Shortcomings of the bond orientational order parameters for the analysis of disordered particulate matter.

Local structure characterization with the bond-orientational order parameters q(4), q(6), ... introduced by Steinhardt et al. [Phys. Rev. B 28, 784 (1983)] has become a standard tool in condensed matter physics, with applications including glass, jamming, melting or crystallization transitions, and cluster formation. Here, we discuss two fundamental flaws in the definition of these parameters that significantly affect their interpretation for studies of disordered systems, and offer a remedy. First, the definition of the bond-orientational order parameters considers the geometrical arrangement of a set of nearest neighboring (NN) spheres, NN(p), around a given central particle p; we show that the choice of neighborhood definition can have a bigger influence on both the numerical values and qualitative trend of q(l) than a change of the physical parameters, such as packing fraction. Second, the discrete nature of neighborhood implies that NN(p) is not a continuous function of the particle coordinates; this discontinuity, inherited by q(l), leads to a lack of robustness of the q(l) as structure metrics. Both issues can be avoided by a morphometric approach leading to the robust Minkowski structure metrics q(l)'. These q(l)' are of a similar mathematical form as the conventional bond-orientational order parameters and are mathematically equivalent to the recently introduced Minkowski tensors [G. E. Schröder-Turk et al., Europhys. Lett. 90, 34001 (2010); S. Kapfer et al., Phys. Rev. E 85, 030301(R) (2012)].

A bicontinuous mesophase geometry with hexagonal symmetry.

We report that a specific realization of Schwarz's triply periodic hexagonal minimal surface is isotropic with respect to the Doi-Ohta interface tensor and simultaneously has minimal packing and stretching frustration similar to those of the commonly found cubic bicontinuous mesophases. This hexagonal surface, of symmetry P6(3)/mmc with a lattice ratio of c/a = 0.832, is therefore a likely candidate geometry for self-assembled lipid/surfactant or copolymer mesophases. Furthermore, both the peak position ratios in its powder diffraction pattern and the elastic moduli closely resemble those of the cubic bicontinuous phases. We therefore argue that a genuine possibility of experimental misidentification exists.

Transport, phase transitions, and wetting in micro/nanochannels: a phase field/DDFT approach.

While the flow of a liquid in a macroscopic channel is usually described using hydrodynamics with no-slip boundary conditions at the walls of the channel, transport phenomena in microchannels involve physics at many different scales due to the interplay between the micrometric section of the channel and the micro- or nanometric roughness of the boundaries. Roughness can have many different effects such as increasing the friction between the liquid and the walls (leading to the macroscopic no-slip boundary condition) or on the contrary reduce it thanks to the Wenzel-Cassie-Baxter wetting transition induced by capillarity. Here we detail a phase-field/dynamic density functional theory model able to account for the wetting transitions, the resulting friction between the wall and the fluid, and compressible hydrodynamics at high viscosity contrast.

Robust pore size analysis of filamentous networks from three-dimensional confocal microscopy.

We describe a robust method for determining morphological properties of filamentous biopolymer networks, such as collagen or other connective tissue matrices, from confocal microscopy image stacks. Morphological properties including pore size distributions and percolation thresholds are important for transport processes, e.g., particle diffusion or cell migration through the extracellular matrix. The method is applied to fluorescently labeled fiber networks prepared from rat-tail tendon and calf-skin collagen, at concentrations of 1.2, 1.6, and 2.4 mg/ml. The collagen fibers form an entangled and branched network. The medial axes, or skeletons, representing the collagen fibers are extracted from the image stack by threshold intensity segmentation and distance-ordered homotopic thinning. The size of the fluid pores as defined by the radii of largest spheres that fit into the cavities between the collagen fibers is derived from Euclidean distance maps and maximal covering radius transforms of the fluid phase. The size of the largest sphere that can traverse the fluid phase between the collagen fibers across the entire probe, called the percolation threshold, was computed for both horizontal and vertical directions. We demonstrate that by representing the fibers as the medial axis the derived morphological network properties are both robust against changes of the value of the segmentation threshold intensity and robust to problems associated with the point-spread function of the imaging system. We also provide empirical support for a recent claim that the percolation threshold of a fiber network is close to the fiber diameter for which the Euler index of the networks becomes zero.

Tensorial Minkowski functionals of triply periodic minimal surfaces.

A fundamental understanding of the formation and properties of a complex spatial structure relies on robust quantitative tools to characterize morphology. A systematic approach to the characterization of average properties of anisotropic complex interfacial geometries is provided by integral geometry which furnishes a family of morphological descriptors known as tensorial Minkowski functionals. These functionals are curvature-weighted integrals of tensor products of position vectors and surface normal vectors over the interfacial surface. We here demonstrate their use by application to non-cubic triply periodic minimal surface model geometries, whose Weierstrass parametrizations allow for accurate numerical computation of the Minkowski tensors.

Jammed spheres: Minkowski tensors reveal onset of local crystallinity.

The local structure of disordered jammed packings of monodisperse spheres without friction, generated by the Lubachevsky-Stillinger algorithm, is studied for packing fractions above and below 64%. The structural similarity of the particle environments to fcc or hcp crystalline packings (local crystallinity) is quantified by order metrics based on rank-four Minkowski tensors. We find a critical packing fraction φ(c)≈0.649, distinctly higher than previously reported values for the contested random close packing limit. At φ(c), the probability of finding local crystalline configurations first becomes finite and, for larger packing fractions, increases by several orders of magnitude. This provides quantitative evidence of an abrupt onset of local crystallinity at φ(c). We demonstrate that the identification of local crystallinity by the frequently used local bond-orientational order metric q(6) produces false positives and thus conceals the abrupt onset of local crystallinity. Since the critical packing fraction is significantly above results from mean-field analysis of the mechanical contacts for frictionless spheres, it is suggested that dynamic arrest due to isostaticity and the alleged geometric phase transition in the Edwards framework may be disconnected phenomena.