Interface Distribution Function Research Articles

Computationally efficient high-fidelity plasma simulations by coupling multi-species kinetic and multi-fluid models on decomposed domains

A numerical method is developed for coupling a multi-species kinetic plasma model with a 5N-moment multi-fluid plasma model. The simulation domain is decomposed such that the local conditions satisfy the corresponding plasma model's region of validity. The method allows for hybrid simulations by formulating each model as a set of conservation laws and using a continuum numerical method to solve each model's governing equations in the subdomains of the decomposed domain. The models are coupled through fluxes across subdomain interfaces. Two methods are explored for the formulation of the fluxes that can be self-consistently represented by both plasma models. One method allows for flux calculations consistent with the 5N-moment multi-fluid plasma model and assumes thermodynamic equilibrium within each species of the kinetic plasma model. The second method ensures conservation of the distribution function as well as mass, momentum, and energy by formulating the fluxes using a composite underlying distribution function at the subdomain interfaces. The methods are compared in 1D1V simulations of a double rarefaction wave and a plasma sheath using the WARPXM framework, which solves each model using the discontinuous Galerkin finite element method. Both methods for formulating the fluxes perform well as the subdomain interface distribution function approaches a Maxwellian, with the consistent method being more robust to larger deviations. A simulation of the magnetized Kelvin-Helmholtz instability in 2D2V is also performed using the consistent method, which demonstrates the potential of the domain-decomposed hybrid method in facilitating speedup and reduction in required computational resources for high-fidelity plasma simulations, allowing for the investigation of problems that are beyond current capabilities.

IpyChord: a package for evaluating small-angle X-ray scattering data of fiber symmetry

This article presents a Python-based package, ipyChord, to compute the 2D chord distribution function (CDF) from the small-angle X-ray scattering (SAXS) pattern from polymer materials with fiber-symmetrical nanostructure. The program allows construction of a harmonized SAXS pattern from a raw SAXS pattern, by normalization of the incident-beam intensity, absorption correction for sample thickness, masking blind areas on the detector, and filling in the shadow of the beamstop and its holder using symmetry operations. Patterns from modular detectors with inter-module gaps can still be fully constructed satisfactorily after determining the optimized beam position and a radial basis function. A CDF pattern computed from the full SAXS pattern can be used to determine the domain size and its variability using a graphical method. An interface distribution function computed from Bonart's longitudinal projection or sliced from a CDF meridian can quantify differently stacked hard and soft domains. Two cases of the application of ipyChord are presented. The software is open source and available at https://github.com/isaxs/ipyChord.

Suppression of Iodide Ion Migration via Sb2S3 Interfacial Modification for Stable Inorganic Perovskite Solar Cells.

In mixed halide perovskite, the halide phase segregation is commonly observed due to halide ion migration, which causes severe stability issues in perovskite devices. Here, we directly revealed the iodide-migration process via potentiostatic treatment in CsPbIBr2 perovskite. The absence of iodide ions was reduced significantly via a Sb2S3 interfacial modification. We further employed the density functional theory (DFT) calculation to optimize the geometry positions at the perovskite interface and radial distribution functions (RDF) to analyze the atom perturbation. The simulation yielded a slight distortion of the perovskite lattice at the Sb2S3-CsPbIBr2 interface and iodide ion fluctuation was reduced due to the decrease of halide vacancies. In addition, the thermally stimulated current was calculated to evaluate the defect density in the modified perovskite device. Due to the Sb2S3 interaction with perovskite, the device became stable against humidity and maintained its photoactivity over 400 h. The champion efficiency of 9.31% with 26.31% improvement was obtained in modified CsPbIBr2 perovskite solar cells.

A new Fourier transformation method for SAXS of polymer lamellar crystals

The interface distribution function is composed mainly of the self-interference item of the first interfaceF11, the interference term of the first and the second interfacesF12, and the interference term of the first and the third interfacesF13.

