Particle Form Factor Research Articles

Reinforcement induced microcracking during the conversion of polymer-derived ceramics

This study investigates the role of discontinuous reinforcement on the microcracking of a preceramic polymer matrix during polymer to ceramic conversion. The material system comprised a carbosilane-based, preceramic polymer reinforced with mullite particles. The preceramic resin slurry was formulated for photopolymerization on a digital light projection 3D printer. Micro X-ray computed tomography, using a synchrotron light source, monitored a printed composite part during pyrolysis. The conversion of the carbosilane matrix into Si(O)C generated microcracks in the matrix that radially extended from particles. The likelihood of microcrack formation positively correlated with particle size. The largest particles (>104 µm3 volume or >60 µm side length) always abutted microcracks, while the matrix surrounding smaller particles (<5 µm) was free of microcracks. Numerical calculations showed the particles resist the shrinking matrix during its conversion. This created tensile stresses within the matrix. The driving force for microcrack growth was also analyzed with regard to the influence of matrix material parameters, particle form-factor and crack length. These results reveal the need to consider the form factor of discontinuous reinforcements, with regard to the material properties of the polymer-derived ceramic, in order to reduce or eliminate defects in the final part.

Structure and Conformation of Hydroxypropylmethyl Cellulose with a Wide Range of Molar Masses in Aqueous Solution─Effects of Hydroxypropyl Group Addition.

The structure of hydroxypropylmethyl cellulose (HpMC) samples with a wide range of weight average molar masses (Mw) from 23 to 5000 kg mol-1, a controlled degree of substitution (DS) of 1.9 by methyl groups, and a molar substitution number (MS) of 0.25 by hydroxypropyl groups dissolved in aqueous solution was examined using static light scattering (SLS), dynamic light scattering (DLS), small-to-wide angle neutron scattering (S-WANS) techniques, and intrinsic viscosity ([η]) measurements. The determined Mw and the radius of gyration (Rg) showed the relationships Rg ∝ Mw1.0 and [η] ∝ Mw1.7 in a range of Mw < 100 kg mol-1, similar to rigid rod molecules in solution. However, exponents in the relationships decreased gradually with increasing Mw and reached ∼0.5 in a high Mw region, which is a typical value of flexible chain molecules for both Rg and [η]. These observations suggest that the HpMC samples behave as semiflexible rods with a certain persistence length (lp). The ratios of the hydrodynamic radius via DLS measurements to Rg also supported semiflexible rod behavior. Particle form factors and the average lengths (L) resulting from SLS and S-WANS experiments are well described with rigid rod particles in the range of Mw < 100 kg mol-1 and semiflexible rods with lp ∼ 100 nm in Mw > 100 kg mol-1. Because the average contour length (lc) calculated from Mw is approximately twice as long as L in the Mw range < 100 kg mol-1, the formed HpMC particles possess a folded hairpin-like elongated rigid rod structure. However, the lc/L value increases gradually in the range Mw > 200 kg mol-1, where the formed HpMC particles behave as semiflexible rods. The formed particle structure was substantially different from that found in methyl cellulose samples with a similar DS value, which showed rod-like behavior over a wide Mw range. The addition of hydroxypropyl groups only at MS = 0.25 effectively changed the formed particle structure.

Resonance form factors from finite-volume correlation functions with the external field method

A novel method for the extraction of form factors of unstable particles on the lattice is proposed. The approach is based on the study of two-particle scattering in a static, spatially periodic external field by using a generalization of the Lüscher method in the presence of such a field. It is shown that the resonance form factor is given by the derivative of the resonance pole position in the complex plane with respect to the coupling constant to the external field. Unlike the standard approach, this proposal does not suffer from problems caused by the presence of the triangle diagram.

