Three-dimensional reconstruction of liquid phases in disordered mesopores usingin situsmall-angle scattering

On the nanoscale structural evolution of solid discharge products in lithium-sulfur batteries using operando scattering

The inadequate understanding of the mechanisms that reversibly convert molecular sulfur (S) into lithium sulfide (Li₂S) via soluble polysulfides (PSs) formation impedes the development of high-performance lithium-sulfur (Li-S) batteries with non-aqueous electrolyte solutions. Here, we use operando small and wide angle X-ray scattering and operando small angle neutron scattering (SANS) measurements to track the nucleation, growth and dissolution of solid deposits from atomic to sub-micron scales during real-time Li-S cell operation. In particular, stochastic modelling based on the SANS data allows quantifying the nanoscale phase evolution during battery cycling. We show that next to nano-crystalline Li₂S the deposit comprises solid short-chain PSs particles. The analysis of the experimental data suggests that initially, Li₂S₂ precipitates from the solution and then is partially converted via solid-state electroreduction to Li₂S. We further demonstrate that mass transport, rather than electron transport through a thin passivating film, limits the discharge capacity and rate performance in Li-S cells.

Understanding lithium sulfide’s electrodeposition and stripping is key to developing practical Li-S batteries. Here, the authors demonstrate that the discharge product in Li-S batteries consists of nano-size solid polysulfide particles and nano-crystalline lithium sulfide.

Fast reconstruction of multiphase microstructures based on statistical descriptors

In this paper, we propose a hierarchical simulated annealing of erosion method (HSAE) to improve the computational efficiency of multiphase microstructure reconstruction, whose computational efficiency can be improved by an order of magnitude. Reconstruction of the two-dimensional (2D) and three-dimensional (3D) multiphase microstructures (pore, grain, and clay) based on simulated annealing (SA) and HSAE are performed. In the reconstruction of multiphase microstructure with HSAE and SA, three independent two-point correlation functions are chosen as the morphological information descriptors. The two-point cluster function which contains significant high-order statistical information is used to verify the reconstruction results. From the analysis of 2D reconstruction, it can find that the proposed HSAE technique not only improves the quality of reconstruction, but also improves the computational efficiency. The reconstructions of our proposed method are still imperfect. This is because the used two-point correlation functions contain insufficient information. For the 3D reconstruction, the two-point correlation functions of the 3D generation are in excellent agreement with those of the original 2D image, which illustrates that our proposed method is effective for the reconstruction of 3D microstructure. The comparison of the energy vs computational time between the SA and HSAE methods shows that our presented method is an order of magnitude faster than the SA method. That is because only some of the pixels in the overall hierarchy need to be considered for sampling.

Inelastic neutron scattering analysis with time-dependent Gaussian-field models

Converting neutron scattering data to real-space time-dependent structures can only be achieved through suitable models, which is particularly challenging for geometrically disordered structures. We address this problem by introducing time-dependent clipped Gaussian field models. General expressions are derived for all space- and time-correlation functions relevant to coherent inelastic neutron scattering for multiphase systems and arbitrary scattering contrasts. Various dynamic models are introduced that enable one to add time-dependence to any given spatial statistics, as captured, e.g., by small-angle scattering. In a first approach, the Gaussian field is decomposed into localized waves that are allowed to fluctuate in time or to move either ballistically or diffusively. In a second approach, a dispersion relation is used to make the spectral components of the field time-dependent. The various models lead to qualitatively different dynamics, which can be discriminated by neutron scattering. The methods of this paper are illustrated with oil/water microemulsion studied by small-angle scattering and neutron spin-echo. All available data-in both film and bulk contrasts, over the entire range of q and τ-are analyzed jointly with a single model. The analysis points to the static large-scale structure of the oil and water domains while the interfaces are subject to thermal fluctuations. The fluctuations have an amplitude of around 60 Å and contribute to 30% of the total interface area.

In situ small-angle X-ray scattering reveals solution phase discharge of Li-O2 batteries with weakly solvating electrolytes

Electrodepositing insulating lithium peroxide (Li₂O₂) is the key process during discharge of aprotic Li-O₂ batteries and determines rate, capacity, and reversibility. Current understanding states that the partition between surface adsorbed and dissolved lithium superoxide governs whether Li₂O₂ grows as a conformal surface film or larger particles, leading to low or high capacities, respectively. However, better understanding governing factors for Li₂O₂ packing density and capacity requires structural sensitive in situ metrologies. Here, we establish in situ small- and wide-angle X-ray scattering (SAXS/WAXS) as a suitable method to record the Li₂O₂ phase evolution with atomic to submicrometer resolution during cycling a custom-built in situ Li-O₂ cell. Combined with sophisticated data analysis, SAXS allows retrieving rich quantitative structural information from complex multiphase systems. Surprisingly, we find that features are absent that would point at a Li₂O₂ surface film formed via two consecutive electron transfers, even in poorly solvating electrolytes thought to be prototypical for surface growth. All scattering data can be modeled by stacks of thin Li₂O₂ platelets potentially forming large toroidal particles. Li₂O₂ solution growth is further justified by rotating ring-disk electrode measurements and electron microscopy. Higher discharge overpotentials lead to smaller Li₂O₂ particles, but there is no transition to an electronically passivating, conformal Li₂O₂ coating. Hence, mass transport of reactive species rather than electronic transport through a Li₂O₂ film limits the discharge capacity. Provided that species mobilities and carbon surface areas are high, this allows for high discharge capacities even in weakly solvating electrolytes. The currently accepted Li-O₂ reaction mechanism ought to be reconsidered.

