3D Periodic Boundary Conditions Research Articles

Molecular dynamics simulations of liquid-liquid interfaces in an electric field: The water-1,2-dichloroethane interface.

The polarized interface between two immiscible liquids plays a central role in many technological processes. In particular, for electroanalytical and ion extraction applications, an external electric field is typically used to selectively induce the transfer of ionic species across the interfaces. Given that it is experimentally challenging to obtain an atomistic insight into the ion transfer process and the structure of liquid-liquid interfaces, atomistic simulations have often been used to fill this knowledge gap. However, due to the long-range nature of the electrostatic interactions and the use of 3D periodic boundary conditions, the use of external electric fields in molecular dynamics simulations requires special care. Here, we show how the simulation setup affects the dielectric response of the materials and demonstrate how by a careful design of the system it is possible to obtain the correct electric field on both sides of a liquid-liquid interface when using standard 3D Ewald summation methods. In order to prove the robustness of our approach, we ran extensive molecular dynamics simulations with a rigid-ion and polarizable force field of the water/1,2-dichloroethane interface in the presence of weak external electric fields.

Mesoscale finite element analysis of cracked composite laminates under out-of-plane loads using 3D periodic boundary conditions

The behavior of composite materials under out-of-plane loads is strongly affected by the presence of transverse ply cracks. The cracks perturb the distribution of stresses leading to large out-of-plane shear stiffness reductions. It is crucial to include these effects in the damage material models to improve their accuracy. Therefore, the stress transfer and stiffness reduction in cracked laminates have been studied with a mesoscale finite element model (FEM) under general in-plane, out-of-plane normal and shear loads. A symmetric laminate containing ply cracks in a single orientation has been considered under the hypothesis of periodicity using a novel relaxed three-dimensional formulation of Periodic Boundary Conditions (PBCs). The local stresses have been verified versus different analytical and numerical methods. In addition, the degraded effective thermo-elastic constants involving out-of-plane properties have been calculated as a function of crack density. Both uniform and non-uniform distributions of cracks have been considered for different lay-ups including angle-ply and unbalanced laminates. The effect of contact between the crack surfaces has been studied for specific loading conditions. It is shown that a single formulation based on three-dimensional periodic boundary conditions is sufficient to determine the interfacial stresses and the complete thermo-elastic constants under in-plane and out-of-plane loads accurately.

Topological shape optimization of 3D micro-structured materials using energy-based homogenization method

This paper proposes an effective method for the design of 3D micro-structured materials to attain extreme mechanical properties, which integrates the firstly developed 3D energy-based homogenization method (EBHM) with the parametric level set method (PLSM). In the 3D EBHM, a reasonable classification of nodes in periodic material microstructures is introduced to develop the 3D periodic boundary formulation consisting of 3D periodic boundary conditions, 3D boundary constraint equations and the reduced linearly elastic equilibrium equation. Then, the effective elasticity properties of material microstructures are evaluated by the average stress and strain theorems rather than the asymptotic theory. Meanwhile, the PLSM is applied to optimize microstructural shape and topology because of its positive characteristics, like the perfect demonstration of geometrical features and high optimization efficiency. Numerical examples are provided to demonstrate the advantages of the proposed design method. Results indicate that the optimized 3D material microstructures with expected effective properties are featured with smooth structural boundaries and clear interfaces.

Nonequilibrium molecular dynamics simulation for studying the effect of pressure difference and periodic boundary conditions on water transport through a CNT membrane

ABSTRACTA NEMD simulation system is constructed to simulate at two-dimensional (2D) periodic boundary conditions (PBCs) and to create two different pressures on two sides of the carbon nanotube (CNT) membrane. The simulation results show that water permeation through the same CNT membrane driven by different pressure differences exhibit similar transport phenomenon including unusually fast water permeation and a periodic (non-parabolic) radial velocity distribution unlike the parabolic form characteristic of continuum flow in the CNT membrane. A three-dimensional (3D) PBC system is also constructed to simulate water permeation through the same CNT membrane at the same pressure differences, to show the effect of PBC and simulation methodologies on transport phenomenon. The two systems both show that the forward/backward water flux increases/decreases with increasing the pressure difference from 1.0 MPa to 8.0 MPa. However, the net flux is higher for the 3D PBC system, especially at higher pressure difference is high. In general, the NEMD simulation method using the 2D PBC system is shown to be a feasible and valuable tool for studying pressure-driven permeation processes such as nanofiltration through these studies with model CNT membrane.