Scattering phase delay and momentum transfer of light in disordered media

Disordered dielectric materials with short-range spatial correlations on length scales comparable to the wavelength of light display a rich variety of optical phenomena: photonic band gaps, structural coloring, strong scattering, and whiteness. However, a lack of reliable and straightforward analytical models complicates the rationale design of optical materials for specific applications. Here, we demonstrate how to accurately introduce collective scattering and define the effective medium in single scattering from heterogeneous dielectrics with a substantial refractive index contrast, starting from fundamental principles. Our model captures the effective medium's role in the momentum transfer definition for the particle form and structure factor in the forward scattering regime. We support our claims through transfer matrix calculations scattering from particle clusters.

Quantifying Nanoparticle Assembly States in a Polymer Matrix through Deep Learning

There is great interest in controlling the spatial dispersion of inorganic nanoparticles (NPs) in an organic polymer matrix because this centrally underpins the property enhancements obtained from these hybrid materials. Currently, qualitative information on NP spatial distribution is obtained by visual inspection of transmission electron microscopy (TEM) images. Quantitative information is only indirectly obtained through the use of scattering probes such as small-angle X-ray/neutron scattering (SAXS/SANS). While the main challenge, that scattering probes operate in reciprocal space, can be remedied by Fourier inverting the data into real space, a much harder issue deconvolves the contribution of the particle form factor (which is affected by the details of the NP size and shape) from the structure factor that contains information on NP spatial distribution. These problems become acute when we deal with the popular topic of NPs grafted with polymer chains because the polymeric corona and hence the particle form factor becomes context-dependent and is hard to quantify. To make progress, we develop and apply a deep-learning-based image analysis method to quantify the distribution of spherical NPs in a polymer matrix directly from their real-space TEM images. A dataset of NP detection (DOPAD) is built by manually labeling particle positions on experimental TEM images of diverse polymer composite systems. A convolutional neural network object detection model is then trained on DOPAD. Together with sliding-window and merging algorithms, an automated pipeline is established, which takes a large TEM image as input and extracts NP locations and sizes. We validate the structural information resulting from this method against SAXS-derived structural information for NPs ordered by polymer crystallization and then use it to distinguish between different states of the assembly of polymer-grafted NPs in a polymer matrix achieved by using their surfactancy. We show that this data-rich protocol allows us to draw critical facets of experimental behavior which have previously not been accessible. The DOPAD dataset, Python source code, and trained model are shared on GitHub at https://dopad.github.io.

Influence of 80-mesh Traditional Chinese Medicine Particle Stack Thickness on Percolation Performance

In order to research the influence of 80-mesh traditional Chinese medicine particle characteristics and particle stack thickness on percolation performance, wire screen was used to carry out filtration by the vibratory action of oscillator, screen No. and screen pore size were recorded and weight of screen residue was measured, so as to calculate average distribution density of particles, distribution function of particle size, form factor and specific surface area of particles. Percolation pressure drop was utilized as the index to evaluate percolation performance. Ethanol solution at 20°C with volumetric concentration of 47% was selected as percolation solution to measure and calculate the percolation pressure drop when ethanol solution flowed through 100mm, 150mm, 180mm, 250mm and 300mm 80-mesh particle layer. The results showed that percolation pressure drop is proportional to particle stack thickness, and it is high relatively due to the small size of 80-mesh particle, which shall result in high energy consumption of percolation system.

Non-sintered dredged sediments artificial cobblestones: Preparation, structure and properties

A novel preparation process of non-sintered dredged sediments artificial cobblestones (DSACs) was conducted in this study. DSACs with a multilayer core–shell structure was manufactured by wrap-shell process. The performance characteristics, such as particle form factor, water absorption, particle size distribution, strength, density, frost resistance, and salt resistance of different particle sizes of DSACs were investigated. The results showed that DSACs was nearly spherical, and with a three-dimensional network-like structure. The single DSACs strength increased with the decrease of its particle size. When the particle size of DSACs was between 10 and 20 mm, the single strength of DSACs reached the maximum of 1.25 MPa. After 50 freeze–thaw cycles and 50 days of soaking in salt solution, the mass of DSACs showed no obvious mass loss. However, with the increase of the particle size, the strength of the DSACs got weakened. With the feasibility of preparation process, this technology paves the avenue to the resource utilization of dredged sediments and avoids excessive exploitation of mineral resources.

