The role of pressure and defects in the wurtzite to rock salt transition in cadmium selenide.

Using molecular dynamics and path sampling techniques we investigated the effect of pressure and defects in the wurtzite to rock salt transition in cadmium selenide (CdSe). In the pressure range 2-10 GPa, rate constants of transition are in the order of 10-23 to 105 s-1 for the transformation of a relatively small wurtzite crystal consisting of 1024 atoms with periodic boundary conditions. The transition paths predominantly evolve through an intermediate 5-coordinated structure, as reported before, though its typical lifetime within the transition paths is particularly long in the intermediate pressure range (4-6 GPa). The defects were created by removing Cd-Se pairs from an otherwise perfect crystal. The removals were either selected fully randomized or grouped in clusters (cavity creation). We find that the rate of transition due to the defects increases by several orders of magnitude even for a single pair removal. This is caused by a change in the transition mechanism that no longer proceeds via the intermediate 5-coordinated structure, when defects are present. Further, the cavity creation yields a lower rate than the fully randomized removal.

Precursors of fluidisation in the creep response of a soft glass.

Via extensive numerical simulations, we study the fluidisation process of dense amorphous materials subjected to an external shear stress, using a three-dimensional colloidal glass model. In order to disentangle possible boundary effects from finite size effects in the process of fluidisation, we implement a novel geometry-constrained protocol with periodic boundary conditions. We show that this protocol is well controlled and that the longtime fluidisation dynamics is, to a great extent, independent of the details of the protocol parameters. Our protocol, therefore, provides an ideal tool to investigate the bulk dynamics prior to yielding and to study finite size effects regarding the fluidisation process. Our study reveals the existence of precursors to fluidisation observed as a peak in the strain-rate fluctuations, that allows for a robust definition of a fluidisation time. Although the exponents in the power-law creep dynamics seem not to depend significantly on the system size, we reveal strong finite size effects for the onset of fluidisation.

Foundations and latest advances in replica exchange transition interface sampling.

Nearly 20 years ago, transition path sampling (TPS) emerged as an alternative method to free energy based approaches for the study of rare events such as nucleation, protein folding, chemical reactions, and phase transitions. TPS effectively performs Monte Carlo simulations with relatively short molecular dynamics trajectories, with the advantage of not having to alter the actual potential energy surface nor the underlying physical dynamics. Although the TPS approach also introduced a methodology to compute reaction rates, this approach was for a long time considered theoretically attractive, providing the exact same results as extensively long molecular dynamics simulations, but still expensive for most relevant applications. With the increase of computer power and improvements in the algorithmic methodology, quantitative path sampling is finding applications in more and more areas of research. In particular, the transition interface sampling (TIS) and the replica exchange TIS (RETIS) algorithms have, in turn, improved the efficiency of quantitative path sampling significantly, while maintaining the exact nature of the approach. Also, open-source software packages are making these methods, for which implementation is not straightforward, now available for a wider group of users. In addition, a blooming development takes place regarding both applications and algorithmic refinements. Therefore, it is timely to explore the wide panorama of the new developments in this field. This is the aim of this article, which focuses on the most efficient exact path sampling approach, RETIS, as well as its recent applications, extensions, and variations.

Light propagation in two-dimensional and three-dimensional slabs of reflective colloidal particles in solution: The effect of interfaces and interparticle correlations.

The propagation of light across 2D and 3D slabs of reflective colloidal particles in a fluidlike state has been investigated by simulation. The colloids are represented as hard spheres with and without an attractive square-well tail. Representative configurations of particles have been generated by Monte Carlo. The path of rays entering the slab normal to its planar surface has been determined by exact geometric scattering conditions, assuming that particles are macroscopic spheres fully reflective at the surface of their hard-core potential. The analysis of light paths provides the transmission and reflection coefficients, the mean-free path, the average length of transmitted and reflected paths, the distribution of scattering events across the slab, the angular spread of the outcoming rays as a function of dimensionality, and thermodynamic state. The results highlight the presence of a sizable population of very long paths, which play an important role in random lasing from solutions of metal particles in an optically active fluid. The output power spectrum resulting from the stimulated emission amplification decays asymptotically as an inverse power law. The present study goes beyond the standard approach based on a random walk confined between two planar interfaces and parametrized in terms of the mean-free path and scattering matrix. Here, instead, the mean-free path, the correlation among scattering events, and memory effects are not assumed a priori, but emerge from the underlying statistical mechanics model of interacting particles. In this way the dependence of properties on the thermodynamic state, the effect of particle-particle and particle-interface correlations and of spatial inhomogeneity, and memory effects are accounted for in a transparent way. Moreover, the approach joins smoothly the ballistic regime of light propagation at low density with the diffusive regime at high density of scattering centers. These properties are exploited to investigate the effect of weak polydispersivity and of large density fluctuations at the critical point of the model with the attractive potential tail.

