On uniform edge-n-colorings of tilings.

An edge-n-coloring of a uniform tiling {\cal T} is uniform if for any two vertices of {\cal T} there is a symmetry of {\cal T} that preserves the colors of the edges and maps one vertex onto the other. This paper gives a method based on group theory and color symmetry theory to arrive at uniform edge-n-colorings of uniform tilings. The method is applied to give a complete enumeration of uniform edge-n-colorings of the uniform tilings of the Euclidean plane, for which the results point to a total of 114 colorings, n = 1, 2, 3, 4, 5.

Enzymatic Degradation Behavior of Self-Degradable Lipase-Embedded Aliphatic and Aromatic Polyesters and Their Blends.

Over the past decade, the preparation of novel materials by enzyme-embedding into biopolyesters has been proposed as a straightforward method to produce self-degrading polymers. This paper reports the preparation and enzymatic degradation of extruded self-degradable films of three different biopolyesters: poly(lactic acid) (PLA), poly(butylene adipate--terephthalate) (PBAT), and poly(butylene succinate) (PBS), as well as three binary/ternary blends. lipase B (CalB) has been employed for the enzyme-embedding procedure, and to the best of our knowledge, the use of this approach in biopolyester blends has not been reported before.

Crystallization-Induced Self-Assembly of Poly(ethylene glycol) Side Chains in Dithiol-yne-Based Comb Polymers: Side Chain Spacing and Molecular Weight Effects.

The chain architecture and topology of macromolecules impact their physical properties and final performance, including their crystallization process. In this work, comb polymers constituted by poly(ethylene glycol), PEG, side chains, and a dithiol-yne-based ring polymer backbone have been studied, focusing on the micro- and nanostructures of the system, thermal behavior, and crystallization kinetics. The designed comb system allows us to investigate the role of a ring backbone, the impact of varying the distance between two neighboring side chains, and the effect of the molecular weight of the side chain.

Salt-induced Fmoc-tripeptide supramolecular hydrogels: a combined experimental and computational study of the self-assembly.

Delving into the mechanism behind the molecular interactions at the atomic level of short-sequence peptides plays a key role in the development of nanomaterials with specific structure-property-function relationships from a bottom-up perspective. Due to their poor water solubility, the self-assembly of Fmoc-bearing peptides is usually induced by dissolution in an organic solvent, followed by a dilution step in water, pH changes, and/or a heating-cooling process. Herein, we report a straightforward methodology for the gelation of Fmoc-FFpY (F: phenylalanine; Y: tyrosine; and p: PO), a negatively charged tripeptide, in NaCl solution.

Symmetry groups of two-way twofold and three-way threefold fabrics.

This work discusses the symmetry groups of two classes of woven fabrics, two-way twofold fabrics and three-way threefold fabrics. A method to arrive at a design of a fabric is presented, employing methods in color symmetry theory. Geometric representations of all possible layer group or diperiodic symmetry structures of the fabrics are derived.