Molecular Insights into Gas Nanofilms Confined Between Bulk Liquid Phases

Abstract: Nanometer-thick fluid films play a critical role in confined multiphase processes, yet the thermodynamics and stability of free gas nanofilms remain poorly understood compared with their liquid counterparts. Here, molecular dynamics (MD) simulations are employed to systematically investigate gas nanofilms confined between bulk liquid phases using Lennard-Jones argon as a model system. The results show that the surface tension decreases exponentially with decreasing film thickness, accompanied by an increasing magnitude of the negative disjoining pressure. Upon thinning, the planar gas film undergoes a distinct morphological transition from a stable planar state to a transient or persistent spherical bubble through the formation and growth of a liquid bridge. The film surface area strongly affects its thermodynamic properties, with larger areas producing stronger thickness dependence and larger deviations from classical density functional theory (cDFT) predictions. The closer agreement between MD and cDFT at smaller surface areas suggests that the discrepancy primarily arises from thermal capillary-wave fluctuations, which are included in MD but omitted in mean-field cDFT. Moreover, at small film thicknesses, the magnitude of the disjoining pressure increases with decreasing temperature, consistent with the enhanced sensitivity of the confined gas phase to thickness variations and contrasting with the trend generally reported for liquid nanofilms. These findings provide molecular insights into the thermodynamics and stability of gas nanofilms, with implications for confined multiphase transport and droplet coalescence.

• The paper disentangles the molecular dynamics of gas nanofilms, particularly emphasizing thickness-induced morphological transitions.
• Unique findings, such as surface tension and disjoining pressure dependence on temperature and a temperature-reversed trend of the disjoining pressure
• Surface area effects indicate capillary-wave fluctuations as a dominant factor in discrepancies between molecular dynamics and classical density functional theory

This paper reports molecular dynamics (MD) simulations of free gas nanofilms sandwiched between bulk liquid phases, using Lennard-Jones argon as a model system (2608.18891). While the thermodynamics of liquid nanofilms—particularly disjoining-pressure isotherms—has been extensively characterized by simulation and classical density functional theory (cDFT), the corresponding behavior of gas nanofilms has remained essentially unexplored at the molecular level. The study establishes a Gibbs surface thermodynamic framework for the gas-film geometry and uses it to extract surface tension and disjoining pressure as functions of film thickness, lateral system size, and temperature. Two results are particularly notable: a thinning-induced morphological transition from planar film to spherical bubble via liquid-bridge formation, and a temperature dependence of the disjoining pressure that is opposite in sign to that reported for liquid nanofilms.

Thermodynamic framework and simulation methodology

The authors adapt the Toshev–Ivanov Gibbs surface formulation, originally developed for thin liquid films, to the case of a single-component gas film of thickness $h$ bounded by two bulk liquid reservoirs. Starting from the excess Helmholtz free energy $\tilde{F}$ and using Rusanov's relation between film tension and film surface tension, $\gamma^f = 2\sigma^f + \Pi h$, they derive

$$\Pi = -2\left(\frac{\partial \sigma^f}{\partial h}\right)_T,$$

which is formally identical to the liquid-film result but employs a different dividing-surface definition of film thickness,

$h=\frac{N/A-\rho_{l}L}{\rho_{g}-\rho_{l}}.$

The framework is restricted to single-component systems with constant chemical potentials of any additional species; multicomponent extension requires explicit treatment of all surface excesses.

Simulations were performed in LAMMPS on reparameterized Lennard-Jones argon, with short-range interactions truncated at half the shortest box dimension and long-range dispersion handled by PPPM—an important detail, since the authors' earlier work showed that neglecting long-range dispersion introduces substantial errors in $\Pi$. Production runs used $NVT$ dynamics (Nosé-Hoover thermostat, 5 fs timestep, 22.5 ns after 7.5 ns equilibration), with surface tension computed from the Bakker integral over the pressure tensor. The exponential fit $\sigma^f(h) = a e^{bh} + c$ was then differentiated to obtain $\Pi(h)$.

Thickness dependence and morphological stability

At 120 K, the film surface tension increases monotonically and exponentially with thickness, converging to approximately 5.11 mN/m at large $h$—in close agreement with the experimental value of 5.06 mN/m. Disjoining pressures are consistently negative across all thicknesses studied (15–50 Å), implying that the bulk gas phase is at higher pressure than the bulk liquid; the resulting meniscus curvature in the Plateau border is therefore opposite to the conventional schematic depiction. The data follow the Hamaker scaling $\tilde{F}$0 well, yielding a fitted Hamaker constant of $\tilde{F}$1 J.

The stability analysis identifies three regimes of morphological evolution:

• Large thicknesses: the planar film remains stable throughout the simulated time.
• Moderate thicknesses: a liquid bridge forms and grows radially, converting the film into a transient spherical bubble that later disappears, restoring the planar state.
• Small thicknesses: the same bridge-mediated pathway produces a persistent spherical bubble that does not revert within the simulation window.

The authors interpret this through surface free-energy minimization ($\tilde{F}$2): bridge formation increases interfacial area at large $\tilde{F}$3 (unfavorable), leaves it comparable at intermediate $\tilde{F}$4 (metastable coexistence), and reduces it substantially at small $\tilde{F}$5 (favorable). Notably, this pathway differs qualitatively from liquid nanofilm rupture, which proceeds via hole nucleation rather than bridge growth.

Because surface tension here was computed only for intact planar films, the systematic decrease of $\tilde{F}$6 with decreasing $\tilde{F}$7 cannot be attributed to ruptured configurations. This directly contradicts Filippini et al.'s claim that intact liquid films show no intrinsic thickness dependence of surface tension (2608.18891), and instead supports Peng et al.'s regime-dependent picture of genuine thickness-dependent surface properties. The evidence thus favors an intrinsic confinement effect rather than an artifact of hole formation.

