Structural properties of pure simple alcohols from ethanol, propanol, butanol, pentanol, to hexanol: comparing Monte Carlo simulations with experimental SAXS data

The primary liquid alcohols from ethanol to 1-hexanol were studied utilizing the configurational-bias Monte Carlo (MC) simulations of the modeled alcohols (transferable potential for phase equilibria-united atom model) and the small-angle X-ray scattering (SAXS) method. A novel approach for calculating the scattering intensities from the theoretically obtained MC data by utilizing the Debye equation and their further validation with experimental results was introduced. This procedure is important, since the common problem of how to initially separate the intra- and intermolecular contributions to the scattering when comparing the calculated and experimental data was successfully avoided. Nevertheless, the intra- and intermolecular contributions to the scattering were able to be investigated directly from the MC results. The most pretentious task of the procedure was the suppression of the MC box background scattering, which was solved by utilizing the averaging of the scattering intensities over the different box sizes. This method of the scattering intensity calculations enabled us to make a theoretical analog to the well-known small-angle neutron scattering contrast matching experiment that, in our case, nicely revealed the origin of the two alcohol scattering peaks in the SAXS regime of the scattering curves (0.3 A(-1) < q < 3 A(-1)). For the example of butanol, the outer alcohol scattering peaks at approximately 1.40 A(-1) were unambiguously ascribed to the correlations between the alcohol hydrocarbon tails described by the gCH(x)CH(x)(r) pair correlation function. Similarly, the inner alcohol scattering peaks that shift from approximately 0.8 to approximately 0.4 A(-1) with an increasing alkyl chain length of the alcohol molecule are mainly the consequence of the O-O correlations. These findings were tested on pentanol/water mixtures and further applied to the results of the structural investigations on the binary and ternary microemulsion systems of the nonionic surfactant Brij 35 (Tomsic, et al. J. Phys. Chem. B 2004, 108, 7021; Tomsic, et al. J. Colloid Interface Sci. 2006, 294, 194), which were in fact the actual motivation for this present study.     

A small-angle scattering study on equilibrium clusters in lysozyme solutions

We use small-angle scattering experiments to investigate the structural properties of aqueous lysozyme solutions under conditions where the existence of equilibrium clusters has recently been demonstrated (Nature 2004, 432, 492). We also discuss the possible emergence of a low angle scattering contribution, which recently attracted interest due to its appearance in solutions of various proteins. We demonstrate that in lysozyme solutions under our experimental conditions such rising low q intensities can only be observed under special circumstances and can thus not be attributed to the existence of a universal long-range attraction. We then focus on the structural properties of the equilibrium clusters as a function of protein concentration, temperature, and ionic strength. We show that the experimental structure factors obtained from the scattering measurements exhibit the typical cluster-cluster peak q(c) reflecting the mean distance between charged clusters as well as a monomer-monomer peak q(m), which represents the nearest neighbor shell of monomers within a single cluster. The underlying principle for the formation of these structures is the coexistence of two opposing forces, a short-range attraction and a long-range repulsion due to residual charges. We can quantitatively analyze our scattering data by applying a simple equilibrium cluster model and calculate an average cluster aggregation number, N(c). The thus obtained cluster aggregation number increases linearly with volume fraction. We also observe an increasing N(c) as temperature decreases and as the screening of residual charges increases. We point out the importance of the existence of equilibrium clusters and the universality of this phenomenon for self-assembling processes observed in nature. Finally, we discuss the limitations of our simple globular cluster model in view of recent findings from computer simulations.     

Molecular dynamics simulation of polymer electrolytes based on poly(ethylene oxide) and ionic liquids. I. Structural properties

Molecular dynamics (MD) simulations have been performed for prototype models of polymer electrolytes in which the salt is an ionic liquid based on 1-alkyl-3-methylimidazolium cations and the polymer is poly(ethylene oxide), PEO. The MD simulations were performed by combining the previously proposed models for pure ionic liquids and polymer electrolytes containing simple inorganic ions. A systematic investigation of ionic liquid concentration, temperature, and the 1-alkyl- chain length, [1,3-dimethylimidazolium]PF6, and [1-butyl-3-methylimidazolium]PF6, effects on resulting equilibrium structure is provided. It is shown that the ionic liquid is dispersed in the polymeric matrix, but ionic pairs remain in the polymer electrolyte. Imidazolium cations are coordinated by both the anions and the oxygen atoms of PEO chains. Probability density maps of occurrences of nearest neighbors around imidazolium cations give a detailed physical picture of the environment experienced by cations. Conformational changes on PEO chains upon addition of the ionic liquid are identified. The equilibrium structure of simulated systems is also analyzed in reciprocal space by using the static structure factor, S(k). Calculated S(k) display a low wave-vector peak, indicating that spatial correlation in an extended-range order prevail in the ionic liquid polymer electrolytes. Long-range correlations are assigned to nonuniform distribution of ionic species within the simulation box.     

