Viscosity as a Smoking Gun for Complex Formation in Solution: Fe$^{2+}$ and Mg$^{2+}$ Chlorides as Examples

Abstract

Electrolyte solutions at high concentration are indispensable and yet poorly understood. In particular, the extent of speciation -- the formation of complexes composed of multiple species -- in concentrated ionic solutions is very challenging to obtain theoretically and experimentally, but can have a strong effect on solution properties. The literature is rife with contradictory estimates of speciation from experiments. We find that speciation affects transport properties, and is therefore, a prerequisite to accurately model concentrated solutions. We turn this to our advantage by showing that the viscosity can be used to determine the extent of complexation in concentrated aqueous solutions. Results of simulations as well as experimental measurements are presented. The atomistic Madrid-2019 force-field is extended to model FeCl$_2$. Solutions of FeCl$_2$ and MgCl$_2$ are compared and the observed difference in viscosity explained by more complexation in the former, a conclusion supported by recently reported X-ray absorption and neutron scattering experiments.

Figures (10)

• Figure 1: Viscosity of FeCl_2 and MgCl_2 from experiments, obtained from laliberte2007model and this work. The blue shaded region corresponds to a $2\,\%$ relative uncertainty in the FeCl2 viscosity measurements reported in this work. The red shaded region represents the $1.8\,\%$ mean relative deviation of the Laliberté model for MgCl2 from the experimental data laliberte2007model. Inset, bottom: Zoomed-in view of viscosities at low concentration, which are similar in value. Inset, top: Close-up view of the stark difference between the experimental viscosity of FeCl2 and MgCl2 at high concentration.
• Figure 2: Density of FeCl2 and MgCl2 from fits to experiments (solid blue and magenta line, respectively) from this work and Laliberte2004laliberte2007model, respectively, as well as the density from atomic-scale simulations without complexes (squares and circles). Agreement is within $0.5 \%$ for all concentrations.
• Figure 3: Comparison of the viscosity of FeCl2 and MgCl2 obtained from simulations using the Madrid-2019 model (blue and red squares) with those from experiments (solid blue and red line, respectively). Inset: The viscosity obtained from the Green-Kubo formalism for a $4$ m MgCl2 solution, showing that the viscosity plateaus at about $100$ ps at the converged value.
• Figure 4: Illustration of the complexes considered in the atomic-scale simulations. The bond between the metal cation and Cl- anion is rigid, but the water molecules are free to move. The black dashed lines indicate the octahedral shape of the solvation shell. Left: The monomer complex, wherein the cation is part of a monochloro complex (where M corresponds to an Fe^2+ or Mg^2+ cation). Right: The dimer complex, consisting of a linear dichloro unit Cl-M-Cl.
• Figure 5: The experimentally measured viscosity of a $4$ m solution of MgCl_2 laliberte2007model and FeCl_2 depicted as magenta and cyan horizontal lines, respectively, as well as the calculated viscosity (squares) of solutions containing a varying fraction of monomer complexes and free ions, shown as a function of the percentage of free cations, $\alpha$. The orange circles depict calculated viscosity of MgCl_2 using the Madrid-2019 force-field with a charge of $0.80 \ e$. Insets on top illustrate solutions with no free cations, 50% free cations and only free cations.