a third pseudophase (40). Strong experimental evidence suggests that surfactant adsorption takes place from the surfactant monomer phase but not from the micelles (84), behavior that leads to competition of both the micelles and the adsorbed phase for surfactant molecules from the monomer phase. Adsorption from a surfactant solution above the CMC then depends not only on the affinity of the surfactant for the solid surface but also on its tendency to form micelles. If a mixture can be formulated such that at least one of the surfactants is incorporated into micelles preferentially over the adsorbed phase, then the micelles act as a sink for the surfactant and thus prevent it from being adsorbed. 

There are two basic approaches to modeling the thermodynamics of micelle formation. The mass action model views the micelles as reversible complexes of the monomer that are aggregating and predicts the sharp change in tendency of incremental surfactant to form micelles instead of monomer at the CMC this sharp transition is a consequence of the relatively large number of molecules forming the aggregate. The mass action model predicts that micelles are present below the CMC but at very low concentrations. The ocher major model used to describe micelle formation is the pseudophase separation model, which views micelles as a separate thermodynamic phase in equilibrium with monomer. Because micelle formation is a second-order phase transition, micelles are not a true thermodynamic phase, and this model is an approximation. However, the assumption that there are no mi-celies present below the CMC, and that the surfactant activity becomes constant above the CMC. is close to reality. and the mathematical simplicity of the pseudophase... 

Holterman, H.A.J. and Engberts, J.B.F.N., Heat capacities of activation for the neutral hydrolysis of two acyl-activated esters in water-rich 2-n-butoxyethanol-water mixtures. Analysis in terms of the pseudophase-separation model, /. Org. Chem., 1983, 48, 4025-4030. 

This important equation relates the dependence of the Kralft temperature on composition (composition in units of mole fraction of surfactant, Xi) to three terms. These are the magnitude of T, the differential molar heat of solution of the crystal H, and the dependence of surfactant chemical potential (pi) on surfactant composition. (Pressure, p, is presumed to remain constant.) In the pseudophase separation model this dependence equals zero, which does not correspond to the actual data. However, the dependence of Krafft temperature on composition in this system is small, and this approximation is numerically satisfactory. 

Mukerjee et al. [125] have emphasized that calculations based on the mass action model or the pseudophase separation model give significantly different en-thalphy values. However, the discrepancies between both models diminish if the aggregation number increases to infinity [107,127]. 

The pseudophase separation model of micellar solutions considers a micelle to be a pseudophase in a liquid state. Because the micelles are assumed to have a liquidlike core, the mutual solubility of a fluorinated surfactant and a hydrocarbon surfactant in mixed micelles is, according to the pseudophase model, governed by the miscibility of the fluorocarbon and hydrocarbon chain. For example, heptane and perfluoroheptane are immiscible at 25°C, but above 50°C, these liquids are miscible in all proportions [75]. A terminal substitution of a hydrophilic group depresses the enthalpy of mixing and makes the components miscible at 25°C. 

Kamrath and Franses [85] developed a single-micelle-size mass action model for binary solutions of surfactants with the same hydrophilic group and counterion. The mass action model predicts micellar behavior more accurately than the pseudophase separation model [73] if the number of surfactant monomers in the mixed micelle is less than about 50. 

Binary surfactant mixtures have traditionally been modeled using the pseudophase-separation approach, in which the micelles are treated as a separate, inLnite phase in equilibrium with the... 

The CMC has its most clear-cut interpretation within the (pseudo) phase separation model of micelle formation. Although the micelles and the surrounding solution form a single phase, the amphiphile association shows a cooperativity that makes an analogy with a phase transition useful. Within this model, the CMC is the concentration at which the system enters a two phase region the two pseudophases formed being the aqueous system and the micelles. 

