Solution micelles second virial coefficient

The diffuse part of the double layer is of little concern to us at this point. Chapters 11 and 12 explore in detail various models and phenomena associated with the ion atmosphere. At present it is sufficient for us to note that the extension in space of the ion atmosphere may be considerable, decreasing as the electrolyte content of the solution increases. As micelles approach one another in solution, the diffuse parts of their respective double layers make the first contact. This is the origin of part of the nonideality of the micellar dispersion and is reflected in the second virial coefficient B as measured by osmometry or light scattering. It is through this connection that z can be evaluated from experimental B values. 

P = 2RTM l is called the second virial coefficient it yields the same qualitative information about interaction as A[nq]2 in Eq. (4.6). Membrane osmometry seldom requires an accuracy to more than P cf. Doi and Edwards (1986) define a dilute solution as one in which P = 0—the ideal condition for accurately measuring Mn. Te is that temperature where P = 0 (Alberty and Silby, 1992). The fact that P provides information about solute-solute interactions, micellization and demicellization studies are made possible by the use of Eqs. (4.29) and (4.30). 

Therefore, the present approach was initiated, together with the second virial coefficient, Bg, analyses. It was also shown for the first time (15) that in the case of ionic micelles, the Donnan term of Bg is proportional to the added salt concentration, mg1, as expected from theory. This relationship was valid only in those systems where the aggregation number, N, did not change appreciably with increased mg. It is thus obvious that ionic micelles must be treated as macro-ions (macromolecules). In the same context, we showed that B2 goes to zero as the temperature of non-ionic micellar solutions approaches this eloudpoint ("poor solvent") (15). 

By experimentally measuring the turbidity as a function of concentration, one can obtain the molecular weight of solute and the second virial coefficient, B2, which characterizes interactions between solute molecules (or particles). In systems containing charged particles, such as e.g. micelles of ionic surfactants, the second virial coefficient describes the effective charge of particles. The molecular weight and the second virial coefficient can be determined by plotting the quantity Hc/x as a function of concentration, c. 

Among other approaches, a theory for intermolecular interactions in dilute block copolymer solutions was presented by Kimura and Kurata (1981). They considered the association of diblock and triblock copolymers in solvents of varying quality. The second and third virial coefficients were determined using a mean field potential based on the segmental distribution function for a polymer chain in solution. A model for micellization of block copolymers in solution, based on the thermodynamics of associating multicomponent mixtures, was presented by Gao and Eisenberg (1993). The polydispersity of the block copolymer and its influence on micellization was a particular focus of this work. For block copolymers below the cmc, a collapsed spherical conformation was assumed. Interactions of the collapsed spheres were then described by the Hamaker equation, with an interaction energy proportional to the radius of the spheres. 

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