Hydrogen–Water Demixing: Planetary & Materials Insights

• Hydrogen–water demixing is the thermodynamic phase separation of a hydrogen-water mixture into distinct hydrogen-rich and water-rich phases, defined by Gibbs free energy criteria.
• Models of planetary interiors leverage demixing to explain compositional layering, gravitational harmonics, and thermal evolution in ice giants like Uranus and Neptune.
• Both experimental setups and ab initio computational methods, including Flory–Huggins representations, are used to elucidate hydrogen–water separation under extreme pressures.

Searching arXiv for papers on hydrogen–water demixing and related planetary interior studies. Hydrogen–water demixing is the phase separation of a nominally mixed $\mathrm{H_2}$–$\mathrm{H_2O}$ system into coexisting hydrogen-rich and water-rich phases under conditions where mixing is thermodynamically disfavored. In planetary science, the topic is primarily associated with the interiors of Uranus and Neptune, where the miscibility of major volatile constituents affects interior stratification, gravitational harmonics, magnetic-field interpretation, thermal evolution, and atmospheric composition constraints (Bailey et al., 2020, Amoros et al., 2024, Howard et al., 8 Jul 2025). In condensed-matter and cryogenic materials research, hydrogen removal from hydrogen-filled ice provides a distinct but related manifestation of hydrogen–water separation, producing a metastable porous water framework known as ice XVII (Rosso et al., 2016). Across these settings, the central question is whether hydrogen and water remain a single phase or undergo immiscibility governed by the Gibbs free energy of mixing, chemical-potential equalities, and the geometry of binodal and spinodal boundaries (Amoros et al., 2024, Howard et al., 8 Jul 2025).

1. Thermodynamic definition and phase-separation criteria

For a binary mixture of hydrogen and water at pressure $P$, temperature $T$, and composition $x$, demixing is formulated through the Gibbs free energy of mixing. One representation writes

$$\Delta G_{\rm mix}(x,T,P)=G_{\rm mix}-\left[x\,G_{\mathrm{H_2}}+(1-x)\,G_{\mathrm{H_2O}}\right],$$

with $x$ taken as the $\mathrm{H_2O}$ particle fraction in one formulation (Amoros et al., 2024) and as the water mole fraction $x\equiv x_{\mathrm{H_2O}}$ in another (Howard et al., 8 Jul 2025). In the planetary demixing literature summarized here, phase separation occurs when the free-energy surface develops a composition range associated with an immiscibility gap, and coexistence is determined by equality of chemical potentials between the two phases (Amoros et al., 2024, Howard et al., 8 Jul 2025).

A detailed statement of the coexistence condition uses

$$\mu_{\mathrm{H_2}}(A)=\mu_{\mathrm{H_2}}(B), \qquad \mu_{\mathrm{H_2O}}(A)=\mu_{\mathrm{H_2O}}(B),$$

where $\mathrm{H_2O}$0 is water-poor and $\mathrm{H_2O}$1 is water-rich (Amoros et al., 2024). The same condition is equivalently expressed through a common-tangent construction in the composition-dependent free energy, formulated as solving $\mathrm{H_2O}$2 and $\mathrm{H_2O}$3 (Howard et al., 8 Jul 2025). The spinodal is defined by the vanishing of the curvature of the Gibbs free energy with respect to composition, $\mathrm{H_2O}$4 (Howard et al., 8 Jul 2025). One summary also states that the immiscibility-gap criterion is $\mathrm{H_2O}$5 over some range in $\mathrm{H_2O}$6, with the locus where $\mathrm{H_2O}$7 defining the spinodal and the maximum of the coexistence curve constituting a critical point $\mathrm{H_2O}$8 (Amoros et al., 2024). This discrepancy in sign convention reflects differing definitions and summaries of the free-energy construction rather than a settled controversy in the supplied material.

A simplified thermodynamic parameterization for warm sub-Neptunes adopts a Flory–Huggins–style expression,

$\mathrm{H_2O}$9

with $P$0 and $P$1 an interaction parameter (Piaulet-Ghorayeb et al., 1 Dec 2025). In that representation, absolute instability is written as

$P$2

or equivalently $P$3 (Piaulet-Ghorayeb et al., 1 Dec 2025). The same source states that, in practice, it does not adopt the toy Flory–Huggins parameterization directly, but instead uses ab-initio-derived coexistence curves.

