Surface assembly
is often decomposed into two classes: diffusion
and reaction limited processes. The transition between the two cases
is complex because the dynamics are so different. In this article,
we simulate, explain, and experimentally discuss the evolution of
the spatial distribution for surface assemblies with diffusion limited
and reaction limited processes. Explicitly, we demonstrate that diffusion
limited and reaction limited processes show some temporal differences,
but more importantly, we show that the spatial arrangements are different
enough to discriminate between the two cases. Using fundamental properties,
such as the diffusion constant, we calculate the evolution of the
spatial profile and derive from physical, heuristic models the assembly
rate for reaction and diffusion limited processes based on the individual
particle’s interactions with the surface. Finally, we confirm
the spatial profile differences between diffusion and reaction limited
cases by experimentally measuring the surface assembly between two
molecules of similar size, but having different assembly routes. Unique
to our description is that we have derived and simulated everything
through the particle picture in place of ensemble descriptions such
as the diffusion equation, and we show the equivalence between our
heuristic formulas and those derived from the diffusion equation.