Theoretical Outline - Collective Diffusion and Screening of Hydrodynamic Interactions

1 Theoretical Outline — Collective Diffusion and Screening of Hydrodynamic Interactions 

Transition from Single to Many Chain Behavior 

When the monomer concentration exceeds c [see Eq. (112) and Fig. 38], the different polymer molecules are no longer separated but interpenetrate each other forming a transient network of lifetime xg. At constant temperature this network structure is characterized by a concentration-dependent correlation length (c), which may be considered as the mean mesh size of the pseudo gel. 

Since the transition from dilute to semi-dilute solutions exhibits the features of a second-order phase transition, the characteristic properties of the single- chain statics and dynamics observed in dilute solutions on all intramolecular length scales, are expected to be valid in semi-dilute solutions on length scales r (c), whereas for r E,(c) the collective properties should prevail [90]. 

However, this is true only for good solvent conditions, where (c) is also the correlation length, beyond which both the excluded volume and the hydrodynamic interaction are screened and self-entanglements (intramolecular 

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