Scaling theory of de Gennes

For PEO-PPO-PEO triblock copolymers it was found that the poly(ethylene oxide) chain is in the brush configuration ifDdistance between the chains, Rj is the radius of gyration). When h<2hi a brush-to-brush interaction appears, which can be described by the scaling theory of de Gennes [39,40[, according to which the steric disjoining pressure is given by... 

In summary, it has been established, using microscopic foam films, that films from aqueous solutions of polymeric surfactants (A-B-A block copolymers and AB graft polymers based on inulin) are stabilized by both electrostatic, DLVO and steric, non-DLVO surface forces. Application of the scaling theory of de Gennes [39, 40] to describe the brush-to-brush and loop-to-loop interactions is interesting. 

As indicated above, the term P allows for the diffusion of the stem to the site and is usually described by the WLF equation, h is Planck s constant, J is a dimensionless scaling constant, is a constant (dimensions J mol ) and is the temperature at which diffusion is stopped. If the polymer is of sufficiently high molar mass for entanglement to take place, then instead of the WLF theory the reptation theory of de Gennes should be used ... 

During the decade that has just ended the application of the method of lattice theory (by Hory and Huggins), the scaling theory (by de Gennes) of polymer solutions, and the theory of gelation reaction (by Hory and Stockmayer) has resulted in the development of what has become known as the theory of associating polymer solutions. This has brought the aforementioned unsolved problem markedly nearer to the resolution. 

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 )... 

De Gennes PG (1976) Scaling theory of polymer adsorption. J Phys 37 1445-1452 De Gennes PG (1979) Scaling concepts in polymer physics. Cornell University Press, Ithaca De Gennes PG (1981) Polymer solutions near an interface. 1. Adsorptirai and depletion layers. Macromoleeules 14 1637-1644... 

De Gennes PG (1983) Scaling theory of polymer adsorption proximal expontmt. J Phys Lett 44 L241-L246... 

Using the free-volume theory, the following polymer diffiisivity expression attributed to Achillas and Kiparissides (1992) was used, which in turn was based on the scaling theory predications of De Gennes (1979)... 

The subject of Chapter 4 (originally the third lecture) is the problem of the reduction of turbulent losses by polymer chains in a solvent. The topic appears to be especially intricate in view of the coupling between the hydrodynamic aspects of turbulent flow and the viscoelastic behavior of chains in strongly perturbed conformations. The lecture followed closely a paper Towards a scaling theory of drag reduction published in 1986 by Professor de Gennes in Physica which is here reprinted by permission of the publisher. Because this lecture is the most tentative (and difficult) part in the series we have put it in the last chapter. 

Comments on Flory s Theory by de Gennes According to de Gennes, Hory did not realize the existence of the critical point c in the polymer solution. His mean-field theory of or in the dilute polymer solution leads, indeed, to a correct expression of scaling law,... 

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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