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In this paper, we study electrostatic and structural properties betweenpH-responsive polyelectrolyte brushes by using a strong stretching theoryaccounting for excluded volume interactions, the density of polyelectrolytechargeable sites and the Born energy difference between the inside and outsideof the brush layer.  In a free energy framework, we obtain self-consistent field equations todetermine electrostatic properties between two pH-responsive polyelectrolytebrushes. We elucidate that in the region between two pH-responsivepolyelectrolyte brushes, electrostatic potential at the centerline and osmoticpressure increase not only with excluded volume interaction, but also withdensity of chargeable sites on a polyelectrolyte molecule.  Importantly, we clarify that when two pH-responsive polyelectrolyte brushesapproach each other, the brush thickness becomes short and that a largeexcluded volume interaction and a large density of chargeable sites yield theenhanced contract of polyelectrolyte brushes. In addition, we also demonstratehow the influence of such quantities as pH, the number of Kuhn monomers, thedensity of charged sites, the lateral separation between adjacentpolyelectrolyte brushes, Kuhn length on the electrostatic and structuralproperties between the two polyelectrolyte brushes is affected by the exclusionvolume interaction.  Finally, we investigate the influence of Born energy difference on thethickness of polyelectrolyte brushes and the osmotic pressure between twopH-responsive polyelectrolyte brushes.

Structural and electrostatic properties between pH-responsive polyelectrolyte brushes studied by augmented strong stretching theory