Small-Angle Scattering Indicates Equilibrium Instead of Metastable Capillary Condensation in SBA-15 Mesoporous Silica.

Questions about the origin of the adsorption/desorption hysteresis in mesoporous materials are as old as sorption experiments themselves. The historical conception that underlines most existing methods to extract pore size distributions from sorption data assumes that adsorption is a metastable process and that desorption takes place at thermodynamic equilibrium. In this work, we measure nitrogen and argon sorption on a series of 14 SBA-15 ordered mesoporous silicas and use small-angle X-ray scattering to independently determine their pore sizes. We find that capillary condensation systematically occurs close to thermodynamic equilibrium according to a Derjaguin-Broekhoff-de Boer calculation. Our analysis suggests that many earlier works have significantly underestimated the actual pore size in SBA-15 materials. It also highlights the critical role of the reference isotherm used to calibrate the fluid-solid interaction in the models.

Two-Step Wetting of Nanoporous Carbons: Small-Angle Scattering Analysis of Capillary Rise.

Numerous applications of nanoporous materials require their pores to be filled with liquids. In spite of its huge technological importance, the conditions for the wetting of nanometer-sized pores and its phenomenology are still poorly understood. We report on capillary rise experiments with water in carbon xerogels, with synchrotron small-angle scattering used to follow the process in situ at the nanometer scale. The data reveal a two-step wetting process whereby water permeates first into molecular-sized micropores, which is followed by the imbibition of larger mesopores. A Cassie-Baxter analysis shows that the presence of water in the micropores is central, as it turns the mesopores from being hydrophobic to hydrophilic. Based on the so-calculated contact angles, the mesopore wetting kinetics are found to be quantitatively described by a classical Washburn model. Modeling of the experimental water profile ahead of the Washburn front reveals strong surface barriers opposing water transfer from the mesopores to the micropores.

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.

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.

Revealing the Formation of Copper Nanoparticles from a Homogeneous Solid Precursor by Electron Microscopy.

The understanding of processes leading to the formation of nanometer-sized particles is important for tailoring of their size, shape and location. The growth mechanisms and kinetics of nanoparticles from solid precursors are, however, often poorly described. Here we employ transmission electron microscopy (TEM) to examine the formation of copper nanoparticles on a silica support during the reduction by H2 of homogeneous copper phyllosilicate platelets, as a prototype precursor for a coprecipitated catalyst. Specifically, time-lapsed TEM image series acquired of the material during the reduction process provide a direct visualization of the growth dynamics of an ensemble of individual nanoparticles and enable a quantitative evaluation of the nucleation and growth of the nanoparticles. This quantitative information is compared with kinetic models and found to be best described by a nucleation-and-growth scenario involving autocatalytic reduction of the copper phyllosilicate followed by diffusion-limited or reaction-limited growth of the copper nanoparticles. The plate-like structure of the precursor restricted the diffusion of copper and the autocatalytic reduction limited the probability for secondary nucleation. The combination of a uniform size of precursor particles and the autocatalytic reduction thus offers means to synthesize nanoparticles with well-defined sizes in large amounts. In this way, in situ observations made by electron microscopy provide mechanistic and kinetic insights into the formation of supported nanoparticles, essential for the rational design of nanomaterials.

Mesoscale Characterization of Nanoparticles Distribution Using X-ray Scattering.

The properties of many functional materials depend critically on the spatial distribution of an active phase within a support. In the case of solid catalysts, controlling the spatial distribution of metal (oxide) nanoparticles at the mesoscopic scale offers new strategies to tune their performance and enhance their lifetimes. However, such advanced control requires suitable characterization methods, which are currently scarce. Here, we show how the background in small-angle X-ray scattering patterns can be analyzed to quantitatively access the mesoscale distribution of nanoparticles within supports displaying hierarchical porosity. This is illustrated for copper catalysts supported on meso- and microporous silica displaying distinctly different metal distributions. Results derived from X-ray scattering are in excellent agreement with electron tomography. Our strategy opens unprecedented prospects for understanding the properties and to guide the synthesis of a wide array of functional nanomaterials.

