De Gennes’ scaling theory

This mean-field prediction can be substantiated by constructing a simple de Gennes scaling theory. A similar scaling form for the osmotic pressure is assumed in 0-solutions as was used in good solvent [Eq. (5.43)] ... 

M Doi, SF Edwards. Theory of Liquids. New York Oxford Univ Press, 1986. PG de Gennes. Scaling Concepts in Polymer Physics. 2nd ed. Ithaca NY Cornell Univ Press, 1985. 

As discussed by de Gennes," scaling law focuses attention on the exponents and refrains from the determination of any prefactory constants, which are usually much more difficult to determine. Some predictions of scaling law theory for polymers of high molecular weight in both good solvents and 9 solvents in the semidilnte regime are summarized in Table 7.3. 

The dependence of h on M and a is rather weaker than that predicted by Alexander-de Gennes scaling laws and by the self-consistent field theory of Milner, Witten and Cates (h A self-consistent field theory of... 

P. G. de Gennes, Scaling Concepts in Polymer Physics, Cornell University Press, Ithaca, New York, 1988 M. Doi and S. F. Edwards, The Theory of Polymer Dynamics, Oxford Science, New York, 1989 J. des Cloiseaux and G. Jannink, Polymers in Solution, Clarendon, Oxford, 1990. 

The breakdown of the semi-dilute brush theory was also revealed in the force-distance curve of the high-density PMMA brush. Using the scaling approach [138], de Gennes derived the equation concerning the interaction force between two parallel plates with a semi-dilute polymer brush layer, predicting that the force-distance profiles should be scaled by plotting (F/i )... 

A simple scaling model of block copolymer micelles was derived by de Gennes (1978). He obtained scaling relations assuming uniformly stretched chains for the core radius, RB, of micelles with association number p.This model can be viewed as a development of the Alexander de Gennes theory (Alexander 1977 de Gennes 1976,1980) for polymer brushes at a planar interface, where the density profile normal to the interface is a step function. In the limit of short coronal (A) chains (crew-cut micelles) de Gennes (1978) predicted... 

It is worth emphasizing that all scaling theories (due to de Gennes, Daoud and Cotton, Zhulina and Birshtein, and Halperin) for block copolymer micelles with a small core and large corona predict that the association number and core radius are independent of the coronal chain length. 

This review is intended to complement those of Cohen Stuart et al. (1986) and de Gennes (1987). The former details experimental techniques available for probing polymer-particle interactions and the lattice, i.e., mean field, theories that predict, via numerical solutions, segment-density profiles and interaction potentials. The latter constructs a simple and elegant picture of the same phenomena through scaling theories developed for semidilute solutions. 

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