Bond Order Parameters Research Articles

Dynamic simulation of sediment films of Yukawa-stabilized particles.

The fast lubrication dynamics method is applied to simulate the motion and deposition of charge-stabilized 100-nm-diam particles into sediment films from aqueous dispersions. Colloidal interactions are incorporated with a Yukawa potential and the effects of the screened-Coulomb potential strength and Péclet number (which controls the sedimentation driving force) on particle orientation are quantified with a sixfold bond order parameter. The effect of sediment growth rate on the order parameter is determined and related to a competition between the electrostatic interaction strength and sedimentation driving force. Increasing the electrostatic interaction strength and decreasing the Péclet number lead to lower sediment growth rates and consequently greater sixfold bond order. Our work demonstrates the feasibility of including lubrication interactions in dynamic simulations of sediment films and suggests that these interactions play a central role in the kinetics of film microstructure development and consequently in the degree of order within the film.

Ab initio description of segregation and cohesion of grain boundaries in W–25 at.% Re alloys

We investigate grain boundaries (GBs) in W–25at.% Re alloys with special focus on the segregation of Re to the GBs and the changes in their cohesive properties that arise therefrom. Our simulations rely on density functional theory and a mean-field approximation, the virtual crystal approximation, to model the highly alloyed system. Based on a gamma-surface approach, the geometry of a wide range of GBs, including tilt, twist and mixed GBs, is obtained. Segregation energies are found to vary strongly between different segregation sites, with the strongest segregation energy amounting to −0.75 eVs. We show that bond-order parameters are able to identify strong segregation sites based on purely geometric information only. With a thermodynamic model based on a Bragg–Williams approach, the concentration of Re atoms is calculated as a function of GB character at 1913K and compared with atom probe experiments. The segregation levels are similar, with a trend towards higher segregation levels observed in the calculations for certain misorientation angles. Finally, Re alloying is found to lead to a general increase in the work of separation of the GBs, suggesting a reduction in the tendency for intergranular fracture.

Jammed elastic shells - a 3D experimental soft frictionless granular system.

We present a new experimental system of monodisperse, soft, frictionless, fluorescent labeled elastic shells for the characterization of structure, universal scaling laws and force networks in 3D jammed matter. The elastic shells in a jammed packing are deformed in such a way that at each contact one of the shells buckles with a dimple and the other remain spherical, closely resembling overlapping spheres. Using confocal microscopy, we obtained 3D stacks of images of shells at different volume fractions which were subsequently processed in ImageJ software to find their coordinates. The determination of 3D coordinates involved three steps: locating the edges of shells in all 2D slices, analyzing their shape and subsequently finding their 2D coordinates, and finally determining their 3D centers by grouping the corresponding 2D coordinates. From this analysis routine we obtained particle coordinates with sub-pixel accuracy. In a contact pair we also identified the shell that underwent buckling forming a dimple by analyzing the intensity profile of a line that connects the centers of particle pairs. The amorphous structure of the packing was analyzed as a function of distance to the jamming threshold by investigating the radial distribution function, bond order parameters, contact numbers and the number of dimples per particle (buckling number), which is a unique property of this system. We find that the power law scaling of the contact number with excess volume fraction deviated from theoretical and computer simulation predictions. In addition, the buckling number also showed a similar scaling as that of the contact number with distance to the jamming transition.

Formation of bcc and fcc during the coalescence of free and supported Fe and Ni clusters.

The formation of bcc and fcc during the coalescence of free and supported Fe and Ni clusters has been studied by molecular dynamics simulation using an embedded atom method. Structural evolution of the clusters, coalesced under varying temperature, Ni content and substrate conditions, was explored by interatomic energy, snapshots, pair distribution functions and bond order parameters. The results show that the formation of bcc and fcc is strongly related to Ni content, substrate and coalescence temperature. Free clusters coalesced at 1200 K form bcc at lower Ni contents with fcc forming at higher Ni concentrations and no observable coexistence of bcc and fcc. Differences in coalescence at 1000 K result from the coexistence of bcc and fcc within the Ni range of 50-70%. Free clusters supported on disordered Ni substrates were shown to transform from spherical morphology to islands of supported clusters with preferred epitaxial orientation. The Ni content required to form bcc and fcc coexistence on supported clusters at 1000 K decreased to 30-50% Ni. Free clusters possessing bcc and fcc generally stacked along the bcc (110) and fcc (111) facets, whereas supported clusters stacked along the (111) bcc and (100) fcc planes. Structural transformation was induced by clusters containing greater numbers of atoms. Spread over the substrate enhanced interatomic energy, order substrates affect the epitaxial growth direction and increase the melting points of the supported clusters. This study can be used to predict the nature of fcc and bcc formation in Fe-Ni films.

