It is known that line optical tweezers (LOT) can measure potential of mean force (PMF) between colloidal particles in the bulk. However, PMF obtained with LOT is empirically modified before showing the result of the final form in order to correct the potential rise at long distances. In the present letter, we derive theoretical correction methods for acquisition of PMF by using statistical mechanics. Using the new methods, PMF can be obtained without the empirical fitting equation. Through the new methods, external potential acting on the trapped two colloidal particles induced by LOT can also be obtained. As an additional study, we explain two methods for obtaining PMF between colloidal particles on a substrate surface, in which a normal single optical tweezers with a fixed focal point is used, and for obtaining PMF between colloidal particles trapped by dual-beam optical tweezers in the bulk. These methods can also obtain the external potential acting on the trapped two colloidal particles.
Time-division multiplexing presents an attractive opportunity to probe multi-colloidal interactions in optical traps at short time-scales. In this paper, we demonstrate a stroboscopic system capable of arbitrary control of multiple trapped colloids with sensing at kHz rates and validate it using several simple multi-colloidal experiments. We expect this methodology will be of benefit in the study of group colloidal hydrodynamics and systems of active colloids, particularly where a temporal sensitivity beyond that of camera-based position sensing is required. In addition, our multiplexing enabl…
Viscously damped particles driven past an evenly spaced array of potential energy wells or barriers may become kinetically locked in to the array, or else may escape from the array. The transition between locked-in and free-running states has been predicted to depend sensitively on the ratio between the particles' size and the separation between wells. This prediction is confirmed by measurements on monodisperse colloidal spheres driven through arrays of holographic optical traps.
A method for forming permanent three dimensional structures from colloidal particles using holographic optical trapping is described. Holographic optical tweezers (HOT) are used to selectively position charge stabilized colloidal particles within a flow cell. Once the particles are in the desired location an electrolyte solution is pumped into the cell which reduces the Debye length and induces aggregation caused by the van der Waals attraction. This technique allows for the formation of three dimensional structures both on and away from the substrate that can be removed from solution without …
This paper reports on some new results from the analyses of the video microscopy data obtained in a prior experiment on two-dimensional (2D) colloidal crystals. It was reported previously that optical tweezers can be used to create mono- and di-vacancies in a 2D colloidal crystal. Here we report the results on the creation of a vacancy-interstitial pair, as well as tri-vacancies. It is found that the vacancy-interstitial pair can be long-lived, but they do annihilate each other. The behavior of tri-vacancies is most intriguing, as it fluctuates between a configuration of bound pairs of disloca…
How far a particle moves along the optical axis in a holographic optical trap is not simply dictated by the programmed motion of the trap, but rather depends on an interplay of the trap's changing shape and the particle's material properties. For the particular case of colloidal spheres in optical tweezers, holographic video microscopy reveals that trapped particles tend to move farther along the axial direction than the traps that are moving them and that different kinds of particles move by different amounts. These surprising and sizeable variations in axial placement can be explained by a d…
We demonstrate both experimentally and theoretically that a colloidal sphere trapped in a static optical tweezer does not come to equilibrium, but rather reaches a steady state in which its probability flux traces out a toroidal vortex. This non-equilibrium behavior can be ascribed to a subtle bias of thermal fluctuations by non-conservative optical forces. The circulating sphere therefore acts as a Brownian motor. We briefly discuss ramifications of this effect for studies in which optical tweezers have been treated as potential energy wells.