Nanoparticle growth in supported nickel catalysts during methanation reaction--larger is better.

A major cause of supported metal catalyst deactivation is particle growth by Ostwald ripening. Nickel catalysts, used in the methanation reaction, may suffer greatly from this through the formation of [Ni(CO)4 ]. By analyzing catalysts with various particle sizes and spatial distributions, the interparticle distance was found to have little effect on the stability, because formation and decomposition of nickel carbonyl rather than diffusion was rate limiting. Small particles (3-4 nm) were found to grow very large (20-200 nm), involving local destruction of the support, which was detrimental to the catalyst stability. However, medium sized particles (8 nm) remained confined by the pores of the support displaying enhanced stability, and an activity 3 times higher than initially small particles after 150 h. Physical modeling suggests that the higher [Ni(CO)4 ] supersaturation in catalysts with smaller particles enabled them to overcome the mechanical resistance of the support. Understanding the interplay of particle size and support properties related to the stability of nanoparticles offers the prospect of novel strategies to develop more stable nanostructured materials, also for applications beyond catalysis.

Confinement induced change of microemulsion phase structure in controlled pore glass (CPG) monoliths.

We use small-angle neutron scattering (SANS) to investigate the structure and phase behavior of a complex fluid within meso- and macroporous matrices. Specifically, bicontinuous microemulsions of the temperature-dependent ternary system C10E4-water-n-octane are investigated in controlled pore glass (CPG) membranes with nominal pore diameters of 10 nm, 20 nm, 50 nm, and 100 nm. The scattering data were analyzed using the Teubner-Strey model and a multiphase generalization of clipped Gaussian-field models. The analysis indicates changes in the phase structure of the bicontinuous microemulsion in the membranes with the smallest pores. This is attributed to a shift in the ternary phase diagram toward a three-phase structure at lower surfactant concentrations. This effect is likely related to a larger internal surface area in the membranes with smaller pores, which enhances surfactant adsorption onto the pore walls.

Adsorption, capillary bridge formation, and cavitation in SBA-15 corrugated mesopores: a Derjaguin-Broekhoff-de Boer analysis.

A Derjaguin-Broekhoff-de Boer analysis of adsorption and desorption in SBA-15 mesoporous silica is presented, using realistic geometrical models that account for the pore corrugation in these materials. The model parameters are derived from independent electron tomography and small-angle scattering characterization. A geometrical characteristic of the pore that is found to be important for adsorption is the corrugation length, l(C), which describes the longitudinal size of the geometrical defects along a given pore. Capillary bridges are possible only for large values of l(C). The results are explained in terms of two spinodal and two equilibrium pressures, characterizing the wide and the narrow sections of the pores. Simplified analytical expressions are obtained, which provide necessary conditions for bridge formation and for cavitation in terms of the radii of the narrow and wide sections of the pores, as well as of l(C). Quite generally, the results show that the deviation of the pore shape from that of ideal cylinders is key to understanding adsorption and desorption in corrugated mesopores, notably in SBA-15.

Molecular and morphological aspects of annealing-induced stabilization of starch crystallites.

A unique series of potato (mutant) starches with highly different amylopectin/amylose (AP/AM) ratios was annealed in excess water at stepwise increasing temperatures to increase the starch melting (or gelatinization) temperatures in aqueous suspensions. Small-angle X-ray scattering (SAXS) experiments revealed that the lamellar starch crystals gain stability upon annealing via thickening for high-AM starch, whereas the crystal surface energy decreases for AM-free starch. In starches with intermediate AP/AM ratio, both mechanisms occur, but the surface energy reduction mechanism prevails. Crystal thickening seems to be associated with the cocrystallization of AM with AP, leading to very disordered nanomorphologies for which a new SAXS data interpretation scheme needed to be developed. Annealing affects neither the crystal internal structure nor the spherulitic morphology on a micrometer length scale.

A Time-Dependent Hierarchical Model for Elastic and Inelastic Scattering Data Analysis of Aerogels and Similar Soft Materials.

