Characteristic Length Scales in Polymer Solutions

In Sect. 2.2 we considered the concept of ghost or ideal chains. The segments of such chains do not feel each other. Here we consider excluded volume interactions between the segments Throughout Sect. 4.3 we consider two limiting cases of interacting polymer chains the excluded volume limit (good solvent) and the 

A special situation occurs when the attraction between the segments exactly compensates the (hard-core) excluded volume efifeet In dilute solutions the chains then behave quasi-ideal. This situation is commonly referred to as the -solvent condition. 

For long chains the following scaling relation holds [37] 

For shorter chains an approximate expression for any solvency may be derived using the Flory excluded-volume parameter v, which is unity when the segments experience hard-core repulsion and vanishes in case of a -solvent. Based on Flory s result [37] for the expansion coefficient, the coil size can be written as [39]  

Show that for M 1 this expression reduces to the scaling limits of (4.8) and (4.9). 

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