Propagating waves of self-assembly in organosilane monolayers

Abstract

Wavefronts associated with reaction-diffusion and self-assembly processes are ubiquitous in the natural world. For example, propagating fronts arise in crystallization and diverse other thermodynamic ordering processes, in polymerization fronts involved in cell movement and division, as well as in the competitive social interactions and population dynamics of animals at much larger scales. Although it is often claimed that self-sustaining or autocatalytic front propagation is well described by mean-field ''reaction-diffusion'' or ''phase field'' ordering models, it has recently become appreciated from simulations and theoretical arguments that fluctuation effects in lower spatial dimensions can lead to appreciable deviations from the classical mean-field theory (MFT) of this type of front propagation. The present work explores these fluctuation effects in a real physical system. In particular, we consider a high-resolution near-edge x-ray absorption fine structure spectroscopy (NEXAFS) study of the spontaneous frontal self-assembly of organosilane (OS) molecules into self-assembled monolayer (SAM) surface-energy gradients on oxidized silicon wafers. We find that these layers organize from the wafer edge as propagating wavefronts having well defined velocities. In accordance with two-dimensional simulations of this type of front propagation that take fluctuation effects into account, we find that the interfacial widths w(t) of these SAM self-assembly fronts exhibit a power-law broadening in time, w(t) Ϸ t ␤ , rather than the constant width predicted by MFT. Moreover, the observed exponent values accord rather well with previous simulation and theoretical estimates. These observations have significant implications for diverse types of ordering fronts that occur under confinement conditions in biological or materials-processing contexts.fluctuation-induced interfacial broadening ͉ frontal self-assembly ͉ mean-field Fisher-Kolmogorov equation ͉ reaction-diffusion fronts ͉ self-assembled monolayers I n the early 1990s, Chaudhury and Whitesides developed an extremely facile method of creating surface energy gradients using self-assembled monolayers (SAMs) (1). Rather than using a solution as a carrier for adsorption or a rubber stamp for direct deposition of SAM molecules, these researchers simply placed a volatile fluid of organosilane (OS) molecules at the edge of a silica-covered substrate and enclosed the entire system in a container to avoid convection effects (Fig. 1). The symmetry-breaking perturbation associated with placing the source of diffusing material to the side of the wafer imparts a direction to the self-assembly of the SAM layer and leads to the spontaneous formation of a concentration gradient of OS molecules on the substrate. This gradient may be fixed into position at any point in its development by simply removing the wafer from OS exposure (2). These kinetically ''frozen'' SAM patterns are then ready for further measurements in which surface energy gradients are required.Although this method of ...

Progress in front propagation research

“…And these three key results can be derived only from microscopic models (e.g. that in the previous section) but not from macroscopic ones such as the set (10).…”

“…They describe propagating profiles for the particle concentration, individual number density, temperature, etc. They are widely used in physical models of combustion flames [3], population invasions [4], virus infections [5], tumor growth [6], chemical waves [7], crystallization [8], superconductors [9] and many other interesting phenomena in physical, biophysical, chemical and cross-disciplinary systems [1,2,10].…”

Negative velocity fluctuations of pulled reaction fronts

“…It is one of the most fundamental models in mathematical genetics and population biology [1,2], but similar equations appear in chemical kinetics [3], extreme value statistics [4], disordered systems [5] and even particle physics [6]. The invasion fronts are described by traveling-front solutions (TFSs) of Eq.…”

Spontaneous propagation of self-assembly in a continuous medium

“…Some research has considered self-assembly in the loose sense, which refers to the aggregation of building blocks without forming any ordered pattern. For example, propagating aggregation waves were demonstrated in an organosilane monolayer system [25]. The organic molecules aggregated when the concentration was higher than a critical value.…”