Determination of the local density of polydisperse nanoparticle assemblies

On the absence of structure factors in concentrated colloidal suspensions and nanocomposites

Small-angle scattering is a commonly used tool to analyze the dispersion of nanoparticles in all kinds of matrices. Besides some obvious cases, the associated structure factor is often complex and cannot be reduced to a simple interparticle interaction, like excluded volume only. In recent experiments, we have encountered a surprising absence of structure factors (S(q) = 1) in scattering from rather concentrated polymer nanocomposites (Genix et al. in ACS Appl Mater Interfaces 11(19):17863-17872, 2019). In this case, quite pure form factor scattering is observed. This somewhat "ideal" structure is further investigated here making use of reverse Monte Carlo simulations in order to shed light on the corresponding nanoparticle structure in space. By fixing the target "experimental" apparent structure factor to one over a given q-range in these simulations, we show that it is possible to find dispersions with this property. The influence of nanoparticle volume fraction and polydispersity has been investigated, and it was found that for high concentrations only a high polydispersity allows reaching a state of S = 1. The underlying structure in real space is discussed in terms of the pair-correlation function, which evidences the importance of attractive interactions between polydisperse nanoparticles. The calculation of partial structure factors shows that there is no specific ordering of large or small particles, but that the presence of attractive interactions together with polydispersity allows reaching an almost "structureless" state.

Influence of the Graft Length on Nanocomposite Structure and Interfacial Dynamics

Both the dispersion state of nanoparticles (NPs) within polymer nanocomposites (PNCs) and the dynamical state of the polymer altered by the presence of the NP/polymer interfaces have a strong impact on the macroscopic properties of PNCs. In particular, mechanical properties are strongly affected by percolation of hard phases, which may be NP networks, dynamically modified polymer regions, or combinations of both. In this article, the impact on dispersion and dynamics of surface modification of the NPs by short monomethoxysilanes with eight carbons in the alkyl part (C₈) is studied. As a function of grafting density and particle content, polymer dynamics is followed by broadband dielectric spectroscopy and analyzed by an interfacial layer model, whereas the particle dispersion is investigated by small-angle X-ray scattering and analyzed by reverse Monte Carlo simulations. NP dispersions are found to be destabilized only at the highest grafting. The interfacial layer formalism allows the clear identification of the volume fraction of interfacial polymer, with its characteristic time. The strongest dynamical slow-down in the polymer is found for unmodified NPs, while grafting weakens this effect progressively. The combination of all three techniques enables a unique measurement of the true thickness of the interfacial layer, which is ca. 5 nm. Finally, the comparison between longer (C₁₈) and shorter (C₈) grafts provides unprecedented insight into the efficacy and tunability of surface modification. It is shown that C₈-grafting allows for a more progressive tuning, which goes beyond a pure mass effect.

How Tuning Interfaces Impacts the Dynamics and Structure of Polymer Nanocomposites Simultaneously

Fundamental understanding of the macroscopic properties of polymer nanocomposites (PNCs) remains difficult due to the complex interplay of microscopic dynamics and structure, namely interfacial layer relaxations and three-dimensional nanoparticle (NP) arrangements. The effect of surface modification by alkyl methoxysilanes at different grafting densities has been studied in PNCs made of poly(2-vinylpyridine) and spherical 20 nm silica NPs. The segmental dynamics has been probed by broadband dielectric spectroscopy and the filler structure by small-angle X-ray scattering and reverse Monte Carlo simulations. By combining the particle configurations with the interfacial layer properties, it is shown how surface modification tunes the attractive polymer-particle interactions: bare NPs slow down the polymer interfacial layer dynamics over a thickness of ca. 5 nm, while grafting screens these interactions. Our analysis of interparticle spacings and segmental dynamics provides unprecedented insights into the effect of surface modification on the main characteristics of PNCs: particle interactions and polymer interfacial layers.

A model on an absolute scale for the small-angle X-ray scattering from bovine casein micelles

Casein micelles extracted from milk are 100-400 nm-sized particles, made up of proteins and calcium phosphates, with the latter as colloidal calcium phosphate particles (CCPs) in a size range of 2-4 nm embedded in a protein network. The hierarchical structures give rise to a variation of scattering intensity over many orders of magnitude, which can be measured by small-angle X-ray scattering and static light scattering. Expressions for the scattering intensity of a general simple model for composite particles with polydispersities of overall size and subparticles are derived, and some approximations are checked by generating scattering data for systems generated by Monte Carlo simulations. Based on the simpler models, a new model has been developed for casein micelles, where the scattering is expressed on an absolute scale and where the concentrations of, respectively, protein and CCPs are used as constraints, providing a consistent model. The CCPs are modelled as oblate ellipsoids and the protein as star structures. Correlations between the substructures of CCPs and protein structures are taken into account in terms of partial structure factors. The overall structure as well as some heterogeneities at intermediate length scale are modelled as polydisperse spheres. The model fits the data very well on all length scales and demonstrates that both the scattering from CCPs and protein is important. Thus, the model provides a detailed description of the casein structure, which is consistent with the information available in the literature.

