The Crystallization of Amorphous Calcium Carbonate is Kinetically Governed by Ion Impurities and Water

Abstract Many organisms use amorphous calcium carbonate (ACC) and control its stability by various additives and water; however, the underlying mechanisms are yet unclear. Here, the effect of water and inorganic additives commonly found in biology on the dynamics of the structure of ACC during crystallization and on the energetics of this process is studied. Total X‐ray scattering and pair distribution function analysis show that the short‐ and medium‐range order of all studied ACC samples are similar; however, the use of in situ methodologies allow the observation of small structural modifications that are otherwise easily overlooked. Isothermal calorimetric coupled with microgravimetric measurements show that the presence of Mg2+ and of PO4 3− in ACC retards the crystallization whereas increased water content accelerates the transformation. The enthalpy of ACC with respect to calcite appears, however, independent of the additive concentration but decreases with water content. Surprisingly, the enthalpic contribution of water is compensated for by an equal and opposite entropic term leading to a net independence of ACC thermodynamic stability on its hydration level. Together, these results point toward a kinetic stabilization effect of inorganic additives and water, and may contribute to the understanding of the biological control of mineral stability.

. Scanning electron micrographs of synthetised ACCs. A) additive free ACC, B) Mg-ACC, C) P-ACC,D) comparison of the particle size distribution of ACC, Mg-ACC and P-ACC, E) additive free ACC iso , F) Mg-ACC iso , G) P-ACC iso ,H) comparison of the particle size distribution of ACC iso , Mg-ACC iso and P-ACC iso .     . dPDF/dT maps calculated from x-ray in-situ humidity measurements. A) pure ACC with 200 nm particle size, B) 65 nm particle size, C) P-ACC; 40 nm particle size and D) Mg-ACC; 75 nm particle size.

Text S1. Surface water calculation
The amount of water determined in this work refers mainly to bulk water. For the TG experiments, in fact, the samples were equilibrated for a relatively long time at RT under dry N2. For this reason, most of the surface water was already removed. The residual surface water could be estimated as follows: considering particles of 80 nm in diameter and a density for hydrated ACC of about 2.3 g/cm 3 , the specific surface area of ACC would be about 30-35 m 2 /g. Assuming (overestimating) that the water size is 2.8 Å and that a full monolayer is left after dehydration at RT, we can assess the surface water contribution to be maximally about 10% of the total water. More realistically, only the strongly bound water is left at the surface of ACC after equilibration at low RHs, which has been estimated to be about 3 wat/nm 2 . [42] In this case, the contribution to the surface water here would represent maximally 2% of the total water content.

Text S2. Calculation of the entropic contribution -TdS/dn to the molar free energy
The experimentally standard entropy values of calcite and hydrated calcium carbonates, namely monohydrocalcite (CaCO 3 H 2 O) and ikaite (CaCO 3 6H 2 O) were used to calculate the entropic contribution -TdS/ dn H2O to the molar free energy. The entropy of calcite S calcite was reported to vary between 91.7 and 92.9 J K -1 mol -1 , [50] [51] the entropy of monohydrocalcite S mhc to be 129.7 J K -1 mol -1 [52] [53] and the one of ikaite S ikaite to range from 306.6 [62] to 310.40 J K -1 mol -1 [53] . Therefore, -TdS/ dn H2O for the hydration of calcite to monohydrocalcite at for example 298K is (S mhc -S calcite )*298/1=10.6-10.9 kJ mol -1 and for the hydration of calcite to ikaite (S ikaite -S calcite )*298/6=10.9-11.3 kJ mol -1 . For Figure 2C an average of 10.9 kJ mol -1 with a standard deviation of 0.3 was used for -TdS/ dn H2O . Note that -dΔS/ dn H2O is 0.036 kJ mol -1 .

Text S3 Microgravimetry and isothermal calorimetry.
As the starting material is hydrated, the transformation is accompanied by a weight loss due to water evaporation. The total heat flow measured over time, Q(t) [Js -1 ], then consists of both a (exothermic) contribution due to the ACC crystallization, Q c (t), and a (endothermic) contribution associated to water vaporization Q v (t). To extract the crystallization contribution, the measurement of the heat flow is subtracted for the water vaporization contribution, i.e. Other thermal events, namely, water adsorption and dissolution, may contribute to the total heat flow. We considered these contributions that are however expected to be negligible.

Water adsorption:
For the transformation induced by humidity, as indicated in the SI, samples were equilibrated at a water vapour pressure P/P0 of 0.3. As typical for Calcium salts, at that P/P0 enthalpy of adsorption are not larger than 45-46 kJ/mol [63] . This is in fact the reason why we chose to equilibrate the samples at a relatively high P/P 0 . Unfortunately, there are no such reference data for ACC. If only water with partial enthalpy of adsorption very close to 44 kJ/mol is adsorbed, the measurement is only very slightly (if at all) affected by this phenomenon. It may have been unclear from our text that by simultaneously measuring the weight of the sample, we can compensate not only water evaporation, but also for the condensation of water from gas phase during sorption. After changing the relative humidity from 30% to 85%, therefore, the contribution to the heat of adsorption of water will be maximally 1-2 kJ/mol of water.
Taking an average value of 80 nm for particle diameter, we can easily estimate that the maximum heat produced by adsorption for a full monolayer of water is smaller than 2 J/g of CaCO3. The heat of crystallisation, on the other hand, is, in the worst case (i.e. for the most hydrated samples), around 50 J/g of CaCO3. Therefore, the contribution of water adsorption does not exceed 1-4% of the total measured enthalpy changes. We have added this consideration in the description of the method in the SI.
In addition to these theoretical, overestimated, values, we can show experimentally that water Therefore, we can confidently conclude that our values for the crystallization enthalpy are not Dissolution: We do not exclude that the sample undergoes dissolution and re-precipitation. In fact, we have suggested that this is the mechanism for the transformation at high humidity levels based is then equal to H1+H2. Figure S7. Measure of the crystallization enthalpy for ACC. A) The sample is equilibrated at 303 K at a RH of 30% (blue shadowed area) until its weight (m(t), light green) is constant. Then the humidity is changed to 85% (red shadowed area) to induce the crystallization. After a first weight increase due to water adsorption at the surface of the particles, the material starts crystallizing and a weight loss is observed. The rate of weight change (m'(t), dark green) is easily calculated from the instantaneous weight. B) The heat flow contribution due to crystallization (Q c (t), orange) is obtained from the total heat flow (Q(t), blue) by subtraction of the heat flow due to water vaporization (Q v (t), dashed green) calculated from the rate of weight change. Figure S8. Validation of the accuracy of the calorimeter. A) About 40 mg of water are placed in a crucible inside the calorimeter. The humidity is changed stepwise and the heat flow (Q v (t), blue) as well as the rate of weight change (m'(t), black) are monitored overtime. B) Plotting the linear parts of the curves against each other, the enthalpy of evaporation of water Δ v H as well as the calorimeter baseline Q 0 can be evaluated with a simple linear fit. The obtained value for the enthalpy of vaporization at 303 K. C is about 43.1 kJ mol-1, which is about 1.5% lower than 43.7 kJ mol -1 reported in literature.