When Rank-One Convexity Meets Polyconvexity: An Algebraic Approach to Elastic Binodal

Journal of Nonlinear Science - In the variational problems involving non-convex integral functionals, finding the binodal, the boundary of validity of the quasiconvexity of the energy density, is...     

Host–Guest Chemistry Within Cellulose Nanocrystal Gel Receptors

Cellulose nanocrystals (CNCs) spontaneously assemble into gels when mixed with a polyionic organic or inorganic salt. Here, we have used this ion-induced gelation strategy to create functional CNC gels with a rigid tetracationic macrocycle, cyclobis(paraquat-p-phenylene) ( CBPQT ⁴⁺). Addition of [ CBPQT ]Cl₄ to CNCs causes gelation and embeds an active host inside the material. The fabricated CNC gels can reversibly absorb guest molecules from solution then undergo molecular recognition processes that create colorful host–guest complexes. These materials have been implemented in gel chromatography (for guest exchange and separation), and as elements to encode 2- and 3-dimensional patterns. We anticipate that this concept might be extended to design a set of responsive and selective gel-like materials functioning as, for instance, water-pollutant scavengers, substrates for chiral separations, or molecular flasks.     

The Synthesis and Characterization of the Tri-rhenium(VI) Capped Wells–Dawson Polyoxometalate, [{(C4H9)4N)5(C2H5)3NH}{Re3P2W15O62}]

The tri-rhenium(VI) capped Wells–Dawson polyoxometalate, [Re₃P₂W₁₅O₆₂]^6– with quaternary ammonium cations was synthesized by reacting the trivacant lacunary species, [P₂W₁₅O₅₆]^12– with [ReOCl₃(PPh₃)₂] in an organic solvent. Elemental analysis by thermogravimetry and inductively coupled plasma mass spectroctrometry confirmed the substitution of three rhenium atoms, single-crystal X-ray diffraction as well as infra red spectroscopy showed the complete Wells–Dawson structure. The presence of all three rhenium atoms in one cap is indicated by ³¹P nuclear magnetic resonance spectroscopy and the electron spin resonance spectrum shows that the tri-rhenium(V) species with three unpaired electrons is low spin, S = ½.     

Facile Synthesis and Properties of 2‐λ5‐Phosphaquinolines and 2‐λ5‐Phosphaquinolin‐2‐ones

Treatment of 2‐ethynylanilines with P(OPh)₃ gives either 2,2‐diphenoxy‐2‐λ⁵‐phosphaquinolines or 2‐phenoxy‐2‐λ⁵‐phosphaquinolin‐2‐ones under transition‐metal‐free conditions. This reaction offers access to an underexplored heterocycle, which opens up the study of the fundamental nature of the N?P^V double bond and its potential for delocalization within a cyclic π‐electron system. This heterocycle can serve as a carbostyril mimic, with application as a bioisostere for pharmaceuticals based on the 2‐quinolinone scaffold. It also holds promise as a new fluorophore, since initial screening reveals quantum yields upwards of 40 %, Stokes shifts of 50–150 nm, and emission wavelengths of 380–540 nm. The phosphaquinolin‐2‐ones possess one of the strongest solution‐state dimerization constants for a D–A system (130 M ^?1) owing to the close proximity of a strong acceptor (P?O) and a strong donor (phosphonamidate N? H), which suggests that they might hold promise as new hydrogen‐bonding hosts for optoelectronic sensing.     

The flip side of buckling

Buckling of slender structures under compressive loading is a failure of infinitesimal stability due to a confluence of two factors: the energy density non-convexity and the smallness of Korn’s constant. The problem has been well understood only for bodies with simple geometries when the slenderness parameter is well defined. In this paper, we present the first rigorous analysis of buckling for bodies with complex geometry. By limiting our analysis to the “near-flip” instability, we address the universal features of the buckling phenomenon that depend on neither the shape of the domain nor the degree of constitutive nonlinearity of the elastic material.      

Percolation Thresholds in Ternary Polymer Melt Blends with Separate Dispersions of the Inner Phases: Mathematical Model

A mathematical model based on a straightforward geometrical background is developed which enables predictions of a transition of one dispersed phase to a cocontinuous one (i.e., the percolation threshold) on addition of another dispersed phase during melt mixing in ternary polymer blends. The present work concerns only ternary blends with two separate dispersions of the inner phases in which no encapsulation takes place. In addition, in order to simplify the model, one of the inner phases was represented by hard, nondeformable microspheres The expression developed describes well an experimental relationship between the percolation threshold, the concentration above which the former dispersed phase transforms to a continuous one, and concentrations of both inner phases. The results agree well with the experimental data obtained in a previous work.     

Cosmological Acceleration as a Consequence of Quantum de Sitter Symmetry

Physics of Particles and Nuclei Letters - Physicists usually understand that physics cannot (and should not) derive that $$c \approx 3 \times {{10}^{8}}$$ m/s and $$\hbar \approx 1.054 \times...