Particle laden fluid interfaces: Dynamics and Interfacial rheology

Alma J. Mendoza, Eduardo Guzman, Fernando Martinez-Pedrero, Herman Ritacco, Ramon G. Rubio, Francisco Ortega, Victor M. Starov, Reinhard Miller
We review the dynamics of particle laden interfaces, both particle monolayers and particle + surfactant monolayers. We also discuss the use of the Brownian motion of microparticles trapped at fluid interfaces for measuring the shear rheology of surfactant and polymer monolayers. We describe the basic concepts of interfacial rheology and the different experimental methods for measuring both dilational and shear surface complex moduli over a broad range of frequencies, with emphasis in the micro-rheology methods. In the case of particles trapped at interfaces the calculation of the diffusion coefficient from the Brownian trajectories of the particles is calculated as a function of particle surface concentration. We describe in detail the calculation in the case of subdiffusive particle dynamics. A comprehensive review of dilational and shear rheology of particle monolayers and particle + surfactant monolayers is presented. Finally the advantages and current open problems of the use of the Brownian motion of microparticles for calculating the shear complex modulus of monolayers are described in detail.

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Dislocation reactions, grain boundaries, and irreversibility in two-dimensional lattices using topological tweezers

William T. M. Irvine, Andrew D. Hollingsworth, David G. Grier, and Paul M. Chaikin

Dislocations, disclinations, and grain boundaries are topological excitations of crystals that play a key role in determining out-of-equilibrium material properties. In this article we study the kinetics, creation, and annihilation processes of these defects in a controllable way by applying “topological tweezers,” an array of weak optical tweezers which strain the lattice by weakly pulling on a collection of particles without grabbing them individually. We use topological tweezers to deterministically control individual dislocations and grain boundaries, and reversibly create and destroy dislocation pairs in a 2D crystal of charged colloids. Starting from a perfect lattice, we exert a torque on a finite region and follow the complete step-by-step creation of a disoriented grain, from the creation of dislocation pairs through their reactions to form a grain boundary and their reduction of elastic energy. However, when the grain is rotated back to its original orientation the dislocation reactions do not retrace. Rather, the process is irreversible; the grain boundary expands instead of collapsing.
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Lipid Droplets Purified from Drosophila Embryos as an Endogenous Handle for Precise Motor Transport Measurements

Tobias F. Bartsch, Rafael A. Longoria, Ernst-Ludwig Florin, and George T. Shubeita
Molecular motor proteins are responsible for long-range transport of vesicles and organelles. Recent works have elucidated the richness of the transport complex, with multiple teams of similar and dissimilar motors and their cofactors attached to individual cargoes. The interaction among these different proteins, and with the microtubules along which they translocate, results in the intricate patterns of cargo transport observed in cells. High-precision and high-bandwidth measurements are required to capture the dynamics of these interactions, yet the crowdedness in the cell necessitates performing such measurements in vitro. Here, we show that endogenous cargoes, lipid droplets purified from Drosophila embryos, can be used to perform high-precision and high-bandwidth optical trapping experiments to study motor regulation in vitro. Purified droplets have constituents of the endogenous transport complex attached to them and exhibit long-range motility. A novel method to determine the quality of the droplets for high-resolution measurements in an optical trap showed that they compare well with plastic beads in terms of roundness, homogeneity, position sensitivity, and trapping stiffness. Using high-resolution and high-bandwidth position measurements, we demonstrate that we can follow the series of binding and unbinding events that lead to the onset of active transport.
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Optical trapping of microparticles from a stream in vacuum

D. A. Plutenko, O. M. Sarkisov, V. A. Nadtochenko
The feasibility of trapping microparticles from a stream in vacuum using dynamic optical tweezers is proven theoretically. A new approach to stabilizing particles and cooling the translational degrees of freedom by modulating power in the laser trap is presented.
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High bandwidth optical force clamp for investigation of molecular motor motion

Subhrajit Roychowdhury, Tanuj Aggarwal, Srinivasa Salapaka and Murti V. Salapaka
Use of optical tweezers for load force regulation on processive motors has yielded significant insights into intracellular transport mechanisms. The methodology developed in this letter circumvents the limitations of existing active force clamps with the use of experimentally determined models for various components of the optical tweezing system, thus making it possible to probe motor proteins at higher speeds. This paradigm also allows for real-time step estimation for step sizes as small as 8 nm with dwell time of 5 ms or higher without sacrificing force regulation.
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A Landau-Squire nanojet

