Liquid-phase parallel synthesis of tetrahydro-β-carbolines

Parallel synthesis of β-carbolines on soluble polyethylene glycol (PEG-OH) support is demonstrated. One-pot condensation of polymer-bound tryptophan residues with various aldehydes and ketones has been carried out in the presence of p-TSA as a catalyst to deliver immobilized 1,2,3,4-tetrahydro-β-carbolines. Subsequent disengagement of the appendant from the polymer support afforded the desired products in good yield and acceptable purity.     

Aldol reactions of a cyclobutanone enolate

Addition of an aldehyde and zinc chloride to a cyclobutanone enolate, prepared by the reaction of an α-chlorocyclobutanone with dimethylcopperlithium, gave an aldol adduct in good yield.     

Dehydration of tetrafluoropropanol (TFP) by pervaporation via novel PBI/BTDA-TDI/MDI co-polyimide (P84) dual-layer hollow fiber membranes

A novel PBI/P84 co-polyimide dual-layer hollow fiber membrane has been specifically fabricated through the dry-jet wet phase inversion process, for the first time, for the dehydration pervaporation of tetrafluoropropanol (TFP). Polybenzimidazole (PBI) was chosen as the outer selective layer because of its superior hydrophilic nature and excellent solvent-resistance together with robust thermal stability, while P84 co-polyimide was employed as the inner supporting layer because of its good solvent-resistance and thermal stability. The PBI/P84 membrane exhibits superior water selectivity and relatively high permeation flux. At 60 °C, the PBI/P84 dual-layer hollow fiber membrane shows a permeation flux of 332 g/(m² h) and a separation factor of 1990 for a feed solution containing of 85 wt% TFP. The preferential water sorption and the significant diffusivity difference between TFP and water are the main causes of high separation factor. However, an increase in feed temperature will greatly increase the permeation flux but seriously decrease the water selectivity. The activation energy data verify that water can preferentially permeate the PBI membrane due to the strong water affinity of PBI and a much smaller molecular size of water.     

Pruning of orbits in four-disk and hyperbola billiards

It is shown that for the four-disk system and the hyperbola billiard it is possible to construct a new symbolic plane preserving the orientation existing in the dynamical space. Physical orbits are mapped into the topological well-ordered plane and it is shown that the forbidden and allowed orbits are separated by a monotone pruning front.