The Effect of Phenyl Substitutions on Microstructures and Dynamics of Tetraalkylphosphonium Bis(trifluoro- methylsulfonyl)imide Ionic Liquids

Extensive atomistic simulations demonstrated that a gradual substitution of hexyl chains with phenyl groups in tetraalkylphosphonium cations results in remarkable changes in hydrogen bonding interactions, liquid structures and scattering structural functions, and rotational dynamics of hexyl chains and phenyl groups in tetraalkylphosphonium bis(trifluoromethylsulfonyl)imide ionic liquids. Hydrogen donor sites in hexyl chains present competitive characteristics with those in phenyl groups in coordinating anions, as well as their continuous and intermittent hydrogen bonding dynamics. Cation-cation and anion-anion spatial correlations show concomitant shift to short distances with decreased peak intensities with variations of cation structures, whereas cation-anion correlations have a distinct shift to large radial distances due to decreased associations of anions with neighboring cations. These microstructural changes are qualitatively manifested in shifts of prominent peaks for prevalent charge alternations and adjacency correlations between ion species in scattering structural functions. Meanwhile, rotational dynamics of hexyl chains speed up, which, in turn, slow down rotations of phenyl groups, whereas anions exhibit imperceptible changes in their rotational dynamics. These computational results are intrinsically correlated with conformational flexibilities, molecular sizes, and steric hindrance effects of phenyl groups in comparison with hexyl chains, and constrained distributions of anions around cations in heterogeneous ionic environments.     

Fe68Si32合金液态结构与固态组织的相关性

利用液态X射线衍射仪研究了Fe68Si32合金的液态结构，获得了结构因子、径向分布函数、原子间的最近邻距离和配位数.结果表明，在1250～1450 ℃范围内液态合金的最近邻距离为0.259～0.260 nm，配位数为10.3(±0.2)；液态合金的结构因子在Q=15.5 nm－1处有一明显的预峰存在.根据预峰的特性，建立了Fe68Si32熔体的结构模型，即体心立方结构的有序Fe3Si原子团以共面的方式形成Fe3Si面心立方超结构(DO3)；合金在1250 ℃的径向分布函数的Gauss分解结果与合金的面心立方模型吻合较好.预峰的产生是面心立方超结构原子团中Si原子之间相互关联的外在表现. Fe68Si32合金的固态X射线衍射显示合金中含有Fe3Si相，而且其特征峰与合金的结构因子的峰位基本一致，表明Fe68Si32合金的液固态结构之间联系紧密.     

Simulation of electric double layers with multivalent counterions: ion size effect

In this paper, the structure of the electric double layer in the presence of (mostly) multivalent counterions is investigated through Monte Carlo simulations. Unlike previous similar studies addressing this matter, the difference of this study lies in the use of realistic hydrated ion sizes. Additionally, two different methods for calculating energies in the Metropolis algorithm are applied. The obtained results show that the conclusions of preceding papers must be revised. In particular, our simulations suggest the existence of certain ion layering effects at high surface charge densities, which are not accounted for by integral equation theories in the case of divalent counterions. These layering effects could justify why the overcharging phenomena due to ion size correlations are hardly observable in real colloids with divalent counterions. The existence of charge inversion due to ion size correlations (and without requiring specific counterion adsorption) is probed for trivalent counterions. Moreover, the hypernetted-chain/mean-spherical-approximation is tested under conditions not studied yet.     

Ionic liquid near a charged wall: structure and capacitance of electrical double layer

We study the effects of ion size asymmetry and short-range correlations on the electrical double layer in ionic liquids: we perform molecular dynamics simulations of a model ionic liquid between two "electrodes" and calculate the differential capacitance of each as a function of the electrode potential. The capacitance curve has an asymmetric "bell-shape" character, in qualitative agreement with recent experiments and the mean- field theory (MFT) which takes into account the limitation on the maximal local density of ions. The short-range ionic correlations, not included in the MFT, lead to an overscreening effect which changes radically the structure of the double layer at small and moderate charging. With the radius of cations taken to be twice as large as anions, the position of the main capacitance maximum is shifted positively from the potential of zero charge (PZC), as predicted by MFT. An extension of the theory (EMFT), however, reproduces the simulated capacitance curve almost quantitatively. Capacitance curves for real ionic liquids will be affected by nonspherical shape of ions and sophisticated pair potentials, varying from liquid to liquid. But understanding the capacitance behavior of such model system is a basis for rationalizing those more specific features.     

