Normalized Structure Factors Research Articles

Anomalous friction of confined water in carbon nanotubes

The friction of water within a carbon nanotube (CNT) is influenced by the interplay between energy barriers and water structure. In this work, we employ a series of regular polygonal CNTs, whose energy barriers remain constant with size, to examine the influence of water structure on solid-water friction using the molecular dynamics (MD) method. Polygonal CNTs with radii under 0.45 nm show friction coefficients an order of magnitude higher than their circular counterparts. While water exhibits an ordered phase within 0.5–0.6 nm-radius polygonal CNTs, resulting in a significant 80 % reduction in the friction coefficients compared to bulk like water. The force distribution analysis confirms the constancy of energy barriers. Further analysis of water density, hydrogen bond number distribution, average structure factor, and density correlation time demonstrates that the density correlation time predominantly impacts solid-liquid friction. The observed reduction in friction is primarily due to the collective movement of water molecules in an ordered arrangement. These findings illuminate nanoscale drag reduction mechanisms, offering insights for micro-nano flow system design.

Prediction of Matrix Suction of Unsaturated Granite Residual Soil Slope Based on Electrical Conductivity

To study the relationship between matrix suction and conductivity in unsaturated granite residual soil and realize the matrix suction prediction of soil slope based on conductivity, laboratory and field tests are carried out on undisturbed soil at different depths of the Yandou village landslide in Sanming City, Fujian Province, China. Through physical and chemical property analysis, soil-water characteristic curves and electric parameter matrix suction prediction models for unsaturated granite residual soil at different depths of the target area are obtained. Based on the proposed model, the matrix suction distribution of on-site soil slope is predicted and the dynamic response law under the influence of artificial rainfall is studied. The results show that: (1) The transverse conductivity, average structure factor, average shape factor, and anisotropy coefficient of unsaturated soil are related to the soil saturation degree. By considering the above parameters, the comprehensive structure parameter Re is introduced and its functional relationship with matrix suction is established. (2) Under artificial simulated rainfall, the saturation, hysteresis of the conductivity parameters, and matrix suction response of the slope occurs, which is controlled by soil depth, permeability and rainfall intensity. The matrix suction is distributed in layers on the profile and its recovery rate is slower than saturation. The suction contour map shows a parabola shape with the opening downward. (3) The relationship between the conductivity parameters of the residual soil slope and matrix suction is further revealed and a new method to indirectly measure matrix suction is proposed. Its feasibility is verified based on field tests, which is of great significance to landslide monitoring and early warning.

Molecular Dynamics Investigation of Phenolic Oxidative Coupling Protein Hyp-1 Derived from Hypericum perforatum

Molecular dynamics (MD) simulations provide a physics-based approach to understanding protein structure and dynamics. Here, we used this intriguing tool to validate the experimental structural model of Hyp-1, a pathogenesis-related class 10 (PR-10) protein from the medicinal herb Hypericum perforatum, with potential application in various pharmaceutical therapies. A nanosecond MD simulation using the all-atom optimized potentials for liquid simulations (OPLS–AA) force field was performed to reveal that experimental atomic displacement parameters (ADPs) underestimate their values calculated from the simulation. The average structure factors obtained from the simulation confirmed to some extent the relatively high compliance of experimental and simulated Hyp-1 models. We found, however, many outliers between the experimental and simulated side-chain conformations within the Hyp-1 model, which prompted us to propose more reasonable energetically preferred rotameric forms. Therefore, we confirmed that MD simulation may be applicable for the verification of refined, experimental models and the explanation of their structural intricacies.

Diffusing wave microrheology of highly scattering concentrated monodisperse emulsions

Motivated by improvements in diffusing wave spectroscopy (DWS) for nonergodic, highly optically scattering soft matter and by cursory treatment of collective scattering effects in prior DWS microrheology experiments, we investigate the low-frequency plateau elastic shear moduli [Formula: see text] of concentrated, monodisperse, disordered oil-in-water emulsions as droplets jam. In such experiments, the droplets play dual roles both as optical probes and as the jammed objects that impart shear elasticity. Here, we demonstrate that collective scattering significantly affects DWS mean-square displacements (MSDs) in dense colloidal emulsions. By measuring and analyzing the scattering mean free path as a function of droplet volume fraction φ, we obtain a φ-dependent average structure factor. We use this to correct DWS MSDs by up to a factor of 4 and then calculate [Formula: see text] predicted by the generalized Stokes-Einstein relation. We show that DWS-microrheological [Formula: see text] agrees well with mechanically measured [Formula: see text] over about three orders of magnitude when droplets are jammed but only weakly deformed. Moreover, both of these measurements are consistent with predictions of an entropic-electrostatic-interfacial (EEI) model, based on quasi-equilibrium free-energy minimization of disordered, screened-charge-stabilized, deformable droplets, which accurately describes prior mechanical measurements of [Formula: see text] made on similar disordered monodisperse emulsions over a wide range of droplet radii and φ. This very good quantitative agreement between DWS microrheology, mechanical rheometry, and the EEI model provides a comprehensive and self-consistent view of weakly jammed emulsions. Extensions of this approach may improve DWS microrheology on other systems of dense, jammed colloids that are highly scattering.