Rheology and microstructure of non-Brownian suspensions in the liquid and crystal coexistence region: strain stiffening in large amplitude oscillatory shear.

Concentrated hard-sphere suspensions in the liquid and crystal coexistence region show a unique nonlinear behavior under a large amplitude oscillatory shear flow, the so-called strain stiffening, in which the viscosity or modulus suddenly starts to increase near a critical strain amplitude. Even though this phenomenon has been widely reported in experiments, its key mechanism has never been investigated in a systematic way. To have a good understanding of this behavior, a numerical simulation was performed using the lattice Boltzmann method (LBM). Strain stiffening was clearly observed at large strain amplitudes, and the critical strain amplitude showed an angular frequency dependency. The distortion of the shear stress appeared near the critical strain amplitude, and the nonlinear behavior was quantified by the Fourier transformation (FT) and the stress decomposition methods. Above the critical strain amplitude, an increase in the global bond order parameter Ψ(6) was observed at the flow reversal. The maximum of Ψ(6) and the maximum shear stress occurred at the same strain. These results show how strongly the ordered structure of the particles is related to the stress distortion. The ordered particles maintained a bond number of "two" with alignment with the compressive axis, and they were distributed over a narrow range of angular distribution (110°-130°). In addition, the ordered structure was formed near the lowest shear rate region (the flow reversal). The characteristics of the ordered structure were remarkably different from those of the hydroclusters which are regarded as the origin of shear thickening. It is clear that strain stiffening and shear thickening originate from different mechanisms. Our results clearly demonstrate how the ordering of the particles induces strain stiffening in the liquid and crystal coexistence region.

Conformation and dynamics of a diluted chain in the presence of an adsorbing wall: A simulation with the bond fluctuation model

The bond fluctuation model has been used to simulate the adsorption process of a single long polymer chain on an adsorbing surface. Simulations start at high temperature with the chain in an equilibrium coil structure. The inter- and intra chain energy potential were selected in such a way that on cooling the polymer chain vitrifies without any indication of chain ordering or chain folding. The structure attained on cooling is analysed for a range of values of the interaction potential between the surface and the polymer segments. Adsorption is measured by the fraction of polymer segments situated on the adsorbing wall whilst crystalline ordering is characterized by the pair correlation function g(r), the bond order parameter P2(r) and the bond correlation function M(j). Isothermal adsorption is followed as well as a function of temperature. The work shows that adsorbing surface nucleates crystalline order by suppressing one dimension in the segmental mobility of the polymer chain, along with factors as thermal treatment and inter and intra-potentials.

Bond orientation properties in lipid molecules of membranes: molecular dynamics simulations

Atomistic molecular dynamics simulations have been carried out for 16 different fully hydrated phosphatidylcholine lipid bilayers, having 16 or 18 carbon atoms in fully saturated sn − 1 chain and from 18 to 22 carbon atoms in sn − 2 chain with different degree of unsaturation, with the purpose to investigate the effect of unsaturation on physical properties of lipid bilayers. Special attention has been paid to profiles of C-C and C-H bond order parameters of lipid molecules and the orientational fluctuations of these bond vectors. It was shown that the study of anisotropy degree of bond orientations probability distributions allows distinguishing extended regions with different types of angular fluctuations of bonds in a membrane formed by lipid molecules with unsaturated chains.

Mean-field theory of competing orders in metals with antiferromagnetic exchange interactions

It has long been known that two-dimensional metals with antiferromagnetic exchange interactions have a weak-coupling instability to the superconductivity of spin-singlet, $d$-wave electron pairs. We examine additional possible instabilities in the spin-singlet particle-hole channel and study their interplay with superconductivity. We perform an unrestricted Hartree-Fock-BCS analysis of bond order parameters in a single-band model on the square lattice with nearest-neighbor exchange and repulsion, while neglecting on-site interactions. The dominant particle-hole instability is found to be an incommensurate, bidirectional, bond density wave with wave vectors along the $(1,1)$ and $(1,\ensuremath{-}1)$ directions and an internal $d$-wave symmetry. The magnitude of the ordering wave vector is close to the separation between points on the Fermi surface, which intersect the antiferromagnetic Brillouin zone boundary. The temperature dependence of the superconducting and bond order parameters demonstrates their mutual competition. We also obtain the spatial dependence of the two orders in a vortex lattice induced by an applied magnetic field: ``halos'' of the bond order appear around the cores of the vortices.

