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Register a new userModelling textile structures using bicontinuous surfaces
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We present a method for modelling textile structures, such as weft knits, on families of bicontinuous surfaces. By developing a tangible interpretation of mathematical theory, we combine perspectives of art, design, engineering, and science to understand how the architecture of the knit relates to its physical and mathematical properties. While modelling and design tools have become ubiquitous in many industries, there is still a significant lack of predictive advanced manufacturing techniques available for the design and manufacture of textiles. We describe a mathematical structure as a system for dynamic modelling of textiles in the form of a physical prototype which may be used to inform and predict relevant textile parameters prior to fabrication. This includes dimensional changes due to yarn relaxation, which would streamline production of knit textiles for industry, makers and textile artists.
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Amphiphiles are molecules which have both hydrophilic and hydrophobic parts. In water- and/or oil-like solvent, they self-assemble into extended sheet-like structures due to the hydrophobic effect. The free energy of an amphiphilic system can be written as a functional of its interfacial geometry, and phase diagrams can be calculated by comparing the free energies following from different geometries. Here we focus on bicontinuous structures, where one highly convoluted interface spans the whole sample and thereby divides it into two separate labyrinths. The main models for surfaces of this class are triply periodic minimal surfaces, their constant mean curvature and parallel surface companions, and random surfaces. We discuss the geometrical properties of each of these types of surfaces and how they translate into the experimentally observed phase behavior of amphiphilic systems.
Coarsening of bicontinuous microstructures is observed in a variety of systems, such as nanoporous metals and mixtures that have undergone spinodal decomposition. To better understand the morphological evolution of these structures during coarsening, we compare the morphologies resulting from two different coarsening mechanisms, surface and bulk diffusion. We perform phase-field simulations of coarsening via each mechanism in a two-phase mixture at nominal volume fractions of 50%-50% and 36%-64%, and the simulated structures are characterized in terms of topology (genus density), the interfacial shape distribution, structure factor, and autocorrelations of phase and mean curvature. We observe self-similar evolution of morphology and topology and agreement with the expected power laws for dynamic scaling, in which the characteristic length scale increases over time proportionally to $t^{1/4}$ for surface diffusion and $t^{1/3}$ for bulk diffusion. While we observe the expected difference in the coarsening kinetics, we find that differences in self-similar morphology due to coarsening mechanism are relatively small, although typically they are larger at 36% volume fraction than at 50% volume fraction. In particular, we find that bicontinuous structures coarsened via surface diffusion have lower scaled genus densities than structures coarsened via bulk diffusion. We also compare the self-similar morphologies to those in literature and to two model bicontinuous structures, namely, constant-mean-curvature surfaces based on the Schoen G minimal surface and random leveled-wave structures. The average scaled mean curvatures of these model structures agree reasonably with those of the coarsened structures at both 36% and 50%, but we find substantial disagreements in the scaled genus densities and the standard deviations of mean curvature.
A simple model was constructed to describe the polar ordering of non-centrosymmetric supramolecular aggregates formed by self assembling triblock rodcoil polymers. The aggregates are modeled as dipoles in a lattice with an Ising-like penalty associated with reversing the orientation of nearest neighbor dipoles. The choice of the potentials is based on experimental results and structural features of the supramolecular objects. For films of finite thickness, we find a periodic structure along an arbitrary direction perpendicular to the substrate normal, where the repeat unit is composed of two equal width domains with dipole up and dipole down configuration. When a short range interaction between the surface and the dipoles is included the balance between the up and down dipole domains is broken. Our results suggest that due to surface effects, films of finite thickness have a none zero macroscopic polarization, and that the polarization per unit volume appears to be a function of film thickness.
A method for forming permanent three dimensional structures from colloidal particles using holographic optical trapping is described. Holographic optical tweezers (HOT) are used to selectively position charge stabilized colloidal particles within a flow cell. Once the particles are in the desired location an electrolyte solution is pumped into the cell which reduces the Debye length and induces aggregation caused by the van der Waals attraction. This technique allows for the formation of three dimensional structures both on and away from the substrate that can be removed from solution without the aid of critical point drying. This technique is inexpensive, fast, and versatile as it relies on forces acting on almost all colloidal suspensions.
Rough or textured hydrophobic surfaces are dubbed superhydrophobic due to their numerous desirable properties, such as water repellency and interfacial slip. Superhydrophobicity stems from an aversion for water to wet the surface texture, so that a water droplet in the superhydrophobic Cassie state, contacts only the tips of the rough hydrophobic surface. However, superhydrophobicity is remarkably fragile, and can break down due to the wetting of the surface texture to yield the Wenzel state under various conditions, such as elevated pressures or droplet impact. Moreover, due to large energetic barriers that impede the reverse (dewetting) transition, this breakdown in superhydrophobicity is widely believed to be irreversible. Using molecular simulations in conjunction with enhanced sampling techniques, here we show that on surfaces with nanoscale texture, water density fluctuations can lead to a reduction in the free energetic barriers to dewetting by circumventing the classical dewetting pathways. In particular, the fluctuation-mediated dewetting pathway involves a number of transitions between distinct dewetted morphologies, with each transition lowering the resistance to dewetting. Importantly, an understanding of the mechanistic pathways to dewetting and their dependence on pressure, allows us to augment the surface texture design, so that the barriers to dewetting are eliminated altogether and the Wenzel state becomes unstable at ambient conditions. Such robust surfaces, which defy classical expectations and can spontaneously recover their superhydrophobicity, could have widespread importance, from underwater operation to phase change heat transfer applications.
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