Insight into the electrical properties and chain conformation of spherical polyelectrolyte brushes by dielectric spectroscopy

Abstract

We report here a dielectric study on three kinds of anionic spherical polyelectrolyte brush (SPBs, consisting of a polystyrene (PS) core and three different poly (acrylic acid) chains grafted onto the core) suspensions over a frequency ranging from 40 Hz to 110 MHz. The relaxation behavior of the SPB suspensions shows significant changes in the brush-layer properties when the mass fraction of SPBs and the pH of the suspensions change. Two definite relaxations related to the interfacial polarization are observed around 100 kHz and 10 MHz. A single-layer spherical-shell model is applied to describe the SPB suspensions wherein the suspended SPB is modeled as a spherical-shell composite particle in which an insulated PS sphere is surrounded by a conducting ion-permeable shell (the polyelectrolyte chain layer). We developed the curve-fitting procedure to analyze the dielectric spectrum in order to obtain the dielectric properties of the components of the SPBs, especially the properties of the polyelectrolyte brush. Based on this method and model, the permittivity and conductivity of the brush layer, ζ potential, etc are calculated. The ordered orientation of the water molecules in the layer leads to an additional electrical dipole moment; increasing pH causes the brush layer to swell. In addition, the repulsive force between the SPB particles are evaluated using the brush-layer thickness, which is obtained by fitting dielectric spectra, combined with relative theoretical formulas. Increasing PH values or SPB concentration would improve the stability of the SPBs dispersion.

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

“…Under electrostatic repulsion and strong osmotic pressure [10], the PAEMH brush layer is changed into a collapsed state from the swelling state [9]. This is probably a good explanation for why the Ф of the PAEMH-SPB in the suspension decreases with the increase in the pH, while for the PAA-SPB (diagram [41]; all the data related to it in this work is from [41]), its brush layer gradually becomes swollen, and the specific reasons will be discussed in the following section.…”

“…The geometric area of the electrodes is 13.72 mm 2 and the distance between them is 9.82 mm. To eliminate the errors from residual inductance (L r ) and stray capacitance (C r ) (the values of L r , C r and the cell constant C l are 7.21 nF ⋅ S −2 , 0.0523 pF and 0.892 pF, respectively, which have been determined by using three standard substances (air, ethanol, water) and a KCl solution of different concentrations), the capacitance C x and conductance G x of the raw experimental data need further processing; the specific information has been described in [41].…”

“…Afterward, Grosse and Zimmerman [40] extended the Dukhin-Shilove model to a new one in which the sphere core is covered with a charged single shell, and presented a calculation method for obtaining the analytical solution. Recently, using the Gross-Zimmerman (GZ) model, we [41] successfully obtained the electrical properties of the PAA brush and its suspension.…”

“…In this work, we measured the dielectric spectra of PAEMH-SPB and analyzed the suspensions made up of PAEMH-SPB theoretically. Taking into account that PAEMH has the same structure as PAA [41], PAEMH-SPB is also modeled as a PS core covered with an ion-permeable PAEMH layer. The dielectric data is recorded as a function of the mass fraction of the SPBs as well as the pH of the solution.…”

Effect of dielectric discontinuity on a spherical polyelectrolyte brush

“…Spherical PEBs also carry a number of advantages in comparison with planar ones. They can be studied by a wide variety of distinct methods coined for colloidal particles investigation, from scattering methods 31-34 to, more recently, dielectric spectroscopy 35 . Furthermore, the colloidal dimensions of the spherical PEB may be used to create well defined surfaces of the order of many m 2 that can be used for nanoparticle/protein immobilization 36,37 , and they can also be viewed as models for the study of carboxylated latex particles that constitute a major industrial product 38 .…”