Light scattering from colloidal aggregates on a hierarchy of length scales

Disordered dielectrics with structural correlations on length scales comparable to visible light wavelengths exhibit interesting optical properties. Such materials exist in nature, leading to beautiful structural non-iridescent color, and they are also increasingly used as building blocks for optical materials and coatings. In this article, we explore the angular resolved single-scattering properties of micron-sized, disordered colloidal assemblies. The aggregates act as structurally colored supraparticles or as building blocks for macroscopic photonic glasses. We obtain first experimental data for the differential scattering and transport cross-section. Based on existing macroscopic models, we develop a theoretical framework to describe the scattering from densely packed colloidal assemblies on a hierarchy of length scales.

Assessment of structure factors for analysis of small-angle scattering data from desired or undesired aggregates

Aggregation processes are central features of many systems ranging from colloids and polymers to inorganic nanoparticles and biological systems. Some aggregated structures are controlled and desirable, e.g. in the design of size-controlled clustered nanoparticles or some protein-based drugs. In other cases, the aggregates are undesirable, e.g. protein aggregation involved in neurodegenerative diseases or in vitro studies of single protein structures. In either case, experimental and analytical tools are needed to cast light on the aggregation processes. Aggregation processes can be studied with small-angle scattering, but analytical descriptions of the aggregates are needed for detailed structural analysis. This paper presents a list of useful small-angle scattering structure factors, including a novel structure factor for a spherical cluster with local correlations between the constituent particles. Several of the structure factors were renormalized to get correct limit values in both the high-q and low-q limit, where q is the modulus of the scattering vector. The structure factors were critically evaluated against simulated data. Structure factors describing fractal aggregates provided approximate descriptions of the simulated data for all tested structures, from linear to globular aggregates. The addition of a correlation hole for the constituent particles in the fractal structure factors significantly improved the fits in all cases. Linear aggregates were best described by a linear structure factor and globular aggregates by the newly derived spherical cluster structure factor. As a central point, it is shown that the structure factors could be used to take aggregation contributions into account for samples of monomeric protein containing a minor fraction of aggregated protein. After applying structure factors in the analysis, the correct structure and oligomeric state of the protein were determined. Thus, by careful use of the presented structure factors, important structural information can be retrieved from small-angle scattering data, both when aggregates are desired and when they are undesired.

Resolving Segmental Polymer Dynamics in Nanocomposites by Incoherent Neutron Spin-Echo Spectroscopy

The segmental dynamics of styrene-butadiene nanocomposites with embedded silica nanoparticles (NPs, ca. 20 vol. %) has been studied by broadband dielectric (BDS) and neutron spin-echo spectroscopy (NSE). It is shown by BDS that overlapping contributions only allow us to conclude on a range of distributions of relaxation times in simplified industrial nanocomposites formed with highly polydisperse NPs. For comparison, structurally similar but less aggregated colloidal nanocomposites have a well-defined distribution of relaxation times due to the reduced influence of interfacial polarization processes. This distribution is widened with respect to the neat polymer, without change in the position of the maximum and at most a small slowing down visible in the average time. We then demonstrate that incoherent NSE can be used to resolve small modifications of segmental dynamics of the industrial samples. By carefully choosing the q-vector of the measurement, experiments with fully hydrogenated polymer give access to the self-dynamics of the polymer in the presence of silica on the scale of approximately 1 nm. Our high-resolution measurements show that the segmental motion is slightly but systematically slowed also by the presence of the industrial filler NPs.

Structural identification of percolation of nanoparticles

We propose a method relying on structural measurements by small-angle scattering to quantitatively follow aggregation of nanoparticles (NPs) in concentrated colloidal assemblies or suspensions up to percolation, regardless of complex structure factors arising due to interactions. As an experimental model system, the dispersion of silica NPs in a styrene-butadiene matrix has been analyzed by small-angle X-ray scattering and transmission electron microscopy (TEM), as a function of particle concentration. A reverse Monte Carlo analysis applied to the NP scattering compared favorably with TEM. By combining it with an aggregate recognition algorithm, series of representative real space structures and aggregation number distribution functions have been determined up to high concentrations, taking into account particle polydispersity. Our analysis demonstrates that the formation of large percolating aggregates on the scale of the simulation box (of linear dimension 1/q_min, here micron-sized) can be mapped onto the macroscopic percolation characterized by rheology. Our method is thus capable of determining aggregate structure in dense NP systems with strong - possibly unknown - interactions visible in scattering. It is hoped to be useful in many other colloidal systems, beyond the case of polymer nanocomposites exemplarily studied here.

