Measurement of the Gaussian curvature of the surfactant film in an isometric bicontinuous one-phase microemulsion

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.

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.

Using X-Ray Scattering to Elucidate the Microstructural Instability of 3D Bicontinuous Nanoporous Metal Scaffolds for Use in an Aperiodic 3D Tricontinuous Conductor-Insulator-Conductor Nanocapacitor

The development of three-dimensional aperiodic energy storage devices is in part impeded by the lack of appropriate aperiodic templates that can withstand the thermal conditions required to deposit energy storage materials within their void space. Herein, the feasibility of an aperiodic three-dimensional architecture for energy storage is demonstrated for the first time by constructing a tricontinuous conductor-insulator-conductor (CIC) nanocapacitor on an aperiodic nanoporous gold scaffold. To accomplish this, the scaffold was characterized using in situ small-angle X-ray scattering (SAXS) during exposure to a thermal environment, revealing that its microstructure eventually stabilizes after undergoing a phase of rapid coarsening, indicating a departure from the 1/4 time-dependent power-law coarsening behavior usually observed at the early stage of the coarsening process. Using this stability regime, we created the CIC by intentionally precoarsening and stabilizing the scaffold before depositing two dissimilar metal oxide films in its void space by atomic layer deposition. Current-voltage characteristics and electrochemical impedance spectroscopy measurements revealed that the un-optimized 3D CIC outperformed its 2D counterpart by ∼4× in terms of capacitance. This proof-of-concept device will pave the way to the development of aperiodic three-dimensional energy storage systems with enhanced energy and power densities.

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.

Toughening of Thermoresponsive Arrested Networks of Elastin-Like Polypeptides To Engineer Cytocompatible Tissue Scaffolds

Formulation of tissue engineering or regenerative scaffolds from simple bioactive polymers with tunable structure and mechanics is crucial for the regeneration of complex tissues, and hydrogels from recombinant proteins, such as elastin-like polypeptides (ELPs), are promising platforms to support these applications. The arrested phase separation of ELPs has been shown to yield remarkably stiff, biocontinuous, nanostructured networks, but these gels are limited in applications by their relatively brittle nature. Here, a gel-forming ELP is chain-extended by telechelic oxidative coupling, forming extensible, tough hydrogels. Small angle scattering indicates that the chain-extended polypeptides form a fractal network of nanoscale aggregates over a broad concentration range, accessing moduli ranging from 5 kPa to over 1 MPa over a concentration range of 5-30 wt %. These networks exhibited excellent erosion resistance and allowed for the diffusion and release of encapsulated particles consistent with a bicontinuous, porous structure with a broad distribution of pore sizes. Biofunctionalized, toughened networks were found to maintain the viability of human mesenchymal stem cells (hMSCs) in 2D, demonstrating signs of osteogenesis even in cell media without osteogenic molecules. Furthermore, chondrocytes could be readily mixed into these gels via thermoresponsive assembly and remained viable in extended culture. These studies demonstrate the ability to engineer ELP-based arrested physical networks on the molecular level to form reinforced, cytocompatible hydrogel matrices, supporting the promise of these new materials as candidates for the engineering and regeneration of stiff tissues.

Arrested Phase Separation of Elastin-like Polypeptide Solutions Yields Stiff, Thermoresponsive Gels

The preparation of new responsive hydrogels is crucial for the development of soft materials for various applications, including additive manufacturing and biomedical implants. Here, we report the discovery of a new mechanism for forming physical hydrogels by the arrested phase separation of a subclass of responsively hydrophobic elastin-like polypeptides (ELPs). When moderately concentrated solutions of ELPs with the pentapeptide repeat (XPAVG)n (where X is either 20% or 60% valine with the remainder isoleucine) are warmed above their inverse transition temperature, phase separation becomes arrested, and hydrogels can be formed with shear moduli on the order of 0.1-1 MPa at 20 wt % in water. The longest stress relaxation times are well beyond 10(3) s. This result is surprising because ELPs are classically known for thermoresponsive coacervation that leads to macrophase separation, and solids are typically formed in the bulk or by supplemental cross-linking strategies. This new mechanism can form gels with remarkable mechanical behavior based on simple macromolecules that can be easily engineered. Small angle scattering experiments indicate that phase separation arrests to form a network of nanoscale domains, exhibiting rheological and structural features consistent with an arrested spinodal decomposition mechanism. Gel nanostructure can be modeled as a disordered bicontinuous network with interdomain, intradomain, and curvature length scales that can be controlled by sequence design and assembly conditions. These studies introduce a new class of reversible, responsive materials based on a classic artificial biopolymer that is a versatile platform to address critical challenges in industrial and medical applications.

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.

Columnar and lamellar phases in attractive colloidal systems

In colloidal suspensions, at low volume fraction and temperature, dynamical arrest occurs via the growth of elongated structures that aggregate to form a connected network at gelation. Here we show that, in the region of parameter space where gelation occurs, the stable thermodynamical phase is a crystalline columnar one. Near and above the gelation threshold, the disordered spanning network slowly evolves and finally orders to form the crystalline structure. At higher volume fractions the stable phase is a lamellar one, which seems to have a still longer ordering time.

Morphological characterization of bicontinuous structures in polymer blends and microemulsions by the inverse-clipping method in the context of the clipped-random-wave model

A method is proposed to determine the spectral function of the clipped-random-wave (CRW) model directly from scattering data. The spectral function f(k) (k is a wave number) gives the distribution of the magnitude of wave vectors of the sinusoidal waves that describes the essential features of the two-phase morphology. The proposed method involves "inverse clipping" of a correlation function to obtain f(k) and does not require any a priori assumptions for f(k). A critical test of the applicability of the inverse-clipping method was carried out by using three-component bicontinuous microemulsions. The method was then used to determine f(k) of the bicontinuous structure of a phase-separating polymer blend. f(k) for the polymer blend turned out to be a multipeaked function, while f(k) for the microemulsions exhibits a single broad maximum representing periodicity of the morphology. These results indicate the presence of the long-range regularity in the morphology of the polymer blend. Three-dimensional (3D) morphology corresponding to the scattering data of the polymer blend was generated using the CRW model together with the multipeaked f(k). Interface curvatures of the 3D morphology calculated from f(k) were measured and compared with those experimentally determined directly from the laser scanning confocal microscopy in the same blend.

Clipped random wave analysis of isometric lamellar microemulsions

We have made small angle neutron scattering studies of C10E4-D2O-octane isometric microemulsions in the lamellar phase at the hydrophile-lipophile balance temperature. The scattering intensity distributions were then analyzed with a particular choice of a spectral density function (SDF) derived by maximization of generalized entropy. The model agrees well with the measured intensities on an absolute scale, and allowed us to derive various length scales associated with the microemulsion mesoscopic structure as well as the average interfacial curvatures. We also used the experimentally determined SDF to generate a three-dimensional snapshot of the fluctuating microemulsion microstructure. Unlike conventional pictures of extended lamellar planes, we observed small domains which were internally lamellar but randomly oriented with respect to each other. Finally, we computed the probability distributions of the mean curvature H and the Gaussian curvature K on the oil-water interface. The former showed a symmetric distribution centered around H = 0, while the latter showed a skewed distribution peaked at a negative value of K, but with a wing extending to positive values.