Prenucleation Cluster Pathway is Inconsistent with CaCO3 Kinetics.

It has been debated whether CaCO3 nucleates classically with the attainment of a critical cluster size or nonclassically with the restructuring of a prenucleation cluster (PNC). Here, we determine from the nucleation kinetics of CaCO3 that the transition state is composed of about 10 formula units, irrespective of the supersaturation. Crucially, the size of the transition state is considerably smaller than the average PNC size estimated from experimental characterization. This size discrepancy suggests the PNCs are uninvolved in nucleation, and the kinetics indicate that if CaCO3 nucleates classically, the transition state must be an abnormally unstable (antimagic) cluster.

Accelerating Solvent Dynamics with Replica Exchange for Improved Free Energy Sampling.

Molecular reactions in solution typically involve solvent exchange; for example, a surface must partly desolvate for a molecule to adsorb onto it. When these reactions are simulated, slow solvent dynamics can limit the sampling of configurations and reduce the accuracy of free energy estimates. Here, we combine Hamiltonian replica exchange (HREX) with well-tempered metadynamics (WTMD) to accelerate the sampling of solvent configurations orthogonal to the collective variable space. We compute the formation free energy of a carbonate vacancy in the calcite-water interface and find that the combination of WTMD with HREX significantly improves the sampling relative to WTMD without HREX.

Polyamines Promote Aragonite Nucleation and Generate Biomimetic Structures.

Calcium carbonate biomineralization is remarkable for the ability of organisms to produce calcite or aragonite with perfect fidelity, where this is commonly attributed to specific anionic biomacromolecules. However, it is proven difficult to mimic this behavior using synthetic or biogenic anionic organic molecules. Here, it is shown that cationic polyamines ranging from small molecules to large polyelectrolytes can exert exceptional control over calcium carbonate polymorph, promoting aragonite nucleation at extremely low concentrations but suppressing its growth at high concentrations, such that calcite or vaterite form. The aragonite crystals form via particle assembly, giving nanoparticulate structures analogous to biogenic aragonite, and subsequent growth yields stacked aragonite platelets comparable to structures seen in developing nacre. This mechanism of polymorph selectivity is captured in a theoretical model based on these competing nucleation and growth effects and is completely distinct from the activity of magnesium ions, which generate aragonite by inhibiting calcite. Profiting from these contrasting mechanisms, it is then demonstrated that polyamines and magnesium ions can be combined to give unprecedented control over aragonite formation. These results give insight into calcite/aragonite polymorphism and raise the possibility that organisms may exploit both amine-rich organic molecules and magnesium ions in controlling calcium carbonate polymorph.

Calcite Kinks Grow via a Multistep Mechanism.

The classical model of crystal growth assumes that kinks grow via a sequence of independent adsorption events where each solute transitions from the solution directly to the crystal lattice site. Here, we challenge this view by showing that some calcite kinks grow via a multistep mechanism where the solute adsorbs to an intermediate site and only transitions to the lattice site upon the adsorption of a second solute. We compute the free energy curves for Ca and CO3 ions adsorbing to a large selection of kink types, and we identify kinks terminated both by Ca ions and by CO3 ions that grow in this multistep way.

Calcite Kinetics for Spiral Growth and Two-Dimensional Nucleation.

Calcite crystals grow by means of molecular steps that develop on {10.4} faces. These steps can arise stochastically via two-dimensional (2D) nucleation or emerge steadily from dislocations to form spiral hillocks. Here, we determine the kinetics of these two growth mechanisms as a function of supersaturation. We show that calcite crystals larger than ∼1 µm favor spiral growth over 2D nucleation, irrespective of the supersaturation. Spirals prevail beyond this length scale because slow boundary layer diffusion creates a low surface supersaturation that favors the spiral mechanism. Sub-micron crystals favor 2D nucleation at high supersaturations, although diffusion can still limit the growth of nanoscopic crystals. Additives can change the dominant mechanism by impeding spiral growth or by directly promoting 2D nucleation.

Positively Charged Additives Facilitate Incorporation in Inorganic Single Crystals.

