Bond-orientational Correlation Research Articles

Confinement controlled dynamical structural rearrangement in a quasi-2D dusty plasma crystal

In this work, we present experimental results on the structural transition of a two-dimensional dust crystal through controlled adjustment of its radial confinement while keeping all other discharge parameters constant. The experiments are performed in an L-shaped Dusty Plasma Experimental device in a DC glow discharge argon plasma environment. Initially, a purely 2D dust crystal is formed inside a circular confining ring at the interface of the plasma-cathode sheath region. This monolayer with a hexagonal lattice configuration of the dust particles gets buckled when the sheath thickness around the radial confinement ring is reduced. A bilayer with a square lattice configuration emerges in the dust system due to the onset of a transverse instability. The multiple crystalline domains at this lower confinement show signatures of a constant structural rearrangement in the system. The timescale associated with this rearrangement is quantified from the bond-orientational correlation function. It is found that the heterogeneous cooperative micro-motion of particles in the quasi-layered system is responsible for the rearrangement over the passage of time.

Molecular simulation of an initial stage of the ordered-structure formation of linear and ring polymers upon cooling from the melts

Monte Carlo (MC) simulation of the coarse-grained ring and linear polyethylene (PE) models were employed to study the early stage of the ordered-structure formation upon cooling from the melts. The simulations suggest that the ordered structure with the single domain can be formed for both linear and ring PE chains which have the same mean square radius of gyration in the molten state. Molecular and structural properties evaluated from the simulation are the fraction of trans conformation and the sequence length of trans state, the anisotropic change of chain dimension, the overall orientation correlation function, intra- and inter-molecular bond orientation correlation functions and intermolecular pair correlation function. All these properties reveal an ordering process as the sign of crystallization especially for linear chains whereas it is more difficult for ring polymer to form an ordered phase. For ring chains, the ordered structures were formed with multiple folded conformations and smaller magnitude for the fraction of trans conformation, chain orientation, degree of chain packing, intra- and inter-molecular bond ordering. The simulations suggest that PE chains are needed to stretch to some extent before the chain alignment can proceed. Compared to the linear polymers with comparable molecular size, ring PE chains tend to form the less-ordered crystalline structure, have higher melting temperature and exhibit slower crystallization rates.

Coincident Correlation between Vibrational Dynamics and Primary Relaxation of Polymers with Strong or Weak Johari-Goldstein Relaxation.

The correlation between the vibrational dynamics, as sensed by the Debye-Waller factor, and the primary relaxation in the presence of secondary Johari-Goldstein (JG) relaxation, has been investigated through molecular dynamics simulations. Two melts of polymer chains with different bond length, resulting in rather different strength of the JG relaxation are studied. We focus on the bond-orientation correlation function, exhibiting higher JG sensitivity with respect to alternatives provided by torsional autocorrelation function and intermediate scattering function. We find that, even if changing the bond length alters both the strength and the relaxation time of the JG relaxation, it leaves unaffected the correlation between the vibrational dynamics and the primary relaxation. The finding is in harmony with previous studies reporting that numerical models not showing secondary relaxations exhibit striking agreement with experimental data of polymers also where the presence of JG relaxation is known.

Liquid-hexatic-solid phase transition of a hard-core lattice gas with third neighbor exclusion.

The determination of phase behavior and, in particular, the nature of phase transitions in two-dimensional systems is often clouded by finite size effects and by access to the appropriate thermodynamic regime. We address these issues using an alternative route to deriving the equation of state of a two-dimensional hard-core particle system, based on kinetic arguments and the Gibbs adsorption isotherm, by the use of the random sequential adsorption with a surface diffusion model. Insight into coexistence regions and phase transitions is obtained through direct visualization of the system at any fractional surface coverage via local bond orientation order. The analysis of the bond orientation correlation function for each individual configuration confirms that first-order phase transition occurs in a two-step liquid-hexatic-solid transition at high surface coverage.

Role of many-body interactions in the structure of coarse-grained polymers.