Particle shape and medium chirality are two key features recently used to control anisotropic colloidal self-assembly and dynamics in liquid crystals. Here, we study magnetically responsive gourd-shaped colloidal particles dispersed in cholesteric liquid crystals with periodicity comparable or smaller than the particle's dimensions. Using magnetic manipulation and optical tweezers, which allow one to position colloids near the confining walls, we measured the elastic repulsive interactions of these particles with confining surfaces and found that separation-dependent particle-wall interaction …
Since their invention in 1986 by Arthur Ashkin and colleagues, optical tweezers have become an essential tool in several fields of physics, spectroscopy, biology, nanotechnology, and thermodynamics. In this Tutorial, we provide a primer on how to calibrate optical tweezers and how to use them for advanced applications. After a brief general introduction on optical tweezers, we focus on describing and comparing the various available calibration techniques. Then, we discuss some cutting-edge applications of optical tweezers in a liquid medium, namely to study single-molecule and single-cell mech…
Using laser tweezers and fluorescence confocal polarizing microscopy, we study colloidal interactions of solid microspheres in the nematic bulk caused by elastic distortions around the particles with strong tangential surface anchoring. The particles aggregate into chains directed at about 30 degrees to the far field director and, at higher concentrations, form complex kinetically trapped structures. We characterize the distance and angular dependencies of the colloidal interaction forces.
We present the first direct measurement of three-body interactions in a colloidal system comprised of three charged colloidal particles. Two of the particles have been confined by means of a scanned laser tweezers to a line-shaped optical trap where they diffused due to thermal fluctuations. Upon the approach of a third particle, attractive three-body interactions have been observed. The results are in qualitative agreement with additionally performed nonlinear Poissson-Boltzmann calculations, which also allow us to investigate the microionic density distributions in the neighborhood of the in…
We demonstrate scaffolding of plasmonic nanoparticles by topological defects induced by colloidal microspheres to match their surface boundary conditions with a uniform far-field alignment in a liquid crystal host. Displacing energetically costly liquid crystal regions of reduced order, anisotropic nanoparticles with concave or convex shapes not only stably localize in defects but also self-orient with respect to the microsphere surface. Using laser tweezers, we manipulate the ensuing nanoparticle-microsphere colloidal dimers, probing the strength of elastic binding and demonstrating self-asse…
Electrostatic forces between small groups of colloidal particles are measured using blinking optical tweezers. When the electrostatic screening length is significantly larger than the particle radius, forces are found to be non-pairwise additive. Both pair and multi-particle forces are well described by the linearized Poisson-Boltzmann equation with constant potential boundary conditions. These findings may play an important role in understanding the structure and stability of a wide variety of systems, from micron-sized particles in oil to aqueous nanocolloids.
We study the relaxation of a single colloidal sphere which is periodically driven between two nonequilibrium steady states. Experimentally, this is achieved by driving the particle along a toroidal trap imposed by scanned optical tweezers. We find that the relaxation time after which the probability distributions have been relaxed is identical to that obtained by a steady state measurement. In quantitative agreement with theoretical calculations the relaxation time strongly increases when driving the system further away from thermal equilibrium.
We study the Brownian motion of particles trapped by optical tweezers inside a colloidal glass (Laponite) during the sol-gel transition. We use two methods based on passive rheology to extract the effective temperature from the fluctuations of the Brownian particles. All of them give a temperature that, within experimental errors, is equal to the heat bath temperature. Several interesting features concerning the statistical properties and the long time correlations of the particles are observed during the transition.