Various approaches have been employed to tackle the problem of micelle formation. The most simple approach treats micelles as a single phase, and this is referred to as the phase-separation model. In this model, micelle formation is considered as a phase-separation phenomenon, and the cmc is then taken as the saturation concentration of the amphiphile in the monomeric state, whereas the micelles constitute the separated pseudophase. Above the cmc, a phase equilibrium exists with a constant activity of the surfactant in the micellar phase. The Krafft point is viewed as the temperature at which a solid-hydrated surfactant, the micelles, and a solution saturated with undissociated surfactant molecules are in equiUbrium at a given pressure. 

The simplest thermodynamic model for solubilization is the pseudophase or phase separation model. The micelles are treated as a separate phase consisting of surfactant and the solubilized molecules. Solubilization is regarded as a simple distribution or equilibrium of the solute between the aqueous and the miceUar phases, i.e.. 

Data published on thermodynamic properties of fluorinated surfactants are scarce. Shinoda and Hutchinson [42] treated the micelle as a separate pseudophase of very small dimensions. The phase-separation model describes the micelle as a separate phase which begins to form at cmc. If micelle formation is analogous to phase separation, the heat and entropy of micellization can be calculated from the temperature dependence of the activities of micelle-forming species. 

Advances in the theory of mixed-micelle formation have made it possible to calculate the composition of mixed micelles formed by two or more surfactants. A thermodynamic treatment of micellar solutions of mixed surfactants is usually based on the pseudophase separation theory [61,71-74]. The pseudophase models developed for binary surfactant solutions assume ideal mixing of the surfactants in the micelle. 

The anionic fluorinated surfactant (SPFO) forms with the nonionic or the amphoteric hydrocarbon surfactant mixed micelles containing both types of surfactants. Both systems exhibit a negative deviation from ideality. Changes of the F and H chemical shifts of the two surfactants upon mixing are consistent with pseudophase diagrams, calculated from the cmc dependence on the fluorinated surfactant mole fraction. The interpretation of data was based a modified regular solution theory and the phase-separation model. 

The kinetic data are essentially always treated using the pseudophase model, regarding the micellar solution as consisting of two separate phases. The simplest case of micellar catalysis applies to unimolecTilar reactions where the catalytic effect depends on the efficiency of bindirg of the reactant to the micelle (quantified by the partition coefficient, P) and the rate constant of the reaction in the micellar pseudophase (k ) and in the aqueous phase (k ). Menger and Portnoy have developed a model, treating micelles as enzyme-like particles, that allows the evaluation of all three parameters from the dependence of the observed rate constant on the concentration of surfactant". ... 

In contrast to SDS, CTAB and C12E7, CufDSjz micelles catalyse the Diels-Alder reaction between 1 and 2 with enzyme-like efficiency, leading to rate enhancements up to 1.8-10 compared to the reaction in acetonitrile. This results primarily from the essentially complete complexation off to the copper ions at the micellar surface. Comparison of the partition coefficients of 2 over the water phase and the micellar pseudophase, as derived from kinetic analysis using the pseudophase model, reveals a higher affinity of 2 for Cu(DS)2 than for SDS and CTAB. The inhibitory effect resulting from spatial separation of la-g and 2 is likely to be at least less pronoimced for Cu(DS)2 than for the other surfactants. 

Both the Menger-Portnoy model and the model by Berezin were effectively derived on the assumption that micellar solutions contain two pseudophases, namely the micellar pseudophase and bulk water. However, both models can be expanded to take more than one micellar pseudophase into account. For example, this could be done when the micellar pseudophase is seen to consist of two separate pseudophases (zones) itself, namely a pseudophase corresponding to the hydrophobic core and a pseudophase corresponding to the micellar Stern region. " If one then assumes a reaction to occur with a rate constant k in the Stern region while the reaction does not occur in the micellar core, the expression for k includes the distribution of the reactant over different zones [Equation (6)]. " ... 

The synthesis of sodium decanesulfonate from the alkyl halide and Na2S03 can be carried out very conveniently in microemulsions based on nonionic surfactants [108]. The rate data fit a pseudophase model, and the nonionic surfactants make this method preparatively very useful because phase separation with a change of temperature allows recovery of the surfactants. This approach is very useful because surfactants have high molecular weights and large amounts are needed in preparative reactions and the solubilizing ability of surfactants complicates product isolation. Therefore, more research is needed... 