An improved lattice Boltzmann model for high gas and liquid density ratio in composite grids

Lattice Boltzmann method is one of the widely used in multiphase fluid flow. However, the two main disadvantages of this method are the instability of numerical calculations due to the large density ratio of two phases and impossibility of the temperature distribution to be fed back into the velocity distribution function when the temperature is simulated. Based on the combination prescribed by Inamuro, the large density ratio two-phase flow model and thermal model makes the density ratio of the model simulation to be increased to 2778:1 by optimizing the interface distribution function of two-phase which improves the accuracy of differential format. The phase transition term is added as source term into the distribution function controlling two phase order parameters to describe the temperature effect on the gas-liquid phase transition. The latent heat generated from the phase change is also added as a source term into the temperature distribution function which simulates the movement of the flow under the common coupling of density, velocity, pressure and temperature. The density and the temperature distribution of single bubble are simulated. Comparison of the simulation results with experimental results indicates a good agreement pointing out the effectiveness of the improved model.

Crystallization of hard segments in MDI/BD-based polyurethanes deformed at elevated temperature and their dependence on the MDI/BD content

Morphological variation of thermoplastic polyurethanes (TPUs) with different hard segment contents (HSCs) stretched at 100 °C higher than the Tg of hard domain was monitored by in-situ wide-angle X-ray scattering (WAXS) and small-angle X-ray scattering (SAXS) techniques. WAXS patterns reveal that the crystalline modification of TPUs with high HSCs transforms from paracrystal (termed as form I) to form III of 4,4′-methylene diphenyl diisocyanate/1,4-butanediol (MDI/BD) segment, and TPUs with low HSCs show the direct transition from amorphous MDI/BD packing to form III packing. The form III crystals are fibrillar hard domains. Chord distribution functions (CDFs) computed from the SAXS patterns were employed to illustrate the domain topology. The streak-like CDF peaks off the meridian indicate the existence of cylindrical microfibrils which are composed of very low inhomogeneities between the destructured hard domains and stretched soft domains along the straining direction. These microfibrils of TPUs with low HSCs present a periodically lateral correlation. Interface distribution function (IDF) and chord length distribution (CLD) were computed from Bonart's longitudinal and transverse projection to quantify the domain stacking and microfibril arrangement respectively. The average size of hard domains increases up to a constant size with the increasing macroscopic strain which may be related to the maximal sequence length of hard segment. The average size of soft domain also reaches up to a constant size at large strain that is smaller than the fully-extended length of soft segment. The variation of domain size is different from deformation at room temperature. The HSC affects the behaviors of morphological evolution significantly.

Performance evaluation of the general characteristics based off-lattice Boltzmann scheme and DUGKS for low speed continuum flows

The general characteristics based off-lattice Boltzmann scheme proposed by Bardow et al. [1] (hereafter Bardow's scheme) and the discrete unified gas kinetic scheme (DUGKS) [2] are two methods that successfully overcome the time step restriction by the collision time, which is commonly seen in many other kinetic schemes. In this work, we first perform a theoretical analysis of the two schemes in the finite volume framework by comparing their numerical flux evaluations. It is found that the effect of collision term is considered in the evaluation of the cell interface distribution function in both schemes, which explains why they can overcome the time step restriction and can give accurate results even as the time step is much larger than the collision time. The difference between the two schemes lies in the treatment of the integral of the collision term when evaluating the cell interface distribution function, in which Bardow's scheme uses the rectangular rule while DUGKS uses the trapezoidal rule. The performance of the two schemes, i.e., accuracy, stability, and efficiency are then compared by simulating several two dimensional flows, including the unsteady Taylor–Green vortex flow, the steady lid-driven cavity flow, and the laminar boundary layer problem. It is observed that, DUGKS can give more accurate results than Bardow's scheme with a same mesh size. Furthermore, the numerical stability of Bardow's scheme decreases as the Courant–Friedrichs–Lewy (CFL) number approaches to 1, while the stability of DUGKS is not affected by the CFL number apparently as long as CFL<1. It is also observed that DUGKS is twice as expensive as the Bardow's scheme with the same mesh size.