First principles modeling of the structural, electronic, and vibrational properties of Ni40Pd40P20 bulk metallic glass

Abstract The structural, vibrational, and electronic properties of Ni40Pd40P20 bulk metallic glass have been studied using ab initio molecular-dynamics simulations and total-energy optimization. Structural analyses of the resulting ab initio models show the presence of a few to no P P bonds and two main building blocks, consisting of tricapped trigonal prism (TTP) and capped square anti-prism (CSAP) with P as the center of these blocks. The computed Pd and Ni K-edge spectra of extended X-ray absorption fine structure (EXAFS) are found to be in good agreement with experimental data. The configurational averaged static structure factor and the generalized vibrational density of states are also observed to be in good agreement with experimental data.

Protein-Protein Interactions of Highly Concentrated Monoclonal Antibody Solutions via Static Light Scattering and Influence on the Viscosity.

The ability to design and formulate mAbs to minimize attractive interactions at high concentrations is important for protein processing, stability, and administration, particularly in subcutaneous delivery, where high viscosities are often challenging. The strength of protein-protein interactions (PPIs) of an IgG1 and IgG4 monoclonal antibody (mAb) from low to high concentration was determined by static light scattering (SLS) and used to understand viscosity data. The PPI were tuned using NaCl and five organic ionic co-solutes. The PPI strength was quantified by the normalized structure factor S(0)/ S(0)HS and Kirkwood-Buff integral G22/ G22,HS (HS = hard sphere) determined from the SLS data and also by fits with (1) a spherical Yukawa potential and (2) an interacting hard sphere (IHS) model, which describes attraction in terms of hypothetical oligomers. The IHS model was better able to capture the scattering behavior of the more strongly interacting systems (mAb and/or co-solute) than the spherical Yukawa potential. For each descriptor of PPI, linear correlations were obtained between the viscosity at high concentration (200 mg/mL) and the interaction strengths evaluated both at low (20 mg/mL) and high concentrations (200 mg/mL) for a given mAb. However, the only parameter that provided a correlation across both mAbs was the oligomer mass ratio ( moligomer/ mmonomer+dimer) from the IHS model, indicating the importance of self-association (in addition to the direct influence of the attractive PPI) on the viscosity.

Simulation of phase separation with temperature-dependent viscosity using lattice Boltzmann method.

This paper presents an exploration of the phase separation behavior and pattern formation in a binary fluid with temperature-dependent viscosity via a coupled lattice Boltzmann method (LBM). By introducing a viscosity-temperature relation into the LBM, the coupling effects of the viscosity-temperature coefficient [Formula: see text] , initial viscosity [Formula: see text] and thermal diffusion coefficient [Formula: see text] , on the phase separation were successfully described. The calculated results indicated that an increase in initial viscosity and viscosity-temperature coefficient, or a decrease in the thermal diffusion coefficient, can lead to the orientation of isotropic growth fronts over a wide range of viscosity. The results showed that droplet-type phase structures and lamellar phase structures with domain orientation parallel or perpendicular to the walls can be obtained in equilibrium by controlling the initial viscosity, thermal diffusivity, and the viscosity-temperature coefficient. Furthermore, the dataset was rearranged for growth kinetics of domain growth and thermal diffusion fronts in a plot by the spherically averaged structure factor and the ratio of separated and continuous phases. The analysis revealed two different temporal regimes: spinodal decomposition and domain growth stages, which further quantified the coupled effects of temperature and viscosity on the evolution of temperature-dependent phase separation. These numerical results provide guidance for setting optimum temperature ranges to obtain expected phase separation structures for systems with temperature-dependent viscosity.