Confounding the paradigm: peculiarities of amyloid fibril nucleation.

Fibrils of amyloid proteins are currently of great interest because of their involvement in various amyloid-related diseases and nanotechnological products. In a recent kinetic Monte Carlo simulation study (Cabriolu, R.; Kashchiev, D.; Auer, S. J. Chem. Phys.2012, 137, 204903), we found that our simulation data for the rate of amyloid fibril nucleation occurring by direct polymerization of monomeric protein could not be described adequately by nucleation theory. It turned out that the process occurred in a peculiar way, thus confounding the nucleation paradigm and demanding a new theoretical treatment. In the present study, we reconsider the theoretical approach to nucleation of amyloid fibrils and derive new expressions for the stationary rate of the process. As these expressions provide a remarkably good description of the simulation data, by using them we propose a theoretical dependence of the amyloid-ß(40) fibril nucleation rate on the concentration of monomeric protein in the solution. This dependence reveals the existence of a threshold concentration below which the fibril nucleation in small enough solution volumes is practically arrested, and above which the process occurs vigorously, because then each monomeric protein in the solution acts as fibril nucleus. The presented expressions for the threshold concentration and for the dependence of the fibril nucleation rate on the concentration of monomeric protein can be a valuable guide in designing new therapeutic and/or technological strategies for prevention or stimulation of amyloid fibril formation.

Effect of Organic Ions on The Formation and Collapse of Nanometric Bubbles in Ionic Liquid/Water Solutions: A Molecular Dynamics Study.

Molecular dynamics simulation is applied to investigate the effect of two ionic liquids (IL) on the nucleation and growth of (nano)cavities in water under tension and on the cavities' collapse following the release of tension. Simulations of the same phenomena in two pure water samples of different sizes are carried out for comparison. The first IL, i.e., tetra-ethylammonium mesylate ([Tea][Ms]), is relatively hydrophilic and its addition to water at 25 wt % concentration decreases its tendency to nucleate cavities. Apart from quantitative details, cavity formation and collapse are similar to those taking place in water and qualitatively follow the Rayleigh-Plesset (RP) equation. The second IL, i.e., tetrabutyl phosphonium 2,4-dimethylbenzenesulfonate ([P4444][DMBS]), is amphiphilic and forms nanostructured solutions with water. At 25 wt % concentrations, [P4444][DMBS] favors the nucleation of bubbles that tend to form at the interface between water-rich and IL-rich domains. Cavity collapse in [P4444][DMBS]/water solutions are greatly hindered by a shell of ions decorating the interface between the solution and the vapor phase. A similar effect is observed for the equilibration of a population of bubbles of different sizes. The drastic slowing down of the bubbles' relaxation processes suggests ways to produce long-lived nanometric cavities in the liquid phase that could be useful for nanotechnology and drug delivery.

Breakdown of nucleation theory for crystals with strongly anisotropic interactions between molecules.

We study the nucleation of model two-dimensional crystals in order to gain insight into the effect of anisotropic interactions between molecules on the stationary nucleation rate J. With the aid of kinetic Monte Carlo simulations, we determine J as a function of the supersaturation s. It turns out that with increasing degree of interaction anisotropy the dependence of ln J on s becomes step-like, with jumps at certain s values. We show that this J(s) dependence cannot be described by the classical and atomistic nucleation theories. A formula that predicts the identified J(s) behavior is yet to be derived and verified, and the present study provides the necessary data and understanding for doing that.

Effects of Degrees of Freedom on Calculating Diffusion Properties in Nanoporous Materials.

If one carries out a molecular simulation of N particles using periodic boundary conditions, linear momentum is conserved, and hence, the number of degrees of freedom is set to 3N - 3. In most programs, this number of degrees of freedom is the default setting. However, if one carries out a molecular simulation in an external field, one needs to ensure that degrees of freedom are changed from this default setting to 3N, as in an external field the velocity of the center of mass can change. Using the correct degrees of freedom is important in calculating the temperature and in some algorithms to simulate at constant temperature. For sufficiently large systems, the difference between 3N and 3N - 3 is negligible. However, there are systems in which the comparison with experimental data requires molecular dynamics simulations of a small number of particles. In this work, we illustrate the effect of an incorrect setting of degrees of freedom in molecular dynamic simulations studying the diffusion properties of guest molecules in nanoporous materials. We show that previously published results have reported a surprising diffusion dependence on the loading, which could be traced back to an incorrect setting of the degrees of freedom. As the correct settings are convoluted and counterintuitive in some of the most commonly used molecular dynamics programs, we carried out a systematic study on the consequences of the various commonly used (incorrect) settings. Our conclusion is that for systems smaller than 50 particles the results are most likely unreliable as these are either performed at an incorrect temperature or the temperature is incorrectly used in some of the results. Furthermore, a novel and efficient method to calculate diffusion coefficients of guest molecules into nanoporous materials at zero-loading conditions is introduced.

