Rotational diffusion in concentrated colloidal dispersions of hard spheres

Rotational diffusion of colloidal microspheres near flat walls

Recently, colloids with an off-center fluorescent core and homogeneous composition have been developed to measure the rotational diffusivity of microparticles using 3D confocal microscopy in refractive index-matched suspensions. Here, we show that the same particles may be imaged using a standard fluorescence microscope to yield their rotational diffusion coefficients. Trajectories of the off-center core may be combined with known expressions for the correlation decay of particle orientations to determine an effective rotational diffusivity. For sedimented particles, we also find the rotational diffusivity about axes perpendicular and parallel to the interface by adding some bright field illumination and simultaneously tracking both the core and the particle. Trajectories for particles of different sizes yield excellent agreement with hydrodynamic models of rotational diffusion near flat walls, taking the sedimentation-diffusion equilibrium into account. Finally, we explore the rotational diffusivity of particles in crowded two-dimensional monolayers, finding a different reduction of the rotational motion about the two axes depending on the colloidal microstructure.

Fractional Extended Diffusion Theory to capture anomalous relaxation from biased/accelerated molecular simulations

Biased and accelerated molecular simulations (BAMS) are widely used tools to observe relevant molecular phenomena occurring on time scales inaccessible to standard molecular dynamics, but evaluation of the physical time scales involved in the processes is not directly possible from them. For this reason, the problem of recovering dynamics from such kinds of simulations is the object of very active research due to the relevant theoretical and practical implications of dynamics on the properties of both natural and synthetic molecular systems. In a recent paper [A. Rapallo et al., J. Comput. Chem. 42, 586-599 (2021)], it has been shown how the coupling of BAMS (which destroys the dynamics but allows to calculate average properties) with Extended Diffusion Theory (EDT) (which requires input appropriate equilibrium averages calculated over the BAMS trajectories) allows to effectively use the Smoluchowski equation to calculate the orientational time correlation function of the head-tail unit vector defined over a peptide in water solution. Orientational relaxation of this vector is the result of the coupling of internal molecular motions with overall molecular rotation, and it was very well described by correlation functions expressed in terms of weighted sums of suitable time-exponentially decaying functions, in agreement with a Brownian diffusive regime. However, situations occur where exponentially decaying functions are no longer appropriate to capture the actual dynamical behavior, which exhibits persistent long time correlations, compatible with the so called subdiffusive regimes. In this paper, a generalization of EDT will be given, exploiting a fractional Smoluchowski equation (FEDT) to capture the non-exponential character observed in the relaxation of intramolecular distances and molecular radius of gyration, whose dynamics depend on internal molecular motions only. The calculation methods, proper to EDT, are adapted to implement the generalization of the theory, and the resulting algorithm confirms FEDT as a tool of practical value in recovering dynamics from BAMS, to be used in general situations, involving both regular and anomalous diffusion regimes.

3-D rotation tracking from 2-D images of spherical colloids with textured surfaces

Tracking the three-dimensional rotation of colloidal particles is essential to elucidate many open questions, e.g. concerning the contact interactions between particles under flow, or the way in which obstacles and neighboring particles affect self-propulsion in active suspensions. In order to achieve rotational tracking, optically anisotropic particles are required. We synthesise here rough spherical colloids that present randomly distributed fluorescent asperities and track their motion under different experimental conditions. Specifically, we propose a new algorithm based on a 3-D rotation registration, which enables us to track the 3-D rotation of our rough colloids at short time-scales, using time series of 2-D images acquired at high frame rates with a conventional wide-field microscope. The method is based on the image correlation between a reference image and rotated 3-D prospective images to identify the most likely angular displacements between frames. We first validate our approach against simulated data and then apply it to the cases of: particles flowing through a capillary, freely diffusing at solid-liquid and liquid-liquid interfaces, and self-propelling above a substrate. By demonstrating the applicability of our algorithm and sharing the code, we hope to encourage further investigations in the rotational dynamics of colloidal systems.

Rotational Dynamics of Discoid Colloidal Particles in Attractive Quasi-Two-Dimensional Plastic Crystals

Plastic crystals formed from anisotropic molecules or particles are an important state of matter characterized by the presence of long-range positional order and the lack of long-range orientational order. The rotational motion of molecules or particles in plastic crystals is the most attractive characteristic of the system. Here the rotational dynamics of the discoid particles in quasi-two-dimensional colloidal plastic crystals stabilized via depletion interactions are quantitatively studied using time-resolved confocal microscopy. The measured probability distribution of particle orientation reveals the existence of a strong coupling between the lattice symmetry and particle rotation, resulting in anisotropic rotational dynamics modes resembling the underlying hexagonal crystalline symmetry. Furthermore, the orientational distribution function provides information about the potential surface of rotational dynamics. The observed slow rotational diffusion can be attributed to the presence of orientational minima and potential barriers on the potential surface. Our findings with a real experimental system provide important insights into the role of attraction in the phase behaviors of plastic crystals.

