Dimensions of Cellulose Nanocrystals from Cotton and Bacterial Cellulose: Comparison of Microscopy and Scattering Techniques.

Different microscopy and scattering methods used in the literature to determine the dimensions of cellulose nanocrystals derived from cotton and bacterial cellulose were compared to investigate potential bias and discrepancies. Atomic force microscopy (AFM), small-angle X-ray scattering (SAXS), depolarized dynamic light scattering (DDLS), and static light scattering (SLS) were compared. The lengths, widths, and heights of the particles and their respective distributions were determined by AFM. In agreement with previous work, the CNCs were found to have a ribbon-like shape, regardless of the source of cellulose or the surface functional groups. Tip broadening and agglomeration of the particles during deposition cause AFM-derived lateral dimensions to be systematically larger those obtained from SAXS measurements. The radius of gyration determined by SLS showed a good correlation with the dimensions obtained by AFM. The hydrodynamic lateral dimensions determined by DDLS were found to have the same magnitude as either the width or height obtained from the other techniques; however, the precision of DDLS was limited due to the mismatch between the cylindrical model and the actual shape of the CNCs, and to constraints in the fitting procedure. Therefore, the combination of AFM and SAXS, or microscopy and small-angle scattering, is recommended for the most accurate determination of CNC dimensions.

Analysing Sources of Error in Total Internal Reflection Microscopy (TIRM) Experiments and Data Analysis.

Many phenomena observed in synthetic and biological colloidal suspensions are dominated by the static interaction energies and the hydrodynamic interactions that act both between individual particles and also between colloids and macroscopic interfaces. This calls for methods that allow precise measurements of the corresponding forces. One method used for this purpose is total internal reflection microscopy (TIRM), which has been employed for around three decades to measure in particular the interactions between a single particle suspended in a liquid and a solid surface. However, given the importance of the observable variables, it is crucial to understand the possibilities and limitations of the method. In this paper, we investigate the influence of technically unavoidable noise effects and an inappropriate choice of particle size and sampling time on TIRM measurement results. Our main focus is on the measurement of diffusion coefficients and drift velocities, as the influence of error sources on dynamic properties has not been investigated so far. We find that detector shot noise and prolonged sampling times may cause erroneous results in the steep parts of the interaction potential where forces of the order of pico-Newtons or larger act on the particle, while the effect of background noise is negligible below certain thresholds. Furthermore, noise does not significantly affect dynamic data but we find that lengthy sampling times and/or probe particles with too small a radius will cause issues. Most importantly, we observe that dynamic results are very likely to differ from the standard hydrodynamic predictions for stick boundary conditions due to partial slip.

The effect of morphology and particle-wall interaction on colloidal near-wall dynamics.

We investigated the near-wall Brownian dynamics of different types of colloidal particles with a typical size in the 100 nm range using evanescent wave dynamic light scattering (EWDLS). In detail we studied dilute suspensions of silica spheres and shells with a smooth surface and silica particles with controlled surface roughness. While the near wall dynamics of the particle with a smooth surface differ only slightly from the theoretical prediction for hard sphere colloids, the rough particles diffuse significantly slower. We analysed the experimental data by comparison with model calculations and suggest that the deviating dynamics of the rough particles are not due to increased hydrodynamic interaction with the wall. Rather, the particle roughness significantly changes their DLVO interaction with the wall, which in turn affects their diffusion.

Thermophoresis of a Colloidal Rod: Contributions of Charge and Grafted Polymers.

In this study, we investigated the thermodiffusion behavior of a colloidal model system as a function of the Debye length, λDH, which is controlled by the ionic strength. Our system consists of an fd-virus grafted with poly(ethylene glycol) (PEG) with a molecular mass of 5000 g mol-1. The results are compared with recent measurements on a bare fd-virus and with results of PEG. The diffusion coefficients of both viruses are comparable and increase with the increasing Debye length. The thermal diffusion coefficient, DT, of the bare virus increases strongly with the Debye length, whereas DT of the grafted fd-virus shows only a very weak increase. The Debye length dependence of both systems can be described with an expression derived for charged rods using the surface charge density and an offset of DT as adjustable parameters. It turns out that the ratio of the determined surface charges is inverse to the ratio of the surfaces of the two systems, which means that the total charge remains almost constant. The determined offset of the grafted fd-virus describing the chemical contributions is the sum of DT of PEG and the offset of the bare fd-virus. At high λDH, corresponding to the low ionic strength, the ST values of both colloidal model systems approach each other. This implies a contribution from the polymer layer, which is strong at short λDH and fades out for the longer Debye lengths, when the electric double layer reaches further than the polymer chains and therefore dominates interactions with the surrounding water.