Scattering from colloidal cubic silica shells: Part I, particle form factors and optical contrast variation

HypothesisColloidal cubic silica shells, prepared from cuprous oxide cubes, with a typical size of 100 nm are promising model particles for scattering studies on dilute, as well as concentrated fluids, of non-spherical colloids. ExperimentsSmall angle X-ray scattering, and static light scattering are employed to determine form factors of cubic silica shells and silica covered cuprous oxide cubes. Contrast variation experiments are performed to assess the refractive index and optical homogeneity of the cubic silica shells, which is important for the extension of the scattering study to concentrated dispersions of cubic shells in Part II (Dekker, submitted for publication). ResultsThe experimental form factors, which compare well to theoretical form factors, manifest cubic silica shells that are dispersed as single stable colloids with a shape intermediate between a sphere and a perfect cube. Contrast variation demonstrates that the silica shells are optically homogeneous, with a refractive index that is independent of the shell thickness. The results presented here open up the possibility to extract structure factors from light scattering measurements on concentrated cube dispersions in Part II.

Modelling of multicomponent polydisperse systems using small-angle scattering data

Algorithms for modelling of multicomponent polydisperse systems using small-angle scattering data have been developed. They cover a wide range of particle form-factors and take into account interparticle interactions. The algorithms are implemented in computer programs MIXTURE and POLYSAS, and their performance is tested on a number of simulated and experimental examples. The stability of the solution search is explored for the case of a two-component polydisperse system of spherical particles.

Constituent-Quark Model with Pionic Contributions: Electromagnetic {varvec{Nrightarrow varDelta }} Transition

We report on ongoing work to determine the pion-cloud contribution to the electromagnetic Nrightarrow varDelta transition form factors. The starting point is an SU(6) spin-flavor symmetric constituent-quark model with instantaneous confinement that is augmented by dynamical pions which couple directly to the quarks. This system is treated in a relativistically invariant way within the framework of point-form quantum mechanics using a multichannel formulation. The first step is to determine the electromagnetic form factors of the bare particles that consist only of three quarks. These form factors are basic ingredients for calculating the pion-cloud contributions. Already without the pion cloud, electromagnetic nucleon and Nrightarrow varDelta transition form factors compare reasonably well with the data. By inclusion of the pion-cloud contribution coming from the pi -N intermediate state the reproduction of the data is further improved.

Unambiguous extraction of the electromagnetic form factors for spin-1 particles on the light-front

The electromagnetic form factors of a composite vector particle within the light-front formulation of the Mandelstam formula is investigated. In order to extract the form factors from the matrix elements of the plus component of the current in the Drell–Yan frame, where the momentum transfer is chosen such that q+=q0+q3=0, one has in principle the freedom to choose between different linear combinations of matrix elements of the current operator. The different prescriptions to calculate the electromagnetic form factors, G0,G1 and G2, i.e.; charge form factor, magnetic and quadrupole respectively. If the covariance is respected, all prescriptions give the same results; misfortune, is not the situation; the light-front approach produce different results, which depend of the prescriptions as utilized to extract the electromagnetic form factors in the case of the spin-1 particles. The main differences of the prescriptions appear because of the light-front matrix elements of the electromagnetic current are contaminated by the zero-modes contributions to the same with the plus component of the matrix elements of the electromagnetic current. However, the Inna Grach prescription is immune to the zero-modes contributions to the electromagnetic current, then the electromagnetic form factors extracted with that prescriptions do not have zero-modes contribution and give the same result compared with the instant form quantum field theory. Another's prescriptions with the light-front approach are contaminated by the zero-modes contributions to the matrix elements of the electromagnetic current with the plus component of the current. With some relations between the electromagnetic matrix elements of the electromagnetic current Jji+, as demonstrated analytical here, it was possible to calculate the electromagnetic form factors for spin-1 particles without zero-modes or non-valence contributions.

