Reconsidering Calcium Dehydration as the Rate-Determining Step in Calcium Mineral Growth

Abstract

The dehydration of cations is generally accepted as the rate-limiting step in many processes. Molecular dynamics (MD) can be used to investigate the dynamics of water molecules around cations, and two different methods exist to obtain trajectory-based water dehydration frequencies. Here, these two different post-processing methods (direct method versus survival function) have been implemented to obtain calcium dehydration frequencies from a series of trajectories obtained using a range of accepted force fields. None of the method combinations reproduced the commonly accepted experimental water exchange frequency of 10–8.2 s–1. Instead, our results suggest much faster water dynamics, comparable with more accurate ab initio MD simulations and with experimental values obtained using neutron scattering techniques. We obtained the best agreement using the survival function method to characterize the water dynamics, and we show that different method combinations significantly affect the outcome. Our work strongly suggests that the fast water exchange kinetics around the calcium ions is not rate-limiting for reactions involving dissolved/solvated calcium. Our results further suggest that, for alkali and most of the earth alkali metals, mechanistic rate laws for growth, dissolution, and adsorption, which are based on the principle of rate-limiting cation dehydration, need careful reconsideration.

Density functional theory based molecular dynamics study of solution composition effects on the solvation shell of metal ions

“…The procedure of first conducting classical MD (NPT) simulations to equilibrate the volume of the simulation box followed by AIMD (NVT) simulations has been routinely adopted to study the properties of hydrated ions. 18,20,22,42 We did not attempt to run AIMD in the NPT ensemble, which could determine the ''correct'' system density at zero pressure, because depending on the DFT method (functional and dispersion correction) equilibrium density of water can change significantly. 43 Instead, we chose to fix the system size to match the one obtained using the classical MD simulation of these systems.…”

“…13,14 An important contribution to this field was the development of ab initio MD (AIMD), where forces are derived from the electronic structure, 15,16 usually in the framework of density functional theory (DFT), 17 which provides the capability of studying non-additivity effects in the dynamics of ions solvation shells. AIMD simulations, using the Car-Parrinello and Born-Oppenheimer schemes, of cations [18][19][20][21][22][23] and anions, 24,25 have been mostly conducted on an isolated ion in pure liquid water, with no counterions in solution. Electrolyte solutions, on the other hand, have been subject to only a few AIMD studies, including the characterization of the dissociation of the NaCl in water, 26 the cooperative ionic effects are of the Na + and Cl À on the hydrogen bonding network, 27 and the influence of a static electric fields.…”

Solution chemistry effects on the solvation shell of metal ions

“…[44][45][46][47] We have characterized the dynamics of the first and second hydration shells of the alkali metal ions (Li + , Na + , K + and Cs + ) and alkaline earth metal ions (Mg 2+ and Ca 2+ ) in pure liquid water and electrolyte solutions using the "direct" method proposed by Hofer and co-workers. 48 This methodology has been previously applied for, among others, the characterization of ligand exchange between coordination shells of hydrated alkaline earth metal ions and their carbonate and bicarbonate complexes, [49][50][51] as well as the quantification of the water exchange frequency around calcium sites in calcite-water interface 52,53 and hydroxyapatite nanopores. 54 In the "direct" method, the MD trajectories are analyzed for water molecule movements and whenever a water molecule crosses the boundary of the cation coordination shell its path is followed; if its new position outside or inside this shell lasts for more than τ* = 0.5 ps then the event is accounted as a real exchange event (N ex ).…”

Ion Pairing and Multiple Ion Binding in Calcium Carbonate Solutions Based on a Polarizable AMOEBA Force Field and Ab Initio Molecular Dynamics

“…Recently it has been shown that water exchange at carbonate has a timescale of the order of 12.7 ps from ab initio molecular dynamics, 58 while estimates for calcium are far slower and typically lie in the range of 60-80 ps. 59,60 It should be noted that the water exchange rate of calcium is particularly sensitive to the coordination number; exchange within between 6, 7 and 8 waters being faster than states where less than 6 waters are present, such as at surfaces. 54 Analysis of the free energy landscape for ion pairing from ab initio molecular dynamics shows that both the contact and solvent-shared ion pair states are composed of multiple minima.…”