Characterization of novel extremely extended regime in conductive rod-like polyaniline nanobrush-covered poly(ethylene glycol) single crystals

The fourth regime of polymer brushes was innovated for first time based on conductive rod polyaniline (PANI) brush-covered polyethylene glycol (PEG) single crystals. The three ordinary regimes for coily brushes (i.e., non-interaction, crossover, and highly stretched regimes) were also investigated and compared by the novel extremely extended regime coined for the rod PANI nano-brushes. It was revealed that in the conductive rod polymer brushes, the type of oxidant (ammonium peroxydisulfate (APS) and potassium hydrogen diiodate (PHD)), uniformity (in PEG5000-b-PANIn and PANIn-b-PEG6000-b-PANIn single crystals) or dispersity (in PANIn-b-PEG35000-b-PANIn single crystals) of arranged nanofibers diameter wise, and the morphology of tethered nanofibers on the crystalline substrate surface did not affect the brush regimes. We demonstrated that the equations of the substrate thickness, tethering density and reduced tethering density, which were quite applicable for coily brush systems, did not satisfy the conductive rigid PANI brushes. In these systems, the thicknesses were directly obtained from the interface distribution function (IDF) of small angle X-ray scattering (SAXS) analyses, and the brush regimes were judged based on the slopes of the reciprocal of substrate thickness (1/dc) versus crystallization temperature (Tc) graphs.

Micro/nano conductive-dielectric channels designed by poly(ethylene glycol) single crystals covered by polyaniline nanofibers

Dielectric-conductive single crystal channel-wire structures were developed using diblock and triblock copolymers of poly(ethylene glycol) (PEG) and polyaniline (PANI). Conductive PANI nanofiber-covered nano/micro wires were designed between the dielectric homo-PEG channels via controlling the effective parameters, including the molecular weight of substrate building blocks, mixing with dielectric PEG chains, and arranging different channels in the vicinity of each other. Due to being synthesized by interfacial polymerization, conductive PANI nanobrushes had a diameter distribution on the PEG substrate. The conductivities of PANI nanofibers synthesized by stronger, potassium hydrogen biiodate (PHD), and weaker, ammonium peroxydisulfate (APS), oxidants varied in 70–80 and 0.005–0.01 S/cm, respectively. Furthermore, the electrical conductivities of the diblock and triblock copolymers prepared by PHD and APS ranged in 3–5 S/cm and 8 × 10−5−1 × 10−4 S/cm, respectively. The mats of grown single crystals to some extent were as electroactive as bulk block copolymers. This was proved through the cyclic voltammetry (CV). The widths and thicknesses of dielectric channels and conductive wires were detected by the atomic force microscopy and the interface distribution function of small angle X-ray scattering. The lateral sizes of nanowires were 13–16 nm, those of microwires were 0.45–3.25 μm, however. The overall thicknesses of the channel-wire single crystals changed from 10 to 294 nm.

A subtle insight into nano-convergence of substrate thickness in melt-grown single-co-crystals

To precisely investigate the nano-convergence, single-co-crystals of poly(ethylene glycol) (PEG) homopolymers with molecular weights of 5000, 35,000, and 100,000 g/mol and poly(ethylene glycol)-b-polystyrene (PEG-b-PS) and poly(ethylene glycol)-b-poly(methyl methacrylate) (PEG-b-PMMA) diblock copolymers were grown from melt state. In PEG35000/PEG5000-b-PS, PEG35000/PEG5000-b-PMMA, PEG100000/PEG5000-b-PS, and PEG100000/PEG5000-b-PMMA single-co-crystals, a considerable convergence was detected by atomic force microscopy (AFM) and the interface distribution function of small angle X-ray scattering (SAXS) analyses. Whereas in previously grown PEG5000/PEG5000-b-PS and PEG5000/PEG5000-b-PMMA single-co-crystals, the characteristics of PEG5000-b-PS and PEG5000-b-PMMA phase regions were independent of the presence of homo-PEG5000 chains. The convergence in melt-grown single-co-crystals was ascribed to the variance of molecular weight of PEG blocks in homopolymer and diblock copolymers. The higher molecular weight of homo-PEG chains were utilized for co-crystallization; the more significant convergence was observed between the substrates of bared and brush-covered phase regions. The lower increase in the thickness of PMMA-covered substrate in comparison with PS-covered substrate was attributed to higher osmotic pressure of PMMA chains on the surface of single crystals. Hence, to reach the equilibrium convergence in single-co-crystal structure, the decrease of PEG35000 and PEG100000 substrate thicknesses from respective homopolymer single crystals to PEG/PEG-b-PMMA single-co-crystals was higher than the decrease in thickness of PEG/PEG-b-PS ones.

