Simon Hanna

Hydration of Nafion® studied by AFM and X-ray scattering

Nafion® is a commercially available perfluorosulphonate cation exchange membrane commonly used as a perm-selective separator in chlor-alkali electrolysers and as the electrolyte in solid polymer fuel cells. This usage arises because of its high mechanical, thermal and chemical stability coupled with its high conductivity and ionic selectivity, which depend strongly on the water content. The membrane was therefore studied in different states of hydration with two complementary techniques: atomic force microscopy (AFM) and small angle X-ray scattering (SAXS) combined with a maximum entropy (MaxEnt) reconstruction. Tapping mode phase imaging was successfully used to identify the hydrophobic and hydrophilic regions of Nafion. The images support the MaxEnt interpretation of a cluster model of ionic aggregation, with spacings between individual clusters ranging from 3 to 5 nm, aggregating to form cluster agglomerates with sizes from 5 to 30 nm. Both techniques indicate that the number density of ionic clusters changes as a function of water content, and this explains why the bulk volumetric swelling in water is observed to be significantly less than the swelling inferred from scattering measurements.

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.

The swelling behaviour of perfluorinated ionomer membranes in ethanol/water mixtures

Abstract The microscopic and bulk swelling of “Nafion®” perfluorinated ionomer membranes in mixtures of ethanol and water was studied using small angle X-ray diffraction and optical microscopy. The microscopic swelling decreased with increasing ethanol content, in contrast to the bulk swelling which increased dramatically, reaching a maximum in a mixture containing 75% ethanol and 25% water. Uniaxially oriented membranes swollen with such an optimal mixture were found to relax back to an almost isotropic state, which could not be achieved by using water alone. The conclusion is that the ethanol plasticises the fluorocarbon matrix in Nafion, allowing the ionic material to be redistributed into smaller, more numerous clusters than in membranes swollen with water alone.

An optically actuated surface scanning probe

We demonstrate the use of an extended, optically trapped probe that is capable of imaging surface topography with nanometre precision, whilst applying ultra-low, femto-Newton sized forces. This degree of precision and sensitivity is acquired through three distinct strategies. First, the probe itself is shaped in such a way as to soften the trap along the sensing axis and stiffen it in transverse directions. Next, these characteristics are enhanced by selectively position clamping independent motions of the probe. Finally, force clamping is used to refine the surface contact response. Detailed analyses are presented for each of these mechanisms. To test our sensor, we scan it laterally over a calibration sample consisting of a series of graduated steps, and demonstrate a height resolution of ∼ 11 nm. Using equipartition theory, we estimate that an average force of only ∼ 140 fN is exerted on the sample during the scan, making this technique ideal for the investigation of delicate biological samples.

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.

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.

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.

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.

Atomistic simulation of a model liquid crystal

We present atomistic molecular dynamics computer simulations of the bulk phases of a model liquid crystal system based on 8CB. The model differs from real 8CB because it employs a united-atom description to eliminate all hydrogen atoms, and neglects all long-range electrostatic interactions. Despite this simplification, the pressure-temperature phase diagram shows an order-disorder transition, in which isotropic, smectic, and nematiclike behaviors are observed. A detailed analysis of the inter- and intramolecular structures of the ordered phases is given, together with an examination of finite size effects and the equilibration times of the system. It is shown that, whereas a system may appear to be thermodynamically and mechanically equilibrated after a period of 10-15 ns, it is possible for an imprint of the starting configuration to persist for much longer time scales. In the present case, however, such an imprint does not appear to affect the observed phase behavior.

Force sensing with a shaped dielectric micro-tool

We analyse the thermal motion of a holographically trapped non-spherical force probe, capable of interrogating arbitrary samples with nanometer resolution. High speed video stereo-microscopy is used to track the translational and rotational coordinates of the micro-tool in three dimensions, and the complete 6 × 6 stiffness matrix for the system is determined using equipartition theorem. The Brownian motion of the extended structure is described in terms of a continuous distribution of thermal ellipsoids. A centre of optical stress, at which rotational and translational motion is uncoupled, is observed and controlled. Once calibrated, the micro-tool is deployed in two modes of operation: as a force sensor with <150 femto-Newton sensitivity, and in a novel form of photonic force microscopy.