Soft nanomaterials like aerogels are subject to thermal fluctuations, so that their structure randomly fluctuates with time. Neutron elastic and inelastic scattering experiments provide unique structural and dynamic information on such systems with nanometer and nanosecond resolution. The data, however, come in the form of space- and time-correlation functions, and models are required to convert them into time-dependent structures. We present here a general time-dependent stochastic model of hierarchical structures, with scale-invariant fractals as a particular case, which enables one to jointly analyze elastic and inelastic scattering data. In order to describe thermal fluctuations, the model builds on time-dependent generalisations of the Boolean model of penetrable spheres, whereby each sphere is allowed to move either ballistically or diffusively. Analytical expressions are obtained for the correlation functions, which can be used for data fitting. The model is then used to jointly analyze previously published small-angle neutron scattering (SANS) and neutron spin-echo (NSE) data measured on silica aerogels. In addition to structural differences, the approach provides insight into the different scale-dependent mobility of the aggregates that make up the aerogels, in relation with their different connectivities.

Remodelling of the fibre-aggregate structure of collagen gels by cancer-associated fibroblasts: A time-resolved grey-tone image analysis based on stochastic modelling.

Introduction: Solid tumors consist of tumor cells associated with stromal and immune cells, secreted factors and extracellular matrix (ECM), which together constitute the tumor microenvironment. Among stromal cells, activated fibroblasts, known as cancer-associated fibroblasts (CAFs) are of particular interest. CAFs secrete a plethora of ECM components including collagen and modulate the architecture of the ECM, thereby influencing cancer cell migration. The characterization of the collagen fibre network and its space and time-dependent microstructural modifications is key to investigating the interactions between cells and the ECM. Developing image analysis tools for that purpose is still a challenge because the structural complexity of the collagen network calls for specific statistical descriptors. Moreover, the low signal-to-noise ratio of imaging techniques available for time-resolved studies rules out standard methods based on image segmentation. Methods: In this work, we develop a novel approach based on the stochastic modelling of the gel structure and on grey-tone image analysis. The method is then used to study the remodelling of a collagen matrix by migrating breast cancer-derived CAFs in a three-dimensional spheroid model of cellular invasion imaged by time-lapse confocal microscopy. Results: The structure of the collagen at the scale of a few microns consists in regions with high fibre density separated by depleted regions, which can be thought of as aggregates and pores. The approach developped captures this two-scale structure with a clipped Gaussian field model to describe the aggregates-and-pores large-scale structure, and a homogeneous Boolean model to describe the small-scale fibre network within the aggregates. The model parameters are identified by fitting the grey-tone histograms and correlation functions of the images. The method applies to unprocessed grey-tone images, and it can therefore be used with low magnification, noisy time-lapse reflectance images. When applied to the CAF spheroid time-resolved images, the method reveals different matrix densification mechanisms for the matrix in direct contact or far from the cells. Conclusion: We developed a novel and multidisciplinary image analysis approach to investigate the remodelling of fibrillar collagen in a 3D spheroid model of cellular invasion. The specificity of the method is that it applies to the unprocessed grey-tone images, and it can therefore be used with noisy time-lapse reflectance images of non-fluorescent collagen. When applied to the CAF spheroid time-resolved images, the method reveals different matrix densification mechanisms for the matrix in direct contact or far from the cells.

Small-angle scattering for beginners.

Many experimental methods are available for the characterization of nanostructures, but most of them are limited by stringent experimental conditions. When it comes to analysing nanostructures in the bulk or in their natural environment - even as ordinary as water at room temperature - small-angle scattering (SAS) of X-rays or neutrons is often the only option. The rapid worldwide development of synchrotron and neutron facilities over recent decades has opened unprecedented possibilities for using SAS in situ and in a time-resolved way. But, in spite of its huge potential in the field of nanomaterials in general, SAS is covered far less than other characterization methods in non-specialized curricula. Presented here is a rigorous discussion of small-angle scattering, at a technical level comparable to the classical undergraduate coverage of X-ray diffraction by crystals and which contains diffraction as a particular case.

