Search Results (8)

Polyhedral cages (p-cages) are Euclidean geometric structures corresponding to polyhedra with holes. They are a good example of the geometry of some artificial protein cages. In this paper we identify p-cages made out of two families of equivalent polygonal faces, where the face of one family is attached to three other faces while the faces of the other family are attached to three, four, five or six other faces. To restrict ourselves to p-cages with small holes, we consider p-cages where each hole comprises at most four faces. The construction starts from planar graphs made out of two families of equivalent nodes. One can then construct the dual of the solid corresponding to that graph and tile its faces with regular or nearly regular polygons. An energy function is then defined to quantify the amount of irregularity of the p-cages which is then minimised using a simulated annealing algorithm. We have analysed nearly 100,000 possible configurations, ruling out the p-cages made out of faces with deformations exceeding 10%. We then present graphically some of the most interesting geometries. Full article

The primary objective of this contribution is to numerically and graphically evaluate engineering stress–strain curves, transform them into true stress–strain curves, and de-scribe the key points of material processed by cold rolling with strains of ε_Roll = 0%, 10%, 30%, and 50%. The initial and final conditions for uniform plastic deformations have been described. The initial point of uniform deformation lies above the onset yield strength value (σ_T,S > R_P0,2). The necking point, as the final point of uniform deformation, was determined as the intersection point of the curves of the true stress–strain and strain hardening rate. The strain hardening coefficient and the recovery rate, as a function of cold rolling deformations, were derived. Convex polyhedra were derived which describe the dependencies of the development of maximal strain hardening rate values (θ_Max) and initial strain hardening rates (θ₀) as a function of cold rolling deformations and the diameter of grain. The decisive point at which the curves showed a local maximum was a cold rolling deformation ε_Roll = 30%. The saturation stress required to initiate dynamic recovery of the microstructure is significantly higher than the stress necessary for necking (σ_T,Sat > σ_T,Neck). The saturation strain required to initiate dynamic recovery of the microstructure is significantly higher than the strain needed for necking formation (ε_T,Sat > ε_T,Neck). Full article

Polyhedral cages (p-cages) provide a good description of the geometry of some families of artificial protein cages. In this paper we identify p-cages made out of two families of equivalent polygonal faces/protein rings, where each face has at least four neighbours and where the holes are contributed by at most four faces. We start the construction from a planar graph made out of two families of equivalent nodes. We construct the dual of the solid corresponding to that graph, and we tile its faces with regular or nearly regular polygons. We define an energy function describing the amount of irregularity of the p-cages, which we then minimise using a simulated annealing algorithm. We analyse over 600,000 possible geometries but restrict ourselves to p-cages made out of faces with deformations not exceeding 10%. We then present graphically some of the most promising geometries for protein nanocages. Full article

Polyhedral cages (p-cages) describe the geometry of some families of artificial protein cages. We identify the p-cages made out of families of equivalent polygonal faces such that the faces of one family have five neighbors and $P_1$ edges, while those of the other family have six neighbors and $P_2$ edges. We restrict ourselves to polyhedral cages where the holes are adjacent to four faces at most. We characterize all p-cages with a deformation of the faces, compared to regular polygons, not exceeding 10%. Full article

This study explores a simple method of fabricating hybrid supercapacitor electrodes, which could potentially broaden the application of this technology. The method involves electrospinning a uniform solution of Matrimid/Metal−Organic Polyhedra 18 (MOP−18) followed by carbonization at a relatively low temperature of 700 °C in air, rather than in an inert atmosphere, to create free−standing, redox−active hybrid supercapacitor electrodes. Additionally, the synthesis procedure requires no stabilization or activation steps, which enhances the cost effectiveness of the synthesized electrode materials. The resulting C/CuO composite was used as the working electrode, with a polyacrylonitrile (PAN)/Poly(methyl methacrylate) (PMMA) carbon nanofiber (CNF) electrode as the counter and 6 M KOH as the electrolyte in a T−cell configuration. The cell performance and redox activity were evaluated using cyclic voltammetry (CV), galvanostatic charge–discharge (GCD), electrochemical impedance spectroscopy (EIS) and cycling stability tests. Additionally, the physical and chemical structures of the electrode materials were assessed using X−ray photoelectron spectroscopy (XPS), scanning electron microscopy (SEM), transmission electron spectroscopy (TEM), X−ray diffractometry (PXRD), surface area analysis and other characterization techniques. The electrode material demonstrated a specific capacitance of up to 206 F/g. Supercapacitors utilizing this material display an energy density of 10.3 Wh/kg (active material) at a current density of 1 A/g in electrochemical testing. Full article

Following the discovery of an artificial protein cage with a paradoxical geometry, we extend the concept of homogeneous symmetric congruent equivalent near-miss polyhedral cages, for which all the faces are equivalent, and define bi-homogeneous symmetric polyhedral cages made of two different types of faces, where all the faces of a given type are equivalent. We parametrise the possible connectivity configurations for such cages, analytically derive p-cages that are regular, and numerically compute near-symmetric p-cages made of polygons with 6 to 18 edges and with deformation not exceeding 10%. Full article

Following the experimental discovery of several nearly symmetric protein cages, we define the concept of homogeneous symmetric congruent equivalent near-miss polyhedral cages made out of P-gons. We use group theory to parameterize the possible configurations and we minimize the irregularity of the P-gons numerically to construct all such polyhedral cages for $P=6$ to $P=20$ with deformation of up to 10%. Full article

We review recent results from extensive simulations of the crystallization of athermal polymer packings. It is shown that above a certain packing density, and for sufficiently long simulations, all random assemblies of freely-jointed chains of tangent hard spheres of uniform size show a spontaneous transition into a crystalline phase. These polymer crystals adopt predominantly random hexagonal close packed morphologies. An analysis of the local environment around monomers based on the shape and size of the Voronoi polyhedra clearly shows that Voronoi cells become more spherical and more symmetric as the system transits to the ordered state. The change in the local environment leads to an increase in the monomer translational contribution to the entropy of the system, which acts as the driving force for the phase transition. A comparison of the crystallization of hard-sphere polymers and monomers highlights similarities and differences resulting from the constraints imposed by chain connectivity. Full article