Pincus brush

Fig. 7 Scaling theory phase diagram at v2//B3< 1 in logarithmic scales with quasi-neutral (NB), osmotic (OsB), Pincus (PB) and collapsed (CB) brush regimes...

The important thickness and high monomer and charge densities encountered in polyelectrolyte brushes are expected to provide emulsion droplets with large steric and electrostatic repulsions. As a consequence, diblock polyelectrolyte surfactants are suitably designed to be effective emulsion stabilizers. Pincus [212] has proposed a description of polyelectrolyte brushes using an approach similar to that of Alexander and de Gennes for neutral brushes [75,213,214], The latter model is thus first presented before developing that of polyelectrolyte brushes. 

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 ... 

Ross RS, Pincus P. The polyelectrolyte brush poor solvent. Macromolecules 1992 25 2177-2183. 

Both forces act into opposite directions the osmotic force tries to stretch the chain into the continuous phase, whereas the elastic force pulls the chain back to the interface. Setting Pci = Posm shows that AP a This is a much lower electrolyte dependence than in the case of low-molecular-weight ionic stabilizers where an exponential dependence of Vim is predicted (cf. equations (8.20)). Note, this scaling behavior of AR with Cl is the same as for polyelectrolyte chains in solution [2]. Regarding colloid stability, this means that polyelectrolyte-decorated droplets/particles possess an extraordinary electrolyte stability when compared to low-molecular-weight ionic stabilizers. Indeed, the Pincus brush behaviour (AP oc was experimen-... 

Klein, J., Kamiyama, Y., Yoshizawa, H., IsraelachviH, J.N., Fredrickson, G.H., Pincus, P., Fetters, L.J. Lubrication forces between surfaces bearing polymer brushes. Macromolecules 26, 5552-5560 (1993). doi 10.1021/ma00073a004... 

Ross, R.S., Pincus, P. The polyelectrolyte brush—poor solvent Macromolecules 25, 2177-2183 (1992). doi 10.1021/ma00 034a018... 

The first term is the interaction free energy associated with repulsive monomer-monomer contacts as given by the Flory theory. For a brush, this free energy is valid for any N since the chains lose their translational entropy upon grafting. The handling of the elastic free energy penalty is the core of the Pincus approxi-... 

Pincus TYAPA (2011) Collapse of polyelectrolyte brushes in electric fields. EPL 95 48003... 

Farina R, Laugel N, Pincus P, Tirrell M (2013) Brushes of strong polyelectrolytes in mixed mono- and tri-valent ionic media at fixed total ionic strengths. Soft Matter 9 10458-10472... 

Figure 3. A stretched brush comprising of chains depicted as strings of Pincus blobs. In distinction to the semi-dilute solution behavior the blobs are not close packed.

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