Osmotic brush regime

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 threshold salt concentration above which the brush contraction sets in is given by the salt concentration which equals the counterion concentration inside the brush. This means that the higher the grafting density (and consequently the higher the internal counterion concentration in the osmotic brush regime), the larger the salt concentration necessary to see any salt effects at all. 

From the measured core radii the grafting distance b can be calculated. Its variation as a function of added salt concentration is shown in Fig. 6 a. In the osmotic brush regime at low added salt concentrations the grafting distances are practically constant. At concentrations above c s 0.05 mol/1 ( salted brush ) the grafting distances decrease with increasing salt due to screening of the repulsive interactions between the corona chains [49]. 

Fig. 13. A universal curve of force profiles in the osmotic brush regime, incorporating data for three different molecular weights. One force curve is shown for each salt concentration. The separations are normalised by twice the equilibrium brush height at the corresponding salt concentration, and the measured force F/R is normalised by the prefactor (InkTcaN), which is derived from the scaling theory. The solid line is a fit based on equations from this theory (see Ref. [158]). Redrawn with permission from Ref [158]. 2002, American Chemical Society.

Lateral Inhomogeneity and Non-Linear Osmotic Brush Regime. 92... 

We can conclude that that the charged osmotic brush regime, in which counterions escape into bulk solvent, can be observed when the experiments are performed in solutions with pH close to p A at very low ionic strength. Because our study provided the very first indirect evidence of behavior of PE micelles that, at that time, was only hypothetical and highly doubted by recognized theoreticians, we were looking for independent support and performed an MC study (see Sect. 4.2). 

All polyelectrolyte brushes, both weakly and strongly charged, are responsive to the ionic strength in (aqueous) solution (Balastre et al., 2002 Borisov et al., 1994 Israels, Leermakers, Fleer, 1994). At a low salt concentration (the osmotic brush regime),... 

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