Size distribution of amyloid nanofibrils.

We consider the size distribution of amyloid nanofibrils (protofilaments) in nucleating protein solutions when the nucleation process occurs by the mechanism of direct polymerization of ß-strands (extended peptides or protein segments) into ß-sheets. Employing the atomistic nucleation theory, we derive a general expression for the stationary size distribution of amyloid nanofibrils constituted of successively layered ß-sheets. The application of this expression to amyloid ß(1-40) (Aß(40)) fibrils allows us to determine the nanofibril size distribution as a function of the protein concentration and temperature. The distribution is most remarkable with its exhibiting a series of peaks positioned at "magic" nanofibril sizes (or lengths), which are due to deep local minima in the work for fibril formation. This finding of magic sizes or lengths is consistent with experimental results for the size distribution of aggregates in solutions of Aß(40) proteins. Also, our approach makes it possible to gain insight into the effect of point mutations on the nanofibril size distribution, an effect that may play a role in experimentally observed substantial differences in the fibrillation lag-time of wild-type and point-mutated amyloid-ß proteins.

Atomistic theory of amyloid fibril nucleation.

We consider the nucleation of amyloid fibrils at the molecular level when the process takes place by a direct polymerization of peptides or protein segments into ß-sheets. Employing the atomistic nucleation theory (ANT), we derive a general expression for the work to form a nanosized amyloid fibril (protofilament) composed of successively layered ß-sheets. The application of this expression to a recently studied peptide system allows us to determine the size of the fibril nucleus, the fibril nucleation work, and the fibril nucleation rate as functions of the supersaturation of the protein solution. Our analysis illustrates the unique feature of ANT that the size of the fibril nucleus is a constant integer in a given supersaturation range. We obtain the ANT nucleation rate and compare it with the rates determined previously in the scope of the classical nucleation theory (CNT) and the corrected classical nucleation theory (CCNT). We find that while the CNT nucleation rate is orders of magnitude greater than the ANT one, the CCNT and ANT nucleation rates are in very good quantitative agreement. The results obtained are applicable to homogeneous nucleation, which occurs when the protein solution is sufficiently pure and/or strongly supersaturated.

Ice nucleation on carbon surface supports the classical theory for heterogeneous nucleation.

The prevalence of heterogeneous nucleation in nature was explained qualitatively by the classical theory for heterogeneous nucleation established over more than 60 years ago, but the quantitative validity and the key conclusions of the theory have remained unconfirmed. Employing the forward flux sampling method and the coarse-grained water model (mW), we explicitly computed the heterogeneous ice nucleation rates in the supercooled water on a graphitic surface at various temperatures. The independently calculated ice nucleation rates were found to fit well according to the classical theory for heterogeneous nucleation. The fitting procedure further yields the estimate of the potency factor, which measures the ratio of the heterogeneous nucleation barrier to the homogeneous nucleation barrier. Remarkably, the estimated potency factor agrees quantitatively with the volumetric ratio of the critical nuclei between the heterogeneous and homogeneous nucleation. Our numerical study thus provides a strong support to the quantitative power of the theory and allows understanding ice nucleation behaviors under the most relevant freezing conditions.

Amyloid fibrillation kinetics: insight from atomistic nucleation theory.

We consider the nucleation of nanosized amyloid fibrils composed of successively layered ß-sheets at the molecular level when this process takes place by direct polymerization of protein segments (ß-strands) into ß-sheets. Application of the atomistic nucleation theory (ANT) to amyloid nucleation of ß(2)-microglobulin and amyloid ß(40) allows us to predict the fibril nucleus size and the fibril nucleation rate as functions of the supersaturation of the protein solution. The ANT predictions are compared to recent time-resolved optical experiments where they measure the effect of the protein concentration and mutations on the initial lag time before amyloid fibrils form in the protein solution. The presented analysis reveals the general principles underlying the nucleation kinetics of nanosized amyloid fibrils and indicates that it can be treated in the framework of existing general theories of the nucleation of new phases.