Dielectric analysis based on spherical-shell model for cationic and anionic spherical polyelectrolyte brushes.

We report here a dielectric study on cationic and anionic spherical polyelectrolyte brush (SPB) (consisting of a polystyrene (PS) core and poly (2-aminoethylmethacrylate hydrochloride (PAEMH) chains or poly (acrylic acid) (PAA) chains grafted onto the core) suspensions over a frequency range of 40 Hz-110 MHz. The relaxation behavior of the suspensions shows significant changes in the brush layer properties when changing the particle mass fraction or pH of the system. After eliminating the electrode polarization effect at a low frequency, two definite relaxations related to interfacial polarization, around 100 kHz and 10 MHz respectively, are observed. Based on a single layer spherical-shell model, we developed a curve-fitting procedure to analyze such dielectric spectra for soft particles, and then calculated the dielectric properties of the components of the SPBs (such as the permittivities and conductivities of the layer and solution phase), especially the layer thickness d of the polyelectrolyte chain (PE) layer. We also found a larger confinement degree of counterions in the PAEMH brush due to the protonation of the amino group. Moreover, the repulsive force between the SPB particles is evaluated by using the d combined with the relative theoretical formulas. We conclude that by raising (reducing) the acidity of the system, the stability of the PAEMH-SPB (PAA-SPB) suspension was improved. An increase in particle concentration can also improve the stability of these two dispersions.