Free energy barriers from biased molecular dynamics simulations.

Atomistic simulation methods for the quantification of free energies are in wide use. These methods operate by sampling the probability density of a system along a small set of suitable collective variables (CVs), which is, in turn, expressed in the form of a free energy surface (FES). This definition of the FES can capture the relative stability of metastable states but not that of the transition state because the barrier height is not invariant to the choice of CVs. Free energy barriers therefore cannot be consistently computed from the FES. Here, we present a simple approach to calculate the gauge correction necessary to eliminate this inconsistency. Using our procedure, the standard FES as well as its gauge-corrected counterpart can be obtained by reweighing the same simulated trajectory at little additional cost. We apply the method to a number of systems-a particle solvated in a Lennard-Jones fluid, a Diels-Alder reaction, and crystallization of liquid sodium-to demonstrate its ability to produce consistent free energy barriers that correctly capture the kinetics of chemical or physical transformations, and discuss the additional demands it puts on the chosen CVs. Because the FES can be converged at relatively short (sub-ns) time scales, a free energy-based description of reaction kinetics is a particularly attractive option to study chemical processes at more expensive quantum mechanical levels of theory.

Effects of CO2 adsorption on proton migration on a hydrated ZrO2 surface: an ab initio molecular dynamics study.

Hydration reactions on a carbonate-terminated cubic ZrO2(110) surface were analyzed using ab initio molecular dynamics (AIMD) simulations. After hydration reactions, carbonates were still present on the surface at 500 K. However, these carbonates are very weak conjugate bases and only act as steric hindrance in proton hopping processes between acidic chemisorbed H2O molecules (Zr-OH2) and monodentate hydroxyl groups (Zr-OH-). Similar to a carbonate-free hydrated surface, Zr-OH2, Zr-OH-, and polydentate hydroxyl groups ([double bond splayed left]OH+) were observed, while the ratio of acidic Zr-OH2 was significantly larger than that on the carbonate-free hydrated surface. A thermodynamic discussion and bond property analysis reveal that CO2 adsorption significantly decreases the basicity of surface oxide ions ([double bond splayed left]O), whereas the acidity of Zr-OH2 is not affected. As a result, protons released from [double bond splayed left]OH+ react with Zr-OH- to form Zr-OH2, leading to a deficiency of proton acceptor sites, which decreases the proton conductivity by the hopping mechanism.

Predicting long-term trends in physical properties from short-term molecular dynamics simulations using long short-term memory.

This study proposes a novel long short-term memory (LSTM)-based model for predicting future physical properties based on partial data of molecular dynamics (MD) simulation. It extracts latent vectors from atomic coordinates of MD simulations using graph convolutional network, utilizes LSTM to learn temporal trends in latent vectors and make one-step-ahead predictions of physical properties through fully connected layers. Validating with MD simulations of Ni solid-liquid systems, the model achieved accurate one-step-ahead prediction for time variation of the potential energy during solidification and melting processes using residual connections. Recursive use of predicted values enabled long-term prediction from just the first 20 snapshots of the MD simulation. The prediction has captured the feature of potential energy bending at low temperatures, which represents completion of solidification, despite that the MD data in short time do not have such a bending characteristic. Remarkably, for long-time prediction over 900 ps, the computation time was reduced to 1/700th of a full MD simulation of the same duration. This approach has shown the potential to significantly reduce computational cost for prediction of physical properties by efficiently utilizing the data of MD simulation.

Predicting materials properties with generative models: applying generative adversarial networks for heat flux generation.

In the realm of materials science, the integration of machine learning techniques has ushered in a transformative era. This study delves into the innovative application of generative adversarial networks (GANs) for generating heat flux data, a pivotal step in predicting lattice thermal conductivity within metallic materials. Leveraging GANs, this research explores the generation of meaningful heat flux data, which has a high degree of similarity with that calculated by molecular dynamics simulations. This study demonstrates the potential of artificial intelligence (AI) in understanding the complex physical meaning of data in materials science. By harnessing the power of such AI to generate data that is previously attainable only through experiments or simulations, new opportunities arise for exploring and predicting properties of materials.