Quantitative structural analysis of binary nanocrystal superlattices by electron tomography.

Binary nanocrystal superlattices, that is, ordered structures of two sorts of nanocolloids, hold promise for a series of functional materials with novel collective properties. Here we show that based on electron tomography a comprehensive, quantitative, three-dimensional characterization of these systems down to the single nanocrystal level can be achieved, which is key in understanding the emerging materials properties. On four binary lattices composed of PbSe, CdSe, and Au nanocrystals, we illustrate that ambiguous interpretations based on two-dimensional transmission electron microscopy can be prevented, nanocrystal sizes and superlattice parameters accurately determined, individual crystallographic point and plane defects studied, and the order/disorder at the top and bottom surfaces imaged. Furthermore, our results suggest that superlattice nucleation and growth occurred at the suspension/air interface and that the unit cells of some lattices are anisotropically deformed upon drying.

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.

Ostwald ripening of confined nanoparticles: chemomechanical coupling in nanopores.

Ostwald ripening is a major source of deactivation of functional nanomaterials. It consists in the growth of large nanoparticles at the expense of smaller ones via the formation and decomposition of intermediate chemical species. In most materials of practical interest nanoparticles are dispersed in porous supports with which they interact mechanically. We analyze the consequences of this chemo-mechanical coupling on both kinetic and equilibrium aspects of Ostwald ripening. We show that the long-term stability of a collection of confined nanoparticles depends on nucleation-like events, whereby few particles break through the pore walls early in the process and later grow at the expense of all other particles. This notably explains why the stability of confined nanoparticles depends critically on their initial size distribution; it also provides an explanation for the occasional observation of bimodal particle size distributions in aged materials.

Structure development of resorcinol-formaldehyde gels: microphase separation or colloid aggregation.

Time-resolved small-angle x-ray scattering (SAXS) is used to follow the formation of resorcinol-formaldehyde (RF) gels. An existing morphological model based on Gaussian random fields, and validated on RF aerogels, is generalized to analyze the data. The generalization is done in two different ways, one being relevant to colloid aggregation and the other to microphase separation. The SAXS data do not enable discrimination between the two mechanisms of gel formation, which shows that aggregation and microphase separation can generate very similar morphologies at the length scales explored by SAXS. Furthermore, physical arguments suggest that, in the case of RF gels, aggregation and microphase separation can be regarded as two idealizations of the same complex physical process.

Positive curvature effects and interparticle capillary condensation during nitrogen adsorption in particulate porous materials.

The adsorption of nitrogen in a collection of spheres that touch or merge in a sintering-like manner is modeled using a Derjaguin-Broeckhof-de Boer approach. The proposed model accounts for both positive curvature effects and for capillary condensation at the contact between two spheres. A methodology is proposed to fit the P/P(0)>0.4 adsorption region with the coordination number of the spheres as the only adjustable parameter. The use of the model is illustrated on a series of silica aerogels. The suitability of various standard isotherms needed for the modeling is also discussed.

Structure of silica xerogels synthesized with organoalkoxysilane co-reactants hints at multiple phase separation.

The microstructure of hybrid silica xerogels synthesized by the base-catalyzed polymerization of tetraethoxysilane (TEOS) in ethanol in the presence of 3-aminopropyltriethoxysilane (AES) and of 3-(2-aminoethylamino)propyltrimethoxysilane (EDAS) as co-reactants, and dried in subcritical conditions, is analyzed. A thorough structural characterization of the samples is performed combining nitrogen adsorption, small-angle X-ray scattering (SAXS), and transmission electron microscopy coupled with digital image analysis. The use of these methods shows that, for both co-reactants, the xerogels are made of macropores supported by filaments, with each filament being formed of smaller structures. The quantitative impact of the additive on each structural level is assessed. The data are compared with a previous time-resolved SAXS study conducted during the formation of the gels (J. Phys. Chem. B 2004, 108, 8983-8991). The results are analyzed in the framework of a double phase separation model.