Elucidation of spin echo small angle neutron scattering correlation functions through model studies

Several single-modal Debye correlation functions to approximate part of the overall Debey correlation function of liquids are closely examined for elucidating their behavior in the corresponding spin echo small angle neutron scattering (SESANS) correlation functions. We find that the maximum length scale of a Debye correlation function is identical to that of its SESANS correlation function. For discrete Debye correlation functions, the peak of SESANS correlation function emerges at their first discrete point, whereas for continuous Debye correlation functions with greater width, the peak position shifts to a greater value. In both cases, the intensity and shape of the peak of the SESANS correlation function are determined by the width of the Debye correlation functions. Furthermore, we mimic the intramolecular and intermolecular Debye correlation functions of liquids composed of interacting particles based on a simple model to elucidate their competition in the SESANS correlation function. Our calculations show that the first local minimum of a SESANS correlation function can be negative and positive. By adjusting the spatial distribution of the intermolecular Debye function in the model, the calculated SESANS spectra exhibit the profile consistent with that of hard-sphere and sticky-hard-sphere liquids predicted by more sophisticated liquid state theory and computer simulation.     

Determination of pair correlation functions of dense colloidal systems by means of indirect Fourier transformation

The interparticle pair correlation gr function is determined by the small angle scattering data of interacting, monodisperse, globular colloidal particles. The new approach to this problem requires that the form factor and the particle number density must be known. Instrumental broadening effects and experimental imperfections are included in a way that makes it unnecessary to deconvolute the scattering function from beam profiles. The applicability of the approach is demonstrated by the simulated data of a charged colloidal dispersion and by way of the neutron scattering data of nonionic micellar solutions. In both cases, gr functions are obtained that are in good agreement with the known behavior of the systems.     

Structured water in polyelectrolyte dendrimers: understanding small angle neutron scattering results through atomistic simulation

Based on atomistic molecular dynamics (MD) simulations, the small angle neutron scattering (SANS) intensity behavior of a single generation-4 polyelectrolyte polyamidoamine starburst dendrimer is investigated at different levels of molecular protonation. The SANS form factor, P(Q), and Debye autocorrelation function, γ(r), are calculated from the equilibrium MD trajectory based on a mathematical approach proposed in this work. The consistency found in comparison against previously published experimental findings (W.-R. Chen, L. Porcar, Y. Liu, P. D. Butler, and L. J. Magid, Macromolecules 40, 5887 (2007)) leads to a link between the neutron scattering experiment and MD computation, and fresh perspectives. The simulations enable scattering calculations of not only the hydrocarbons but also the contribution from the scattering length density fluctuations caused by structured, confined water within the dendrimer. Based on our computational results, we explore the validity of using radius of gyration R(G) for microstructure characterization of a polyelectrolyte dendrimer from the scattering perspective.     

Colloidal particles coated and stabilized by DNA-wrapped carbon nanotubes

Single-walled carbon nanotubes (SWNTs) are dispersed in water via wrapping with short segments of single-stranded DNA (ssDNA). Small angle neutron scattering suggests a power-law exponent that is consistent with clustered nanotubes and hence marginal stability. The SWNT-ssDNA complex is used to stabilize dispersions of hydrophilic colloidal particles with the nanotubes adhered to the surface of the colloids. Near-infrared fluorescence microscopy demonstrates the interfacial band-gap fluorescence of these SWNT-coated particles, suggesting potential routes to novel platforms and applications.     

Effective charges of colloidal particles obtained from collective diffusion experiments

In this work, the collective diffusion coefficient of highly charged colloidal particles in dilute dispersions has been measured by means of dynamic light scattering. The possibility of obtaining valuable information about the particle charge from these data is looked into with the help of electrophoresis experiments. Our results suggest that this is possible in the case of slight or moderately interacting particles as long as experimental data are properly treated. For highly interacting colloids, however, such information could not be so reliable, presumably due to certain shortcomings of the experimental technique at low angle. The role of charge renormalization is also discussed in this work.     

Sol-Gel Routes to Zeolite Membranes and Thin Films

The synthesis of zeolite membranes and thin films using the secondary growth process is briefly described. In this process colloidal zeolite particles (sols) are prepared hydrothermally and then subsequently deposited on substrates to produce uniform layers of controlled thickness, as illustrated with silicalite and zeolite-A. The formation and growth of the zeolite sols has been investigated in situ by small angle neutron scattering (SANS). SANS measurements on silicalite sols at progressively higher concentrations have provided details of the colloid interactions which lead to zeolite gel-layer structures which are uniform and free of defects.     