Versatile application of indirect Fourier transformation to structure factor analysis: from X-ray diffraction of molecular liquids to small angle scattering of protein solutions

We highlight versatile applicability of a structure-factor indirect Fourier transformation (IFT) technique, hereafter called SQ-IFT. The original IFT aims at the pair distance distribution function, p(r), of colloidal particles from small angle scattering of X-rays (SAXS) and neutrons (SANS), allowing the conversion of the experimental form factor, P(q), into a more intuitive real-space spatial autocorrelation function. Instead, SQ-IFT is an interaction potential model-free approach to the 'effective' or 'experimental' structure factor to yield the pair correlation functions (PCFs), g(r), of colloidal dispersions like globular protein solutions for small-angle scattering data as well as the radial distribution functions (RDFs) of molecular liquids in liquid diffraction (LD) experiments. We show that SQ-IFT yields accurate RDFs of liquid H(2)O and monohydric alcohol reflecting their local intermolecular structures, in which q-weighted structure function, qH(q), conventionally utilized in many LD studies out of necessity of performing direct Fourier transformation, is no longer required. We also show that SQ-IFT applied to theoretically calculated structure factors for uncharged and charged colloidal dispersions almost perfectly reproduces g(r) obtained as a solution of the Ornstein-Zernike (OZ) equation. We further demonstrate the relevance of SQ-IFT in its practical applications, using SANS effective structure factors of lysozyme solutions reported in recent literatures which revealed the equilibrium cluster formation due to coexisting long range electrostatic repulsion and short range attraction between the proteins. Finally, we present SAXS experiments on human serum albumin (HSA) at different ionic strength and protein concentration, in which we discuss the real space picture of spatial distributions of the proteins via the interaction potential model-free route.     

液态纯铁微观结构的温度变化特性

利用液态金属高温X射线衍射仪对纯铁熔体的微观结构进行了研究, 获得了结构因子、双体分布函数、原子间最近邻距离以及配位数. 结果表明, 随着温度的升高, 结构因子和双体分布函数第一峰的高度逐渐降低; 原子间最近邻距离则先降低然后基本保持不变; 纯铁熔体的配位数和原子团相关半径在1600～1650 ℃的温度范围内有一个突变, 表明熔体中发生了结构转变; 对相关半径的物理意义进行了探讨.     

Cu-12％Al合金熔体内中程有序原子团簇

通过高温X射线衍射仪研究了Cu 12％Al（质量分数,下同）合金熔体结构,并用纯铜作对比实验.在1250 ℃时,发现Cu 12％Al合金熔体结构因子曲线上18.5 nm－1位置有预峰出现.随着温度的下降,预峰变得更加明锐.预峰的出现是液体中存在中程有序的标志.通过熔态旋淬法获得该合金的快速凝固条带,对条带进行固态X射线衍射分析,其结构是具有有序体心立方晶格的Cu3Al.熔体内的中程有序结构单元尺寸与快凝Cu3Al（111）晶面面间距d111数值一致.由双体分布函数得到的最近邻原子距离、配位数.结合原子团簇结构单元的几何模型,计算得出该体心立方的棱边长(a=3.00 10－10m)与文献中所提供的固态晶格常数（a=2.95 10－10 m）基本吻合.可证明该合金熔体中存在以DO3结构为基本单元的中程有序原子团簇,在液相线以上200 ℃温度范围内这种中程有序都能稳定存在,并随着温度的下降,中程有序的相关尺寸逐渐增大.     

Intermolecular association in liquid N-methylacetamide as studied by x-ray scattering

A structural investigation of liquid N methylacetamide was performed at 308 K using x-ray scattering. To extract the molecular form factor F1(q), the geometry of the conformer which has been found in the crystal is considered. The intermolecular structure function DM(q) is interpreted in terms of H-bonding interactions. The crystal N...O distance is taken into accounted and the number of H bond(s) is assumed to be, respectively, equal to one and two. The liquid structure can be described by a linear dimer or chainlike trimer similar to the ones existing in the crystal. The structure factors SM(q) extracted from these clusters fairly agree with the experimental one beyond q=2.5 A(-1).     