Effect of Temperature and Ionic Strength on Micellar Aggregates of Oppositely Charged Thermoresponsive Block Copolymer Polyelectrolytes

The self-assembly of two oppositely charged diblock copolymers that have a common thermosensitive nonionic block of poly(N-isopropylacrylamide) (pNIPAAM) has been investigated. The effect of the mixing ratio and total polymer concentrations on the self-assembly of the components and on the phase stability of the mixtures was studied by dynamic light scattering, electrophoretic mobility, and turbidimetry measurements in water at 20 °C. The effect of the competing electrostatic and hydrophobic interactions on the nanostructure of negatively charged electrostatically self-assembled micelles bearing a pNIPAAM corona was investigated by small-angle X-ray scattering (SAXS). The electrostatic and hydrophobic interactions were controlled independently by tuning the ionic strength (from pure water to 50 mM NaCl) and the temperature (20-50 °C) of the investigated mixtures. The SAXS data could be fitted by a spherical micelle model, which has a smoothly decaying radial profile and a Gaussian star term that describes the internal structure of the micellar structures and possible attractive interactions between the polymer chains. At high temperature, a cluster structure factor was included for describing the formation of bulky clusters of the formed micelles. At low temperature and ionic strength, the formation of micelles with a coacervate core and hydrated pNIPAAM shell was observed. The structural evolution of the self-assembled micelles with increasing ionic strength and temperature could be followed, and finally at high ionic strength and temperature, the formation of inverted micelles with a hydrophobic core and polyelectrolyte shell could be identified.

THE PAYNE EFFECT: PRIMARILY POLYMER-RELATED OR FILLER-RELATED PHENOMENON?

The hysteretic softening at small dynamic strains (Payne effect)—related to the rolling resistance and viscoelastic losses of tires—was studied as a function of particle size, filler volume fraction, and temperature for carbon black (CB) reinforced uncrosslinked styrene–butadiene rubber (SBR) and a paste-like material composed of CB-filled paraffin oil. The low-strain limit for dynamic storage modulus was found to be remarkably similar for CB-filled oil and the CB-filled SBR. Small-angle X-ray scattering (SAXS) measurements on the simple composites and detailed data analysis confirmed that the aggregate structures and nature of filler branching/networking of carbon black were virtually identical within oil compared to the high molecular weight polymer matrix. The combined dynamic rheology and SAXS results provide clear evidence that the deformation-induced breaking (unjamming) of the filler network—characterized by filler–filler contacts that are percolated throughout the material—is the main cause for the Payne effect. However, the polymer matrix does play a secondary role as demonstrated by a reduction in Payne effect magnitude with increasing temperature for the CB-reinforced rubber, which was not observed to a significant extent for the oil–CB system.

Unfolding and partial refolding of a cellulase from the SDS-denatured state: From β-sheet to α-helix and back

Globular proteins are typically unfolded by SDS to form protein-decorated micelle-like structures. Several proteins have been shown subsequently to refold by addition of the nonionic surfactant octaethylene glycol monododecyl ether (C₁₂E₈). Thus SDS converts β-lactoglobulin, which has mainly β-sheet secondary structure, into a state rich in α-helicality, while addition of C₁₂E₈ leads to refolding and recovery of the original β-sheet structure. Here we extend these studies to the large β-sheet-rich cellulase Cel7b from Humicola insolens whose enzymatic activity provides a very sensitive refolding parameter. The enzymes widespread usage in the detergent industry makes it an obvious model system for protein-surfactant interactions. SDS-unfolding and subsequent refolding using C₁₂E₈ were investigated at pH 4.2 using near- and far-UV circular dichroism (CD), small-angle X-ray scattering (SAXS), isothermal titration calorimetry (ITC), size-exclusion chromatography (SEC) and activity measurements. The Cel7b:SDS complex can be described as a random configuration of 3-4 connected core-shell structures in which the protein is converted to a mainly α-helical secondary structure. Addition of C₁₂E₈ recovers almost all the secondary structure, part of the tertiary structure, about 50% of the activity and dissociates part of the protein population completely from detergent micelles. The lack of complete refolding may be due to charge neutralisation of Cel7b by SDS, kinetically trapping the enzyme into aggregated structures. In support of this, aggregates did not form when C₁₂E₈ was first mixed with Cel7b followed by addition of SDS. Formation of such aggregates may be a general phenomenon hampering quantitative refolding from the SDS-denatured state.

