Chapter 6 Solution and Speciation Effects
6.4 Experimental Studies of Precipitation
During the controlled titration of 10 mM CaCl2 solution into a 10 mM carbon- ate buffer solution at pH=9.75, precipitation of calcium carbonate was found and a highly reproducible LaMer diagram (shown in Figure 6.8) was obtained. In the LaMer diagram the concentration of precursor solute increases until the critical concentration for nucleation is reached; the time before this point is known as the
Figure 6.8: Titration curve showing the development of free Ca2+ ions (red line) compared to the total amount of dosed calcium (black) at pH=9.75, as a function of time normalised with respect totσmax(the time at which the red curve reached a maximum). Different stages of the experiment are defined in the plot (t= 1.3tσmax is the time when solubility is reached).
prenucleation stage. Nucleation occurs at the critical concentration, but the concen- tration of free solute continues to increase up to a maximum, where the nucleation rate is balanced by the consumption rate of solute. The subsequent decrease in the concentration of solute occurs as the consumption rate is higher than the nucleation rate. Once the solute concentration falls below the critical concentration to nucle- ation, any nucleation ceases and the postnucleation stage is entered, where solute is consumed by growing nuclei. Finally, the solute concentration reaches the solubility limit for the bulk phase of growing solid.
Prenucleation Stage
The time axes in the LaMer diagrams from multiple experiments were normalised according to the maximum (tσmax) in the free Ca2+ concentration (see Figure 6.8), and the critical concentration was 0.88tσmax. 62.9±1.0 mol% of dosed calcium was measured to be bound in solution in the prenucleation stage, corroborating with the findings of Gebaueret al. [Gebauer et al., 2008]. Constant pH was maintained by the constant linear addition of sodium hydroxide solution.
The free and bound calcium in solution before nucleation can be considered to be in equilibrium, in which case an equilibrium constant can be defined as follows,
Keq = h Cax(CO3)xy−y i h Caf ree2+ ixhCO32f ree− iy , (6.2)
with a similar function for bicarbonate binding. As the free (bi)carbonate concen- tration is excessive in the prenucleation stage, this can be considered as constant. The function reduces to,
Keq= h Cax(CO3)xy−y i h Caf ree2+ ix . (6.3)
As the ratio of bound to free calcium was found to be constant, it follows thatx= 1 and that one calcium ion is incorporated into prenucleation complexes. This fits with classical ion pair formation in solution before nucleation.
As the pH is constant before nucleation, the ratio of bicarbonate to carbon- ate must also be constant. 7.24 mM of bicarbonate is present in 10 mM buffer solution. On anion binding to calcium, this ratio will be re-established as the equi- librium of free anions (HCO3−⇋CO2−
3 +H+) shifts to replenish the relative amounts
of (de)protonated species. 1 mmol of carbonate binding to 1 mmol of calcium re- sults in the release of 0.724 mmol of H+, while 1 mmol of bicarbonate binding to 1 mmol of calcium requires consumption of 0.276 mmol of H+. If these processes
were taking place, then 0.724 mmol of OH− or 0.276 mmol of H+ would need to be added per mmol of added Ca2+, respectively, to keep the pH constant. The amount of added NaOH across the prenucleation stage can, therefore, be used to calculate the ratio of bicarbonate to carbonate binding: NaOH/Cabound2+ = 0.724 for only carbonate binding and NaOH/Cabound2+ =−0.276 for only bicarbonate binding. As the experiment is conducted under atmospheric conditions, the effect of CO2 indiffusion must also be accounted for. When CO2 dissolves into solution H2CO3 is generated, from which bicarbonate and carbonate is produced by loss of protons. NaOH is added to account for the release of 1.31H+ (measured from the
relative activities of bicarbonate and carbonate) per molecule of CO2.
Accounting for the indiffusion of CO2 (which is distinctly different to the studies of Gebauer et al.), during the prenucleation stage NaOH/Cabound2+ = 0.31± 0.06. Using all of the titration data in a speciation program (Visual MINTEQ), the concentration of species in solution at t = 0,0.2,0.4,0.8 and 1.0×tσmax were estimated. The software determined that 99 % of bound calcium before nucleation
was present as CaCO30 and CaHCO3+, with calcium carbonate ion pairs dominating (97% of ion complexes were of this type). The titration profiles were reproduced with high accuracy, providing further evidence that bound calcium in solution before nucleation can be descried in terms of simple ion pairs.
Further support for the lack of prenucleation clusters was provided by cryo– TEM. The TEM images which were obtained following analysis of samples extracted from solution at t= 0.86tσmax were subjected to an analysis procedure. Firstly, a smoothing filter was applied to a TEM image which resulted in the smoothing of each pixel according to the intensity of 250 surrounding pixels. The standard deviation in pixel intensity was 0.004% of the mean. Objects were identified according to the pixel intensity once background noise (from the filtered image) was extracted, so long as a minimum of four-way pixel connectivity was found. A minimum of three pixels were, therefore, required to define the diameter of an object. The threshold, below which an object cannot be distinguished from noise, was 7–8 pixels (approximately 0.9 nm). An equivalent diameter of objects was measured from the maximum length of connected pixels. No object in the prenucelation stage was measured to be greater than the threshold of 0.9 nm. That is to say, no prenucleation clusters can be identified from cryo–TEM images.
Nucleation and Post–nucleation stages
cryo–TEM was used to analyse the species emerging at nucleation. At t= 0.88− 1.0tσmax TEM images showed the presence of 200-400 nm objects which had a very low contrast for their size, as shown in Figure 6.9. The low contrast could be due to high degrees of hydration in the objects, similar to those observed for polymer induced liquid precursor phases [Cantaertet al., 2012]. No long range atomic order was found in the objects from low dose electron diffraction analysis, and so these objects were proposed to be a dense liquid phase formed via liquid–liquid separation. Att= 0.96tσmax objects of size 2 nm were identified in solution using cryo– TEM; these were much higher contrast than the dense liquid phase. These objects were too small for diffraction analysis. However, SEM revealed that the high contrast objects had reached micrometer sizes with spherical morphology by t = 1.03tσmax (see Figure 6.9). In-situ FTIR identified characteristic vibrations for vaterite (875, 1072 and 1087 cm−1) in these objects. As in the prenucleation stage, NaOH/Ca2+
bound in the post-nucleation stage was found to be constant. The change in the concen- tration of sodium hydroxide, ∆[NaOH] and bound calcium, ∆[Cabound2+ ], in solution during the growth stage can be used to determine the number of protons and cal- cium involved in the nucleation and growth of solid. ∆[NaOH]/∆[Ca2+ ] was
Figure 6.9: Images of (sub)micron sized objects during the nucleation and growth stages. cryo-TEM images were taken at (A)t = 0.92tσmax, and (B) t= 0.96tσmax showing low contrast objects of 215 nm and 320–350 nm, respectively (indicated by arrows; scale bar is 0.5µm). C shows a SEM image taken att= 1.03tσmax showing spherical–framboidal objects typical of vaterite; scale bar is 2µm.
measured to be 1.47±0.14. Growth and nucleation of solid from free ions would give ∆[NaOH]/∆[Cabound2+ ]= 1.38 (1/0.724 H+released per Cabound2+ ). The data sug- gest that vaterite is grown by addition of free ions to growing nuclei, and this fits with a classical mechanism of nucleation and growth.