Comparison of open boundary conditions realizations for continuous injection of an electron beam into a plasma in the case of the PIC and parabolic form-factors

The paper is devoted to a comparison of methods for realizing open boundary conditions that allow continuous injection of a beam of charged particles into a plasma in the PIC model in the case of different particle form-factors, as well as with two variants of boundary conditions at plasma ends. It is shown that simulation results coincide for the PIC and parabolic form-factors for the problem of injecting an electron beam into a plasma in 1D geometry for all the boundary conditions under consideration. In 2D geometry, we find the discrepancy between these models, as well as the inapplicability of the Mur’s boundary conditions for electromagnetic fields simultaneously with the condition of equality of currents in boundary cells. The number of particles in a cell, which is necessary for convergence of calculations, for each method is determined.

Spin-1 Particles and Perturbative QCD

Due to the angular condition in the light-front dynamics (LFD), the extraction of the electromagnetic form factors for spin-1 particles can be uniquely determined taking into account implicitly non-valence and/or the zero-mode contributions to the matrix elements of the electromagnetic current. No matter which matrix elements of the electromagnetic current is used to extract the electromagnetic form factors, the same unique result is obtained. As physical observables, the electromagnetic form factors obtained from matrix elements of the current in LFD must be equal to those obtained in the instant form calculations. Recently, the Babar collaboration \cite{Aubert2008} has analyzed the reaction $e^+ e^-\rightarrow \rho^+ + \rho^-$ at $\sqrt{s}=10.58 GeV$ to measure the cross section as well as the ratios of the helicity amplitudes $F_{\lambda'\lambda}$. We present our recent analysis of the Babar data for the rho meson considering the angular condition in LFD to put a stringent test on the onset of asymptotic perturbative QCD and predict the energy regime where the subleading contributions are still considerable.

Small-angle neutron scattering modeling of spin disorder in nanoparticles

Magnetic small-angle neutron scattering (SANS) is a powerful technique for investigating magnetic nanoparticle assemblies in nonmagnetic matrices. For such microstructures, the standard theory of magnetic SANS assumes uniformly magnetized nanoparticles (macrospin model). However, there exist many experimental and theoretical studies which suggest that this assumption is violated: deviations from ellipsoidal particle shape, crystalline defects, or the interplay between various magnetic interactions (exchange, magnetic anisotropy, magnetostatics, external field) may lead to nonuniform spin structures. Therefore, a theoretical framework of magnetic SANS of nanoparticles needs to be developed. Here, we report numerical micromagnetic simulations of the static spin structure and related unpolarized magnetic SANS of a single cobalt nanorod. While in the saturated state the magnetic SANS cross section is (as expected) determined by the particle form factor, significant deviations appear for nonsaturated states; specifically, at remanence, domain-wall and vortex states emerge which result in a magnetic SANS signal that is composed of all three magnetization Fourier components, giving rise to a complex angular anisotropy on a two-dimensional detector. The strength of the micromagnetic simulation methodology is the possibility to decompose the cross section into the individual Fourier components, which allows one to draw important conclusions regarding the fundamentals of magnetic SANS.

Distribution functions of magnetic nanoparticles determined by a numerical inversion method

