Thermodynamic and Kinetic Studies on the Conversion of Solvent-Shared to Contact Ion Pairs in Sparingly Soluble MF₂ (M = Mg²⁺ and Ca²⁺) Aqueous Solutions: Implications for Understanding Supersaturated Behavior and Association Constant Determination

Abstract

The thermodynamic and kinetic behaviors of Mg2+-F– ion pairing in aqueous solution are investigated theoretically and experimentally and are contrasted to those of Ca2+-F–. Thermodynamically, similar to CaF x (H2O)14 2–x (x = 1 and 2), MgF­(H2O) y + (y = 14–20) contact ion pairs (CIPs) are more stable than their solvent-shared ion pairs (SSIPs), whereas the CIPs and SSIPs of MF2(H2O) y are almost isoenergetic. However, in kinetics, the conversion of SSIPs to CIPs for M2+-F– (M = Mg2+ and Ca2+) ion pairing must overcome a high energy barrier due to the strong hydration of Mg2+ and F–. The kinetics dominate after the thermodynamics and kinetics are balanced, which hinders the formation of M2+-F– CIPs in practical MF2 aqueous solutions (less than or equal to saturated concentrations). This result is also supported by the 19F nuclear magnetic resonance spectra of saturated MF2 solutions. Although the interaction between Mg2+ and F– is slightly stronger than that between Ca2+ and F– due to the smaller radius of Mg2+, the formation of Mg2+-F– CIPs needs to go through two rate-limiting steps, the dehydration and entrance of F– (i.e., via exchange mode) with a higher energy barrier, due to the ability of strongly bound water molecules and rigorous octahedral coordinated configuration of Mg2+, while the formation of Ca2+-F– CIPs only goes through a single rate-limiting step, the entrance of F– (i.e., via swinging mode) with a lower energy barrier, due to the flexible coordination configuration of Ca2+. This is responsible for precipitation in MgF2 aqueous solution requiring a larger supersaturation degree and a lower precipitation rate than in CaF2. These kinetic factors lead to the association constants previously reported for MF+ determined by a fluoride ion-selective electrode (ISE) combined with the titration method, where the MF2 solutions were always unsaturated at the titration end point, which actually corresponds to those of the ligand process going from completely free M2+ and F– to their SSIPs. A possible strategy to accurately determine the association constants of MF+ and MF2(aq) CIPs by fluoride ISEs is proposed. The present results suggest that judging the formation of M2+-F– CIPs in practical solutions from a theoretical calculation perspective requires significant consideration of the kinetic factors, except for the thermodynamic factors.

Structural hysteresis of dilute fluorine salt aqueous solutions

“…When Zn 2+ is replaced with Mg 2+ , having same charge and ion radius as Zn 2+ , the dissociation energy profile shows that Mg 2+ -F − SSIPs are stable outer-sphere complexes (energy trough locates at the range of 3.8-4.5 Å of Mg 2+ -F − distance.) [9]. To further confirm this anomaly, both clusters, Zn 2+ -F − SSIP and 2SSIP with explicit water molecules (40 H2O), extracted from dynamic trajectory are optimized by static DFT calculations.…”

“…In the solutions with lowest Zn(Cd)F2 concentration (0.001 mol•kg −1 ), a single peak at ~−120 ppm (A) could be observed. This signal has been assigned to the solvated fluoride ion [9]. As the Zn(Cd)F2 concentration increases, the peak gradually shifts upfield, indicating that the 19 F nucleus is shielded.…”

“…The archetypal systems that are well known have been traditionally glass-forming solutions under supercooled conditions [1][2][3] and some easily hydrolysable metal ions in strong alkali and acidic solutions [4][5][6][7][8] where the substitution of ligands or ion aggregation occur. Such slow process makes whole system long-termly keep a non-equilibrium steady state [5,9], even a bistable state observed in nanoparticle-based solutions at a given value of pH [10], and exhibit some peculiar properties that are expected to be regulated, especially in nanoscale self-assembly field [11][12][13]. As a consequence, it still remains a topic of intense experimental and theoretical interest [14].…”