Anisotropic and hindered diffusion of colloidal particles in a closed cylinder

Protocell Effects on RNA Folding, Function, and Evolution

ConspectusCreating a living system from nonliving matter is a great challenge in chemistry and biophysics. The early history of life can provide inspiration from the idea of the prebiotic "RNA World" established by ribozymes, in which all genetic and catalytic activities were executed by RNA. Such a system could be much simpler than the interdependent central dogma characterizing life today. At the same time, cooperative systems require a mechanism such as cellular compartmentalization in order to survive and evolve. Minimal cells might therefore consist of simple vesicles enclosing a prebiotic RNA metabolism.The internal volume of a vesicle is a distinctive environment due to its closed boundary, which alters diffusion and available volume for macromolecules and changes effective molecular concentrations, among other considerations. These physical effects are mechanistically distinct from chemical interactions, such as electrostatic repulsion, that might also occur between the membrane boundary and encapsulated contents. Both indirect and direct interactions between the membrane and RNA can give rise to nonintuitive, "emergent" behaviors in the model protocell system. We have been examining how encapsulation inside membrane vesicles would affect the folding and activity of entrapped RNA.Using biophysical techniques such as FRET, we characterized ribozyme folding and activity inside vesicles. Encapsulation inside model protocells generally promoted RNA folding, consistent with an excluded volume effect, independently of chemical interactions. This energetic stabilization translated into increased ribozyme activity in two different systems that were studied (hairpin ribozyme and self-aminoacylating RNAs). A particularly intriguing finding was that encapsulation could rescue the activity of mutant ribozymes, suggesting that encapsulation could affect not only folding and activity but also evolution. To study this further, we developed a high-throughput sequencing assay to measure the aminoacylation kinetics of many thousands of ribozyme variants in parallel. The results revealed an unexpected tendency for encapsulation to improve the better ribozyme variants more than worse variants. During evolution, this effect would create a tilted playing field, so to speak, that would give additional fitness gains to already-high-activity variants. According to Fisher's Fundamental Theorem of Natural Selection, the increased variance in fitness should manifest as faster evolutionary adaptation. This prediction was borne out experimentally during in vitro evolution, where we observed that the initially diverse ribozyme population converged more quickly to the most active sequences when they were encapsulated inside vesicles.The studies in this Account have expanded our understanding of emergent protocell behavior, by showing how simply entrapping an RNA inside a vesicle, which could occur spontaneously during vesicle formation, might profoundly affect the evolutionary landscape of the RNA. Because of the exponential dynamics of replication and selection, even small changes to activity and function could lead to major evolutionary consequences. By closely studying the details of minimal yet surprisingly complex protocells, we might one day trace a pathway from encapsulated RNA to a living system.

Brownian motion of soft particles near a fluctuating lipid bilayer

The dynamics of a soft particle suspended in a viscous fluid can be changed by the presence of an elastic boundary. Understanding the mechanisms and dynamics of soft-soft surface interactions can provide valuable insights into many important research fields, including biomedical engineering, soft robotics development, and materials science. This work investigates the anomalous transport properties of a soft nanoparticle near a visco-elastic interface, where the particle consists of a polymer assembly in the form of a micelle and the interface is represented by a lipid bilayer membrane. Mesoscopic simulations using a dissipative particle dynamics model are performed to examine the impact of micelle's proximity to the membrane on its Brownian motion. Two different sizes are considered, which correspond to ≈10-20nm in physical units. The wavelengths typically seen by the largest micelle fall within the range of wavenumbers where the Helfrich model captures fairly well the bilayer mechanical properties. Several independent simulations allowed us to compute the micelle trajectories during an observation time smaller than the diffusive time scale (whose order of magnitude is similar to the membrane relaxation time of the largest wavelengths), this time scale being hardly accessible by experiments. From the probability density function of the micelle normal position with respect to the membrane, it is observed that the position remains close to the starting position during ≈0.05τd (where τd corresponds to the diffusion time), which allowed us to compare the negative excess of mean-square displacement (MSD) to existing theories. In that time range, the MSD exhibits different behaviors along parallel and perpendicular directions. When the micelle is sufficiently close to the bilayer (its initial distance from the bilayer equals approximately twice its gyration radius), the micelle motion becomes quickly subdiffusive in the normal direction. Moreover, the temporal evolution of the micelle MSD excess in the perpendicular direction follows that of a nanoparticle near an elastic membrane. However, in the parallel direction, the MSD excess is rather similar to that of a nanoparticle near a liquid interface.

