Scattering Structure Factor Research Articles

A multiscale simulation model for poly(ethylene oxide)

An overview of the recent development of a multiscale simulation of amorphous polymeric materials at the bulk density is presented. Poly(ethylene oxide), (PEO), (CH3O-[CH2-CH2-O]nCH3) was selected to illustrate the method. The model starts from an ab initio quantum chemistry to obtain the statistical weights of polymer conformation based on the rotational isomeric state (RIS) theory. PEO chains were then mapped to a coarse-grained model using the modified RIS model onto the second nearest neighbor diamond (2nnd) lattice. The average non-bonded interactions were treated by the discretized Lennard-Jones (LJ) potential. Bulk PEO melts with molecular weight up to 8000 g/mol was generated and equilibrated. The on-lattice properties such as molecular size and conformational statistics agree well with the theory. Fully atomistic amorphous PEO models can be obtained by the reverse-mapping procedure to recover the missing atoms. After an energy minimization step, properties including torsional angle distribution, solubility parameter and static neutron scattering structure factor are in good agreement with experimental results.

Self-association behaviour of atactic polymethacrylic acid in aqueous solution investigated by atomistic molecular dynamics simulations

The self-association behaviour of atactic poly(methacrylic acid) (a-PMA) in water was investigated by atomistic molecular dynamics (MD) simulations. Simulations show that interchain association of a-PMA occurs only in its un-neutralised form, by hydrogen bonding between –COOH groups, which is in agreement with the experimental observation. Chain conformations, dihedral angle distributions, hydration behaviour, scattering structure factor and enthalpy-of-hydration (i.e. aqueous solvation) were analysed as a function of concentration for un-neutralised PMA, across dilute to concentrated regimes. The average 〈Rg〉 of the chain remains unaffected in solution and also for amorphous undissolved a-PMA phase, confirming the occurrence of the approximate theta-solution condition for the first time, as revealed by simulations, in a polar hydrogen-bonding polymer aqueous solution. Chain hydration behaviour and scattering structure factor show significant changes in concentrated regime. Scattering intensity collapse occurs in concentrated PMA solution, due to the existence of the swollen regime captured for the first time by explicit-MD-simulations. The hydration of PMA is driven by H-bonding, specifically between H atoms of the COOH groups and O atoms of water molecules in the closest coordination shell. The enthalpy of hydration of PMA is dominated by PMA–water interactions (charges and H-bonding). The thermodynamic contributions of PMA–PMA and PMA–water interactions towards the electrostatics as well as the dispersion components of the total solvation-enthalpy become more favourable than water–water interactions.

Understanding the structure of molecular liquids via combinations of molecular dynamics simulations and Reverse Monte Carlo modeling: Handling information deficiency

The problem of information deficiency, i.e., when the number of available diffraction (and/or EXAFS) experiments is (in many cases, much) lower than the number of partial radial distribution function in the system, is considered, with a focus on molecular liquids. Two approaches, both relying heavily on Reverse Monte Carlo (RMC) modeling [R.L. McGreevy, L. Pusztai, Molec. Simul. 1, 359 (1988)] are sketched: (1) molecular dynamics simulation, followed by RMC modeling (‘RMCMD’), and (2) RMC modeling that incorporates the extensive use of interatomic potential functions (‘RMC_POT’). We show that applying either method is useful, although the ‘RMCMD’ is restricted to smaller molecules. With larger molecules, the molecular structure begins to dominate the measurable total scattering structure factor and therefore, Reverse Monte Carlo is expected to play a more and more important role in conformational analyses in the liquid state.

Pair correlations in a bidisperse ferrofluid in an external magnetic field: theory and computer simulations

The pair distribution function g(r) for a ferrofluid modeled by a bidisperse system of dipolar hard spheres is calculated. The influence of an external uniform magnetic field and polydispersity on g(r) and the related structure factor is studied. The calculation is performed by diagrammatic expansion methods within the thermodynamic perturbation theory in terms of the particle number density and the interparticle dipole-dipole interaction strength. Analytical expressions are provided for the pair distribution function to within the first order in number density and the second order in dipole-dipole interaction strength. The constructed theory is compared with the results of computer (Monte Carlo) simulations to determine the range of its validity. The scattering structure factor is determined using the Fourier transform of the pair correlation function g(r) − 1. The influence of the granulometric composition and magnetic field strength on the height and position of the first peak of the structure factor that is most amenable to an experimental study is analyzed. The data obtained can serve as a basis for interpreting the experimental small-angle neutron scattering results and determining the regularities in the behavior of the structure factor, its dependence on the fractional composition of a ferrofluid, interparticle correlations, and external magnetic field.