Molecular Dynamics Simulation of Adhesion of Additive Molecules in Paint Materials toward Enhancement of Anticorrosion Performance.

Adsorption energies of additive molecules in paint materials on the iron oxide substrate are investigated by molecular dynamics (MD) simulations to find the key feature of adhesion, which is one of the indispensable elements for the corrosion resistance of coated materials. Both edge-on and face-on adsorptions are observed for most additive molecules such as phenylsuccinic acid and benzoic acid. On the other hand, only the edge-on adsorption is observed for the specific molecule having a benzothiazole ring due to the effect of steric conformation. The largest adsorption energy per functional group is observed for two nitrogen atoms in the thiazole ring and amino group, which influences the relationship between face-on and edge-on adsorption energies. Moreover, a correlation analysis using RDKit descriptors is performed to discuss the dominant factor for the adsorption energy of additive molecules. The descriptor for the magnitude of partial charge relative to the molecular surface area and the one for the topological polar surface area have the largest correlation with the adsorption energy of the target molecules. It is significant in this study to extract key factors that contribute to molecular adhesion through MD simulations in combination with correlation analysis using RDKit descriptors. This study is a good example of the computer-assisted design of new paint materials.

Fast-Decoding Algorithm for Electrode Processes at Electrified Interfaces by Mean-Field Kinetic Model and Bayesian Data Assimilation: An Active-Data-Mining Approach for the Efficient Search and Discovery of Electrocatalysts.

The microscopic origins of the activity and selectivity of electrocatalysts has been a long-lasting enigma since the 19th century. By applying an active-data-mining approach, employing a mean-field kinetic model and a statistical approach of Bayesian data assimilation, we demonstrate here a fast decoding to extract key properties in the kinetics of complicated electrode processes from current-potential profiles in experimental and literary data. As the proof-of-concept, kinetic parameters on the four-electron oxygen reduction reaction in the 0.1 M HClO4 solution (ORR: O2 + 4e- + 4H+ → 2H2O) of various platinum-based single-crystal electrocatalysts are extracted from our own experiments and third-party literature to investigate the microscopic electrode processes. Furthermore, data assimilation of the mean-field ORR model and experimental data is performed based on Bayesian inference for the inductive estimation of kinetic parameters, which sheds light on the dynamic behavior of kinetic parameters with respect to overpotential. This work shows that a fast-decoding algorithm based on a mean-field kinetic model and Bayesian data assimilation is a promising data-driven approach to extract key microscopic features of complicated electrode processes and therefore will be an important method toward building up advanced human-machine collaborations for the efficient search and discovery of high-performance electrochemical materials.

Ultrastrong underwater adhesion on diverse substrates using non-canonical phenolic groups.

Robust underwater adhesion is challenging because a hydration layer impedes the interaction between substrates and adhesives. Phenolic adhesives inspired by marine creatures such as mussels were extensively studied, but these adhesives have not reached the adhesion strength and substrate diversity of Man-made dry adhesives. Here, we report a class of ultrastrong underwater adhesives with molecular phenolic designs extending beyond what nature has produced. These non-canonical phenolic polymers show versatile adhesion on various materials, with adhesion strengths exceeding 10 MPa on metal. Incorporating even just a small amount (<10%) of non-canonical phenolic groups into a polymer is sufficient for dramatically enhancing underwater adhesion, suggesting that this new class of phenolic materials will be incorporated into various industrial polymer systems in the future.

Free energy surface of initial cap formation in carbon nanotube growth.

Initial cap formation is an important process of carbon nanotube (CNT) growth where a hexagonal carbon network is lifted off from the catalyst surface. In this study, free energy surface (FES) of initial cap formation in the CNT growth is investigated by metadynamics simulation. A two-dimensional collective variable (CV) space is newly developed to examine the complicated formation process of the cap structure, which consists of the formation of a hexagonal carbon network and lift-off of the network from the catalyst surface. States before and after the lift-off of the carbon network are clearly distinguished in the two-dimensional FES. Therefore, free energy difference before and after the lift-off can be directly derived from the two-dimensional FES. It was revealed that the cap structure is stable at a high temperature due to the entropy effect, while the carbon network covering the catalyst surface is energetically stable. The new insight in this study is achieved owing to metadynamics simulation in conjunction with a newly developed two-dimensional CV space since it is impossible to explore FES for such complicated processes in the framework of conventional molecular dynamics simulation.