Effects of Interfacial Shear on Particle Aggregation at an Oil/Water Interface

Using a Stokesian dynamics simulation, the microstructure of particle aggregates at an oil/water interface with an applied Couette flow is studied. The results of the aggregation are consistent with previously published experimental work demonstrating multiple regimes of behavior based on the relative strength of shear and capillary forces. In previous work, densification of aggregates at low shear rates was theorized to occur due to short time scale fragmentation/reaggregation of aggregates with rigid particle bonds. In simulations, densification is observed at low shear rates but occurs due to local reorganization of particles due to capillary torques over long time scales. Moderate shear rates create mobile bonds between particles at shorter time scales, allowing aggregates to fragment without reaggregation into smaller isolated clusters, consistent with prior experimental work. At the highest shear rates, aggregation is inhibited completely.

Dynamical effective field model for interacting ferrofluids: II. The proper relaxation time and effects of dynamic correlations

The recently proposed dynamical effective field model (DEFM) is quantitatively accurate for ferrofluid dynamics. It is derived in paper I within the framework of dynamical density functional theory (DDFT) along with a phenomenological description of nonadiabatic effects. However, it remains to clarify how the characteristic rotational relaxation time of a dressed particle, denoted byτ_r, is quantitatively related to that of a bare particle, denoted byτr0. By building macro-micro connections via two different routes, I reveal that under some gentle assumptionsτ_rcan be identified with the mean time characterizing long-time rotational self-diffusion. I further introduce two simple but useful integrated correlation factors, describing the effects of quasi-static (adiabatic) and dynamic (nonadiabatic) inter-particle correlations, respectively. In terms of both the dynamic magnetic susceptibility is expressed in an illuminating and elegant form. Remarkably, it shows that the macro-micro connection is established via two successive steps: a dynamical coarse-graining with nonadiabatic effects accounted for by the dynamic factor, followed by equilibrium ensemble averaging captured by the static factor. By analyzing data from Brownian dynamics simulations on monodisperse interacting ferrofluids, I findτr/τr0is, somehow unexpectedly, insensitive to changes of particle volume fraction. A physical picture is proposed to explain it. Furthermore, an empirical formula is proposed to characterize the dependence ofτr/τr0on dipole-dipole interaction strength. The DEFM supplemented with this formula leads to parameter-free predictions in good agreement with results from Brownian dynamics simulations. The theoretical developments presented in this paper may have important consequences to studies of ferrofluid dynamics in particular and other systems modeled by DDFTs in general.

Roughness induced rotational slowdown near the colloidal glass transition

HYPOTHESIS

In concentrated suspensions, the dynamics of colloids are strongly influenced by the shape and topographical surface characteristics of the particles. As the particles get into close proximity, surface roughness alters the translational and rotational Brownian motions in different ways. Eventually, the rotations will get frustrated due to geometric hindrance from interacting asperities.

EXPERIMENTS

We use model raspberry-like colloids to study the effect of roughness on the translational and rotational dynamics. Using Confocal Scanning Laser Microscopy and particle tracking, we simultaneously resolve the two types of Brownian motion and obtain the corresponding Mean Squared Displacements for varying concentrations up to the maximum packing fraction.

FINDINGS

Roughness not only lowers the concentration of the translational colloidal glass transition, but also generates a broad concentration range in which the rotational Brownian motion changes signature from high-amplitude diffusive to low-amplitude rattling. This hitherto not reported second glass transition for rough spherical colloids emerges when the particle intersurface distance becomes comparable to the roughness length scale. Our work provides a unifying understanding of the surface characteristics' effect on the rotational dynamics during glass formation and provides a microscopic foundation for many roughness-related macroscale phenomena in nature and technology.

Two-dimensional Brownian motion of anisotropic dimers

We study the two-dimensional motion of colloidal dimers by single-particle tracking and compare the experimental observations obtained by bright-field microscopy to theoretical predictions for anisotropic diffusion. The comparison is based on the mean-square displacements in the laboratory and particle frame as well as generalizations of the self-intermediate scattering functions, which provide insights into the rotational dynamics of the dimer. The diffusional anisotropy leads to a measurable translational-rotational coupling that becomes most prominent by aligning the coordinate system with the initial orientation of the particles. In particular, we find a splitting of the time-dependent diffusion coefficients parallel and perpendicular to the long axis of the dimer which decays over the orientational relaxation time. Deviations of the self-intermediate scattering functions from pure exponential relaxation are small but can be resolved experimentally. The theoretical predictions and experimental results agree quantitatively.

Probing roto-translational diffusion of small anisotropic colloidal particles with a bright-field microscope

Soft and biological materials are often composed of elementary constituents exhibiting an incessant roto-translational motion at the microscopic scale. Tracking this motion with a bright-field microscope becomes increasingly challenging when the particle size becomes smaller than the microscope resolution, a case which is frequently encountered. Here we demonstrate squared-gradient differential dynamic microscopy (SG-DDM) as a tool to successfully use bright-field microscopy to extract the roto-translational dynamics of small anisotropic colloidal particles, whose rotational motion cannot be tracked accurately in direct space. We provide analytical justification and experimental demonstration of the method by successful application to an aqueous suspension of peanut-shaped particles.