Phase densities and lamellar morphologies of semicrystalline polyethylenesviaabsolute small-angle X-ray scattering measurements

With the crystalline volume fraction from small-angle X-ray scattering (SAXS) and the density of the crystalline phase from wide-angle X-ray diffraction, the amorphous phase density of two representative polyethylenes was calculated as a function of temperature using the absolute total SAXS scattering power or invariant. The density of the amorphous phase in semicrystalline polyethylene is crystallinity independent and is lower than melt-extrapolated values reported in the literature. Model-independent SAXS-based crystallinity values can be calculated with the aid of the densities of the crystalline and amorphous phase and the absolute SAXS invariant. Such model-independent crystallinity values can be used in SAXS curve-shape analysis procedures to obtain the average thickness of the crystalline and amorphous layers also in the case of non-ideal lamellar semicrystalline polymer morphologies for which the number-average long period cannot be retrieved from the maxima in correlation functions or interface distribution functions.

Structure development during isothermal crystallisation of high-density polyethylene: Synchrotron small-angle X-ray scattering study

Isothermal melt crystallisation in high-density polyethylene (HDPE) was studied using the time-resolved SAXS method with synchrotron radiation over a wide range of crystallisation temperatures. The SAXS profile was analysed by an interface distribution function, g1(r), which is a superposition of three contributions associated with the size distributions of crystalline (LC) and amorphous (LA) layers and a distribution of long period (LP). The morphological parameters extracted from the g1(r) functions show that the lamellar thickness increases with time, obeying a logarithmic time dependence. The time evolution of LC observed for the sample crystallised at 122°C leads to the conclusion that crystallisation proceeds according to the mechanism of thickening growth. For samples crystallised at lower temperatures (116°C and 118°C), the lamellar thickening mechanism has been observed. The rate of lamellar thickening in these cases is much lower than that at 122°C. At 40°C, thickening of the crystalline layer does not occur. The interface distribution functions were deconvoluted, and the relative standard deviation σC/LC obtained in this way is an additional parameter that is varied during crystallisation and can be used for analysis of this process. Time-dependent changes in the σC/LC at large supercooling (TC=40°C) indicates that LC presents a broad distribution in which the relative standard deviation increases with time. At lower supercooling (TC=122°C), LC shows a much sharper distribution. In this case, the relative standard deviation decreases with time.

Correlation analysis of the side-chains conformational distribution in bound and unbound proteins

BackgroundProtein interactions play a key role in life processes. Characterization of conformational properties of protein-protein interactions is important for understanding the mechanisms of protein association. The rapidly increasing amount of experimentally determined structures of proteins and protein-protein complexes provides foundation for research on protein interactions and complex formation. The knowledge of the conformations of the surface side chains is essential for modeling of protein complexes. The purpose of this study was to analyze and compare dihedral angle distribution functions of the side chains at the interface and non-interface areas in bound and unbound proteins.ResultsTo calculate the dihedral angle distribution functions, the configuration space was divided into grid cells. Statistical analysis showed that the similarity between bound and unbound interface and non-interface surface depends on the amino acid type and the grid resolution. The correlation coefficients between the distribution functions increased with the grid spacing increase for all amino acid types. The Manhattan distance showing the degree of dissimilarity between the distribution functions decreased accordingly. Short residues with one or two dihedral angles had higher correlations and smaller Manhattan distances than the longer residues. Met and Arg had the slowest growth of the correlation coefficient with the grid spacing increase. The correlations between the interface and non-interface distribution functions had a similar dependence on the grid resolution in both bound and unbound states. The interface and non-interface differences between bound and unbound distribution functions, caused by biological protein-protein interactions or crystal contacts, disappeared at the 70° grid spacing for interfaces and 30° for non-interface surface, which agrees with an average span of the side-chain rotamers.ConclusionsThe two-fold difference in the critical grid spacing indicates larger conformational changes upon binding at the interface than at the rest of the surface. At the same time, transitions between rotamers induced by interactions across the interface or the crystal packing are rare, with most side chains having local readjustments that do not change the rotameric state. The analysis is important for better understanding of protein interactions and development of flexible docking approaches.

