Stable Prenucleation Calcium Carbonate Clusters
Denis Gebauer,
Antje Völkel and
Helmut Cölfen*
Max Planck Institute of Colloids and Interfaces, Research Campus Golm, Am Mühlenberg 1, D-14424 Potsdam, Germany.
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Fig. 1. (A) Development of the free calcium ions measured by the calcium ion selective electrode (black line) at pH = 9.25 in comparison with the dosed amount of calcium ions (red line). The solubility concentration of the precipitated phase defines the undersaturated and supersaturated stages of the prenucleation stage. Already in undersaturated solution, calcium ions are bound. (B) Averaged amount of bound calcium ions as calculated from the difference between the measured amount of free calcium ions and the dosed amount of calcium ions shown in (A) for five pH levels. The arithmetic average of a sample of three measurements is calculated in the prenucleation stage and the postnucleation stage. Averaging during nucleation is not appropriate, and the particular developments are indicated by fine lines. Error bars depict ±1 SD of a sample of three measurements; the center of the error bars gives the arithmetic average of the particular data points (see also fig. S2).
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Fig. 2. Schematic illustration of the free reaction enthalpy  RG versus the reaction coordinate. In the classical view (bold line), metastable clusters form and nucleation occurs when the critical nucleation enthalpy G* is overcome. In fact, stable clusters (dashed line) are formed with an activation barrier negligible compared to thermal energy. The structure and depth of the indicated minimum remain unknown, as well as the height of the activation barrier for nucleation.
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Fig. 3. Time development of the free ion product. Shown are averaged values obtained from a sample of three measurements. Because averaging is not appropriate during nucleation, the particular developments are indicated by dashed lines. We find two different ACC phases with solubility products of  3.1 x 10–8 M2 (ACC I) and 3.8 x 10–8 M2 (ACC II), corresponding to the pH dependency of the prenucleation cluster equilibrium. Also given are the solubilities of vaterite, aragonite, and calcite (27) (SOM section 2.5.)
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Fig. 4. Schema of the classical and novel view on precipitation (not to scale). Prenucleation-stage calcium carbonate clusters provide an early precursor species of different ACC phases giving rise to an alternative crystallization-reaction channel.
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