Structure and Dynamics of Ribonuclease A during Thermal Unfolding: The Failure of the Zimm Model

Disordered regions as found in intrinsically disordered proteins (IDP) or during protein folding define response time to stimuli and protein folding times. Neutron spin-echo spectroscopy is a powerful tool to directly access the collective motions of the unfolded chain to enlighten the physical origin of basic conformational relaxation. During the thermal unfolding of native ribonuclease A, we examine the structure and dynamics of the disordered state within a two-state transition model using polymer models, including internal friction, to describe the chain dynamics. The presence of four disulfide bonds alters the disordered configuration to a more compact configuration compared to a Gaussian chain that is defined by the additional links, as demonstrated by coarse-grained simulation. The dynamics of the disordered chain is described by Zimm dynamics with internal friction (ZIF) between neighboring amino acids. Relaxation times are dominated by mode-independent internal friction. Internal friction relaxation times show an Arrhenius-like behavior with an activation energy of 33 kJ/mol. The Zimm dynamics is dominated by internal friction and suggest that the characteristic motions correspond to overdamped elastic modes similar to the motions observed for folded proteins but within a pool of disordered configurations spanning the configurational space. For IDP, internal friction dominates while solvent friction and hydrodynamic interactions are smaller corrections.

Extended diffusion theory: Recovering dynamics from biased/accelerated molecular simulations

Dynamical properties are of great importance in determining the behavior of synthetic and natural molecules, but capturing them by computational methods is a nontrivial task. Very often the time scales of the relevant phenomena are far beyond the typical time windows accessible by classical Molecular Dynamics (MD) simulations, currently limited to the order of microseconds on standard laboratory workstations. On the other hand, biased and accelerated simulations allow for fast and thorough exploration of the molecular conformational space, but they lose the dynamic information. The problem of recovering dynamics from biased/accelerated simulations is a very active field of research, but no totally robust/reliable solutions have been given yet. In this paper it is shown how the Smoluchowski equation, in the framework of Diffusion Theory (DT), can be used to bridge this gap, and dynamical properties, in the form of time correlation functions (TCFs), can be extracted also from such kind of simulations. DT is first extended (EDT) to express the mobility tensors entering the Smoluchowski operator in terms of a recently introduced unified and regularized Rotne-Prager-Yamakawa approximation, [P. J. Zuk, E. Wajnryb, K. A. Mizerski, P. Szymczak, J. Fluid. Mech. 2014, 741, R5, 1-13] also involving mixed rotation-translation contributions, and rotation-rotation terms beside the classical translation-translation ones, so far used in DT. Then, the method is applied to recover the dynamics of a nontrivial example of a peptide in explicit water from the first 200 ns of a Replica Exchange Molecular Dynamics simulation, which is a popular computational method that destroys the long time dynamics. EDT dynamics were found to favorably compare against those coming from a standard MD simulation of the same system, requiring a time window of 30 μs to converge. This result shows that EDT is a tool of practical value to recover the long time dynamics of systems in diffusive regimes from biased/accelerated simulations, to be exploited in those cases when direct evaluation by standard MD is unfeasible.

Magnetic viscoelastic behavior in a colloidal ferrofluid

Based on the stochastic Langevin equation, we derived the total friction experienced by a tracer particle diffusing in thermally equilibrated colloidal magnetic fluids. This transport property leads to new expressions for its long-time diffusion coefficients, which satisfy an Einstein relation with the frictions of its translational and rotational Brownian motion. Further use of the nano-rheology theory allowed us to derive also the viscoelastic modulus of the colloid from such a property. The temporal relaxation of the viscoelasticity and transport coefficient turns out to be governed by the intermediate scattering function of the colloid. We derived an explicit formula for this evolution function within a hydrodynamic theory to include rotational degrees of freedom of the particles. In the limit of short frequencies, the viscous moduli render a new expression for the static viscosity. We found that its comparison with known experiments, at low and high concentration of ferroparticles in magnetite ferrofluids, is fair. However, comparing the predicted viscoelastic moduli with computer simulations as a function of frequency yields poor agreement.

Effect of red blood cell shape changes on haemoglobin interactions and dynamics: a neutron scattering study

By using a combination of experimental neutron scattering techniques, it is possible to obtain a statistical perspective on red blood cell (RBC) shape in suspensions, and the inter-relationship with protein interactions and dynamics inside the confinement of the cell membrane. In this study, we examined the ultrastructure of RBC and protein-protein interactions of haemoglobin (Hb) in them using ultra-small-angle neutron scattering and small-angle neutron scattering (SANS). In addition, we used the neutron backscattering method to access Hb motion on the ns time scale and Å length scale. Quasi-elastic neutron scattering (QENS) experiments were performed to measure diffusive motion of Hb in RBCs and in an RBC lysate. By using QENS, we probed both internal Hb dynamics and global protein diffusion, on the accessible time scale and length scale by QENS. Shape changes of RBCs and variation of intracellular Hb concentration were induced by addition of the Na⁺-selective ionophore monensin and the K⁺-selective one, valinomycin. The experimental SANS and QENS results are discussed within the framework of crowded protein solutions, where free motion of Hb is obstructed by mutual interactions.

