Self-assembly of twisted,multi-sheet aggregates

ABSTRACT

Hierarchical self-assembly underpins much of the diversity of form and function seen in soft systems, yet the pathways by which they achieve their final form are not always straightforward – intermediate steps, kinetic effects and finite sizes of aggregates all influence the self-assembly pathways of these systems. In this paper, we use molecular dynamics simulations of binary mixtures of spheres and ellipsoidal discs to investigate the self-assembly of anisotropic aggregates with internal structures. Through this, the full aggregation pathways of spontaneously chiral, multi-bilayer and multi-layer assemblies have been tracked and characterised via a semi-qualitative analysis. This includes the unambiguous identification of first-, second- and third-generation hierarchical assemblies within a single simulation. Given the significant challenge of tracking full aggregation pathways in experimental systems, our findings strongly support the notion that molecular simulation has much to contribute to improving our understanding of hierarchical self-assembling systems.     

Molecular simulation of chemical reaction equilibria by Kinetic Monte Carlo

ABSTRACT

We describe a new algorithm for the molecular simulation of chemical reaction equilibria, which we call the Reactive Kinetic Monte Carlo (ReKMC) algorithm. It is based on the use of the equilibrium Kinetic Monte Carlo (eKMC) method (Ustinov et al., J. Colloid Interface Sci., 2012, 366, 216–223) to generate configurations in the underlying nonreacting system and to calculate the species chemical potentials at essentially zero marginal computational cost. We consider in detail the typical case of specified temperature, T and pressure, P, but extensions to other thermodynamic constraints are straightforward in principle. In the course of this work, we also demonstrate an alternative method for calculating simulation box volume changes in NPT ensemble simulations to achieve the specified P. We consider two sets of example reacting systems previously considered in the literature, and compare the ReKMC results and computational efficiencies with those of different implementations of the REMC algorithm (Turner et al., Molec. Simulation, 2008, 34, 119–146).     

Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview

Here, we review the basic concepts and applications of the phase-field-crystal (PFC) method, which is one of the latest simulation methodologies in materials science for problems, where atomic- and microscales are tightly coupled. The PFC method operates on atomic length and diffusive time scales, and thus constitutes a computationally efficient alternative to molecular simulation methods. Its intense development in materials science started fairly recently following the work by Elder et al. [Phys. Rev. Lett. 88 (2002), p. 245701]. Since these initial studies, dynamical density functional theory and thermodynamic concepts have been linked to the PFC approach to serve as further theoretical fundamentals for the latter. In this review, we summarize these methodological development steps as well as the most important applications of the PFC method with a special focus on the interaction of development steps taken in hard and soft matter physics, respectively. Doing so, we hope to present today's state of the art in PFC modelling as well as the potential, which might still arise from this method in physics and materials science in the nearby future.     

Convergence acceleration of molecular dynamics methods for shocked materials using velocity scaling

ABSTRACT

In this work, a convergence acceleration method applicable to extended system molecular dynamics techniques for shock simulations of materials is presented. The method uses velocity scaling to reduce the instantaneous value of the Rankine–Hugoniot conservation of energy constraint used in extended system molecular dynamics methods to more rapidly drive the system towards a converged Hugoniot state. When used in conjunction with the constant stress Hugoniostat method, the velocity scaled trajectories show faster convergence to the final Hugoniot state with little difference observed in the converged Hugoniot energy, pressure, volume and temperature. A derivation of the scale factor is presented and the performance of the technique is demonstrated using the boron carbide armour ceramic as a test material. It is shown that simulation of boron carbide Hugoniot states, from 5 to 20 GPa, using both a classical Tersoff potential and an ab initio density functional, are more rapidly convergent when the velocity scaling algorithm is applied. The accelerated convergence afforded by the current algorithm enables more rapid determination of Hugoniot states thus reducing the computational demand of such studies when using expensive ab initio or classical potentials.     

Giant SALR cluster reproduction,with implications for their chemical evolution

ABSTRACT

Particles with SALR (short-range attraction and long-range repulsion) interactions are common to many physical systems, especially biological and soft matter, yet their behaviour is still not completely understood. Using Monte Carlo simulations and a thermodynamic model, it is shown here that giant SALR clusters can grow and reproduce in these fluids. Giant cluster growth and reproduction should therefore be common to a wide range of natural and synthetic systems under suitable conditions. If, in addition, cluster fitness selection occurs then chemical evolution of giant SALR cluster might be observed in suitable systems.     