Nadanai Laohakunakorn , Benjamin Gollnick , Fernando Moreno-Herrero , Dirk Aarts , Roel P.A. Dullens , Sandip Ghosal , and Ulrich F Keyser
Fluid jets are found in nature at all length scales – microscopic to cosmological. Here we report on an electroosmotically driven jet from a single glass nanopore about 75 nm in radius with a maximum flow rate ~ 30 pL/s. A novel anemometry technique allows us to map out the vorticity and velocity fields which show excellent agreement with the classical Landau-Squire solution of the Navier Stokes equations for a point jet. We observe a phenomenon that we call flow rectification: an asymmetry in the flow rate with respect to voltage reversal. Such a nanojet could potentially find applications in micro manipulation, nano patterning, and as a diode in microfluidic circuits.
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Enhanced Optical Forces by Hybrid Long-Range Plasmonic Waveguides

Lin Chen, Tian Zhang, and Xun Li
Compared with optical resonant structures, current plasmonic waveguides have the advantage of enhancing optical forces in a broad range of wavelengths, but the enhancement can only be maintained for several dozens of microns at 1.55 μm. Here, a hybrid long-range plasmonic waveguide, consisting of two identical dielectric nanowires symmetrically placed on each side of a thin metal film, is proposed for optical forces. Strong optical coupling between the dielectric waveguide mode and long-range plasmonic mode leads to enhanced optical forces on the dielectric nanowire at low input optical power due to the deep subwavelength optical energy confinement. The enhancement can be maintained for distances of 1∼2 orders of magnitude larger than that of previous plasmonic waveguides. The deep subwavelength optical confinement as well as enhanced field gradient also allows eff icient trapping of single nanoscale particle, while the smaller propagation loss ensures a much larger trapping region at the same input optical power. The present results enable the potential applications of precisely controlling the positions of dielectric nanowires as well as manipulating a single nanoparticle such as a biomolecule and one quantum dot.
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Tailoring photonic forces on a magnetodielectric nanoparticle with a fluctuating optical source

Juan Miguel Auñón, Cheng Wei Qiu, and Manuel Nieto-VesperinasWe address the forces exerted by the random electromagnetic field emitted by a fluctuating optical source on a kind of dielectric nanoparticles that have arisen much interest because of their recently shown magnetodielectric behavior. The illumination with light, or other electromagnetic wave, of a given state of coherence allows us to create photonic forces, a particular case of which are optical analogous to the Casimir-Polder and van der Waals forces, as well as of thermal forces out of thermodynamic equilibrium. This leads to a deeper understanding of the conditions and limitations under which some theories of these forces were established. We also study the effects of the coherence length and of sharp changes in the particle differential scattering cross section due to Kerker minimum forward or zero backward conditions. We show how the nanoparticle Mie resonances, constituted by the induced electric and magnetic dipoles, lead to long distance attractions to the source, as well as to the possible predominance of magnetic forces. In addition, it is shown how, by manipulating the fluctuating source, either pushing or tractor beams are obtained, even in the far zone. These effects are specially relevant when quasimonochromatic emission is employed, and manifest the possibility of performing a monitoring of these mechanical interactions, in particular by a photonic analogy of those aforementioned classical thermal forces. This opens paths to nanoparticle ensembling and manipulation. The influence of the excitation of surface waves of the source is also considered.
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Direct measurement of osmotic pressure via adaptive confinement of quasi hard disc colloids

Ian Williams, Erdal C. Oguz, Paul Bartlett, Hartmut Lowen and C. Patrick Royall
Confining a system in a small volume profoundly alters its behaviour. Hitherto, attention has focused on static confinement where the confining wall is fixed such as in porous media. However, adaptive confinement where the wall responds to the interior has clear relevance in biological systems. Here we investigate this phenomenon with a colloidal system of quasi hard discs confined by a ring of particles trapped in holographic optical tweezers, which form a flexible elastic wall. This elasticity leads to quasi-isobaric conditions within the confined region. By measuring the displacement of the tweezed particles, we obtain the radial osmotic pressure. We further find a novel bistable state of a hexagonal structure and concentrically layered fluid mimicking the shape of the confinement. The hexagonal configurations are found at lower pressure than those of the fluid, thus the bistability is driven by the higher entropy of disordered arrangements, unlike bulk hard systems.

