Determining nanorod dimensions in dispersion with size anisotropy nanoparticle tracking analysis.

Control over nanorod dimensions is critical to their application, requiring fast, robust characterisation of their volume and aspect ratio whilst in their working medium. Here, we present an extension of Nanoparticle Tracking Analysis which determines the aspect ratio of nanoparticles from the polarisation state of scattered light in addition to a hydrodynamic diameter from Brownian motion. These data, in principle, permit the determination of nanorod dimensions of any composition using Nanoparticle Tracking Analysis. The results are compared with transmission electron microscopy and show that this technique can additionally determine the aggregation state of the nanorod dispersion if single nanorod dimensions are determined with a complementary technique. We also show it is possible to differentiate nanoparticles of similar hydrodynamic diameter by their depolarised scattering. Finally, we assess the ability of the technique to output nanorod dimensions and suggest ways to further improve the approach. This technique will enable rapid characterisation of nanorods in suspension, which are important tools for nanotechnology.

Scale-invariance in miniature coarse-grained red blood cells by fluctuation analysis.

To accurately represent the morphological and elastic properties of a human red blood cell, Fu et al. [Fu et al., Lennard-Jones type pair-potential method for coarse-grained lipid bilayer membrane simulations in LAMMPS, 2017, 210, 193-203] recently developed a coarse-grained molecular dynamics model with particular detail in the membrane. However, such a model accrues an extremely high computational cost for whole-cell simulation when assuming an appropriate length scaling - that of the bilayer thickness. To date, the model has only simulated "miniature" cells in order to circumvent this, with the a priori assumption that these miniaturised cells correctly represent their full-sized counterparts. The present work assesses the validity of this approach, by testing the scale invariance of the model through simulating cells of various diameters; first qualitatively in their shape evolution, then quantitatively by measuring their bending rigidity through fluctuation analysis. Cells of diameter of at least 0.5 µm were able to form the characteristic biconcave shape of human red blood cells, though smaller cells instead equilibrated to bowl-shaped stomatocytes. Thermal fluctuation analysis showed the bending rigidity to be constant over all cell sizes tested, and consistent between measurements on the whole-cell and on a planar section of bilayer. This is as expected from the theory on both counts. Therefore, we confirm that the evaluated model is a good representation of a full-size RBC when the model diameter is ≥0.5 µm, in terms of the morphological and mechanical properties investigated.

Optical Binding of Nanowires.

Multiple scattering of light induces structured interactions, or optical binding forces, between collections of small particles. This has been extensively studied in the case of microspheres. However, binding forces are strongly shape dependent: here, we turn our attention to dielectric nanowires. Using a novel numerical model we uncover rich behavior. The extreme geometry of the nanowires produces a sequence of stationary and dynamic states. In linearly polarized light, thermally stable ladder-like structures emerge. Lower symmetry, sagittate arrangements can also arise, whose configurational asymmetry unbalances the optical forces leading to nonconservative, translational motion. Finally, the addition of circular polarization drives a variety of coordinated rotational states whose dynamics expose fundamental properties of optical spin. These results suggest that optical binding can provide an increased level of control over the positions and motions of nanoparticles, opening new possibilities for driven self-organization and heralding a new field of self-assembling optically driven micromachines.

Photonic Torque Microscopy of the Nonconservative Force Field for Optically Trapped Silicon Nanowires.

We measure, by photonic torque microscopy, the nonconservative rotational motion arising from the transverse components of the radiation pressure on optically trapped, ultrathin silicon nanowires. Unlike spherical particles, we find that nonconservative effects have a significant influence on the nanowire dynamics in the trap. We show that the extreme shape of the trapped nanowires yields a transverse component of the radiation pressure that results in an orbital rotation of the nanowire about the trap axis. We study the resulting motion as a function of optical power and nanowire length, discussing its size-scaling behavior. These shape-dependent nonconservative effects have implications for optical force calibration and optomechanics with levitated nonspherical particles.

Mass-manufacturable polymer microfluidic device for dual fiber optical trapping.