2. Phase diagrams, critical curves, and experimental-computational disagreements

Two lines of evidence for possible hydrogen–water immiscibility in ice-giant interiors were identified in work on thermodynamically governed interior models of Uranus and Neptune (Bailey et al., 2020). The first arises from crude extrapolation of the experimental hydrogen–water critical curve to $P$4 GPa using data obtained for an impure system containing silicates, as reported by Bali et al. (2013); the same source notes that Uranus and Neptune could also be “dirty” (Bailey et al., 2020). The second invokes reasoning based on the gravitational and magnetic fields (Bailey et al., 2020). That work also states that current ab initio models disagree and cites Soubiran and Militzer (2015), while remarking that hydrogen and water are difficult to model from first-principles quantum mechanics with the necessary precision (Bailey et al., 2020).

A more systematic planetary treatment constructs seven $P$5–$P$6 phase diagrams from available experimental and computational data (Amoros et al., 2024). These are the SFB-linear-3 GPa, SFB-linear-4 GPa, and SFB-linear-5 GPa extrapolations of Seward and Franck (1981) and Bali et al. (2013); the V23 flat, V23 conv–1800 K, and V23 conv–2000 K extensions of Vlasov et al. (2023); and Berg24, based on ab initio DFT-MD results from Bergermann et al. (2024) up to $P$7 GPa (Amoros et al., 2024). For each critical curve $P$8, the low-pressure U-shape of the $P$9 GPa binodal observed by Seward and Franck (1981) is shifted vertically by $T$0, yielding approximate isobaric boundaries $T$1 and $T$2 (Amoros et al., 2024). Clausius–Clapeyron,

$T$3

is given but not explicitly required in the interpolation procedure (Amoros et al., 2024).

A later study of Uranus, Neptune, K2-18 b, and TOI-270 d uses recent ab initio calculations and an analytic fit to the demixing temperature:

$T$4

with coefficients $T$5, $T$6, $T$7, $T$8, $T$9, $x$0, $x$1, $x$2, and $x$3 (Howard et al., 8 Jul 2025). The same work introduces constant temperature offsets,

$x$4

with explored values $x$5, $x$6 K, and $x$7 K, and for exoplanets up to $x$8 K, in order to bracket uncertainties in the miscibility gap (Howard et al., 8 Jul 2025).

For warm sub-Neptunes, a merged low-pressure and high-pressure critical-curve construction is described as

$x$9

and full $$\Delta G_{\rm mix}(x,T,P)=G_{\rm mix}-\left[x\,G_{\mathrm{H_2}}+(1-x)\,G_{\mathrm{H_2O}}\right],$$0–$$\Delta G_{\rm mix}(x,T,P)=G_{\rm mix}-\left[x\,G_{\mathrm{H_2}}+(1-x)\,G_{\mathrm{H_2O}}\right],$$1 coexistence curves are computed for metallicities from $$\Delta G_{\rm mix}(x,T,P)=G_{\rm mix}-\left[x\,G_{\mathrm{H_2}}+(1-x)\,G_{\mathrm{H_2O}}\right],$$2 to $$\Delta G_{\rm mix}(x,T,P)=G_{\rm mix}-\left[x\,G_{\mathrm{H_2}}+(1-x)\,G_{\mathrm{H_2O}}\right],$$3 solar (Piaulet-Ghorayeb et al., 1 Dec 2025). At $$\Delta G_{\rm mix}(x,T,P)=G_{\rm mix}-\left[x\,G_{\mathrm{H_2}}+(1-x)\,G_{\mathrm{H_2O}}\right],$$4 solar, the dome of immiscibility peaks at $$\Delta G_{\rm mix}(x,T,P)=G_{\rm mix}-\left[x\,G_{\mathrm{H_2}}+(1-x)\,G_{\mathrm{H_2O}}\right],$$5 K around $$\Delta G_{\rm mix}(x,T,P)=G_{\rm mix}-\left[x\,G_{\mathrm{H_2}}+(1-x)\,G_{\mathrm{H_2O}}\right],$$6 kbar, whereas at $$\Delta G_{\rm mix}(x,T,P)=G_{\rm mix}-\left[x\,G_{\mathrm{H_2}}+(1-x)\,G_{\mathrm{H_2O}}\right],$$7 solar the dome peaks above $$\Delta G_{\rm mix}(x,T,P)=G_{\rm mix}-\left[x\,G_{\mathrm{H_2}}+(1-x)\,G_{\mathrm{H_2O}}\right],$$8 K near $$\Delta G_{\rm mix}(x,T,P)=G_{\rm mix}-\left[x\,G_{\mathrm{H_2}}+(1-x)\,G_{\mathrm{H_2O}}\right],$$9 kbar (Piaulet-Ghorayeb et al., 1 Dec 2025).