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Radiation force of abruptly autofocusing Airy beams on a Rayleigh particle

Yunfeng Jiang, Kaikai Huang, and Xuanhui Lu
The radiation force of circular Airy beams (CAB) on a dielectric Rayleigh particle is investigated in this paper. Our results show that the CAB can be used to trap the particle whose refractive index is larger than the ambient at different positions along the beam axis. Comparing with the Gaussian beam under the same conditions, the longitudinal and the transverse gradient force of CAB on the Rayleigh particle are increased, and the particle can be trapped more stable. Our analyses also demonstrate that the trapping properties of CAB can be modulated by controlling corresponding parameters of CAB.
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Laser trapping-induced crystallization of L-phenylalanine through its high concentration domain formation

Ken-ichi Yuyama, Chi-Shiun Wu, Teruki Sugiyama and Hiroshi Masuhara
We present laser trapping-induced crystallization of L-phenylalanine through high concentration domain formation in H2O and D2O solutions which is achieved by focusing a continuous-wave (CW) near-infrared laser beam at the solution surface. Upon the laser irradiation into the H2O solution, laser trapping of the liquid-like clusters increases local concentration, accompanying laser heating, and a single plate-like crystal is eventually prepared at the focal spot. On the other hand, in the D2O solution, a lot of the monohydrate needle-like crystals are observed not at the focal spot where concentration is high enough to trigger crystal nucleation, but in 0.5–1.5 millimetres range from the focal spot. The dynamics and mechanism of the amazing crystallization behaviour induced by laser trapping are discussed from the viewpoints of concentration increase due to laser heating depending on solvent, large high concentration domain formation by laser trapping of liquid-like clusters, and orientational disorder of molecules/clusters at the domain edge.
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Phase-separation and photoresponse in binary azobenzene-containing polymer vesicles

Guosheng Xue, Kun Chen, Guangyong Shen, Ziqiang Wang, Qijin Zhang, Jun Cai , Yinmei Li

Understanding the photoresponse of azobenzene polymer in different conditions is essential for the potential application of azobenzene-based technologies. Herein, the microscale, photoresponsive hybrid polymersomes (polymer vesicles) composed of binary blends of azobenzene-containing block copolymers is prepared. The Janus morphology which presents phase-separation within the surface of hybrid polymersomes is observed. The composition and photoisomerization characteristic time of different domains are studied with Laser Trapping Raman Spectroscope (LTRS) system. The results indicated that the morphology of polymersomes can be tuned by the ratio of azobenzene-containing copolymer contents. We find the photoisomerization rate of azobenzene in hybrid vesicles is marginally slower than those in pure vesicles. These experiments provide a quantitative measurement method for dynamic photoresponse of azobenzene hybrid polymersomes.

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The Role of Vimentin Intermediate Filaments in Cortical and Cytoplasmic Mechanics

Ming Guo, Allen J. Ehrlicher, Saleemulla Mahammad|, Hilary Fabich, Mikkel H. Jensen, Jeffrey R. Moore, Jeffrey J. Fredberg, Robert D. Goldman, David A. Weitz
The mechanical properties of a cell determine many aspects of its behavior, and these mechanics are largely determined by the cytoskeleton. Although the contribution of actin filaments and microtubules to the mechanics of cells has been investigated in great detail, relatively little is known about the contribution of the third major cytoskeletal component, intermediate filaments (IFs). To determine the role of vimentin IF (VIF) in modulating intracellular and cortical mechanics, we carried out studies using mouse embryonic fibroblasts (mEFs) derived from wild-type or vimentin−/− mice. The VIFs contribute little to cortical stiffness but are critical for regulating intracellular mechanics. Active microrheology measurements using optical tweezers in living cells reveal that the presence of VIFs doubles the value of the cytoplasmic shear modulus to ∼10 Pa. The higher levels of cytoplasmic stiffness appear to stabilize organelles in the cell, as measured by tracking endogenous vesicle movement. These studies show that VIFs both increase the mechanical integrity of cells and localize intracellular components.
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A microengineered cell fusion approach with combined optical tweezers and microwell array technologies