We present a microfluidic chip in Polymethyl methacrylate (PMMA) for optical trapping of particles in an 80µm wide microchannel using two counterpropagating single-mode beams. The trapping fibers are separated from the sample fluid by 70µm thick polymer walls. We calculate the optical forces that act on particles flowing in the microchannel using wave optics in combination with non-sequential ray-tracing and further mathematical processing. Our results are compared with a theoretical model and the Mie theory. We use a novel fabrication process that consists of a premilling step and ultraprecision diamond tooling for the manufacturing of the molds and double-sided hot embossing for replication, resulting in a robust microfluidic chip for optical trapping. In a proof-of-concept demonstration, we show the trapping capabilities of the hot embossed chip by trapping spherical beads with a diameter of 6µm, 8µm and 10µm and use the power spectrum analysis of the trapped particle displacements to characterize the trap strength.

Optimal hydrodynamic synchronization of colloidal rotors.

Synchronization of driven oscillators is a key aspect of flow generation in artificial and biological filaments such as cilia. Previous theoretical and numerical studies have considered the "rotor" model of a cilium in which the filament is coarse grained into a colloidal sphere driven with a given force law along a predefined trajectory to represent the oscillating motion of the cilium. These studies pointed to the importance of two factors in the emergence of synchronization: the modulation of the driving force around the orbit and the deformability of the trajectory. In this work it is shown via experiments, supported by numerical simulations and theory, that both of these factors are important and can be combined to produce strong synchronization (within a few cycles) even in the presence of thermal noise.

Optical lift from dielectric semicylinders.

A wave optics numerical analysis of the force and torque on a semicylindrical optical wing is presented. Comparisons with a recently reported ray optics analysis indicate good agreement when the radius is large compared with the wavelength of light, as expected. Surprisingly, we find that the dominant rotationally stable angle of attack at α≈-15° is relatively invariant to changes in radius and refractive index. However, the torsional stiffness at the equilibrium point is found to increase, approximately, as the cubic power of the radius. Quasi-resonant internal modes of light produce complex size-dependent variations of the angle and magnitude of the optical lift force.

Application of the discrete dipole approximation to optical trapping calculations of inhomogeneous and anisotropic particles.

The accuracy of the discrete dipole approximation (DDA) for computing forces and torques in optical trapping experiments is discussed in the context of dielectric spheres and a range of low symmetry particles, including particles with geometric anisotropy (spheroids), optical anisotropy (birefringent spheres) and structural inhomogeneity (core-shell spheres). DDA calculations are compared with the results of exact T-matrix theory. In each case excellent agreement is found between the two methods for predictions of optical forces, torques, trap stiffnesses and trapping positions. Since the DDA lends itself to calculations on particles of arbitrary shape, the study is augmented by considering more general systems which have received recent experimental interest. In particular, optical forces and torques on low symmetry letter-shaped colloidal particles, birefringent quartz cylinders and biphasic Janus particles are computed and the trapping behaviour of the particles is discussed. Very good agreement is found with the available experimental data. The efficiency of the DDA algorithm and methods of accelerating the calculations are also discussed.

Optical trapping of microrods: variation with size and refractive index.

Optical traps can be characterized in terms of two simple parameters: the stiffness, given by the gradient of the force at mechanical equilibrium, and the strength, as expressed by the maximum restoring force available for displacement in a given direction. We present numerical calculations of these quantities for dielectric microrods of varying radius and refractive index held horizontally in pairs of holographically generated Gaussian beams. The resulting variations are seen to be influenced by optical resonances, as well as by the relative sizes of the beam waist and rod diameter. In addition, it is shown that trapping in these systems is sensitive to the polarization state of the incident field; i.e., for certain rods, trapping will occur for beams polarized perpendicular to the long axis of the rod, but not for beams polarized parallel to the long axis. Finally, friction coefficients are evaluated and used to estimate the maximum rates at which the rods may be dragged through the ambient medium.

Orbital motion of optically trapped particles in Laguerre-Gaussian beams.

