Solution length scale polymer size

Topological constraints do not influence polymer motion on length scales smaller than the size of an entanglement strand. In entangled polymer solutions, chain sections with end-to-end distance shorter than the tube... 

Fig. 9 Schematic representation of (sections of) multi-arm star polymers in semidilute solution in good solvent. The three different length scales, the radius ofthe star R, the coat ri, hard core are indicated. The open circles denote the correlation length blob size)...

Nevertheless, from a physical point of view, it is better to use other parameters. First, instead of choosing z to define the interaction, we can use the osmotic parameter g which is related to it. In this connection, let us recall that the function g = g(z) was studied in detail at the beginning of this chapter, Section 1.1. Secondly, instead of choosing the size S1/2 of the non-interacting polymer as the length scale, we can use the size x = (R2/d)112 of the isolated polymer in solution [the variable x is defined by (13.1.1)]. Thus, the osmotic pressure can be expressed in the form... 

Figure 5.6. Schematic plots of the polymer segment concentration as a function of the distance in bulk polymer solutions. In (a) the concentration of chains is low enough that on average different polymer chains do not overlap. The segment concentration has large spatial fluctuations this is a dilute solution. In (b) chains start to overlap, but there are still strong composition fluctuations imposed by the connectivity of the chains characterised by a correlation length This is the so-called semi-dilute concentration regime. In (c) the solution is concentrated and there are no concentration fluctuations on length scales larger than the monomer size.

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