Revealing Liquid-Gas Transitions with Finite-Size Scaling in Confined Systems

TL;DR

Confining external fields can mask liquid-gas phase transitions, so the paper develops a finite-size scaling criterion based on density-profile scaling to distinguish one-phase from two-phase states. The approach yields scaling forms: for a single-phase system, the density profile $n(r,N)$ collapses onto a master curve when plotted versus $\hat{r} = r / N^{1/d}$ at fixed $\bar{n}$; for a two-phase system, the profiles intersect at a single interface position $\hat{r}_c$, indicating a LGPT. The authors validate the framework with colloidal experiments under gravity, molecular-dynamics simulations of colloids with attraction, and simulations of complex plasmas under a central confining potential, showing intersections in the two-phase regime and collapses in the one-phase regime. The method provides a robust, field-invariant criterion for detecting LGPTs in laboratory systems and yields precise interface position and width, with broad applicability to systems where confinement is intrinsic.

Abstract

The application of an external field often renders empirical criteria for identifying liquid-gas phase transitions ambiguous. Here, we demonstrate that the finite-size scaling of the density profile provides a definitive criterion to distinguish liquid-gas coexistence from a single fluid phase in field-confined systems. Our scaling method collapses the density profiles of different system sizes onto a single master curve for a one-phase system, while causing the profiles to intersect at the interface in a two-phase system. We validate this theoretical proposal through experiments and simulations of two model systems: colloidal suspensions under gravity and/or two-dimensional complex plasmas confined by a central potential. Our method is broadly applicable for detecting liquid-gas phase transitions in laboratory systems where external fields are inherent.

Figures (6)

• Figure 1: Results of colloidal experiments. (a-c) Single fluid phase systems with the hard-sphere-like inter-particle interaction. (a) Images of three typical subsystems in the wedge-shaped cell with different $H$ ($\Delta \rho = 0.0472~\rm{g/cm^3}$). For comparison, we also show an image of a system under microgravity ($\Delta \rho \approx 0$ and $l_g \gg H$). (b) Density profiles $n(z,H)$ of the subsystems with different $H$ in the cell. (c) $n(z,H)$ as a function of $\hat{z} = z/H$ for different $H$, with a constant $l_g/H=0.159$. (d-f) Corresponding results for liquid-gas coexistence systems where particles interact with additional attraction.
• Figure 2: Simulated complex plasmas. Snapshots of a Kompaneets system with $T_{\rm c}=0.0038$: (a) without a confining potential, at $T=0.0031<T_{\rm c}$; (b) confined by a central potential, at $T=0.0050>T_{\rm c}$; (c) confined by a central potential, at $T=0.0031$. (d) Density profile of the system in a confining potential at a few different $T$, with $N=20480$. We fix $T/k=6100$.
• Figure 3: Density profiles of simulated complex plasmas. (a) A supercritical system with the Kompaneets interaction at $T=0.006$, above $T_{\rm c}=0.0038$. The $n(r, N)$ data of different $N$ are plotted as functions of $\hat{r}=r/N^{1/2}$. (b,c) A subcritical system with the Kompaneets interaction at $T=0.0031$ below $T_{\rm c}$. The intersection point in (b) gives $\hat{r}_{\rm c}=1.44$. In (c), the density profiles are zoomed in around the interface (blue) region. (d) Yukawa systems at $T=0.0031$. We set $Nk=2.62\times 10^{-3}$ for Kompaneets systems and $Nk=2.62\times 10^{-2}$ for Yukawa systems.
• Figure 4: Schematic of the wedge-shaped sample cell. We show three typical windows where images are taken (dahsed lines); such images are shown in Fig. \ref{['fig:colloidal_experiments']}(a,d).
• Figure 5: Density profiles of experimental colloidal suspensions near $z_{\rm c}$. (a) Data for hard-sphere-like colloids, where $z_{\rm c}$ is the position at half height. (b) Data for colloids with effective attraction, where $z_{\rm c}$ is the intersection point determined in Fig. \ref{['fig:colloidal_experiments']}f.