Critical Casimir forces emerge between objects, such as colloidal particles, whenever their surfaces spatially confine the fluctuations of the order parameter of a critical liquid used as a solvent. These forces act at short but microscopically large distances between these objects, reaching often hundreds of nanometers. Keeping colloids at such distances is a major experimental challenge, which can be addressed by the means of optical tweezers. Here, we review how optical tweezers have been successfully used to quantitatively study critical Casimir forces acting on particles in suspensions. A…
Appropriate combinations of laser beams can be used to trap and manipulate small particles with "optical tweezers" as well as to induce significant "optical binding" forces between particles. These interaction forces are usually strongly anisotropic depending on the interference landscape of the external fields. This is in contrast with the familiar isotropic, translationally invariant, van der Waals and, in general, Casimir-Lifshitz interactions between neutral bodies arising from random electromagnetic waves generated by equilibrium quantum and thermal fluctuations. Here we show, both theore…
Three-body and four-body interactions have been directly measured in a colloidal system comprised of three (or four) charged colloidal particles. Two of the particles have been confined by means of a scanned laser tweezers to a line-shaped optical trap where they diffused due to thermal fluctuations. By means of an additional focused optical trap a third particle has been approached and attractive three-body interactions have been observed. These observations are in qualitative agreement with additionally performed nonlinear Poissson-Boltzmann calculations. Two configurations of four particles…
We demonstrate a novel method of introducing point defects (mono and di-vacancies) in a confined mono-layer colloidal crystal by manipulating individual particles with optical tweezers. Digital video microscopy is used to study defect dynamics in real space and time. We analyze the topological arrangements of the particles in the defect core and establish their connection with the energetics of the system. It is found that thermal fluctuations excite point defects into \textit{dislocation multipole} configurations. We extract the dislocation pair potential at near field, where cores overlap an…
We demonstrate that the active thermocapillary stresses induced by multiple microbubbles offer simple routes to directed self-assembly and complex but controllable micromanipulation of mesoscopic colloidal particles embedded in a liquid. The microbubbles are nucleated on a liquid-glass interface using optical tweezers. The flow around a single bubble causes self-assembly of the particles in rings at the bubble-base, while an asymmetric temperature profile generated across the bubble interface breaks the azimuthal symmetry of the flow, and induces simultaneous accumulation and repulsion of part…
We examine the behavior of spherical silica particles trapped at an air-nematic liquid crystal interface. When a strong normal anchoring is imposed, the beads spontaneously form various structures depending on their area density and the nematic thickness. Using optical tweezers, we determine the pair potential and explain the formation of these patterns. The energy profile is discussed in terms of capillary and elastic interactions. Finally, we detail the mechanisms that control the formation of an hexagonal lattice and analyze the role of gravity for curved interfaces.
The progress of realizing colloidal structures mimicking natural forms of organization in condensed matter is inherently limited by the availability of suitable colloidal building blocks. To enable new forms of crystalline and quasicrystalline self-organization of colloids, we develop truncated pyramidal particles that form nematic elastic dipoles with long-range electrostaticlike and geometry-guided low-symmetry short-range interactions. Using a combination of nonlinear optical imaging, laser tweezers, and video microscopy, we characterize colloidal pair interactions and demonstrate unusual f…
Particles that are immersed in a fluid exchange momentum via the fluid, hence their Brownian motion is correlated. By means of multiparticle-collision dynamics simulations we study the interactions between two colloidal beads in a sheared fluid suspension. Recently, this topic has been addressed in experiments on colloidal particles trapped by optical tweezers in a microfluidic device [PRL, 103, 230602 (2009)] and theoretically by means of a Langevin model [Eur. Phys. J E, 33, 313 (2010)]. Although we neglect the rotational degrees of freedom of the colloids, and employ a very simple coupling …
This work is devoted to the study of displacement fluctuations of micron-sized particles in an aging colloidal glass. We address the issue of the validity of the fluctuation dissipation theorem (FDT) and the time evolution of viscoelastic properties during aging of aqueous suspensions of a clay (Laponite RG) in a colloidal glass phase. Given the conflicting results reported in the literature for different experimental techniques, our goal is to check and reconcile them using \emph{simultaneously} passive and active microrheology techniques. For this purpose we measure the thermal fluctuations …