Xiaolin Wang, Shuxun Chen, Yu Ting Chow, Chi-Wing Kong, Ronald A Li and Dong Sun

Cell fusion in vitro can be artificially achieved through microengineering technology. This paper presents a laser-induced cell fusion methodology on the microwell array-based microfluidic chip, with high selectivity and controllability at the single cell level. Optical tweezers and optical scissors are employed to achieve cell pairing and fusion, respectively. The specific cells are first characterized with high spatio-temporal resolution and preselected from the mixture through an on-chip isolation method prior to pairing. The paired cells are then transported, deposited, fused, and released at the desired location with high controllability. Biophysical analysis on the fused cells shows that the fusion efficiency of the homotypical pairs is higher than that of the heterogenic pairs obtained based on different combinations of sample cells, such as human embryonic stem cells and Jurkat cells. This laser-induced cell fusion technique offers a new opportunity to explore specific targeted therapy in stem cell research for the treatment of human diseases.
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Invited Article: A review of haptic optical tweezers for an interactive microworld exploration

Cécile Pacoret and Stéphane Régnier
This paper is the first review of haptic optical tweezers, a new technique which associates force feedback teleoperation with optical tweezers. This technique allows users to explore the microworld by sensing and exerting picoNewton-scale forces with trapped microspheres. Haptic optical tweezers also allow improved dexterity of micromanipulation and micro-assembly. One of the challenges of this technique is to sense and magnify picoNewton-scale forces by a factor of 10^12 to enable human operators to perceive interactions that they have never experienced before, such as adhesion phenomena, extremely low inertia, and high frequency dynamics of extremely small objects. The design of optical tweezers for high quality haptic feedback is challenging, given the requirements for very high sensitivity and dynamic stability. The concept, design process, and specification of optical tweezers reviewed here are focused on those intended for haptic teleoperation. In this paper, two new specific designs as well as the current state-of-the-art are presented. Moreover, the remaining important issues are identified for further developments. The initial results obtained are promising and demonstrate that optical tweezers have a significant potential for haptic exploration of the microworld. Haptic optical tweezers will become an invaluable tool for force feedback micromanipulation of biological samples and nano- and micro-assembly parts.
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The molecular yo-yo method: Live jump detection improves throughput of single-molecule force spectroscopy for out-of-equilibrium transitions

A. H. Mack, D. J. Schlingman, M. Kamenetska, R. Collins, L. Regan, and S. G. J. Mochrie

By monitoring multiple molecular transitions, force-clamp, and trap-position-clamp methods have led to precise determinations of the free energies and free energy landscapes for molecular states populated in equilibrium at the same or similar forces. Here, we present a powerful new elaboration of the force-clamp and force-jump methods, applicable to transitions far from equilibrium. Specifically, we have implemented a live jump detection and force-clamp algorithm that intelligently adjusts and maintains the force on a single molecule in response to the measured state of that molecule. We are able to collect hundreds of individual molecular transitions at different forces, many times faster than previously, permitting us to accurately determine force-dependent lifetime distributions and reaction rates. Application of our method to unwinding and rewinding the nucleosome inner turn, using optical tweezers reveals experimental lifetime distributions that comprise a statistically meaningful number of transitions, and that are accurately single exponential. These measurements significantly reduce the error in the previously measured rates, and demonstrate the existence of a single, dominant free energy barrier at each force studied. A key benefit of the molecular yo-yo method for nucleosomes is that it reduces as far as possible the time spent in the tangentially bound state, which minimizes the loss of nucleosomes by dissociation.
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Vesicle Photonics

A.E. Vasdekis, E.A. Scott, S. Roke, J.A. Hubbell, and D. Psaltis
Amphiphiles, under appropriate conditions, can self-assemble into nanoscale thin membrane vessels (vesicles) that encapsulate and hence protect and transport molecular payloads. Vesicles assemble naturally within cells but can also be artificially synthesized. In this article, we review the mechanisms and applications of light-field interactions with vesicles. By being associated with light-emitting entities (e.g., dyes, fluorescent proteins, or quantum dots), vesicles can act as imaging agents in addition to cargo carriers. Vesicles can also be optically probed on the basis of their nonlinear response, typically from the vesicle membrane. Light fields can be employed to transport vesicles by using optical tweezers (photon momentum) or can directly perturb the stability of vesicles and hence trigger the delivery of the encapsulated payload (photon energy). We conclude with emerging vesicle applications in biology and photochemical microreactors.
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Potential energy profile of colloidal nanoparticles in optical confinement

