Effects of Nonionic and Mixed Cationic-Nonionic Micelles on the Rate of Alkaline Hydrolysis of 4-Nitrophthalimide

Pseudo-first-order rate constants (k_obs) for alkaline hydrolysis of 4-nitrophthalimide show a monotonic decrease with increase in [C₁₂E₂₃]_T (total concentration of Brij 35) at constant [CH₃CN] and [NaOH]. This micellar effect is explained in terms of a pseudophase micelle model. The rate of hydrolysis becomes too slow to monitor at [C₁₂E₂₃]_T≥0.03 M in the absence of cetyltrimethylammonium bromide (CTABr) and at [C₁₂E₂₃]_T≥0.04 M in the presence of 0.006–0.02 M CTABr at 0.01 M NaOH. The plots of k_obs versus [C₁₂E₂₃]_T show minima at 0.006 and 0.01 M CTABr, while such a minimum is not visible at 0.02 M CTABr.     

A formula for the powers of fractional order operators

We derive none some explicit formula for the power of fractional order (differential and integral) operators.     

Observation of Persistent Currents in Finely Dispersed Pyrolytic Graphite

The trapped magnetic flux in the finely ground pyrolytic graphite sample annealed at 670 K in air has been observed. Flux trapping occurs on cooling of the sample from room temperature to 10 K in a magnetic field of 1 T. The magnitude and sign of the induced trapped moment remain unchanged when the applied magnetic field is varied within ±1 T at T K. The trapped magnetic flux is manifested in the displacement of the magnetization curve relative to that of the sample cooled in zero field. Displacement magnitude gradually decreases with the temperature increase up to 350 K, not reaching zero. The set of experimental observations probably reflects the presence in the sample of a granular high-temperature superconducting phase.