The structure of PX3 (X = Cl, Br, I) molecular liquids from X-ray diffraction, molecular dynamics simulations, and reverse Monte Carlo modeling

Synchrotron X-ray diffraction measurements have been conducted on liquid phosphorus trichloride, tribromide, and triiodide. Molecular Dynamics simulations for these molecular liquids were performed with a dual purpose: (1) to establish whether existing intermolecular potential functions can provide a picture that is consistent with diffraction data and (2) to generate reliable starting configurations for subsequent Reverse Monte Carlo modelling. Structural models (i.e., sets of coordinates of thousands of atoms) that were fully consistent with experimental diffraction information, within errors, have been prepared by means of the Reverse Monte Carlo method. Comparison with reference systems, generated by hard sphere-like Monte Carlo simulations, was also carried out to demonstrate the extent to which simple space filling effects determine the structure of the liquids (and thus, also estimating the information content of measured data). Total scattering structure factors, partial radial distribution functions and orientational correlations as a function of distances between the molecular centres have been calculated from the models. In general, more or less antiparallel arrangements of the primary molecular axes that are found to be the most favourable orientation of two neighbouring molecules. In liquid PBr3 electrostatic interactions seem to play a more important role in determining intermolecular correlations than in the other two liquids; molecular arrangements in both PCl3 and PI3 are largely driven by steric effects.

Atomistic Simulations of Gel and Liquid Crystalline Lipid Bilayers

A re-parametrized united atom force field that can describe the gel as well as the liquid crystalline phase with reasonable accuracy is presented. It is based on new quantum mechanically determined (using CPMD calculations on sets of representative molecular conformations) fractional charges and tail dihedral potentials. For the Lennard-Jones parameters of the tail hydrocarbons we have chosen a set that has been fitted to give a good description of liquid hydrocarbons. Experimental data as area per lipid, x-ray and neutron scattering structure factors and NMR order parameters are well reproduced for both phases. The tilt angle of the gel phase is also reproduced. The experimental phase transition enthalpy is obtained with good accuracy. Still, it is noted that even better accuracy with experiment can be obtained by doing a separate parametrization for the two phases.

Modeling Dendrimers Charge Interaction in Solution: Relevance in Biosystems

Dendrimers are highly branched macromolecules obtained by stepwise controlled, reaction sequences. The ability to be designed for specific applications makes dendrimers unprecedented components to control the structural organization of matter during the bottom-up synthesis of functional nanostructures. For their applications in the field of biotechnology the determination of dendrimer structural properties as well as the investigation of the specific interaction with guest components are needed. We show how the analysis of the scattering structure factor S(q), in the framework of current models for charged systems in solution, allows for obtaining important information of the interdendrimers electrostatic interaction potential. The finding of the presented results outlines the important role of the dendrimer charge and the solvent conditions in regulating, through the modulation of the electrostatic interaction potential, great part of the main structural properties. This charge interaction has been indicated by many studies as a crucial factor for a wide range of structural processes involving their biomedical application. Due to their easily controllable properties dendrimers can be considered at the crossroad between traditional colloids, associating polymers, and biological systems and represent then an interesting new technological approach and a suitable model system of molecular organization in biochemistry and related fields.

The liquid structure of tetrachloroethene: Molecular dynamics simulations and reverse Monte Carlo modeling with interatomic potentials

The liquid structure of tetrachloroethene has been investigated on the basis of measured neutron and X-ray scattering structure factors, applying molecular dynamics simulations and reverse Monte Carlo (RMC) modeling with flexible molecules and interatomic potentials. As no complete all-atom force field parameter set could be found for this planar molecule, the closest matching all-atom Optimized Potentials for Liquid Simulations (OPLS-AA) intra-molecular parameter set was improved by equilibrium bond length and angle parameters coming from electron diffraction experiments [I. L. Karle and J. Karle, J. Chem. Phys. 20, 63 (1952)]. In addition, four different intra-molecular charge distribution sets were tried, so in total, eight different molecular dynamics simulations were performed. The best parameter set was selected by calculating the mean square difference between the calculated total structure factors and the corresponding experimental data. The best parameter set proved to be the one that uses the electron diffraction based intra-molecular parameters and the charges qC = 0.1 and qCl = -0.05. The structure was further successfully refined by applying RMC computer modeling with flexible molecules that were kept together by interatomic potentials. Correlation functions concerning the orientation of molecular axes and planes were also determined. They reveal that the molecules closest to each other exclusively prefer the parallel orientation of both the molecular axes and planes. Molecules forming the first maximum of the center-center distribution have a preference for <30° and >60° axis orientation and >60° molecular plane arrangement. A second coordination sphere at ∼11 Å and a very small third one at ∼16 Å can be found as well, without preference for any axis or plane orientation.