Exploring the structure of inter-platelet galleries in organically modified montmorillonite using the small-angle X-ray scattering interface distribution function approach

Small-angle X-ray scattering interface distribution function (IDF) analysis is successfully applied to evaluate the two- and three-phase inter-platelet gallery structure in synthetic montmorillonite (MMT) modified with a mixture of chemically grafted and physically adsorbed chains of a typical organic modifier, octadecyl trimethyl ammonium bromide. Two distinctly different states of adsorbed chains in the inter-platelet galleries are identified. The first one corresponds to a fully cation-exchanged structure with an inter-platelet distance of about 21 Å. In this case the organic modifier is in a liquid-like state, and the system does not exhibit any structural or thermal transitions between ambient temperature and 433 K. When the number of adsorbed chains exceeds the cation-exchange capacity of the MMT platelets the inter-platelet spacing is increased to 43 Å. In this case, the variable-temperature IDFs reveal partially crystalline order in the inter-platelet galleries, which vanishes at the melting point of the alkyl tails confined in the galleries.

On the lamellar width distributions of starch

Advances in the structural understanding of the lamellar organization of starch obtained through small-angle X-ray scattering (SAXS) technique are presented. An accurate starch sample preparation followed by appropriate background subtraction and Lorentz correction were able to evidence the second harmonic SAXS peak. Interface distribution functions (IDF) were generated from SAXS data to obtain dimensions and distributions of starch lamellae without any constraints or predefined assumptions. Dimensions and distributions of crystalline and amorphous lamellae were consistent with the molecular architecture of amylopectin. IDF fit results clearly indicate that amorphous and crystalline lamellae present different degrees of paracrystallinity, i.e. peak width/peak position ratios. The results of lamellar domain boundary are interpreted as a consequence of enzymatic trimming required to generate order in the amorphous lamellae for subsequent synthesis of the crystalline lattice. Amylose content seems to affect amorphous and crystalline lamellar distributions while the allomorph-type content is only reflected within the distribution of crystalline lamellae.

SAXS Analysis of Polypropylene-Layered Silicate Nanocomposites: An Integrated Correlations Functions Approach Using an Exfoliation Factor

Use of correlation function and interface distribution function to obtain the morphological parameters from Small Angle X-ray Scattering data makes it as an important quantitative method to evaluate lamellar morphology. Analysis using correlation function assumes lamellar stack morphology with variation of electron density along one dimension where lateral width of lamellae is much larger than the long period normal to the lamellae and the electron density varies with a rectangular profile for alternating crystalline and amorphous layers. In this work, a modified Porod law approach is used for the deviation from ideal two phase model and the thickness of transition zone with variation in electron densities is calculated. Morphological parameters of various grades of organically modified Polypropylene clay nanocomposites, such as long period, linear crystallinity, lamellar thickness and amorphous thickness are estimated using a combination of correlation and interface distribution function. Presence of transition zones does not influence the values for amorphous layer thickness, crystalline layer thickness and long period. Variations in values of long period calculated from correlation and interface function suggest a distribution of lamellar sizes in the polymer and nanocomposites. A new model consisting of the integrated correlation function of polymer and organoclay was developed to quantify the extent of exfoliation of organoclay in the nanocomposites by introducing a parameter, the exfoliation factor, beta. For a highly non-exfoliated system, the large number of clay tactoids is highly correlated and interacting, the correlation function of nanocomposites will be similar to that of nanoclay samples with low values of exfoliation factor. The correlation function of well exfoliated nanocomposites is similar to neat polymer, and such systems have high values of the exfoliation factor. Moreover, the exfoliation factor, which is easily determined by a scattering experiment, correlated well to the important engineering properties of the nanocomposites.

SAXS study on the crystallization of PET under physical confinement in PET/PC multilayered films

The present work is concerned with the study of the development of the crystalline structure of poly(ethylene terephthalate) in multilayered films of poly(ethylene terephthalate)/polycarbonate (PET/PC) prepared by means of layer multiplying coextrusion. Small angle X-ray scattering patterns were recorded during isothermal crystallization experiments and evaluated by means of Ruland's interface distribution function. Thus, structural parameters describing the thickness distribution of crystalline and amorphous layers were determinated. It is shown that the crystallization of PET is delayed with increasing confinement. However when the crystallization process comes to an end, the values of the nanostructural parameters of the lamellar system are nearly the same for the confined and non-confined PET.

