Explaining the Transition from Diffusion Limited to Reaction Limited Surface Assembly of Molecular Species through Spatial Variations

Abstract

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.

Direct observation of nanoparticle-surfactant assembly and jamming at the water-oil interface

“…1C , a substantially longer time is required to attach the same number of 500-nm NPs to the already densely assembled interface than onto a bare interface. Because the 500-nm NPs must first displace the 70-nm NPs before or during attachment, the attachment can be viewed as a reaction-controlled process ( 32 ). In movies S1 and S2, it is evident that the 500-nm NPs (green) diffuse to the assembled interfacial layer, but many do not attach, indicating that attachment requires multiple attachment attempts, further supporting the conclusion that this is a reaction-controlled process, i.e., attachment with an energy barrier.…”

Thermal scanning probe lithography—a review

“…e A second organic layer under the temperature-sensitive resist that is selectively removed in wet chemistry can be used to create an undercut for lift-off 68,69 . f A functional layer under the temperature-sensitive resist can be locally accessed when the resist is removed and simultaneously activated by the thermal probe [70][71][72] or in a subsequent step by oxygen plasma 73 . g A three-layer stack composed of a temperature-sensitive resist, a thin inorganic hard mask and an organic transfer layer is suitable for high aspect ratio and high-resolution etching 29,43,69,[74][75][76] .…”

“…While PPA is negatively charged in aqueous solution, the exposed amine groups become protonated. These patterns were used to study the interplay between diffusion and surface reactions in the assembly process of negatively charged particles in dilute solutions which are relevant for modern sensor applications [70][71][72] .…”

“…f Selective removal of PPA for accessing a functional material to study nanoparticle assembly processes. Reproduced with permission from ref 72 ,. Copyright 2018 ACS.…”

Metal nanoparticles entrapped in metal matrices

“…9(a) shows that the reaction complies with this equation and the value of the activation energy derived from it is 88±9 kJ/mol. This value indicates that the reaction is not controlled by the diffusion of the substances (usually resulting in activation energies smaller than 21 kJ/mol 27 ), but rather a surface- 26,28 . Recyclability for three cycles was tested and the results are shown in Fig.…”