Leveraging Torsional and Steric Strains: A Pre-macrocyclization Strategy Enables Conformation-Specific Fullerene Binding in m-Cyclophanes

Though the chemistry of resorcinarenes is half a century old, the conformationally-locked resorcinarene crowns are generally constructed using hydrogen bonds or covalent tethers. Often, covalent tethering involves extra post-macrocyclization steps involving upper-rim functionalities. We have leveraged the torsional and steric strains through α-substituents of the lower-rim C-alkyl chains and accomplished conformationally-rigid fluorescent m-cyclophane deep-crowns in a predetermined way. The strategy offers a pre-macrocyclization route conserving upper-rim functionalities, an aspect overlooked in resorcinarene chemistry. X-ray structural and computational analyses unveil the cause for conformational rigidity in m-cyclophanes due to α-branching in C-alkyls (linear vs. α-/β-branched). The conformationally-locked fluorescent deep-crown with a preorganized cavity captures hydrophobic spherical guest C₆₀ in both solution and solid states specifically, when compared to conformationally-dynamic boats, enabling conformation-specific binding.     

Solution to the Riemann problem for drift-flux model with modified Chaplygin two-phase flows

In this paper, we concern about the Riemann problem for compressible no-slip drift-flux model which represents a system of quasi-linear partial differential equations derived by averaging the mass and momentum conservation laws with modified Chaplygin two-phase flows. We obtain the exact solution of Riemann problem by elaborately analyzing characteristic fields and discuss the elementary waves namely, shock wave, rarefaction wave and contact discontinuity wave. By employing the equality of pressure and velocity across the middle characteristic field, two nonlinear algebraic equations with two unknowns as gas density ahead and behind the middle wave are formed. The Newton–Raphson method of two variables is applied to find the unknowns with a series of initial data from the literature. Finally, the exact solution for the physical quantities such as gas density, liquid density, velocity, and pressure are illustrated graphically.     

Dielectric Properties of Beta Barium Borate and Potassium Pentaborate Single Crystals

Single crystals of beta barium borate and potassium pentaborate (commonly known as β-BaB₂O₄ or BBO and KB₅O₈. 4 H₂O or KB5) were grown by high and low temperature solution growth methods, respectively. The dielectric constant and loss tangent were determined as a function of temperature. Frequency response of the dielectric constant and tan δ have been studied over a frequency range of 0.1 −100 kHz; it is found that both the dielectric constant and tan δ decrease with increase in frequency for both crystals. The dielectric constant and tan δ are found to increase with increase in temperature for both the crystals. Further, the dielectric constant and tan δ measured on different orientations of the grown crystals reveal the anisotropic nature of the crystals.