Thermal Hysteresis Involving Reversible Self-Catalytic Reactions

Hysteresis is ubiquitous in nature and biology. It appears in ferromagnetism, ferroelectrism, traffic congestion, river sedimentation, electronics, thermoresponses, cell division, differentiation, and apoptosis. Hysteresis phenomena are beyond equilibrium and involve nonlinear, bistable, time delay, and memory events, which are described in input/output profiles by different outputs during continuous decreases and increases in input intensity. Although hysteresis profiles in these phenomena appear similar, the mechanisms underlying them are complex, and their basic understanding is desired. In this Account, I describe thermal hysteresis caused by molecules dispersed in dilute solutions containing optically active helicene oligomers, which form homo- and heterodouble helices, the cooling and heating processes of which cause different structural changes with regard to their relative concentrations. Reversible self-catalytic reactions are involved in the formation of a double helix, which catalyzes its own formation. The reactions accelerate as they progress, in contrast to ordinary reactions, which exhibit monotonic retardation as they progress. Thermal hysteresis involving reversible self-catalytic reactions exhibits notable phenomena, when various cooling/heating inputs are applied during the reaction; these phenomena are shown herein with profiles of experimental results of Δε outputs obtained by circular dichroism (CD) plotted against temperature inputs. Thermal hysteresis is discussed in terms of (1) two states of the homodouble helix and a random coil involving one reversible self-catalytic reaction and (2) three states of enantiomeric heterodouble helices and a random coil involving two reversible self-catalytic reactions. Repeated cooling and heating processes provide the same stable thermal hysteresis loops, when the initial and final high-temperature states are under equilibrium, and nonloop and unstable thermal hysteresis appears when whole the systems are beyond equilibrium. Diverse thermal hysteresis loops are obtained under different temperature change conditions for different oligomers. The mechanism of thermal hysteresis involves different macroscopic mechanisms at a fixed temperature, when the relative concentrations of substrates/products and the reaction direction differ. Microscopic mechanisms, which are shown by energy diagrams, are fixed at a temperature irrespective of cooling or heating. A comparison of thermal hysteresis loops and equilibrium curves provides distances to the metastable states on the loops from equilibrium, and reactions occur from the metastable states toward equilibrium. Notable phenomena described herein include bistability, high sensitivity to small concentration changes, equilibrium crossing, three-state one-directional structural change caused by a single heating procedure, reaction shortcuts, the memory effect on thermal history, figure-eight thermal hysteresis, chemical oscillation, stable and unstable thermal hysteresis, double-helix formation only under heating, and chiral symmetry breaking.