Density Functional Theory of a Curved Liquid-Vapour Interface: Evaluation of the rigidity constants

It is argued that to arrive at a quantitative description of the surface tension of a liquid drop as a function of its inverse radius, it is necessary to include the bending rigidity k and Gaussian rigidity k_bar in its description. New formulas for k and k_bar in the context of density functional theory with a non-local, integral expression for the interaction between molecules are presented. These expressions are used to investigate the influence of the choice of Gibbs dividing surface and it is shown that for a one-component system, the equimolar surface has a special status in the sense that both k and k_bar are then the least sensitive to a change in the location of the dividing surface. Furthermore, the equimolar value for k corresponds to its maximum value and the equimolar value for k_bar corresponds to its minimum value. An explicit evaluation using a short-ranged interaction potential between molecules, shows that k is negative with a value around minus 0.5-1.0 kT and that k_bar is positive with a value which is a bit more than half the magnitude of k. Finally, for dispersion forces between molecules, we show that a term proportional to log(R)/R^2 replaces the rigidity constants and we determine the (universal) proportionality constants.Comment: 28 pages; 5 figures; accepted for publication in J. Phys.: Condens. Matter (2013

Three-dimensional cross-linked F-actin networks:Relation between network architecture and mechanical behavior

Numerical simulations are reported for the response of three-dimensional cross-linked F-actin networks when subjected to large deformations. In addition to the physiological parameters such as actin and cross-linker concentration, the model explicitly accounts for filament properties and network architecture. Complementary to two-dimensional studies, we find that the strain-stiffening characteristics depend on network architecture through the local topology around cross-links

Clearing-induced tissue shrinkage:A novel observation of a thickness size effect

The use of clearing agents has provided new insights in various fields of medical research (developmental biology, neurology) by enabling examination of tissue architecture in 3D. One of the challenges is that clearing agents induce tissue shrinkage and the shrinkage rates reported in the literature are incoherent. Here, we report that for a classical clearing agent, benzyl-alcohol benzyl-benzoate (BABB), the shrinkage decreases significantly with increasing sample size, and present an analytical formula describing this

Unified scenario for the morphology of crack paths in two-dimensional disordered solids

A combined experimental and numerical investigation of the roughness of intergranular cracks in two-dimensional disordered solids is presented. We focus on brittle materials for which the characteristic length scale of damage is much smaller than the grain size. Surprisingly, brittle cracks do not follow a persistent path with a roughness exponent ζ≈0.6-0.7 as reported for a large range of materials. Instead, we show that they exhibit monoaffine scaling properties characterized by a roughness exponent ζ=0.50±0.05, which we explain theoretically from linear elastic fracture mechanics. Our findings support the description of the roughening process in two-dimensional brittle disordered solids by a random walk. Furthermore, they shed light on the failure mechanism at the origin of the persistent behavior with ζ≈0.6-0.7 observed for fractures in other materials, suggesting a unified scenario for the geometry of crack paths in two-dimensional disordered solids