Reaction rate theory for supramolecular kinetics: application to protein aggregation

ABSTRACT

Probing reaction mechanisms of supramolecular processes in soft and biological matter, such as protein aggregation, is inherently challenging. This is because these processes involve multiple molecular mechanisms that are associated with the rearrangement of large numbers of weak bonds, resulting in complex free energy landscapes with many kinetic barriers. Reaction rate measurements at different temperatures can offer unprecedented insights into the underlying molecular mechanisms. However, to be able to interpret such measurements, a key challenge is to establish which properties of the complex free energy landscapes are probed by the reaction rate. Here, we present a reaction rate theory for supramolecular kinetics based on Kramers theory of diffusive reactions over multiple kinetic barriers. We find that reaction rates for protein aggregation are of the Arrhenius–Eyring type and that the associated activation energies probe only one relevant barrier along the respective free energy landscapes. We apply this advancement to interpret, in experiments and in coarse-grained computer simulations, reaction rates of amyloid aggregation in terms of molecular mechanisms and associated thermodynamic signatures. These results suggest a practical extension of the concept of rate-determining steps for complex supramolecular processes and establish a general platform for probing the underlying energy landscape using kinetic measurements.     

The discrete-dipole-approximation code ADDA: Capabilities and known limitations

The open-source code ADDA is described, which implements the discrete dipole approximation (DDA), a method to simulate light scattering by finite 3D objects of arbitrary shape and composition. Besides standard sequential execution, ADDA can run on a multiprocessor distributed-memory system, parallelizing a single DDA calculation. Hence the size parameter of the scatterer is in principle limited only by total available memory and computational speed. ADDA is written in C99 and is highly portable. It provides full control over the scattering geometry (particle morphology and orientation, and incident beam) and allows one to calculate a wide variety of integral and angle-resolved scattering quantities (cross sections, the Mueller matrix, etc.). Moreover, ADDA incorporates a range of state-of-the-art DDA improvements, aimed at increasing the accuracy and computational speed of the method. We discuss both physical and computational aspects of the DDA simulations and provide a practical introduction into performing such simulations with the ADDA code. We also present several simulation results, in particular, for a sphere with size parameter 320 (100-wavelength diameter) and refractive index 1.05.     

Comparison of modern Langevin integrators for simulations of coarse-grained polymer melts

For a wide range of phenomena, current computational ability does not always allow for atomistic simulations of high-dimensional molecular systems to reach time scales of interest. Coarse-graining (CG) is an established approach to alleviate the impact of computational limits while retaining the same algorithms used in atomistic simulations. It is important to understand how algorithms such as Langevin integrators perform on non-trivial CG molecular systems, and in particular how large of an integration time step can be used without introducing unacceptable amounts of error into averaged quantities of interest. To investigate this, we examined three different Langevin integrators on a CG polymer melt: the recently developed BAOAB method by Leimkuhler and Matthews [J. Chem. Phys. 138 (17), 05B601_1 (2013)], the Grønbech-Jensen and Farago method [Mol. Phys. 111 (8), 983-991 (2013)], or G-JF, and the frequently used Brünger–Brooks–Karplus integrator [Chem. Phys. Lett. 105 (5), 495-500 (1984)], known as BBK. We compute and analyse key statistical properties for each. Our results indicate that the integrators perform similarly for a small friction parameter; however outside this regime, the use of large integration steps produces significant deviations from the predicted diffusivity and steady-state distributions for all methods examined with the exception of G-JF.     