Conformational analysis of bis(methylthio)methane and diethyl sulfide molecules in the liquid phase: reverse Monte Carlo studies using classical interatomic potential functions

Series of flexible molecule reverse Monte Carlo calculations, using bonding and non-bonding interatomic potential functions (FMP-RMC), were performed starting from previous molecular dynamics results that had applied the OPLS-AA and EncadS force fields. During RMC modeling, the experimental x-ray total scattering structure factor was approached. The discrepancy between experimental and calculated structure factors, in comparison with the molecular dynamics results, decreased substantially in each case. The room temperature liquid structure of bis(methylthio)methane is excellently described by the FMP-RMC simulation that applied the EncadS force field parameters. The main conformer was found to be AG with 55.2%, followed by 37.2% of G+G+ (G−G−) and 7.6% of AA; the stability of the G+G+ (G−G−) conformer is most probably caused by the anomer effect. The liquid structure of diethyl sulfide can be best described by applying the OPLS-AA force field parameters during FMP-RMC simulation, although in this case the force field parameters were found to be not fully compatible with experimental data. Here, the two main conformers are AG (50.6%) and the AA (40%). In addition to findings on the actual real systems, a fairly detailed comparison between traditional and FMP-RMC methodology is provided.

Comparison of the atomic level structure of the plastic crystalline and liquid phases of CBr2Cl2: neutron diffraction and reverse Monte Carlo modelling

Neutron diffraction results obtained for plastic crystalline dichlorodibromomethane (CBr2Cl2) have been modelled by means of the reverse Monte Carlo method. Comparison with its liquid phase is provided at several levels of the atomic structure (total scattering structure factors, partial radial distribution functions, orientational and dipole–dipole correlations). The results reveal that the relative orientation of neighbouring molecules largely depends on the steric effect. The small dipole moment does not have as strong an influence as the steric effect on the short-range order. Our observations fit well with earlier findings presented for the series CBrnCl4−n (n = 0, 1, 2, 4).

The Conformation of a Ribose Derivative in Aqueous Solution: A Neutron‐Scattering and Molecular Dynamics Study

The structure of aqueous solutions of methyl β-D-ribofuranoside was investigated by coupling molecular dynamics (MD) simulations and neutron scattering measurements with isotopic substitution. Using a sample of the sugar isotopically-labeled at a single unique position, neutron scattering structure factors and radial distribution functions can be compared with MD simulations constrained to different conformations to determine which conformer best fits the experimental results. Three different simulations were performed with the methyl ether group of the sugar unconstrained and constrained in each of its staggered orientations. The results of the unconstrained simulation showed that the methyl ester group occupied predominantly the 300° position, which is in agreement with the diffraction experimental results. This result suggests that the molecular mechanics force field used in the simulation adequately describes the conformation of the 1-methyl ether group in the methyl β-D-ribofuranoside.

Driving Force for Crystallization of Anionic Lipid Membranes Revealed by Atomistic Simulations

Crystalline vesicles are promising nanomaterials due to their mechanical stability in various environments. To control their fabrication, it is essential to understand the effects of different experimental conditions on crystallization. Here we perform atomistic molecular dynamics simulations of anionic lipid membranes of 1,2-dilauroyl-sn-glycero-3-phosphol-L-serine. In the presence of Na(+) monovalent counterions, we access the phase transition from the liquid-like disordered liquid-crystalline phase to the ordered gel phase by lowering the temperature of the system. The phase transition is conclusively evidenced by the scattering structure factor. Quantitative calculations show that the enhancement of the intertail van der Waals interaction (about -6 k(B)T) plays a dominant role in driving the phase transition rather than the increase in the cohesive interaction (-0.5 k(B)T) between lipids and counterions. Meanwhile, in the presence of multivalent counterions of Zn(2+) or La(3+) the gel phase is found throughout the temperature range investigated. Moreover, the van der Waals interaction per hydrocarbon group is ∼20% stronger in the gel phase (∼ -1.8 k(B)T regardless of the counterions) than in the liquid-crystalline phase (-1.5 k(B)T).