3. Demixing in Uranus and Neptune

Interior models that assume discrete layers are only directly justified if the major constituents are immiscible; otherwise, diffuse interfaces may arise from accretion that centrally concentrates the least volatile and most dense constituents, with resulting compositional gradients likely inhibiting convection (Bailey et al., 2020). Within that framework, hydrogen–water immiscibility has been treated as a candidate explanation for the contrasting internal properties of Uranus and Neptune (Bailey et al., 2020, Amoros et al., 2024).

Adiabatic structure calculations compare planetary adiabats $x$0 to the various demixing boundaries to infer the onset and depth of phase separation (Amoros et al., 2024). The onset occurs where the planetary adiabat intersects the phase boundary, stated as $x$1–$x$2 GPa and $x$3–$x$4 K (Amoros et al., 2024). Rain-out then proceeds until the adiabat of the depleted outer layer just grazes the binodal at a single transition pressure $x$5 (Amoros et al., 2024). In this formalism, $x$6 is the outer-envelope water mass fraction after demixing, $x$7 is the deep-interior water mass fraction, and $x$8 is the pressure of the sharp transition between the water-poor and water-rich layers (Amoros et al., 2024).

For Uranus with $x$9 K, the inferred upper limit is $\mathrm{H_2O}$0 with $\mathrm{H_2O}$1–$\mathrm{H_2O}$2 GPa (Amoros et al., 2024). For Neptune with $\mathrm{H_2O}$3 K, the inferred upper limit is $\mathrm{H_2O}$4 with the same $\mathrm{H_2O}$5–$\mathrm{H_2O}$6 GPa range (Amoros et al., 2024). The sensitivity to phase-diagram choice is explicit: SFB-linear models are shallow with $\mathrm{H_2O}$7 GPa, V23 extensions give $\mathrm{H_2O}$8–$\mathrm{H_2O}$9 GPa, and Berg24 yields the deepest $x\equiv x_{\mathrm{H_2O}}$0 GPa and the widest tangential region, $x\equiv x_{\mathrm{H_2O}}$1–$x\equiv x_{\mathrm{H_2O}}$2 GPa (Amoros et al., 2024).

An earlier thermodynamic interior study drew a different asymmetry between the two planets. It found that Neptune models with envelopes containing a substantial water mole fraction, as much as $x\equiv x_{\mathrm{H_2O}}$3 relative to hydrogen, can satisfy observations, whereas Uranus models appear to require $x\equiv x_{\mathrm{H_2O}}$4, potentially suggestive of fully demixed hydrogen and water (Bailey et al., 2020). The same study argued that different hydrogen–water demixing states could account for the different heatflows of Uranus and Neptune (Bailey et al., 2020). This suggests that the sharper depletion inferred for Uranus in some models is linked not only to present-day composition but also to a specific thermodynamic and evolutionary pathway.

4. Interior structure, gravitational harmonics, and layered envelopes

The adiabatic-structure approach for the ice giants combines equations of state for an H/He mixture, water, and rock with hydrostatic equilibrium and mass continuity:

$x\equiv x_{\mathrm{H_2O}}$5

and an adiabatic gradient $x\equiv x_{\mathrm{H_2O}}$6 computed from the equation of state mixture including ideal-mixing entropy (Amoros et al., 2024). The H/He equation of state is given as the SCvH-like EoS by Chabrier and Debras (2021), the water equation of state as AQUA EoS, and the rock core as the Hubbard and Marley (1989) silicate/iron mixture (Amoros et al., 2024).

