A thermodynamic solution model for calcium carbonate: Towards an understanding of multi-equilibria precipitation pathways

Abstract

a b s t r a c tThermodynamic solubility calculations are normally only related to thermodynamic equilibria in solution. In this paper, we extend the use of such solubility calculations to help elucidate possible precipitation reaction pathways during the entire reaction. We also estimate the interfacial energy of particles using only solubility data by a modification of Mersmann's approach. We have carried this out by considering precipitation reactions as a succession of small quasi-equilibrium states. Thus possible equilibrium precipitation pathways can be evaluated by calculating the evolution of surface charge, particle size and/ or interfacial energy during the ongoing reaction. The approach includes the use of the Kelvin's law to express the influence of particle size on the solubility constant of precipitates, the use of Nernst's law to calculate surface potentials from solubility calculations and relate this to experimentally measured zeta potentials. Calcium carbonate precipitation and zeta potential measurements of well characterised high purity calcite have been used as a model system to validate the calculated values. The clarification of the change in zeta potential on titration illustrates the power of this approach as a tool for reaction pathway prediction and hence knowledge based tailoring of precipitation reactions.

Growth modification of seeded calcite using carboxylic acids: Atomistic simulations

“…Even stable surfaces such as the ð1 0 1 4Þ surface have been shown to reconstruct in moist air via pit formation and film growth [57], making it reasonable to consider defective stepped surfaces in our simulations. In order to have an estimate of the number of carbonate groups to be removed, experimental zeta-potential measurements (À13 mV) at low CO 2 partial pressure [58] were considered and the surface charge density u calculated via the surface potential w as given by [59].…”

“…To replicate the experimental zeta potential [58], 4-5 carbonate groups have to be removed per simulation box with a surface measuring about 25 Â 27 Å. An acute step with five carbonate vacancies was created by subsequent removal of CO 2À 3 groups followed by equilibration for 0.5 ns after each removal.…”

Contribution of Aggregation to the Growth Mechanism of Seeded Calcium Carbonate Precipitation in the Presence of Polyacrylic Acid

“…Results were analyzed using thermodynamic solubility calculations developed by Donnet et al 29 All equilibria were solved simultaneously considering the activity of each species in solution. This approach allows the calculation of reaction progress, crystallite size, and surface charge from experimentally measured pH values as a function of time.…”

“…With a higher amount of PAA giving a higher number of calcite seeds, the final crystallite size should be smaller if growth of the calcite is uniquely on the seeds. This evolution can be calculated from our thermodynamic model 29 and advancement of reaction (from the pH evolution) and is shown in Figure 7. We report the simulated size of calcite by considering the number of calcite seeds of 11 × 10 15 dm -3 with 0.0100 wt % of PAA, and 4 × 10 15 dm -3 with 0.0010 wt % of PAA.…”

“…The surface potential of the particles, Φ 0 , and the interfacial energy between the crystal and the solution, γ, were calculated from the thermodynamic solubility model (Figure 7), described in more detail elsewhere. 29 At the beginning of the reaction, the surface potential, Φ 0 , is close to the isoelectric point, and the formation of a hydrate phase gives a low interfacial energy, γ. This leads to a chaotic agglomeration of the first precipitated nanoparticles and, thus, to the formation of an open network: our so-called pseudogel.…”