Predicting XAFS scattering path cumulants and XAFS spectra for metals (Cu,Ni, Fe,Ti, Au) using molecular dynamics simulations

The ability of molecular dynamics (MD) simulations to support the analysis of X‐ray absorption fine‐structure (XAFS) data for metals is evaluated. The low‐order cumulants (ΔR, σ², C₃) for XAFS scattering paths are calculated for the metals Cu, Ni, Fe, Ti and Au at 300 K using 28 interatomic potentials of the embedded‐atom method type. The MD cumulant predictions were evaluated within a cumulant expansion XAFS fitting model, using global (path‐independent) scaling factors. Direct simulations of the corresponding XAFS spectra, χ(R), are also performed using MD configurational data in combination with the FEFFab initio code. The cumulant scaling parameters compensate for differences between the real and effective scattering path distributions, and for any errors that might exist in the MD predictions and in the experimental data. The fitted value of ΔR is susceptible to experimental errors and inadvertent lattice thermal expansion in the simulation crystallites. The unadjusted predictions of σ² vary in accuracy, but do not show a consistent bias for any metal except Au, for which all potentials overestimate σ². The unadjusted C₃ predictions produced by different potentials display only order‐of‐magnitude consistency. The accuracy of direct simulations of χ(R) for a given metal varies among the different potentials. For each of the metals Cu, Ni, Fe and Ti, one or more of the tested potentials was found to provide a reasonable simulation of χ(R). However, none of the potentials tested for Au was sufficiently accurate for this purpose.     

Monte Carlo simulations of primitive models for ionic systems using the Wolf method

Thermodynamic and structural properties of primitive models for electrolyte solutions and molten salts were studied using NVT and NPT Monte Carlo simulations. The Coulombic interactions were simulated using the Wolf method [D. Wolf, Phys. Rev. Lett. 68, 3315 (1992); D. Wolf, P. Keblinnski, S. R. Phillpot, and J. Eggebrecht, J. Chem. Phys. 110, 8254 (1999)]. Results for 1?:?1 and 2?:?1 charge ratio electroneutral systems are presented, using the restricted and non-restricted primitive models, as well as a soft PM pair potential for a monovalent salt [J.-P. Hansen and I. R. McDonald, Phys. Rev. A 11, 2111 (1975)] that has also been used to model 2?:?12 and 1?:?20 asymmetric colloidal systems, with size ratios 1?:?10 and 2?:?15, respectively [B. Hribar, Y. V. Kalyuzhnyi, and V. Vlachy, Molec. Phys. 87, 1317 (1996)]. We present the predictions obtained for these systems using the Wolf method. Our results are in very good agreement with simulation data obtained with the Ewald sum method as well as with integral-equation theories results. We discuss the relevance of the Wolf method in the context of variable-ranged potentials in molecular thermodynamic theories for complex fluids.     

snapMRF: GPU-accelerated magnetic resonance fingerprinting dictionary generation and matching using extended phase graphs

Purpose:Magnetic resonance fingerprinting (MRF) is a state-of-the-art quantitative MRI technique with a computationally demanding reconstruction process, the accuracy of which depends on the accuracy of the signal model employed. Having a fast, validated, open-source MRF reconstruction would improve the dependability and accuracy of clinical applications of MRF.Methods:We parallelized both dictionary generation and signal matching on the GPU by splitting the simulation and matching of dictionary atoms across threads. Signal generation was modeled using both Bloch equation simulation and the extended phase graph (EPG) formalism. Unit tests were implemented to ensure correctness. The new package, snapMRF, was tested with a calibration phantom and an in vivo brain.Results:Compared with other online open-source packages, dictionary generation was accelerated by 10–1000× and signal matching by 10–100×. On a calibration phantom, T₁ and T₂ values were measured with relative errors that were nearly identical to those from existing packages when using the same sequence and dictionary configuration, but errors were much lower when using variable sequences that snapMRF supports but that competitors do not.Conclusion:Our open-source package snapMRF was significantly faster and retrieved accurate parameters, possibly enabling real-time parameter map generation for small dictionaries. Further refinements to the acquisition scheme and dictionary setup could improve quantitative accuracy.     

Atomistic mechanism of NaCl nucleation from an aqueous solution

Despite great technological relevance, the initial steps of nucleation and crystal growth from solution are still poorly understood. While experimentally difficult to access, simulations in principle may provide insight at the atomic level. However, in most cases the computational demand dramatically exceeds the scope of current hardware. Since crystallization usually occurs on time scales much larger than the few ns of a molecular dynamics simulation, special techniques for the study of rare events are of particular interest. In the present work the nucleation of sodium chloride aggregates from aqueous solution is investigated from path sampling molecular dynamics simulation. The introduced simulation schemes appear to be widely applicable.     

