  By implementing the nonlinear Poisson-Boltzmann theory in a cell model, we
theoretically investigate the influence of polyelectrolye gel permeability on
ion densities and pH deviations inside the cavities of ionic microcapsules. Our
calculations show that variations in permeability of a charged capsule shell
cause a redistribution of ion densities within the capsule, which ultimately
affects the pH deviation and Donnan potential induced by the electric field of
the shell. We find that semipermeable capsules can induce larger pH deviations
inside their cavities that can permeable capsules. Furthermore, with increasing
capsule charge, the influence of permeability on pH deviations progressively
increases. Our theory, while providing a self-consistent method for modeling
the influence of permeability on fundamental properties of ionic microgels,
makes predictions of practical significance for the design of microcapsules
loaded with fluorescent dyes, which can serve as biosensors for diagnostic
purposes.
