Calcite Crystals with Platonic Shapes and Minimal Surfaces

Abstract

Platonic solids [1] are the five polyhedrons with equivalent facets composed of congruent convex regular polygons, in which the same number of facets meet at every vertex. The octahedron, with eight facets, is a platonic shape composed of triangles, and the dodecahedron, with 12 facets, is the only one with pentagonal facets. In nature, pyrite frequently occurs as octahedral or dodecahedral crystals. Certain viruses and radiolaria also routinely take the form of these regular polyhedral shapes.[2] A number of synthetic inorganic crystals with platonic shapes have been reported recently, such as gold nanocrystals, [3a] mesoporous silicate dodecahedra and octahedra, [3b,c] [4k] and from sea urchins. [4l,m] The mechanisms of crystal growth of these calcite pseudo-dodecahdra are additive adsorption on the {011} faces, [4l, n] the inhibiting effect of additives on step-growth, [4c] or the combination of the two functions.[4] Calcite mesocrystals with pseudo-octahedral morphology [5a,b] and otoconia-like morphology [5c] were also described.However, a unified route towards more than one platonic calcite shape based on one same mechanistic approach has not yet been revealed. Herein, we present a nonclassical crystallization approach towards calcite with a platonic shape based on nanoparticle aggregation. We show that a commercial co-polyelectrolyte can be used to manoeuvre the crystallization of CaCO 3 into meso-crystalline calcite structures with curved surfaces and platonic shapes. Significantly, the intermediates are consistent with rhombohedral primitive (P)-surface morphology (see Supporting Information Figure S1)-one of the mathematical minimal surfaces, which were found in nature and in synthetic bicontinuous mesophases. [6a,b, 7] The most striking example is the skeleton of Cidaris rugosa, in which self-assembled 3D networks have a continuous curvature. The importance of the P-surface structure was also recognized in other sea-urchin skeletal plates and has been connected with their functions in nutrient permeation, stress distribution, and their unique optical properties. [6,8] The platonic calcite crystals were generated by a simple gas-diffusion method [9] in the presence of poly(4-styrenesulfonate-co-maleic acid) (PSS-co-MA). This polymer was chosen as it combines the maleic acid, which stabilizes {011} faces of calcite, [4e] with the mesocrystal-inducing properties of PSS [10] in one molecule. Pseudo-dodecahedral crystals were obtained for a polymer concentration of 0.1 g L À1 and [CaCl 2 ] = 1.25 mm after 2 weeks crystallization.

The multiple effects of amino acids on the early stages of calcium carbonate crystallization

“…6c and d). Similar morphologies have previously been obtained in the presence of different polymeric additives [14,37,[63][64][65] as well as negatively charged silicate species [66]. In some of these cases, truncation of edges and corners was ascribed to face-selective adsorption of the additives, which thus be- came stabilized and exposed.…”

Mesocrystals—Ordered Nanoparticle Superstructures

“…[137] Even during the aggregation of clusters to amorphous but solid species, there appear to be liquid intermediates, which can transform to mesocrystals or single crystal-liquid hybrid particles exhibiting a soap film like texture or the typical minimal surfaces of liquids like the P-surface. [139] The corresponding time scales related to mesocrystal formation are even broader spanning from the sub-ms range for primary particle formation [140,141] to many hours of structural ripening, as observed for the (NH 4 ) 3 PW 12 O 40 example. [42] This spans at least about 8 decades in time (10 À3 -10 5 s).…”

Polymer‐Controlled Crystallization of Unique Mineral Superstructures

“…In the presence of PSS-co-MA (poly(4-styrenesulfonate)-co-(maleic acid)), the platonic calcite crystals with pseudododecahedral and pseudooctahedral shapes consist of nanoparticles and polymer incorporated in the voids in the microcrystal. [22] A continuous evolution of the crystallization mechanism from polycrystalline to mesocrystalline and then to single crystalline in the presence of poly(ethylene oxide)-bpoly(sodium 4-styrenesulfonate) (PEO 22 -PNaStS 49 ) was investigated, based on aggregation of nonoriented larger nanoparticles, to oriented smaller nanoparticles, and then to classical Oswald-ripening ion-to-ion growth. [23] A thin layer of polymer on the fine crystallites of polycrystalline crystals (2.2 nm) and mesocrystals (3.7 nm) was observed, which can be further proved by thermogravimetric analysis (TGA).…”