Pseudophase models, as well as other forms of quantitatively analyzing the effects of supramolecular aggregates on reaction rates, were derived for micellar solutions [21]. The full description, as well as critical analysis of the models, has been reviewed [22]. Pseudophase models start by considering that a system can be treated as if it were composed of two separate pseudophases, micelles and an intermicellar aqueous phase. It is further assumed that monomers, substrates and ions equilibrate much faster than reaction rates. This last assumption renders these treatments only applicable to some ground state reactions, since excited state processes and some electron transfer reactions, can be faster than equilibration rates [21,23]. Further assuming that the reaction rate in the two pseudophases can be characterized by two separate and independent rate constants (k, in the micelle and in the intermicellar aqueous phase) the rate constant kij/) of a spontaneous monomolecular decomposition of a substrate S is described by... 

Pseudophase models " were originally developed to treat mixed micellization of binary surfactants." The concept has been generahzed to mean that the totality of the surfactant aggregates present, for example, micelles, microemnlsions, vesicles, and so on, in homogeneous solutions are treated conceptually as a separate phase, or... 

Pseudophase models work for several reasons (i) Reactions in association coUoids can be carried out under conditions of dynamic equilibrium. Thus the totality of the interfacial regions of all the aggregates in micelle, microemulsion, or vesicle solutions, and the totalities of their oil and water regions can be modeled as single interfacial, oil, and water reaction volumes of uniform properties with a separate rate constant for the reaction in each volume. Scheme 4. (ii) The requirement of dynamic equilibrium is met because the rate constants for diffusion of ions and molecules in association colloid solutions are near the diffusion-controlled limit. For example, the entrance and exit rate constants in micellar solutions in Table 1 are orders of magnitude faster than the example rate constants for thermal bimolecular reactions in micellar solutions in Table 4. Many additional examples are compiled in reviews. (iii) Measured rate constants for spontaneous reactions and... 

Pseudophase model The properties of the totality of the aggregates in homogeneous solutions are treated as a separate phase, a pseudophase. The totality of the association colloid present (micelle, vesicle, microemulsion) is modeled as three regions oil, interfacial, and water. 

Eventually, let us compare the adsorption behavior with what we had found in Chapter 13 for simplified hybrid lattice models of polymers and peptides near attractive substrates. The adhesion of the jjeptides at the Si(lOO) substrate exhibits very similar features. Exemplified for peptide S3, Fig. 14.13 shows the plot of the canonical probability distributionpcan E, q) 8 E — E(X))S(q — q(X))) at room temperature (T = 300 K). The peak at E, q) (80.5 kcal/mole, 0.0) corresponds to conformations that are not in contact with the substrate. It is separated from another peak near (E, q) (74.5 kcal/mole, 0.2) and belongs to conformations with about 17% of the heavy atoms with distances < 5 A from the substrate surface (compare with Fig. 14.12). That means adsorbed and desorbed conformations coexist and the gap in between the peaks separates the two pseudophases in g -space, which causes a kinetic free-energy barrier. Thus, the adsorption transition is a first-order-like pseudophase transition in q, but since both structural phases (adsorbed and desorbed) coexist almost at the same energy, the transition in E space is weakly of first order. ... 

In view of assumption 1, each micelle acts as a microreactor of one domain that provides a new reaction medium and alters the distributions of reactants in solution. Thus, the classical PP model may also be called the two-domain pseudophase model of micelles, in which the bulk aqueous region and the entire micellar pseudophase are considered to be two different reaction domains. A refinement of Equation 3.2 consists of including the possibility of different reaction domains within the micelle. A three-domain pseudophase model is one in which, for example, the bulk aqueous region, the Stem region, and the hydro-phobic micellar core are treated as separate reaction regions. ... 

---