A theoretical examination of off-axial trapping in non-paraxial Laguerre-Gaussian beams is presented for both the Rayleigh and Mie regimes. It is well known that the force acting on a particle may be divided into a term proportional to the intensity gradient and another representing the scattering force. The latter term may be further sub-divided into a dissipative radiation force and a term dependent on the electric field gradient. For Rayleigh particles in Laguerre-Gaussian beams, it is shown that the field gradient term contributes exactly half of the scattering force. This may be compared with a plane wave, in which it makes zero contribution. The off-axis trapping positions for spheres with radii varying from 0.1 to 0.5 mum and a range of refractive indices are calculated numerically in the Mie regime, using a conjugate gradient approach. Azimuthal forces and orbital torques are presented for particles in their trapping positions, for beams with different orbital angular momentum and polarization states. The components of a "spin" torque, acting through the center of the particle, are also computed for absorbing particles in the Mie regime.

Holographic optical trapping of microrods and nanowires.

Holographic optical tweezing permits the trapping of objects with less than spherical symmetry in appropriately distributed sets of beams thereby permitting control to be exerted over both the orientation and position. In contrast to the familiar case of the singly trapped sphere, the stiffness and strength of such compound traps will have rotational components. We investigate this for a simple model system consisting of multiply trapped dielectric cylinder. Optically induced forces and torques are evaluated using the discrete dipole approximation and the resulting trap stiffnesses are presented. A variety of configurations of trapping beams are considered. Hydrodynamic resistances for the cylinder are also calculated and used to estimate translation and rotation rates. A number of conclusions are reached concerning the optimal trapping and dragging conditions for the rod. In particular, it is clear that it is advantageous to drag a rod in a direction perpendicular rather than parallel to its length. In addition, it is observed that the polarization of the incident light plays a significant role. Finally, it is noted that the non-conservative nature of the optical force field manifests itself directly in the stiffness of the trapped cylinder. The consequences of this last point are discussed.

First-order nonconservative motion of optically trapped nonspherical particles.

It is well known that optical force fields are not conservative. This has important consequences for the thermal motion of optically trapped dielectric spheres. In particular, the spheres do not reach thermodynamic equilibrium. Instead, a steady state is achieved in which the stochastic trajectory contains an underlying deterministic bias toward cyclic motion, and the energy of the sphere deviates from that implied by the equipartition theorem. Such effects are second order and only observed at low trap powers when the sphere is able to explore regions of the trap beyond the linear regime. Analogous effects may be expected for particles of less than spherical symmetry. However, in this case the effects are first order and depend on the linear term in the optical force field. As such they are not suppressed by increases in beam power, although the frequency and amplitude of the cyclic motion will be affected by it. In this paper, we present an analysis of the first-order nonconservative behavior of nonspherical particles in optical traps. The analysis is supported by optical force calculations and brownian dynamics simulations of dielectric microrods held vertically in gaussian optical traps.

Thermal motion of a holographically trapped SPM-like probe.

By holding a complex object in multiple optical traps, it may be harmonically bound with respect to both its position and its orientation. In this way a small probe, or nanotool, can be manipulated in three dimensions and used to measure and apply directed forces, in the manner of a scanning probe microscope. In this paper we evaluate the thermal motion of such a probe held in holographic optical tweezers, by solving the Langevin equation for the general case of a set of spherical vertices linked by cylindrical rods. The concept of a corner frequency, familiar from the case of an optically trapped sphere, is appropriately extended to represent a set of characteristic frequencies given by the eigenvalues of the product of the stiffness matrix and the inverse hydrodynamic resistance matrix of the tool. These eigenvalues may alternatively be interpreted as inverses of a set of characteristic relaxation times for the system. The approach is illustrated by reference to a hypothetical tool consisting of a triangular arrangement of spheres with a lateral probe. The characteristic frequencies and theoretical resolution of the device are derived; variations of these quantities with tool size and orientation and with the optical power distribution, are also considered.

Optical angular momentum transfer by Laguerre-Gaussian beams.