Dynamics of interacting Brownian particles

A memory function formulation has been used for the dynamics of interacting Brownian particles in colloidal systems and polymer dispersions. By introducing approximations at the level of the force correlation function, the theoretical scattering functions agree well with the experimental photon correlation spectroscopy data.     

Non-affine structural evolution of soft colloidal crystalline latex films under stretching as observed via synchrotron X-ray scattering

A polymer dispersion consisting of soft latex spheres with a diameter of 135 nm was used to produce a crystalline film with face-centered cubic (fcc) packing of the spheres. Different from conventional small-molecule and hard-sphere colloidal crystals, the crystalline latex film in the present case is soft (i.e., easily deformable). The structural evolution of this soft colloidal latex film under stretching was investigated by in-situ synchrotron ultra-small-angle X-ray scattering. The film exhibits polycrystalline scattering behavior corresponding to fcc structure. Stretching results not only in a large deformation of the crystallographic structure but also in considerable nonaffine deformation at high draw ratios. The unexpected nonaffine deformation was attributed to slippage between rows of particles and crystalline grain boundaries. The crystalline structure remains intact even at high deformation, suggesting that directional anisotropic colloidal crystallites can be easily produced.     

Small angle neutron scattering studies on non-aqueous dispersions of calcium carbonate. Part III. Concentrated dispersions

Small angle neutron scattering has been used to examine calcium carbonate dispersions in toluene over the w/w concentration range 5 to 40 %. The particles were stabilised by a combination of a surface active agent and a linear polymeric molecule. Analysis of the experimental data gave results for the structure factorS(Q) and the pair correlation functiong(r).Theoretical computations of the structure factor were made using a hard sphere model and the mean spherical approximation approach. These analyses indicated that the interaction was essentially soft at low volume fractions but became hard at the higher volume fractions.     

Structural properties of thermoresponsive poly(N-isopropylacrylamide)-poly(ethyleneglycol) microgels

We present investigations of the structural properties of thermoresponsive poly(N-isopropylacrylamide) (PNiPAM) microgels dispersed in an aqueous solvent. In this particular work poly(ethyleneglycol) (PEG) units flanked with acrylate groups are employed as cross-linkers, providing an architecture designed to resist protein fouling. Dynamic light scattering (DLS), static light scattering (SLS), and small angle neutron scattering (SANS) are employed to study the microgels as a function of temperature over the range 10 °C ≤ T ≤ 40 °C. DLS and SLS measurements are simultaneously performed and, respectively, allow determination of the particle hydrodynamic radius, R(h), and radius of gyration, R(g), at each temperature. The thermal variation of these magnitudes reveals the microgel deswelling at the PNiPAM lower critical solution temperature (LCST). However, the hydrodynamic radius displays a second transition to larger radii at temperatures T ≤ 20 °C. This feature is atypical in standard PNiPAM microgels and suggests a structural reconfiguration within the polymer network at those temperatures. To better understand this behavior we perform neutron scattering measurements at different temperatures. In striking contrast to the scattering profile of soft sphere microgels, the SANS profiles for T ≤ LCST of our PNiPAM-PEG suspensions indicate that the particles exhibit structural properties characteristic of star polymer configurations. The star polymer radius of gyration and correlation length gradually decrease with increasing temperature despite maintenance of the star polymer configuration. At temperatures above the LCST, the scattered SANS intensity is typical of soft sphere systems.     

Synthesis and characterization of non-spherical gold colloids in block-copolymer micelles

Gold colloids of well-defined shape, size and polydispersity are synthesized by heterogeneous reduction of gold salts in amphiphilic block-copolymer micelles. The resulting hybride systems consisting of the noble metal colloid and the stabilizing shell of block-copolymers are characterized by electron microscopy and small-angle x-ray scattering. Opposite to classical noble metal colloids, the block-copolymer stabilized systems exhibit an extra-ordinary high colloidal stability which makes analysis and sample handling very simple.It turned out that non-spherical metal colloids are formed in the early stages of the reduction process where the amount of gold exceeds the reduction agent. At later stages, the colloids break up to globular subunits again. The reaction period of colloidal anisometry is reflected in a violet color of the reaction solution, which is caused by a typical structured, double-resonance plasmon band.Small-and wide-angle x-ray scattering reveal a quantitative measure for the size, shape, anisometry and local order in each step of the reduction process. It is suggested that the primary aubergine-shaped particles consist of globular primary particles which are glued together via non reacted gold salt. This observation gives rise to some interesting possibilities of the supramolecular handling of colloids.     