Idealized vs. Realistic Microstructures: An Atomistic Simulation Case Study on γ/γ' Microstructures.

Single-crystal Ni-base superalloys, consisting of a two-phase γ/ microstructure, retain high strengths at elevated temperatures and are key materials for high temperature applications, like, e.g., turbine blades of aircraft engines. The lattice misfit between the γ and phases results in internal stresses, which significantly influence the deformation and creep behavior of the material. Large-scale atomistic simulations that are often used to enhance our understanding of the deformation mechanisms in such materials must accurately account for such misfit stresses. In this work, we compare the internal stresses in both idealized and experimentally-informed, i.e., more realistic, γ/ microstructures. The idealized samples are generated by assuming, as is frequently done, a periodic arrangement of cube-shaped particles with planar γ/ interfaces. The experimentally-informed samples are generated from two different sources to produce three different samples—the scanning electron microscopy micrograph-informed quasi-2D atomistic sample and atom probe tomography-informed stoichiometric and non-stoichiometric atomistic samples. Additionally, we compare the stress state of an idealized embedded cube microstructure with finite element simulations incorporating 3D periodic boundary conditions. Subsequently, we study the influence of the resulting stress state on the evolution of dislocation loops in the different samples. The results show that the stresses in the atomistic and finite element simulations are almost identical. Furthermore, quasi-2D boundary conditions lead to a significantly different stress state and, consequently, different evolution of the dislocation loop, when compared to samples with fully 3D boundary conditions.

Parameter Tuning for the NFFT Based Fast Ewald Summation

The computation of the Coulomb potentials and forces in charged particle systems under 3d-periodic boundary conditions is possible in an efficient way by utilizing the Ewald summation formulas and applying the fast Fourier transform (FFT). In this paper we consider the particle-particle NFFT (P$^2$NFFT) approach, which is based on the fast Fourier transform for nonequispaced data (NFFT) and compare the error behaviors regarding different window functions, which are used in order to approximate the given continuous charge distribution by a mesh based charge density. Typically B-splines are applied in the scope of particle mesh methods, as for instance within the well known particle-particle particle-mesh (P$^3$M) algorithm. The publicly available P$^2$NFFT algorithm allows the application of an oversampled FFT as well as the usage of different window functions. We consider for the first time also an approximation by Bessel functions and show how the resulting root mean square errors in the forces can be predicted precisely and efficiently. The results show that, if the parameters are tuned appropriately, the Bessel window function is in many cases even the better choice in terms of computational costs. Moreover, the results indicate that it is often advantageous in terms of efficiency to spend some oversampling within the NFFT while using a window function with a smaller support.

Fast Ewald summation based on NFFT with mixed periodicity

In this paper we develop new fast Fourier-based methods for the Coulomb problem. We combine the Ewald summation formulas and the fast summation approach based on the nonequispaced fast Fourier transform (NFFT) in order to develop efficient methods for calculating the Coulomb energies as well as the acting forces in charged particle systems subject to mixed periodic boundary conditions. Therewith, we extend the applicability of NFFT based methods, which already exist for open as well as for 3d-periodic boundary conditions, to arbitrary combinations of periodic and open boundary conditions. We reconsider the derivation of the Ewald formulas for 2d- and 1d-periodic systems, introduce the new algorithms and present high precision numerical results.

DMG-α--a computational geometry library for multimolecular systems.