It is well known that Laguerre-Gaussian beams carry angular momentum and that this angular momentum has a mechanical effect when such beams are incident on particles whose refractive indices differ from those of the background medium. Under conditions of tight focusing, intensity gradients arise that are sufficiently large to trap micrometer-sized particles, permitting these mechanical effects to be observed directly. In particular, when the particles are spherical and absorbing, they rotate steadily at a rate that is directly proportional to the theoretical angular momentum flux of the incident beam. We note that this behavior is peculiar to absorbing spheres. For arbitrary, axially placed particles the induced torque for rotation angle zeta is shown to be Gammaz=Asin(2zeta+delta)+B, where A, B, and delta are constants that are determined by the mechanisms coupling optical and mechanical angular momentum. The resulting behavior need not be directly related to the total angular momentum in the beam but can, nonetheless, be understood in terms of an appropriate torque density. This observation is illustrated by calculations of the torque induced in optically and geometrically anisotropic particles using a T-matrix approach.

Rotation of absorbing spheres in Laguerre-Gaussian beams.

It is well known that optical vortex beams carry orbital as well as spin angular momentum. This optical angular momentum can manifest itself mechanically, for example in tightly focused Laguerre-Gaussian beams, where trapped, weakly absorbing spheres rotate at a rate proportional to the total angular momentum carried by the beam. In the present paper we subject this system to a rigorous analysis involving expansions in vector spherical wave functions that culminates in a simple expression for the torque on the sphere. It is seen that, for large weakly absorbing spheres, the induced torque per unit power is independent of the detailed structure of the incident field, being a simple function of two indices that describe the helicity and polarization state of the beam, the relative refractive indices of the sphere and ambient medium, the absorption index of the sphere, and its radius. A number of relationships between the coefficients of these expansions are also developed.

FDTD simulations of forces on particles during holographic assembly.

We present finite-difference time-domain (FDTD) calculations of the forces and torques on dielectric particles of various shapes, held in one or many Gaussian optical traps, as part of a study of the physical limitations involved in the construction of micro- and nanostructures using a dynamic holographic assembler (DHA). We employ a full 3-dimensional FDTD implementation, which includes a complete treatment of optical anisotropy. The Gaussian beams are sourced using a multipole expansion of a fifth order Davis beam. Force and torques are calculated for pairs of silica spheres in adjacent traps, for silica cylinders trapped by multiple beams and for oblate silica spheroids and calcite spheres in both linearly and circularly polarized beams. Comparisons are drawn between the magnitudes of the optical forces and the Van der Waals forces acting on the systems. The paper also considers the limitations of the FDTD approach when applied to optical trapping.

Computer simulations of wetting of solid surfaces by liquid crystals.

Atomistic computer simulations are presented, consisting of droplets of model liquid crystal molecules wetting a generic crystalline surface. It is shown that the type of wetting that occurs is highly dependent on the value of the surface interaction parameter epsilon{fs} , switching between partial wetting (no spreading) for epsilon{fs}=2.0 to complete wetting for epsilon{fs}=2.5 . epsilon{fs} is the multiplicative factor which scales the well depth of the fluid-surface interaction energy. During complete wetting, the spreading occurs through the growth of a precursor layer, and a set of secondary terraces. The temperature affects the structure of the droplet, as might be expected when different phases are sampled, and also the shape of the spreading droplet, and the rate of spreading. In particular, in the smectic-A phase at 350K, for values of epsilon{fs} just large enough to induce complete wetting, the precursor film assumes a diamond shape, with edges normal to the [110] directions in the crystal surface. It is shown that spreading occurs through diffusion across the surface, with the radius of the precursor layer increasing with the square root of time. Mass flow studies indicate that the spreading occurs by molecules cascading over the top of the droplet to feed the growing precursor layer. Calculations of contact angle relaxation are in qualitative agreement with experimental findings.

Optical trapping of spheroidal particles in Gaussian beams.

The T matrix method is used to compute equilibrium positions and orientations for spheroidal particles trapped in Gaussian light beams. It is observed that there is a qualitative difference between the behavior of prolate and oblate ellipsoids in linearly polarized Gaussian beams; the former generally orient with the symmetry axis parallel to the beam except at very small particle sizes, while the latter orient with the symmetry axis perpendicular to the beam. In the presence of a circularly polarized beam, it is demonstrated that oblate ellipsoids will experience a torque about the beam axis. However, for a limited range of particle sizes, where the particle dimensions are comparable with the beam waist, the particles are predicted to rotate in a sense counter to the sense of rotation of the circular polarization. This unusual prediction is discussed in some detail.