Spatial correlations of density and structural fluctuations in liquid water: a comparative simulation study

We use large-scale classical simulations employing different force fields to study spatial correlations between local density and structural order for water in the liquid temperature range. All force fields investigated reproduce the main features of the experimental SAXS structure factor S(q), including the minimum at small q, and the recent TIP4P/2005 parametrization yields almost quantitative agreement. As local structural order parameters we consider the tetrahedrality and the number of hydrogen bonds and calculate all pure and mixed spatial two-point correlation functions. Except for the density-density correlation function, there are only weak features present in all other correlation functions, showing that the tendency to form structural clusters is much weaker than the well-known tendency of water to form density clusters (i.e., spatially correlated regions where the density deviates from the mean). In particular, there are only small spatial correlations between local density and structural fluctuations, suggesting that features in density-density correlations (such as measured by the structure factor) are not straightforwardly related to spatial correlations of structure in liquid water.     

Local Structure Evolution in Particle Network Formation Studied by Brownian Dynamics Simulation

The effect of solid content and colloidal interactions on the structure of forming networks of colloidal particles is studied by Brownian dynamics simulation. The different situations are compared in terms of the pair distribution function and the distribution of nearest neighbors around each particle. The results indicate that, in fast coagulation, the higher solid contents lead to a freezing-in of the liquid structure. Nevertheless, this effect can be reduced substantially by the introduction of a shallow secondary minimum and an energy barrier in the interaction potential. However, the structures resulting from such slow coagulation show a substantial degree of porosity, larger than those produced at the same solid content but by fast coagulation. It is also shown how the porosity (defined on a few particle diameters) is reflected in the distribution of nearest neighbors around the center particle, i.e., the very local conformation in the particle network. Fractal analysis shows that, at the relatively high volume fractions considered in this study, no intermediate fractal regime exists. Copyright 2000 Academic Press.     

A model for transits in dynamic response theory

The first goal of vibration-transit (V-T) theory was to construct a tractable approximate Hamiltonian from which the equilibrium thermodynamic properties of monatomic liquids can be calculated. The Hamiltonian for vibrations in an infinitely extended harmonic random valley, together with the universal multiplicity of such valleys, gives an accurate first-principles account of the measured thermodynamic properties of the elemental liquids at melt. In the present paper, V-T theory is extended to nonequilibrium properties, through an application to the dynamic structure factor S(q,omega). It was previously shown that the vibrational contribution alone accurately accounts for the Brillouin peak dispersion curve for liquid sodium, as compared both with molecular-dynamics (MD) calculations and inelastic x-ray scattering data. Here it is argued that the major effects of transits will be to disrupt correlations within the normal-mode vibrational motion and to provide an additional source of inelastic scattering. We construct a parametrized model for these effects and show that it is capable of fitting MD results for S(q,omega) in liquid sodium. A small discrepancy between model and MD at large q is attributed to multimode vibrational scattering. In comparison, mode coupling theory formulates S(q,omega) in terms of processes through which density fluctuations decay. While mode coupling theory is also capable of modeling S(q,omega) very well, V-T theory is the more universal since it expresses all statistical averages, thermodynamic functions, and time correlation functions alike, in terms of the same motional constituents, vibrations and transits.     

Molecular dynamics simulations on the local order of liquid and amorphous ZnTe

Molecular dynamics studies of structural and dynamical correlations of molten and vitreous states under several conditions of density and temperature were performed. We use an effective recently proposed interatomic potential, consisting of two- and three-body covalent interactions which has successfully described the structural, dynamical, and structural phase transformation induced by pressure in ZnTe [D. S. Borges and J. P. Rino, Phys. Rev. B 72, 014107 (2005)]. The two-body term of the interaction potential consists of Coulomb interaction resulting from charge transfer, steric repulsion due to atomic sizes, charge-dipole interaction to include the effect of electronic polarizability of anions, and dipole-dipole (van der Waals) interactions. The three-body covalent term is a modification of the Stillinger-Weber potential. Molecular dynamics simulations in isobaric-isenthalpic ensemble have been performed for systems amounting to 4096 and 64 000 particles. Starting from a crystalline zinc-blende (ZB) structure, the system is initially heated until a very homogeneous liquid is obtained. The vitreous zinc telluride phase is attained by cooling the liquid at sufficiently fast cooling rates, while slower cooling rates lead to a disordered ZB crystalline structure. Two- and three-body correlations for the liquid and vitreous phases are analyzed through pair distribution functions, static structure factors, and bond angle distributions. In particular, the neutron static structure factor for the liquid phase is in very good agreement with both the reported experimental data and first-principles simulations.     

