Entropy repulsion effects

The behavior of hA in real micellar systems is more complex as seen in Fig. 2.12. Similar data have been obtained for several other amphiphiles148,149). The deviations in hA from the standard value at infinite dilution appear clearly below the CMC, but at these concentrations one has a compensating change in the partial molar entropy. This effect might be due to a repulsive interaction between the hydrophobically hydrated alkyl chains leading to a breakdown of the water structure with a concomitant increase in entropy. 

The first reason lies in the fact that the interaction between solvent molecules (usually water) is stronger than the interaction between the solvent and the solute. This effect alone would lead to a precipitation of the solute. In the case of amphiphiles which form micelles, however, the head groups are strongly hydrated and repulse each other. The hydration forces and steric forces which are made responsible for this repulsion effect prevent crystallization above the Krafft point and also above the cmc. Where the formation of 3D crystals is impeded, the smallest possible droplet is formed, removing the alkyl chains from the solvent. The interactions between solvent molecules are therefore disturbed to a minimal extent, allowing the head groups to be solvated with a minimal entropy loss. It is irrelevant whether the solvent contains clusters or not. Micelle formation only occurs as a result of a solvation of head groups and non-solvation of a solvophobic core. ... 

The second repulsive effect resulting from the presence of the adsorbed layers is the loss in configurational entropy of the chains when significant overlap occurs. This effect, which is always repulsive, is referred to as an entropic, volume-restriction or elastic interaction, Gei. 

In this section we study a system with purely repulsive interactions which demonstrates the importance of entropy effects on the stability of phases when the effect of the corrugation potential due to the structured surface is completely neglected. The phase diagrams are determined by finite size scaling methods, in particular the methods of Sec. IV A. 

In Eq. (15) the second term reflects the gain in entropy when a chain breaks so that the two new ends can explore a volume Entropy is increased because the excluded volume repulsion on scales less than is reduced by breaking the chain this effect is accounted for by the additional exponent 9 = y — )/v where 7 > 1 is a standard critical exponent, the value of 7 being larger in 2 dimensions than in 3 dimensions 72 = 43/32 1.34, 73j 1.17. In MFA 7 = 1, = 0, and Eq. (15) simplifies to Eq. (9), where correlations, brought about by mutual avoidance of chains, i.e., excluded volume, are ignored. 

The effect of the leaving group is illustrated in the comparison of fluoro- and chloro-nitrobenzenes (Table VIII) in their reactions with ethoxide ion (lines 5 and 8) and with piperidine (lines 7 and 9). Rate ratios F Cl are 23 1 (opposing and entropy of activation changes) and 201 1 (E effect), respectively, for the two nucleophiles. For the reasons discussed in Section II, D, 1, a fluorine substituent produces a lower energy of repulsion of the nucleophile and thus facilitates reaction. 

The ring size (degree of oligomerization x) and conformation of M-E heterocycles strongly depends on steric effects of the substituents (repulsive interactions), ring strain effects and on entropy factors. This was shown for instance by Beachley and Racette for several heterocyclic aminoalanes [R2A1NR2]X97 and confirmed by our own results. However, predictions whether four- or six-membered heterocycles will be formed are... 

The FvdM as well as the BMVW model neglects thermal fluctuation effects both are T = 0 K theories. Pokrovsky and Talapov (PT) have studied the C-SI transition including thermal effects. They found that, for T 0 K the domain walls can meander and collide, giving rise to an entropy-mediated repulsive force of the form F where I is the distance between nearest neighbor walls. Because of this inverse square behavior, the inverse wall separation, i.e. the misfit m, in the weakly incommensurate phase should follow a power law of the form... 

This entropic force is important where adsorption of polymers occnrs on colloidal particles. This is due to interaction between polymer chains on the interacting particles As the particles approach each other to the point where the polymer chains of the two particles interact, there is an decrease in entropy due to confinement of the chains, in an analogous manner to the solution species discussed earher, with the same result— repulsion. This is the basis of polymeric stabilization of colloids it is generally undesirable in CD, since adhesion and aggregation are preferred in this case. However, in view of the fact that the presence of such polymers (and other stabilizing adsorbates) may prevent the aggregation needed to build up a CD layer, it is important to be aware of the effect. 

The hard-core repulsion prevents spherocylinders from overlapping. This effect reduces the space available for the cylinders, and gives rise to a loss of their translational entropy ( —S ). Many statistical thermodynamic techniques were used to calculate it, as has been extensively reviewed by Vroege and Lekkerkerker [9]. 

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