Effect of the Hartmann number on phase separation controlled by magnetic field for binary mixture system with large component ratio

This paper presents an exploration for phase separation in a magnetic field using a coupled lattice Boltzmann method (LBM) with magnetohydrodynamics (MHD). The left vertical wall was kept at a constant magnetic field. Simulations were conducted by the strong magnetic field to enhance phase separation and increase the size of separated phases. The focus was on the effect of magnetic intensity by defining the Hartmann number (Ha) on the phase separation properties. The numerical investigation was carried out for different governing parameters, namely Ha and the component ratio of the mixed liquid. The effective morphological evolutions of phase separation in different magnetic fields were demonstrated. The patterns showed that the slant elliptical phases were created by increasing Ha, due to the formation and increase of magnetic torque and force. The dataset was rearranged for growth kinetics of magnetic phase separation in a plot by spherically averaged structure factor and the ratio of separated phases and total system. The results indicate that the increase in Ha can increase the average size of separated phases and accelerate the spinodal decomposition and domain growth stages. Specially for the larger component ratio of mixed phases, the separation degree was also significantly improved by increasing magnetic intensity. These numerical results provide guidance for setting the optimum condition for the phase separation induced by magnetic field.

Solving proteins at non-atomic resolution by direct methods: update

Direct methods can be used to solve proteins of great structural complexity even when diffraction data are at non-atomic resolution. However, one of the main obstacles to the wider application of direct methods is that they reliably phase only a small fraction of the observed reflections, those with a sufficiently large value of the normalized structure factor amplitude. The subsequent phase expansion and refinement required for full structure solution are difficult. Here a new phase refinement procedure is described, which combines (1–2) difference Fourier synthesis with electron density modification techniques and thevive la differenceand Free Lunch algorithms. This procedure is able to solve data resistant to other direct space refinement procedures.

Accounting for thermodynamic non-ideality in the Guinier region of small-angle scattering data of proteins.

Hydrodynamic studies of the solution properties of proteins and other biological macromolecules are often hard to interpret when the sample is present at a reasonably concentrated solution. The reason for this is that solutions exhibit deviations from ideal behaviour which is manifested as thermodynamic non-ideality. The range of concentrations at which this behaviour typically is exhibited is as low as 1–2 mg/ml, well within the range of concentrations used for their analysis by techniques such as small-angle scattering. Here we discuss thermodynamic non-ideality used previously used in the context of light scattering and sedimentation equilibrium analytical ultracentrifugation and apply it to the Guinier region of small-angle scattering data. The results show that there is a complementarity between the radially averaged structure factor derived from small-angle X-ray scattering/small-angle neutron scattering studies and the second virial coefficient derived from sedimentation equilibrium analytical ultracentrifugation experiments.

Simulation of phase separation with large component ratio for oil-in-water emulsion in ultrasound field

This paper presents an exploration for separation of oil-in-water and coalescence of oil droplets in ultrasound field via lattice Boltzmann method. Simulations were conducted by the ultrasound traveling and standing waves to enhance oil separation and trap oil droplets. The focus was to the effect of ultrasound irradiation on oil-in-water emulsion properties in the standing wave field, such as oil drop radius, morphology and growth kinetics of phase separation. Ultrasound fields were applied to irradiate the oil-in-water emulsion for getting flocculation of the oil droplets in 420kHz case, and larger dispersed oil droplets and continuous phases in 2MHz and 10MHz cases, respectively. The separated phases started to rise along the direction of sound propagation after several periods. The rising rate of the flocks was significantly greater in ultrasound case than that of oil droplets in the original emulsion, indicating that ultrasound irradiation caused a rapid increase of oil droplet quantity in the progress of the separation. The separation degree was also significantly improved with increasing frequency or irradiation time. The dataset was rearranged for growth kinetics of ultrasonic phase separation in a plot by spherically averaged structure factor and the ratio of oil and emulsion phases. The analyses recovered the two different temporal regimes: the spinodal decomposition and domain growth stages, which further quantified the morphology results. These numerical results provide guidance for setting the optimum condition for the separation of oil-in-water emulsion in the ultrasound field.

Kinetics of fluid demixing in complex plasmas: Domain growth analysis using Minkowski tensors.

A molecular dynamics simulation of the demixing process of a binary complex plasma is analyzed and the role of distinct interaction potentials is discussed by using morphological Minkowski tensor analysis of the minority phase domain growth in a demixing simulated binary complex plasma. These Minkowski tensor methods are compared with previous results that utilized a power spectrum method based on the time-dependent average structure factor. It is shown that the Minkowski tensor methods are superior to the previously used power-spectrum method in the sense of higher sensitivity to changes in domain size. By analysis of the slope of the temporal evolution of Minkowski tensor measures, qualitative differences between the case of particle interaction with a single length scale compared to particle interactions with two different length scales (dominating long-range interaction) are revealed. After proper scaling the graphs for the two length scale scenarios coincide, pointing toward universal behavior. The qualitative difference in demixing scenarios is evidenced by distinct demixing behavior: in the long-range dominated cases demixing occurs in two stages. At first, neighboring particles agglomerate, then domains start to merge in cascades. However, in the case of only one interaction length scale only agglomeration but no merging of domains can be observed. Thus, Minkowski tensor analysis is likely to become a useful tool for further investigation of this (and other) demixing processes. It is capable to reveal (nonlinear) local topological properties, probing deeper than (linear) global power-spectrum analysis, however, still providing easily interpretable results founded on a solid mathematical framework.

