Chain anchoring brushes

V( ) X(>T) Zap volume fraction gradient along z axis 2.1 composition of N-mer brush chains in brush layer 4.1 Flory-Huggins interaction parameter 2.1,2.2.2 interaction parameter between species of anchor block A and matrix P-mer 4.1 ... 

In most of the experimental studies, the copolymer chains are not so long relative to the homopolymers. Thus, mixing of the copolymer and homopolymer chains should be taken into account due to the penetration of homopolymers into the layer of chains anchored at the interface, whereas the copolymer chains can be either stretched (wet brush regime) or not (wet mushroom). Neglecting the composition gradients in the bmsh (Hory approximation), g, is given by [40, 75, 287] ... 

Poly(methyl methacrylate) with a variable degree of polymerization anchored to silica surfaces was synthesized following the room temperature ATRP polymerization scheme described earlier [45,46]. In the main part of Fig. 25 we plot the variation of the PMMA brush thickness after drying (measured by SE) as a function of the position on the substrate. Thickness increases continuously from one end of the substrate to the other. Since the density of polymerization initiators is (estimated to be 0.5 chains/nm ) uniform on the substrate, we ascribe the observed change in thickness to different lengths of polymer chains grown at various positions. 

Fig. 12 Density profiles of monomers open symbols) and counterions (filled symbols) as a function of the distance from the anchoring sirnface. Shown are profiles for fully charged brushes of 36 chains of N = 30 monomers at grafting densities (from bottom to top) = 0.042 (circles), 0.063 (squares), 0.094 (diamonds), and 0.12 (triangles). As can be clearly seen, the counterions stay inside the brush for aU considered grafting densities and the local electroneutrality condition is satisfied very well...

When calculating the theoretical force curves shown in Fig. 9 we used the XPS results to obtain the value of s and twice the length of the polymer brush was set to 23 nm. The anchoring points for the grafted PEO-chains were set at a distance 1.5 nm away from the mica surface. This value was chosen to be equal to the undisturbed layer thickness of the adsorbed chitosan polymer without grafted side-chains. When the prefactor is set equal to 1, the lower curve in Fig. 9 is obtained, and when a prefactor equal to two is used the upper curve is obtained. 

There are several ways of forming surface layers of polymer chains, and various solid/polymer systems have been used. The silica/PDMS system is quite convenient since both end-grafted layers with high grafting densities (i.e., brushes) and irreversibly adsorbed layers (i.e., pseudo-brushes) can be formed with controlled molecular characteristics (polymerization index of the tethered chains and surface density), allowing a detailed investigation of the structure and properties of these two different classes of surface anchored polymer layers. 

In order to understand the role played by surface-anchored chains in adhesion and friction, it is essential to understand under which conditions a surface layer, when in contact with a melt, is penetrated by free chains. The question has been addressed theoretically mostly for polymer brushes, and more recently for Guiselin s pseudo-brushes. We want to review here some of these analysis, and compare the predictions of the models with the available experimental data. 

Finally, the case of a polar A - B type supramolecular polymer chain with two complementary but different chain-ends is worth considering. If such a system is brought into contact of a surface grafted with an anchoring group bearing only A functions, then a theoretical model shows that the supramolecular brushes formed should exert repulsive forces between approaching surfaces [170,171]. 

Figure 3.96. Brush height as a function of grafting density for terminally anchored PEO chains. The chain length (A/) is indicated. (Redrawn after Currie et al., loc. cit.)...

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