# Difference between revisions of "Micro-and nanotechnology via reaction–diffusion"

## Introduction

The term reaction-diffusion is used to describe systems in which the components are both reacting with in some way (local production/consumption) and diffusing. The general form of the PDE for these systems is $\partial_t C_i =\nabla \cdot(D_i\nabla C_i)+R_i(\{C\},r,t)$

where $C_i$is the concentration of the ith component and $D_i$ and $R_i$ the diffusive and reactive constants of the ith component. Solutions to the reaction-diffusion (RD) equation can have some interesting properties; some solutions have traveling waves. Others show spontaneous formation of patterns, which can be quite intricate. The RD equation first gained interest after Alan Turing showed that stable patterns could exist in these systems. Since then, many phenomena in nature have been found to obey RD. Zebra stripes, cave stalactites, and certain chemical reactions are all patterns that can be described as an outcome of RD. Below we show some of the now classic images assosciated with RD, patterns arising from the Belousov–Zhabotinsky chemical reaciton.

As nature is able to use RD to form intricate patterns, the questions arises as to whether or not we can utilize this method as a way to fabricate patterns. This paper describes a variety RD techniques that were used to controllably engineer micro- and nano-patterns.

## Color Micropatterning

The group employed a stamping technique to create color patterns in gels. In this process, a micropatterned hydrogel (the stamp) is soaked in one or more salt solutions. This hydrogel is then stamped onto a film of dry gel (here, gelatin) which had been chemically doped. The ions were chosen such that their reaction with the chemical led to colored precipitates. As the ions from the stamp diffused into the film, different colored patterns could be created, depending on the diffusitivity and reaction rates of the components. Below is an example of the patterns they were able to achieve with a description of the ion and chemical solutions that were used.

## Surface Micropatterning via Periodic Precipitation

Another technique employed by the group relied on periodic precipitation (PP), which they define as "when inorganic salts diffusing through a gel form mobile colloidal precipitates that can subsequently aggregate into an immobile phase." In PP, waves of the various concentrations propagate outwards from a source; if the surface is made to deform via reaction with the precipitate, then the deformation will be higher in areas of higher concentrations, and patterns can emerge. Using PP the group was able to create patterned surface that have traditionally been fabricated via techniques such as photolithography.

## RD Sensing

The RD equation is very sensitive to changes in the diffusivity and reaction terms and can therefore in principle be used to detect small changes in the parameters of a system. This is a bit difficult to achieve in practice, as it is not easy to predict which patterns will emerge for a given system. However, the group was able to show on situation where RD sensing could come into play. They stamped the same micropattern on two gel films. The gel films differed in thickness by only 1 micron, yet the patterns that emerged via RD were very different because the difference in thickness had a large effect on the diffusive properties. The two pictures in the middle below show the two patterns. On the right, the patterns that emerged from a film that varied continuously in thickness from 10-35 microns. As can be seen, this shows promise for applications in thickness measurement, and perhaps in measurements of more difficult quantities.

## Conclusion

RD systems can form intricate patterns. Though controlling and modeling these systems can sometimes be difficult, the group showed a variety of techniques which can use RD in a useful engineering setting.