Size fractionation and characterization of natural colloids by flow-field flow fractionation coupled to multi-angle laser light scattering

Flow-field flow fractionation (FlFFF) coupled to multi-angle laser light scattering (MALLS) was evaluated for size and shape determination of standard spherical and arbitrarily shaped natural colloids. Different fitting methods for light scattering data retrieved from MALLS were evaluated to determine the particle size of spherical standards and natural colloids. In addition, FlFFF was optimized for best fractionation in connection to MALLS, minimal colloids-membrane interaction, and minimal sample losses. FlFFF, calibrated with standard particles, was used to determine hydrodynamic diameter, or radius (D(h) or R(h)), of the fractionated colloids, whereas the MALLS was used to determine root mean square radius of gyration (R(g)) for fractionated colloids. Combining both results, by calculating the R(g)/R(h) ratio, allows an estimation of colloid deviation from the shape of homogeneous sphere. Accordingly, this study demonstrates that, FlFFF-MALLS is a valuable technique for characterizing heterogeneous and arbitrarily shaped natural colloidal particles in terms of size and shape. To check the usefulness of FlFFF-MALLS in natural colloid studies, the technique was used to investigate the sedimentation behavior of extracted soil colloidal particles. Results illustrate that, in a silty till sample, carbonates function as cement between the colloidal particles, and consequently, change their sedimentation behavior. On the other hand, carbonate dissolution generates a more homogeneous colloidal sample.     

Small-angle neutron scattering on a core-shell colloidal system: a contrast-variation study

Small-angle neutron scattering (SANS) measurements are reported on a sterically stabilized, core-shell colloidal system using contrast variation. Aqueous dispersions of polystyrene particles bearing grafted poly(ethylene glycol) (PEG) have been studied over a large range of particle concentrations and two different solvent conditions for the PEG polymer. SANS data are analyzed quantitatively by modeling the particles as core-shell colloids. In a good solvent and under particle contrast conditions, an effective hard-sphere interaction captures excluded-volume interactions up to high concentrations. Contrast variation, through isotopic substitution of both the core and solvent, expedite a detailed study of the PEG layer, both in the dilute limit and as a function of the particle concentration. Upon diminishing the solvent quality, subtle changes in the PEG layer translate into attractions among particles of moderate magnitude.     

Tunable rheology of dense soft deformable colloids

In the last two decades, advances in synthetic, experimental and modeling/simulation methodologies have considerably enhanced our understanding of colloidal suspension rheology and put the field at the forefront of soft matter research. Recent accomplishments include the ability to tailor the flow of colloidal materials via controlled changes of particle microstructure and interactions. Whereas hard sphere suspensions have been the most widely studied colloidal system, there is no richer type of particles than soft colloids in this respect. Yet, despite the remarkable progress in the field, many outstanding challenges remain in our quest to link particle microstructure to macroscopic properties and eventually design appropriate soft composites. Addressing them will provide the route towards novel responsive systems with hierarchical structures and multiple functionalities. Here we discuss the key structural and rheological parameters which determine the tunable rheology of dense soft deformable colloids. We restrict our discussion to non-crystallizing suspensions of spherical particles without electrostatic or enthalpic interactions.     

Light and neutron scattering study of PEG-oleate and its use in emulsion polymerization

Steric stabilization of colloids forms a robust mechanism to obtain colloids that are stable in a variety of environments, and that can be used to study the phase behavior of hard or soft spheres. We report the synthesis of sterically stabilized colloids in an aqueous environment using readily dissolvable surfactants, with an unsaturated hydrophobic tail. We synthesized a new surfactant by esterification of a poly(ethylene glycol) (PEG) chain of 4.1 kg/mol with oleic acid, called PEG4OA. The micellization of PEG4OA was characterized by light and neutron scattering, which yielded values for the aggregation number and the overall size that are in excellent agreement with a comparable surfactant with a saturated octadecane chain, Brij 700. We successfully used PEG4OA in the emulsion polymerization of polystyrene colloids. In comparison with the smaller surfactant Tween 80, PEG4OA yielded smaller colloids with radii around 50 nm, and the addition of 1-dodecanethiol reduced the formation of aggregates during the synthesis. A contrast variation study with small angle neutron scattering (SANS) showed that a dense PEG layer was grafted to the colloid surface.     

