Measurement of surface charge densities on Brownian particles using total internal reflection microscopy

Study on defect imaging technology of optical elements based on micro-Raman spectroscopy

An optical element defect detection imaging method based on micro-Raman spectroscopy is proposed to achieve high-precision imaging of optical element defects and their distribution. The detection precision of the system is immediately reflected in the imaging quality. The sharpness value of the mapping images is calculated using the Sum of Modulus of Gray Difference function. The selection of the Raman peak is an important step, and when a borosilicate glass sample with standard defects is measured for verification, it is found that the Raman peak light intensity changes at -37 and 28 cm-1. When these two peaks were used for 2D mapping, obvious defect contours can be obtained, while the light intensity at other sites could not be used for imaging, and remained essentially constant. Through the detection of laser burning defects, new peaks appear at the burned defect location that could be used for imaging, and the burning defect area can be clearly distinguished from the non-burning area. By changing the laser burning conditions, the Raman shift changes, which verifies that there is a certain correlation between the laser burning degree and the Raman shift, which also provides a basis for 2D mapping imaging of defect detection.

Effect of photon counting shot noise on total internal reflection microscopy

Total internal reflection microscopy (TIRM) measures changes in the distance between a colloidal particle and a transparent substrate by measuring the scattering intensity of the particle illuminated by an evanescent wave. From the distribution of the recorded separation distances, the height-dependent effective potential φ(z) between the colloidal particle and the substrate can be measured. In this work, we show that spatial resolution with which TIRM can measure φ(z) is limited by the photon counting statistics of the scattered laser light. We develop a model to evaluate the effect of photon counting statistics on different potential profiles using Brownian dynamics simulations and experiments. Our results show that the effect of photon counting statistics depends on spatial gradients ∂φ/∂z of the potential, with the result that sharp features tend to be significantly blurred. We further establish the critical role of photon counting statistics and the intensity integration time τ in TIRM measurements, which is a trade-off between narrowing the width of the photon counting distribution and capturing the instantaneous position of the probe particle.

Critical Casimir interactions of colloids in micellar critical solutions

We study the temperature-dependence of critical Casimir interactions in a critical micellar solution of the nonionic surfactant C12E5 dissolved in water. Experimentally, this is achieved with total internal reflection microscopy (TIRM) which measures the interaction between a single particle and a flat wall. For comparison, we also studied the pair interactions of a two dimensional layer of colloidal particles in the identical micellar system which yields good agreement with the TIRM results. Although, at the surfactant concentration considered here, the fluid forms a dynamical network of wormlike micelles whose structure is considerably more complex than that of simple critical molecular fluids, the temperature-dependence of the measured interactions is - for surface-to-surface distances above 160 nm - in excellent quantitative agreement with theory. Below 160 nm, deviations arise which we attribute to the adsorption of micelles to the interacting surfaces.

Interactions between charged particles with bathing multivalent counterions: experiments vs. dressed ion theory

We compare the recent experimentally measured forces between charged colloidal particles, as well as their effective surface potentials (surface charge) in the presence of multivalent counterions in a bathing monovalent salt solution, with the predictions of the dressed ion theory of strongly charged colloidal systems. The benchmark for comparison is provided by the DLVO theory and the deviations from its predictions at small separations are taken as an indication of the additional non-DLVO attractions that can be fitted by an additional phenomenological exponential term. The parameters characterizing this non-DLVO exponential term as well as the dependencies of the effective potential on the counterion concentration and valency predicted by the dressed ion theory are well within the experimental values. This suggests that the deviations from the DLVO theory are probably caused by ion correlations as formalized within the dressed ion theory.

Interactions between silica particles in the presence of multivalent coions

Forces between charged silica particles in solutions of multivalent coions are measured with colloidal probe technique based on atomic force microscopy. The concentration of 1 : z electrolytes is systematically varied to understand the behavior of electrostatic interactions and double-layer properties in these systems. Although the coions are multivalent the Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory perfectly describes the measured force profiles. The diffuse-layer potentials and regulation properties are extracted from the forces profiles by using the DLVO theory. The dependencies of the diffuse-layer potential and regulation parameter shift to lower concentration with increasing coion valence when plotted as a function of concentration of 1 : z salt. Interestingly, these profiles collapse to a master curve if plotted as a function of monovalent counterion concentration.