Recrystallization studies on isotropic cold-crystallized PET: Influence of heating rate

The nanostructural changes associated to the multiple melting behaviour of isotropic cold-crystallized poly(ethylene terephthalate) (PET) have been investigated by means of simultaneous wide- and small-angle X-ray scattering, using a synchrotron radiation source. Variations in the degree of crystallinity, coherent lateral crystal size and long period values, as a function of temperature, for two different heating rates are reported for cold-crystallized samples in the 100–190°C range. The Interface Distribution Function analysis is also employed to provide the crystalline and amorphous layer thickness values at various temperatures of interest. Results suggest that samples crystallized at both low (Ta=100–120°C) and high (Ta=160–190°C) temperatures are subjected to a nearly continuous nanostructural reorganization process upon heating, starting immediately above Tg (≈80°C) and giving rise to complete melting at ≈260°C. For all the Ta investigated, a melting–recrystallization mechanism seems to take place once Ta is exceeded, concurrently to the low-temperature endotherm observed in the DSC scans. For low-Ta and slow heating rates (2°C/min), a conspicuous recrystallization process is predominant within Ta+30°C≤T≤200°C. In contrast, for high-Ta, an increasingly strong melting process is observed. For both, high- and low-Ta, an extensive structural reorganization takes place above 200°C, involving the appearance of new lamellar stacks simultaneously to the final melting process. The two mechanisms should contribute to the high-temperature endotherm in the DSC scan. Finally, the use of a high heating rate is found to hinder the material's overall recrystallization process during the heating run and suggests that the high-temperature endotherm is ascribed to the melting of lamellae generated or thickened during the heating run.

Mechanism of sintering of polyoxymethylene powders investigated by small-angle X-ray scattering

AbstractThe structural reorganization of polyoxymethylene powders during sintering has been investigated through a detailed analysis of the SAXS data in order to determine the origin of the mechanical property improvement with regard to the compression-moulded counterpart. Two approaches afford a quantitative evaluation of the structural parameter evolutions. On one hand, the correlation and interface distribution functions were calculated for the samples submitted to various thermo-mechanical treatments. On the other hand, the Hosemann’s paracrystalline model modified with Reinhold distributions of the crystal and amorphous phase thicknesses was used to evaluate the disorder in the lamella stacking. Both approaches suggest that a more perfect and regular crystalline structure with thicker and wider crystals develops in the sintered samples as compared with the parent powders and the material crystallized from the melt. Theses morphological modifications are discussed in relation to the very high stiffness and brittleness of the sintered materials. Two possible mechanisms of coalescence of the powder grains via the crystalline phase are proposed to account for these specific mechanical properties of the sintered materials.

Melting behavior of polymorphic crystals of poly(trimethylene 2,6-naphthalate) studied by simultaneous synchrotron X-ray scattering and thermal analysis

The polymorphic crystallization and melting behavior of poly(trimethylene 2,6-naphthalate) (PTN) have been investigated using small-angle X-ray scattering and simultaneous wide-angle X-ray scattering (WAXS) and differential scanning calorimetry (DSC). The α-crystal, the β-crystal and the coexistence of both crystal forms of PTN develop at an isothermal temperature below 393 K, above 453 K and between these two temperatures, respectively. The simultaneous WAXS/DSC measurement provides a good way to identify the origin of multiple melting peaks and to get equilibrium melting temperatures. During the PTN melting process, the thermal evolutions of crystallinities, Bragg diffraction intensities and DSC thermograms reveal that the \alpha \rightarrow \beta phase transformation and primary and secondary crystallizations arise to generate the multiple melting peaks. The β-crystal with high equilibrium melting temperature (T^{0}_{{\rm m},\beta}} = 510 K) is a structurally stable phase while the α-crystal with low equilibrium melting temperature (T^{0}_{{\rm m},\alpha}} = 488 K) is a metastable phase. The temperature-dependent structural parameters such as the long period, lamellar thickness and amorphous thickness were extracted from the interface distribution function. Two-step changes in the lamellar thickness and the invariant during the subsequent melting of PTN crystallized at 383 K are consistent with the \alpha \rightarrow \beta transformation obtained by WAXS/DSC. The \alpha \rightarrow \beta transformation, a typical melting–recrystallization, proceeds firstly via surface melting of α-lamellae, and then the PTN chains near the boundaries of surviving α-lamellae modify their conformation to form the β-crystal resulting in thickening lamellae.