The resulting density structures are evaluated against the observed gravitational harmonics. The even zonal harmonics are written as

$x\equiv x_{\mathrm{H_2O}}$7

In a case with a water-only deep envelope adjusted to fit the observed $x\equiv x_{\mathrm{H_2O}}$8, the comparison with $x\equiv x_{\mathrm{H_2O}}$9 discriminates among demixing prescriptions (Amoros et al., 2024). SFB-linear-3 GPa models with $$\mu_{\mathrm{H_2}}(A)=\mu_{\mathrm{H_2}}(B), \qquad \mu_{\mathrm{H_2O}}(A)=\mu_{\mathrm{H_2O}}(B),$$0 GPa yield $$\mu_{\mathrm{H_2}}(A)=\mu_{\mathrm{H_2}}(B), \qquad \mu_{\mathrm{H_2O}}(A)=\mu_{\mathrm{H_2O}}(B),$$1 larger than observed, including dynamic wind correction, and are therefore excluded (Amoros et al., 2024). SFB-linear-5 GPa and V23 conv–2000 K models with $$\mu_{\mathrm{H_2}}(A)=\mu_{\mathrm{H_2}}(B), \qquad \mu_{\mathrm{H_2O}}(A)=\mu_{\mathrm{H_2O}}(B),$$2–$$\mu_{\mathrm{H_2}}(A)=\mu_{\mathrm{H_2}}(B), \qquad \mu_{\mathrm{H_2O}}(A)=\mu_{\mathrm{H_2O}}(B),$$3 GPa can just match Neptune’s $$\mu_{\mathrm{H_2}}(A)=\mu_{\mathrm{H_2}}(B), \qquad \mu_{\mathrm{H_2O}}(A)=\mu_{\mathrm{H_2O}}(B),$$4 but overpredict Uranus’s $$\mu_{\mathrm{H_2}}(A)=\mu_{\mathrm{H_2}}(B), \qquad \mu_{\mathrm{H_2O}}(A)=\mu_{\mathrm{H_2O}}(B),$$5 unless $$\mu_{\mathrm{H_2}}(A)=\mu_{\mathrm{H_2}}(B), \qquad \mu_{\mathrm{H_2O}}(A)=\mu_{\mathrm{H_2O}}(B),$$6 GPa (Amoros et al., 2024). Berg24 with $$\mu_{\mathrm{H_2}}(A)=\mu_{\mathrm{H_2}}(B), \qquad \mu_{\mathrm{H_2O}}(A)=\mu_{\mathrm{H_2O}}(B),$$7 GPa matches both $$\mu_{\mathrm{H_2}}(A)=\mu_{\mathrm{H_2}}(B), \qquad \mu_{\mathrm{H_2O}}(A)=\mu_{\mathrm{H_2O}}(B),$$8 and $$\mu_{\mathrm{H_2}}(A)=\mu_{\mathrm{H_2}}(B), \qquad \mu_{\mathrm{H_2O}}(A)=\mu_{\mathrm{H_2O}}(B),$$9 within uncertainties (Amoros et al., 2024).

The inferred deep compositions depend on whether rocks are permitted below a “rock-cloud” level. In a water-only deep envelope, $\mathrm{H_2O}$00–$\mathrm{H_2O}$01 for Uranus and $\mathrm{H_2O}$02–$\mathrm{H_2O}$03 for Neptune (Amoros et al., 2024). If a rock fraction is allowed below a “rock-cloud” level at $\mathrm{H_2O}$04 K and $\mathrm{H_2O}$05–$\mathrm{H_2O}$06 GPa, with the ice-to-rock ratio fixed to $\mathrm{H_2O}$07 solar ($\mathrm{H_2O}$08), the enhanced central condensation lowers $\mathrm{H_2O}$09 and improves agreement (Amoros et al., 2024). In that case, $\mathrm{H_2O}$10–$\mathrm{H_2O}$11 and $\mathrm{H_2O}$12–$\mathrm{H_2O}$13 for Uranus, while Neptune yields $\mathrm{H_2O}$14–$\mathrm{H_2O}$15 and $\mathrm{H_2O}$16–$\mathrm{H_2O}$17 (Amoros et al., 2024).