Using single nanoparticle tracking obtained by nanophotonic force microscopy to simultaneously characterize nanoparticle size distribution and nanoparticle-surface interactions

Comprehensive characterization of nanomaterials for medical applications is a challenging and complex task due to the multitude of parameters which need to be taken into consideration in a broad range of conditions. Routine methods such as dynamic light scattering or nanoparticle tracking analysis provide some insight into the physicochemical properties of particle dispersions. For nanomedicine applications the information they supply can be of limited use. For this reason, there is a need for new methodologies and instruments that can provide additional data on nanoparticle properties such as their interactions with surfaces. Nanophotonic force microscopy has been shown as a viable method for measuring the force between surfaces and individual particles in the nano-size range. Here we outline a further application of this technique to measure the size of single particles and based on these measurement build the distribution of a sample. We demonstrate its efficacy by comparing the size distribution obtained with nanophotonic force microscopy to established instruments, such as dynamic light scattering and differential centrifugal sedimentation. Our results were in good agreement to those observed with all other instruments. Furthermore, we demonstrate that the methodology developed in this work can be used to study complex particle mixtures and the surface alteration of materials. For all cases studied, we were able to obtain both the size and the interaction potential of the particles with a surface in a single measurement.

Interactions of Colloidal Particles and Droplets with Water-Oil Interfaces Measured by Total Internal Reflection Microscopy

Total internal reflection microscopy (TIRM) is a well-known technique to measure weak forces between colloidal particles suspended in a liquid and a solid surface by using evanescent light scattering. In contrast to typical TIRM experiments, which are carried out at liquid-solid interfaces, here we extend this method to liquid-liquid interfaces. Exemplarily, we demonstrate this concept by investigating the interactions of micrometer-sized polystyrene particles and oil droplets near a flat water-oil interface for different concentrations of added salt and ionic surfactant (SDS). We find that the interaction is well described by the superposition of van der Waals and double layer forces. Interestingly, the interaction potentials are, within the SDS concentration range studied here, rather independent of the surfactant concentration, which suggests a delicate counter play of different interactions at the oil-water interface and provides interesting insights into the mechanisms relevant for the stability of emulsions.

Nanophotonic force microscopy: characterizing particle-surface interactions using near-field photonics

Direct measurements of particle-surface interactions are important for characterizing the stability and behavior of colloidal and nanoparticle suspensions. Current techniques are limited in their ability to measure pico-Newton scale interaction forces on submicrometer particles due to signal detection limits and thermal noise. Here we present a new technique for making measurements in this regime, which we refer to as nanophotonic force microscopy. Using a photonic crystal resonator, we generate a strongly localized region of exponentially decaying, near-field light that allows us to confine small particles close to a surface. From the statistical distribution of the light intensity scattered by the particle we are able to map out the potential well of the trap and directly quantify the repulsive force between the nanoparticle and the surface. As shown in this Letter, our technique is not limited by thermal noise, and therefore, we are able to resolve interaction forces smaller than 1 pN on dielectric particles as small as 100 nm in diameter.

Crystallization kinetics of colloidal model suspensions: recent achievements and new perspectives

Colloidal model systems allow studying crystallization kinetics under fairly ideal conditions, with rather well-characterized pair interactions and minimized external influences. In complementary approaches experiment, analytic theory and simulation have been employed to study colloidal solidification in great detail. These studies were based on advanced optical methods, careful system characterization and sophisticated numerical methods. Over the last decade, both the effects of the type, strength and range of the pair-interaction between the colloidal particles and those of the colloid-specific polydispersity have been addressed in a quantitative way. Key parameters of crystallization have been derived and compared to those of metal systems. These systematic investigations significantly contributed to an enhanced understanding of the crystallization processes in general. Further, new fundamental questions have arisen and (partially) been solved over the last decade: including, for example, a two-step nucleation mechanism in homogeneous nucleation, choice of the crystallization pathway, or the subtle interplay of boundary conditions in heterogeneous nucleation. On the other hand, via the application of both gradients and external fields the competition between different nucleation and growth modes can be controlled and the resulting microstructure be influenced. The present review attempts to cover the interesting developments that have occurred since the turn of the millennium and to identify important novel trends, with particular focus on experimental aspects.

Sizing of metallic nanoparticles confined to a microfluidic film applying dark-field particle tracking

We present Brownian motion-based sizing of individual submicron and nanoparticles in liquid samples. The advantage of our approach is that particles can freely diffuse in a 10 μm thin liquid film and are therefore always within the focal depth of a low numerical aperture objective. Particles are visualized with dark-field microscopy, and the resulting diffraction-limited spots are tracked over a wide field of view of several hundred micrometers. Consequently, it is ascertained that long 2D trajectories are acquired, which leads to significantly increased particle sizing precision. The hydrodynamic diameters of metal particles with nominal sizes ranging from 70 to 200 nm in aqueous solution were determined by tracking for up to 2 min, and it was investigated if the diffusion characteristics were influenced by the proximity of substrates. This was not the case, and the estimated diameters were in good agreement with the values obtained by electron microscopy, thus validating the particle sizing principle. Furthermore, we measured a sample mixture to demonstrate the distinction of close particle sizes and performed the conjugation of a model protein (BSA) on the nanoparticle surface. An average increase in the radius of 9 nm was determined, which corresponds to the size of the BSA protein.