In developing coarse-grained (CG) polymer models it is important to reproduce both local and molecule-scale structure. We develop a procedure for fast calculation of the bond-orientation correlation and the internal squared distance 〈R^{2}(M)〉 through evaluation of the probability distribution functions that represent a CG model. Different CG models inherently contain or omit correlations between CG variables. Here, we construct CG models that contain specific correlations between CG variables. The importance of different correlations is tested on CG models of polyethylene, polytetrafluoroethylene, and poly-L-lactic acid. The chain stiffness and 〈R^{2}(M)〉 are calculated using both analytic evaluation and Monte Carlo sampling, and approximate model results are compared with exact results from all-atom simulations. For polymers with an exponential correlation decay, the bond-orientation correlation and 〈R^{2}(M)〉 indicate which CG variable correlations are most important to reproduce molecule-scale structure. Analysis of the bond-orientation correlation and internal-squared distance indicates that for poly-L-lactic acid the bond-orientation correlation requires qualitatively different additional terms in CG models and quantifies the error in neglecting this important behavior.

Persistence Length, End-to-End Distance, and Structure of Coarse-Grained Polymers.

Coarse-grained (CG) polymer simulations can access longer times and larger lengths than all-atom (AA) molecular dynamics simulations; however, not all CG models correctly reproduce polymer properties on all length scales. Here we coarse-grain atomistic position data from polyethylene (PE) and polytetrafluoroethylene (PTFE) melt simulations by combining λ backbone carbon atoms in a single CG bead. Resulting CG variables have correlations along the chain backbone that depend on the coarse-graining scale λ and are generally not reproduced by independent bond-length, bond-angle and torsion-angle distributions. By constructing distributions of CG variables equivalent to those from simulated CG potentials we are able to evaluate the bond-orientation correlation for different CG models at reduced computational cost. CG models and potentials that include only nonbonded, bond-length, and bond-angle interactions computed by Boltzmann inversion correctly reproduce the CG variable distributions but do not necessarily reproduce the chain stiffness, overestimating the persistence length Lp and end-to-end distance ⟨ R2⟩1/2 with increasing λ. While CG models that include an independent torsion angle match the bond-orientation correlation and ⟨ R2⟩1/2 better, only approximate models that include correlations between bond and torsion angles match the true bond-orientation correlation.

Bond-orientational order and Frank’s constant in two-dimensional colloidal hard spheres

Recently, the full phase behaviour of 2D colloidal hard spheres was experimentally established, and found to involve a first order liquid to hexatic transition and a continuous hexatic to crystal transition (Thorneywork et al 2017 Phys. Rev. Lett. 118 158001). Here, we expand upon this work by considering the behaviour of the bond-orientational correlation time and Frank’s constant in the region of these phase transitions. We also consider the excess entropy, as calculated from the radial distribution functions, for a wide range of area fractions covering the liquid, hexatic and crystal phases. In all cases, the behaviour of these quantities further corroborates the previously reported melting scenario of 2D colloidal hard spheres.

Dynamic heterogeneity in two-dimensional supercooled liquids: comparison of bond-breaking and bond-orientational correlations

We compare the spatial correlations of bond-breaking events and bond-orientational relaxation in a model two-dimensional liquid undergoing Newtonian dynamics. We find that the relaxation time of the bond-breaking correlation function is much longer than the relaxation time of the bond-orientational correlation function and self-intermediate scattering function. However, the relaxation time of the bond-orientational correlation function increases faster with decreasing temperature than the relaxation time of the bond-breaking correlation function and the self-intermediate scattering function. Moreover, the dynamic correlation length that characterizes the size of correlated bond-orientational relaxation grows faster with decreasing temperature than the dynamic correlation length that characterizes the size of correlated bond-breaking events. We also examine the ensemble-dependent and ensemble-independent dynamic susceptibilities for both bond-breaking correlations and bond-orientational correlations. We find that for both correlations, the ensemble-dependent and ensemble-independent susceptibilities exhibit a maximum at nearly the same time, and this maximum occurs at a time slightly shorter than the peak position of the dynamic correlation length.