Probability diffusion in non-Markhovian,non-Gaussian molecular ensembles: A theoretical analysis and computer simulation

A theoretical generalisation of the Fokker/Planck equation for atomic and molecular diffusion is compared with the results of a molecular dynamics simulation of a triatomic molecule ofC _2v symmetry. The molecular dynamics results are non-Markhovian and non-Gaussian in nature, markedly so in the case of the centre of mass linear velocityV. This may be ascertained by simulating the long-time limit of the three dimensional kinetic energy autocorrelation function <V ²(t)V ²(0)>/<V ²(0)V ²(0)>, which falls well below the theoretical Gaussian value of 3/5. By expressing the Mori continued fraction as a multidimensional Markhovian chain of differential equations and expressing this in turn as a non-Gaussian probability-diffusion equation of the Kramers/Moyal type it is possible to account for the simulation results in a qualitative fashion.     

Nearsightedness-related indices of finite systems based on linear response function: one-dimensional cases

ABSTRACT

We have investigated nearsightedness of electronic matter (NEM) of finite systems on the basis of linear response function to examine theoretical foundation of contemporary computational chemistry such as quantum mechanics/molecular mechanics methods. In this study, we introduce several nearsightedness-related indices to assess the magnitude of localisability of responses for one-dimensional finite model systems. We started from two electrons' systems, which are beyond the scope of the original concept of NEM, and increased the number of electrons (N) to a hundred electrons to analyse dependency of such indices on N. In the process of construction of the indices, we analysed the factors, because of which the magnitude of nonlocal parts of linear response functions becomes small, into several ones, and extracted purely the magnitude of propagation of responses.     

MuMax: A new high-performance micromagnetic simulation tool

We present MuMax, a general-purpose micromagnetic simulation tool running on graphical processing units (GPUs). MuMax is designed for high-performance computations and specifically targets large simulations. In that case speedups of over a factor 100 × can be obtained compared to the CPU-based OOMMF program developed at NIST. MuMax aims to be general and broadly applicable. It solves the classical Landau-Lifshitz equation taking into account the magnetostatic, exchange and anisotropy interactions, thermal effects and spin-transfer torque. Periodic boundary conditions can optionally be imposed. A spatial discretization using finite differences in two or three dimensions can be employed. MuMax is publicly available as open-source software. It can thus be freely used and extended by community. Due to its high computational performance, MuMax should open up the possibility of running extensive simulations that would be nearly inaccessible with typical CPU-based simulators.     

Dynamic adaptive chemistry for turbulent flame simulations

The use of large chemical mechanisms in flame simulations is computationally expensive due to the large number of chemical species and the wide range of chemical time scales involved. This study investigates the use of dynamic adaptive chemistry (DAC) for efficient chemistry calculations in turbulent flame simulations. DAC is achieved through the directed relation graph (DRG) method, which is invoked for each computational fluid dynamics cell/particle to obtain a small skeletal mechanism that is valid for the local thermochemical condition. Consequently, during reaction fractional steps, one needs to solve a smaller set of ordinary differential equations governing chemical kinetics. Test calculations are performed in a partially-stirred reactor (PaSR) involving both methane/air premixed and non-premixed combustion with chemistry described by the 53-species GRI-Mech 3.0 mechanism and the 129-species USC-Mech II mechanism augmented with recently updated NO _x pathways, respectively. Results show that, in the DAC approach, the DRG reduction threshold effectively controls the incurred errors in the predicted temperature and species concentrations. The computational saving achieved by DAC increases with the size of chemical kinetic mechanisms. For the PaSR simulations, DAC achieves a speedup factor of up to three for GRI-Mech 3.0 and up to six for USC-Mech II in simulation time, while at the same time maintaining good accuracy in temperature and species concentration predictions.     

Equilibrium molecular dynamics calculation of the bulk viscosity of liquid water

Twenty independent equilibrium molecular dynamics simulations were performed in NVE ensemble to calculate the bulk viscosity of water at a temperature of 303 K and a density of 0.999 gcm^?3. The energy of each simulation with a production time of 200ps was conserved within 1 part in 10⁴. By stopping the velocity-scaling procedure at a proper step, the energies of independent simulations were specified precisely. This caused the simulations of different start configurations to sample the same NVE ensemble. The shear viscosity of SPC/E water obtained in the present study was 6.5±0.4 × 10^?4 Pas, which is in close agreement with a previous calculation in the NVT ensemble (Balasubramanian, S., Mundy, C. J., and Klein, M. L., 1996, J. clzern. Phys., 105, 11 190). The bulk viscosity was 15.5 ± 1.6 × 10^?4 Pas, which is 27% smaller than the experimental value. Thus, like its behaviour in predicting the shear viscosity, the SPC/E model also underestimates the bulk viscosity of real water.     