Comparison of the TIP4P-2005, SWM4-DP and BK3 interaction potentials of liquid water with respect to their consistency with neutron and X-ray diffraction data of pure water

Following a fairly comprehensive study on popular interaction potentials of water (Pusztai et al., J. Chem. Phys., 2008, 129, 184103), here two more recent polarizable potential sets, SWM4-DP (Lamoureux et al., Chem. Phys. Lett., 2006, 418, 245) and BK3 (Kiss et al., J. Chem. Phys., 2013, 138, 204507) are compared to the TIP4P-2005 water potential (Abascal et al., J. Chem. Phys., 2005, 123, 234505) that had previously appeared to be most favoravble. The basis of comparison was the compatibility with the results of neutron and X-ray diffraction experiments on pure water, using the scheme applied by Pusztai et al. (2008). The scheme combines the experimental total scattering structure factors (TSSF) and partial radial distribution functions (PRDF) from molecular dynamics simulations in a single structural model. Goodness-of-fit values to the O-O, O-H and H-H simulated PRDF-s and to the experimental neutron and X-ray TSSF provided a measure that can characterize the level of consistency between interaction potentials and diffraction experiments. Among the sets of partial RDF-s investigated here, the ones corresponding to the SWM4-DP potential parameters have proven to be the most consistent with the particular diffraction results taken for the present study, by a hardly significant margin ahead of BK3. Perhaps more importantly, it is shown that the three sets of potential parameters produce nearly equivalent PRDF-s that may all be made consistent with diffraction data at a very high level. The largest differences can be detected in terms of the O-O partial radial distribution function.

Hydration structure in concentrated aqueous lithium chloride solutions: A reverse Monte Carlo based combination of molecular dynamics simulations and diffraction data

We report on a comparison of three interaction potential models of water (SPC/E, TIP4P-2005, and SWM4-DP) for describing the structure of concentrated aqueous lithium chloride solutions. Classical molecular dynamics simulations have been carried out and total scattering structure factors, calculated from the particle configurations, were compared with experimental diffraction data. Later, reverse Monte Carlo structural modelling was applied for refining molecular dynamics results, so that particle configurations consistent with neutron and X-ray diffraction data could be prepared that, at the same time, were as close as possible to the final stage of the molecular dynamics simulations. Partial radial distribution functions, first neighbors, and angular correlations were analysed further from the best fitting particle configurations. It was found that none of the water potential models describe the structure perfectly; overall, the SWM4-DP model seems to be the most promising. At the highest concentrations the SPC/E model appears to provide the best approximation of the water structure, whereas the TIP4P-2005 model proved to be the most successful for estimating the lithium-oxygen partial radial distribution function at each concentration.

Microscopic and mesoscopic structural features of an activated carbon sample, prepared from sorghum via activation by phosphoric acid

An acidic chemical activation procedure has been used for preparing activated carbon with a surface area exceeding 1000m2/g from sorghum. In order to reveal structural features, synchrotron X-ray diffraction measurements have been performed. The structure of the material has been characterized by the total scattering structure factor and the radial distribution function describing short-range arrangement of atoms at distances of the order of a few atomic diameters as well as correlations at a longer scale, of the order of nanometers. The atomic arrangement has been found to be consistent with that of amorphous graphite-like carbon. As far as the mesoscopic structure is concerned, the presence of a characteristic distance is suggested on the basis of the clear nanometer scale oscillations of the radial distribution function, which distance may be assigned as the mesopore size in the material. It is suggested that the approach devized here may later be applied routinely for other activated carbon samples, too, for characterizing atomic and nanoscale order simultaneously.

On the Structure of Aqueous Cesium Fluoride and Cesium Iodide Solutions: Diffraction Experiments, Molecular Dynamics Simulations, and Reverse Monte Carlo Modeling

A detailed study of the microscopic structure of two electrolyte solutions, cesium fluoride (CsF) and cesium iodide (CsI) in water, is presented. For revealing the influence of salt concentration on the structure, CsF solutions at concentrations of 15.1 and 32.3 mol % and CsI solutions at concentrations of 1.0 and 3.9 mol % are investigated. For each concentration, we combine total scattering structure factors from neutron and X-ray diffraction and 10 partial radial distribution functions from molecular dynamics simulations in one single structural model, generated by reverse Monte Carlo modeling. For the present solutions we show that the level of consistency between simulations that use simple pair potentials and experimental structure factors is at least semiquantitative for even the extremely highly concentrated CsF solutions. Remaining inconsistencies seem to be caused primarily by water-water distribution functions, whereas slightly problematic parts appear on the ion-oxygen partials, too. As a final result, we obtained particle configurations from reverse Monte Carlo modeling that were in quantitative agreement with both sets of diffraction data and most of the MD simulated partial radial distribution functions. From the particle coordinates, distributions of the number of first neighbors as well as angular correlation functions were calculated. The average number of water molecules around cations in both materials decreases from about 8.0 to about 5.1 as concentration increases, whereas the same quantity for the anions (X) changes from about 5.3 to about 3.7 in the case of CsF and from about 6.2 to about 4.0 in the case of CsI. The average angle of X···H-O particle arrangements, characteristic of anion-water hydrogen bonds, is closer to 180° than that found for O···H-O arrangements (water-water hydrogen bonds) at higher concentrations.