Numerical simulations of confined Brownian-yet-non-Gaussian motion

Brownian motion is a central scientific paradigm. Recently, due to increasing efforts and interests towards miniaturization and small-scale physics or biology, the effects of confinement on such a motion have become a key topic of investigation. Essentially, when confined near a wall, a particle moves much slower than in the bulk due to friction at the boundaries. The mobility is therefore locally hindered and space-dependent, which in turn leads to the apparition of so-called multiplicative noises, and associated non-Gaussianities which remain difficult to resolve at all times. Here, we exploit simple, optimized and efficient numerical simulations to address Brownian motion in confinement in a broadrange and quantitative way. To do so, we integrate the overdamped Langevin equation governing the thermal dynamics of a negatively-buoyant single spherical colloid within a viscous fluid confined by two rigid walls, including surface charges. From the produced large set of long random trajectories, we perform a complete statistical analysis and extract all the key quantities, such as the probability distributions in displacements and their main moments. In particular, we propose a novel method to compute high-order cumulants by reducing convergence problems, and employ it to efficiently characterize the inherent non-Gaussianity of the confined process.

The Curvature Effect on the Diffusion of Single Brownian Squares on a Cylindrical Surface in the Presence of Depletion Attractions

The diffusion of single micron-sized Brownian square platelets on cylindrical surfaces with different radii of curvature in the presence of depletion attractions was studied experimentally by video microscopy. The translational motion of a square is found to be diffusive along the axial direction of the cylinder but sub-diffusive along the circumferential direction due to the confinement induced by gravity, while its rotational motion displays a sub-diffusive behavior due to the confinement induced by orientation-dependent depletion attractions. Such a confinement effect decreases as the radius of curvature increases and can be tuned both through surface curvatures and/or depletion attractions. Our work provides a new way to control the translational and rotational dynamics of anisotropic particles through curved surfaces in the presence of depletion attractions.

Droplet Characteristics at the Maximum Adhesion on Curved Surfaces

For applications involving droplet detachment from solid surfaces, it is vital to study the droplet characteristics (e.g., contact angle and base width) when the droplet is experiencing the maximum force that detaches the droplet (maximum adhesion state). Historically, such investigations were mainly conducted on flat two-dimensional surfaces and the characteristics on curved surfaces with the third dimension remain unknown. Thus, the generalized description of such characteristics has not been established yet. Here, by vertically pulling liquid droplets using a microbalance, we study the droplet characteristics at the maximum adhesion on curved homogeneous surfaces. Variables in this study include liquid surface tension, initial droplet base area, and the asymmetry in solid surface curvature. Results show that the contact angle is identical everywhere along the droplet perimeter on curved surfaces irrespective of the asymmetry in surface curvature. In addition, we found that the droplet base is nonaxisymmetric (not circular) at the maximum adhesion, opposing previous understanding that was formulated for flat surfaces. As a result, we propose a more generalized and quantitative description of the droplet characteristics at the maximum adhesion, derived from the component of the surface tension force acting along the droplet perimeter.

Height distribution and orientation of colloidal dumbbells near a wall

Geometric confinement strongly influences the behavior of microparticles in liquid environments. However, to date, nonspherical particle behaviors close to confining boundaries, even as simple as planar walls, remain largely unexplored. Here, we measure the height distribution and orientation of colloidal dumbbells above walls by means of digital in-line holographic microscopy. We find that while larger dumbbells are oriented almost parallel to the wall, smaller dumbbells of the same material are surprisingly oriented at preferred angles. We determine the total height-dependent force acting on the dumbbells by considering gravitational effects and electrostatic particle-wall interactions. Our modeling reveals that at specific heights both net forces and torques on the dumbbells are simultaneously below the thermal force and energy, respectively, which makes the observed orientations possible. Our results highlight the rich near-wall dynamics of nonspherical particles and can further contribute to the development of quantitative frameworks for arbitrarily shaped microparticle dynamics in confinement.