Bayesian Data Assimilation of Temperature Dependence of Solid-Liquid Interfacial Properties of Nickel.

Temperature dependence of solid-liquid interfacial properties during crystal growth in nickel was investigated by ensemble Kalman filter (EnKF)-based data assimilation, in which the phase-field simulation was combined with atomic configurations of molecular dynamics (MD) simulation. Negative temperature dependence was found in the solid-liquid interfacial energy, the kinetic coefficient, and their anisotropy parameters from simultaneous estimation of four parameters. On the other hand, it is difficult to obtain a concrete value for the anisotropy parameter of solid-liquid interfacial energy since this factor is less influential for the MD simulation of crystal growth at high undercooling temperatures. The present study is significant in shedding light on the high potential of Bayesian data assimilation as a novel methodology of parameter estimation of practical materials an out of equilibrium condition.

Non-classical nucleation in vapor-liquid-solid growth of monolayer WS2 revealed by in-situ monitoring chemical vapor deposition.

The very early nucleation stage of a transition metal dichalcogenide (TMD) was directly observed with in-situ monitoring of chemical vapor deposition and automated image analysis. Unique nucleation dynamics, such as very large critical nuclei and slow to rapid growth transitions, were observed during the vapor-liquid-solid (VLS) growth of monolayer tungsten disulfide (WS2). This can be explained by two-step nucleation, also known as non-classical nucleation, in which metastable clusters are formed through the aggregation of droplets. Subsequently, nucleation of solid WS2 takes place inside the metastable cluster. Furthermore, the detailed nucleation dynamics was systematically investigated from a thermodynamic point of view, revealing that the incubation time of metastable cluster formation follows the traditional time-temperature transformation diagram. Quantitative phase field simulation, combined with Bayesian inference, was conducted to extract quantitative information on the growth dynamics and crystal anisotropy from in-situ images. A clear transition in growth dynamics and crystal anisotropy between the slow and rapid growth phases was quantitatively verified. This observation supports the existence of two-step nucleation in the VLS growth of WS2. Such detailed understanding of TMD nucleation dynamics can be useful for achieving perfect structure control of TMDs.

Phase transition in substrate-supported molybdenum nanoparticles: a molecular dynamics study.

The phase transition between liquid and solid phases of substrate-supported molybdenum nanoparticles with size ranging from 2000 to 16,000 atoms was investigated using molecular dynamics simulation. The effect of the interaction energy between the nanoparticle and the substrate on the contact angle, melting point and nucleation temperature was focused on. Unidirectional solidification and inward melting after surface melting were observed in the substrate-supported nanoparticles during cooling and heating, respectively. The depression of the melting point from the bulk melting point was proportional to the inverse of the effective radius of the substrate-supported nanoparticles. The gradient of proportionality increased with decreasing contact angle and deviated from that of freestanding nanoparticles. On the other hand, the undercooling temperature for solidification decreased with decreasing contact angle, which agrees with the theory of heterogeneous nucleation.

Bayesian inference of solid-liquid interfacial properties out of equilibrium.

Solid-liquid interfacial properties out of equilibrium provide the essential information required for understanding and controlling solidification microstructures in metallic materials. However, few studies have attempted to reveal all interfacial properties out of equilibrium in detail. The present study proposes an approach for simultaneously estimating all interfacial properties in a pure metal below the melting point on the basis of the Bayesian inference theory. The solid-liquid interfacial energy, interfacial mobility, and anisotropy parameters in pure Fe are estimated by combining molecular dynamics simulation with phase-field simulation using an ensemble Kalman filter, which is a data assimilation technique. Furthermore, the temperature dependences of all interfacial parameters are computed and discussed. In summary, the proposed multiscale approach integrates atomistic and microstructural simulations within the framework of data science and it has considerable potential for a wide variety of applications in materials engineering.