The same work emphasizes that a sharp transition at $\mathrm{H_2O}$18–$\mathrm{H_2O}$19 GPa emerges because the binodal is nearly vertical in $\mathrm{H_2O}$20, and that gradual layering would require more complex binodal shapes at these pressures (Amoros et al., 2024). This is significant because it links a microscopic phase boundary directly to the macroscopic legitimacy of “classical few-layer models” for Uranus and Neptune (Amoros et al., 2024).

5. Thermal evolution, rain-out energetics, and planetary consequences

Hydrogen–water demixing is not only a structural effect but also an energy source. In thermodynamically governed interior models of Uranus and Neptune, enough gravitational potential energy is available from gradual hydrogen–water demixing to supply Neptune’s present-day heatflow for roughly ten solar system lifetimes (Bailey et al., 2020). The same study states that hydrogen–water demixing could slow Neptune’s cooling rate by an order of magnitude (Bailey et al., 2020). Within the scope of the supplied material, these statements are presented as consequences of gradual phase separation and settling rather than of a transient catastrophic event.

A later evolutionary treatment couples phase separation directly into a 1D structure–energy solver, CEPAM, using

$\mathrm{H_2O}$21

and the internal-energy equation

$\mathrm{H_2O}$22

where the last term accounts for chemical work associated with composition changes (Howard et al., 8 Jul 2025). At each timestep, layers satisfying $\mathrm{H_2O}$23 are flagged as unstable; the local water mass fraction is reduced to its saturation value, and the excess water is instantaneously redeposited below, maintaining a smooth and monotonic water-versus-depth profile (Howard et al., 8 Jul 2025). The chemical potential difference appears as a positive source term and physically includes both latent heat release and gravitational potential energy as water sinks (Howard et al., 8 Jul 2025). The additional energy raises the intrinsic luminosity and can slow contraction or even cause transient radius inflation (Howard et al., 8 Jul 2025).

The following summary organizes the planetary outcomes explicitly stated for the evolutionary models (Howard et al., 8 Jul 2025):

Planet	$\mathrm{H_2O}$24	Stated consequence
Uranus	$\mathrm{H_2O}$25 K	no demixing; $\mathrm{H_2O}$26 remains $\mathrm{H_2O}$27
Uranus	$\mathrm{H_2O}$28 K	outer $\mathrm{H_2O}$29 mass fully depleted; $\mathrm{H_2O}$30
Uranus	$\mathrm{H_2O}$31 K	outer $\mathrm{H_2O}$32 mass fully depleted; $\mathrm{H_2O}$33
Neptune	$\mathrm{H_2O}$34 K	no demixing; $\mathrm{H_2O}$35 remains $\mathrm{H_2O}$36
Neptune	$\mathrm{H_2O}$37 K	outer $\mathrm{H_2O}$38 depleted; $\mathrm{H_2O}$39
Neptune	$\mathrm{H_2O}$40 K	outer $\mathrm{H_2O}$41 fully depleted; $\mathrm{H_2O}$42

For Uranus, a $\mathrm{H_2O}$43 K offset gives onset at $\mathrm{H_2O}$44 kbar at $\mathrm{H_2O}$45 Gyr and complete depletion of the outer $\mathrm{H_2O}$46 mass, while a $\mathrm{H_2O}$47 K offset yields onset at $\mathrm{H_2O}$48 kbar at $\mathrm{H_2O}$49 Gyr and full demixing of the outer $\mathrm{H_2O}$50 by mass, with a radius increase of nearly $\mathrm{H_2O}$51 (Howard et al., 8 Jul 2025). For Neptune, a $\mathrm{H_2O}$52 K offset gives onset at $\mathrm{H_2O}$53–$\mathrm{H_2O}$54 kbar at $\mathrm{H_2O}$55 Gyr with the outer $\mathrm{H_2O}$56 depleted, and a $\mathrm{H_2O}$57 K offset gives onset at $\mathrm{H_2O}$58–$\mathrm{H_2O}$59 kbar at $\mathrm{H_2O}$60 Gyr with full depletion of the outer envelope and again nearly $\mathrm{H_2O}$61 radius increase (Howard et al., 8 Jul 2025).

A plausible implication is that thermodynamic uncertainty in the phase diagram propagates directly into uncertainty in the inferred luminosity history, contraction rate, and present-day stratification. That implication is explicitly anticipated in calls for coupled thermal-evolution models including latent heat release and gravitational energy from rain-out to refine cooling-time predictions and address Uranus’s anomalously low luminosity (Amoros et al., 2024).

