Adsorbate-Induced Phase Transition Model

Abstract

In 1990, Jakubith et al. (Phys. Rev. Lett. 65:3013–3016, 1990) and Ertl (Science 254:1750–1755, 1991) found out that, in the catalytic oxidation of CO molecules on a Pt(110) surface, adsorbed CO molecules and O atoms form various types of spatio-temporal patterns, such as propagating wave, spiral, target, stripe, and chaotic patterns. To understand the mechanism of these phenomena from macroscopic point of view, Hildebrand–Kuperman–Wio–Mikhailov–Ertl and Hildebrand–Ipsen–Mikhailov–Ertl presented a simple kinematic model of the surface reaction coupled to a structural phase transition of the surface, i.e.,

$$\begin{cases}\frac{\partial u}{\partial t}=a\varDelta u-\mu\nabla\cdot[u(1-u)\nabla\chi(\rho)]-fe^{-\alpha\chi(\rho)}u-gu+h(1-u)\\\quad\text{in}\ \varOmega \times(0,\infty),\\\noalign{\vspace{3pt}}\frac{\partial\rho}{\partial t}=b\varDelta\rho+d\rho(\rho+u-1)(1-\rho)-\nu(\rho-\frac{1}{2})\quad\text{in}\ \varOmega \times(0,\infty).\end{cases}$$

(14.1)