Evaluation of the particle growth of amorphous calcium carbonate in water by means of the Porod invariant from SAXS.

A time-resolved SAXS study has been carried out on the formation of amorphous calcium carbonate from supersaturated aqueous solutions at an initial concentration of 5 mmol/L CaCO(3). Particle formation was induced by mixing equal volumes of equinormal CaCl(2) and Na(2)CO(3) solutions with a stopped-flow device installed at the SAXS beamline. The resulting scattering curves were analyzed without any model assumption with respect to the particle shape. The analysis is based on the intercept of the scattering curve, its initial slope, and the Porod invariant. These parameters give access to the average particle mass, the average particle size, and the mass concentration of the particles, respectively. The evolution of particle mass and concentration with time gives access to the trend in the particle number density. The size and mass values were found to be correlated by characteristic exponents. Two different mass values can be used for this correlation: direct use of the intercept of the scattering curve or alternatively a ratio of this intercept with the corresponding Porod invariant. The resulting exponents depend on the particle growth mechanism. These exponents, together with the evolution of the number density, are capable of discriminating between a monomer-addition mechanism and a particle-particle coagulation mechanism as two alternative building mechanisms for the resulting amorphous CaCO(3) nanoparticles. A detailed description of the data analysis and its merit in establishing a particle growth mechanism is presented.