Spherical probes for simultaneous measurement of rotational and translational diffusion in 3 dimensions

Real time visualization and tracking of colloidal particles with 3D resolution is essential for probing the local structure and dynamics in complex fluids. Although tracking translational motion of spherical particles is well-known, accessing rotational dynamics of such particles remains a great challenge. Here, we report a novel approach of using fluorescently labeled raspberry-like colloids with an optical anisotropy to concurrently track translational and rotational dynamics in 3 dimensions. The raspberry-like particles are coated by a silica layer of adjustable thickness, which allows tuning the surface roughness. The synthesis and applicability of the proposed method is demonstrated by two types of probes: rough and smoothened. The accuracies of measuring Mean Squared (Angular) Displacements are also demonstrated by using these 2 probes dispersed in 2 different solvents. The presented 3D trackable colloids offer a high potential for wide range of applications and studies, such as probing the dynamics of crystallization, phase transitions, biological interactions and the effect of surface roughness on diffusion.

Shape anisotropic colloidal particle fabrication using 2-photon polymerization

HYPOTHESIS

Our ability to dictate the colloid geometry is intimately related to self-assembly. The synthesis of anisotropic colloidal particles is currently dominated by wet chemistry and lithographic techniques. The wet chemical synthesis offers limited particle geometries at bulk quantities. Lithographic techniques, on the other hand, provide precise control over the particle shape, although at lower yields. In this respect, two-photon polymerization (2PP)¹ has attracted growing attention due to its ability to automatically fabricate complex micro/nano structures with high resolution.

EXPERIMENTS

We manufacture precisely designed colloids with sizes ranging from 1 µm to 10 µm with 2PP and optimize the process parameters for each dimension. Moreover, we study the shape dependent Brownian motion of these particles with video microscopy and estimate their diffusion coefficients.

FINDINGS

We observe that increasing the geometrical anisotropy leads to a pronounced deviation from the analytically predicted diffusion coefficient for disks with a given aspect ratio. The deviation is attributed to stronger hydrodynamic coupling with increasing anisotropy. We demonstrate, for the first time, 2PP manufacturing of colloids with tailored geometry. This study opens synthesis of colloidal building blocks to a broader audience with limited access to cleanrooms or wet-chemistry know-how.

Diffusive Escape of a Nanoparticle from a Porous Cavity

Narrow escape from confinement through a nanochannel is the critical step of complex transport processes including size-exclusion-based separations, oil and gas extraction from the microporous subsurface environment, and ribonucleic acid translocation through nuclear pore complex channels. While narrow escape has been studied using theoretical and computational methods, experimental quantification is rare because of the difficulty in confining a particle into a microscopic space through a nanoscale hole. Here, we studied narrow escape in the context of continuous nanoparticle diffusion within the liquid-filled void space of an ordered porous material. Specifically, we quantified the spatial dependence of nanoparticle motion and the sojourn times of individual particles in the interconnected confined cavities of a liquid-filled inverse opal film. We found that nanoparticle motion was inhibited near cavity walls and cavity escape was slower than predicted by existing theories and random-walk simulations. A combined computational-experimental analysis indicated that translocation through a nanochannel is barrier controlled rather than diffusion controlled.

Diffusion Decoupling in Binary Colloidal Systems Observed with Contrast Variation Multispeckle Diffusing Wave Spectroscopy

In the study of colloidal glasses, crystallization is often suppressed by leveraging size polydispersity, ranging from systems where particle sizes exhibit a continuous distribution to systems composed of particles of two or more distinct sizes. The effects of the disparities in size of the particles on the colloidal glass transition are not yet completely understood. Especially, the question of the existence of a decoupled glass transition between the large and small population remains. In order to measure colloidal dynamics on very long time scales and to disentangle the dynamics of the two populations, we employ contrast variation multispeckle diffusing wave spectroscopy. With this method, we aim to analyze the effect of size ratio, a = rPS/ rpNIPAM, on particle dynamics near the glass transition of a binary colloidal system. We find that both for long-time (α-) and short-time (β-) relaxation, the dynamics of the small particles either completely decouple from the large ones ( a = 0.2), moving freely through a glassy matrix, or are identical to the dynamics of the larger-sized population ( a = 0.37 and 1.44). For a size ratio of 0.37, we find a single-glass transition for both particle populations. The postulated double-glass transition in simulations and theory is not observed.