Localised contacts lead to nanosecond hinge motions in dimeric bovine serum albumin

Domain motions in proteins are crucial for biological function. In the present manuscript, we present a neutron spin-echo spectroscopy (NSE) study of native bovine serum albumin (BSA) in solution. NSE allows to probe both global and internal dynamics of the BSA monomer and dimer equilibrium that is formed in solution. Using a model independent approach, we were able to identify an internal dynamic process in BSA that is visible in addition to global rigid-body diffusion of the BSA monomer and dimer mixture. The observed internal protein motion is characterised by a relaxation time of 43 ns. The overdamped Brownian oscillator was considered as an alternative analytical theory that was able to describe the internal process as first-order approximation. More detailed information on the physical nature of the internal protein motion was extracted from the q-dependent internal diffusion coefficients ΔDeff(q) that were detected by NSE in addition to global rigid-body translational and rotational diffusion. The ΔDeff(q) were interpreted using normal mode analysis based on the available crystal structures of the BSA monomer and dimer as structural test models. Normal mode analysis demonstrates that the observed internal dynamic process can be attributed to bending motion of the BSA dimer. The native BSA monomer does not show any internal dynamics on the time- and length-scales probed by NSE. An intermolecular disulphide bridge or a direct structural contact between the BSA monomers forms a localised link acting as a molecular hinge in the BSA dimer. The effect of that hinge on the observed motion of BSA in the used dimeric structural model is discussed in terms of normal modes in a molecular picture.

2D Stokesian Approach to Modeling Flow Induced Deformation of Particle Laden Interfaces

A Stokesian dynamics simulation of the effect of surface Couette flow on the microstructure of particles irreversibly adsorbed to an interface is presented. Rather than modeling both bulk phases, the interface, and particles in a full 3D simulation, known interfacial interactions between adsorbed particles are used to create a 2D model from a top down perspective. This novel methodology is easy to implement and computationally inexpensive, which makes it favorable to simulate behavior of particles under applied flow at fluid-fluid interfaces. The methodology is used to examine microstructure deformation of monodisperse, rigid spherical colloids with repulsive interactions when a surface Couette flow is imposed. Simulation results compare favorably to experimental results taken from literature, showing that interparticle forces must be 1 order of magnitude greater than viscous drag for microstructure to transition from aligned particle strings to rotation of local hexagonal domains. Additionally, it is demonstrated that hydrodynamic interactions between particles play a significant role in the magnitude of these microstructure deformations.

Measuring viscosity inside mesoporous silica using protein-bound molecular rotor probe

Fluorescence spectroscopy of protein-bound molecular rotors Cy3 and Cy5 is used to monitor the effective viscosity inside the pores of two types of mesoporous silica (SBA-15 and MCF) with pore diameters between 8.9 and 33 nm.

Real-space imaging of translational and rotational dynamics of hard spheres from the fluid to the crystal

Using real-space imaging of single particles, we investigate the interplay between translational and rotational motion of tracer particles in suspensions of colloidal particles over a wide range of volume fractions from dilute fluid to densely packed crystal. To this end, we introduce a new type of spherical colloidal tracer particles containing two differently labelled fluorescent cores. The tracer particles can be combined with host particles enclosing a single fluorescent core and chemical and physical properties identical to the tracers. This leads to a system of spherical colloidal particles, in which spatio-temporal trajectories of rotation and translation of individual particles can be recorded simultaneously with full 360° resolution of rotational dynamics. Our analysis shows that translation and rotation of colloidal particles are uncorrelated and decoupled for all volume fractions irrespective of the phase of the particle system.

Semi-batch synthesis of colloidal spheres with fluorinated cores and varying grafts of poly(ethylene glycol)

Fluorinated spheres with grafted poly(ethylene glycol) (PEG) have been synthesized using a semi-batch emulsion polymerization in which the initiator is fed slowly to the reaction. In this way, PEG-grafted colloidal spheres can be fabricated with varying PEG chain length, different cores and varying degrees of crosslinking. The resulting batches have been characterized using disc centrifuge photosedimentometry and small-angle X-ray scattering. The size distribution is shown to be a sensitive function of the molar ratio of the reactive PEG macromonomer to fluorinated monomer, and with some optimization latices of very low polydispersity can be obtained with this simple synthesis method. For short PEG grafts too high a molar ratio results in a build up of smaller size particles and a broadening of the size distribution, whereas for longer grafts the mean particle size increases with decreasing molar ratio.

Structure and domain dynamics of human lactoferrin in solution and the influence of Fe(III)-ion ligand binding

Background

Human lactoferrin is an iron-binding protein of the innate immune system consisting of two connected lobes, each with a binding site located in a cleft. The clefts in each lobe undergo a hinge movement from open to close when Fe³⁺ is present in the solution and can be bound. The binding mechanism was assumed to relate on thermal domain fluctuations of the cleft domains prior to binding. We used Small Angle Neutron Scattering and Neutron Spin Echo Spectroscopy to determine the lactoferrin structure and domain dynamics in solution.