Evaluation of small-angle x-ray scattering data of a Raney-type Ni catalyst with computer simulation

A reverse Monte Carlo-type simulation method was developed for the evaluation of anomalous small-angle x-ray scattering data of a Raney-type Ni catalyst. Based on other experimental data the catalytic Ni particles were modeled as small crystalline cylinders dispersed in the matrix. The average size of the Ni particles and their pair-correlation function were determined. Despite the unknown density of the catalyst, it is shown that each particle has about 2 neighbors in the first neighboring shell independent of the modeling density, and the position of the first peak of the pair-correlation function does not depend on the modeling density. A method was elaborated to get reasonable performance of the Reverse Monte Carlo-type simulation. The scattered intensity was calculated on the basis of probe scattering atoms put inside the cylinders. The effects of the omission of the real number of the atoms, the unknown density, the lack of normalization and the uncertainties in the cross sections were unified in two constants that were determined during the simulation. The method can be used for nanoparticles with other shape, where analytic form factors are complicated, and it may be powerful in the investigation of the usually neglected or simplified inter-particle structure of these systems.     

A molecular dynamics investigation of the structural and dynamic properties of the ionic liquid 1-n-butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide

Molecular dynamics simulations have been performed to investigate the structure and dynamics of the ionic liquid, 1-n-butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide ([C(4)mim][Tf(2)N]) in the temperature range of 283-460 K. Extensive analysis was carried out to characterize a number of structural and dynamic features. Transport properties were computed using a variety of equilibrium methods that employed the Green-Kubo and Einstein formulations. Nonequilibrium techniques were also used. In general, different methods mostly yielded consistent results, although some differences were observed. Computed self-diffusivities and ionic conductivities tended to be slightly lower than experimental values, while computed viscosities were significantly higher than experiment. Computed thermal conductivities agreed reasonably well with experimental data. Despite these discrepancies, the simulations capture the experimental temperature-dependent trends for all these transport properties. Single ion dynamics were studied by examining diffusional anisotropy, the self-part of the van Hove function, non-Gaussian parameters, and incoherent intermediate scattering functions. It is found that cations diffuse faster than anions and are more dynamically heterogeneous. A clear anisotropy is revealed in cation displacement, with the motion normal to the imidazolium ring plane being the most hindered and the motion along the alkyl chain in the plane of the ring being the most facile. Cations structurally relax faster than anions but they rotationally relax slower than anions. There is a pronounced temperature dependence to the rotational anisotropy of the cations, but only a weak temperature dependence for the anions. The ionic conductivity deviates from the Nernst-Einstein relation due to the correlated motion of cations and anions. The results suggest that the dynamical behavior of this and related ionic liquids is extremely complex and consists of many different modes with widely varying timescales, making the prediction of dynamical trends extremely difficult.     

HUG and SQUEEZE: using CRYSTALS to incorporate resonant scattering in the SQUEEZE structure‐factor contributions to determine absolute structure

The resonant‐scattering contributions to single‐crystal X‐ray diffraction data enable the absolute structure of crystalline materials to be determined. Crystal structures can be determined even if they contain considerably disordered regions because a correction is available via a discrete Fourier transform of the residual electron density to approximate the X‐ray scattering from the disordered region. However, the corrected model cannot normally account for resonant scattering from atoms in the disordered region. Straightforward determination of absolute structure from crystals where the strongly resonantly scattering atoms are not resolved has therefore not been possible. Using an approximate resonant‐scattering correction to the X‐ray scattering from the disordered regions, we have developed and tested a procedure (HUG) to recover the absolute structure using conventional Flack x refinement or other post‐refinement determination methods. Results show that in favourable cases the HUG method works well and the absolute structure can be correctly determined. It offers no useful improvement in cases where the original correction for the disordered region scattering density is problematic, for example, when a large fraction of the scattering density in the crystal is disordered, or when voids are not occupied equally by the disordered species. Crucially, however, if the approach does not work for a given structure, the statistics for the absolute structure measures are not improved, meaning it is unlikely to lead to misassignment of absolute structure.