Near wall dynamics of a spherical particle in crowded suspensions of colloidal rods - dynamic information from TIRM revisited.

We performed total internal reflection microscopy (TIRM) experiments to determine the depletion potentials between probe spheres and a flat glass wall which are induced by long and thin, rod-shaped colloids (fd-virus), and probe the spatially resolved dynamics of the probe spheres. The dynamic information from the same raw TIRM intensity time traces is extracted in three different ways: by determining the spatially averaged diffusion constant of the probe sphere normal to the wall, by measuring the position dependence of the diffusion coefficient, and by measuring the particle's local drift velocity. Up to a concentration of about 6 times the overlap concentration of the rod-like colloids, the spatially averaged diffusion coefficient and the amplitude of the depletion potential are in surprisingly good agreement with theoretical predictions in which mutual interactions between the rods are neglected, that is, where the concentration is less than the overlap concentration. On increasing the depletant content even further, however, both the static and the averaged dynamic quantities begin to deviate from such theoretical predictions. In particular we find large deviations from the prediction by Mao, Cates, and Lekkerkerker [J. Chem. Phys., 1997, 106, 3721] based on the third order virial expansion for the rod concentration. It is shown that there are significant inaccuracies in TIRM measurements of diffusion coefficients due to the limited time range in which the mean squared displacements vary linearly in time, whereas mean displacements give much more accurate information concerning the probe sphere dynamics.

A combined 3D and 2D light scattering study on aqueous colloidal model systems with tunable interactions.

In this article we report on the synthesis and characterization of a system of colloidal spheres suspended in an aqueous solvent which can be refractive index-matched, thus allowing for investigations of the particle near-wall dynamics by evanescent wave dynamic light scattering at concentrations up to the isotropic to ordered transition and beyond. The particles are synthesized by copolymerization of a fluorinated acrylic ester monomer with a polyethylene-glycol (PEG) oligomer by surfactant free emulsion polymerization. Static and dynamic light scattering experiments in combination with cryo transmission electron microscopy reveal that the particles have a core shell structure with a significant enrichment of the PEG chains on the particles surface. In index-matching DMSO/water suspensions the particles arrange in an ordered phase at volume fraction above 7%, if no additional electrolyte is present. The near-wall dynamics at low volume fraction are quantitatively described by the combination of electrostatic repulsion and hydrodynamic interaction between the particles and the wall. At volume fractions close to the isotropic to ordered transition, the near-wall dynamics are more complex and qualitatively reminiscent of the behaviour which was observed in hard sphere suspensions at high concentrations.

Near-wall dynamics of concentrated hard-sphere suspensions: comparison of evanescent wave DLS experiments, virial approximation and simulations.

In this article we report on a study of the near-wall dynamics of suspended colloidal hard spheres over a broad range of volume fractions. We present a thorough comparison of experimental data with predictions based on a virial approximation and simulation results. We find that the virial approach describes the experimental data reasonably well up to a volume fraction of ϕ≈ 0.25 which provides us with a fast and non-costly tool for the analysis and prediction of evanescent wave DLS data. Based on this we propose a new method to assess the near-wall self-diffusion at elevated density. Here, we qualitatively confirm earlier results [Michailidou, et al., Phys. Rev. Lett., 2009, 102, 068302], which indicate that many-particle hydrodynamic interactions are diminished by the presence of the wall at increasing volume fractions as compared to bulk dynamics. Beyond this finding we show that this diminishment is different for the particle motion normal and parallel to the wall.

Translational and rotational near-wall diffusion of spherical colloids studied by evanescent wave scattering.

In this article we extend recent experimental developments [Rogers et al., Phys. Rev. Lett., 2012, 109, 098305] by providing a suitable theoretical framework for the derivation of exact expressions for the first cumulant (initial decay rate) of the correlation function measured in Evanescent Wave Dynamic Light Scattering (EWDLS) experiments. We focus on a dilute suspension of optically anisotropic spherical Brownian particles diffusing near a planar hard wall. In such a system, translational and rotational diffusion are hindered by hydrodynamic interactions with the boundary which reflects the flow incident upon it, affecting the motion of colloids. The validity of the approximation by the first cumulant for moderate times is assessed by juxtaposition to Brownian dynamics simulations, and compared with experimental results. The presented method for the analysis of experimental data allows the determination of penetration-depth-averaged rotational diffusion coefficients of spherical colloids at low density.