Machine learning wall effects of eccentric spheres for convenient computation

In confined systems, such as the inside of a biological cell, the outer boundary or wall can affect the dynamics of internal particles. In many cases of interest both the internal particle and outer wall are approximately spherical. Therefore, quantifying the wall effects from an outer spherical boundary on the motion of an internal eccentric sphere is very useful. However, when the two spheres are not concentric, the problem becomes nontrivial. In this paper we improve existing analytical methods to evaluate these wall effects and then train a feed-forward artificial neural network within a broader model. The final model generally performed with ∼0.001% error within the training domain and ∼0.05% when the outer spherical wall was extrapolated to an infinite plane. Through this model, the wall effects of an outer spherical boundary on the arbitrary motion of an internal sphere for all experimentally achievable configurations can now be conveniently and efficiently determined.

Rheology of colloidal suspensions in confined flow: Treatment of hydrodynamic interactions in particle-based simulations inspired by dynamical density functional theory

We investigate the microstructure and rheology of a hard-sphere suspension in a Newtonian fluid confined in a cylindrical channel and undergoing pressure-driven flow using Monte Carlo simulations. We develop a hydrodynamic framework inspired by dynamical density functional theory approaches in which the contributions due to various flow-induced hydrodynamic interactions (HI) are included in the form of thermodynamic work done by these HI-derived forces in displacing the hard spheres. Using this framework, we can self-consistently determine the effect of the local microstructure on the average flow field, and vice versa, and coevolve the inhomogeneous density distribution and the flattening velocity profile with increase in the density of suspended particles. Specifically, we explore the effect on the local microstructure due to the inclusion of forces arising from confinement-induced inertial effects, forces due to solvent-mediated interparticle interactions, and the dependence of the diffusivity on the local density. We examine the dependence of the apparent viscosity of the suspension on the volume fraction of hard spheres in the cylinder, the flow rate, and the diameter of the cylinder and investigate their effects on the local microstructure.

Brownian motion near an elastic cell membrane: A theoretical study

Elastic confinements are an important component of many biological systems and dictate the transport properties of suspended particles under flow. In this paper, we review the Brownian motion of a particle moving in the vicinity of a living cell whose membrane is endowed with a resistance towards shear and bending. The analytical calculations proceed through the computation of the frequency-dependent mobility functions and the application of the fluctuation-dissipation theorem. Elastic interfaces endow the system with memory effects that lead to a long-lived anomalous subdiffusive regime of nearby particles. In the steady limit, the diffusional behavior approaches that near a no-slip hard wall. The analytical predictions are validated and supplemented with boundary-integral simulations.

Impact of complex surfaces on biomicrorheological measurements using optical tweezers

The characterisation of physical properties in biologically relevant processes and the development of novel microfluidic devices for this purpose are experiencing a great resurgence at present. In many of measurements of this type where a probe in a fluid is used, the strong influence of the boundaries of the volume used is a serious problem. In these geometries the proximity of a probe to a wall can severely influence the measurement. However, although much knowledge has been gained about flat walls, to date, the effect of non-planar surfaces at microscopic scale on rotational motion of micro-objects has not been studied. Here we present for the first time both experimental measurements and numerical computations which aim to study the drag torque on optically trapped rotating particles moving near 3D-printed conical and cylindrical walls on-chip. These results are essential for quantifying how curved walls can effect the torque on particles, and thus enable accurate hydrodynamic simulations at the micron-scale. This opens the potential for new sensing approaches under more complex conditions, allowing both dynamic and microrheological studies of biological systems and lab-on-chip devices.

