General theoretical considerations

Let us come back to the definition (10.8.1), (10.8.6) of this coefficient. It is clear that a negative value for A2 reflects the existence of attractive forces between the chains in solution. 

When the temperature of the solution is again lowered, we can observe that the solution which was limpid and transparent becomes turbid. Then, if the temperature remains constant, a meniscus appears after some time and separates two phases in the sample. We have demixtion, and this is the second characteristic effect. Precise measurements of the demixtion temperature have been made, in particular by the Japanese school. 

What we have said concerns the lowest demixtion temperature. Let us note that if we heat a good polymer solution, a phase separation may also occur, but this second demixtion domain has not been studied very much.  

The third observation concerns the swelling of chains in very dilute solutions, when T becomes smaller than the temperature for which A2 = 0 (see the beginning of this section). Then the second virial coefficient becomes negative, and this phenomenon is an effect of the attractive forces existing between chains. These attractive forces produce another effect. In fact, Per-zynski, Adam, and Delsanti3 observed that the hydrodynamic swelling XH which is nearly equal to unity when A2 = 0, becomes smaller than 1 when the temperature of the solution decreases (see Fig. 14.2). In other words, in this case, the chain is smaller than the equivalent Brownian chain. 

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Muller, V.M., Yushchenko, V.S. and Derjaguin, B.V., General theoretical consideration of... 

Before leaving general theoretical considerations we must briefly examine the consequences of the simple radiation theory of unimolecular reactions. The only unimolecular reactions to which, on purely a priori grounds, it would be necessary to apply this theory would be those in which the value of the velocity constant showed no diminution whatever as the concentration was indefinitely decreased. 

Much equipment for the separation of liquids and finely divided solids was invented independently in a number of industries and is of diverse character. These developments have occurred without benefit of any but the most general theoretical considerations. Even at present, the selection of equipment for specific solid-liquid separation applications is largely a process of scale-up based on direct experimentation with the process material. 

General Theoretical Considerations in Cation Radical Cycloadditions... 

Carrier-Facilitated Coupled Transport Through Liquid Membranes General Theoretical Considerations and Influencing Parameters... 

A. General Theoretical Considerations Common to All Ab Initio Methods... 

Solubility of the precipitate in excess of antiserum has been reported for a few systems, such as diphtheria toxin and horse antitoxin, but not for antigen-antibody systems in general. Theoretical considerations indicate that solubility in antibody excess should occur for antigens wi small valence (such as the dihaptenic substances of Table IV) but not for antigens with large valence, which would only witii difificulty be saturated with antibody to form a soluble complex. 

General theoretical considerations are given with emphasis on the possibility of making deductions about preferential solvation phenomena from the variation of relaxation rate (extrapolated to infinite dilution of the electrolyte to eliminate ion-ion contributions) with... 

II. GENERAL THEORETICAL CONSIDERATIONS A. The Origin of Self-Assembly... 

Muller, V. M., Yushchenko, V. S. and Derjaguin, B. V., General theoretical consideration of the influence of surface forces on contact deformations and the reciprocal adhesion of elastic spherical particles, J. Colloid Interface ScL, 92, 92-101 (1983). 

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