Electric double-layer potentials and surface regulation properties measured by colloidal-probe atomic force microscopy

We show how the colloidal-probe technique, which is based on force measurements made with the atomic force microscope, can be used to accurately determine the charging parameters of water-solid interfaces. Besides yielding accurate values of the double-layer or diffuse-layer potential, the method also allows reliable determination of the charge regulation properties of the surfaces. The latter can be quantified with a regulation parameter, which is essential to properly describe forces between interfaces, especially in asymmetric situations when one of the interfaces is charged and the other one is close to neutral. The technique relies on a highly charged probe particle, for which the charging properties are accurately determined by interpreting the double-layer contribution of the measured force profiles in the symmetric sphere-sphere geometry with Poisson-Boltzmann (PB) theory. Once the probe particle is calibrated, this particle is used to measure the force profile between an unknown substrate in the asymmetric sphere-sphere or sphere-plane geometry. From this profile, the diffuse-layer potential and regulation parameter of the substrate can be again determined with PB theory. The technique is highly versatile, as it can be used for a wide variety of substrates, including colloidal particles and planar substrates. The technique is also applicable in salt solutions containing multivalent ions. The current drawbacks of the technique are that it can only be applied up to moderately high salt levels, typically to 10 mM, and only for relatively large particles, typically down to about 1 μm in diameter. How the technique could be extended to higher salt levels and smaller particle size is also briefly discussed.

Rectification of ion current in nanopipettes by external substrates

We describe ion distribution and the current-voltage (i-V) response of nanopipettes at different probe-to-substrate distances (Dps) as simulated by finite-element methods. Results suggest electrostatic interactions between a charged substrate and the nanopipette dominate electrophoretic ion transport through the nanopipette when Dps is within 1 order of magnitude of the Debye length (∼10 nm for a 1 mM solution as employed in the simulation). Ion current rectification (ICR) and permselectivity associated with a neutral or charged nanopipette can be reversibly enhanced or reduced dependent on Dps, charge polarity, and charge density (σ) of the substrate. Regulation of nanopipette current is a consequence of the enrichment or depletion of ions within the nanopipette interior, which influences conductivity of the nanopipette. When the external substrate is less negatively charged than the nanopipette, the substrate first reduces, and then enhances the ICR as Dps decreases. Surprisingly, both experimental and simulated data show that a neutral substrate was also able to reduce and reverse the ICR of a slightly negatively charged nanopipette. Simulated results ascribe such effects to the elimination of ion depletion within the nanopipette at positive potentials.

Particle dynamics in two-dimensional random-energy landscapes: experiments and simulations

The dynamics of individual colloidal particles in random potential energy landscapes was investigated experimentally and by Monte Carlo simulations. The value of the potential at each point in the two-dimensional energy landscape follows a Gaussian distribution. The width of the distribution, and hence the degree of roughness of the energy landscape, was varied and its effect on the particle dynamics studied. This situation represents an example of Brownian dynamics in the presence of disorder. In the experiments, the energy landscapes were generated optically using a holographic setup with a spatial light modulator, and the particle trajectories were followed by video microscopy. The dynamics is characterized using, e.g., the time-dependent diffusion coefficient, the mean squared displacement, the van Hove function, and the non-Gaussian parameter. In both experiments and simulations the dynamics is initially diffusive, showing an extended subdiffusive regime at intermediate times before diffusive motion is recovered at very long times. The dependence of the long-time diffusion coefficient on the width of the Gaussian distribution agrees with theoretical predictions. Compared to the dynamics in a one-dimensional potential energy landscape, the localization at intermediate times is weaker and the diffusive regime at long times reached earlier, which is due to the possibility to avoid local maxima in two-dimensional energy landscapes.

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].

Force measurement in the presence of Brownian noise: equilibrium-distribution method versus drift method

The study of microsystems and the development of nanotechnologies require alternative techniques to measure piconewton and femtonewton forces at microscopic and nanoscopic scales. Among the challenges is the need to deal with the ineluctable thermal noise, which, in the typical experimental situation of a spatial diffusion gradient, causes a spurious drift. This leads to a correction term when forces are estimated from drift measurements [G. Volpe, L. Helden, T. Brettschneider, J. Wehr, and C. Bechinger, Phys. Rev. Lett. 104, 170602 (2010)]. Here we provide a systematic study of such an effect by comparing the forces acting on various Brownian particles derived from equilibrium-distribution and drift measurements. We discuss the physical origin of the correction term, its dependence on wall distance and particle radius, and its relation to the convention used to solve the respective stochastic integrals. Such a correction term becomes more significant for smaller particles and is predicted to be on the order of several piconewtons for particles the size of a biomolecule.

