Dielectric analysis of different spherical polyelectrolyte brushes: Influence of pH and mass fraction on movement of counterions and electrical properties for different SPBs

Two remarkable relaxations are observed for the SPBs (composed of PS core and PAA and PAEMH chains) suspension, and the mechanisms of the relaxations are confirmed the movement of the counterions (low-frequency relaxation) and the interface polarization between SPB and solution (high-frequency relaxation). The movements of counterion in the SPBs suspension are revealed as two kinds of modes: tangential movement of counterions along the SPB particles for SPBs with collapsed brushes (the collapsed PS-PAA in the acidic solution) and diffusion movement of counterions along the brush between the brush and the bulk solution for SPBs with stretched brushes (the strentching PS-PAA in the basic solution and PS-PAEMH in the acidic solution). From high-frequency relaxation the response of polyelectrolyte brush to acidity of medium is detected. Further, combining dielectric parameters obtained and the theory equations presented by O'Konski, surface conductivity λ and the particle surface charge densityσ and the Zeta potential ς of PS-PAA1, 2, 3 are obtained. Combining dielectric parameters obtained and the cell model, the phase parameters of the SPBs can be obtained.