Results

When Fe³⁺ is present in solution interparticle interactions change from repulsive to attractive in conjunction with emerging metas aggregates, which are not observed without Fe³⁺. The protein form factor shows the expected change due to lobe closing if Fe³⁺ is present. The dominating motions of internal domain dynamics with relaxation times in the 30–50 ns range show strong bending and stretching modes with a steric suppressed torsion, but are almost independent of the cleft conformation. Thermally driven cleft closing motions of relevant amplitude are not observed if the cleft is open.

Conclusion

The Fe³⁺ binding mechanism is not related to thermal equilibrium fluctuations closing the cleft. A likely explanation may be that upon entering the cleft the iron ion first binds weakly which destabilizes and softens the hinge region and enables large fluctuations that then close the cleft resulting in the final formation of the stable iron binding site and, at the same time, stable closed conformation.

Electronic supplementary material

The online version of this article (doi:10.1186/s13628-016-0032-3) contains supplementary material, which is available to authorized users.

Coupling and Decoupling of Rotational and Translational Diffusion of Proteins under Crowding Conditions

Molecular motion of biopolymers in vivo is known to be strongly influenced by the high concentration of organic matter inside cells, usually referred to as crowding conditions. To elucidate the effect of intermolecular interactions on Brownian motion of proteins, we performed (1)H pulsed-field gradient NMR and fluorescence correlation spectroscopy (FCS) experiments combined with small-angle X-ray scattering (SAXS) and viscosity measurements for three proteins, αB-crystalline (αBc), bovine serum albumin, and hen egg-white lysozyme (HEWL) in aqueous solution. Our results demonstrate that long-time translational diffusion quantitatively follows the expected increase of macro-viscosity upon increasing the protein concentration in all cases, while rotational diffusion as assessed by polarized FCS and previous multi-frequency (1)H NMR relaxometry experiments reveals protein-specific behavior spanning the full range between the limiting cases of full decoupling from (αBc) and full coupling to (HEWL) the macro-viscosity. SAXS was used to study the interactions between the proteins in solution, whereby it is shown that the three cases cover the range between a weakly interacting hard-sphere system (αBc) and screened Coulomb repulsion combined with short-range attraction (HEWL). Our results, as well as insights from the recent literature, suggest that the unusual rotational-translational coupling may be due to anisotropic interactions originating from hydrodynamic shape effects combined with high charge and possibly a patchy charge distribution.

Measuring rotational diffusion of colloidal spheres with confocal microscopy

We report an experimental method to measure the translational and rotational dynamics of colloidal spheres in three dimensions with confocal microscopy and show that the experimental values reasonably agree with the theoretical values. This method can be extended to study rotational dynamics in concentrated colloidal systems and complex bio-systems.

Fast antibody fragment motion: flexible linkers act as entropic spring

A flexible linker region between three fragments allows antibodies to adjust their binding sites to an antigen or receptor. Using Neutron Spin Echo Spectroscopy we observed fragment motion on a timescale of 7 ns with motional amplitudes of about 1 nm relative to each other. The mechanistic complexity of the linker region can be described by a spring model with Brownian motion of the fragments in a harmonic potential. Displacements, timescale, friction and force constant of the underlying dynamics are accessed. The force constant exhibits a similar strength to an entropic spring, with friction of the fragment matching the unbound state. The observed fast motions are fluctuations in pre-existing equilibrium configurations. The Brownian motion of domains in a harmonic potential is the appropriate model to examine functional hinge motions dependent on the structural topology and highlights the role of internal forces and friction to function.

Rotational self-diffusion in suspensions of charged particles: simulations and revised Beenakker-Mazur and pairwise additivity methods

We present a comprehensive joint theory-simulation study of rotational self-diffusion in suspensions of charged particles whose interactions are modeled by the generic hard-sphere plus repulsive Yukawa (HSY) pair potential. Elaborate, high-precision simulation results for the short-time rotational self-diffusion coefficient, D(r), are discussed covering a broad range of fluid-phase state points in the HSY model phase diagram. The salient trends in the behavior of D(r) as a function of reduced potential strength and range, and particle concentration, are systematically explored and physically explained. The simulation results are further used to assess the performance of two semi-analytic theoretical methods for calculating D(r). The first theoretical method is a revised version of the classical Beenakker-Mazur method (BM) adapted to rotational diffusion which includes a highly improved treatment of the salient many-particle hydrodynamic interactions. The second method is an easy-to-implement pairwise additivity (PA) method in which the hydrodynamic interactions are treated on a full two-body level with lubrication corrections included. The static pair correlation functions required as the only input to both theoretical methods are calculated using the accurate Rogers-Young integral equation scheme. While the revised BM method reproduces the general trends of the simulation results, it significantly underestimates D(r). In contrast, the PA method agrees well with the simulation results for D(r) even for intermediately concentrated systems. A simple improvement of the PA method is presented which is applicable for large concentrations.