Persistent and reversible solid iodine electrodeposition in nanoporous carbons

Aqueous iodine based electrochemical energy storage is considered a potential candidate to improve sustainability and performance of current battery and supercapacitor technology. It harnesses the redox activity of iodide, iodine, and polyiodide species in the confined geometry of nanoporous carbon electrodes. However, current descriptions of the electrochemical reaction mechanism to interconvert these species are elusive. Here we show that electrochemical oxidation of iodide in nanoporous carbons forms persistent solid iodine deposits. Confinement slows down dissolution into triiodide and pentaiodide, responsible for otherwise significant self-discharge via shuttling. The main tools for these insights are in situ Raman spectroscopy and in situ small and wide-angle X-ray scattering (in situ SAXS/WAXS). In situ Raman confirms the reversible formation of triiodide and pentaiodide. In situ SAXS/WAXS indicates remarkable amounts of solid iodine deposited in the carbon nanopores. Combined with stochastic modeling, in situ SAXS allows quantifying the solid iodine volume fraction and visualizing the iodine structure on 3D lattice models at the sub-nanometer scale. Based on the derived mechanism, we demonstrate strategies for improved iodine pore filling capacity and prevention of self-discharge, applicable to hybrid supercapacitors and batteries.

Iodide based energy storage is a potential candidate to improve performance of hybrid supercapacitors and batteries. Here, the authors revisit the previous understanding and show that electrochemical oxidation of iodide results in solid iodine deposits stabilized by the confinement of nanoporous carbons.

Stochastic models of dense or hollow nanoparticles and their scattering properties

A family of stochastic models of disordered particles is proposed, obtained by clipping a Gaussian random field with a function that is space dependent. Depending on the shape of the clipping function, dense or hollow particles can be modelled. General expressions are derived for the form factor of the particles, for their average volume and surface area, and for their density and surface-area distributions against the distance to the particle centre. A general approximation for the form factor is also introduced, based on the density and surface-area distributions, which coincides with the Guinier and Porod expressions in the limits of low and high scattering vector magnitude q. The models are illustrated with the fitting of small-angle X-ray scattering (SAXS) data measured on Pt/Ni hollow nanoparticles. The SAXS analysis and modelling notably capture the collapse of the particles' porosity after being used as oxygen-reduction catalysts.

Small-angle scattering by supported nanoparticles: exact results and useful approximations

In functional materials, nanoparticles are often dispersed in a porous support for the purpose of stabilizing them. This makes their characterization by small-angle scattering challenging because the signal comprises contributions from the nanoparticles of interest, from the inert support and from their cross-correlation. Exact analytical expressions for all three contributions are derived in the case of a Gaussian-field model of the porous support, with nanoparticles randomly distributed over the surface. For low nanoparticle loading, the expressions simplify to the addition of properly scaled support and particle scattering. For higher loadings, however, the cross-correlation cannot be ignored. Two approximations are introduced, which capture correlation effects in cases where the pores of the support are much larger or only slightly larger than the nanoparticles. The methods of the paper are illustrated with the small-angle X-ray scattering analysis of hollow metallic nanoparticles supported on porous carbon.

Stochastic analysis of capillary condensation in disordered mesopores

Most mesoporous materials of practical interest are inherently disordered, which has a significant impact on the condensation and evaporation of vapours in their pores. Traditionally, the effect of disorder is theoretically analyzed in a perturbative approach whereby slight elements of disorder (constriction, corrugation) are added to geometrically ideal pores. We propose an alternative approach, which consists of using a stochastic geometrical model to describe both the porous material and the condensate within the pores. This is done through a multiphase generalisation of the standard Gaussian random field model of disordered materials. The model parameters characterising the condensate provide a low-dimensional approximation of its configuration space, and we use a Derjaguin-Broekhoff-de Boer approximation to calculate the free-energy landscape. Our analysis notably questions the existence of vapour-like metastable states in realistically disordered mesoporous materials. Beyond capillary condensation, our general methodology is applicable to a broad array of confined phenomena.