Accurate Description of Aqueous Carbonate Ions: An Effective Polarization Model Verified by Neutron Scattering

The carbonate ion plays a central role in the biochemical formation of the shells of aquatic life, which is an important path for carbon dioxide sequestration. Given the vital role of carbonate in this and other contexts, it is imperative to develop accurate models for such a high charge density ion. As a divalent ion, carbonate has a strong polarizing effect on surrounding water molecules. This raises the question whether it is possible to describe accurately such systems without including polarization. It has recently been suggested the lack of electronic polarization in nonpolarizable water models can be effectively compensated by introducing an electronic dielectric continuum, which is with respect to the forces between atoms equivalent to rescaling the ionic charges. Given how widely nonpolarizable models are used to model electrolyte solutions, establishing the experimental validity of this suggestion is imperative. Here, we examine a stringent test for such models: a comparison of the difference of the neutron scattering structure factors of K2CO3 vs KNO3 solutions and that predicted by molecular dynamics simulations for various models of the same systems. We compare standard nonpolarizable simulations in SPC/E water to analogous simulations with effective ion charges, as well as simulations in explicitly polarizable POL3 water (which, however, has only about half the experimental polarizability). It is found that the simulation with rescaled charges is in a very good agreement with the experimental data, which is significantly better than for the nonpolarizable simulation and even better than for the explicitly polarizable POL3 model.

Modeling particle scattering structure factor for branched bio-inspired polymers in solution: A small angle X-ray scattering study

We present a study which illustrates the modeling of the Particle Scattering Structure Factor of an hyperbranched biopolymer in water solution using the Small Angle X-ray Scattering (SAXS) data. The studied sample was a sodium carboxilate terminated poly(amidoamine) dendrimer (generation 2.5) dispersed in water medium. The experimental inter-dendrimer structure factor S(q) has been analyzed in the framework of liquid integral equation theory for charged systems in solution. From that, we derive an effective interparticle interaction composed of a screened Coulombic plus hard-sphere repulsion potential, which allows the estimation of the dendrimer effective charge Zeff. The present analysis strongly supports the finding that structures and interaction of dendrimer are strongly influenced by charge effects. As a result, this quantity can be considered as a crucial parameter for the modulation of the degree of structural organization in solution, suitable for a number of potential applications. We conclude our form factor analysis with the investigation of the long-range assembly conditions during the growth of the intermediate nanoaggregates generated by the inclusion of aluminosilicate components of zeolite 13X on the surface of dendrimers.

Oscillatory acoustic phonon relaxation of excitons in quantum dot molecules

We study electrically tunable self-assembled InAs quantum dot molecules through photoluminescence (PL) and time-resolved PL measurements. For the model we assume quantum dots with cylindrical symmetry, for which the confinement potentials have been modeled as narrow quantum wells in the growth and in-plane directions matched to parabolic potentials. We focus on the hole scattering rates by bulk acoustic phonons, as these rates are the leading contribution for the neutral indirect exciton relaxation rate when the electron localizes primarily on one dot. The hole–phonon scattering structure factor for acoustic phonons is found to contain a phase relationship between the phonon wave and the hole wave function, which can be tuned by an external electric field. The phase relationship leads to interference effects and tunable oscillatory relaxation rates of indirect excitons, in agreement with experiments.

Modeling of the particle scattering structure factor for branched bio-polymers in solution: A X-ray scattering study

We present a study which illustrates the modeling of the Particle Scattering Structure Factor from Small Angle X-ray Scattering (SAXS) data. The studied sample was a poly(amidoamine) Pamam dendrimers in water solution. The intra-particle form factor P(q) has been analyzed employing an inverse Fourier transformation which allows to obtain the particle pair distance distribution function and to gain information about dendrimer shape. The experimental inter-dendrimer structure factor S(q) has been analysed in the framework of liquid integral equation theory for charged systems in solution. From that, we derive an effective interparticle interaction composed of a screened Coulombic plus hard-sphere repulsion potential, which allow the estimation of the dendrimer effective surface charge Z eff . The present analysis, applied to a Pamam dendrimers in water solution, strongly supports the finding that structures and interaction of dendrimer is strongly influenced by charge effects. As a result, this quantity can be considered as a crucial parameters for the modulation of the degree of structural organization in solution, suitable for a number of potential applications.