The pressure dependence of the electrical conductivity of SU is very much similar to that of water and ammonia where there is a sharp rise in conductivity at low pressures followed by a plateau above 30 GPa (refs 8, 9). The low pressure conductivity is dominated by conduction via H+ ions that have an effective mean free path comparable to the nearest neighbour distance and travel at thermal velocity. The interpretation is that below 30 GPa, the molecular bonds are being broken generating an increasing population of H+ charge carriers. Based on this picture one can apply the Drude model to the conductivity in which one H+ ion per molecule is available as a charge carrier, one finds the electrical conductivity to be of order 30 (Ω-cm)−1 roughly in agreement with the data. It is interesting that if one applies this picture to increasing pressure, a decrease in conductivity would result because of the shortening of the mean free path, which is contrary to the current experimental data that show a monotonic increase with pressure.

The further increase in electrical conductivity is due to the gradual onset of electronic conduction. The temperature independence of the electrical conductivity ≤74 GPa is consistent with ionic dominated conduction. At higher pressures, electronic conduction will become more pronounced and eventually dominate the ionic contribution. Electronic conduction at higher pressures is expected to be hydrogen-like wherein the electrical conductivity is thermally activated (semi-conductor-like) and temperature dependent with an energy gap that closes with pressure11. The electrical conductivity would become metallic-like on the closing of the gap. The transition from ionic dominated to electronic dominated conduction is smooth and continuous, and not accompanied by any observable discontinuities.

In laser shock experiments on water, metallic-like conductivity was reported at very high pressures and different temperatures from this study12,13. The laser experiments are only sensitive to the electronic part of the conductivity and are lower than our reported conductivity, which includes both the ionic and electronic contributions. As the pressure and temperature increases, the electronic contribution to the conductivity will increase and eventually dominate the ionic contribution. The onset of electronic conduction also leads to electronic contributions to the specific heat and thermal conductivity. We do not have estimates of these contributions but their effect on the thermal profiles of the planet's interior cannot be neglected.

The similarity of the pressure dependence of the electrical conductivity of SU and water is not surprising, as SU is mostly composed of water. The fact that the conductivity versus pressure relation for SU appears to be shifted down from that of water by a factor of two, suggested a possible scaling of the electrical conductivity. The conductivity of water and SU are plotted in Figure 1b as a function of density. As a function of density, the electrical conductivity of water and SU are identical. The density is a measure of the next nearest neighbour distance or effectively the scattering distance for an ion. This makes sense for the ionic conductivity in which the ions have a mean free path that is approximately the next nearest neighbour spacing. It is unclear why this works for the electronic contribution. Ignoring the specific effects of chemistry, the fluid ice layers of Uranus and Neptune can be effectively modelled by density-scaled water.

It is instructive to compare the SU mixture to simpler systems, such as water, methane, and water–methane mixtures (1:1), in particular, in the reticulating phase (4,000 K and 176 GPa). In the region denoted as the reticulating phase in Figure 2 (~4,000 K and 176 GPa), FPMD simulations of pure water predict it to be in the superionic phase14 with a solid oxygen lattice. This is no longer the case in FPMD simulations of mixtures of water–methane or SU, in which the addition of carbon promotes the diffusion of oxygen atoms. Such a change in the location of phase lines in mixtures compared with the pure components is to be expected, and we recover a 'superionic' phase at the same density (3 g cm−3) but at much lower temperature (1,837 K), in which the larger atoms are essentially frozen (diffusion coefficient of ~10−6 cm2 s−1), whereas the hydrogen (deuterium) are still fluid (diffusion coefficient of 7.7×10−5 cm2 s−1). However, at this scale no long-range order is apparent in the simulations.

From the simulations we find that under these extreme conditions of pressure and temperature, molecules dissociate and react at very rapid rates. In the reticulating phase, as the bond lifetime of C–C and C–N bonds is much longer than other type of bonds, the large organic molecules observed in the simulation may be the first stage of growing clusters (containing mostly carbon but also nitrogen). The dissociation of pure methane has been suggested to lead to the precipitation of the carbon in the form of diamond15. But, in the case of the shock recovery experiments and the static high pressure experiments on methane, the presence of aggregated carbon is confirmed only on release to ambient conditions and does not indicate the state of the carbon at high pressure and temperatures. Under the influence of gravity, these small clusters (which are denser than the surrounding fluid) are expected to sink deeper into the core of the planet and constitute a large source of (gravitational) energy that will be converted into thermal energy deeper in the planet.

If the clusters forming in the reticulating phase of the SU mixture, indeed, lead to segregation and precipitation of the carbon and nitrogen content of the mixture, one would go from a fluid highly conducting mixture to an essentially solid superionic water fraction with a rather low conductivity (only ionic through proton hopping with no electronic component), whereas carbon would be in the diamond phase, which has essentially no conductivity. This would then support a stratified core with very low conductivity in line with the models of Stanley and Bloxham1.

To highlight the role of water on the carbon chemistry in the reticulating part of the P–T space, we compare the BACF for C–C and C–H bonds in methane, water–methane (1:1) and SU (which is 1.75:1 O to C ratio) at 4,000 K and 176 GPa (see Fig. 3c). We find that the C–C bonds have a longer lifetime for water-richer mixtures. This suggests that the water-rich SU mixture favours the formation of larger carbon network or clusters than the water–methane (1:1) mixture. This tendency could also be due to the presence of N.

In the reticulating phase, although the SU mixture is still fluid, because of the C–C and C–N bonding and the formation of large networks, its viscosity is expected to be quite different from that of the higher temperature fluid. The calculated viscosity for SU and other mixtures are shown in Figure 4. We find that the viscosity is indeed six times higher at 4,000 K than at 7,260 K. Moreover, at 4,000 K and 176 GPa, the viscosity of the SU mixture is higher than that of the other fluids considered such as methane and water–methane (1:1). This is consistent with the results from the BACF in that the carbon clusters are more stable in the SU mixture.

Figure 4: The calulated viscocity of synthetic Uranus and other mixtures. (a) Calculated viscosity of the synthetic Uranus mixture as a function of temperature. The viscosity is six times higher at 4,000 K than at 7,260 K. (b) Calculated viscosity of different mixtures at 4,000 K and 176 GPa. At 4,000 K and 176 GPa, the viscosity of the SU mixture is higher than that of the other fluids considered such as methane and water–methane (1:1). Full size image

In applying shock compression data to planetary problems, the vast difference between laboratory and planetary timescales needs to be addressed. On the experimental timescale of hundreds of nanoseconds, we expect that the number of particle collisions is sufficiently high for thermal equilibrium to be achieved. However, the ice fluid at planetary pressures and temperatures is expected to be a dissociated fluid and it becomes unclear over planetary timescales whether the effects of gravity and other forces such as convection lead to chemical separation of the dissociated products or if rough chemical balance is maintained. Shock recovery experiments on a variety of hydrocarbons typically show irreversible dissociation of the hydrocarbons and the formation of small amorphous carbon particles. In the case of methane, our preliminary data suggest this process occurs within hundreds of nanoseconds or less. This suggests that any methane within planetary interiors would likely have dissociated and precipitated out as some form of carbon. The situation is less clear for the dissociation products of water and ammonia, but from the simulation, it is likely that the nitrogen is incorporated in the carbon clusters. Any separation and segregation of dissociated products would support the possibility of a stratified inner core for Uranus and Neptune.