Polymer-micelle complexes Thermodynamics

Abstract A molecular interaction model of nonionic polymer-surfactant complex formation was developed by modifying the free-energy expression of micelles for interaction with polymer segments. Using the small systems thermodynamics the composition of the surfactant aggregates with respect to the aggregation number, the number of polymer segments involved in the... 

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. 

Interactions between soluble polymer and either colloidal particles, surfactant micelles, or proteins control the behavior and viability of a large number of chemical and biochemical products and processes. Considerable scientific interest also centers on these interactions because of their profound and, sometimes, unexpected effects on the thermodynamics and dynamics of the dispersions or solutions, known collectively as complex fluids. Syntheses of novel block copolymers, improved scattering and optical techniques for characterization, and predictions emerging from sophisticated statistical mechanical approaches provide additional stimulus. Thus, the area is vigorous academically and industrially as evidenced by the broad and international participation in this volume. 

Finally, topological and chemical complexity can be combined within the individual maaomolecule diblock star copolymer or comblike copolymers are the examples of polymer architectures capable of forming thermodynamically stable molecular solutions in the form of unimolecular micelles. 

The thermodynamic framework to describe electrostatically driven micellization naturally builds upon previous work on the micellization of amphiphilic polymers and theories of macro-ion complex formation [1-5, 7, 9, 10,12, 13, 27, 28]. A full treatise of the state of the art is beyond the scope of this chapter we here restrict ourselves to a simple description of the free energy of micellization per chain as the sum of several terms which are positive when opposing and negative when driving micellization (Eq. 1). 

When So = 2, this model reduces to the variable multiplicity model in which junctions of arbitrary multiplicity can coexist at the probability determined by the thermodynamic balance. In the case of micro-crystalline junctions, for instance, it is natural to assume that a minimum number Sq greater than 2 of the crystalline chains is required for a junction formation. This is because, the surface energy terms will prevent small-k units from being stable, leading to the existence of the critical multiplicity for the nucleation of the crystallites. Similarly, a minimum aggregation number is required for the stability of micelles formed by hydrophobes on water-soluble polymers. As we will see later, surfactants added to the solution cause complex interaction with hydrophobically modified polymers due to the existence of this minimum multiplicity. 

For present purposes, solubilization is defined as a spontaneous process leading to a thermodynamically stable, isotropic solution of a substance (the additive) normally insoluble or only slightly soluble in a given solvent produced by the addition of one or more amphiphilic compounds, including polymers, at or above their critical micelle concentration. Using such a definition, we can cover a broad area that includes both dilute and concentrated surfactant solutions, aqueous and nonaqueous solvents, all classes of surfactants and additives, and the effects of complex interactions such as mixed micelle formation. It does not, however, limit the phenomenon to any single mechanism of action. 

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