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When polyelectrolyte chains are densely grafted onto a spherical particle, the interaction between the polyelectrolyte chain molecules causes each polymer chain to orient nearly perpendicular to the surface, resulting in the formation of a spherical polyelectrolyte brush.
While planar polyelectrolyte brushes are mainly formed in nanochannels and exhibit various functions, such as current rectifiers, ion sensing, flow valves, spherical polyelectrolyte brushes are designed and used to sensitively emit drug solution under partial heterogeneity pH condition for the precise delivery of drug solution to damaged cell or tissue. Spherical polyelectrolyte brushes also seek their active use in such fields as oil recovery and emulsion stabilization.
Studies on spherical polyelectrolyte brush were mostly based on scaling theory and rigorous self-consistent field model.
However, such models assume that the hydrogen ion distribution inside and outside the polyelectrolyte layer follows the Boltzmann distribution.
Recently, it has been discovered that the description of such hydrogen ion concentration indeed violates thermodynamics and a research has been done to accept a description of hydrogen ion concentration that properly takes account of the ionization of the polyelectrolyte layer.
A more advanced version of strong stretching, a self-consistent field theory that takes account of excluded volume effect and generic mass action law, was proposed and applied to various transport and interfacial phenomena in a nanochannel grafted by planar polyelectrolyte brushes.
We have applied for the first time the strong stretching theory that takes into account the excluded volume effect and mass action law to spherical polyelectrolyte brushes and have studied their structure and properties.
First of all, we defined free energy of the system taking account of electrostatic effect, elastic and excluded volume effects, and ionization energy. Then, based on the variation principle, we determine the self-consistent field equations to define the electric field distribution and ion distribution around the spherical polyelectrolyte brushes, the monomer distribution of the polyelectrolyte chain, and the polyelectrolyte chain end distribution.
We found that the smaller the inner core particle radius, the thicker the polyelectrolyte brush, and furthermore, the smaller the monomer density function.
It was also demonstrated that a larger excluded volume interaction of monomers, a larger chargeable site density, a smaller concentration of electrolyte solution and a higher pH of electrolyte solution result in a thicker polyelectrolyte brush.
This theory can be applied to a more general case, not requiring any strong, necessary conditions such as constancy of polyelectrolyte chain length in previous studies. It requires only grafting density to be large enough. We expect the results to promote the development of pH-responsive polyelectrolyte grafted nanoparticles such as drug courier.
Our results have been published in "Physics of Fluidis" under the title "Electric double layer of spherical pH-responsive polyelectrolyte brushes in an electrolyte solution: A strong stretching theory accounting for excluded volume interaction and mass action law"(https://doi.org/10.1063/5.0115975).