Brownian Dynamics of a Sphere Between Parallel Walls

We describe direct imaging measurements of a colloidal sphere's diffusion between two parallel surfaces. The dynamics of this deceptively simple hydrodynamically coupled system have proved difficult to analyze. Comparison with approximate formulations of a confined sphere's hydrodynamic mobility reveals good agreement with both a leading-order superposition approximation as well as a more general all-images stokeslet analysis.Comment: 4 pages, 3 figures, REVTeX with PostScript figure

Strain-dependent solid surface stress and the stiffness of soft contacts

Surface stresses have recently emerged as a key player in the mechanics of highly compliant solids. The classic theories of contact mechanics describe adhesion with a compliant substrate as a competition between surface energies driving deformation to establish contact and bulk elasticity resisting this. However, it has recently been shown that surface stresses provide an additional restoring force that can compete with and even dominate over elasticity in highly compliant materials, especially when length scales are small compared to the ratio of the surface stress to the elastic modulus, $\Upsilon/E$. Here, we investigate experimentally the contribution of surface stresses to the force of adhesion. We find that the elastic and capillary contributions to the adhesive force are of similar magnitude, and that both are required to account for measured adhesive forces between rigid silica spheres and compliant, silicone gels. Notably, the strain-dependence of the solid surface stress contributes significantly to the stiffness of soft solid contacts.Comment: 6 pages, 3 figure

Many-Body Electrostatic Forces Between Colloidal Particles at Vanishing Ionic Strength

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.Comment: 5 pages 2 figure

The Deformation of an Elastic Substrate by a Three-Phase Contact Line

Young's classic analysis of the equilibrium of a three-phase contact line ignores the out-of-plane component of the liquid-vapor surface tension. While it has long been appreciated that this unresolved force must be balanced by elastic deformation of the solid substrate, a definitive analysis has remained elusive because conventional idealizations of the substrate imply a divergence of stress at the contact line. While a number of theories of have been presented to cut off the divergence, none of them have provided reasonable agreement with experimental data. We measure surface and bulk deformation of a thin elastic film near a three-phase contact line using fluorescence confocal microscopy. The out-of-plane deformation is well fit by a linear elastic theory incorporating an out-of-plane restoring force due to the surface tension of the gel. This theory predicts that the deformation profile near the contact line is scale-free and independent of the substrate elastic modulus.Comment: 4 pages, 3 figure

A minimal model for kinetic arrest

To elucidate slow dynamics in glassy materials, we introduce the {\it Figure-8 model} in which $N$ hard blocks undergo Brownian motion around a circuit in the shape of a figure-8. This system undergoes kinetic arrest at a critical packing fraction $\phi=\phi_g < 1$, and for $\phi\approx\phi_g$ long-time diffusion is controlled by rare, cooperative `junction-crossing' particle rearrangements. We find that the average time between junction crossings $\tau_{JC}$, and hence the structural relaxation time, does not simply scale with the configurational volume \OmegaLow of transition states, because $\tau_{JC}$ also depends on the time to complete a junction crossing. The importance of these results in understanding cage-breaking dynamics in glassy systems is discussed.Comment: 4 pages, 4 figure

Parabolic lithium refractive optics for x rays

Excellent x-ray optics for photons at around 10 keV can be expected with lithium metal. One of the best compound refractive lens designs [Lengeler et al., J. Appl. Phys. 84, 5855 (1998)] is now produced routinely in aluminum, and more recently has been demonstrated using beryllium [M. Kuhlmann et al. (unpublished)]. Here, we report a similar refractive lens made from lithium. At 10.87 keV, this lens has a ≃2 m focal length, more than 90% peak transmission, and an average transmission of 49%. The lens shows a very useful gain of up to 40. The full widths at half maximum (FWHM) of the focus are blurred by roughly 20 μm, resulting in a horizontal and vertical FWHM of 33 and 17 μm for an image distance of 2.13 m. The lens produces speckle on the x-ray beam, which is likely due to the inhomogeneities of the lens surface: Coherent x-ray scattering is useful in understanding imperfections in x-ray optics, such as mirrors and lenses. Better molding techniques should result in improved performance and enable microbeam techniques with this type of Li lens. © 2004 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70176/2/RSINAK-75-1-37-1.pd

An Imaging System for Focusing Tests of Li Multiprism X‐ray Refractive Lenses

For rapid and efficient tests of novel X‐rays optics, such as lithium‐based compound refractive lenses, we have built a fast X‐ray sensitive CCD imaging system. We report on the linearity, response and resolution of the microscope‐based imaging system. For the low magnifications used here (X2‐X10), we find that a thinly doped YAG screen has a poorer resolution than a thick YAG screen. We provide an example of its use in testing a new 2D focusing multiprism X‐ray lens. © 2004 American Institute of PhysicsPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87661/2/780_1.pd