6. Materials manifestation: hydrogen removal from filled ice and ice XVII

Outside planetary interiors, hydrogen–water demixing also appears in cryogenic solid-state systems. A hydrogen-filled crystalline water compound called C$\mathrm{H_2O}$62 filled ice can be emptied to produce a new porous form of ice, termed ice XVII, while retaining the water-lattice framework (Rosso et al., 2016). The precursor is synthesized by exposing finely powdered $\mathrm{H_2O}$63 ice to $\mathrm{H_2O}$64 gas at $\mathrm{H_2O}$65 MPa and $\mathrm{H_2O}$66 K; the sample adsorbs hydrogen above $\mathrm{H_2O}$67 MPa, and the pressure is maintained for several days to assure full conversion to the C$\mathrm{H_2O}$68 phase (Rosso et al., 2016). Room-pressure X-ray diffraction at $\mathrm{H_2O}$69 K is fitted by the C$\mathrm{H_2O}$70-II structural model in space group $\mathrm{H_2O}$71 with lattice constants $\mathrm{H_2O}$72 Å and $\mathrm{H_2O}$73 Å (Rosso et al., 2016).

Hydrogen release is monitored by Raman spectroscopy in four spectral regions: lattice phonons, H–O–H stretch, $\mathrm{H_2O}$74 rotational lines, and $\mathrm{H_2O}$75 vibrons (Rosso et al., 2016). As temperature is slowly raised under vacuum, the intensity of the $\mathrm{H_2O}$76 rotational lines decreases until they vanish after $\mathrm{H_2O}$77–$\mathrm{H_2O}$78 h at $\mathrm{H_2O}$79 K, with no abrupt shifts or splittings in lattice phonon or OH bands, implying no change of the water-lattice framework (Rosso et al., 2016). Hydrogen content is quantified using

$\mathrm{H_2O}$80

with calibration giving $\mathrm{H_2O}$81 (Rosso et al., 2016). Freshly synthesized C$\mathrm{H_2O}$82 samples have $\mathrm{H_2O}$83–$\mathrm{H_2O}$84, hence $\mathrm{H_2O}$85 (Rosso et al., 2016).

The equilibrium condition for guest hydrogen is stated as

$\mathrm{H_2O}$86

with ideal-gas chemical potential

$\mathrm{H_2O}$87

From adsorption isotherms at fixed uptake $\mathrm{H_2O}$88, the adsorption enthalpy is obtained through

$\mathrm{H_2O}$89

and experimentally $\mathrm{H_2O}$90 decreases from $\mathrm{H_2O}$91 kJ/mol at $\mathrm{H_2O}$92 to $\mathrm{H_2O}$93 kJ/mol at $\mathrm{H_2O}$94 (Rosso et al., 2016). The corresponding Gibbs free-energy change is given as $\mathrm{H_2O}$95 (Rosso et al., 2016).

Neutron powder diffraction on deuterated ice XVII yields an empty-lattice structure in space group $\mathrm{H_2O}$96, with lattice constants at $\mathrm{H_2O}$97 K of $\mathrm{H_2O}$98 Å and $\mathrm{H_2O}$99 Å (Rosso et al., 2016). The framework contains helical channels parallel to $P$00, with free bore of $P$01 Å and channel diameter $P$02 Å (Rosso et al., 2016). The same work describes the demixing mechanism as smooth, diffusion-mediated desorption under vacuum, with guest molecules leaving the spiraling channels while the host framework persists (Rosso et al., 2016). Upon emptying, the OH-stretch mode downshifts by $P$03 and phonons upshift by $P$04, indicating loss of guest-induced strain (Rosso et al., 2016).

Adsorption–desorption isotherms show strong hysteresis at $P$05 K, two kinetic regimes at $P$06 K, and nearly reversible behavior for $P$07 K (Rosso et al., 2016). The emptied crystal can adsorb hydrogen again and release it repeatedly, and ice XVII can be refilled to $P$08 at $P$09 K and $P$10 bar within minutes, with no detectable loss of crystallinity or capacity (Rosso et al., 2016). In this materials context, hydrogen–water demixing refers not to liquid immiscibility in a planetary envelope but to removal of guest $P$11 from a host water lattice while preserving a metastable porous ice framework.

