Design of equidistant and revert type precipitation patterns in reaction–diffusion systems

In the past years considerable attention has been devoted to designing and controlling patterns at the microscale using bottom-up self-assembling techniques. The precipitation process proved itself to be a good candidate for building complex structures. Therefore, the techniques and ideas to control the precipitation processes in space and in time play an important role. We present here a simple and technologically applicable technique to produce arbitrarily shaped precipitation (Liesegang) patterns. The precipitation process is modelled using a sol coagulation model, in which the precipitation occurs if the concentration of the intermediate species (sol) produced from the initially separated reactants (inner and outer electrolytes) reaches the coagulation threshold. Spatial and/or temporal variation of this threshold can result in equidistant and revert (inverse) type patterns in contrast to regular precipitation patterns, where during the pattern formation a constant coagulation threshold is supposed and applied in the simulations. In real systems, this threshold value may be controlled by parameters which directly affect it (e.g. temperature, light intensity or ionic strength).