Hydrodynamic and entropic effects on colloidal diffusion in corrugated channels

In the absence of advection, confined diffusion characterizes transport in many natural and artificial devices, such as ionic channels, zeolites, and nanopores. While extensive theoretical and numerical studies on this subject have produced many important predictions, experimental verifications of the predictions are rare. Here, we experimentally measure colloidal diffusion times in microchannels with periodically varying width and contrast results with predictions from the Fick-Jacobs theory and Brownian dynamics simulation. While the theory and simulation correctly predict the entropic effect of the varying channel width, they fail to account for hydrodynamic effects, which include both an overall decrease and a spatial variation of diffusivity in channels. Neglecting such hydrodynamic effects, the theory and simulation underestimate the mean and standard deviation of first passage times by 40% in channels with a neck width twice the particle diameter. We further show that the validity of the Fick-Jacobs theory can be restored by reformulating it in terms of the experimentally measured diffusivity. Our work thus shows that hydrodynamic effects play a key role in diffusive transport through narrow channels and should be included in theoretical and numerical models.

Hydrodynamic interaction between particles near elastic interfaces

We present an analytical calculation of the hydrodynamic interaction between two spherical particles near an elastic interface such as a cell membrane. The theory predicts the frequency dependent self- and pair-mobilities accounting for the finite particle size up to the 5th order in the ratio between particle diameter and wall distance as well as between diameter and interparticle distance. We find that particle motion towards a membrane with pure bending resistance always leads to mutual repulsion similar as in the well-known case of a hard-wall. In the vicinity of a membrane with shearing resistance, however, we observe an attractive interaction in a certain parameter range which is in contrast to the behavior near a hard wall. This attraction might facilitate surface chemical reactions. Furthermore, we show that there exists a frequency range in which the pair-mobility for perpendicular motion exceeds its bulk value, leading to short-lived superdiffusive behavior. Using the analytical particle mobilities we compute collective and relative diffusion coefficients. The appropriateness of the approximations in our analytical results is demonstrated by corresponding boundary integral simulations which are in excellent agreement with the theoretical predictions.

Dynamics of colloids confined in microcylinders

We studied both global and local effects of cylindrical confinement on the diffusive behavior of hard sphere (HS) colloids. Using confocal scanning laser microscopy (CSLM) and particle tracking, we measured the mean squared displacement (MSD) of 1 micron sized silica particles in water-glycerol. This combination of fluid and setup allowed us to measure MSDs in a 4-dimensional parameter space, defined by the HS volume fraction (Φ: 0.05-0.39), cylinder radius (R: 2.5-20 micron), distance to the wall (z) and lagtime (τ: 0.03-60 s). MSDs for the entire cylinder confirm earlier findings that both narrowing the cylinder and populating it cause a slower dynamics. Additionally a decrease in R was found to cause a stronger ordering of the fluid. The effect of confinement on dynamics was further examined as a function of (z) location. For the largest cylinder (with minor curvature), we found that the strong decrease in MSD near the wall, becomes much less pronounced for higher Φ. Analyzing the radial (r) and azimuthal (θ) components, we found pronounced differences in the z-dependence that were 'hidden' in the total MSD. Near the wall, the r-MSD shows a much steeper z-dependence while at larger z, it shows a remarkable anti-correlation with the (peaked) density n(z). Also the dependence of the r-MSD on lagtime correlates with n(z): diffusive in between layers, but subdiffusive inside layers. These observations bring earlier findings together, while also shedding new light on the diffusive dynamics of concentrated colloids in narrow capillaries.

Broadband boundary effects on Brownian motion

Brownian motion of particles in confined fluids is important for many applications, yet the effects of the boundary over a wide range of time scales are still not well understood. We report high-bandwidth, comprehensive measurements of Brownian motion of an optically trapped micrometer-sized silica sphere in water near an approximately flat wall. At short distances we observe anisotropic Brownian motion with respect to the wall. We find that surface confinement not only occurs in the long time scale diffusive regime but also in the short time scale ballistic regime, and the velocity autocorrelation function of the Brownian particle decays faster than that of a particle in bulk fluid. Furthermore, at low frequencies the thermal force loses its color due to the reflected flow from the no-slip boundary. The power spectrum of the thermal force on the particle near a no-slip boundary becomes flat at low frequencies. This detailed understanding of boundary effects on Brownian motion opens a door to developing a 3D microscope using particles as remote sensors.

