Equilibrium Conformations and Surface Charge Regulation of Spherical Polymer Brushes in Stretched Regimes

Abstract

In the present work, we study the equilibrium conformations of linear polyelectrolytes tethered onto a spherical, oppositely charged core in equilibrium with an ionic reservoir of fixed concentration. Particular focus is placed on the situation of stretched chains, where the monomer concentration is known to display an inverse square-law decay far away from the spherical surface, which is then further extrapolated all the way down to the grafting core. While the equilibrium distributions of mobile ions are computed in the framework of a classical density functional theory (cDFT) that incorporates both their size and electrostatic correlations within the grafted polyelectrolyte, the equilibrium configuration of the latter is described by its average radius of gyration, which is taken as a variational parameter that guarantees mechanical equilibrium across the polymer–solvent interface. The average particle size is then analyzed over a wide range of polymerization degrees, ionic concentrations, and functionality of the polymer backbones. Two distinct regimes can be identified: at high ionic strengths, swelling of the grafted polymers is dominated by ionic entropic contribution as well as polymer size effects, whereas at low ionic concentrations, a balance between electrostatic and entropic effects is the main driven mechanism for particle stretching. Using Monte Carlo simulations, we then proceed to investigate the effects of charge regulation when the brush core is further decorated with active functional sites randomly distributed over its surface, which act as receptors onto which dissolved acidic ions can be adsorbed.

Controlling the two components modified on nanoparticles to construct nanomaterials

“…On this basis of a lot of work on theoretical simulations of single-component polymer grafted nanoparticles, 22,61,62,[64][65][66][67][68][69][70][71][72][73] theoretical simulations of two-component polymer grafted nanoparticles has also gradually attracted attention. Koski et al 12 used the theoretically-informed Langevin dynamics (TILD) to study the self-assembly of nanoparticles modified with different polymers to form different structures of vesicle, droplet and dispersed, respectively (Fig.…”

Theory of Charge Regulation of Colloidal Particles in Electrolyte Solutions

“…The Baxter model of protonation also showed that there is a change in equilibrium constant when an acidic group is moved from bulk to the surface [38][39][40][41] . In general, the renormalization of the equilibrium constant is due to the broken rotational and translational symmetry at the surface compared to the bulk.…”

“…Indeed PB theory is known to be very accurate for suspensions with monovalent 1:1 electrolytes. However recent works, based on Baxter's model of sticky spheres to describe protoa) Electronic mail: bakhshandeh.amin@gmail.com b) Electronic mail: derek.frydel@usm.cl c) Electronic mail: levin@if.ufrgs.br nation/deprotonation equilibrium, showed [38][39][40][41] that discreteness of surface groups affects significantly the effective charge predicted by the NP theory. The importance of ion polarizability and of finite ion size was also explored in reference 42 .…”

Theory of Charge Regulation of Colloidal Particles in Electrolyte Solutions

“…The Baxter model of protonation also showed that there is a change in equilibrium constant when an acidic group is moved from bulk to the surface. − Generally, the renormalization of the equilibrium constant is due to the broken rotational and translational symmetry at the surface, compared to the bulk. However, the theory developed showed that both the discrete charge effects and the renormalization of the bulk equilibrium constant by the surface can be included within the NP framework.…”

“…The NP approach is based on Poisson–Boltzmann (PB) theory, which neglects the discrete nature of colloidal surface groups and electrostatic correlation effects. − Indeed, PB theory is known to be very accurate for suspensions with monovalent 1:1 electrolytes. However, recent works, based on Baxter’s model of sticky spheres to describe protonation/deprotonation equilibrium, showed − that discreteness of surface groups significantly affects the effective charge predicted by the NP theory. The importance of ion polarizability and of finite ion size was also explored in ref .…”