Promoter-Induced Reactive Phase Separation in Surface Reactions

Promoters are adsorbed mobile species which do not directly participate in a catalytic surface reaction, but can influence its rate. Often, they are characterized by strong attractive interactions with one of the reactants. We show that these conditions lead to a Turing instability of the uniform state and to the formation of reaction-induced periodic concentration patterns. Experimentally such patterns are observed in catalytic water formation on a Rh(110) surface in the presence of coadsorbed potassium.

Figure 1

Formation of a stationary concentration pattern in catalytic water formation on a Rh(110) surface predosed with potassium (${\theta }_{\mathrm{K}}=0.08$). (a) PEEM images showing the development of stationary patterns during the transition from reducing to oxidizing conditions. Experimental conditions: $T=518\mathrm{K}$, $p_{{\mathrm{H}}_{\mathrm{2}}}=2.2\times {10}^{-6}\mathrm{mbar}$, $p_{{\mathrm{O}}_{\mathrm{2}}}=1\times {10}^{-6}\mathrm{mbar}$ ($t=0$), $1.5\times {10}^{-6}\mathrm{mbar}$ ($t=175\mathrm{s}$), $2\times {10}^{-6}\mathrm{mbar}$ ($t=285\mathrm{s}$). The dimensions of imaged area are $210\times 35\mu \mathrm{m}$. (b) PEEM image of a stationary concentration pattern recorded 840 s after adjusting reaction conditions. Experimental conditions: $T=565\mathrm{K}$, $p_{{\mathrm{O}}_{\mathrm{2}}}=2\times {10}^{-7}\mathrm{mbar}$, $p_{{\mathrm{H}}_{\mathrm{2}}}=1.8\times {10}^{-7}\mathrm{mbar}$. The diameter of the imaged area is $400\mu \mathrm{m}$.

Figure 2

Concentration profiles of potassium and oxygen in a stationary pattern obtained from in situ SPEM measurements of O $1s$ and K $3d$ core levels. Experimental conditions: $T=583\mathrm{K}$, $p_{{\mathrm{O}}_{\mathrm{2}}}=2\times {10}^{-7}\mathrm{mbar}$, $p_{{\mathrm{H}}_{\mathrm{2}}}=0.76\times {10}^{-7}\mathrm{mbar}$, ${\theta }_{\mathrm{K}}=0.08$.

Figure 3

Patterns in the general three-component model. (a) Asymptotic spatial profiles of coverages ${\theta }_A$ (dotted line), ${\theta }_B$ (solid line), and ${\theta }_C$ (dashed line) for $P=1$, $\gamma =10$, $c=0.3$, $u_0{k}_{B}T=8$, $r_0=0.5L_{\mathrm{diff}\mathrm{,}\mathrm{A}}$, and $D_{B}D=0.1$. (b),(c) Snapshots of the distributions of coverages ${\theta }_B$ (b) and ${\theta }_C$ (c) in the two-dimensional simulation with the same parameters; white regions correspond to higher coverages. Periodic boundary and random initial conditions, the linear size is 30 $L_{\mathrm{diff}\mathrm{,}\mathrm{A}}$.

Figure 4

Stationary pattern obtained by numerical simulations of the realistic model. Realistic 1D simulations showing the formation of a stationary pattern in $\mathrm{Rh}(110)/\mathrm{K}/{\mathrm{O}}_{\mathrm{2}}+{\mathrm{H}}_{\mathrm{2}}$. The model parameters are $p_{{\mathrm{H}}_{\mathrm{2}}}=2.2\times {10}^{-6}\mathrm{mbar}$, $p_{{\mathrm{O}}_{\mathrm{2}}}=2.0\times {10}^{-6}\mathrm{mbar}$, $T=518\mathrm{K}$. Initial conditions: ${\theta }_{\mathrm{H}}=0.0$, ${\theta }_{\mathrm{O}}=0.2$, ${\theta }_{\mathrm{K}}=0.1$, with $20\mu \mathrm{m}$ wide adsorbate free region in the center of a $1200\mu \mathrm{m}$ wide interval (the figure shows a $400\mu \mathrm{m}$ wide section). $T$-independent constants: $k_1=2.186\times {10}^6\mathrm{ML}{\mathrm{s}}^{-1}{\mathrm{mbar}}^{-1}$, $k_2=0.546\times {10}^6\mathrm{ML}{\mathrm{s}}^{-1}{\mathrm{mbar}}^{-1}$, $\beta =1.1$, $\gamma =4\times {10}^{-4}$, $\delta =6$, $E_b=0.2491\times {10}^{-22}\mathrm{kJ}$. $T$-dependent constants: ${\nu }_{\mathrm{i}}[{\mathrm{s}}^{-1}]$, $E_{\mathrm{i}}[{10}^{-22}\mathrm{kJ}]$ preexponentials for diffusion in $[{\mathrm{cm}}^2{\mathrm{s}}^{-1}]$: $k_3:{10}^{13},1.1956$; $k_4:{10}^{12},3.4041$; $k_5:{10}^{13},1.4945$; $D_{\mathrm{H}}:4\times {10}^{-3},0.2989$; $D_{\mathrm{O}}:2.5\times {10}^1,1.9926$; for K diffusion (see text): $D_{\mathrm{K}}^0=0.4{\mathrm{cm}}^2{\mathrm{s}}^{-1}$, $E_{\mathrm{diff}\mathrm{,}\mathrm{K}}^{\prime }=0.6277\times {10}^{-22}\mathrm{kJ}$, and $E_{\mathrm{diff}\mathrm{,}\mathrm{K}}^{\prime \prime }=1.4081\times {10}^{-22}\mathrm{kJ}$.