Novel perspectives for the application of total internal reflection microscopy

Total Internal Reflection Microscopy (TIRM) is a sensitive non-invasive technique to measure the interaction potentials between a colloidal particle and a wall with femtonewton resolution. The equilibrium distribution of the particle-wall separation distance z is sampled monitoring the intensity I scattered by the Brownian particle under evanescent illumination. Central to the data analysis is the knowledge of the relation between I and the corresponding z, which typically must be known a priori. This poses considerable constraints to the experimental conditions where TIRM can be applied (short penetration depth of the evanescent wave, transparent surfaces). Here, we introduce a method to experimentally determine I(z) by relying only on the distance-dependent particle-wall hydrodynamic interactions. We demonstrate that this method largely extends the range of conditions accessible with TIRM, and even allows measurements on highly reflecting gold surfaces where multiple reflections lead to a complex (z).

Colloidal model system for island formation

We present model calculations to explore the possibility of colloidal island formation over strained surfaces. Colloids, aggregating due to attractive depletion interactions, are deposited onto a colloidal surface whose lattice constant and geometry can be varied by optical forces. This allows precise control of the strain between the substrate and the colloidal adsorbate. Three different strain fields are considered: fields with either an unidirectional or a hexagonal variation of strain, and fields with a combination of both variations. We find that the unidirectional field induces the formation of infinitely extended ridges, while hexagonal strain fields lead to regular pyramidal island structures which can be distorted in a controlled way by adding the unidirectional strain component. We furthermore study the dependence of island size on strain strength for the hexagonal strain pattern and find that the area occupied by an island is a constant fraction of the strain field's repeat unit.

Vesicle diffusion close to a membrane: intermembrane interactions measured with fluorescence correlation spectroscopy

The protein machinery controlling membrane fusion (or fission) has been well studied; however, the role of vesicle diffusion near membranes in these critical processes remains unclear. We experimentally and theoretically investigated the dynamics of small vesicles (approximately 50 nm in diameter) that are diffusing near supported planar bilayers acting as "target" membranes. Using total internal reflection-fluorescence correlation spectroscopy, we examined the validity of theoretical analyses of vesicle-membrane interactions. Vesicles were hindered by hydrodynamic drag as a function of their proximity to the planar bilayer. The population distributions and diffusion kinetics of the vesicles were further affected by changing the ionic strength and pH of the buffer, as well as the lipid composition of the planar membrane. Effective surface charges on neutral bilayers were also analyzed by comparing experimental and theoretical data, and we show the possibility that vesicle dynamics can be modified by surface charge redistribution of the planar bilayer. Based on these results, we hypothesize that the dynamics of small vesicles, diffusing close to biomembranes, may be spatially restricted by altering local physiological conditions (e.g., salt concentration, lipid composition, and pH), which may represent an additional mechanism for controlling fusion (or fission) dynamics.

Frustration-induced magic number clusters of colloidal magnetic particles

We report the formation of stable two-dimensional clusters consisting of long-range-interacting colloidal particles with predefined magnetic moments. The symmetry and arrangement of the particles within the cluster are imposed by the magnetic frustration. By satisfying the criteria of stability, a series of magic number clusters is formed. The magic clusters are close packed and have compensating magnetic moments and chirality. Thus, the system can be regarded as a classical mesoscopic model for spin arrangements in two-dimensional triangular antiferromagnets, although the exact nature of the interactions between the macroscopic magnetic moments is different.

Single-particle evanescent light scattering simulations for total internal reflection microscopy

We simulate and measure light scattering of a micrometer-sized spherical particle suspended in solution close to a glass substrate. The model, based on the discrete sources method, is developed to describe the experimental situation of total internal reflection microscopy experiments; i.e., the particle is illuminated by an evanescent light field originating from the glass-solvent interface. In contrast to the well-established assumption of a simple exponential decay of the scattering intensity with distance, we demonstrate significant deviations for a certain range of penetration depths and polarization states of the incident light.