Synthesis and self-assembly of squarelike PbCrO4 nanoplatelets via micelle-mediated depletion attraction.

The self-assembly of nanoparticles triggered by attractive depletion forces presents a versatile pathway for building nanostructural superlattices directly in solution. In this work, the synthesis of squarelike lead chromate (PbCrO4) nanoplatelets is described, and their assembly into well-defined stacks by introducing various types of micelles as depletion agents is studied. The kinetics of the reversible assembly process in solution is probed by light scattering, and the depletion-induced self-assembly of the nanoplatelets is investigated by transmission electron microscopy. For nonionic surfactants, rodlike micelles are found to be more efficient at producing self-assembled particles than are spherelike micelles, in accordance with an increased depletion force. Adding ionic surfactants additionally leads to a segregation of PbCrO4 rod reaction byproducts.

One-particle correlation function in evanescent wave dynamic light scattering.

In order to interpret measured intensity autocorrelation functions obtained in evanescent wave scattering, their initial decay rates have been analyzed recently [P. Holmqvist, J. K. G. Dhont, and P. R. Lang, Phys. Rev. E 74, 021402 (2006); B. Cichocki, E. Wajnryb, J. Blawzdziewicz, J. K. G. Dhont, and P. R. Lang, J. Chem. Phys. 132, 074704 (2010); J. W. Swan and J. F. Brady, ibid. 135, 014701 (2011)]. A theoretical analysis of the longer time dependence of evanescent wave autocorrelation functions, beyond the initial decay, is still lacking. In this paper we present such an analysis for very dilute suspensions of spherical colloids. We present simulation results, a comparison to cumulant expansions, and experiments. An efficient simulation method is developed which takes advantage of the particular mathematical structure of the time-evolution equation of the probability density function of the position coordinate of the colloidal sphere. The computer simulation results are compared with analytic, first and second order cumulant expansions. The only available analytical result for the full time dependence of evanescent wave autocorrelation functions [K. H. Lan, N. Ostrowsky, and D. Sornette, Phys. Rev. Lett. 57, 17 (1986)], that neglects hydrodynamic interactions between the colloidal spheres and the wall, is shown to be quite inaccurate. Experimental results are presented and compared to the simulations and cumulant expansions.

Flow dichroism as a reliable method to measure the hydrodynamic aspect ratio of gold nanoparticles.

Particle shape plays an important role in controlling the optical, magnetic, and mechanical properties of nanoparticle suspensions as well as nanocomposites. However, characterizing the size, shape, and the associated polydispersity of nanoparticles is not straightforward. Electron microscopy provides an accurate measurement of the geometric properties, but sample preparation can be laborious, and to obtain statistically relevant data many particles need to be analyzed separately. Moreover, when the particles are suspended in a fluid, it is important to measure their hydrodynamic properties, as they determine aspects such as diffusion and the rheological behavior of suspensions. Methods that evaluate the dynamics of nanoparticles such as light scattering and rheo-optical methods accurately provide these hydrodynamic properties, but do necessitate a sufficient optical response. In the present work, three different methods for characterizing nonspherical gold nanoparticles are critically compared, especially taking into account the complex optical response of these particles. The different methods are evaluated in terms of their versatility to asses size, shape, and polydispersity. Among these, the rheo-optical technique is shown to be the most reliable method to obtain hydrodynamic aspect ratio and polydispersity for nonspherical gold nanoparticles for two reasons. First, the use of the evolution of the orientation angle makes effects of polydispersity less important. Second, the use of an external flow field gives a mathematically more robust relation between particle motion and aspect ratio, especially for particles with relatively small aspect ratios.

Depletion interactions effected by different variants of fd virus.

The depletion interaction between a probe sphere and a flat wall induced by fd virus is investigated by means of total internal reflection microscopy (TIRM). The viruses serve as a model system for monodisperse, rod-like colloids. We find that the experimental potentials are well described by the first-order density approximation up to an fd content of several overlap concentrations. This is in accordance with higher order density theory as confirmed by numerical calculations. Since the first-order analytical description still holds for all measurements, this exemplifies that higher order terms of the theory are unimportant for our system. Comparing the potentials induced by wild-type fd to those induced by a more rigid fd variant, it can be shown that the influence of the virus stiffness is beyond our experimental resolution and plays only a negligible role for the measured depletion potentials.