7. Extensions to sub-Neptunes, observational implications, and open questions

Hydrogen–water demixing has been extended from Solar System ice giants to sub-Neptunes. One study finds that demixing may occur in Uranus, Neptune, K2-18 b, and TOI-270 d and could lead to complete depletion of water in the outermost regions of Uranus and Neptune (Howard et al., 8 Jul 2025). For K2-18 b, a temperature offset of $P$12 K is required to obtain complete depletion of water in the atmosphere, and the model is proposed as an explanation for the absence of water features in its JWST spectrum (Howard et al., 8 Jul 2025). For TOI-270 d, the same offset yields partial atmospheric depletion, consistent with JWST’s detection of water (Howard et al., 8 Jul 2025).

A later atmosphere–interior inference framework, ATHENAIA, argues for “a window for demixing” on warm metal-rich sub-Neptunes (Piaulet-Ghorayeb et al., 1 Dec 2025). The atmosphere is modeled with SCARLET and the interior with one-dimensional structure models following Thorngren et al. (2016, 2019), linked by minimizing

$P$13

at $P$14 (Piaulet-Ghorayeb et al., 1 Dec 2025). For solar-type irradiation levels equivalent to TOI-270 d, the region in which demixing first appears is approximately

$P$15

and the window broadens for lower $P$16, higher mass, or larger envelope mass fraction (Piaulet-Ghorayeb et al., 1 Dec 2025).

That framework emphasizes the role of adiabatic gradients. The dry adiabatic gradient is

$P$17

and water-rich mixtures have systematically smaller $P$18 than pure H$P$19/He mixtures (Piaulet-Ghorayeb et al., 1 Dec 2025). The reported values are $P$20–$P$21 for pure H$P$22/He, $P$23–$P$24 for $P$25 by mass H$P$26O, and $P$27–$P$28 for $P$29 H$P$30O in the $P$31–$P$32 kbar region (Piaulet-Ghorayeb et al., 1 Dec 2025). Because a shallower adiabat heats up more slowly with depth, a water-rich envelope can remain below $P$33 and therefore enter the demixing region (Piaulet-Ghorayeb et al., 1 Dec 2025).

For TOI-270 d specifically, the inferred posterior is bimodal: either a thin ($P$34–$P$35 wt %) solar-metallicity envelope or a thick ($P$36–$P$37 wt %) water-rich one (Piaulet-Ghorayeb et al., 1 Dec 2025). The JWST water abundance, stated as $P$38, lies inside the demixing window $P$39–$P$40 and $P$41–$P$42, so the planet is argued likely to host compositional gradients, with the true bulk $P$43 possibly $P$44–$P$45 higher than the photospheric $P$46 (Piaulet-Ghorayeb et al., 1 Dec 2025). The same models place the envelope–mantle boundary at $P$47 kbar and $P$48 K for $P$49 K and $P$50, which is below high-pressure silicate melting curves of $P$51–$P$52 K; on that basis, no molten magma ocean is predicted for TOI-270 d (Piaulet-Ghorayeb et al., 1 Dec 2025).

Several unresolved issues recur across the literature. Consensus remains lacking on the phase boundary itself, because extrapolated experiments, newer experiments, and ab initio calculations do not yield a unique miscibility curve (Bailey et al., 2020, Amoros et al., 2024). The predicted atmospheric water abundance limits are upper limits for water alone, while real atmospheres also contain CH$P$53, NH$P$54, and He (Amoros et al., 2024). If $P$55–$P$56 demixing does not occur, alternative explanations for low outer-envelope water include cloud-inhibited convection and progressive planetesimal enrichment during formation (Amoros et al., 2024). Other demixing processes—H–He at Mbar pressures, H–C forming diamonds, and MgO–H$P$57O in the deep mantle—may superpose additional layering (Amoros et al., 2024). Reduced uncertainty in $P$58, better estimates of dynamic corrections, atmospheric water-abundance measurements from an orbiter-plus-probe mission, and laboratory and ab initio studies of multicomponent phase behavior remain the stated priorities for testing the hydrogen–water demixing hypothesis (Amoros et al., 2024).