Inverted regions induced by geometric constraints on a classical encounter-controlled binary reaction

TL;DR

This study investigates how geometric constraints and boundary conditions induce non-monotonic reaction times in a classical two-reactant lattice system, revealing regimes where increased 'temperature' can decrease reaction efficiency.

Contribution

It demonstrates the emergence of inverted regions in reaction times due to classical geometric effects, contrasting with quantum Marcus inversion phenomena.

Findings

Reaction time can have a local minimum or maximum as a function of temperature parameter p.

Inverted regions depend on initial conditions and boundary constraints.

Classical geometric effects can cause non-monotonic reaction efficiencies.

Abstract

The efficiency of an encounter-controlled two-channel reaction between two independently-mobile reactants on a lattice is characterized by the mean number $\rt$ of steps to reaction. The two reactants are distinguished by their mass with the "light" walker performing a jump to a nearest-neighbor site in each time step, while the "heavy" walker hops only with a probability $p$; we associate $p$ with the "temperature" of the system. Lattices subject to periodic and to confining boundary conditions are considered. For periodic lattices, depending on the initial state, the reaction time either falls off monotonically with $p$ or displays a local minimum with respect to $p$; occurrence of the latter signals a regime where the efficiency of the reaction effectively decreases with increasing temperature. Such behavior disappears if the jump probability of the light walker falls below a characteristic threshold value. In lattices subject to confining boundary conditions, the behavior is more complex. Depending on the initial conditions, the reaction time as a function of $p$ may increase monotonically, decrease monotonically, display a single maximum or even a maximum and minimum. These inverted regions are a consequence of a strictly classical interplay between excluded volume effects implicit in the specification of the two reaction channels, and the system's dimensionality and spatial extent. Our results highlight situations where the description of an encounter-controlled reactive event cannot be described by a single, effective diffusion coefficient. We also distinguish between the inversion region identified here and the Marcus inverted region which arises in electron transfer reactions.