Incorporation of guest additives within inorganic single crystals offers a unique strategy for creating nanocomposites with tailored properties. While anionic additives have been widely used to control the properties of crystals, their effective incorporation remains a key challenge. Here, we show that cationic additives are an excellent alternative for the synthesis of nanocomposites, where they are shown to deliver exceptional levels of incorporation of up to 70 wt % of positively charged amino acids, polymer particles, gold nanoparticles, and silver nanoclusters within inorganic single crystals. This high additive loading endows the nanocomposites with new functional properties, including plasmon coupling, bright fluorescence, and surface-enhanced Raman scattering (SERS). Cationic additives are also shown to outperform their acidic counterparts, where they are highly active in a wider range of crystal systems, owing to their outstanding colloidal stability in the crystallization media and strong affinity for the crystal surfaces. This work demonstrates that although often overlooked, cationic additives can make valuable crystallization additives to create composite materials with tailored composition-structure-property relationships. This versatile and straightforward approach advances the field of single-crystal composites and provides exciting prospects for the design and fabrication of new hybrid materials with tunable functional properties.

Critical Step Length as an Indicator of Surface Supersaturation during Crystal Growth from Solution.

The surface processes that control crystal growth from solution can be probed in real-time by in situ microscopy. However, when mass transport (partly) limits growth, the interfacial solution conditions are difficult to determine, precluding quantitative measurement. Here, we demonstrate the use of a thermodynamic feature of crystal surfaces-the critical step length-to convey the local supersaturation, allowing the surface-controlled kinetics to be obtained. Applying this method to atomic force microscopy measurements of calcite, which are shown to fall within the regime of mixed surface/transport control, unites calcite step velocities with the Kossel-Stranski model, resolves disparities between growth rates measured under different mass transport conditions, and reveals why the Gibbs-Thomson effect in calcite departs from classical theory. Our approach expands the scope of in situ microscopy by decoupling quantitative measurement from the influence of mass transport.

Magnesium-rich nanoprecipitates in calcite: atomistic mechanisms responsible for toughening in Ophiocoma wendtii.

The brittlestar Ophiocoma wendtii is theorised to employ a technique already used in metallurgy in order to optimise the mechanical properties of calcitic microlenses within their skeletons. These microlenses contain arrays of Mg-rich nanoprecipitates, which are proposed to inhibit crack propagation through the compression of the local host lattice. Here, we employ classical molecular dynamics in order to study the effects of Mg-rich nanoprecipitates on lattice strain, stress distributions and crack propagation in calcite. Our quantitative results on lattice strain and stress induced on the host matrix are compatible with empirical estimates. Simulations of crack propagation demonstrate that the inclusion of a Mg-rich region results in an increase in stress required to fracture the crystal, as well as higher residual stress in the fractured crystal. This is the result of an inhomogeneous stress distribution causing a more disordered fracture, as well as deflections of the crack away from the lowest energy (10.4) surface. The results agree with the proposal that the compression of the host lattice inhibits propagation, and offer insight into other mechanisms through which the nanoprecipitates affect crack propagation.

Hydroxyl-rich macromolecules enable the bio-inspired synthesis of single crystal nanocomposites.

Acidic macromolecules are traditionally considered key to calcium carbonate biomineralisation and have long been first choice in the bio-inspired synthesis of crystalline materials. Here, we challenge this view and demonstrate that low-charge macromolecules can vastly outperform their acidic counterparts in the synthesis of nanocomposites. Using gold nanoparticles functionalised with low charge, hydroxyl-rich proteins and homopolymers as growth additives, we show that extremely high concentrations of nanoparticles can be incorporated within calcite single crystals, while maintaining the continuity of the lattice and the original rhombohedral morphologies of the crystals. The nanoparticles are perfectly dispersed within the host crystal and at high concentrations are so closely apposed that they exhibit plasmon coupling and induce an unexpected contraction of the crystal lattice. The versatility of this strategy is then demonstrated by extension to alternative host crystals. This simple and scalable occlusion approach opens the door to a novel class of single crystal nanocomposites.

Stress in titania nanoparticles: an atomistic study.

Stress engineering is becoming an increasingly important method for controlling electronic, optical, and magnetic properties of nanostructures, although the concept of stress is poorly defined at the nanoscale. We outline a procedure for computing bulk and surface stress in nanoparticles using atomistic simulation. The method is applicable to ionic and non-ionic materials alike and may be extended to other nanostructures. We apply it to spherical anatase nanoparticles ranging from 2 to 6 nm in diameter and obtain a surface stress of 0.89 N m(-1), in agreement with experimental measurements. Based on the extent that stress inhomogeneities at the surface are transmitted into the bulk, two characteristic length-scales are identified: below 3 nm bulk and surface regions cannot be defined and the available analytic theories for stress are not applicable, and above about 5 nm the stress becomes well-described by the theoretical Young-Laplace equation. The effect of a net surface charge on the bulk stress is also investigated. It is found that moderate surface charges can induce significant bulk stresses, on the order of 100 MPa, in nanoparticles within this size range.