In the present study, we applied a regularized inversion method to extract the particle size, magnetic moment and relaxation-time distribution of magnetic nanoparticles from small-angle x-ray scattering (SAXS), DC magnetization (DCM) and AC susceptibility (ACS) measurements. For the measurements the particles were colloidally dispersed in water. At first approximation the particles could be assumed to be spherically shaped and homogeneously magnetized single-domain particles. As model functions for the inversion, we used the particle form factor of a sphere (SAXS), the Langevin function (DCM) and the Debye model (ACS). The extracted distributions exhibited features/peaks that could be distinctly attributed to the individually dispersed and non-interacting nanoparticles. Further analysis of these peaks enabled, in combination with a prior characterization of the particle ensemble by electron microscopy and dynamic light scattering, a detailed structural and magnetic characterization of the particles. Additionally, all three extracted distributions featured peaks, which indicated deviations of the scattering (SAXS), magnetization (DCM) or relaxation (ACS) behavior from the one expected for individually dispersed, homogeneously magnetized nanoparticles. These deviations could be mainly attributed to partial agglomeration (SAXS, DCM, ACS), uncorrelated surface spins (DCM) and/or intra-well relaxation processes (ACS). The main advantage of the numerical inversion method is that no ad hoc assumptions regarding the line shape of the extracted distribution functions are required, which enabled the detection of these contributions. We highlighted this by comparing the results with the results obtained by standard model fits, where the functional form of the distributions was a priori assumed to be log-normal shaped.

(Invited) Recent Progress in Fundamental Photoelectrochemical Studies Relevant to New Low-Cost Designs for Z-Scheme Solar Water Splitting Reactors

Particle suspension reactors for solar water splitting are capable of generating hydrogen at a cost that is competitive with hydrogen produced from steam methane reforming. One reactor design resembles Nature’s Z-scheme where two side-by-side and connected photocatalyst reactor beds together drive overall solar water splitting.1,2 The photocatalyst in each reactor bed also performs a half-reaction with a redox shuttle, i.e. oxidation or reduction, and therefore to prevent complete depletion of the redox shuttle, the electrolyte must transport between the beds via a nanoporous gas separator. While this design facilitates separation of the H2 and O2 reaction products, and therefore can circumvent formation of an explosive mixture of gases, transport of the redox shuttle between the beds requires active pumping which equates to additional capital expenditures that result in a near doubling of the reactor cost.1,2 Our team is evaluating the feasibility of new reactor designs where the beds are simply stacked. This generates a true tandem light-absorbing reactor where the theoretical maximum solar-to-hydrogen conversion efficiency is over 50% larger than a side-by-side or single light-absorber design. Each bed is projected to be < 10 cm tall and therefore, this design greatly decreases the distance required for redox shuttle transport, reducing or even eliminating the need for pipes, pumps, and forced convection. In my presentation I will report on our team’s recent progress on this design. We used finite-element numerical methods to model and simulate in two dimensions the transient mass transport processes, light absorption, and electrochemical kinetics in the proposed reactor. Model results suggest that a reactor operating at a ~4% solar-to-hydrogen conversion efficiency can operate indefinitely without complete loss of the active form of the redox shuttle at any location in the reactor beds. Experimentally, we are investigating and characterizing photocatalyst nanomaterials over many length scales, from single nanoparticles (~10 nm to ~1 µm in diameter) to mesoporous thin films (~10 µm thick) to laboratory-scale prototype particle-suspension reactors (on the scale of feet). On the single-particle level we jammed and covalently bound TiO2 nanoparticles into a single nanopore in a plastic sheet, wetted the particles with liquid electrolyte on both sides, and measured photovoltages that resulted from optical excitation of the particles. This was significant because it allowed, for the first time, in situ photoelectrochemical characterization of nanoparticle(s). We also synthesized, characterized, and evaluated the photo(electro)chemical performance of BiVO4, WO3, and Rh-doped SrTiO3 nanocrystallites as mesoporous thin films and as particles in model reactors, and evaluated the transport properties of several redox shuttles. As a model system, H2-evolving Rh-doped SrTiO3 was evaluated as a mesoporous electrode and in particle form factor in the absence and presence of the ferric and/or ferrous iron redox shuttle. Based on this suite of results, we demonstrated that in the presence of FeII the limiting rate of reduction of FeIII is attenuated and the rate of catalysis for H2 evolution is enhanced. This is important because both halves of the iron redox shuttle are present in the reactor bed containing Rh-doped SrTiO3 and therefore this suggests that reduction of H+ can outcompete reduction of at least some FeIII under certain circumstances. Collectively, our efforts represent strides toward achieving a high-level of techno-economic viability in solar water splitting reactors. Acknowledgments: This work was supported by the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, Fuel Cell Technologies Incubator Program under Award No. DE-EE0006963 and Lawrence Berkeley National Laboratory under Contract No. DE-AC02-05CH11231.