Understanding the Static Interfacial Polymer Layer by Exploring the Dispersion States of Nanocomposites

The dynamic and static properties of the interfacial region between polymer and nanoparticles have wide-ranging consequences on performances of nanomaterials. The thickness and density of the static layer are particularly difficult to assess experimentally due to superimposing nanoparticle interactions. Here, we tune the dispersion of silica nanoparticles in nanocomposites by preadsorption of polymer layers in the precursor solutions, and by varying the molecular weight of the matrix chains. Nanocomposite structures ranging from ideal dispersion to repulsive order or various degrees of aggregation are generated and observed by small-angle scattering. Preadsorbed chains are found to promote ideal dispersion, before desorption in the late stages of nanocomposite formation. The microstructure of the interfacial polymer layer is characterized by detailed modeling of X-ray and neutron scattering. Only in ideally well-dispersed systems a static interfacial layer of reduced polymer density over a thickness of ca. 2 nm is evidenced based on the analysis with a form-free density profile optimized using numerical simulations. This interfacial gradient layer is found to be independent of the thickness of the initially adsorbed polymer, but appears to be generated by out-of-equilibrium packing and folding of the preadsorbed layer. The impact of annealing is investigated to study the approach of equilibrium, showing that initially ideally well-dispersed systems adopt a repulsive hard-sphere structure, while the static interfacial layer disappears. This study thus promotes the fundamental understanding of the interplay between effects which are decisive for macroscopic material properties: polymer-mediated interparticle interactions, and particle interfacial effects on the surrounding polymer.

A methodology to calculate small-angle scattering profiles of macromolecular solutions from molecular simulations in the grand-canonical ensemble

The theoretical framework to evaluate small-angle scattering (SAS) profiles for multi-component macromolecular solutions is re-examined from the standpoint of molecular simulations in the grand-canonical ensemble, where the chemical potentials of all species in solution are fixed. This statistical mechanical ensemble resembles more closely scattering experiments, capturing concentration fluctuations that arise from the exchange of molecules between the scattering volume and the bulk solution. The resulting grand-canonical expression relates scattering intensities to the different intra- and intermolecular pair distribution functions, as well as to the distribution of molecular concentrations on the scattering volume. This formulation represents a generalized expression that encompasses most of the existing methods to evaluate SAS profiles from molecular simulations. The grand-canonical SAS methodology is probed for a series of different implicit-solvent, homogeneous systems at conditions ranging from dilute to concentrated. These systems consist of spherical colloids, dumbbell particles, and highly flexible polymer chains. Comparison of the resulting SAS curves against classical methodologies based on either theoretical approaches or canonical simulations (i.e., at a fixed number of molecules) shows equivalence between the different scattering intensities so long as interactions between molecules are net repulsive or weakly attractive. On the other hand, for strongly attractive interactions, grand-canonical SAS profiles deviate in the low- and intermediate-q range from those calculated in a canonical ensemble. Such differences are due to the distribution of molecules becoming asymmetric, which yields a higher contribution from configurations with molecular concentrations larger than the nominal value. Additionally, for flexible systems, explicit discrimination between intra- and inter-molecular SAS contributions permits the implementation of model-free, structural analysis such as Guinier's plots at high molecular concentrations, beyond what the traditional limits are for such analysis.

Nanoparticle self-assembly: from interactions in suspension to polymer nanocomposites

Recent experimental results using in particular small-angle scattering to characterize the self-assembly of mainly hard spherical nanoparticles into higher ordered structures ranging from fractal aggregates to ordered assemblies are reviewed. The crucial control of interparticle interactions is discussed, from chemical surface-modification, or the action of additives like depletion agents, to the generation of directional patches and the use of external fields. It is shown how the properties of interparticle interactions have been used to allow inducing and possibly controlling aggregation, opening the road to the generation of colloidal molecules or potentially metamaterials. In the last part, studies of the microstructure of polymer nanocomposites as an application of volume-spanning and stress-carrying aggregates are discussed.

Introduction to soft matter and neutron scattering

As an opening lecture to the French-Swedish neutron scattering school held in Uppsala (6th to 9th of December 2016), the basic concepts of both soft matter science and neutron scattering are introduced. Typical soft matter systems like self-assembled surfactants in water, microemulsions, (co-)polymers, and colloids are presented. It will be shown that widely different systems have a common underlying physics dominated by the thermal energy, with astonishing consequences on their statistical thermodynamics, and ultimately rheological properties – namely softness. In the second part, the fundamentals of neutron scattering techniques and in particular small-angle neutron scattering as a powerful method to characterize soft matter systems will be outlined.