PMMA/PMMA core-shell particles with ellipsoidal, fluorescent cores: accessing rotational dynamics

For several decades, nonaqueous dispersions of PMMA particles have played an important role in colloid research. They have found application as colloidal model systems, which are used to probe glassy dynamics or to explore crystal nucleation. To date, most research has focused on spherical particles, in which only translational motion can be investigated. Recently, however, there has been a surge of interest in analyzing also rotational dynamics. In this contribution, we introduce a new class of core-shell particles, which can be used as rotational probes. The colloids described herein are composed of shape anisotropic, fluorescent cores covered with nonfluorescent PMMA shells. The core-shell particles are built up in four steps. In a first step, we produce fluorescent and photo-cross-linkable PMMA colloids. In the second step, these particles are thermomechanically elongated and fixed in defined ellipsoidal shapes by photo-cross-linking. Subsequently, we cover the cross-linked, fluorescent core with a nonfluorescent PMMA shell. The shape of the resulting core-shell colloids is tunable between the initial anisotropic and perfect spherical shape. For shaping, we apply a simple solvent swelling procedure. As one option, this method yields perfect PMMA spheres with ellipsoidal, fluorescent centers. We also report morphological particle characterization using various fluorescence microscopy techniques. Finally, we demonstrate that the rotational dynamics of individual colloids can be tracked and analyzed.

Slow internal protein dynamics in solution

Large-scale domain dynamics in proteins are found when flexible linkers or hinges connect domains. The related conformational changes are often related to the function of the protein,for example by arranging the active center after substrate binding or allowing transport and release of products. The adaptation of a specific active structure is referred to as ‘induced fit’ and is challenged by models such as ‘conformational sampling’. Newer models about protein unction include some flexibility within the protein structure or even internal dynamics of the protein. As larger domains contribute to the configurational changes, the timescale of the involved motions is slowed down. The role of slow domain dynamics is being increasingly recognized as essential to understanding the function of proteins. Neutron spin echospectroscopy (NSE) is a technique that is able to access the related timescales from 0.1 up to several hundred nanoseconds and simultaneously covers the length scale relevant for protein domain movements of several nanometers distance between domains. Here we focus on these large-scale domain fluctuations and show how the structure and dynamics of proteins can be assessed by small-angle neutron scattering and NSE.

How nonmagnetic particles intensify rotational diffusion in magnetorheological fluids

In this work we propose a mechanism to explain the enhancement of the magnetic-field-induced yield stress when nonmagnetic particles are added to magnetic particulate suspensions, i.e., two-component suspensions. Our main hypothesis is that the nonmagnetic particles collide with the field-induced magnetic aggregates under shear flow. Consequently, supplementary fluctuations of the orientations of the magnetic aggregates occur, resulting in an effective rotary diffusion process, which increases the dynamic yield stress of the suspension. Furthermore, the collision rate and the rotary diffusivity of the aggregates should increase with the concentration of nonmagnetic particles. Rheological measurements in plate-plate and cylindrical Couette geometries confirm the increase of the yield stress with the volume fraction of nonmagnetic particles. In addition, such an effect appears to be more important in Couette geometry, for which orientation fluctuations of the magnetic aggregates play a more significant role. Finally, a theoretical model based on this rotary diffusion mechanism is developed, providing a quantitative explanation of the experimentally observed trends.

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.

Monodisperse PEGylated spheres: an aqueous colloidal model system

Fluorinated core–shell spheres have been synthesized using a novel semibatch emulsion polymerization protocol employing slow feeding of the initiator. The synthesis results in aqueous dispersions of highly monodisperse spheres bearing a well-defined poly(ethylene glycol) graft (PEGylation). Measurements are consistent with the synthesis achieving a high grafting density that moreover consists of a single PEG layer with the polymer significantly elongated beyond its radius of gyration in bulk. The fluorination of the core of the particles confers a low index of refraction such that the particles can be refractive index matched in water through addition of relatively small amounts of a cosolvent, which enables the use of optical and laser-based methods for studies of concentrated systems. The systems exhibit an extreme stability in NaCl solutions, but attractions among particles can be introduced by addition of other salts, in which case aggregation is shown to be reversible. The PEGylated sphere dispersions are expected to be ideally suited as model systems for studies of the effect of PEG-mediated interactions on, for instance, structure, dynamics, phase behavior, and rheology.

Shape-tailored polymer colloids on the road to become structural motifs for hierarchically organized materials

Anisometric polymer colloids are likely to behave differently when compared with centrosymmetric particles. Their study may not only shine new light on the organization of matter; they may also serve as building units with specific symmetries and complexity to build new materials from them. Polymer colloids of well-defined complex geometries can be obtained by packing a limited number of spherical polymer particles into clusters with defined configurations. Such supracolloidal architectures can be fabricated at larger scales using narrowly dispersed emulsion droplets as templates. Assemblies built from at least two different types of particles as elementary building units open perspectives in selective targeting of colloids with specific properties, aiming for mesoscale building blocks with tailor-made morphologies and multifunctionality. Polymer colloids with defined geometries are also ideal to study shape-dependent properties such as the diffusion of complex particles.

