Suppression of spatiotemporal chaos in the oscillatory CO oxidation on Pt(110) by focused laser light

Chemical turbulence in the oscillatory catalytic CO oxidation on Pt(110) is suppressed by means of focused laser light. The laser locally heats the platinum surface which leads to a local increase of the oscillation frequency, and to the formation of a pacemaker which emits target waves. These waves slowly entrain the medium and suppress the spatiotemporal chaos present in the absence of laser light. Our experimental results are confirmed by a detailed numerical analysis of one- and two-dimensional media using the Krischer-Eiswirth-Ertl model for CO oxidation on Pt(110). Different control regimes are identified and the dispersion relation of the system is determined using the pacemaker as an externally tunable wave source.

Figure 1

(Color online) Experimental setup. Upon reflection at the platinum surface (sample) the light changes polarization because the Pt(110) surface is optically anisotropic. When covered with CO, the optical properties of the crystal surface change slightly compared to a clean or oxygen covered surface. This is visualized using the polarizing beam splitter cube which acts as a filter. Light reflected from reactive surface areas is blocked, but light reflected from surface regions covered with CO can pass. The platinum surface is imaged onto the chip of a CCD camera using a simple achromatic lens. The light of an Ar-ion laser is focused onto the surface and can be positioned via computer controlled mirrors. Reproduced from [50].

Figure 2

(Color online) Suppression of turbulence by a laser induced target pattern. (a)–(c) Snapshots at indicated time moments after initiation of the laser spot. (d) Frequency spectrum at the center of the target pattern compared to frequency of the background dynamics. The white arrow in (a) indicates the position of the laser spot. The reaction parameters are $P_{\text{Laser}}=49\text{mW}$, $p_{{\text{O}}_2}=1.84\times {10}^{-4}\text{mbar}$, $p_{\text{CO}}=7.84\times {10}^{-5}\text{mbar}$, and $T=538\text{K}$.

Figure 3

(Color online) Moving the laser spot. (a) Snapshot 10 s prior to move, arrows indicate old (1) and new (2) position of the laser spot, (b) snapshot 80 s after move, (c) frequency evolution at the old (black) and the new (red) location of the laser spot. The reaction parameters are $P_{\text{Laser}}=53\text{mW}$, $p_{{\text{O}}_2}=1.84\times {10}^{-4}\text{mbar}$, $p_{\text{CO}}=7.84\times {10}^{-5}\text{mbar}$, and $T=538\text{K}$.

Figure 4

Partial control. (a)–(c) Snapshots of the system at indicated time moments. (d) space-time plots along the line indicated in (a). After the oxygen pressure is decreased from $2.064\times {10}^{-4}\text{mbar}$ to $2.058\times {10}^{-4}\text{mbar}$ at $t=45\text{s}$, the target pattern collapses via a cascade of phase slips. The reaction parameters are $P_{\text{Laser}}=63\text{mW}$, $p_{\text{CO}}=8.40\times {10}^{-5}\text{mbar}$, $T=539\text{K}$, $p_{{\text{O}}_2}=2.068\times {10}^{-4}\text{mbar}$ for $t>95\text{s}$.

Figure 5

(Color online) Frequency analysis of the data shown in Fig. 4. (a) Thick red curve, frequency of the pacemaker; thick black curve, frequency far away from the target pattern (natural frequency), the curves in different shades of gray indicate the frequency at distances of $4\lambda$ (dark gray) to $10\lambda$ (light gray) from the pacemaker along the white line in Fig. 4a. (b) Blue lines indicate the frequency at distances of $11\lambda$ (dark blue) to $14\lambda$ (light blue) from the pacemaker.

Figure 6

Spatiotemporal dynamics in the KEE model. Parameters: $T_0=543.5\text{K}$, $p_{\text{CO}}=4.46\times {10}^{-5}\text{mbar}$, and $p_{{\text{O}}_2}=1.1\times {10}^{-4}\text{mbar}$. Shown are space-time diagrams in gray scale for $u$. Black (white) denotes minimum (maximum) values of $u$ in the shown simulation. (a) Development of intermittent turbulence from an initial perturbation (strong, momentary, localized increase of $u$ in the center of the medium). System size is $L=800\mu \text{m}$, shown time interval $t=\left[0,200\right]\text{s}$. (b) Complete control: Full suppression of turbulence by a heterogeneous pacemaker $\left(\Delta T=0.13\text{K},\sigma =16\mu \text{m}\right)$. System size is $L=1400\mu \text{m}$, heterogeneity is switched on at $t=0\text{s}$. Shown are time intervals $t=\left[200,400\right]\text{s}$ (upper panel) and $t=\left[839,1039\right]\text{s}$ (lower panel). (c) Partial control: Spatially confined suppression of turbulence by a heterogeneous pacemaker $\left(\Delta T=0.17\text{K},\sigma =16\mu \text{m}\right)$. System size is $L=1400\mu \text{m}$, heterogeneity is switched on at $t=0\text{s}$. Shown are time intervals $t=\left[200,400\right]\text{s}$ (upper panel) and $t=\left[1300,1500\right]\text{s}$ (lower panel).

Figure 7

Analysis of patterns induced by the pacemaker. (a) Control diagram. Depending on the choice of parameters $\Delta T$ (temperature shift) and $\sigma$ (size of the heterogeneity) we find regions of partial and complete control. (b) Wavelength of the generated target patterns as a function of temperature shift for $\sigma =2\mu \text{m}$ (solid curve) and $\sigma =24\mu \text{m}$ (dashed curve). Solid symbols indicate simulations that lie in the regime of partial control.

Figure 8

(Color online) Diagram showing the main solutions of the CO oxidation system in the parameter space spanned by the partial pressures of oxygen and CO, without (a) and with (b) temperature heterogeneity. In (a), “$U$” denotes uniform oscillations, “$T$” denotes turbulence, “reactive” denotes the reactive-oxygen-covered state, and “CO” the CO-covered state. In (b), “$P$” denotes the area where the temperature heterogeneity constitutes a pacemaker, i.e., gives rise to target patterns. Where this area overlaps with the region “$T$” in (a), control of turbulence (complete or partial) is observed. For more information see text. The system size is $L=800\mu \text{m}$ and the simulation time is $t=2000\text{s}$ [and $t=8000\text{s}$ in the “$T$” region of (a)].

Figure 9

Dispersion relations $\omega \left(k^2\right)$ (a) and $\lambda \left(\tau \right)$ (b). A linear fit to $\omega =\omega \left(k^2\right)$ (dotted curve) is added.

Figure 10

(Color online) Control of chemical turbulence in a two-dimensional system by a temperature induced pacemaker. A temperature heterogeneity of Gaussian shape ($\Delta T=0.3\text{K}$ and $\sigma =40\mu \text{m}$) is induced at $t=0\text{s}$ in the center of the domain. The partial pressures of the reactants are $p_{\text{CO}}=4.46\times {10}^{-5}\text{mbar}$ and $p_{{\text{O}}_2}=10.6\times {10}^{-5}\text{mbar}$, the base temperature is $T_0=543.5\text{K}$. (a) Chemical turbulence at time $t=0\text{s}$. Emerging target pattern at (b) $t=250\text{s}$, (c) $t=500\text{s}$, and (d) $t=750\text{s}$. (e) Space-time diagram along the vertical white line indicated in (a); time axis as in (f). (f) Frequency analysis of time series at four different points in space indicated by colored arrows on the left-hand side of the space-time diagram (e), the dashed black line shows the frequency in the center of the pacemaker.