The DMG-α library grants researchers in the field of computational biology, chemistry, and biophysics access to an open-sourced, easy to use, and intuitive software for performing fine-grained geometric analysis of molecular systems. The library is capable of computing power diagrams (weighted Voronoi diagrams) in three dimensions with 3D periodic boundary conditions, computing approximate projective 2D Voronoi diagrams on arbitrarily defined surfaces, performing shape properties recognition using α-shape theory and can do exact Solvent Accessible Surface Area (SASA) computation. The software is written mainly as a template-based C++ library for greater performance, but a rich Python interface (pydmga) is provided as a convenient way to manipulate the DMG-α routines. To illustrate possible applications of the DMG-α library, we present results of sample analyses which allowed to determine nontrivial geometric properties of two Escherichia coli-specific lipids as emerging from molecular dynamics simulations of relevant model bilayers.

3D numerical simulation for the elastic properties of random fiber composites with a wide range of fiber aspect ratios

A new automatic searching & coupling (ASC) technique is proposed to generate the 3D representative volume element (RVE) to analyze the random fiber composite (RaFC) with a wide range of fiber aspect ratios (FAR), particularly the RaFC with a high FAR. Compared with the conventional model, the present model is easier to generate and more time-saving as it eliminates the drawback of free meshing. In addition, the ASC technique can remove the additional stiffness introduced by the embedded element technique (EET), and hence can improve precision and convergence. Moreover, our technique facilitates the direct application of the 3D periodic boundary conditions (PBC) to the RVE. Using the finite element (FE) method, the elastic properties of RVE are calculated, and the critical RVE size is determined. Furthermore, the 3D elastic properties of RaFC are predicted, which accord well with experimental data. Besides, the RVE is employed to explore the influences of FAR, fiber volume fraction (FVF) and the fiber incline angle on the elastic properties of RaFC, and a comparison with theoretical results is also presented.

Molecular Simulations of Physical and Chemical Properties of Poly(Imino Ketone)s

Six kinds of poly(imino ketone)s (PIKs) with different structures were designed, involving different ratios of carbonyl and imino groups, and the insertion of two types of bulky groups in the main chain. Under 3D periodic boundary conditions, simulations of physical and chemical properties for PIKs with six different structures on the molecular level, including fractional free volume (FFV) and melt density, solubility, and glass transition temperature, were carried out.

Strain engineering via amorphization and recrystallization in Si/Ge heterostructures

We use molecular dynamics with the reactive potential ReaxFF to study strain relaxation during the amorphization and recrystallization of silicon-germanium epitaxial nanolaminates. Starting with a coherent heterostructure with (010) Si/Ge interfaces and 3D periodic boundary conditions, we use local heating and quenching to amorphize half of the simulation cell with crystal-amorphous interfaces normal to [001]. We find strain relaxation along [001] as the crystalline Ge section expands into the amorphous material and crystalline Si contracts from it. The amount of strain relaxation correlates with the atomic transport from the amorphized Ge to Si section and increases as the periodic width of the crystalline-amorphous pattern decreases and the height of the Si/Ge bilayer increases. Recrystallization leads to a decrease in strain relaxation; however, structures with low aspect ratio retain a significant fraction of the strain relaxation. Interestingly, this remnant strain relaxation is not due to misfit dislocations but originates in clusters of lattice defects located on either side of the interface and caused by atomic transport. Our results show that local amorphization followed by recrystallization is a possible avenue for strain engineering in semiconductor heterostructures.

First-Principles Calculations of the Adsorption of Nitromethane and 1,1-Diamino-2,2-dinitroethylene (FOX-7) Molecules on the α-Al2O3(0001) Surface

First-principles calculations based on density functional theory (DFT) and the generalized gradient approximation (GGA) have been used to study the adsorption of nitromethane (NM) and 1,1-diamino-2,2-dinitroethylene (FOX-7) molecules on the basal plane of an alpha-Al(2)O(3) crystal. The calculations employ a (2 x 2) supercell slab model and 3D periodic boundary conditions. On the basis of these calculations, we have determined that both NM and FOX-7 molecules can adsorb nondissociatively on the surface with the most stable adsorption configurations parallel to the surface. The binding energies are in the range 25.3-26.0 kcal/mol for NM and 35.6-48.3 kcal/mol for FOX-7 depending on the relative molecular orientation and the surface sites. The minimum energy pathways for NM dissociation have been determined, and a low-energy pathway leading to H-atom elimination with formation of adsorbed CH(2)NO(2) and hydroxyl species has been identified. Additional calculations have focused on adsorption properties of aci-nitromethane tautomers and on description of the energetic pathways connecting adsorbed nitromethane molecule with these tautomers.