Unexpected slow near wall dynamics of spherical colloids in a suspension of rods.

In this paper, we will show the influence of an additional rodlike component, that is, fd-virus, on the diffusion of spherical polystyrene colloids close to a wall. The sphere diffusivity normal to the wall, D perpendicular, is strongly affected by the presence of the rods, while the effect on the parallel diffusivity, D||, is less pronounced except in the immediate vicinity of the wall. We show that this observation cannot be explained by describing the effect of the rods as a simple mean field depletion potential alone.

Depletion interaction mediated by polydisperse rods.

The interaction between a colloidal hard sphere of radius R and a wall or between two spheres in a dilute suspension of infinitely thin rods of length L is calculated numerically. The method allows the study of depletion potentials for any value of LR and, consequently, the influence of rod length polydispersity can be investigated. It was observed that both the depth and the range of the potential increase drastically if the relative standard deviation sigma of the length distribution is larger than 0.25, while the potential is virtually indistinguishable from that caused by monodisperse rods, if sigma < or similar to 0.1.

Steric repulsion by adsorbed polymer layers studied with total internal reflection microscopy.

Total internal reflection microscopy (TIRM) was applied to measure the interaction potential between charge-stabilized polystyrene latex spheres and a glass wall in dependence on the concentration of additional poly(ethylene oxide). The influence of the polymer can be described by steric repulsion between polymer layers, which are physically adsorbed onto the surfaces of the polystyrene sphere and the glass wall. The expected attractive contribution to the potential due to polymer depletion was not observed. An increase of the polymer bulk concentration is shown to strengthen the steric repulsion. At the highest polymer concentrations studied, it is possible to accurately describe the experimental data for the steric contribution to the total interaction potential with the Alexander-de Gennes model for brush repulsion.

Colloidal dynamics near a wall studied by evanescent wave light scattering: experimental and theoretical improvements and methodological limitations.

The dynamics of colloidal spheres near to a wall is studied with an evanescent wave scattering setup that allows for an independent variation of the components of the scattering wave vector normal and parallel to the wall. The correlation functions obtained with this novel instrumentation are interpreted on the basis of an expression for their short time behavior that includes hydrodynamic interactions between the colloidal spheres and the wall. The combination of the evanescent wave scattering setup and the exact expression for the short time behavior of correlation functions allows for an unambiguous measurement of the particle mobility parallel and normal to the wall by means of light scattering. It is possible to measure the viscous wall drag effect on the dynamics of particles with radii as small as 27 nm, where, however, the method reaches its limits due to the low scattering intensities of such small particles.

Anisotropy of Brownian motion caused only by hydrodynamic interaction with a wall.

The diffusivity of spherical colloidal particles close to a planar hard wall is studied by dynamic light scattering with evanescent illumination. A novel setup allows us to independently vary the scattering vector components parallel Q parallel and normal Q perpendicular to the wall. An expression for the initial decay rate Gamma of the time autocorrelation functions is derived as a function of both Q parallel and Q perpendicular, as well as the penetration depth of the evanescent wave, where hydrodynamic interactions of particles with the wall are included. This makes it possible to study the viscous wall drag effect quantitatively for particles as small as 85 nm in radius.

Depletion interaction mediated by a polydisperse polymer studied with total internal reflection microscopy.

Total internal reflection microscopy (TIRM) was applied to measure depletion forces between a charged colloidal sphere and a charged solid wall induced by dextran, a nonionic nonadsorbing polydisperse polysaccharide. The polymer size polydispersity is shown to greatly influence the depletion potential. Using the theory for the depletion interaction due to ideal polydisperse polymer chains, we could accurately describe the experimental data with a single adjustable parameter.

Interactions and two-phase coexistence in nonionic micellar solutions as determined by static light scattering.

We suggest semi-phenomenological approaches for the pair interaction potential in aqueous C(m)E(n) solutions. These expressions are non-linear least squares fitted to static light scattering data from solutions of C(m)E4 and C(m)E8 surfactants in the long wavelength limit. From the resulting interaction parameters we calculate the location of the liquid/liquid two phase coexistence curves, which are in very good agreement with experimental data reported by others.