A multiscale approach for modeling the early stage growth of single and multiwall carbon nanotubes produced by a metal-catalyzed synthesis process.

A parametrized mesoscale model for the early stage growth of isolated single or multiwall carbon nanotubes (CNTs) has been developed in order to investigate the effects of metal catalyst particle size and composition on CNT growth mechanism during synthesis via a substrate-supported, catalytic chemical vapor deposition process. The model is based on a coarse-grained graphene sheet, represented by a two-dimensional simply connected triangular mesh, with parameters for the surface curvature, bond stretching, carbon-carbon interaction, and carbon-catalyst interaction determined by classical molecular dynamics simulations using a bond-order potential derived from ab initio calculations. The mesoscale simulations show that the initial type of CNT growth is strongly influenced by the surface interaction energy between the graphene sheet and metal catalyst particle, rate of carbon deposition, and particle size. As expected, single wall tubes are produced from small catalyst particles at low deposition rates, but increasing the strength of carbon-catalyst interaction energy or carbon deposition rate results in double or even multiwall CNT structures, formed by folding or involution of the graphene sheet. For the range of model parameters investigated, all single wall CNTs with a diameter greater than 6.6 nm exhibited a kink-collapse transition once a certain critical tube length was reached.

Direction control of chemical wave propagation in self-oscillating gel array.

A chemomechanical actuator utilizing a reaction-diffusion wave across gap junction was constructed toward a novel mircoconveyer by micropatterned self-oscillating gel array. Unidirectional propagation of the chemical wave of the Belousov-Zhabotinsky (BZ) reaction was induced on gel arrays. In the case of using a triangle-shaped gel as an element of the array, the chemical wave propagated from the corner side of the triangle gel to the plane side of the other gel (C-to-P) across the gap junction, whereas it propagated from the plane side to the corner side (P-to-C) in the case of the pentagonal gel array. Numerical analysis based on the Keener-Tyson model was done for understanding the mechanism of unidirectional propagation in triangle and pentagonal gel arrays. The swelling and deswelling changes of the gels followed the unidirectional propagation of the chemical wave.

A molecular dynamics study of the phase transition in bcc metal nanoparticles.

The phase transition between liquid and solid phases in body-centered cubic (bcc) metal nanoparticles of iron, chromium, molybdenum, and tungsten with size ranging from 2000 to 31,250 atoms was investigated using a molecular dynamics simulation. The nucleation from an undercooled liquid droplet was observed during cooling in all nanoparticles considered. It was found that a nucleus was generated near one side of the particle and solidification spread toward the other side the during nucleation process. On the other hand, the surface melting and subsequent inward melting of the solid core of the nanoparticles were observed during heating. The depression of the melting point was proportional to the inverse of the particle radius due to the Gibbs-Thomson effect. On the other hand, the depression of the nucleation temperature during cooling was not monotonic with respect to the particle radius since the nucleation from an undercooled liquid depends on the event probability of an embryo or a nucleus.

Variational formulation of a quantitative phase-field model for nonisothermal solidification in a multicomponent alloy.

A variational formulation of a quantitative phase-field model is presented for nonisothermal solidification in a multicomponent alloy with two-sided asymmetric diffusion. The essential ingredient of this formulation is that the diffusion fluxes for conserved variables in both the liquid and solid are separately derived from functional derivatives of the total entropy and then these fluxes are related to each other on the basis of the local equilibrium conditions. In the present formulation, the cross-coupling terms between the phase-field and conserved variables naturally arise in the phase-field equation and diffusion equations, one of which corresponds to the antitrapping current, the phenomenological correction term in early nonvariational models. In addition, this formulation results in diffusivities of tensor form inside the interface. Asymptotic analysis demonstrates that this model can exactly reproduce the free-boundary problem in the thin-interface limit. The present model is widely applicable because approximations and simplifications are not formally introduced into the bulk's free energy densities and because off-diagonal elements of the diffusivity matrix are explicitly taken into account. Furthermore, we propose a nonvariational form of the present model to achieve high numerical performance. A numerical test of the nonvariational model is carried out for nonisothermal solidification in a binary alloy. It shows fast convergence of the results with decreasing interface thickness.

