Tuning Thermal, Morphological, and Physicochemical Properties of Thermoplastic Polyurethanes (TPUs) by the 1,4-Butanediol (BDO)/Dipropylene Glycol (DPG) Ratio.

Thermoplastic polyurethanes (TPUs) are versatile polymers presenting a broad range of properties as a result of their countless combination of raw materials­in essence, isocyanates, polyols, and chain extenders. This study highlights the effect of two different chain extenders and their combination on the structure−property relationships of TPUs synthesized by reactive extrusion. The TPUs were obtained from 4,4-diphenylmethane diisocyanate (MDI), polyester diols, and the chain extenders 1,4-butanediol (BDO) and dipropylene glycol (DPG). The BDO/DPG ratios studied were 100/0, 75/25, 50/50, 25/75, and 0/100 wt.%. The TPUs were characterized by size exclusion chromatography (SEC), Fourier-transform infrared spectroscopy (FTIR), differential scanning calorimetry (DSC), small-angle X-ray scattering (SAXS), UV−vis spectroscopy, and physical-mechanical properties. The results indicate that DPG promotes compatibility between rigid (HS) and flexible (SS) segments of TPUs. Consequently, increasing DPG content (>75 wt.%) reduced the organization of the rigid segments and the degree of phase separation, increasing the polydispersity of the interdomain distance and the transparency in the UV−visible spectrum of the TPUs. Furthermore, increasing DPG content also reduced the amount of hydrogen bonds present in the rigid phase, reducing or extinguishing its glass transition temperature (TgHS) and melting temperature (Tm), and increasing the glass transition temperature of the flexible phase (TgSS). Therefore, increasing DPG content leads to a deterioration in mechanical properties and hydrolysis resistance.

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.

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 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.

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.

Scale-dependent diffusion anisotropy in nanoporous silicon.

Nanoporous silicon produced by electrochemical etching of highly B-doped p-type silicon wafers can be prepared with tubular pores imbedded in a silicon matrix. Such materials have found many technological applications and provide a useful model system for studying phase transitions under confinement. This paper reports a joint experimental and simulation study of diffusion in such materials, covering displacements from molecular dimensions up to tens of micrometers with carefully selected probe molecules. In addition to mass transfer through the channels, diffusion (at much smaller rates) is also found to occur in directions perpendicular to the channels, thus providing clear evidence of connectivity. With increasing displacements, propagation in both axial and transversal directions is progressively retarded, suggesting a scale-dependent, hierarchical distribution of transport resistances ("constrictions" in the channels) and of shortcuts (connecting "bridges") between adjacent channels. The experimental evidence from these studies is confirmed by molecular dynamics (MD) simulation in the range of atomistic displacements and rationalized with a simple model of statistically distributed "constrictions" and "bridges" for displacements in the micrometer range via dynamic Monte Carlo (DMC) simulation. Both ranges are demonstrated to be mutually transferrable by DMC simulations based on the pore space topology determined by electron tomography.

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.

The range of validity of sorption kinetic models.

Several hundred papers are published yearly reporting liquid-phase adsorption kinetics data. In general the data is analyzed using a variety of standard models such as the pseudo first- and second-order models and the Intraparticle-Diffusion model. The validity of these models is often assessed empirically via their ability to fit the data, independently of their physicochemical soundness. The aim of the present paper is to rationalize the analysis of liquid-phase adsorption kinetics data, and to investigate experimental factors that influence the adsorption kinetics, in addition to the characteristics of the adsorbent material itself. For that purpose we use a simple Langmuir adsorption-diffusion model, which enables us to identify three dimensionless numbers that characterize the working regime of any batch adsorption experiment: an adsorption Thiele modulus, a saturation modulus, and a loading modulus. The standard models are found to be particular cases of the general adsorption-diffusion model for specific values of the dimensionless numbers. This provides sound physicochemical criteria for the validity of the models. Based on our modeling, we also propose a general yet simple data analysis procedure to practically estimate the diffusion coefficient in adsorbent pellets starting from adsorption half-times.

Small-angle X-ray scattering insights into the architecture-dependent emulsifying properties of amphiphilic copolymers in supercritical carbon dioxide.

The supramolecular assembly of a series of copolymers combining poly(ethylene oxide)-rich hydrophilic and fluorinated CO2-philic sequences is analyzed by synchrotron small-angle X-ray scattering (SAXS) in supercritical CO2, as well as in water/CO2 emulsions. These copolymers were designed to have the same molecular weight and composition and to differ only by their macromolecular architecture. The investigated copolymers have random, block, and palm-tree architectures. Besides, thermoresponsive copolymer is also analyzed, having a hydrophilic sequence becoming water-insoluble around 41 °C, i.e., just above the critical point of CO2. At the length scale investigated by SAXS, only the random copolymer appears to self-assemble in pure CO2, in the form of a disordered microgel-like network. The random, block, and thermoresponsive copolymers are all able to stabilize water/CO2 emulsions but not the copolymer with the palm-tree architecture, pointing at the importance of macromolecular architecture for the emulsifying properties. A modeling of the SAXS data shows that the block and the thermoresponsive copolymers form spherical micelle-like structures containing about 70% water and 30% polymer.

A high pressure cell for supercritical CO2 on-line chemical reactions studied with X-ray techniques.

A versatile high pressure X-ray sample cell has been developed for conducting in situ time-resolved X-ray scattering experiments in the pressure and temperature regime required (pressures up to 210 bars and temperatures up to 120 °C) for chemical reactions in supercritical fluids. The large exit opening angle of the cell allows simultaneous performance of SAXS-WAXS experiments. Diamond windows are used in order to benefit from the combination of maximum strength, minimal X-ray absorption and chemical inertia. The sample cell can also be utilised for X-ray spectroscopy experiments over a wide range of photon energies. Results of the online synthesis of a block copolymer, poly(methyl methacrylate-block-poly(benzyl methacrylate), by Reversible Addition-Fragmentation Chain Transfer (RAFT) in a supercritical CO2 dispersion polymerisation will be discussed. The contribution of the density fluctuations, as function of temperature, to the X-ray scattering signal has been quantified in order to allow appropriate background subtractions.

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.

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.

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.

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.

Morphological models of complex ordered materials based on inhomogeneously clipped Gaussian fields.

Clipping a Gaussian random field at a level that is position-dependent yields statistically inhomogeneous morphologies, relevant to many ordered nanostructured materials. The one-point and two-point probability functions of the morphology are derived, as well as a general relation between the specific surface area and the gradient of the clipping function. The general results are particularized for the comprehensive analysis of small-angle x-ray scattering and nitrogen adsorption of SBA-15 ordered mesoporous silica.