Micelle water interface, chemical potential

This transition may j-.e. reducing the specific surface energy, f. The reduction of f to sufficiently small values was accounted for by Ruckenstein (15) in terms of the so called dilution effect". Accumulation of surfactant and cosurfactant at the interface not only causes significant reduction in the interfacial tension, but also results in reduction of the chemical potential of surfactant and cosurfactant in bulk solution. The latter reduction may exceed the positive free energy caused by the total interfacial tension and hence the overall Ag of the system may become negative. Further analysis by Ruckenstein and Krishnan (16) have showed that micelle formation encountered with water soluble surfactants reduces the dilution effect as a result of the association of the the surfactants molecules. However, if a cosurfactant is added, it can reduce the interfacial tension by further adsorption and introduces a dilution effect. The treatment of Ruckenstein and Krishnan (16) also highlighted the role of interfacial tension in the formation of microemulsions. When the contribution of surfactant and cosurfactant adsorption is taken into account, the entropy of the drops becomes negligible and the interfacial tension does not need to attain ultralow values before stable microemulsions form. 

Rahaman and Hatton [152] developed a thermodynamic model for the prediction of the sizes of the protein filled and unfilled RMs as a function of system parameters such as ionic strength, protein charge, and size, Wq and protein concentration for both phase transfer and injection techniques. The important assumptions considered include (i) reverse micellar population is bidisperse, (ii) charge distribution is uniform, (iii) electrostatic interactions within a micelle and between a protein and micellar interface are represented by nonlinear Poisson-Boltzmann equation, (iv) the equilibrium micellar radii are assumed to be those that minimize the system free energy, and (v) water transferred between the two phases is too small to change chemical potential. 

Because the surfactant concentration in the oil phase (the disperse phase) is higher than the equilibrium concentration, surfactant molecules cross the oil-water interface toward the aqueous phase. Thus, surfactant accumulates within the flhn, because the bulk diffusion throughout the film is not fast enough to transport promptly the excess surfactant into the Plateau border. As the background surfactant concentration in the aqueous phase is not less than CMC, the excess surfactant present in the film is packed in the form of micelles (denoted by black dots in Figure 5.48a). This decreases the chemical potential of the surfactant inside the flhn. Nevertheless,... 

W. Actually, the surfactant does not like to be in water nor in oil because one part of the molecule is always lyophobic, which is why micelles are formed to hide it away from the solvent. Hence, it may be said that in type I phase behaviour the surfactant dislikes more oil than water, and in type II it dislikes more water than oil. Then, in type III phase behaviour, the surfactant equally dislikes both phases and would seek a third alternative, e.g. forming a bicontinuous microemulsion. In thermodynamic terms, it simply means that the chemical potential of the surfactant in such a microemulsion phase is lower than when it is adsorbed at the curved interface of a drop. 

The compact core of a micelle is characterized by a uniform polymer density, fiXBs), chemical potential per monomer unit, plb Xbs), and excess free energy per unit area of the core-water interface, kBTy xBs)- Here, Xbs T) is the Hory-Huggins parameter of monomer (B)-solvent (5) interaction, and Xbs T) > Xbs 0) = 1/2 under poor solvent conditions for the monomer units of block B. Although the solubility of polymers in organic solvents usually decreases with a decrease in temperature, dxiT)fdT < 0, the situation is more complex in aqueous solutions. In particular, it appears that the solubility of thermosensitive block B in water typically decreases with an increase in temperature [11], and hence dXBsiJ)/dT>0. In this case, the collapse of blocks B and the aggregation of the block copolymers into micelles occur at r > LCST, where LCST is the lower critical solution temperature. 

Arguably the most important parameter for any surfactant is the CMC value. This is because below this concentration the monomer level increases as more is dissolved, and hence the surfactant chemical potential (activity) also increases. Above the CMC, the monomer concentration and surfactant chemical potential are approximately constant, so surfactant absorption at interfaces and interfacial tensions show only small changes with composition under most conditions. For liquid crystal researchers, the CMC is the concentration at which the building blocks (micelles) of soluble surfactant mesophases appear. Moreover, with partially soluble surfactants it is the lowest concentration at which a liquid crystal dispersion in water appears. Fortunately there are well-established simple rules which describe how CMC values vary with chain length for linear, monoalkyl surfactants. From these, and a library of measured CMC values (35-38), it is possible to estimate the approximate CMC for branched alkyl chain and di- (or multi-) alkyl surfactants. Thus, most materials are covered. This includes the gemini surfactants, a new fashionable group where two conventional surfactant molecules are linked by a hydrophobic spacer of variable length (38). 

Is it possible to reach 7 = 0 by adding surfactants in carefully chosen systems The answer is no for air/water interfaces. The pressure would have to increase up to 11 = 70, in accordance with equation (8.16). Unfortunately, for such high values of 11, the chemical potential fisuRF invariably turns out to be higher than micelle In the competition between the surface and micelles, the surface is almost always the loser because of the cost of the interfacial energy between the aliphatic tails and air. 

An early version of a CG model with explicit solvent was developed by Smit et al., to study the dynamical interface between water and oil [26]. A similar strategy was also used by Goetz and Lipowsky [30] to simulate the self-assembly of a model surfactant into micelles and bilayers. Later, Klein and coworkers employed thermodynamic properties derived from atomistic simulations to develop a CG model for surfactants that includes the chemical structure [24, 31]. In this form, the procedure used to obtain the simplified potential functions of the CG model bears some level of similarity to the force-matching method used to fit simple potential functions for pairs of atoms against a fully electronic description [32]. Voth and coworkers later essentially followed this latter approach to also define an algorithm based on the force-matching procedure specific for CG-MD [33-35]. 

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