Configurational entropy, stability

We present an improved model for the flocculation of a dispersion of hard spheres in the presence of non-adsorbing polymer. The pair potential is derived from a recent theory for interacting polymer near a flat surface, and is a function of the depletion thickness. This thickness is of the order of the radius of gyration in dilute polymer solutions but decreases when the coils in solution begin to overlap. Flocculation occurs when the osmotic attraction energy, which is a consequence of the depletion, outweighs the loss in configurational entropy of the dispersed particles. Our analysis differs from that of De Hek and Vrij with respect to the dependence of the depletion thickness on the polymer concentration (i.e., we do not consider the polymer coils to be hard spheres) and to the stability criterion used (binodal, not spinodal phase separation conditions). 

Considerations of enthalpy, as illustrated by the rule of reversed stability, and of configurational entropy provided insight into the factors governing the stabilities of the AB5 hydrides. Theoretical understanding to predict dissociation pressures should be developed on heat pump application, for example. Although... 

Hatley and Blair [3.69] presented mean Tg data for anhydrous carbohydrates (Table 3.1), which vary in the literature owing to measurement and interpretation differences. Small amounts of water may depress the data substantially. The physical stability of amorphous formulations below Tg is generally accepted, and a collapse can be avoided. This does not always apply to the chemical stability. If the temperature is reduced below T, the configurational entropy diminishes until it reaches zero. This T0 (also shown in Table 3.1) is called the zero mobility temperature at which the molecular motion stops. The authors define three areas of chemical reactions above Tg, chemical reactions are generally possible at T, reactions such as aggregation, which require substantial molecular motion, stop and between Tg and T0, reactions involv-... 

The second contribution to the steric interaction arises from the loss of configurational entropy of the chains on significant overlap. This effect is referred to as entropic, volume restriction, or elastic interaction, Gei. The latter increases very sharply with a decrease in h when the latter is less than 8. A schematic representation of the variation of Gmix, Gei, G, and Gj =G X + Gei + Ga) is given in Fig. 10. The total energy-distance curve shows only one minimum, at h 25, the depth of which depends on 5, R, and A. At a given R and A, G decreases with an increase in 5. With small particles and thick adsorbed layers (5 > 5 nm), G, becomes very small (approaches thermodynamic stability. This shows the importance of steric stabilization in controlling the flocculation of emulsions and suspensions. 

Also, Schellman s work is pertinent (1809). From studies on heats of dilution of urea in water he concludes that the N—H 0=C bond has an enthalpy of 1.5 kcal/mole in aqueous solution, and he carries this value over to proteins and polypeptides. Among these complicated materials he is forced to approximate—but he deduces relations which show the stability of helices and sheets in terms of H bond enthalpy and configurational entropy. From this he draws the important conclusion that H bonds, taken by themselves, give a marginal stability to ordered structures which may be enhanced or disrupted by the interactions of the side chains. Schellman ends his papers with a discussion of experimental tests needed to eliminate some of the assumptions in his theoretical analysis. 

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