Concentration of ${\mathrm{C}\mathrm{O}}_2$ over Melting Ice Oscillates

We report that the concentration of ${\mathrm{C}\mathrm{O}}_2$ over melting ice oscillates as long as water and ice coexist. A phenomenological model involving melting of ${\mathrm{C}\mathrm{O}}_2$ containing ice leading to its release, readsorption of the vapor on ice, and dissolution in water is proposed. Thermokinetics of these processes lead to nonlinearity of the dynamics. This phenomenon is also observed over impure ice contaminated with salts or in the presence of nitrogen or air. Oscillations have been observed in several other solute or ice-water systems.

Figure 1

Oscillations in mass spectral intensity of gas phase ${\mathrm{C}\mathrm{O}}_2$ (m/z 44) as a function of temperature/time. The bottom $x$ axis is temperature, from 153 to 303 K; at 273 K bulk ice melts. The arrow shows the constant temperature region. The top $x$ axis is the time, measured from the start of warm-up. The inset is an enlarged view of the oscillations.

Figure 2

Mass spectral intensity of varying quantities of ${\mathrm{C}\mathrm{O}}_2$ deposited over 10 g of ice. a, b, c, d, e, and f correspond to $2.66\times {10}^{-4}$, $5.32\times {10}^{-4}$, $7.98\times {10}^{-4}$, $1.06\times {10}^{-3}$, $1.33\times {10}^{-3}$, and $2.13\times {10}^{-3}\mathrm{m}\mathrm{o}\mathrm{l}$ of ${\mathrm{C}\mathrm{O}}_2$, respectively.

Figure 3

Experimental time series of ${\mathrm{C}\mathrm{O}}_2$ for (a) $2.13\times {10}^{-3}\mathrm{m}\mathrm{o}\mathrm{l}$ (no oscillations), (b) $2.66\times {10}^{-4}\mathrm{m}\mathrm{o}\mathrm{l}$ (no oscillations), and (c) $1.33\times {10}^{-3}\mathrm{m}\mathrm{o}\mathrm{l}$. Simulated oscillations for (${\mathrm{a}}^{\prime }$) ${\mu }_0=1.6$, $\epsilon =0.04$, (${\mathrm{b}}^{\prime }$) ${\mu }_0=0.01$, $\epsilon =0.001$, and (${\mathrm{c}}^{\prime }$) ${\mu }_0=0.8$, $\epsilon =0.01$.

Figure 4

Power spectra of (a) experimental data for $1.33\times {10}^{-3}\mathrm{m}\mathrm{o}\mathrm{l}$ of deposited ${\mathrm{C}\mathrm{O}}_2$, (b) $\alpha$ without the noise component, and (c) $\alpha$ with addition of 0.5% Gaussian noise (with zero mean and unit variance) in each iterative solution step of $\theta$, respectively.