Micelles thermodynamic models

Osborne-Lee, I. W., and R. S. Schechter. 1986. Nonideal mixed micelles. Thermodynamic models and experimental comparisonACS Symp. Se(Phenom. Mixed Surfactant Syst.). 311 30—43. 

Other molecular thermodynamic models for protein-reverse micelle complexes have also emerged. Bratko et al. [171] presented a model for phase transfer of proteins in RMs. The shell and core model was combined with the Poisson-Boltzmann approximation for the protein-RM complex and for the protein-free RM. The increase in entropy of counterions released from RMs on solubilization of a protein was the main contribution to the decrease in free energy of com-plexation. Good agreement was found with SANS results of Sheu et al. [151] for cytochrome C solubilization and the effect of electrolytes on it. However, this model assumes that filled and empty RMs are of the same size, independent of salt strength and pH, which is not true according to experimental evidence available since then. 

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. 

The importance of entropic considerations in the formulation of a thermodynamic model for micelle formation in mixtures of ionic and nonionic surfactants has been demonstrated by the ability of the... 

The purpose of this paper will be to develop a generalized treatment extending the earlier mixed micelle model (I4) to nonideal mixed surfactant monolayers in micellar systems. In this work, a thermodynamic model for nonionic surfactant mixtures is developed which can also be applied empirically to mixtures containing ionic surfactants. The form of the model is designed to allow for future generalization to multiple components, other interfaces and the treatment of contact angles. The use of the pseudo-phase separation approach and regular solution approximation are dictated by the requirement that the model be sufficiently tractable to be applied in realistic situations of interest. 

Surfactant Activity in Micellar Systems. The activities or concentrations of individual surfactant monomers in equilibrium with mixed micelles are the most important quantities predicted by micellar thermodynamic models. These variables often dictate practical performance of surfactant solutions. The monomer concentrations in mixed micellar systems have been measured by ultraf i Itration (I.), dialysis (2), a combination of conductivity and specific ion electrode measurements (3), a method using surface tension of mixtures at and above the CMC <4), gel filtration (5), conductivity (6), specific ion electrode measurements (7), NMR <8), chromatograph c separation of surfactants with a hydrophilic substrate (9> and by application of the Bibbs-Duhem equation to CMC data (iO). Surfactant specific electrodes have been used to measure anionic surfactant activities in single surfactant systems (11.12) and might be useful in mixed systems. ... 

Maestro, M. and Luisi, P. L. (1990). A simplified thermodynamic model for protein uptake by reverse micelles. In Surfactants in Solution, ed. K. L. Mittal. Plenum, vol. 9. 

Micelles are formed by association of molecules in a selective solvent above a critical micelle concentration (one). Since micelles are a thermodynamically stable system at equilibrium, it has been suggested (Chu and Zhou 1996) that association is a more appropriate term than aggregation, which usually refers to the non-equilibrium growth of colloidal particles into clusters. There are two possible models for the association of molecules into micelles (Elias 1972,1973 Tuzar and Kratochvil 1976). In the first, termed open association, there is a continuous distribution of micelles containing 1,2,3,..., n molecules, with an associated continuous series of equilibrium constants. However, the model of open association does not lead to a cmc. Since a cmc is observed for block copolymer micelles, the model of closed association is applicable. However, as pointed out by Elias (1973), the cmc does not correspond to a thermodynamic property of the system, it can simply be defined phenomenologically as the concentration at which a sufficient number of micelles is formed to be detected by a given method. Thermodynamically, closed association corresponds to an equilibrium between molecules (unimers), A, and micelles, Ap, containingp molecules ... 

The second important characteristic of the micellar solution that relates to solubilization is the micelle size. Poor aqueous soluble compounds are solubilized either within the hydrocarbon core of the micelle or, very commonly, within the head group layer at the surface of the micelle or in the palisade portion of the micelle. Predictions of the micelle size have relied on the use of empirical relationships employed within a thermodynamic model, for instance the law of mass action where micellization is in equilibrium with the associated and unassociated (monomer) surfactant molecules (Attwood and Florence, 1983). 

Although additional discussion on this topic can be found in the section of case studies, solid micelle dispersion/solution is not the primary scope of this chapter. Readers interested in this topic can refer to a corresponding chapter in this book or literature elsewhere (for characterization and thermodynamic modeling of solid micelles Smirnova, 1995, 1996 Berret, 1997 Fujiwara et al.,... 