We describe colloidal Janus particles with metallic and dielectric faces that swim vigorously when illuminated by defocused optical tweezers without consuming any chemical fuel. Rather than wandering randomly, these optically-activated colloidal swimmers circulate back and forth through the beam of light, tracing out sinuous rosette patterns. We propose a model for this mode of light-activated transport that accounts for the observed behavior through a combination of self-thermophoresis and optically-induced torque. In the deterministic limit, this model yields trajectories that resemble roset…
Colloidal crystals are of extreme importance for applied research, such as photonic crystals technology, and for fundamental studies in statistical mechanics. Long range attractive interactions, such as capillary forces, can drive the spontaneous assembly of such mesoscopic ordered structures. However long range attractive forces are very rare in the colloidal realm. Here we report a novel strong and long ranged attraction induced by a thermal gradient in the presence of a wall. Switching on and off the thermal gradient we can rapidly and reversibly form stable hexagonal 2D crystals. We show t…
We develop an integrated system of holographic optical trapping and multimodal nonlinear microscopy and perform simultaneous three-dimensional optical manipulation and non-invasive structural imaging of composite soft-matter systems. We combine different nonlinear microscopy techniques such as coherent anti-Stokes Raman scattering, multi-photon excitation fluorescence and multi-harmonic generation, and use them for visualization of long-range molecular order in soft materials by means of their polarized excitation and detection. The combined system enables us to accomplish both, manipulation i…
We present an extension of the two-point optical microrheology technique introduced by Crocker \textit{et al.} [Phys. Rev. Lett. \textbf{85}, 888 (2000)] to high frequencies. The correlated fluctuations of two probe spheres held by a pair of optical tweezers within a viscoelastic medium are determined using optical interferometry. A theoretical model is developed to yield the frequency-dependent one- and two-particle response functions from the correlated motion. We demonstrate the validity of this method by determining the one- and two-particle correlations in a semi-dilute solution of polyst…
Colloids held by optical or magnetic tweezers have been used to explore the local rheological properties of a complex medium and to extract work from fluctuations with some appropriate protocols. However, a general theoretical understanding of the interplay between the confinement and the interaction with the environment is still lacking. Here, we explore the statistical properties of the position of a probe confined in a harmonic trap moving at constant velocity and interacting with a bath of colloidal particles maintained at a different temperature. Interactions among particles are accounted…
To date, optical manipulation techniques for aqueous dispersions have been developed that deposit and/or transport nanoparticles not only for fundamental studies of colloidal dynamics, but also for either creating photonic devices or allowing accurate control of liquids on micron scales. Here, we report that optical tweezers (OT) system is able to direct three-dimensional assembly of graphene, graphite, and carbon nanotubes (CNT) into microcapsules of hollow spheres. The OT technique facilitates both to visualize the elasticity of a CNT microcapsule and to arrange a triplet of identical graphe…
The present article provides an overview of the recent progress in the direct force measurements between individual pairs of colloidal particles in aqueous salt solutions. Results obtained by two different techniques are being highlighted, namely with the atomic force microscope (AFM) and optical tweezers. One finds that the classical theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO) represents an accurate description of the force profiles even in the presence of multivalent ions, typically down to distances of few nanometers. However, the corresponding Hamaker constants and diffuse lay…
Brownian vortexes are stochastic machines that use static non-conservative force fields to bias random thermal fluctuations into steadily circulating currents. The archetype for this class of systems is a colloidal sphere in an optical tweezer. Trapped near the focus of a strongly converging beam of light, the particle is displaced by random thermal kicks into the nonconservative part of the optical force field arising from radiation pressure, which then biases its diffusion. Assuming the particle remains localized within the trap, its time-averaged trajectory traces out a toroidal vortex. Unl…
Suspensions of micro and nano particles made of Polystyrene, Poly(methyl methacrylate), Silicon dioxide etc. have been a standard model system to understand colloidal physics. . These systems have proved useful insights into phenomena such as self-assembly. Colloidal model systems are also extensively used to simulate many condensed matter phenomena such as dynamics in a quenched disordered system and glass transition. A precise control of particles using optical or holographic tweezers is essential for such studies. However, studies of collective phenomena such as jamming and flocking behavio…
