  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!