The adsorption of binary mixtures of anionic surfactants of a homologous series (sodium octyl sulfate and sodium dodecyl sulfate) on alpha aluminum oxide was measured. A thermodynamic model was developed to describe ideal mixed admicelle (adsorbed surfactant bilayer) formation, for concentrations between the critical admicelle concentration and the critical micelle concentration. Specific... 

A significant amount of work has demonstrated the feasibility and the interest of reversed micelles for the separation of proteins and for the enhancement or inhibition of specific reactions. The number of micellar systems presently available and studied in the presence of proteins is still limited. An effort should be made to increase the number of surfactants used as well as the set of proteins assayed and to characterize the molecular mechanism of solubilization and the microstructure of the laden organic phases in various systems, since they determine the efficiency and selectivity of the separation and are essential to understand the phenomena of bio-activity loss or preservation. As the features of extraction depend on many parameters, particular attention should be paid to controlling all of them in each phase. Simplified thermodynamic models begin to be developed for the representation of partition of simple ions and proteins between aqueous and micellar phases. Relevant experiments and more complete data sets on distribution of salts, cosurfactants, should promote further developments in modelling in relation with current investigations on electrolytes, polymers and proteins. This work could be connected with distribution studies achieved in related areas as microemulsions for oil recovery or supercritical extraction (74). In addition, the contribution of physico-chemical experiments should be taken into account to evaluate the size and structure of the micelles. 

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.. 

Quantitative predictions of surfactant phase behavior can be made by constructing a thermodynamic model. The classical expression for the free energy of a microemulsion is a function of the interfacial tension, bending moment, and micelle-micelle interactions [47]. Two quantitative models have been developed to describe supercritical microemulsions based on this concept. Here, the key challenge is to find accurate expressions for the oil-surfactant tail interactions and the tail-tail interactions. To do this, the first model uses a modified Flory-Krigbaum theory [43,44], and the second a lattice fluid self-consistent field (SCF) theory [25]. 

The thermodynamic model of micellization, presented here, describes the association of any amphiphilic molecules, including low molecular weight surfactants or polymeric amphiphiles. The physical origin of the minimum in the free energy, as a function of p, is specified by the molecular architecture and the interactions between amphiphilic molecules involved in the assembly, and will be discussed in the corresponding sections. An extension of the model for the case of a continuous distribution of micelles with respect to aggregation number (polydispersity of the aggregates) involves the value of d Fp/dp. If this quantity is small in the vicinity of p = Po, then the micelle distribution is wide, and vice versa [37]. The approximation of micelle monodispersity is essential for application of the numerical SCF model which is discussed in Sect. 9. 

Moreira L, Firoozaqbadi A (2010) Molecular thermodynamics modelling of specific ion effects on micellization of ionic surfactants. Langmuir 26 15177-15191 Nandi PK, Robinson DR (1972a) The effects of salts on the free energy of the peptide group. J Am Chem Soc 94 1299-1308... 

DRIVING FORCES OF MICELLE FORMATION AND THERMODYNAMIC MODELS... 

The model calculations utilise a recently developed small systems thermodynamic model for polymer surfactant complex formation [9]. In the framework of this model the polymer-surfactant macroscopic system is considered as a three-component (water, polymer and surfactant) macroscopic ensemble in which the surfactant can be present in monomer, polymer surfactant complex and free micelle forms. The polymer surfactant complex molecules and the micelles are considered as small systems that contain a fluctuating number of building blocks (surfactant molecules in the case of micelles and surfactant aggregate subsystems in the case of the complex molecules). The description of the microstructure of the polymer-surfactant small system is based on Shirahama s necklace model. The subsystem of the polymer-surfactant complex molecules is an individual surfactant aggregate wrapped around by the polymer segments in which both the number of surfactant molecules and the number of polymer segments can fluctuate. 

Surf] plot and A refers to the equivalent conductivity of the surfactant counterion at infinite dilution. Models that are more sophisticated are also available for calculating (a i,) from conductivity data at various (T) and ionic strengths these are based on the mass action micellization thermodynamics and the Debye-Hiickel-Onsager conductivity theory [32]. 

Application of other thermodynamic models to the micellization process... 

In addition to the thermodynamic models, Khokhlov et al proposed a model for the hydrophobic interaction of an ionic surface active agent and electrolyte gel where the volume changes discontinuously in a gel due to the micelle formation [45]. For actual descriptions, the readers are referred to the original monograph. 

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