Equilibrium molecular dynamics simulation of shear viscosity of two-dimensional complex (dusty) plasmas

Shear viscosity is examined throughout the entire range of strongly coupled states of two-dimensional complex (dusty) plasma liquids (CDPLs). We have employed equilibrium molecular dynamics (EMD) simulation to compute the shear viscosity coefficients of CDPLs. In the strongly coupled liquid region, the values of valid viscosity coefficient can be estimated only in order of magnitude. The variations in the valid viscosity coefficients with screening strength (κ) and Coulomb coupling strengths (Γ) are observed. A systematic dependence of shear viscosity on κ is observed for an intermediate and higher Γ. The investigations showed that the position of the minimum viscosity coefficient shifts towards higher Γ as κ increases. The computational results for the entire range of liquid states of the strongly coupled dusty plasma obtained using the shear autocorrelation functions are in good agreement with the available simulation results and experimental data. It is shown that new simulations extended the range of plasma states (Γ, κ) used in our earlier simulation results for the existence of a finite minimum possible viscosity coefficient and it is also dependent on plasma states.     

CONFORMATIONAL ANALYSIS AND MOLECULAR MODELING OF CHOLESTERIC LIQUID CRYSTAL POLYESTERS BASED ON XRD,RAMAN, AND TRANSITION THERMAL ANALYSIS

Molecular modeling of the cholesteric liquid crystal polyester poly[oxy(1,2 - dodecane)oxycarbonyl-1,4-phenyleneoxycarbonyl-1,4-phenylenecarbonyloxy-1,4-phenylenecarbonyl] (PTOBDME), [C₃₄H₃₆O₈] _n , synthesized in our laboratory and thermally characterized by differential scanning calorimetry (DSC), was performed to explain both its cholesteric mesophase and 3D crystalline structure. Conformational analysis (CA) was run for the monomer both by systematic search and with molecular dynamics (MD) simulations. Minima energy conformers were “polymerized” with Cerius² and helical, cholesteric molecules were obtained in all cases. Our models agree with the chiral behavior observed by X-ray diffraction (XRD), thermooptical analysis (TOA) and circular dichroism (CD) experiments. Crystal packing of the polymer molecules were simulated in cells with parameters a and b obtained from experimental powder X-ray diffraction patterns and c calculated from the translational repetitive unit during the theoretical polymerization. Recalculated X-ray powder diffraction patterns of our models matched the observed ones. Morphology simulation from those crystal models is in good agreement with the crystals observed by optical microscopy. We have also modeled the self-associating nature of those polyesters when dispersed in aqueous media. Simulation of our models surrounded by different solvents, such as water and chloroform, were performed by calculating their interaction energies, coordination numbers, and mixing energies, applying Monte Carlo simulation techniques based on the Flory-Huggins theory. These results were compared with their experimental vibrational Fourier transform (FT)–Raman spectra in the regions in which structural marker bands of the polymer appear.     

Canopy Gradients in δ18O of Organic Matter as Ecophysiological Tool

Abstract

We determined vertical oxygen isotope gradients of leaf organic matter for a grassland in Switzerland and a mountain beech forest (Fagus sylvatica) in Northern Italy. A distinctly positive ¹⁸O/¹⁶O gradient with height above ground was found for the grassland (7.9‰m^?1, p < 0.001), whereas the gradient was negative for the forest (–0.077‰m^?1, p < 0.001). The results are consistent with microclimatic measurements, although large isotope variations between the species have to be taken into account for the grassland. A conceptual scheme is shown which relates the isotope enrichment to the canopy density, considering the effects of transpiration and canopy structure. We conclude that the analysis of the within canopy variation in δ¹⁸O of organic matter can be used to provide long-term estimates of leaf water isotope composition, thus improving existing isotope methods to determine the gas-exchange between vegetation and atmosphere.