Preferential synthesis of (6,4) single-walled carbon nanotubes by controlling oxidation degree of Co catalyst.

Chirality-selective synthesis of single-walled carbon nanotubes (SWNTs) has been a research goal for the last two decades and is still challenging due to the difficulty in controlling the atomic structure in the one-dimensional material. Here, we develop an optimized approach for controlling the chirality of species by tuning the oxidation degree of Co catalyst. Predominant synthesis of (6,4) SWNTs is realized for the first time. The detailed mechanism is investigated through a systematic experimental study combined with first-principles calculations, revealing that the independent control of tube diameter and chiral angle achieved by changing the binding energy between SWNTs (cap and tube edge) and catalyst causes a drastic transition of chirality of SWNTs from (6,5) to (6,4). Since our approach of independently controlling the diameter and chiral angle can be applied to other chirality species, our results can be useful in achieving the on-demand synthesis of specific-chirality SWNTs.

Heterogeneity in homogeneous nucleation from billion-atom molecular dynamics simulation of solidification of pure metal.

Can completely homogeneous nucleation occur? Large scale molecular dynamics simulations performed on a graphics-processing-unit rich supercomputer can shed light on this long-standing issue. Here, a billion-atom molecular dynamics simulation of homogeneous nucleation from an undercooled iron melt reveals that some satellite-like small grains surrounding previously formed large grains exist in the middle of the nucleation process, which are not distributed uniformly. At the same time, grains with a twin boundary are formed by heterogeneous nucleation from the surface of the previously formed grains. The local heterogeneity in the distribution of grains is caused by the local accumulation of the icosahedral structure in the undercooled melt near the previously formed grains. This insight is mainly attributable to the multi-graphics processing unit parallel computation combined with the rapid progress in high-performance computational environments.Nucleation is a fundamental physical process, however it is a long-standing issue whether completely homogeneous nucleation can occur. Here the authors reveal, via a billion-atom molecular dynamics simulation, that local heterogeneity exists during homogeneous nucleation in an undercooled iron melt.

Variational formulation and numerical accuracy of a quantitative phase-field model for binary alloy solidification with two-sided diffusion.

We present the variational formulation of a quantitative phase-field model for isothermal low-speed solidification in a binary dilute alloy with diffusion in the solid. In the present formulation, cross-coupling terms between the phase field and composition field, including the so-called antitrapping current, naturally arise in the time evolution equations. One of the essential ingredients in the present formulation is the utilization of tensor diffusivity instead of scalar diffusivity. In an asymptotic analysis, it is shown that the correct mapping between the present variational model and a free-boundary problem for alloy solidification with an arbitrary value of solid diffusivity is successfully achieved in the thin-interface limit due to the cross-coupling terms and tensor diffusivity. Furthermore, we investigate the numerical performance of the variational model and also its nonvariational versions by carrying out two-dimensional simulations of free dendritic growth. The nonvariational model with tensor diffusivity shows excellent convergence of results with respect to the interface thickness.

Wafer-scale fabrication and growth dynamics of suspended graphene nanoribbon arrays.

Adding a mechanical degree of freedom to the electrical and optical properties of atomically thin materials can provide an excellent platform to investigate various optoelectrical physics and devices with mechanical motion interaction. The large scale fabrication of such atomically thin materials with suspended structures remains a challenge. Here we demonstrate the wafer-scale bottom-up synthesis of suspended graphene nanoribbon arrays (over 1,000,000 graphene nanoribbons in 2 × 2 cm(2) substrate) with a very high yield (over 98%). Polarized Raman measurements reveal graphene nanoribbons in the array can have relatively uniform-edge structures with near zigzag orientation dominant. A promising growth model of suspended graphene nanoribbons is also established through a comprehensive study that combined experiments, molecular dynamics simulations and theoretical calculations with a phase-diagram analysis. We believe that our results can contribute to pushing the study of graphene nanoribbons into a new stage related to the optoelectrical physics and industrial applications.