*5.1. Supersaturation*

Supersaturation is defined as:

$$S\_{\circ} = \left(\frac{a\_{Ca^{2+}}a\_{CO\_3^{2-}}}{K\_{sp}}\right)^{1/2} \tag{7}$$

where aCa2<sup>+</sup> and aCO32- are activities of a calcium and carbonate ions, respectively, and Ksp is a solubility product. In the liquid-liquid systems, vaterite particles precipitate at room temperature from moderately supersaturated aqueous solutions, i.e., when S < 6.5 [21,33,69,70]. The supersaturation can influence the size of the crystallite forming vaterite particles, and a smaller crystal subunit was observed when supersaturation increased [69,70]. When precipitation is carried out by a carbonation route, the composition of the gas stream can impact on the supersaturation, i.e., an increase in the CO2 concentration in the gas phase resulted in the higher supersaturation. The high supersaturation in the buffered pH range (from about 9.5 to 7.7) helps to trap metastable vaterite, preventing its transformation in calcite [19]. Also, more regular spherical particles are produced at higher concentrations of CO2 in feed gas mixtures [71].

#### *5.2. Temperature*

Usually, vaterite particles can be formed in a broad range of temperatures using a solution method of calcium carbonate precipitation [24,42,58,72]. The comparison of vaterite concentrations in calcium carbonate samples precipitated at various conditions is shown in Figure 3. The favored range of temperatures for vaterite precipitation in various experiments is up to 40 ◦C. This range is also valid when the carbonation route is applied to produce CaCO3 in the vaterite form [59,71].

**Figure 3.** Influence of temperature on vaterite concentration in CaCO3 samples; (**a**) L-L, S = 6.5, pH = 9, based on data from [21]; (**b**) with carbamate, [Ca2+] = 1.5 M, based on data from [58]; (**c**) L-L, [Ca2+] = 0.25 M, based on data from [24]; (**d**) L-L, [Ca2+] = 0.015 M [73]; (**e**) L-L, [Ca2+] = 0.015 M with ethylene glycol based on data from [73]; (**f**) G-L, pH = 9–10, xCO2 = 1, VG = 50 dm3/h (gray), VG = 100 dm3/h (orange) based on data from [59].

The application of the hydrothermal or solvothermal method allowed the precipitation of vaterite at temperatures above 100 ◦C [23,68]. Some additives, e.g., ethylene glycol, can promote vaterite formation at temperatures above 40 ◦C [42] A higher concentration of vaterite was observed in the CaCO3 product precipitated in an ethylene glycol-water solution at a temperature of 50 ◦C compared to the reaction carried out in an aqueous solution (see Figure 3d,e).
