Non-Exponential Decays in First-Order Kinetic Processes. The Case of"Squeezed Exponential"

Abstract

Dedicated to the memory of late Professor Jerzy ProchorowKinetics of processes, in which the reaction rate increases with conversion, is discussed and illustrated with an example of the chemical reaction of isomerization of an azobenzene derivative in a liquid crystalline matrix. A simple phenomenological model is put forward explaining the effect by dynamic changes of interactions between the reacting species and the matrix.

Size Dependence and Role of Decoherence in Hot Electron Relaxation within Fluorinated Silicon Quantum Dots: A First-Principles Study

“…Notably, the energy decay curve does not obey the conventional stretched exponential with β < 1, 59,60 but rather the compressed exponential decay with 1 < β < 2. 61,62 Overall, the relaxation process is roughly 1.6−2 times faster in the large QD than in the small QD. This faster relaxation can be attributed to several factors including the absence of the unique shuttling mechanism in the large QD as discussed above and also to the closely spaced energy levels.…”

Degradation Kinetics of Organic–Inorganic Hybrid Materials from Micro‐Raman Spectroscopy and Density‐Functional Theory: The Case of β‐ZnTe(en)0.5

“…In contrast to the simple exponential decay where a global rate (k) is assumed, the stretched-exponential views the process as a linear combination of different rates, whose weights can be described using a continuous distribution. [34,35] In the expression of the stretched exponential decay [Equation ( 4)], k describes the effective rate, and b describes the width of the rate distribution. In ambient degradation, accumulation of the tellurium on the sample surface from the early stage of the reaction effectively shields the hybrid from further attack by oxidation agents such as O 2 and H 2 O molecules.…”