# 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 <math>\partial_t C_i =\nabla \cdot(D_i\nabla C_i)+R_i(\{C\},r,t) </math>

where <math>C_i </math>is the concentration of the ith component and <math>D_i</math> and <math>R_i</math> 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.