Characterization of local structures with bond-order parameters and graphs of the nearest neighbors, a comparison

We compare two methods for the characterization of local order in samples undergoing crystal nucleation and growth. Particles with a crystal-like surrounding need to be identified to follow the nucleation process. Both methods are based on the knowledge of the particle positions in a small volume of the sample. (i) Local bond-order parameters are used to quantify the orientation of the nearest neighbors of a particle, while (ii) the graph method determines the topological arrangement of the nearest neighbors and the bonds between them. Both methods are used to detect crystal-like particles and crystal nuclei in a supercooled fluid surrounding and to determine the structure of small crystal nuclei. The properties of these nuclei are of great interest for a deeper understanding of crystal nucleation, and they can be studied in detail in colloidal model systems that allow to follow the evolution of the nuclei with single particle resolution.

Effect of single nanoparticle on the polymer crystallization behavior

Molecular dynamics simulation with a coarse grain model is performed to study the influence of single nanoparticle on the polymer crystallization behavior. By changing the mode of action of the polymer-nanoparticle (i.e. attraction or repulsion), the strength of the polymer-nanoparticle interactions, as well as the chain length of the polymer molecular, and by calculating the bond order parameter to characterize the influence in the cooling process, different effects of single nanoparticle on the polymer crystallization behavior are studied. This study has shown that the nanoparticle has no obvious effect on the whole polymer system composed of single nanoparticles. However, nanoparticles can promote the degree of order of polymer chains in crystallization process and enhance partially the polymer crystallization. Under the attraction and strong strength of the polymer-nanoparticle interaction, it is found that obviously the nanoparticle enhances the polymer crystallization partially. Furthermore, the chain length of the polymer molecular also shows some effect on the crystallization and the long-chain sample has a better enhancement for the polymer crystallization than the short-chain one under a strong attraction strength.

Optimising reaction coordinates for crystallisation by tuning the crystallinity definition

We apply maximum likelihood analysis to optimise crystallisation measures based on Steinhardt bond order parameters. Assuming that the size of the largest cluster of crystalline particles serves as a good reaction coordinate for the freezing transition, we write down the likelihood to observe the committor values computed for a large number of configurations. We then maximise the likelihood function by varying the parameters that enter the definition of crystallinity. For the crystallinity definition considered here this parameter set consists of the thresholds for the next-neighbour distance, the strength of the crystalline bonds and the number of crystalline connections. The optimum parameter set found by the likelihood maximisation differs considerably from the parameters that are commonly used, but leads only to a marginal improvement of the quality of the reaction coordinate.

Hard-core bosons in a zig-zag optical superlattice

We study a system of hard-core bosons at half-filling in a one-dimensional optical superlattice. The bosons are allowed to hop to nearest and next-nearest neighbor sites producing a zig-zag geometry and we obtain the ground state phase diagram as a function of microscopic parameters using the finite-size density matrix renormalization group (FS-DMRG) method. Depending on the sign of the next-nearest neighbor hopping and the strength of the superlattice potential the system exhibits three different phases, namely the bond-order (BO) solid, the superlattice induced Mott insulator (SLMI) and the superfluid (SF) phase. When the signs of both hopping amplitudes are the same (the "unfrustrated" case), the system undergoes a transition from the SF to the SLMI at a non-zero value of the superlattice potential. On the other hand, when the two amplitudes differ in sign (the "frustrated" case), the SF is unstable to switching on a superlattice potential and also exists only up to a finite value of the next nearest neighbor hopping. This part of the phase diagram is dominated by the BO phase which breaks translation symmetry spontaneously even in the absence of the superlattice potential and can thus be characterized by a bond order parameter. The transition from BO to SLMI appears to be first order.

How to quantify solid–liquid phase transition: Lennard–Jones system case study

AbstractIn this paper we analyzed different measures, characterizing the melting of Lennard–Jones solid, and associated with the properties of both the translational and the orientational local order. It has been shown that the most sensitive indicator of melting is the cumulant of the probability distribution function over w6 bond-order parameter. The criterion of melting based on the indicator is proposed; the criterion can be used for any solids, having fcc/hcp types of symmetry.

