On The Effect Of Size On The Kinetics Of Reactions In Solutions

TL;DR

This paper investigates how particle size influences reaction kinetics in solutions, revealing that memory effects from previous collisions significantly alter collision rates and cluster lifetimes, deviating from traditional models.

Contribution

The study introduces a new understanding of reaction kinetics in solutions by incorporating memory effects and size dependence, supported by Brownian dynamics simulations.

Findings

Collision rates are proportional to particle size over Kuhn length.

Particles form long-lived clusters even without attractive forces.

Traditional Smoluchowski model does not account for memory effects.

Abstract

Reactions in solution require "contact" between the reagents. We can predict the rate at which reagents come into "contact" (at least in dilute conditions), but if the initial collision does not lead to reaction, what happens then? The collision rates in solution-phase reactions are generally described (explicitly or implicitly) with the Smoluchowski equation. Unfortunately, that model describes coagulations in gases, not reactions in solutions. The model is memory-less, i.e., collisions are treated as random processes, unaware of each other in space and time. The reality is that unreactive collisions create memory: particles (even molecules) "remember" they just collided, i.e, the probability of collision depends on how far back in time their prior collision happened. As we show here, this purely geometric and statistical fact is valid as long as their size is larger than the Kuhn length of their Brownian motion in solution. Under these conditions, particles in solution form, even in the absence of attractive interactions, relatively long-lived "clusters" kept together by the statistical unlikeliness of separating. We show here through Brownian dynamics simulations that, as a result of this memory, the collision rates and the lifetimes of these clusters, differently from what predicted by Smoluchowski's model, are proportional to the ratio between the radius of the colliders and the Kuhn length of their path in solution, with a coefficient close to unity!