Low-capacity channel designed for particle separation with controlled electric fields and evaluation of involved forces

Electric field is one of the suitable physical fields applicable to particle separations. Although long rectangular channel is used for particle separation in usual electrical field flow fractionation (FFF), a short low-capacity channel can replace it if the field is precisely controlled. Several separation principles are proposed with this channel. The elution behavior of particles has revealed that the gravitational, diffusion, and hydrodynamic lift force (HLF) play important roles in the determination of the elution behavior of particles. The elution threshold voltage (V(th)) was defined and experimentally determined for various system configurations and particles. The electric force no longer overcomes the other forces, and particles are taken off the wall, when the applied voltage becomes lower than V(th). V(th) values have allowed us not only to estimate surface charge density of a particle but also to evaluate the hydrodynamic lift force against particle.

Experimental verification of near-wall hindered diffusion for the Brownian motion of nanoparticles using evanescent wave microscopy

A total internal reflection fluorescence microscopy technique coupled with three-dimensional tracking of nanoparticles is used to experimentally verify the theory on near-wall hindered Brownian motion [Goldman et al., Chem. Eng. Sci. 22, 637 (1967); Brenner, Chem. Eng. Sci. 16, 242 (1967)] very close to the solid surface (within approximately 1 microm). The measured mean square displacements (MSDs) in the lateral x-y directions show good agreement with the theory for all tested nanoparticles of radii 50, 100, 250, and 500 nm. However, the measured MSDs in the z direction deviate substantially from the theory particularly for the case of smaller particles of 50 and 100 nm radius. Since the theory considers only the hydrodynamic interaction of moving particles with a stationary solid wall, additionally possible interaction forces like gravitational forces, van der Waals forces, and electro-osmotic forces have been examined to delineate the physical reasons for the discrepancy.

Many-particle tracking with nanometer resolution in three dimensions by reflection interference contrast microscopy

We have developed and characterized a method, based on reflection interference contrast microscopy, to simultaneously determine the three-dimensional positions of multiple particles in a colloidal monolayer. To evaluate this method, the interaction of 6.8 microm (+/-5%) diameter lipid-derivatized silica microspheres with an underlying planar borosilicate substrate is studied. Measured colloidal height distributions are consistent with expectations for an electrostatically levitated colloidal monolayer. The precision of the method is analyzed using experimental techniques in addition to computational bootstrapping algorithms. In its present implementation, this technique achieves 16 nm lateral and 1 nm vertical precision.

Novel optical and statistical methods reveal colloid–wall interactions inconsistent with DLVO and Lifshitz theories

We present an experimental method based on video microscopy to perform nanometer scale position detection of a micrometer bead in the direction along the propagation of the detection light. Using the same bead for calibration and detection significantly improves the in depth resolution in comparison to video microscopy methods from literature. This method is used together with an optical trap to measure interaction potentials between a glass surface and colloids made of polystyrene or silica at different electrolyte concentrations. The results are confirmed by an independent method where the optical trap is used in connection with a quadrant photodiode. Also, we present a maximum likelihood analysis method which considerably improves the spatial resolution of interaction potentials by optimizing the underlying potential function to fit all observed position distributions. The measured interaction potentials agree well with DLVO theory for small electrolyte concentrations; however, for larger electrolyte concentrations the potentials differ qualitatively from both DLVO and Lifshitz theory.

Three-dimensional characterization of tethered microspheres by total internal reflection fluorescence microscopy

Tethered particle microscopy is a powerful tool to study the dynamics of DNA molecules and DNA-protein complexes in single-molecule experiments. We demonstrate that stroboscopic total internal reflection microscopy can be used to characterize the three-dimensional spatiotemporal motion of DNA-tethered particles. By calculating characteristic measures such as symmetry and time constants of the motion, well-formed tethers can be distinguished from defective ones for which the motion is dominated by aberrant surface effects. This improves the reliability of measurements on tether dynamics. For instance, in observations of protein-mediated DNA looping, loop formation is distinguished from adsorption and other nonspecific events.

Depletion potentials induced by charged colloidal rods

We present direct depletion potential measurements for a single colloidal sphere close to a wall in suspensions of charged colloidal rods. In contrast to earlier studies of purely entropic systems (Helden et al. Phys. Rev. Lett. 2003, 90, 048301), here electrostatic interactions are important. These enhance the depletion attraction and lead to repulsive parts in the interaction potentials, indicating correlation effects between the rods.

Direct measurement of entropic forces induced by rigid rods

We present the first direct depletion potential measurements for a single colloidal sphere close to a wall in a suspension of rigid colloidal rods. Since all particle interactions are as good as hard-core-like, the depletion potentials are of entirely entropic origin. We developed a density functional theory approach that accurately accounts for this experimental situation. The depletion potentials calculated for different rod number densities are in very good quantitative agreement with the experimental results.