Diffusive dynamics of nanoparticles in ultra-confined media

Differential dynamic microscopy (DDM) was used to investigate the diffusive dynamics of nanoparticles of diameter 200-400 nm that were strongly confined in a periodic square array of cylindrical nanoposts. The minimum distance between posts was 1.3-5 times the diameter of the nanoparticles. The image structure functions obtained from the DDM analysis were isotropic and could be fit by a stretched exponential function. The relaxation time scaled diffusively across the range of wave vectors studied, and the corresponding scalar diffusivities decreased monotonically with increased confinement. The decrease in diffusivity could be described by models for hindered diffusion that accounted for steric restrictions and hydrodynamic interactions. The stretching exponent decreased linearly as the nanoparticles were increasingly confined by the posts. Together, these results are consistent with a picture in which strongly confined nanoparticles experience a heterogeneous spatial environment arising from hydrodynamics and volume exclusion on time scales comparable to cage escape, leading to multiple relaxation processes and Fickian but non-Gaussian diffusive dynamics.

Hydrodynamics and Brownian motions of a spheroid near a rigid wall

In this work, we study in detail the hydrodynamics and the Brownian motions of a spheroidal particle suspended in a Newtonian fluid near a flat rigid wall. We employ 3D Finite Element Method (FEM) simulations to compute how the mobility tensor of the spheroid varies with both the particle-wall separation distance and the particle orientation. We then study the Brownian motion of the spheroid by means of a discretized Langevin equation. We specifically focus on the additional drift terms arising from the position and orientational dependence of the mobility matrix. In this respect, we also propose a numerically convenient approximation of the orientational divergence of the mobility matrix that is required in the solution of the Langevin equation. Our results illustrate that both hydrodynamics and Brownian motions of a spheroidal particle near a confining wall display novel features from those of a sphere in the same type of confinement.

Measuring advection and diffusion of colloids in shear flow

An analysis of the dynamics of colloids in shear flow can be challenging because of the superposition of diffusion and advection. We present a method that separates the two motions, starting from the time-dependent particle coordinates. The restriction of the tracking to flow lanes and the subtraction of estimated advective displacements are combined in an iterative scheme that eventually makes the spatial segmentation redundant. Tracking errors due to the neglect of lateral diffusion are avoided, while drifts parallel and perpendicular to the flow are eliminated. After explaining the principles of our method, we validate it against both computer simulations and experiments. A critical overall test is provided by the mean square displacement function at high Peclet numbers (up to 50). We demonstrate via simulations how the measurement accuracy depends on diffusion coefficients and flow rates, expressed in units of camera pixels and frames. Also, sample-specific issues are addressed: inaccuracies in the velocity profile for dilute suspensions (volume fraction ≤0.03) and tracking errors for concentrated ones (VF ≥ 0.3). An analysis of experiments with colloidal spheres flowing through microchannels corroborates these findings and indicates perspectives for studies on transport, mixing, or rheology in microfluidic environments.

Hindered Brownian diffusion in a square-shaped geometry

We study the spatial dependence of the mobility of microparticles diffusing close to an edge of a square microtube. Confocal particle tracking is used to measure the local diffusion coefficients of fluorescent latex 1.1μm particles suspended in an aqueous solution in a borosilicate square capillary of 50μm section side. Observations are made for a set of planes obtained by confocal sectioning of the capillary volume. The translational diffusion coefficients parallel to the axis channel and perpendicular to one of the walls are measured as a function of the distance from both the two channel walls concurring in an edge. A complete 3D spatial map of the colloid diffusion coefficients is thus obtained. Near the corner, the diffusion is hindered up to about 40% as compared to its bulk value. The three translational diffusion coefficients pertaining to the motions along the channel axis and within the channel cross-section turn out to be different from each other and differently affected by the confinement, i.e., we are in the presence of an anisotropic diffusion. The hindered diffusion phenomenon is also examined by finite element numerical simulations, and the numerical predictions fairly agree with the measured diffusion coefficients.