We study elastic interactions between colloidal particles and deformation landscapes of undulations in a cholesteric liquid crystal under an electric field applied normal to cholesteric layers. The onset of undulation instability is influenced by the presence of colloidal inclusions and, in turn, layers' undulations mediate the spatial patterning of particle locations. We find that the bending of cholesteric layers around a colloidal particle surface prompts the local nucleation of an undulations lattice at electric fields below the well-defined threshold known for liquid crystals without incl…
Colloidal particles disturb the alignment of rod-like molecules of liquid crystals, giving rise to long-range interactions that minimize the free energy of distorted regions. Particle shape and topology are known to guide this self-assembly process. However, how chirality of colloidal inclusions affects these long-range interactions is unclear. Here we study the effects of distortions caused by chiral springs and helices on the colloidal self-organization in a nematic liquid crystal using laser tweezers, particle tracking and optical imaging. We show that chirality of colloidal particles inter…
Line optical tweezer and colloidal-probe atomic force microscopy can measure force curves between two large colloidal particles of chemically the same surfaces in a suspension of small colloidal particles. Recently, the authors proposed a transform theory to obtain the number density distribution of the small colloidal particles on the large colloidal particle from the force curve. In this short letter, we propose another method which utilizes Ornstein-Zernike equation coupled with a closure equation instead of Kirkwood superposition approximation. The new transform theory uses a structure fac…
Critical Casimir forces can play an important role for applications in nano-science and nanotechnology, owing to their piconewton strength, nanometric action range, fine tunability as a function of temperature, and exquisite dependence on the surface properties of the involved objects. Here, we investigate the effects of critical Casimir forces on the free dynamics of a pair of colloidal particles dispersed in the bulk of a near-critical binary liquid solvent, using blinking optical tweezers. In particular we measure the time evolution of the distance between the two colloids to determine thei…
We introduce a model gel system in which colloidal forces, structure, and rheology are measured by balancing the requirements of rheological and microscopy techniques with those of optical tweezers. Sterically stabilized poly(methyl methacrylate) (PMMA) colloids are suspended in cyclohexane (CH) and cyclohexyl bromide (CHB) with dilute polystyrene serving as a depletion agent. A solvent comprising of 37% weight fraction CH provides sufficient refractive index contrast to enable optical trapping, while maintaining good confocal imaging quality and minimal sedimentation effects on the bulk rheol…
Understanding the out-of equilibrium behaviour of point defects in crystals, yields insights into the nature and fragility of the ordered state, as well as being of great practical importance. In some rare cases defects are spontaneously healed - a one-dimensional crystal formed by a line of identical charged particles, for example, can accommodate an interstitial (extra particle) by a re-adjusting all particle positions to even out the spacing. In sharp contrast, particles organized into a perfect hexagonal crystal in the plane cannot accommodate an interstitial by a simple re-adjustment of t…
Optical tweezers (OTs) can detect pico-Newton range forces operating on a colloidal particle trapped in a medium and have been successfully utilized to investigate complex systems with internal structures. Laponite clay particles in an aqueous medium self-assemble to form microscopic networks over time as electrostatic interactions between the particles gradually evolve in a physical aging process. We investigate the forced movements of an optically trapped micron-sized colloidal probe particle, suspended in an aging Laponite suspension, as the underlying Laponite microstructures gradually dev…
We measure hydrodynamic interactions between colloidal particles confined in a thin sheet of fluid. The reduced dimensionality, compared to a bulk fluid, increases dramatically the range of couplings. Using optical tweezers we force a two body system along the eigenmodes of the mobility tensor and find that eigen-mobilities change logarithmically with particle separation. At a hundred radii distance, the mobilities for correlated and anti-correlated motions differ by a factor of two, whereas in bulk fluids, they would be practically indistinguishable. We derive the two dimensional counterpart …
We have developed a new in situ method to calibrate optical tweezers experiments and simultaneously measure the size of the trapped particle or the viscosity of the surrounding fluid. The positional fluctuations of the trapped particle are recorded with a high-bandwidth photodetector. Next, we compute the mean-square displacement, as well as the velocity autocorrelation function of the sphere and compare it to the theory of Brownian motion including hydrodynamic memory effects. A careful measurement and analysis of the time scales characterizing the dynamics of the harmonically bound sphere fl…