Computer simulation of structure and ferroelectric phase transition of vinylidene fluoride copolymers. 5. Influence of orientational disorder of dipole moments and domain walls on phase transitional behavior

Molecular dynamics (MD) simulations have been performed in order to clarify the mechanism of ferroelectric phase transition in vinylidene fluoride–trifluoroethylene (VDF–TrFE) copolymers. Influence of orientational disorder of CF 2 dipoles and domain walls on the ferroelectric phase transition behavior has been investigated for VDF 50 mol.% copolymer system. Two types of MD unit cells were constructed by packing the 36 and 16 infinitely long chains, each of which consisted of random sequences of five VDF and five TrFE monomer units under the 3D periodic boundary conditions. For the models with all the CF 2 dipoles arrayed in parallel, the trans-to- gauche conformational change occurred at 450–500 K. Introduction of orientational disorder of one or two chains to the model, in which the dipoles are oriented into the opposite direction along the b axis, caused the reorientation of these dipoles to the original parallel direction at low temperature and the trans-to- gauche conformational change at 450 K. However, by making the dipole packing more irregular, the trans-to- gauche conformational change was found to occur quite easily even below the room temperature. An existence of the domain boundary, which was made in-between the domains consisting of the parallel packing of dipoles, was also found to cause similar structural changes. In this way, the irregular dipole array and/or the domain boundary were found to induce the trans– gauche structural transformation more easily at lower temperature, different from the models of regular dipole arrangements.

Large scale atomistic simulations of screw dislocation structure, annihilation and cross-slip in FCC Ni

Using QM-Sutton-Chen many-body potential, we have studied the 1/2 a〈1 1 0〉 screw dislocation in nickel (Ni) via molecular dynamics (MD) simulations. We have studied core energy and structure using a quadrupolar dislocation system with 3D periodic boundary conditions. The relaxed structures show dissociation into two partials on {1 1 1} planes. The equilibrium separation distance between the two partials is 2.5 nm, which is larger than the derived value according to experimental data, due to low stacking fault energy given by the QM-Sutton-Chen force field. From our calculations, the core energy for the 1/2 a〈1 1 0〉 screw dislocation is 0.5 eV/ b. We also studied motion and annihilation process of opposite signed dislocations. We build the dipole system with two combinations of dissociation planes: (a) two dislocations dissociated on intersecting slip planes and (b) two on parallel planes. The process of cross-slip and associated energy barriers are also calculated from these simulations.

Molecular Atomistic Simulations of Clay Swelling in Water Dispersions

An atomistic model has been constructed for a dimeric montmorillonite type clay aggregate. The solid was supposed to be dispersed in water. The surrounding aqueous phase was modified from pure water to either salt or polymer solution, and finally represented by a mixed solution containing electrolytes and polyols. A combined energy minimisation procedure followed by a 100 ps real time molecular dynamic simulation was performed on each amorphous cell modelling the solid dispersion. 3D periodic boundary conditions were established to ensure fluid spatial continuity and the calculations proceeded at room temperature. Sodium, potassium and calcium chlorides were tested as shale swelling inhibition additives. The lower hydration energy cation K+ was the most effective swelling inhibitor. The adsorption of poly(propylene glyco)s to the ideal smectite surface was also studied. Their tendency to remain adsorbed was associated with the irreversibility of the polymer adsorption process. The conformational changes obtained for organic molecules were responsible for the final orientation of the clay sheets. So it was possible to conclude from qualitative observations that intramolecular interactions may determine a clay dispersion–agglomeration transition by modifying the system entropy. Finally, it was also concluded that specific combinations of additives could enhance their individual capabilities by synergistic effects, determining the effectiveness for some water-based mud formulations.