Surface area effects and capillary-wave fluctuations

A central result concerns the role of lateral system size. A 250% increase in surface area produces an approximately two-order-of-magnitude increase in the fitted prefactor $\tilde{F}$8, i.e., a dramatically stronger thickness dependence of surface tension. Conversely, smaller surface areas yield weaker thickness dependence and better agreement with one-dimensional PC-SAFT-based cDFT predictions. The discrepancy in fitted Hamaker constants between MD and cDFT shrinks systematically from roughly two orders of magnitude at the largest area to about a factor of three at the smallest.

This trend provides indirect but strong evidence that thermal capillary-wave fluctuations—the dominant source of MD–cDFT disagreement—are progressively suppressed as the lateral dimension shrinks, bringing the finite system closer to the fluctuation-free mean-field limit implicit in cDFT. Density profiles reinforce this interpretation: with decreasing film thickness or increasing surface area, the intrinsic sigmoidal density transition softens markedly, producing profile crossings that cDFT cannot reproduce since it yields essentially thickness-independent profile slopes. The authors acknowledge, however, that this capillary-wave explanation, while consistent with all observations, has not been directly verified—for example by explicit spectral analysis of interfacial height fluctuations—and remains a plausible hypothesis supported by circumstantial evidence.

Two caveats qualify these comparisons. First, smaller boxes use shorter interaction cutoffs (half the shortest box length), which systematically lowers the calculated bulk surface tension at small areas; this confounds the area-dependence analysis somewhat, although it affects primarily the large-$\tilde{F}$9 asymptote rather than the thickness dependence. Second, for the largest surface area, deviations from linear $\gamma^f = 2\sigma^f + \Pi h$0 Hamaker scaling emerge at larger thicknesses, indicating that continuum slab-profile assumptions break down when fluctuations are strong.

Temperature dependence: a contrast with liquid nanofilms

At fixed surface area ($\gamma^f = 2\sigma^f + \Pi h$1 Ų), temperatures of 110, 120, and 130 K produce distinct behaviors. Bulk surface tensions (7.69 and 2.92 mN/m at 110 and 130 K) match NIST reference data. At low temperatures the surface tension varies rapidly with thickness and reaches its bulk value at small $\gamma^f = 2\sigma^f + \Pi h$2, whereas at high temperatures the convergence is gradual and asymptotic. The authors attribute this to temperature-controlled interfacial sharpness: sharp interfaces at low temperature couple strongly across narrow overlap regions and decouple abruptly, while thermally broadened interfaces at high temperature remain partially correlated over longer distances.

The disjoining pressure exhibits a crossover structure: at small film thicknesses its magnitude increases with decreasing temperature, while at larger thicknesses the trend reverses. Most strikingly, reducing temperature from 130 to 110 K increases the fitted Hamaker constant by approximately 140-fold. This contrasts sharply with liquid nanofilms, where higher temperatures generally yield lower disjoining pressures in the thin-film regime. The authors explain the reversal through compressibility: an incompressible confined liquid resists thickness-induced structural change and develops weak disjoining pressures, whereas a highly compressible gas film responds strongly to confinement—especially at low temperature where thermal motion is suppressed—and generates large negative disjoining pressures. Density profiles confirm the structural basis: transition layers are markedly steeper at 110 K than at 130 K for comparable thicknesses.

Limitations and open questions

Several limitations should be weighed alongside the conclusions. The capillary-wave mechanism explaining the MD–cDFT gap is inferred from area-scaling trends rather than demonstrated through direct fluctuation measurements, leaving open whether a quantitative fluctuation-corrected theory can be constructed. The bulk gas density entering the film-thickness definition is approximated from the thickest film rather than measured against a true bulk reservoir; the authors argue this is negligible because gas density is one to two orders of magnitude below liquid density and $\gamma^f = 2\sigma^f + \Pi h$3 is governed mainly by $\gamma^f = 2\sigma^f + \Pi h$4, but the approximation's error bounds are not quantified. All results pertain to a single-component LJ fluid at three temperatures near the triple point region; whether the identified trends—including the 140-fold Hamaker constant variation and the bridge-to-bubble transition pathway—persist in multicomponent or chemically realistic systems remains untested. The persistence timescale distinguishing "transient" from "persistent" bubbles is defined only relative to the ~30 ns simulation window, so the long-time stability landscape is not fully resolved. Finally, the cutoff-length confound at small surface areas means the pure surface-area effect on thermodynamics cannot be fully separated from truncation effects without additional simulations at fixed cutoff.

Conclusion

This work provides the first systematic molecular-level characterization of free gas nanofilms, extending nanofilm thermodynamics beyond the well-studied liquid-film regime. Its principal contributions are threefold: demonstration of genuine, intrinsic thickness dependence of gas-film surface tension (contradicting the hole-artifact interpretation); identification of a bridge-mediated planar-film-to-bubble transition pathway distinct from liquid-film rupture; and resolution of the long-standing MD–cDFT discrepancy in favor of capillary-wave fluctuations as the dominant origin, evidenced by systematic convergence upon lateral-size reduction. The reversed temperature trend of the disjoining pressure, traced to the compressibility of the confined gas phase, establishes that nanofilm thermodynamics is fundamentally governed by the mechanical response of the confined phase. These results bear directly on confined multiphase transport in nanoporous geological media and on droplet/bubble coalescence mediated by intervening gas films, and they define a clear open problem: incorporating fluctuation effects into predictive mean-field theories of nanoscale free films.