Conclusions

From MD simulations at equilibrium, ion pairs and free ions were found to dominate species probability distributions at pH and concentration levels close to experiment. No calcium carbonate clusters in the size ranges expected for prenucleation clusters (PNCs) were found. Only when the concentration of ions was much higher than experiment (51 mM) were large calcium carbonate clusters observed. DOLLOP has been suggested as the structural form of PNCs, but at the concentrations investi- gated, only a small concentration of ion associates containing up to three to four ions are likely to be found in solution at experimental concentrations and pH. Even at the limit of high pH, and at a concentration of 20 mM, clusters containing a maximum of six ions were found.

The findings are in contrast with the proposed thermodynamic equilibria of ion association in solution [Demichelis et al., 2011]. However, speciation data for the highest concentrations studied in the work of Demichelis et al. was used to fit a speciation model at the experimental conditions of 10 mM buffer solution and a calcium concentration of 0.4 mM [Demicheliset al., 2011]. The fraction of calcium bound in CaCO₃0, CaHCO₃+ and DOLLOP was suggested to be 0.2, 0.03 and 0.73, respectively. The authors note that this shows good agreement with the fraction of

bound calcium (fCa−bound) in experiment: at pH 9.75±0.05,fCa−bound= 0.69±0.07, and at pH 10.0_±0.05,fCa−_bound = 0.76±0.08 [Demichelis et al., 2011]. However,

at pH 9.5-10 and 0.06 M, the fraction of Ca2+ bound in DOLLOP is likely to be extremely smaller than this. At the pH range and concentrations considered in this study, the fractions of calcium bound in solution are provided in Table 6.5. Reasonable agreement to the experimental values is found, especially for ionic solutions simulated at an initial pH of 9.9, but none of the bound calcium was present as DLNPs. While Demicheliset al. note that bond orders at low concentration are system size limited, this was not the case in the current study: at the same pH, coordination probabilities for different system sizes were equivalent within statistical noise.

Table 6.5: Fraction of bound calcium,fCa−_bound, in solution at equilibrium. System fCa₋bound

I22₋14 0.84±0.07

C22₋14 0.90±0.04

I46₋29 0.77±0.04

I64₋47 0.89±0.02

Simulations at higher concentrations were consistent with recent computa- tional studies [Demicheliset al., 2011; Wallaceet al., 2013] showing that dense liquid phases are stable in solution. The possibility of dense liquid phases forming locally in solution is relevant. During experiments, concentration gradients are likely to be found in solution, which may lead to the association of ions and a liquid–liquid phase separation. As these studies have shown, dense liquid clusters which form are likely to be long lived and could possibly be detected by experimental analysis. Furthermore, as others have pointed out [Faatz et al., 2004; Wallace et al., 2013], the formation of solid phases in the dense liquid may offer a low energy route to the precipitation of calcium carbonate.

The results of computer simulations are in good agreement with the exper- imental findings presented in section 6.4. Only free ions and ion pairs CaCO₃0 and CaHCO₃+ were found in solution in the prenucleation stage of titrations. No PNCs in the size ranges suggested by Gebauer et al. [Gebauer et al., 2008] and Pouget

et al. [Pouget et al., 2009] were found in TEM images. To reconcile differences in this study and previous experiments, it is useful to consider the experimental methods. In the analytical ultracentrifugation experiments used to determine the size distribution of PNCs [Gebauer et al., 2008], it is likely that large concentra- tion gradients exist in solution. At relatively high concentrations, clusters may be

metastable, as shown from simulations here. In the experiments of Pougetet al. the Kitano method for nucleation was adopted in which local high supersaturations at the gas–liquid interface will be found, and so direct comparison to these experiments is difficult [Pougetet al., 2009]. However, at the interface it is likely that metastable clusters would form in these high concentration regions, and vitrification for TEM analysis would capture clusters which would otherwise dissolve in an equilibrated homogeneous solution.

The fact that only free ions and ion pairs are found at low concentration and moderate pH levels in both experiment and simulation is evidence that PNCs are unstable. Instead, a classical mechanism of growth of crystalline phases from free ions or ion pairs seems more likely. Indeed, analyses of objects formed during nucleation in experiment support this. From the simulation side, a thermodynamic link between ion pairs and nanocrystalline particles may help to understand the likelihood of this mechanism. Nonetheless, the data presented here does compare reasonably well with the findings of Hu et al. where classical nucleation of calcite on self assembled monolayers was observed [Huet al., 2013].

The observation of low contrast spherical objects (from cryo–TEM) which reach considerable sizes is consistent with the formation of a dense liquid phase. The formation of a dense liquid via binodal demixing was suggested by Wallace et al.

[Wallaceet al., 2013], and is further indication of the emergence of liquid (precursor) phases. It is possible that the DLNP found at high concentration is the structural form of the dense liquid phase in experiment. At very high supersaturation a homo- geneous solution of free ions and ion pairs will be unstable and so phase separation becomes likely. However, nucleation of crystal (as found in the experiment) will not be seen on the time-scales of the simulation. Liquid–liquid phase separation, where there is a low energy barrier due to a low surface tension of dense liquid phases, is, on the other hand, more likely to be observed. Further analysis must be performed in order to compare the dense liquid phases found in experiment and DLNPs from simulation.