Jinxin Fu, Qiwen Zhan, Min Yao Lim, Zhiyuan Li, and H. Daniel Ou-Yang
An optical bottle method is developed to determine the potential-energy profile of colloidal Rayleigh nanoparticles in an optical trap. The three-dimensional distribution of fluorescent particles in the trap is measured by laser scanning confocal fluorescence microscopy. At sufficiently low concentrations at which interactions between the particles are negligible, the single-particle trapping potential-energy profile is determined from the equilibrium number-density profile by use of the Boltzmann distribution. Fluorescence imaging as well as calculations based on a discrete dipole approximation show that effects due to scattering forces are negligible for polystyrene particles of size less than 10% of the wavelength of the trapping laser, thus justifying the assumption of conservative forces in the equilibrium potential-energy determinations. The new optical bottle method measures the entire two-dimensional trapping-potential profile for an individual nanoparticle without the restriction that only one particle be contained in the trap, thus obviating the need for high laser power.

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Fast Detection of Saxitoxin Using Laser Tweezers Surface Enhanced Raman Spectroscopy

Qiyong Huai, Chunlei Gao, Jinlai Miao, huilu yao and Zongling Wang
Saxitoxin (STX) is a potent marine biotoxin which can cause paralytic shellfish poisoning when consumed. With the development of research, STX has become more and more important in red tide detection, medical research, food safety and warfare agent application. However, new methods for the fast analysis of STX are required. In this study, we used laser optical tweezers Raman spectroscopy (LTRS) combined with surface-enhanced Raman scattering (SERS) to detect STX. Very strong intensity and sharp Raman peaks were achieved. The spectra were obtained at 2 seconds without accumulations. Tentative vibrational mode assignments of the observed peaks for SERS spectra of STX are described. The detection limit and the minimum quantitative limit of this method were 2 nM and 16 nM, respectively. This study supports LTRS - SERS as a new fast, convenient analytical method for STX and other toxicants and pollutants in the environment.
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Motor Domain Phosphorylation Modulates Kinesin-1 Transport

Hannah A. DeBerg, Benjamin H. Blehm, Janet Sheung, Andrew R. Thompson, Carol S. Bookwalter, Seyed F. Torabi, Trina A. Shroer, Christopher L. Berger, Yi Lu, Kathleen M. Trybus and Paul R. Selvin
Disruptions in microtubule motor-transport are associated with a variety of neurodegenerative diseases. Post-translational modification of the cargo binding domain of the light- and heavy-chains of kinesin has been shown to regulate transport, but less is known about how modifications of the motor domain affect transport. Here we report on the effects of phosphorylation of a mammalian kinesin motor domain by the kinase JNK3 at a conserved serine residue (S175 in the B isoform and S176 in the A and C isoforms). Phosphorylation of this residue has been implicated in Huntington's disease, but the mechanism by which S175 phosphorylation affects transport is unclear. The ATPase, microtubule binding affinity, and processivity, are unchanged between a phosphomimetic S175D and a non-phosphorylatable S175A construct. However, we find that application of force differentiates between the two. Placement of negative charge at S175, through phosphorylation or mutation, leads to a lower stall force and decreased velocity under a load of 1 pN or greater. Sedimentation velocity experiments also show that addition of a negative charge at S175 favors the autoinhibited conformation of kinesin. These observations imply that when cargo is transported by both dynein and phosphorylated kinesin, a common occurrence in the cell, there may be a bias that favors motion toward the minus-end of microtubules. Such bias could be used to tune transport in healthy cells when properly regulated, but contribute to a disease state when misregulated.

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Enhancement of ADP release from the RAD51 presynaptic filament by the SWI5-SFR1 complex

Guan-Chin Su, Chan-I Chung, Chia-Yu Liao, Sheng-Wei Lin, Cheng-Ting Tsai,Tao Huang, Hung-Wen Li and Peter Chi

Homologous recombination catalyzed by the RAD51 recombinase eliminates deleterious DNA lesions from the genome. In the presence of ATP, RAD51 forms a nucleoprotein filament on single-stranded DNA, termed the presynaptic filament, to initiate homologous recombination-mediated DNA double-strand break repair. The SWI5-SFR1 complex stabilizes the presynaptic filament and enhances its ability to mediate the homologous DNA pairing reaction. Here we characterize the RAD51 presynaptic filament stabilization function of the SWI5-SFR1 complex using optical tweezers. Biochemical experiments reveal that SWI5-SFR1 enhances ATP hydrolysis by single-stranded DNA-bound RAD51. Importantly, we show that SWI5-SFR1 acts by facilitating the release of ADP from the presynaptic filament. Our results thus provide mechanistic understanding of the function of SWI5-SFR1 in RAD51-mediated DNA recombination.

