Charged osmotic brush

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). 

Comparison of (20) and (21) shows that at large separations, the force T decays as jd, irrespective of the charge density created on the particle surface by the PE brush. In the case of a sparse PE brush with fairly uniform distribution of counterions within the layer of thickness = A, the crossover to logarithmic force decay occurs smoothly at d = A. By contrast, in the case of the osmotic brush with strongly inhomogenous distribution of counterions (most of them trapped inside the brush), the repulsive force T sharply increases at d = H(°o), i.e., when the coronas of colloidal PE brushes approach close contact. 

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),... 

The presence of the brush suppresses the adsorption of these model-proteins. At cT1 = 12 nm2 adsorption of HSA is more strongly reduced than for the smaller LSZ and PLG. Furthermore, at higher grafting densities, LSZ adsorption is relatively poorly suppressed. Apparently, the positively charged LSZ molecules are pulled into the brush by the negative electric field. Thus, there seems to be a trade-off between repulsive steric and osmotic interactions on the one hand and an attractive electrostatic interaction on the other. 

The electrostatic interaction force Pe(h) per unit area between the two charged brush layers at separation h when they are separated (h > Ido) is given by the osmotic pressure at the midpoint between the plates x = hH minus that in the bulk solution phase, namely,... 

Pincus [212] has studied polyelectrolyte chains the monomers of which are in 0 solvent conditions, i.e., the excluded volume is zero. This assumption is justified by the fact that most polyelectrolytes are rather hydrophobic and their solubility in water is only due the presence of charges along the chains. The author shows that electroneutrality is locally achieved within the brush, providing that the fraction of charged monomers p and the densities of adsorption points l/d2 are not too low. Actually, the high concentrations of charged monomers and counterions lead to a Debye length much lower than the brush thickness. Consequently, the only relevant electrostatic contribution to the forces within the brush is the osmotic pressure of the counterions, which behave as a constraint ideal gas with a pressure equal to pckT, in the absence of added salt. Hence the equilibrium thickness of the brush results from the balance between the elastic force and the counterions ... 

The characteristic branching parameter (grafting density), n/m = specifies the onset of counterion localization inside the molecular brush. Note that in the osmotic regime, the spacers get fully extended, /t m. It is therefore not surprising, that the counterion localization in a cylindrical molecular brush coincides (in scaling terms) with the Manning condensation threshold [25] for a charged cylinder, qh = 1. 

FIGURE 20.7 Gibbs energy of adhesion of a particle at a brush-coated, charged substratum surface as a function of separation distance (—), made up of four types of contributions (1) short-range particle-substratum attraction (2) dispersive attraction (3) electrostatic repulsion due to overlap of Uke-charged electrical double layers and (4) osmotic repulsion due to compression of the polymer brush. 

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