Microstructure and properties of random heterogeneous materials: A review of theoretical results

Silkworm and spider silk electrospinning: a review

Issues of fossil fuel and plastic pollution are shifting public demand toward biopolymer-based textiles. For instance, silk, which has been traditionally used during at least 5 milleniums in China, is re-emerging in research and industry with the development of high-tech spinning methods. Various arthropods, e.g. insects and arachnids, produce silky proteinic fiber of unique properties such as resistance, elasticity, stickiness and toughness, that show huge potential for biomaterial applications. Compared to synthetic analogs, silk presents advantages of low density, degradability and versatility. Electrospinning allows the creation of nonwoven mats whose pore size and structure show unprecedented characteristics at the nanometric scale, versus classical weaving methods or modern techniques such as melt blowing. Electrospinning has recently allowed to produce silk scaffolds, with applications in regenerative medicine, drug delivery, depollution and filtration. Here we review silk production by the spinning apparatus of the silkworm Bombyx mori and the spiders Aranea diadematus and Nephila Clavipes. We present the biotechnological procedures to get silk proteins, and the preparation of a spinning dope for electrospinning. We discuss silk's mechanical properties in mats obtained from pure polymer dope and multi-composites. This review highlights the similarity between two very different yarn spinning techniques: biological and electrospinning processes.

High impact resistance in graphyne

Graphyne was recently facilely synthesized with superior mechanical and electrical performance. We investigate the ballistic protection properties of α-, β-, δ-, and γ-graphyne sheets using molecular dynamics simulations in conjunction with elastic theory. The velocities of the in-plane elastic wave and out-of-plane cone wave are obtained by both membrane theory and molecular dynamics simulations. The specific penetration energies are approximately 83% that of graphene, indicating high impact resistance. γ-Graphyne has high sound wave speeds comparable to those of graphene, and its Young's modulus is approximately 60% that of graphene. δ-Graphyne has the highest cone wave speed among the four structures, while α-graphyne possesses the highest penetration energy and impact resistance at most tested projectile speeds. Our results indicate that graphyne is a good protective structural material.

Graphyne was recently facilely synthesized with superior mechanical and electrical performance.

Necessary and sufficient conditions for the two-point phase probability function of two-phase random media

Constructing realizations of random media with a specified two-point phase probability function S 2 has attracted considerable attention in the recent literature. However, little is known about conditions under which a prescribed S 2 is realizable. The only known necessary and sufficient condition, due to McMillan, involves a class of square matrices, called corner-positive matrices, about which almost nothing is known except their definition. As a result, McMillan's theorem has gone mostly unused in the literature for over 50 years. In this paper, we present a general decomposition formula for corner-positive matrices, which allows McMillan's theorem to be written in a significantly more tractable and testable form. We also connect McMillan's theorem with many known but heretofore unrelated necessary conditions on S 2 , extending many of these conditions.

Statistical and sampling issues when using multiple particle tracking

Video microscopy can be used to simultaneously track several microparticles embedded in a complex material. The trajectories are used to extract a sample of displacements at random locations in the material. From this sample, averaged quantities characterizing the dynamics of the probes are calculated to evaluate structural and/or mechanical properties of the assessed material. However, the sampling of measured displacements in heterogeneous systems is singular because the volume of observation with video microscopy is finite. By carefully characterizing the sampling design in the experimental output of the multiple particle tracking technique, we derive estimators for the mean and variance of the probes' dynamics that are independent of the peculiar statistical characteristics. We expose stringent tests of these estimators using simulated and experimental complex systems with a known heterogeneous structure. Up to a certain fundamental limitation, which we characterize through a material degree of sampling by the embedded probe tracking, these estimators can be applied to quantify the heterogeneity of a material, providing an original and intelligible kind of information on complex fluid properties. More generally, we show that the precise assessment of the statistics in the multiple particle tracking output sample of observations is essential in order to provide accurate unbiased measurements.

Granule-by-granule reconstruction of a sandpile from x-ray microtomography data

Mesoscale disordered materials are ubiquitous in industry and in the environment. Any fundamental understanding of the transport and mechanical properties of such materials must follow from a thorough understanding of their structure. However, in the overwhelming majority of cases, experimental characterization of such materials has been limited to first- and second-order structural correlation functions, i.e., the mean filling fraction and the structural autocorrelation function. We report here the successful combination of synchrotron x-ray microtomography and image processing to determine the full three-dimensional real-space structure of a model disordered material, a granular bed of relatively monodisperse glass spheres. Specifically, we determine the center location and the local connectivity of each granule. This complete knowledge of structure can be used to calculate otherwise inaccessible high-order correlation functions. We analyze nematic order parameters for contact bonds to characterize the geometric anisotropy or fabric induced by the sample boundary conditions. Away from the boundaries we find short-range bond orientational order exhibiting characteristics of the underlying polytetrahedral structure.

Design of inhomogeneous materials with given structural properties

We describe a technique applicable to optimize certain quantities associated with the two-phase structure described by a model of penetrable grains. The solution is given in a form of an intensity surface that controls locations of the grains. Particular examples include maximization of the expected phase 2 volume and design of functionally graded materials with a given density profile.

Microstructure functions for random media with impenetrable particles

We introduce a model consisting of nonaligned and impenetrable particles. This model is obtained by placing particles of random orientation within "security spheres," typically chosen to be spheres in thermal equilibrium. The particles in general are allowed to be nonspherical. We obtain an analytical expression for the function S(n), the probability that n points simultaneously lie outside of the particle phase. This characterization of the microstructure appears in certain rigorous bounds on the effective properties of random materials. We also evaluate S2 for various specific examples of this model, including nonaligned impenetrable ellipsoids.