Charge Regulation Effect on Nanoparticles Interaction Mediated by Polyelectrolyte

TL;DR

The paper addresses how charge regulation (CR) on both polyelectrolyte (PE) and nanoparticle (NP) surfaces modulates PE-mediated interactions between two NPs in monovalent electrolyte, accounting for dynamic ionizable groups on both components. A hybrid charge-regulation Monte Carlo / molecular dynamics (CR-MC/MD) framework is developed to sample ionization states and compare CR with constant-charge (CC) simulations while varying $pH$, salt concentration via $pIp$/$pIm$, and PE length $N$. Key findings show that at low salt CR enhances adsorption of the PE onto a single NP, suppressing bridging and yielding weak repulsion at larger interparticle separations, whereas CC promotes bridging and stronger attraction; increasing salt screens and reduces CR effects, with differences most pronounced at intermediate ionization defined by $\\Delta pK = pK_a + pK_b - 2pH$. The results demonstrate that CR is a critical determinant of NP–PE assembly and stability, offering a framework for tuning interactions via the chemical environment and suggesting fast, robust adsorption dynamics under CR. These insights have implications for designing CR-enabled nanomaterials and guiding experimental studies of NP suspensions in complex electrolytes.

Abstract

The ability to precisely control surface charge using charged polymers is fundamental to many nanotechnology applications, enabling the design and fabrication of materials with tailored properties and functionalities. Here, we study the effect of charge regulation (CR) on the interaction between two nanoparticles (NPs) mediated by an oppositely charged polyelectrolyte (PE) in an electrolyte solution. To this end, we employ a hybrid CR Monte Carlo / molecular dynamics simulation framework to systematically explore the effects of pH, salt concentration, and polymer chain length on NP surface charge behavior. For comparison, we also conduct molecular simulations under constant charge (CC) conditions. Our results reveal that CR enhances PE adsorption onto NP surfaces compared to the CC case, where polymer bridging dominates across a wide range of NP intersurface separations. This enhanced adsorption under CR leads to a weak net repulsion driven by osmotic forces. In contrast, the CC model yields a stronger net attraction due to the bridging force. Furthermore, we find that the CR effects are more pronounced at low salt concentration, whereas at high salt concentration, counterion screening dominates in both CR and CC cases, diminishing the CR effect. These findings highlight the importance of incorporating charge regulation in characterizing nanoparticle interactions within a complex biochemical environment, particularly in low salt concentrations.

Figures (7)

• Figure 1: The initial configurations of our modeled systems. (a) A snapshot of the charge regulation (CR) simulation, where nanoparticles (NPs) coated with base groups ($pK_b = 5$) are separated by an intersurface distance ($D=15 \ell_B$). A polyelectrolyte (PE) chain composed of $N=40$ acid groups ($pK_a = 5$) is positioned between the NPs. Red beads represent the charged monomers of the PE, while blue and white sites correspond to the NPs charged and neutral base groups, respectively. Green and magenta beads represent positively and negatively charged ions, respectively. (b) A snapshot of the constant charge (CC) simulation approximates the CR model. Here, NPs are assigned a fixed charge equal to the average charge on NPs in the CR simulation, and this charge is placed at the center of the NPs. A PE chain of $N=40$ monomers, bearing fixed charges equal to the average monomer charge obtained in the CR simulation, is positioned between the NPs.
• Figure 2: Schematic of the system for the force calculation. A fictitious plane, $S$, of width $0.25\ell_B$ is placed at the midpoint, which divides the system into two halves, $V_1$ and $V_2$. The color scheme is the same as in Fig. \ref{['fig:fig1']}.
• Figure 3: Charge regulation (CR) effects on NPs–PE interactions at a low salt concentration ($pIp = pIm = 7$) with PE bearing acidic groups ($pK_a = 5$) and NPs coated with basic groups ($pK_b = 5$). (a) Top: Snapshot of CR simulation at intersurface separation between colloids, $D = 7\ell_B$. Red and white beads denote charged and neutral acid monomers of the PE, while blue and white sites represent charged and neutral base sites. Bottom: Simulation snapshot of a constant charge (CC) simulation at the same $D$. (b) The average charge on NPs and PE as a function of $D$. (c) The total force ($F_X$) between NPs for CR and CC as a function of $D$. (d) Adsorbed monomer fraction ($f_{ad}$), within $2\sigma$ of the colloid surface as a function of $D$. (e) The radius of gyration ($R_g$) of the PE as a function of $D$. The averages are calculated over 7 (CR) and 30 (CC) equilibrated configurations.
• Figure 4: Effect of PE chain length on interaggregate force and PE adsorption across different simulation models, under the same conditions as in Fig. \ref{['fig:fig3']}. (a) The total force ($F_X$) between NPs in the CR simulation. (b) Adsorbed monomer fraction onto NPs in CR simulations. (c) $F_X$ between NPs in CC simulations. (d) Adsorbed monomer fraction onto NPs in CC simulation.
• Figure 5: Effect of net acid and base dissociation constants on adsorbed monomer fraction ($f_{ad}$) at salt concentration $pIp = pIm = 7$ and $pH=7$ (a) Total charge on macromolecules and (b) $f_{ad}$ as a function net ionization parameter $\Delta pK = pK_a + pK_b - 2pH$.