Size, flexibility, and scattering functions of semiflexible polyelectrolytes with excluded volume effects: monte carlo simulations and neutron scattering experiments

Evidence of Size Stratification in Colloidal Glass Microgranules Realized by Rapid Evaporative Assembly

Evaporation is a ubiquitous phenomenon. Rapid evaporation of the continuous phase from micrometric colloidal droplets can be used to realize nanostructured microgranules, constituting the assembled nanoparticles. One of the important aspects of such nonequilibrium assembly is the nature of the packing of nanoparticles in the microgranules. The present work demonstrates the evidence of size stratification of the nanoparticles in such far-from-equilibrium configurations. Small-angle X-ray scattering, in combination with particle packing simulation, reveals the "large on top"-type stratification in such assembled microgranules, where the larger particles get concentrated at the outer shell of the granules while the smaller particles reside in the core region. It also reveals the presence of local clusters in such a rapid evaporative assembly in aerosolized colloidal droplets.

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.

Aggregate Formation of Surface-Modified Nanoparticles in Solvents and Polymer Nanocomposites

A new method based on the combination of small-angle scattering, reverse Monte Carlo simulations, and an aggregate recognition algorithm is proposed to characterize the structure of nanoparticle suspensions in solvents and polymer nanocomposites, allowing detailed studies of the impact of different nanoparticle surface modifications. Experimental small-angle scattering is reproduced using simulated annealing of configurations of polydisperse particles in a simulation box compatible with the lowest experimental q-vector. Then, properties of interest like aggregation states are extracted from these configurations and averaged. This approach has been applied to silane surface-modified silica nanoparticles with different grafting groups, in solvents and after casting into polymer matrices. It is shown that the chemistry of the silane function, in particular mono- or trifunctionality possibly related to patch formation, affects the dispersion state in a given medium, in spite of an unchanged alkyl-chain length. Our approach may be applied to study any dispersion or aggregation state of nanoparticles. Concerning nanocomposites, the method has potential impact on the design of new formulations allowing controlled tuning of nanoparticle dispersion.

Determination of the local density of polydisperse nanoparticle assemblies

Quantitative characterization of the average structure of dense nanoparticle assemblies and aggregates is a common problem in nanoscience. Small-angle scattering is a suitable technique, but it is usually limited to not too big assemblies due to the limited experimental range, low concentrations to avoid interactions, and monodispersity to keep calculations tractable. In the present paper, a straightforward analysis of the generally available scattered intensity - even for large assemblies, at high concentrations - is detailed, providing information on the local volume fraction of polydisperse particles with hard sphere interactions. It is based on the identical local structure of infinite homogeneous nanoparticle assemblies and their subsets forming finite-sized clusters. This approach is extended to polydispersity, using Monte-Carlo simulations of hard and moderately sticky hard spheres. As a result, a simple relationship between the observed structure factor minimum - termed the correlation hole - and the average local volume fraction κ on the scale of neighboring particles is proposed and validated through independent aggregate simulations. This relationship shall be useful as an efficient tool for the structural analysis of arbitrarily aggregated colloidal systems.

Wormlike micelles: where do we stand? Recent developments, linear rheology and scattering techniques

Wormlike micelles are elongated flexible self-assembly structures formed by the aggregation of amphiphiles. Above a threshold concentration, they entangle into a dynamic network, reminiscent of polymer solutions, and display remarkable visco-elastic properties, which have been exploited in numerous industrial and technological fields. Relating the microstructure of these intricate structures with their bulk properties is still an ongoing quest. In this review, we present a classification of wormlike micelles, with a focus on novel systems and applications. We describe the current state of understanding of their linear rheology and give a detailed account of recent progress in small-angle neutron scattering, a particularly powerful technique to elucidate their microstructure on a wide range of length-scales.

Structural Properties of Pure Simple Alcohols from Ethanol, Propanol, Butanol, Pentanol, to Hexanol: Comparing Monte Carlo Simulations with Experimental SAXS Data

The primary liquid alcohols from ethanol to 1-hexanol were studied utilizing the configurational-bias Monte Carlo (MC) simulations of the modeled alcohols (transferable potential for phase equilibria-united atom model) and the small-angle X-ray scattering (SAXS) method. A novel approach for calculating the scattering intensities from the theoretically obtained MC data by utilizing the Debye equation and their further validation with experimental results was introduced. This procedure is important, since the common problem of how to initially separate the intra- and intermolecular contributions to the scattering when comparing the calculated and experimental data was successfully avoided. Nevertheless, the intra- and intermolecular contributions to the scattering were able to be investigated directly from the MC results. The most pretentious task of the procedure was the suppression of the MC box background scattering, which was solved by utilizing the averaging of the scattering intensities over the different box sizes. This method of the scattering intensity calculations enabled us to make a theoretical analog to the well-known small-angle neutron scattering contrast matching experiment that, in our case, nicely revealed the origin of the two alcohol scattering peaks in the SAXS regime of the scattering curves (0.3 A(-1) < q < 3 A(-1)). For the example of butanol, the outer alcohol scattering peaks at approximately 1.40 A(-1) were unambiguously ascribed to the correlations between the alcohol hydrocarbon tails described by the gCH(x)CH(x)(r) pair correlation function. Similarly, the inner alcohol scattering peaks that shift from approximately 0.8 to approximately 0.4 A(-1) with an increasing alkyl chain length of the alcohol molecule are mainly the consequence of the O-O correlations. These findings were tested on pentanol/water mixtures and further applied to the results of the structural investigations on the binary and ternary microemulsion systems of the nonionic surfactant Brij 35 (Tomsic, et al. J. Phys. Chem. B 2004, 108, 7021; Tomsic, et al. J. Colloid Interface Sci. 2006, 294, 194), which were in fact the actual motivation for this present study.

Incorporating intermicellar interactions in the fitting of SANS data from cationic wormlike micelles

Small-angle neutron scattering (SANS) from cationic wormlike micellar solutions composed of hexadecyltrimethylammonium bromide (CTABr) and hexadecylpyridinium bromide (CPyBr) in deuterated water was studied at 40 degrees C as a function of surfactant and salt concentrations. Two scattering functions of semiflexible chains incorporating excluded volume effects, with and without the intermicellar interactions, were used in SANS data model fitting. Two needed changes were made in the well-accepted models. Extensive and systematic SANS data analysis suggests the robustness of these corrected scattering functions when the intermicellar interactions are included. The influence of the headgroups and ionic strength on the contour length and micellar flexibility of these two systems was demonstrated on the basis of the quantitative structural information obtained from the model fitting. Micellar flexibility was found to depend on surfactant concentration, even when intermicellar interactions were taken into account, despite predictions to the contrary.

Moments and distribution function of polyelectrolyte chains

It is demonstrated that the moments R(2k) of the end-to-end distance distribution function f(r) of charged wormlike chains with excluded volume effects in solution with added salt, in the Debye-Huckel approximation, obey a remarkably simple relation. It is shown that the R(2k) can be expressed as weighted sums of the corresponding moments of ideal wormlike chains. As an application of this method, we show that the Fourier transform of f(r) can also be represented by a superposition of distribution functions of ideal chains. The quantities so calculated are compared with the results of Monte Carlo simulations. Excellent agreement between them is observed.