Solid-hexatic-liquid transition in a two-dimensional system of charged dust particles

Two-stage melting is observed experimentally in a confined monolayer of dust particles in plasma. The pair correlation and bond-angular correlation functions, the number of topological defects, and the pair potentials are measured and analyzed. The bond-orientational correlation functions show a clear solid-to-hexatic-to-fluid transition, in perfect agreement with the Berezinskii-Kosterlitz-Thouless transition theory.

Quantitatively mimicking wet colloidal suspensions with dry granular media.

Athermal two-dimensional granular systems are exposed to external mechanical noise leading to Brownian-like motion. Using tunable repulsive interparticle interaction, it is shown that the same microstructure as that observed in colloidal suspensions can be quantitatively recovered at a macroscopic scale. To that end, experiments on granular and colloidal systems made up of magnetized particles as well as computer simulations are performed and compared. Excellent agreement throughout the range of the magnetic coupling parameter is found for the pair distribution as well as the bond-orientational correlation functions. This finding opens new ways to efficiently and very conveniently explore phase transitions, crystallization, nucleation, etc in confined geometries.

Comparison of 2D melting criteria in a colloidal system

We use super-paramagnetic spherical particles which are arranged in a two-dimensional monolayer at a water/air interface to investigate the crystal to liquid phase transition. According to the KTHNY theory a crystal melts in thermal equilibrium by two continuous phase transitions into the isotropic liquid state with an intermediate phase, commonly known as the hexatic phase. We verify the significance of several criteria based on dynamical and structural properties to identify the crystal–hexatic and hexatic–isotropic liquid phase transitions for the same experimental data of the given setup. The criteria are the bond orientational correlation function, the Larson–Grier criterion, the 2D dynamic Lindemann parameter, the bond orientational susceptibility, the 2D Hansen–Verlet rule, the Löwen–Palberg–Simon criterion as well as a criterion based on the shape factor of Voronoi cells and Minkowski functionals. For our system with long-range repulsion, the bond order correlation function and bond order susceptibility work best to identify the hexatic–isotropic liquid transition and the 2D dynamic Lindemann parameter identifies unambiguously the hexatic–crystalline transition.

Structure, compressibility factor, and dynamics of highly size-asymmetric binary hard-disk liquids

By using event-driven molecular dynamics simulation, we investigate effects of varying the area fraction of the smaller component on structure, compressibility factor, and dynamics of the highly size-asymmetric binary hard-disk liquids. We find that the static pair correlations of the large disks are only weakly perturbed by adding small disks. The higher-order static correlations of the large disks, by contrast, can be strongly affected. Accordingly, the static correlation length deduced from the bond-orientation correlation functions first decreases significantly and then tends to reach a plateau as the area fraction of the small disks increases. The compressibility factor of the system first decreases and then increases upon increasing the area fraction of the small disks and separating different contributions to it allows to rationalize this non-monotonic phenomenon. Furthermore, adding small disks can influence dynamics of the system in quantitative and qualitative ways. For the large disks, the structural relaxation time increases monotonically with increasing the area fraction of the small disks at low and moderate area fractions of the large disks. In particular, "reentrant" behavior appears at sufficiently high area fractions of the large disks, strongly resembling the reentrant glass transition in short-ranged attractive colloids and the inverted glass transition in binary hard spheres with large size disparity. By tuning the area fraction of the small disks, relaxation process for the small disks shows concave-to-convex crossover and logarithmic decay behavior, as found in other binary mixtures with large size disparity. Moreover, diffusion of both species is suppressed by adding small disks. Long-time diffusion for the small disks shows power-law-like behavior at sufficiently high area fractions of the small disks, which implies precursors of a glass transition for the large disks and a localization transition for the small disks. Therefore, our results demonstrate the generic dynamic features in highly size-asymmetric binary mixtures.