Influence of Uncompensated Solution Resistance on Diffusion Limited Chronocoulometric Response at Rough Electrode

Theory is developed for the charge transient under ohmic effect in reversible charge transfer process at disordered electrodes. Preliminary experimental results are also analyzed using this theory. Our results show that the deviation from Anson response is stemming from surface disorder and solution resistance. Detailed theoretical results are obtained and analyzed for fractal roughness with self-affine statistical properties. Expressions for concentration, charge density, and total charge have operator structure in Fourier transformed (deterministic) surface profile function. An elegant mathematical formula between the average charge transient and surface structure factor of roughness is obtained. Initial response is attributed to resistive effects of the electrolyte. The intermediate response is attributed to the interplay between various characteristics of the power spectrum and “ohmic equilibration layer thickness”. The theory marks that ohmic effects penetrate farther in time so much so to merge with time regimes which are outside the diffusion regimes giving nonideal behavior at electrode/electrolyte interface. Our results help with the quantitative understanding of generalized Anson response for Nernstian system affected by the uncompensated resistance at rough electrode/electrolyte interface.

Structure factor of a Gaussian chain confined between two parallel plates.

We study the structure factor of a single Gaussian chain confined between two macroscopic parallel plates theoretically. The chain propagator is constructed in terms of the eigen-spectrum of the Laplace operator under the Dirichlet boundary condition enforced at the two plates, by which the confinement effect enters the treatment through size-dependent eigen-spectrum. In terms of the series expansion solution for the chain propagator, we first calculate the confinement free energy and the confinement force for an arbitrary confinement strength. It is found that the confinement force scales to the distance between the two confining surfaces with a power of -3 for strong confinements and of -2 for weak confinements. Based on the ground state dominance approximation for strong confinements and the Euler-Maclaurin formula for weak confinements, we develop approximation theories for the two limit situations, which agree with the numerical results well. We further calculate the structure factor of the confined Gaussian chain in this slit geometry. While the scattering function of the transverse chain fluctuations perpendicular to the confinement direction is still a Debye function form, the structure factor for the longitudinal fluctuations along the confinement dimension starts with the monotonic Debye function behavior for weak confinements and develops a decaying oscillation behavior with the increase of confinements. The numerical results for the structure factor are also interpreted by developing approximation theories in different confinement regimes. Finally, the orientational average of the anisotropic structure factor is performed and an analytic expression for the averaged structure factor is derived under the ground state dominance approximation for strong confinements.

X-ray refinement significantly underestimates the level of microscopic heterogeneity in biomolecular crystals

Biomolecular X-ray structures typically provide a static, time- and ensemble-averaged view of molecular ensembles in crystals. In the absence of rigid-body motions and lattice defects, B-factors are thought to accurately reflect the structural heterogeneity of such ensembles. In order to study the effects of averaging on B-factors, we employ molecular dynamics simulations to controllably manipulate microscopic heterogeneity of a crystal containing 216 copies of villin headpiece. Using average structure factors derived from simulation, we analyse how well this heterogeneity is captured by high-resolution molecular-replacement-based model refinement. We find that both isotropic and anisotropic refined B-factors often significantly deviate from their actual values known from simulation: even at high 1.0 Å resolution and Rfree of 5.9%, B-factors of some well-resolved atoms underestimate their actual values even sixfold. Our results suggest that conformational averaging and inadequate treatment of correlated motion considerably influence estimation of microscopic heterogeneity via B-factors, and invite caution in their interpretation.

INSTAT: a program for computing non-ideal probability density functions of |E|

The purpose of this program is to evaluate probability density functions (p.d.f.s) of the magnitude of the normalized structure factor |E| for the space groups of the triclinic, monoclinic and orthorhombic systems, and for any chemical composition of the asymmetric unit, assuming that the atoms are located in general positions. The p.d.f.s are computed by the Fourier and Fourier–Bessel methods [seee.g.Shmueli (2012).J. Appl. Cryst.45, 389–392]. The p.d.f.s evaluated are scaled together with the histogram of observed |E| values and discrepancy criteria are computed. In addition to the above non-ideal p.d.f.s, the ideal p.d.f.s [Wilson (1949).J. Appl. Cryst.2, 318–321] are also computed and prepared for comparison with an experimental histogram.

