Polymer brush height

In Fig. 3 we show the density profiles (normalized to unity) for four different values of obtained with the full mean-field theory [52]. hi (a) the distance from the grafting surface is rescaled by the scahng prediction for the brush height, ho and in (b) it is rescaled by the imperturbed polymer radius Ro. 

Let us now turn to the thermodynamic behavior of a polymer brush. Using the Alexander scaHng model, we can calculate the free energy per chain by putting the result for the optimal brush height, Eq. 13, into the free-energy expression, Eq. 12, and obtain... 

In the nonlinear osmotic brush regime we combine the high-stretching (nonlinear) version of the chain elasticity in Eq. 22 with the nonhnear en-tropic effects of the counterions due to the finite volume of the polymer chains, i.e. we choose a finite effective diameter creff in Eq. 21. The final result for the equihbrium brush height is... 

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... 

The effect of intermolecular interactions is characterized by the Floiy-Huggins interaction parameter. For the polymer brush with 400 bonds, three values of the interaction parameter were selected in the calculations and the segment density profiles are plotted in Fig. 9. x 0 corresponds to a good solvent and x 0.5 to a poor one. With increasing value of x, the height of the polymer bmsb decreases. For the poor solvent ( =0.5), the chant segments tend to be more uniformly distributed (curve 3). 

Figure 2 The height of a polymer brush as a function of temperature, as revealed by neutron reflectometry. The brush is composed of end-grafted deuterated polystyrene, and the environment ispoly(vinyl methyl ether). As the temperature is increased the interaction between polystyrene and poly( vinyl methyl ether) becomes increasingly unfavourable and the brush height decreases reversibly...

Here we outline a mean field Flory-type model introduced by de Gennes [230] and developed by Leibler [231] and Aubouy and Raphael [232]. This approach is less detailed than SCMF models but it captures the main features of the physics of segregated copolymers. Even though it makes a number of assumptions, which are a simplification in comparison with the SCMF models, its predictions of the main features (such as, e.g., variation of mean brush height L vs size and surface density o of the diblocks) agree [226] well with those of more detailed SCMF calculations [236-238]. Because of clearness and simplicity it has been used as a basic framework for many experimental papers on brush conformation [240-245] and segregation properties of end-adsorbing polymers [246-255]. 

Diblock copolymers admixed to a homopolymer matrix segregate to its interface in a specific way. As well as other end-functioned molecules, diblock copolymers, attached by an anchoring block (or by a copolymer joint) to the interface, offer a convenient means for the realization of so-called polymer brushes. The structure of a polymer brush (characterized by its height and average composi-... 

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