Adsorption energy of stoichiometric molecules and surface energy at morphologically important facets of a Ca(OH)2 crystal

Abstract

Abstract Non-dispersive (polar) contribution to adsorption energy of stoichiometric molecules and surface energy of morphologically important {0 0 0 1} and { 1 ¯ 0 1 0 } type facets of a Ca(OH)2 crystal are evaluated on the basis of calculation of the corresponding surface-associated Madelung constants. At the nano-size level, this contribution both of the adsorption and surface energies of indicated types of facets have been obtained to depend predominantly on the characteristic size r1 of a {0 0 0 1} type facet due to much stronger bonding of ions within individual (0 0 0 1) basal planes in comparison with that between ions belonging to adjacent (0 0 0 1) planes. The non-dispersive component of the surface energy of Ca(OH)2 crystal is highly anisotropic, with much higher value calculated for the { 1 ¯ 0 1 0 } type facets. Both for {0 0 0 1} and { 1 ¯ 0 1 0 } facets, the non-dispersive surface energy in the edge and near-edge area substantially exceeds that at center of the facet, regardless of the crystal sizes. In the size range of r1 ≥ 40 nm, out of the marginal area the surface energy of a facet is not practically influenced by the size effect and may be characterized with a sufficient accuracy by corresponding value that is achieved in the limit of large sizes, r1 → ∞. At small sizes r1 ≤ 4 nm, the distribution of the surface energy on each of {0 0 0 1} and { 1 ¯ 0 1 0 } type facets is strongly inhomogeneous and is very sensitive to variation of the characteristic size r1. The non-dispersive adsorption energy of stoichiometric Ca(OH)2 molecules on the {0 0 0 1} and { 1 ¯ 0 1 0 } facets with variation of the size r1 follows the same trend as the corresponding non-dispersive surface energy. Analytical expressions are obtained for the total (sum of non-dispersive and dispersive components) surface and total adsorption energies that incorporate the size effect resulting predominantly from the non-dispersive component. The proposed theoretical approach may be applied to analysis of the same energy characteristics of the materials that are isostructural with the Ca(OH)2: alkaline earth hydroxides – Mg(OH)2, Sr(OH)2, and Ba(OH)2, as well as some other compounds with the brucite structure.