Angle‐dependent light scattering by highly uniform colloidal rod‐shaped microparticles: Experiment and simulation

While extensive theoretical work has been devoted to analyzing scattering behavior for nonspherical particles, few experimental studies of the light‐scattering properties of such particles are available, largely because of the difficulty of synthesizing such particles with uniform geometries. Here we report the synthesis of highly uniform, volume‐equivalent rod‐shaped colloidal particles prepared from their commercial spherical counterparts, on which we performed light scattering experiments as a function of scattering angle for micro rods with varying aspect ratio and volume. These results were compared to values calculated using the T‐Matrix method. Good agreement with theoretical predictions was found for the experimentally measured scattering cross sections and the angular dependence of the scattering intensity. An increase in the forward scattering intensity is observed and predicted for particles with larger aspect ratios relative to their volume equivalent spheres, with only minor differences observed at both mid‐range and backscattering angles. Furthermore, the light scattering results for the rod‐shaped particles did not show the scattering fringes seen in scattering by the spheres, indicating that as three‐dimensional symmetry is broken, the associated Lorenz–Mie resonances are strongly attenuated. This observation also was predicted by theory. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1889–1895     

Analytical coarse-grained description for polymer melts

Starting from the Ornstein-Zernike equation the authors derive an analytical theory, at the level of pair correlation functions, which coarse grains polymer melts into liquids of interacting soft colloidal particles. Since it is analytical, the presented coarse-graining approach will be useful in developing multiscale modeling procedures to simulate complex fluids of macromolecules. The accuracy of the theory is tested by its capacity to reproduce the liquid structure, as given by the center-of-mass intermolecular total pair correlation function. The theory is found to agree well with the structure predicted by molecular dynamics simulations of the liquid described at the united atom level as well as by molecular dynamics simulations of the liquid of interacting colloidal particles. The authors perform simulations of the liquid of interacting colloidal particles having as input the potential obtained from their analytical total pair correlation function by enforcing the hypernetted-chain closure approximation. Tests systems are polyethylene melts of chains with increasing degrees of polymerization and polymer melts of chains with different chemical architectures. They also discuss the effect of adopting different conventional approximations for intra- and intermolecular monomer structure factors on the accuracy of the coarse-graining procedure, as well as the relevance of higher-order corrections to their expression.     

SAXS and SANS studies of polymer colloids

The analysis of latex particles by small-angle scattering (small-angle X-ray scattering, SAXS; small-angle neutron scattering, SANS) is reviewed. Small-angle scattering techniques give information on the radial structure of the particles as well as on their spatial correlation. Recent progress in instrumentation allows to extend SANS and SAXS to the q-range of light scattering. Moreover, contrast variation employed in SANS and SAXS studies may lead to an unambiguous determination of the radial scattering length density of the particles in situ, i.e. in suspension. Hence, these techniques are highly valuable for a comprehensive analysis of polymer colloids as shown by the examples discussed herein.     

Size distribution of colloidal silica in sodium silicate solutions investigated by dynamic light scattering and viscosity measurements

Three types of aqueous sodium silicate solutions characterized by molar SiO(2):Na(2)O ratios of 2.2, 3.3, and 3.9 were investigated by dynamic light scattering and viscosity measurements. The solutions were prepared by diluting concentrated commercial products to SiO(2) content between 0.5 and 15 wt%. Dynamic light scattering (DLS) was used for the investigation of size distributions of colloids immediately after dilution. At least three size classes of colloidal particles were detected, which exist in parallel in the solutions. The respective radii are 0.4 to 0.6 nm, 2.5 to 13 nm, and 75 to 85 nm. The larger colloids dominate the mass distribution, whereas the smaller colloids control the surface area of the colloidal fraction. Material properties such as pH, viscosity, refractive index, and density were measured as a function of dilution. The evaluation of the viscosity data indicated that the colloids have a lower density than dense amorphous silica. Aging effects could be suppressed by measuring within 1 h after dilution.