Microstructure and mechanical properties of hyperuniform heterogeneous materials

A hyperuniform random heterogeneous material is one in which the local volume fraction fluctuations in an observation window decay faster than the reciprocal window volume as the window size increases. Recent studies show that this class of materials are endowed with superior physical properties such as large isotropic photonic band gaps and optimal transport properties. Here we employ a stochastic optimization procedure to systematically generate realizations of hyperuniform heterogeneous materials with controllable short-range order, which is partially quantified using the two-point correlation function S_{2}(r) associated with the phase of interest. Specifically, our procedure generalizes the widely used Yeong-Torquato reconstruction procedure by including an additional constraint for hyperuniformity, i.e., the volume integral of the autocovariance function χ(r)=S_{2}(r)-ϕ^{2} over the whole space is zero. In addition, we only require the reconstructed S_{2} to match the target function up to a certain cutoff distance γ, in order to give the system sufficient degrees of freedom to satisfy the hyperuniform condition. By systematically increasing the γ value for a given S_{2}, one can produce a spectrum of hyperuniform heterogeneous materials with varying degrees of partial short-range order compatible with the specified S_{2}. The mechanical performance including both elastic and brittle fracture behaviors of the generated hyperuniform materials is analyzed using a volume-compensated lattice-particle method. For the purpose of comparison, the corresponding nonhyperuniform materials with the same short-range order (i.e., with S_{2} constrained up to the same γ value) are also constructed and their mechanical performance is analyzed. Here we consider two specific S_{2} including the positive exponential decay function and the correlation function associated with an equilibrium hard-sphere system. For the constructed systems associated with these two specific functions, we find that although the hyperuniform materials are softer than their nonhyperuniform counterparts, the former generally possess a significantly higher brittle fracture strength than the latter. This superior mechanical behavior is attributed to the lower degree of stress concentration in the material resulting from the hyperuniform microstructure, which is crucial to crack initiation and propagation.

Dynamic reconstruction of heterogeneous materials and microstructure evolution

Reconstructing heterogeneous materials from limited structural information has been a topic that attracts extensive research efforts and still poses many challenges. The Yeong-Torquato procedure is one of the most popular reconstruction techniques, in which the material reconstruction problem based on a set of spatial correlation functions is formulated as a constrained energy minimization (optimization) problem and solved using simulated annealing [Yeong and Torquato, Phys. Rev. E 57, 495 (1998)]. The standard two-point correlation function S2 has been widely used in reconstructions, but can also lead to large structural degeneracy for certain nearly percolating systems. To improve reconstruction accuracy and reduce structural degeneracy, one can successively incorporate additional morphological information (e.g., nonconventional or higher-order correlation functions), which amounts to reshaping the energy landscape to create a deep (local) energy minimum. In this paper, we present a dynamic reconstruction procedure that allows one to use a series of auxiliary S2 to achieve the same level of accuracy as those incorporating additional nonconventional correlation functions. In particular, instead of randomly sampling the microstructure space as in the simulated annealing scheme, our procedure utilizes a series of auxiliary microstructures that mimic a physical structural evolution process (e.g., grain growth). This amounts to constructing a series auxiliary energy landscapes that bias the convergence of the reconstruction to a favored (local) energy minimum. Moreover, our dynamic procedure can be naturally applied to reconstruct an actual microstructure evolution process. In contrast to commonly used evolution reconstruction approaches that separately generate individual static configurations, our procedure continuously evolves a single microstructure according to a time-dependent correlation function. The utility of our procedure is illustrated by successfully reconstructing nearly percolating hard-sphere packings and particle-reinforced composites as well as the coarsening process in a binary metallic alloy.

Soft matter in hard confinement: phase transition thermodynamics, structure, texture, diffusion and flow in nanoporous media

Spatial confinement in nanoporous media affects the structure, thermodynamics and mobility of molecular soft matter often markedly. This article reviews thermodynamic equilibrium phenomena, such as physisorption, capillary condensation, crystallisation, self-diffusion, and structural phase transitions as well as selected aspects of the emerging field of spatially confined, non-equilibrium physics, i.e. the rheology of liquids, capillarity-driven flow phenomena, and imbibition front broadening in nanoporous materials. The observations in the nanoscale systems are related to the corresponding bulk phenomenologies. The complexity of the confined molecular species is varied from simple building blocks, like noble gas atoms, normal alkanes and alcohols to liquid crystals, polymers, ionic liquids, proteins and water. Mostly, experiments with mesoporous solids of alumina, gold, carbon, silica, and silicon with pore diameters ranging from a few up to 50 nm are presented. The observed peculiarities of nanopore-confined condensed matter are also discussed with regard to applications. A particular emphasis is put on texture formation upon crystallisation in nanoporous media, a topic both of high fundamental interest and of increasing nanotechnological importance, e.g. for the synthesis of organic/inorganic hybrid materials by melt infiltration, the usage of nanoporous solids in crystal nucleation or in template-assisted electrochemical deposition of nano structures.

Performance of polycapillary X-ray optics for confocal energy-dispersive small-angle X-ray scattering

A confocal energy-dispersive small-angle X-ray scattering (EDSAXS) setup based on polycapillary optics was designed. In this confocal EDSAXS setup, a polycapillary slightly focusing X-ray lens (PSFXRL) and a polycapillary parallel X-ray lens (PPXRL) with a long input focal distance were placed confocally in the excitation channel and detection channel, respectively. This confocal configuration was helpful in improving the signal-to-noise ratio of the EDSAXS. The high gain in power density of the PSFXRL and PPXRL decreased the power requirement of the X-ray source for EDSAXS. The confocal EDSAXS technology could be used to perform nondestructive andin situanalysis of samples such as milk powder in its packaging.