This paper describes the fabrication and characterization of ionic electrets-materials that bear a long-lived electrostatic charge because of an imbalance between the number of cationic and anionic charges in the material. Crosslinked polystyrene microspheres that contain covalently bound ions and mobile counterions transfer some of their mobile ions in air, in the absence of bulk liquid, to another material upon contact. According to the ion-transfer model of contact electrification, this selective transfer of mobile ions yields microspheres that have a net electrostatic charge. A tool that operates on the principle of electrostatic induction measures the charge on individual microspheres (50-450 microm in diameter). Microspheres with a variety of covalently bound ionic functional groups (tetraalkylammonium, alkyltriphenylphosphonium, alkylsulfonate, and arylsulfonate) acquire charges consistent with this ion-transfer mechanism. The charge on a microsphere is proportional to its surface area (ca. 1 elementary charge per 2000 nm2) and close to the theoretical limit imposed by the dielectric breakdown of air. The charge density in an atmosphere of SF6 is more than twice that in an atmosphere of N2. These observations suggest that the charge density of these ionic electret microspheres is limited by the dielectric breakdown of the surrounding gas. Functionalizing the surfaces of glass or silicon with covalently bound ions and mobile counterions generates ionic electrets from these inorganic substrates. Soft lithography can pattern charge on a planar silicon surface (with oxide) and on the surface of 250-mum glass microspheres.
The mechanics governing the lateral cracks that form when a hard object plastically penetrates a ceramic is presented. The roles of indentation load, penetration depth, and work of indentation are all highlighted, as are the influences of the mechanical properties of the material. A closed form solution for cracking induced by expansion of a two‐dimensional cavity is used to bring out essential features related to parametric dependence and scaling. The three‐dimensional axisymmetric problem for an annular crack driven by a rigid spherical or conical indenter is solved using numerical methods. The region of highest tensile stress is identified corresponding to the location where a crack is most likely to nucleate. This location coincides with the depth below the surface where the crack will expand parallel to the surface under mode I conditions. The solutions have been substantiated by comparison with measurements of the cracks that form upon Vickers indentation. The basic formula for the crack radius has been used to predict trends in cracking upon static penetration and impact by a projectile. In both cases, the extent of the cracking is substantially diminished by increasing the toughness of the material. The yield strength has a much smaller effect. The cracks caused by penetration and the volume removed per impact both decrease marginally at higher yield strength.
Surface instabilities on the top surface of a soft elastomeric dielectric layer bonded on its bottom to a stiff substrate are investigated for two electro-static conditions: (I) a voltage difference imposed across the top and bottom surfaces of the layer which are both conducting, and (II) a voltage difference imposed across a rigid planar electrode above the layer and the conducting top surface of the layer. In the absence of surface energy, the critical voltage associated with the onset of instability of the planar state is shown to be a surface mode with any wavelength that is short compared to the layer thickness. With no layer pre-stretch and no surface energy, the uniform state in (I) has hydrostatic compression while that of (II) has hydrostatic tension, nevertheless the critical voltage is the same for both problems if the permittivity is the same for both systems. The role of equi-biaxial pre-stretch and surface energy is presented for both problems for neo-Hookean materials and for the Gent generalization. The thrust of the study is the investigation of the post-bifurcation behavior involving nonlinear interactions among the simultaneous surface modes associated with the critical voltage. The post-bifurcation response of Problem I is a crease-like mode with the top surface probing downward towards the lower surface. The opposite occurs for Problem II with the formation of a sharp ridge protruding towards the upper electrode. The bifurcation behavior is highly unstable leading to an extreme sensitivity to small imperfections. The study complements earlier work and highlights unresolved issues.
Here we describe a method for quantifying traction in cells that are physically constrained within micron-sized adhesive islands of defined shape and size on the surface of flexible polyacrylamide gels that contain fluorescent microbeads (0.2-microm diameter). Smooth muscle cells were plated onto square (50 x 50 microm) or circular (25- or 50-microm diameter) adhesive islands that were created on the surface of the gels by applying a collagen coating through microengineered holes in an elastomeric membrane that was later removed. Adherent cells spread to take on the size and shape of the islands and cell tractions were quantitated by mapping displacement fields of the fluorescent microbeads within the gel. Cells on round islands did not exhibit any preferential direction of force application, but they exerted their strongest traction at sites where they formed protrusions. When cells were confined to squares, traction was highest in the corners both in the absence and presence of the contractile agonist, histamine, and cell protrusions were also observed in these regions. Quantitation of the mean traction exerted by cells cultured on the different islands revealed that cell tension increased as cell spreading was promoted. These results provide a mechanical basis for past studies that demonstrated a similar correlation between spreading and growth within various anchorage-dependent cells. This new approach for analyzing the spatial distribution of mechanical forces beneath individual cells that are experimentally constrained to defined sizes and shapes may provide additional insight into the biophysical basis of cell regulation.
Rice et al. (1994, J. Mech. Phys. Solids 42, 813–843) analyse the propagation of a planar crack with a nominally straight front in a model elastic solid with a single displacement component. Using the form of their results for a strictly linearized perturbation from a straight crack front which moves at uniform speed, we give the corresponding first-order expression for the deviation of a crack front from straightness as a direct integral expression in the deviation of the material toughness from uniformity in the crack plane. We then use this expression to analyse the autocorrelation of the crack front position when the toughness deviations are random. We find that the root mean square deviation in position diverges logarithmically with travel distance across the random toughness region, as do the variances of the propagation velocity and slope of the crack front. That is, according to strictly linearized analysis, perturbed about the solution for a uniformly moving crack front, the perturbations from straightness and from uniform propagation speed should grow without bound in the presence of random deviations in toughness. What is remarkable about this result is that, according to the same strictly linearized analysis, if the toughness is completely uniform over the remaining part of the fracture plane, after encounter with a region of nonuniform toughness, the moving crack front becomes asymptotically straight with increase of time. Nonlinearities, not considered here, must control how statistically disordered the crack front can ultimately become as it propagates through a region of random toughness variation. Also, because of the logarithmic nature of the growth, significant disorder can occur in response to small perturbations only when the crack moves over a great distance compared to the correlation length scale in the fracture toughness.
A series of one-dimensional studies is presented to reveal basic aspects of momentum and energy transfer to plates in air blasts. Intense air waves are initiated as either an isolated propagating wave or by the sudden release of a highly compressed air layer. Wave momentum is determined in terms of the energy characterizing the compressed layer. The interaction of intense waves with freestanding plates is computed with emphasis on the momentum and/or energy transferred to the plate. A simple conjecture, backed by numerical simulations, is put forward related to the momentum transmitted to massive plates. The role of the standoff distance between the compressed air layer and the plate is elucidated. Throughout, dimensionless parameters are selected to highlight the most important groups of parameters and to reduce parametric dependencies to the extent possible.
Self-assembly is a process in which components, either separate or linked, spontaneously form ordered aggregates. Self-assembly can occur with components having sizes from the molecular to the macroscopic, provided that appropriate conditions are met. Although much of the work in self-assembly has focused on molecular components, many of the most interesting applications of self-assembling processes can be found at larger sizes (nanometers to micrometers). These larger systems also offer a level of control over the characteristics of the components and over the interactions among them that makes fundamental investigations especially tractable.
