Thermodynamics of epitaxial calcite nucleation on self-assembled monolayers

Classical heterogeneous nucleation theory is used to describe the epitaxial nucleation of calcite on self-assembled monolayers (SAMs). Both spherical and faceted clusters are considered. The use of faceted clusters reveals a useful relation between the shape of very small crystals and the ratio of the heterogeneous and homogeneous nucleation barriers. The experimental approach of this paper concerns the measurement of the threshold driving forces for both homogeneous and heterogeneous nucleation of calcite. This is accomplished by preparing solutions with well-defined driving forces and by measuring the resulting types of nucleation that are observed after a fixed experimental time. The results of the experiments and the theoretical shape analysis are compared, and it is shown that in the experiments no homogeneous nucleation of calcite occurs for driving forces up to at least Deltamu/k(B)T approximately equal to 6.0. A calculation of the critical cluster size for heterogeneous nucleation results in a range of 2-28 growth units and faceted critical clusters from 3-28 growth units, depending on the value of the surface free energy of calcite. These sizes are 50-100 times smaller than the crystalline domain sizes of SAMs and therefore small enough to explain the promoting effect of the substrate.