Experiment, theory, and simulation are employed to understand the dispersion of colloidal particles in a periodic array of oscillating harmonic traps generated by optical tweezers. In the presence of trap oscillation, a non-monotonic and anisotropic dispersion is observed. Surprisingly, the stiffest traps produce the largest dispersion at a critical frequency, and the particles diffuse significantly faster in the direction of oscillation than those undergoing passive Stokes-Einstein-Sutherland diffusion. Theoretical predictions for the effective diffusivity of the particles as a function of tr…
We measure the colloidal interaction between two silica microspheres in aqueous solution in the distance range from $0.2\,μ$m to $0.5\,μ$m with the help of optical tweezers. When employing a sample with a low salt concentration, the resulting interaction is dominated by the repulsive double-layer interaction which is fully characterized. The double-layer interaction is suppressed when adding $0.22\,$M of salt to our sample, thus leading to a purely attractive Casimir signal. When analyzing the experimental data for the potential energy and force, we find good agreement with theoretical results…
The spin angular momentum in an elliptically polarized beam of light plays several noteworthy roles in optical traps. It contributes to the linear momentum density in a non-uniform beam, and thus to the radiation pressure exerted on illuminated objects. It can be converted into orbital angular momentum, and thus can exert torques even on optically isotropic objects. Its curl, moreover, contributes to both forces and torques without spin-to-orbit conversion. We demonstrate these effects experimentally by tracking colloidal spheres diffusing in elliptically polarized optical tweezers. Clusters o…
The intensity distribution of a holographically-projected optical trap can be tailored to the physical properties of the particles it is intended to trap. Dynamic optimization is especially desirable for manipulating dark-seeking particles that are repelled by conventional optical tweezers, and even more so when dark-seeking particles coexist in the same system as light-seeking particles. We address the need for dexterous manipulation of dark-seeking particles by introducing a class of "dark" traps created from the superposition of two out-of-phase Gaussian modes with different waist diameters…
By exerting mechanical force it is possible to unfold/refold RNA molecules one at a time. In a small range of forces, an RNA molecule can hop between the folded and the unfolded state with force-dependent kinetic rates. Here, we introduce a mesoscopic model to analyze the hopping kinetics of RNA hairpins in an optical tweezers setup. The model includes different elements of the experimental setup (beads, handles and RNA sequence) and limitations of the instrument (time lag of the force-feedback mechanism and finite bandwidth of data acquisition). We investigated the influence of the instrument…
The forces between colloidal particles at a decane-water interface, in the presence of low concentrations of a monovalent salt (NaCl) and of the surfactant sodium dodecylsulfate (SDS) in the aqueous subphase, have been studied using laser tweezers. In the absence of electrolyte and surfactant, particle interactions exhibit a long-range repulsion, yet the variation of the interaction for different particle pairs is found to be considerable. Averaging over several particle pairs was hence found to be necessary to obtain reliable assessment of the effects of salt and surfactant. It has previously…
We introduce a temporal scheme for data sampling, based on a variable delay between two successive data acquisitions. The scheme is designed so as to reduce the average data flow rate, while still retaining the information on the data evolution on fast time scales. The practical implementation of the scheme is discussed and demonstrated in light scattering and microscopy experiments that probe the dynamics of colloidal suspensions using CMOS or CCD cameras as detectors.
A Brownian particle's random motions can be rectified by a periodic potential energy landscape that alternates between two states, even if both states are spatially symmetric. If the two states differ only by a discrete translation, the direction of the ratchet-driven current can be reversed by changing their relative durations. We experimentally demonstrate flux reversal in a symmetric two-state ratchet by tracking the motions of colloidal spheres moving through large arrays of discrete potential energy wells created with dynamic holographic optical tweezers. The model's simplicity and high d…
We show that the interaction potential between sterically stabilized, nearly hard-sphere [poly(methylmethacrylate)-poly(lauryl methacrylate) (PMMA-PLMA)] colloids at a water-oil interface has a negligible unscreened-dipole contribution, suggesting that models previously developed for charged particles at liquid interfaces are not necessarily applicable to sterically stabilized particles. Interparticle potentials, $U(r)$, are extracted from radial distribution functions [$g(r)$, measured by fluorescence microscopy] via Ornstein-Zernike inversion and via a reverse Monte Carlo scheme. The results…