Brownian motion and the hydrodynamic friction tensor for colloidal particles of complex shape

We synthesize colloidal particles with various anisotropic shapes and track their orientationally resolved Brownian trajectories using confocal microscopy. An analysis of appropriate short-time correlation functions provides direct access to the hydrodynamic friction tensor of the particles revealing nontrivial couplings between the translational and rotational degrees of freedom. The results are consistent with calculations of the hydrodynamic friction tensor in the low-Reynolds-number regime for the experimentally determined particle shapes.

Decoupling of rotational and translational diffusion in supercooled colloidal fluids

We use confocal microscopy to directly observe 3D translational and rotational diffusion of tetrahedral clusters, which serve as tracers in colloidal supercooled fluids. We find that as the colloidal glass transition is approached, translational and rotational diffusion decouple from each other: Rotational diffusion remains inversely proportional to the growing viscosity whereas translational diffusion does not, decreasing by a much lesser extent. We quantify the rotational motion with two distinct methods, finding agreement between these methods, in contrast with recent simulation results. The decoupling coincides with the emergence of non-Gaussian displacement distributions for translation whereas rotational displacement distributions remain Gaussian. Ultimately, our work demonstrates that as the glass transition is approached, the sample can no longer be approximated as a continuum fluid when considering diffusion.

Synthesis of PEG-Stabilized Fluoro-Acrylate Particles and Study of their Glass Transition in Aqueous Dispersion

Synthesis of colloidal particles which are sterically stabilized in water and at the same time isorefractive in aqueous dispersion has been achieved by copolymerizing a fluoracrylate monomer with a PEG-macromonomer. Colloidal stability against salt addition and freeze-thawing cycles is demonstrated, indicating that the particles consist of a core of fluoroacrylate and a stabilizing surface layer of grafted PEG. To test the performance as a model system for studies of colloidal vitrification in aqueous media, the dynamics of a binary mixture of these particles with a size ratio of 0.8 and a number ratio of 1.3 (small : large particles) were studied in an isorefractive mixture of water and DMSO (≈ 11 mol % DMSO). The characteristic features of a system close to the glass transition were observed in the density density autocorrelation function f(q, τ) as measured by DLS. However, the glass transition occurred at an unexpectedly low volume fraction of 0.262. This discrepancy correlates with an unusually large difference between TEM and DLS radii and is explained by the presence of a rather extended hairy PEG surface layer.

Large domain fluctuations on 50-ns timescale enable catalytic activity in phosphoglycerate kinase

Large-scale domain motions of enzymes are often essential for their biological function. Phosphoglycerate kinase has a wide open domain structure with a hinge near the active center between the two domains. Applying neutron spin echo spectroscopy and small-angle neutron scattering we have investigated the internal domain dynamics. Structural analysis reveals that the holoprotein in solution seems to be more compact compared to the crystal structure but would not allow the functionally important phosphoryl transfer between the substrates if the protein were static. Brownian large-scale domain fluctuation dynamics on a timescale of 50 ns was revealed by neutron spin echo spectroscopy. The dynamics observed was compared to the displacement patterns of low-frequency normal modes. The displacements along the normal-mode coordinates describe our experimental results reasonably well. In particular, the domain movements facilitate a close encounter of the key residues in the active center to build the active configuration. The observed dynamics shows that the protein has the flexibility to allow fluctuations and displacements that seem to enable the function of the protein. Moreover, the presence of the substrates increases the rigidity, which is deduced from a faster dynamics with smaller amplitude.

Confocal zero-angle dynamic depolarized light scattering

We present a novel Dynamic Depolarized Scattering method based on a tight confocal, zero scattering angle, heterodyne scheme. The method is highly immune from parasitic multiple-scattering contributions, so that it can operate with non-index-matched samples presenting large turbidity. It provides measurements of both rotational and translational diffusion coefficients, the latter via number fluctuation spectroscopy. In addition, the amplitude ratio between the two baselines for the fast rotational mode and the slow translational mode can be used to determine the particles intrinsic birefringence.

3D Brownian diffusion of submicron-sized particle clusters

We report on the translation and rotation of particle clusters made through the combination of spherical building blocks. These clusters present ideal model systems to study the motion of objects with complex shape. Since they could be separated into fractions of well-defined configurations on a sufficient scale and because their overall dimensions were below 300 nm, the translational and rotational diffusion coefficients of particle doublets, triplets, and tetrahedrons could be determined by a combination of polarized dynamic light scattering (DLS) and depolarized dynamic light scattering (DDLS). The use of colloidal clusters for DDLS experiments overcomes the limitation of earlier experiments on the diffusion of complex objects near surfaces because the true 3D diffusion can be studied. When the exact geometry of the complex assemblies is known, different hydrodynamic models for calculating the diffusion coefficients for objects with complex shapes could be applied. Because hydrodynamic friction must be restricted to the cluster surface, the so-called shell model, in which the surface is represented as a shell of small friction elements, was most suitable to describe the dynamics. A quantitative comparison of the predictions from theoretical modeling with the results obtained by DDLS showed an excellent agreement between experiment and theory.

