Semi-dilute solutions definition

However, let note, that the assumption about independence of the osmotic pressure of semi-diluted solutions on the length of a chain is not physically definitely well-founded per se it is equivalent to position that the system of strongly intertwined chains is thermodynamically equivalent to the system of gaped monomeric links of the same concentration. Therefore, both Flory-Huggins method and Scaling method do not take into account the conformation constituent of free energy of polymeric chains. 

In semi dilute (c>c, [B] = 0.3-0.5 mole.l- ) or dilute (c< c, [B] = 10-2 mole.l- -) solution, Kp is significantly greater for copolymers than for the model compounds whatever the solvent is. For semi-dilute solution in a given solvent, the complex influences of composition, unit distribution and tacticity do not result in definite trends on K, values, as illustrated in table 6 by some representative Kj data related to keto-2-picolyl structures at 25°C. 

Most important, however, was the discovery by Simha et al. [152, 153], de Gennes [4] and des Cloizeaux [154] that the overlap concentration is a suitable parameter for the formulation of universal laws by which semi-dilute solutions can be described. Semi-dilute solutions have already many similarities to polymers in the melt. Their understanding has to be considered as the first essential step for an interpretation of materials properties in terms of molecular parameters. Here now the necessity of the dilute solution properties becomes evident. These molecular solution parameters are not universal, but they allow a definition of the overlap concentration, and with this a universal picture of behavior can be designed. This approach was very successful in the field of linear macromolecules. The following outline will demonstrate the utility of this approach also for branched polymers in the semi-dilute regime. 

Nevertheless, we shall apply this formula to the present case, identifying polymer melt and semi-dilute solution. Let ph then be the mass per unit volume of polymer melt. By definition... 

Number of swollen sequences constituting a polymer chain in a semi-dilute solution for a good solvent the size of a sequence is, by definition, the Kuhnian overlap length... 

Reverse osmosis, by definition, is the reverse of conventional osmosis, which is familiar from biology. If a dilute solution and a concentrated solution are separated by a semi-permeable membrane (which allows water molecules to pass through it, but not other solutes), water will flow from the dilute solution into the concentrated one. Under these conditions, a substantial difference in height between the two water columns may be established (Eigure 7). 

The present chapter aims to describe some typical contributions from recent studies on stiff polymers in dilute solution. We will be mainly interested in (1) applicability of the wormlike chain model to actual polymers, (ii) validity of the hydrodynamic theories [2-4] recently developed for this model, and (iii) the onset of the excluded-volume effect on the dimensions of semi-flexible polymers. Yamakawa [5, 6] has generalized the wormlike chain model to one that he named the helical wormlike chain. In a series of papers he and his collaborators have made a great many efforts to formulate its static and dynamic properties in dilute solution. In fact, the theoretical information obtained is now comparable in both breadth and depth to that of the wotmlike chain (see Ref. [6] for an overview). Unfortunately, however, most of the derived expressions are too complex to be of use for quantitative anal) sis and interpretation of experimental data. Thus, we only have a few to be considered with reference to the practical aspects of the helical wormlike chain, and have to be content with mentioning the definition and some basic features of this novel model. 

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