Computer Simulations of Static and Dynamical Properties of Weak Polyelectrolyte Nanogels in Salty Solutions

Abstract

We investigate the chemical equilibria of weak polyelectrolyte nanogels with reaction ensemble Monte Carlo simulations. With this method, the chemical identity of the nanogel monomers can change between neutral or charged following the acid-base equilibrium reaction HA ⇌ A^- + H⁺. We investigate the effect of changing the chemical equilibria by modifying the dissociation constant K a . These simulations allow for the extraction of static properties like swelling equilibria and the way in which charge-both monomer and ionic-is distributed inside the nanogel. Our findings reveal that, depending on the value of K a , added salt can either increase or decrease the gel size. Using the calculated mean-charge configurations of the nanogel from the reaction ensemble simulation as a quenched input to coupled lattice-Boltzmann molecular dynamics simulations, we investigate dynamical nanogel properties such as the electrophoretic mobility μ and the diffusion coefficient D.

Keywords: computer simulations; electrophoresis; molecular dynamics; nanogels; reaction ensemble Monte Carlo; weak polyelectrolytes.

Figure 1

(Color online) Simulation screenshot of the initialized state of 29 crosslinks attached with 40 polymers having 10 monomers in each chain for a total of $N_0=429$ simulation beads. Screenshots shown immediately after the initial placement of the beads (a) and after equilibration (b).

Figure 2

(Color online) Titration curve: The mean fraction of dissociated monomers versus pH-pK_a. The different markers indicate different salt concentrations. The ideal titration curves is shown as a solid black line.

Figure 3

(Color online) The mean monomer dissociation state $\langle {\Sigma }_i{\alpha }_i\rangle$ as a function of the mean distance to the nanogel center of mass. The different subplots (a–c) show an increasing value of the dissociation constant $K_{\mathrm{a}}$. The monomers belonging to a crosslink are colored in orange. All cases shown here have the same salt concentration of $c_s=0.004$ M.

Figure 4

(Color online) (a) The radius of gyration is plotted as a function of the mean degree of dissociation; (b) the radius of gyration is plotted as a function of pH-pK_a. The different markers indicate different salt concentrations.

Figure 5

(Color online) The distributions of ions and monomers around the nanogel center of mass. The inset shows the monomer-ion pair correlation function $g\left(r\right)$ between the monomers and the mobile ions. The two cases are chosen (a) above and (b) below the Manning parameter. Both subplots have the same salt concentration $c_s=0.019$ M.

Figure 6

(Color online) (a) For the selected case corresponding to $\langle \alpha \rangle \approx 0.24$, the total charge density is plotted as a function of the radial distance to the nanogel center of mass. The symbols mark (in ascending order) the value of $R_{\mathrm{H}}$ and critical radial position $r^{*}$ at which 100% of the nanogel monomers are included. (b) The integrated net charge of the nanogel complex (up to $r^{*}$) as a function of pH-pK_a.

Figure 7

(Color online) The diffusion coefficient D plotted as a function of (a) the dissociated fraction and (b) pH-pK_a. In all cases, the y-axis is rescaled with the value at lowest dissociation $\alpha$ ≈ 0 or pH-pK_a ≈ −2.

Figure 8

(Color online) The electrophoretic mobility is plotted as a function of (a) the dissociated fraction and (b) pH-pK_a.