Isomerisation Reactions of α-Methyl Allyl [Acetate, Trifluoroacetate]: Theoretical Study

The [3,3]-sigmatropic rearrangement reactions of α-methyl allyl acetate (1), and α-methyl allyl trifluoroacetate (2) have been studied using ab initio molecular orbital (MO) methods at the HF, B3LYP, B3PW91, and BHandHLYP levels with a 6-31++G** basis set. Among the methods used in this study, the values for activation parameters obtained with the BHandHLYP/6-31++G** method are in good agreement with experimental values. The calculated data demonstrate that in the rearrangement reactions of the compounds studied, the polarisation of the O3–C4 bond is rate determining. Optimised transition states at the BHandHLYP/6-31++G** level were used for calculating the nucleus-independent chemical shift (NICS) and also a natural bond orbital (NBO) analysis was carried out at the same level. Based on the optimised ground state geometries using the BHandHLYP/6-31++G** method, the NBO analysis of donor–acceptor (bonding–antibonding) interactions revealed that the stabilisation energies associated with electronic delocalisation from the σO(3)–C(4) bonding orbital to the π*C(5)=C(6) antibonding orbital, increase from compounds 1 to 2. The σO(3)–C(4) →π*C(5)=C(6) resonance energies for compounds 1 and 2 are 1.59 and 1.62 kcal mol−1, respectively. Also, analysis of the donor–acceptor interactions σO(3)–C(4) →π*C(5)=C(6) suggests that in these rearrangements, the TS structure in compound 2 has more aromatic character than for compound 1. The NBO results revealed that in these rearrangements, activation energies are not controlled by the σO(3)–C(4) →π*C(5)=C(6) resonance energy. NICS results indicate that the aromaticities of the transition states are controlled by the out-of-plane component. The predicted high-pressure-limit rate constants for the rearrangement reactions of compounds 1 and 2 are represented as 6.12 × 1012 exp(–21604/T), and 1.04 × 1013 exp(–17846/T) s−1, respectively. The fall-off pressures for the rearrangement reactions 1 and 2 are found to be 9.56 × 10−5 and 1.09 × 10−3 mmHg, respectively. The fall-off pressures of compounds 1 and 2 in both reactions are in the following order: P1/2(2) > P1/2(1) and the rates follow as: rate(2) > rate(1). Analysis of bond order, NBO charges, bond indices and synchronicity parameters suggest the Claisen rearrangement reactions of 1 and 2 occur through a concerted and slightly asynchronous six-membered cyclic transition state type of mechanism.

Molecular Dynamics Simulation of the Melting Behavior of Crown-Jewel Structured Au–Pd Nanoalloys

Understanding the thermal stability of the novel crown-jewel structured Au–Pd nanoalloys with the Au atoms at the top positions is attractive and significant for their potential application in catalysis. In this work, the melting of crown-jewel structured Au–Pd nanoalloys with atoms from 561 to 2057 is investigated by molecular dynamics simulations, based on the Gupta potential. Melting properties for these clusters are studied based on the indicators such as potential energy curve, specific heat capacity, bond order parameters, and deformation parameters. It is found that there is a monotonic decrease of the melting temperature with the concentration of the Au atoms, indicating that doping of Au atoms on the Pd clusters could decrease the thermal stability of the Pd cluster. In addition, linear decrease in cluster melting point with the inverse cluster diameter is predicted for the same kind of cluster, which is well-known as the Pawlow’s law.

Bond Order in Two-Dimensional Metals with Antiferromagnetic Exchange Interactions

We present an unrestricted Hartree-Fock computation of charge-ordering instabilities of two-dimensional metals with antiferromagnetic exchange interactions, allowing for arbitrary ordering wave vectors and internal wave functions of the particle-hole pair condensate. We find that the ordering has a dominant d symmetry of rotations about lattice points for a range of ordering wave vectors, including those observed in recent experiments at low temperatures on YBa2Cu3O(y). This d symmetry implies the charge ordering is primarily on the bonds of the Cu lattice, and we propose incommensurate bond order parameters for the underdoped cuprates. The field theory for the onset of Néel order in a metal has an emergent pseudospin symmetry which "rotates" d-wave Cooper pairs to particle-hole pairs [M. A. Metlitski and S. Sachdev, Phys. Rev. B 82, 075128 (2010)]; our results show that this symmetry has consequences even when the spin correlations are short ranged and incommensurate.