Rotational dynamics and aging in a magnetic colloidal glass

We follow here the freezing of the orientational degrees of freedom of strongly interacting magnetic and charged nanoparticles, as the colloidal glass transition is approached. Using a magnetoinduced birefringence technique, we show that the rotational dynamics drastically slows down following a Vogel-Fulcher law. More precisely, this slowing down occurs above a volume fraction threshold phi*, the value of which depends on the range of electrostatic repulsion between nanoparticles. An interpretation in terms of effective spheres, slightly anisotropic, is proposed. The aging of the rotational dynamics of the more concentrated samples is reported on long time scales, with an exponential growth of the rotational characteristic time with the age t(w) of the sample. An attempt of age rescaling at different volume fractions leads us to introduce a phi-dependent "birth age" t(w)0(varphi) , which diverges analytically at the Vogel-Fulcher volume fraction.

Universal critical-like scaling of dynamic properties in symmetry-selected glass formers

Evidence for a possible general validity of the critical-like behavior of dielectric relaxation time or viscosity tau,eta proportional to (T-T(C))(-phi) with phi-->9 and T(C)<T(g) on approaching glass temperature (T(g)) is shown. This universal behavior is found in various systems where the vitrification is dominated by a selected element of symmetry. The supporting evidence was obtained on the basis of the distortion-sensitive, derivative-based analysis of tau(T) data for a rodlike liquid crystalline compound (E7), orientationally disordered crystals (plastic crystals), a colloidal nanofluid system, polymer melt (polystyrene), oligomeric liquid (EPON 828), and low molecular weight glass formers (glycerol, threitol, sorbitol, and 1-propanol). Results presented explain the puzzling experimental artifacts supporting the dynamical scaling model [R. H. Colby, Phys. Rev. E 61, 1783 (2000); B. M. Erwin, R. H. Colby, J. Non-Cryst. Solids 307-310, 225 (2002)]. It is suggested that spin-glass-like systems may be linked to the discussed pattern.

Hydrodynamic regimes of active rotators at fluid interfaces

We analyze the collective motion of suspensions of active rotators at low Reynolds numbers which interact hydrodynamically. We introduce a simple model for a rotator which allows us to classify the relevant dynamical regimes of the suspension. We characterize the collective velocity at which rotators displace and analyze its implications at long times, when these rotator suspensions diffuse. We analyze the differences with respect to diffusion in suspensions of passive particles, and assess the relevance of the Stokes-Einstein relation on rotators' diffusivity.

Microrheology of viscoelastic fluids containing light-scattering inclusions

The microrheology of viscoelastic fluids containing light-scattering inclusions is measured by depolarized dynamic light scattering (DDLS) from optically anisotropic spherical colloidal probes. The anisotropy of the probes allows us to measure both their translational and the rotational mean squared displacements simultaneously, and DDLS allows us to suppress the light scattered from the inclusions. The storage and loss moduli are determined from both mean squared displacements and the results compared with mechanical measurements.

Direct observation of hydrodynamic rotation-translation coupling between two colloidal spheres

By combining optical tweezers with polarization microscopy, the hydrodynamic coupling between position and orientation fluctuations in a pair of colloidal spheres has been measured. Imaging of birefringent particles under crossed polarizers allows for the simultaneous determination of the positions and orientations of both particles. The temporal cross-correlation function between random displacements of one particle and orientation fluctuations of its neighbor allows for the quantification of the hydrodynamic rotation-translation coupling between the spheres. Our results are in good agreement with predictions for the hydrodynamic mobility tensors calculated in the creeping-flow limit of the Navier-Stokes equation.

Rotational dynamics of colloidal spheres probed with fluorescence recovery after photobleaching

We report a polarized fluorescence recovery after photobleaching (pFRAP) method to measure the rotational dynamics of fluorescent colloids over a wide dynamic range. The method is based on the polarization anisotropy in the fluorescence intensity, generated by bleaching of fluorescently labeled particles with an intense pulse of linearly polarized laser light. The rotational mobilities of the fluorescent particles can be extracted from the relaxation kinetics of the postbleach fluorescence polarization anisotropy. Our pFRAP setup has access to correlation times over a range of time scales from tens of microseconds to tens of seconds, and is highly sensitive, so very low concentrations of labeled particles can be probed. We present a detailed description of the theoretical background of pFRAP. The performance of the equipment is demonstrated for fluorescent colloidal silica spheres, dispersed in pure solvents as well as in fd-virus suspensions.

Colloid interaction and pair correlation function of one-dimensional colloid-polymer systems

The interaction and pair correlation function of weakly charged colloidal particles in quasi-one-dimensional colloid-polymer systems are determined by enhanced video microscopy and digital image analysis. The pair correlation function is found to depend not only on the polymer concentration, but also on the degree of confinement; in particular, it depends on whether the channel width is such that mutual passage of the colloid particles is possible or not. These findings are compared with exact results on short-range order in linear continuous systems.