Correlation between anisotropy and lattice distortions in single crystal calcite nanowires grown in confinement.

Growing nanostructures in confinement allows for the control of their shape, size and structure, as required in many technological applications. We investigated the crystal structure and morphology of calcite nanowires, precipitated in the pores of track-etch membranes, by employing transmission electron microscopy and selected area electron diffraction (SAED). The data showed that the nanowires show no preferred growth orientation and that the crystallographic orientation rotated along the length of the nanowire, with lattice rotation angles of several degrees per micrometer. Finite element calculations indicated that the rotation is caused by the anisotropic crystallographic nature of the calcite mineral, the nanoscale diameter of the wires and the confined space provided by the membrane pore. This phenomenon should also be observed in other single crystal nanowires made from anisotropic materials, which could offer the potential of generating nanostructures with tailored optical, electronic and mechanical properties.

Adhesion of sodium dodecyl sulfate surfactant monolayers with TiO(2) (rutile and anatase) surfaces.

Surfactants are widely used as templates to control the nucleation and growth of nanostructured metal oxides such as titania. To gain insight into the origin of the surfactant-titania interactions responsible for polymorph and orientation selection, we simulate the self-assembly of an anionic surfactant monolayer on various low-index titania surfaces, for a range of densities. We characterize the binding in each case and compute the adhesion energies, finding anatase (100) and rutile (110) to be the strongest-binding surfaces. The sodium counterions in the monolayer are found to dominate the adhesion. It is also observed that the assembly is directed predominantly by surface-monolayer electrostatic complementarity. Incorporating water displacement into the calculations does not alter the general findings but does cause the adhesion energies to fall within a smaller range.

Accelerating Bayesian hierarchical clustering of time series data with a randomised algorithm.

We live in an era of abundant data. This has necessitated the development of new and innovative statistical algorithms to get the most from experimental data. For example, faster algorithms make practical the analysis of larger genomic data sets, allowing us to extend the utility of cutting-edge statistical methods. We present a randomised algorithm that accelerates the clustering of time series data using the Bayesian Hierarchical Clustering (BHC) statistical method. BHC is a general method for clustering any discretely sampled time series data. In this paper we focus on a particular application to microarray gene expression data. We define and analyse the randomised algorithm, before presenting results on both synthetic and real biological data sets. We show that the randomised algorithm leads to substantial gains in speed with minimal loss in clustering quality. The randomised time series BHC algorithm is available as part of the R package BHC, which is available for download from Bioconductor (version 2.10 and above) via http://bioconductor.org/packages/2.10/bioc/html/BHC.html. We have also made available a set of R scripts which can be used to reproduce the analyses carried out in this paper. These are available from the following URL. https://sites.google.com/site/randomisedbhc/.

Bayesian hierarchical clustering for microarray time series data with replicates and outlier measurements.

BACKGROUND: Post-genomic molecular biology has resulted in an explosion of data, providing measurements for large numbers of genes, proteins and metabolites. Time series experiments have become increasingly common, necessitating the development of novel analysis tools that capture the resulting data structure. Outlier measurements at one or more time points present a significant challenge, while potentially valuable replicate information is often ignored by existing techniques. RESULTS: We present a generative model-based Bayesian hierarchical clustering algorithm for microarray time series that employs Gaussian process regression to capture the structure of the data. By using a mixture model likelihood, our method permits a small proportion of the data to be modelled as outlier measurements, and adopts an empirical Bayes approach which uses replicate observations to inform a prior distribution of the noise variance. The method automatically learns the optimum number of clusters and can incorporate non-uniformly sampled time points. Using a wide variety of experimental data sets, we show that our algorithm consistently yields higher quality and more biologically meaningful clusters than current state-of-the-art methodologies. We highlight the importance of modelling outlier values by demonstrating that noisy genes can be grouped with other genes of similar biological function. We demonstrate the importance of including replicate information, which we find enables the discrimination of additional distinct expression profiles. CONCLUSIONS: By incorporating outlier measurements and replicate values, this clustering algorithm for time series microarray data provides a step towards a better treatment of the noise inherent in measurements from high-throughput genomic technologies. Timeseries BHC is available as part of the R package 'BHC' (version 1.5), which is available for download from Bioconductor (version 2.9 and above) via http://www.bioconductor.org/packages/release/bioc/html/BHC.html?pagewanted=all.