Normalized structure factor analysis with theCentroMKprogram

Statistical analysis of the normalized structure factorEis important during space-group determination. Several approaches to solve this problem have been described in the literature. In this paper, the most popular approach, the ideal asymptotic probability density function developed by Wilson, is compared with the more accurate exact probability density functions described by Shmueli and co-workers. Furthermore, a new computer program,CentroMK, for normalized structure factor analysis, is presented. The program is capable of plotting histograms of the normalized structure factors and exact probability density functions. Moreover, the program calculates five estimators helpful during the space-group determination: 〈|E|〉, 〈|E2 − 1|〉, %E> 2, %E< 0.25 and the discrepancyRfunction. The two approaches and the error rates of the five listed estimators are compared for nearly 30 600 crystal structures obtained fromActa Crystallographica Section E.It is shown that within a space group the means 〈|E|〉 and 〈|E2 − 1|〉 of real crystal structures show high variability. The comparison shows that decisions based on the exact probability density function are more accurate, the computing time is reasonable, and estimators 〈|E|〉, %E< 0.25 andRare the most accurate and should be preferred during space-group determination.

Discontinuous Molecular Dynamics (DMD) Study of Heteropolymer Collapse in an Explicit Solvent

In this study, we employ the discontinuous molecular dynamics simulation method to investigate the collapse properties of a single heteropolymer chain in an explicit solvent. Solvent density ρ, fraction of hydrophobic monomers n H (defined as the ratio of the number of hydrophobic monomers to the total number of monomers) and a hydrophobicity parameter λ (which controls the energy mismatch between the monomers and solvent particles) were systematically varied to examine their role in polymer collapse. The average static structure factor of the polymer was used to find the so-called θ-point characterizing the state of an ideal chain. Phase diagrams of ρ versus λ for the coil-globule transition were mapped out for different values of n H. Increasing the fraction of hydrophobic monomers n H, solvent density ρ, and hydrophobicity parameter λ were all shown to aid in stabilizing the globule phase. In an effort to explore scaling behaviour of the coil-globule phase diagram as a function of n H, and to investigate whether the phase boundaries for different n H collapsed on to one universal curve, we rescaled λ by n H (δ) λ; we determined δ = 1.72, in contrast to mean-field predictions of δ = 2.0.

Momentum-space finite-size corrections for quantum Monte Carlo calculations

Extended solids are frequently simulated as finite systems with periodic boundary conditions, which due to the long-range nature of the Coulomb interaction may lead to slowly decaying finite-size errors. In the case of quantum Monte Carlo simulations, which are based on real space, both real-space and momentum-space solutions to this problem exist. Here, we describe a hybrid method which using real-space data models the spherically averaged structure factor in momentum space. We show that (i) by integration our hybrid method exactly maps onto the real-space model periodic Coulomb-interaction (MPC) method and (ii) therefore our method combines the best of both worlds (real space and momentum space). One can use known momentum-resolved behavior to improve convergence where MPC fails (e.g., at surfacelike systems). In contrast to pure momentum-space methods, our method only deals with a simple single-valued function and hence better lends itself to interpolation with exact small-momentum data as no directional information is needed. By virtue of integration, the resulting finite-size corrections can be written as an addition to MPC.

Monitoring coalescence behavior of soft colloidal particles in water by small-angle light scattering

The fractal dimension (D f) of the clusters formed during the aggregation of colloidal systems reflects correctly the coalescence extent among the particles (Gauer et al., Macromolecules 42:9103, 2009). In this work, we propose to use the fast small-angle light scattering (SALS) technique to determine the D f value during the aggregation. It is found that in the diffusion-limited aggregation regime, the D f value can be correctly determined from both the power law regime of the average structure factor of the clusters and the scaling of the zero angle intensity versus the average radius of gyration. The obtained D f value is equal to that estimated from the technique proposed in the above work, based on dynamic light scattering (DLS). In the reaction-limited aggregation (RLCA) regime, due to contamination of small clusters and primary particles, the power law regime of the average structure factor cannot be properly defined for the D f estimation. However, the scaling of the zero angle intensity versus the average radius of gyration is still well defined, thus allowing one to estimate the D f value, i.e., the coalescence extent. Therefore, when the DLS-based technique cannot be applied in the RLCA regime, one can apply the SALS technique to monitor the coalescence extent. Applicability and reliability of the technique have been assessed by applying it to an acrylate copolymer colloid.