On tuning microgel character and softness of cross-linked polystyrene particles.

Polystyrene (PS) microgel colloids have often been used successfully to model hard sphere behaviour even though the term "gel" invokes inevitably the notion of a more or less soft, deformable object. Here we systematically study the effect of reducing the cross-link density from 1 : 10 (1 cross-link per 10 monomers) to 1 : 100 on particle interactions and "softness". We report on the synthesis and purification of 1 : 10, 1 : 25, 1 : 50, 1 : 75 and 1 : 100 cross-linked PS particles and their characterization in terms of single particle properties, as well as the behaviour of concentrated dispersions. We are able to tune particle softness in the range between soft PNiPAM-microgels and hard PMMA particles while still allowing the mapping of the microgels onto hard sphere behavior with respect to phase diagram and static structure factors. This is mainly due to a rather homogeneous radial distribution of cross-links in contrast to PNiPAM microgels where the cross-link density decreases radially. We find that up to a cross-link density of 1 : 50 particle form factors are perfectly described by a homogeneous sphere model whereas 1 : 75 and 1 : 100 cross-linked spheres are slightly better described as fuzzy spheres. However the fuzziness is rather small compared to typical PNiPAM microgels so that a hard sphere mapping still holds even for these low cross-link densities. Finally, by varying the reaction conditions - changing from batch to semibatch emulsion polymerization and varying the feed rate or by adjusting the monomer to initiator ratio we can tune the fuzziness or significantly alter the inner structure to a more open, star-like architecture.

Bethe Ansatz and exact form factors of the O (N) Gross Neveu-model

We apply previous results on the O(N) Bethe Ansatz [1 to 3] to construct a general form factor formula for the O(N) Gross-Neveu model. We examine this formula for several operators, such as the energy momentum, the spin-field and the current. We also compare these results with the 1/N expansion of this model and obtain full agreement. We discuss bound state form factors, in particular for the three particle form factor of the field. In addition for the two particle case we prove a recursion relation for the K-functions of the higher level Bethe Ansatz.

Scattering Form Factors for Russian Doll Aerosol Droplet Models.

Our molecular dynamics (MD) simulations have shown that nanodroplets containing water and nonane are nonspherical and strongly phase-separated. This "Russian doll" structure may be simply but realistically modeled as a spherical nonane lens that partially wets a spherical water droplet. We call this the lens-on-sphere model. Here, we present an analytical calculation of the particle form factor, P(q), needed to analyze the intensity curves for small-angle neutron and X-ray scattering by aerosol particles with this type of structure. For this model, the particle form factor must be evaluated by numerical integration. In addition, an exact formulation of the particle form factor is presented for cylindrically symmetric droplets with otherwise arbitrary position-dependent scattering length density. This result enables direct calculation of P(q) from numerical MD simulation data. Results using both formulations are compared, and excellent agreement is found between them. Analytical results are also presented for two limiting cases of the general result: the sphere-on-sphere model and the sphere-in-sphere (SIS) model, corresponding to contact angles of 180° and 0°, respectively. Finally, a generalization of the SIS model to ellipsoidal droplets is given.

Form factor of pNIPAM microgels in overpacked states.

We study the form factor of thermoresponsive microgels based on poly(N-isopropylacrylamide) at high generalized volume fractions, ζ, where the particles must shrink or interpenetrate to fit into the available space. Small-angle neutron scattering with contrast matching techniques is used to determine the particle form factor. We find that the particle size is constant up to a volume fraction roughly between random close packing and space filling. Beyond this point, the particle size decreases with increasing particle concentration; this decrease is found to occur with little interpenetration. Noteworthily, the suspensions remain liquid-like for ζ larger than 1, emphasizing the importance of particle softness in determining suspension behavior.