Structural features of a Lennard-Jones system at melting and crystallization

The structural features of the crystallization and melting of a system of particles whose pair interaction is described by the Lennard-Jones potential have been considered. The bond order parameter method is used to quantitatively describe the orientational short-range order. The rotational invariants of the second (ql) and third (wl) orders are calculated for each particle of the system. These calculations require only information on the snapshot of atom positions, which is quite easily obtained in experiments, and provide the distribution functions of particles in ql and wl (where l is the rank of an invariant; the results for l = 4, 6 are presented), which are important characteristics of the phase state of the system. It has been shown that the cumulant of the distribution of particles in w6 is very sensitive to the destruction/formation of the short-range orientational order in the Lennard-Jones system and, correspondingly, can be used as a criterion of the melting and crystallization of this system.

Molecular dynamics simulations of DPPC bilayers using "LIME", a new coarse-grained model.

A new intermediate resolution model for phospholipids, LIME, designed for use with discontinuous molecular dynamics (DMD) simulations is presented. The implicit-solvent model was developed using a multiscale modeling approach in which the geometric and energetic parameters are obtained by collecting data from atomistic simulations of a system composed of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) molecules and explicit water. In the model, 14 coarse-grained sites that are classified as 1 of 6 types represent DPPC. DMD simulations performed on a random solution of DPPC resulted in the formation of a defect-free bilayer in less than 4 h. The bilayer formed quantitatively reproduces the main structural properties (e.g., area per lipid, bilayer thickness, bond order parameters) that are observed experimentally. In addition, the bilayer transitions from a liquid-crystalline phase to a tilted gel phase when the temperature is reduced. Transbilayer movement of a lipid from the bottom leaflet to the top leaflet is observed when the temperature is increased.

Signal intensities in 1H–13C CP and INEPT MAS NMR of liquid crystals

Spectral editing with CP and INEPT in 13C MAS NMR enables identification of rigid and mobile molecular segments in concentrated assemblies of surfactants, lipids, and/or proteins. In order to get stricter definitions of the terms “rigid” and “mobile”, as well as resolving some ambiguities in the interpretation of CP and INEPT data, we have developed a theoretical model for calculating the CP and INEPT intensities as a function of rotational correlation time τc and C–H bond order parameter SCH, taking the effects of MAS into account. According to the model, the range of τc can at typical experimental settings (5kHz MAS, 1ms ramped CP at 80–100kHz B1 fields) be divided into four regimes: fast (τc<1ns), fast-intermediate (τc≈0.1μs), intermediate (τc≈1μs), and slow (τc>0.1ms). In the fast regime, the CP and INEPT intensities are independent of τc, but strongly dependent on |SCH|, with a cross-over from dominating INEPT to dominating CP at |SCH|>0.1. In the intermediate regime, neither CP nor INEPT yield signal on account of fast T1ρ and T2 relaxation. In both the fast-intermediate and slow regimes, there is exclusively CP signal. The theoretical predictions are tested by experiments on the glass-forming surfactant n-octyl-β-d-maltoside, for which τc can be varied continuously in the nano- to millisecond range by changing the temperature and the hydration level. The atomistic details of the surfactant dynamics are investigated with MD simulations. Based on the theoretical model, we propose a procedure for calculating CP and INEPT intensities directly from MD simulation trajectories. While MD shows that there is a continuous gradient of τc from the surfactant polar headgroup towards the methyl group at the end of the hydrocarbon chain, analysis of the experimental CP and INEPT data indicates that this gradient gets steeper with decreasing temperature and hydration level, eventually spanning four orders of magnitude at completely dry conditions.

Contact network topology in tapped granular media

We analyze the contact network of simulated two-dimensional granular packings in different states of mechanical equilibrium obtained by tapping. We show that topological descriptors of the contact network allow one to distinguish steady states of the same mean density obtained with different tap intensities. These equal-density states were recently proven to be distinguishable through the mean force moment tensor. In contrast, geometrical descriptors, such as radial distribution functions, bond order parameters, and Voronoi cell distributions, can hardly discriminate among these states. We find that small-order loops of contacts-the polygons of the network-are especially sensitive probes for the contact structure.