Entropic interactions, clusters

A quantum mechanical approach to ion-water interactions has the up side that it is the kind of development one might think of as inevitable. On the other hand, there is a fundamental difficulty that attends all quantum mechanical approaches to reactions in chemistry. It is that they concern potential energy and do not account for the entropic aspects of the situation. The importance of the latter (cf. the basic thermodynamic equation AG = AH - TAS) depends on temperature, so that at T = 0, the change in entropy in a reaction, AS, has no effect. However, in calculations of solvation at ordinary temperatures, the inaease in order brought about by the effect of the ion on the water molecules is an essential feature of the situation. Thus, a quantum mechanical approach to solvation can provide information on the energy of individual ion-water interactions (clusters in the gas phase have also been calculated), but one has to ask whether it is relevant to solution chemistry. 

One explanation that can be offered to explain the two Tc values obtained for PMA at low values of a is that they represent the independent rotation of small clusters of the polymer chain. The larger value of (approximately 50 ns) can be associated with a rotating spherical cluster of radius 3.8 nm and of polymer molecular weight equal to 19000. Rotating units of similar size have been observed when the probes 9-methylanthracene and 9,10-DMA are solubilized in the PMA hypercoil structure (15,16) and when the more polar fluorescent probes Rhodamine B ( ) and 1,8-anilinonaphthalene sulfonic acid (1,8-ANS) (28) are bound to PMA for a value of a equal to 0. The smaller rotating unit present in PMA and PAA whose value of Tj, is approximately equal to 5 ns (which corresponds to particles whose radii are approximately equal to 2 nm) may arise from the rotation of a small section of the chain which is just sufficient to surround the 9,10-DMA probe and protect it from unfavourable entropic interactions with water. This shorter T, was... 

Hydrophobic bonds, or, more accurately, interactions, form because nonpolar side chains of amino acids and other nonpolar solutes prefer to cluster in a nonpolar environment rather than to intercalate in a polar solvent such as water. The forming of hydrophobic bonds minimizes the interaction of nonpolar residues with water and is therefore highly favorable. Such clustering is entropically driven. The side chains of the amino acids in the interior or core of the protein structure are almost exclusively hydrophobic. Polar amino acids are almost never found in the interior of a protein, but the protein surface may consist of both polar and nonpolar residues. 

Incorporation of long-chain hydrocarbon hydrophobes into a cellulose ether backbone leads to an interesting new class of polymeric surfactants. Their enhanced solution viscosity can be explained in terms of intermolecular associations via the hydrophobe moieties. Entropic forces cause the polymer hydrophobes to cluster to minimize the disruption of water structure. The same thermodynamic principles that are used to explain the micellization of surfactants can be applied to explain the solution behavior of HMHEC. HMHECs interact with surfactants that modify their solution viscosities. The chemical nature and the concentration of the surfactant dictate its effect on HMHEC solution behavior. The unique rheological properties of HMHEC can be exploited to meet industrial demands for specific formulations and applications. 

The first term is the elastic or entropic part of the free energy. M is the size of the ideal fractal, M the total mass. The second term is the mean field approximation of the excluded volume interaction (compare equation 33) due to Flory and de Gennes, v is the excluded volume parameter, i.e. the binary cluster integral. Minimizing the free energy with respect to R one obtains the swollen fractal dimension ... 

The third type of state, deep states in the energy gap are distinct from the band-like localized structures in that their probability ceases to decay rapidly with energy as one draws away from the mobility edge. They represent a noise background of states present across the mobility gap at a roughly fixed concentration determined essentially entropically. They are distinct from the fourth type of state as they include a distinct, if very heavily distorted, bond-like character. Such states could include various reconstructions of the interior of a vacancy or multisite vacancy cluster, which would allow dangling bonds to interact at least weakly to form some sort of bond. This situation is shown schematically in Figure 8.4. 

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