Two-stage melting transition of bilayer systems under geometrical confinement: multicolour domain decomposition Monte Carlo simulation

The nature of the melting transition in a thin film consisting of a bilayer of spheres confined between parallel walls was investigated by the multicolour domain decomposition Monte Carlo (MDDMC) method. The MDDMC method is suitable for distributed memory parallel computers, and the order parameters of the system were calculated numerically. The nature of the melting transition from an ordered phase with square lattice symmetry was clarified, with the number of particles N larger than 105. The profile of the bond-orientational correlation function near the transition point was also shown. At an intermediate density, this function was found to obey a power-law behaviour such as . A comparison with recent experiments is also presented.

Characterization of ordered array of micropores in a polymer film

Microporous polymer films prepared by templating “breath figures” tend to have closely packed, hexagonal arrays of pores. We characterize the hexagonal order of the structured films using Fraunhofer diffraction patterns in reciprocal space, as well as with the use of Voronoi diagrams and bond-orientational correlation functions using real space images. The average spacing of the pores over a wider area can be calculated by two-dimensional Bragg equation, while the analysis of microscope images provides a direct measurement of the average open pore size and its distribution. The use of bond-orientational correlation function is particularly useful in quantifying the order of various films formed under various conditions. Further, we show how the sequential ordering of water drops formed during breath-figure-templated assembly process can also be characterized using Voronoi analysis and bond orientational correlation function.

Standard Definitions of Persistence Length Do Not Describe the Local “Intrinsic” Stiffness of Real Polymer Chains

On the basis of extensive Monte Carlo simulations of lattice models for linear chains under good and Θ solvents conditions, and for bottle-brush polymers under good solvent conditions, different methods to estimate the persistence lengths of these polymers are applied and compared to each other. While for chain molecules at the Θ point standard textbook definitions of the persistence length yield consistent results, under good solvent conditions the persistence length (according to its standard definitions) diverges when the chain length of the macromolecules tends to infinity. Accurate simulation results for chain lengths up to Nb = 6400 allow us to verify the theoretically predicted power laws for the decay of the bond orientational correlation function. For the case of bottle-brush polymers, this dependence of “the” persistence length on the backbone chain length obscures the dependence on the side chain length, that is controversially discussed in the literature. Alternative definitions of a persistence length that do not suffer from this problem, based on the total linear dimension of the chain or on the scattering function via the so-called “Holtzer plateau” are studied as well. We show that the backbone contour length of the bottle-brush needs to be very large (about 100 persistence lengths in typical cases) to reach the asymptotic limit where the bottle-brush satisfies the self-avoiding walk statistics, and where a well-defined persistence length can be extracted. An outlook to pertinent experimental work is given.

Ion hydration in aqueous solutions of lithium chloride, nickel chloride, and caesium chloride in ambient to supercritical water

Neutron diffraction with an isotopic substitution technique was used to determine the structure (bond distance, hydration number, and orientational correlation of water) of ion hydration in concentrated aqueous solutions of lithium chloride, nickel chloride and caesium chloride in ambient to supercritical water (648 K, 169 MPa). The lithium ion has an average hydration number of 4.1 ± 0.3 at 298 ~ 470 K, but 2.8 ± 0.3 at 647 K. The Li–O bond distance was 2.02 ± 0.01 Å over the temperature range measured, whereas the Li–D bond length decreased from 2.60 ± 0.01 Å at 298 K to 2.49 ± 0.01 Å at 647 K, indicating a weakening of the orientational correlation of water molecules around Li + in supercritical water. The Ni–O and Ni–D distances were 2.10 ± 0.01 Å and 2.68 ± 0.01 Å, respectively, irrespective of temperature at 298 ~ 473 K. The hydration number of Ni 2+ was found to be 6.4 ± 0.3 at 298 and 373 K, but decreased to 5.0 ± 0.2 at 473 K, suggesting the ion-pairing of Ni 2+–Cl − at 473 K. The chloride ions in lithium chloride and caesium chloride solutions are hydrogen bonded with water molecules at Cl–D (D 2O) distances of 2.28 ~ 2.33 Å over a temperature range measured. With an increase in temperature, the number of hydrogen bonded Cl–D interactions in the LiCl solutions changed from 5.6 ± 0.1 at 298 ~ 350 K, 4.5 ± 0.1 at 470 K, to 2.5 ± 0.1 at 648 K, showing that there is a marked lessening of the degree of orientational correlation of water molecules around Cl − in high-temperature liquid, in particular, in supercritical water. In the caesium chloride solution, on the other hand, there is a tendency for formation of contact ion-pair Cs +–Cl − at 473 K due to a decrease in n Cl–D of 3.9 ± 0.5, as also evidence from an X-ray diffraction study.