Effects of shear and walls on the diffusion of colloids in microchannels

Colloidal suspensions flowing through microchannels were studied for the effects of both the shear flow and the proximity of walls on the particles' self-diffusion. Use of hydrostatic pressure to pump micron-sized silica spheres dispersed in water-glycerol mixture through poly(dimethylsiloxane) channels with a cross section of 30×24μm(2), allowed variation in the local Peclet number (Pe) from 0.01 to 50. To obtain the diffusion coefficients, image-time series from a confocal scanning laser microscope were analyzed with a method that, after finding particle trajectories, subtracts the instantaneous advective displacements and subsequently measures the slopes of the mean squared displacement in the flow (x) and shear (y) directions. For dilute suspensions, the thus obtained diffusion coefficients (D(x) and D(y)) are close to the free diffusion coefficient at all shear rates. In concentrated suspensions, a clear increase with the Peclet number (for Pe > 10) is found, that is stronger for D(x) than for D(y). This effect of shear-induced collisions is counteracted by the contribution of walls, which cause a strong local reduction in D(x) and D(y).

Hindered nanoparticle diffusion and void accessibility in a three-dimensional porous medium

The inherent pore-scale heterogeneity of many natural and synthetic porous materials can make it difficult to model and predict porous transport because the underlying microscopic processes are often poorly understood. Here we present the results of single-particle tracking experiments in which we followed the pore-scale diffusion of individual nanoparticles, deep within a three-dimensional porous material of moderate porosity. We observed significant hydrodynamic damping of particle motion at subpore length scales, resulting in heterogeneous and spatially dependent mobility. The accessibility of the void space was strongly dependent on particle size, and related to the heterogeneous hydrodynamics. Our results suggest that pore-scale diffusion is more heterogeneous and volume accessibility more limited than previously expected. The method demonstrated here will enable studies of a broad new class of materials including porous polymers of technological interest.

Anisotropic diffusion of spherical particles in closely confining microchannels

We present here the measurement of the diffusivity of spherical particles closely confined by narrow microchannels. Our experiments yield a two-dimensional map of the position-dependent diffusion coefficients parallel and perpendicular to the channel axis with a resolution down to 129 nm. The diffusivity was measured simultaneously in the channel interior, the bulk reservoirs, as well as the channel entrance region. In the channel interior we found strongly anisotropic diffusion. While the perpendicular diffusion coefficient close to the confining walls decreased down to approximately 25% of the value on the channel axis, the parallel diffusion coefficient remained constant throughout the entire channel width. In addition to the experiment, we performed finite element simulations for the diffusivity in the channel interior and found good agreement with the measurements. Our results reveal the distinctive influence of strong confinement on Brownian motion, which is of significance to microfluidics as well as quantitative models of facilitated membrane transport.

Local characterization of hindered Brownian motion by using digital video microscopy and 3D particle tracking

In this article we present methods for measuring hindered Brownian motion in the confinement of complex 3D geometries using digital video microscopy. Here we discuss essential features of automated 3D particle tracking as well as diffusion data analysis. By introducing local mean squared displacement-vs-time curves, we are able to simultaneously measure the spatial dependence of diffusion coefficients, tracking accuracies and drift velocities. Such local measurements allow a more detailed and appropriate description of strongly heterogeneous systems as opposed to global measurements. Finite size effects of the tracking region on measuring mean squared displacements are also discussed. The use of these methods was crucial for the measurement of the diffusive behavior of spherical polystyrene particles (505 nm diameter) in a microfluidic chip. The particles explored an array of parallel channels with different cross sections as well as the bulk reservoirs. For this experiment we present the measurement of local tracking accuracies in all three axial directions as well as the diffusivity parallel to the channel axis while we observed no significant flow but purely Brownian motion. Finally, the presented algorithm is suitable also for tracking of fluorescently labeled particles and particles driven by an external force, e.g., electrokinetic or dielectrophoretic forces.

Separation of microparticles suspended in a minichannel using laser radiation pressure

Optical separation, which is a contactless and accurate technique, has been mostly used to manipulate single particles. This work mainly aims to present an effective technique for optical propulsion and separation of a group of microscopic particles that are suspended in liquids. An experimental study is conducted to assess the effect of radiation pressure of a high-power laser on a dilute dispersion of microparticles in water using microscopic image analysis. Results of separation experiments indicate that the manipulation mechanism is capable of sorting the microscopic particles in two size classes. Compared to common optical separators, this configuration has a benefit of separating many particles simultaneously.

