Brush height grafting density

Fig. 6 Average brush height (filled symbols) and height of the counter-ion layer (open symbols) of completely charged brushes versus grafting density. lB=0.7 b (diamonds) and ZB=0.1 b (triangles). The lines give power laws (ze) pa ...

The chain dimension in the height direction was evaluated as the thickness of the brush layer, I, relative to the chain contour length, io, by atomic force microscopy (AFM). Figure 4.10 shows the solvent dependence of the conformation of the PMMA brush. Whereas the brush chain changes its conformation in response to the solvent quality at the low graft density, the high-density PMMA brush does not show... 

The layer thickness or brush height h in a good solvent scales linear with the degree of polymerization N, as well as with the grafting density [Pg.400]

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. 

For a theta solvent (V2 = 0) the relevant interaction is described by the third virial coefficient using a simple Alexander approach similar to the one leading to Eq. 13, the brush height is predicted to vary with the grafting density as h pa in agreement with computer simulations [65]. 

Fig. 18 Grafting density (a) dependence of average PEO brush height ((h)brush) during the PEO chain stretching. The line represents a least square fitting of (h)brUsh

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.)...

It can be seen that on addition of salt the brush height decreases by a weak power law, ISait oc cs 1/3. This behavior is often called salted brush . Here the surface-linked monolayer behaves like a neutral brush with an enlarged (electrostatic) excluded volume. Note that the grafting density has a strong influence on the amount of free mobile ions per chain inside the brush. Therefore, the height of such polyelectrolyte brushes is expected to become less sensitive to the external salt concentration if chains at high graft density are considered. 

Fig. 9 Brush height versus grafting density at ZB=0-1 b,f=1. Simulation results and theoretical predictions...

Figure 20 shows the dependence of the brush thickness L on the pH (A) and salt concentration (B) of the liquid phase. As expected from mean-field theory, the height of the strong polyelectrolyte brush at various grafting densities and molecular masses of the surface-attached macromolecules is independent of pH at a given constant electrolyte concentration of the medium so that the PSS chains are fully dissociated under all circumstances [71]. 

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