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Optodynamic phenomena in aggregates of polydisperse plasmonic nanoparticles

A. E. Ershov, A. P. Gavrilyuk, S. V. Karpov, P. N. Semina
We propose an optodynamical model of interaction of pulsed laser radiation with aggregates of spherical metallic nanoparticles embedded into host media. The model takes into account polydispersity of particles, pair interactions between the particles, dissipation of absorbed energy, heating and melting of the metallic core of particles and of their polymer adsorption layers, and heat exchange between electron and ion components of the particle material as well as heat exchange with the interparticle medium. Temperature dependence of the electron relaxation constant of the particle material and the effect of this dependence on interaction of nanoparticles with laser radiation are first taken into consideration. We study in detail light-induced processes in the simplest resonant domains of multiparticle aggregates consisting of two particles of an arbitrary size in aqueous medium. Optical interparticle forces are realized due to the light-induced dipole interaction. The dipole moment of each particle is calculated by the coupled dipole method (with correction for the effect of higher multipoles). We determined the role of various interrelated factors leading to photomodification of resonant domains and found an essential difference in the photomodification mechanisms between polydisperse and monodisperse nanostructures.
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Using optical tweezers to investigate the specific single-interaction between apoA-I molecule and ABCA1 on living cells

Jie Yu, Xunliang Tong, Chengbin Li, Yining Huang, and Anpei Ye
We carry out in situ single-molecule measurements of the specific interaction between apolipoprotein A-I (apoA-I) and ATP binding cassette transporter A1 (ABCA1) on THP-1 cells. Single-molecule force spectroscopy shows that similar to normal apoA-I, the dysfunctional apoA-I from diabetes patients interacts with ABCA1 via two different binding sites on the cells. The strength of dysfunctional apoA-I binding to a high-capacity binding site is 26.5+(-)4.9 pN. The minor direct apoA-I/ABCA1 binding strength is 56.7+(-)4.1 pN. These results facilitate a pathological understanding of the mechanisms that underlie the specific interaction of apoA-I and ABCA1 at the single-molecule level.
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Measurement of the binding force between RAS protein and a pathologic BRAF mutant using optical tweezers

Cheng Wen; and Anpei Ye
Activating mutants in rat sarcoma (RAS) and B-rapid accelerated fibrosarcoma (BRAF) are found in at least a third of cases of human tumors and melanoma; hence, numerous therapeutic treatments target this pathway. In this letter, we study the adhesion force of RAS-coated beads with BRAF-coated beads, BRAF (A246P) mutant-coated beads, and GST-coated beads using optical tweezers. One full and two fractional RAS-BRAF specific binding modes are identified using the rupture force distribution. The koff (0) of the full binding mode in RAS-BRAF is 3.71×10-4/s and 1.16×10-4s-1 in RAS-BRAF (A246P), whereas the xb is around 3 \times 10-10 m in both groups.

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Bond elasticity controls molecular recognition specificity in antibody-antigen binding

Anna Alemany, Nuria Sanvicens, Sara de Lorenzo, M.-Pilar Marco, and Felix Ritort
Force-spectroscopy experiments make it possible to characterize single ligand-receptor pairs. Here we measure the spectrum of bond strengths and flexibilities in antibody-antigen interactions using optical tweezers. We characterize the mechanical evolution of polyclonal antibodies generated under infection and the ability of a monoclonal antibody to cross-react against different antigens. Our results suggest that bond flexibility plays a major role in remodeling antibody-antigen bonds in order to improve recognition during the maturation of the humoral immune system.
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Optical manipulation: Momentum exchange effect

Masud Mansuripur
A pulling force can be generated via amplification of the photon linear momentum when a fairly uniform light field passes from one dielectric to another with a higher refractive index. This force can drag small objects over macroscopic distances along dielectric interfaces.
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