Crystalline multilayers of charged colloids in soft confinement: experiment versus theory

We combine real-space experiments and lattice sum calculations to investigate the phase diagram of charged colloidal particles under soft confinement. In the experiments we explore the equilibrium phase diagram of charged colloidal spheres in aqueous suspensions confined between two parallel charged walls at low background salt concentrations. Motivated by the experiments, we perform lattice sum minimizations to predict the crystalline ground state of point-like Yukawa particles which are exposed to a soft confining wall potential. In the multilayered crystalline regime, we obtain good agreement between the experimental and numerical findings: upon increasing the density we recover the sequence [structure: see text].

Measuring single-walled carbon nanotube length distributions from diffusional trajectories

A new method is demonstrated for measuring the length distributions of dispersed single-walled carbon nanotube (SWCNT) samples by analyzing diffusional motions of many individual nanotubes in parallel. In this method, termed "length analysis by nanotube diffusion" (LAND), video sequences of near-IR fluorescence microscope images showing many semiconducting SWCNTs are recorded and processed by custom image analysis software. This processing locates the individual nanotubes, tracks their translational trajectories, computes the corresponding diffusion coefficients, and converts those values to nanotube lengths. The deduced length values are then compiled into a histogram of lengths present in the sample. By using specific excitation wavelengths and emission filters, this analysis is performed on selected (n,m) structural species. The new LAND method has been found to give distributions in very good agreement with those obtained by conventional AFM analysis of the same samples. Because it is fluorescence-based, LAND monitors only semiconducting, relatively pristine SWCNTs. However, it is less sensitive to artifacts from impurities and bundled nanotubes than AFM or light scattering methods. In addition, samples can be analyzed with less time and operator attention than by AFM. LAND is a promising alternative method for characterizing length distributions of SWCNTs in liquid suspension.

Colloidal dynamics near a particle-covered surface

How the diffusive dynamics of colloidal spheres changes in the vicinity of a particle-coated surface is of importance for industrial challenges such as fouling and sedimentation as well as for fundamental studies into confinement effects. We addressed this question by studying colloidal dynamics in a partially coated surface layer, using video microscopy. Particle mean squared displacement (MSD) functions were measured as a function of a (local) effective volume fraction (EVF), which was varied by making use of gravity settling. Comparison of MSDs at the bare and coated surfaces for EVF of 0.2-0.4 revealed that at the latter surface the motion amplitudes are strongly reduced, accompanied by a sharp transition from diffusive to nearly caged motion. This clearly indicates that the surface-attached particles cannot be taken into account via volume fraction and that their immobility has a distinct effect. For EVF > 0.45, the caging becomes dominated by the suspended particles, making the dynamics at the bare and coated surfaces similar.

Wetting of a drop on a sphere

In this work, the equilibrium morphology of a drop on a sphere is analyzed as a function of the contact angle and drop volume experimentally and with analytical effective interfacial energy calculations. Experimentally, a drop on a sphere geometry is realized in an oil bath by placing a water drop on a sphere coated with a dielectric, of which the radii of curvature are comparable with that of the drop. Electrowetting (EW) is used to change the contact angle of the water drop on the sphere. To validate the applicability of EW and the Lippman-Young equation on nonflat surfaces, we systematically investigate the response of the contact angle to the applied voltage (EW response) for various drop volumes and compared the results with the case of a planar surface. The effective interfacial energy of two competing morphologies, namely, the spherically symmetric "completely engulfing" and "partially engulfing" morphologies are calculated analytically. The analytical calculations are then compared to the experimental results to confirm which morphology is energetically more favored for a given contact angle and drop volume. Our findings indicate that the "partially engulfing" morphology is always the energetically more favorable morphology.

Colloidal diffusion inside a spherical cell

The hydrodynamic hindering of a single-particle dynamics under total confinement is measured by optical microscopy. The three-dimensional trajectories of single-colloidal particles confined in spherical water globules of sizes only a few times the particle's diameter are tracked as they sample the entire volume of the globule. The hydrodynamic interactions between the particle and the spherical wall produce a dependence of the short-time diffusion on the particle's distance to the surface and an asymmetry in the radial and tangential components of the local diffusion coefficient, with the diffusion along the tangential direction being faster than along the radial direction. The latter decreasing close to the wall while the former being practically constant.