Monte Carlo study of melting in a finite two-dimensional dusty plasma

Melting in a finite two-dimensional dusty plasma has recently been characterized experimentally [T. E. Sheridan, Phys. Plasmas 15, 103702 (2008)] in a system with ≈3900 dust particles. We model this experiment using the Metropolis algorithm to generate thermodynamic configurations for a two-dimensional system of identical particles confined in a parabolic well and interacting through a Debye (Yukawa) potential. Results are computed for a Debye shielding parameter a/λD=0.24, where a is the lattice constant and λD is the Debye length. Configurations are characterized using the pair and bond-orientational correlation functions, defect fractions, and correlation lengths. Distinct crystalline, hexatic, and liquid phases are observed. In the hexatic phase, the decay of the bond-orientational correlation goes as r−η6 where η6≈1, which is greater than the value η6=0.25 predicted by the theory of Kosterlitz, Thouless, Halperin, Nelson, and Young.

Melting transition in a two-dimensional complex plasma heated by driven acoustic instability

The melting transition in a two-dimensional complex (dusty) plasma is studied experimentally. A system consisting of ≈3900 microspheres is heated by amplitude modulating the rf discharge power with a square wave at the vertical resonance frequency. The vertical motion couples to an in-plane dust-acoustic instability at one-half the modulation frequency, thereby increasing the complex plasma’s effective temperature. The “thermodynamic” phase of the system is characterized for increasing levels of amplitude modulation at constant neutral pressure (35mTorr Ar) and average rf power using the Lindemann ratio, defect density, bond-orientational correlation function, and pair correlation function. A melting transition showing evidence for an intermediate hexatic phase is observed.

Fabrication of Well-Organized and Densely Packed Si Nanopillars Containing SiGe Nanodots by Using Block Copolymer Templates

We present a method to obtain a dense array of well-organized SiGe quantum dots in Si nanopillars on a large substrate area by using a PS-b-PMMA block copolymer template. First, the 2D order of the template is evaluated using a pair correlation function and a bond-orientational correlation function. It is shown that the holes contained in the polystyrene template form a structure presenting a hexatic order. This template is then used to fabricate the nanopillars using the following method: in a first step, the copolymer template serves as a deposition mask to fabricate a hexagonal array of Pt dots. In a second step, the Pt dot pattern is transferred to an alternation of Si and SiGe layers on a silicon substrate with an anisotropically etching using Cl2/O2 plasma.

Implicit-solvent mesoscale model based on soft-core potentials for self-assembled lipid membranes

An efficient implicit-solvent model for self-assembled lipid bilayers is presented and analyzed using Langevin molecular dynamics simulations. The model is based on soft interactions between particles and short-range attractive interaction between lipid tails, leading for the self-assembly of a lipid bilayer without an explicit solvent. This allows for efficient simulations of large membranes over long times. The model exhibits a fluid phase at high temperatures and a gel phase at low temperatures, identified with the Lbeta-phase. The melting transition is investigated via analysis of the diffusivity of the lipid molecules, the chain-orientational order parameter, the sixfold bond-orientational order parameter, and the positional and bond-orientational correlation functions. The analysis suggests the existence of a hexatic phase over a narrow range of temperatures around the melting transition. The elastic properties of the membrane in the fluid phase are also investigated.