Micelle excess free energy

This conclusion implies that the excess entropy of mixing is non-zero and that the mixed micelles presumably acquire more internal order than they would by random mixing. An examination of the magnitude of the deviations from the regular solution approximation shows that there must be a large TS contribution to the excess free energy of mixing. 

The mixed cmc behavior of these (and many other) mixed surfactant systems can be adequately described by a nonideal mixed micelle model based on the psuedo-phase separation approach and a regular solution approximation with a single net interaction parameter B. However, the heats of micellar mixing measured by calorimetry show that the assumptions of the regular solution approximation do not hold for the systems investigated in this paper. This suggests that in these cases the net interaction parameter in the nonideal mixed micelle model should be interpreted as an excess free energy parameter. 

The regular solution theory predicts a symmetrical excess free energy of mixing with respect to the composition of micelles, which contradicts with experimental data. 

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. 

As discussed below, the first two terms in (20) always dominate over the last term, i.e., the area per chain, s, is determined by the balance between the repulsive interactions in the corona and the excess free energy of the interface. The conformational entropy of the core-forming blocks, however, controls the morphology of the aggregates if the size of the core exceeds that of the corona (so-called crew-cut micelles, vesicles). 

For strongly asymmetric copolymers, Na > Nb, the structure of a micelle is controlled by the balance of the coronal free energy, corona, and the excess free energy of the core-corona interface, Finterfaoe-... 

The excess free energy change of micellization,, calculated by the equation (15)... 

The condensed core of a micelle can be assimilated to a polymer globule and is characterized by fairly uniform polymer density (p(x) and by excess free energy per unit area of the core-solvent interface kjiTy(x). Remarkably, the core-forming blocks are extended in the direction perpendicular to the core surface this extension enables minimization of unfavorable core-solvent interface per block copolymer chain. 

The equilibrium structure of the micelle is now determined by a balance between the osmotic pressure of counterions in the corona and excess interfacial free energy of the core-corona boundary. Here, the micellar corona is equivalent to a quasi-planar PE brush in the annealing osmotic regime [31],... 

In the presence of excess added electrolyte, with mole fraction x, the free energy of micellization is given by the expression,... 

The gap between two colliding particles (bubbles, droplets, solid particles, surfactant micelles) in a colloidal dispersion can be treated as a film of uneven thickness. Then, it is possible to utilize the theory of thin films to calculate the energy of interaction between two colloidal particles. Deijaguin [276] has derived an approximate formula which expresses the energy of interaction between two spherical particles of radii and i 2 through integral of the excess surface free energy per unit area, f h), of a plane-parallel film of thickness h [see Eq. (161)] ... 

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