Polymer brushes theory

Polymer brush theory was applied to the compatibilization of homopolymers A and B by an AB diblock by Leibler (1988). The reduction in interfacial tension due to the segregation of copolymers to the interface was calculated. Considering a film of block copolymers at the homopolymer-homopolymer interface, the free energy was found to be... 

Using a self-consistent field theory, Misra et al. [10] examined the effect of the brush charge, electrolyte concentration, and surface charge density on the brush thickness. They extended the self-consistent field polymer brush theory suggested by Milner et al. [11] to the case of a polyelectrolyte brush. The theory involves a parabolic monomer concentration profile rather than the step-function suggested by Alexander [12] and de Gennes [13,14], The repulsion force... 

Szleifer and coworkers. Recently, Wu et al. applied this theory to successfully model the behavior in charged polymer brush systems [89]. More importantly, this theory enables the estimation of system parameters that are not easy (or even possible) to measure experimentally, such as the local dissociation inside the brush and the average charge of the polymer as a function of the distance from the surface. We will not provide any detailed information about the theory here. The interested reader is referred to the original publication and the references cited therein [89]. 

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 )... 

From the theoretical viewpoint, much of the phase behaviour of blends containing block copolymers has been anticipated or accounted for. The primary approaches consist of theories based on polymer brushes (in this case block copolymer chains segregated to an interface), Flory-Huggins or random phase approximation mean field theories and the self-consistent mean field theory. The latter has an unsurpassed predictive capability but requires intensive numerical computations, and does not lead itself to intuitive relationships such as scaling laws. 

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... 

The scaling theory for spherical polymer brushes due to Daoud and Cotton (1982) (Section 3.4.1) has been applied to analyse the coronal density profile of block copolymer micelles by Forster et al. (1996). If the density profile is of the hyperbolic form r as found by FOrster et al. (1996) for the coronal layer of block copolymer micelles, the brush height scales as... 

Many theories were developed to describe the distribution of segments between two polymer brushes. On the basis of a lattice... 

One way is to use scaling theory that predicts that the pressure P(D) between two flat surfaces coated with polymer brushes in a good solvent as given by [22] ... 

Another approach to study the penetration depth is to use computer simulations of simple shear flow. Computer simulations can check the validity of certain assumptions implicit in the theories, such as the assumption that the shear flow does not distort the density profile. However to do this solvent molecules must be included explicitly in the simulation. Almost all previous simulations of polymer brushes have modeled the solvent as a continuum to save CPU time. 

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