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Phase separation
Phase separation
Phase separation
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Mixing of liquids A and B and subsequent phase separation
When mixed, oil and vinegar will phase-separate
A phase diagram for two isotopes of helium, showing at bottom a range of temperatures and ratios at which they will phase-separate.

Phase separation is the creation of two distinct phases from a single homogeneous mixture.[1] The most common type of phase separation occurs between two immiscible liquids, such as oil and water. This type of phase separation is known as liquid-liquid equilibrium. Colloids are formed by phase separation, though not all phase separations form colloids - for example, oil and water can form separated layers under gravity rather than remaining as microscopic droplets in suspension.

A common form of spontaneous phase separation is termed spinodal decomposition; Cahn–Hilliard equation describes it. Regions of a phase diagram in which phase separation occurs are called miscibility gaps. There are two boundary curves of note: the binodal coexistence curve and the spinodal curve. On one side of the binodal, mixtures are absolutely stable. In between the binodal and the spinodal, mixtures may be metastable: staying mixed (or unmixed) in the absence of some large disturbance. The region beyond the spinodal curve is absolutely unstable, and (if starting from a mixed state) will spontaneously phase-separate.

The upper critical solution temperature (UCST) and the lower critical solution temperature (LCST) are two critical temperatures, above which or below which the components of a mixture are miscible in all proportions. It is rare for systems to have both, but some exist: the nicotine-water system has an LCST of 61 °C and also a UCST of 210 °C at pressures high enough for liquid water to exist at that temperature. The components are therefore miscible in all proportions below 61 °C and above 210 °C (at high pressure), and partially miscible in the interval from 61 to 210 °C.[2][3]

Physical basis

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Mixing is governed by the Gibbs free energy, with phase separation or mixing occurring for whichever case lowers the Gibbs free energy. The free energy can be decomposed into two parts: , with the enthalpy, the temperature, and the entropy. Thus, the change of the free energy in mixing is the sum of the enthalpy of mixing and the entropy of mixing. The enthalpy of mixing is zero for ideal mixtures, and ideal mixtures are enough to describe many common solutions. Thus, in many cases, mixing (or phase separation) is driven primarily by the entropy of mixing. It is generally the case that the entropy will increase whenever a particle (an atom, a molecule) has a larger space to explore; thus, the entropy of mixing is generally positive: the components of the mixture can increase their entropy by sharing a larger common volume.

Several distinct processes then drive phase separation. In one case, the enthalpy of mixing is positive, and the temperature is low: the increase in entropy is insufficient to lower the free energy. In another, considerably rarer case, the entropy of mixing is "unfavorable", that is to say, it is negative. In this case, even if the change in enthalpy is negative, phase separation will still occur unless the temperature is low enough. It is this second case which gives rise to the idea of the lower critical solution temperature.

Phase separation in cold gases

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A mixture of two helium isotopes (helium-3 and helium-4) in a certain range of temperatures and concentrations separates into parts. The initial mix of the two isotopes spontaneously separates into -rich and -rich regions.[4] Phase separation also exists in ultracold gas systems.[5] It has been shown experimentally in a two-component ultracold Fermi gas case.[6][7] The phase separation can compete with other phenomena, such as vortex lattice formation or an exotic Fulde-Ferrell-Larkin-Ovchinnikov phase.[8]

See also

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References

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Further reading

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Phase separation

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Phase separation is a fundamental in which a homogeneous or solution spontaneously segregates into two or more distinct phases with differing compositions, densities, and physical properties, driven by the system's tendency to minimize its free energy. This phenomenon occurs when the mixture becomes thermodynamically unstable, often due to changes in , , concentration, or external fields, leading to phase transitions that can be either (involving and growth) or continuous (via ). Phase separation is ubiquitous in nature and technology, manifesting in everyday examples like the separation of oil and or the demixing of alloys upon cooling. In physics and , phase separation is central to understanding the behavior of multicomponent systems, such as binary fluids, blends, and metallic alloys, where it influences microstructure formation and material properties like strength and conductivity. Mechanisms like , characterized by an amplified instability in composition fluctuations, enable rapid phase ordering without energy barriers, contrasting with nucleation processes that require overcoming an activation energy for droplet formation. These dynamics are described by classical theories, including Cahn-Hilliard equations, which model conserved order parameters in diffusive systems. In chemistry, phase separation underpins applications in polymer processing, such as thermally induced phase separation (TIPS) for creating porous scaffolds in , and in colloidal stability where prevent unwanted demixing in emulsions. More recently, in , liquid-liquid phase separation (LLPS) has gained prominence as a mechanism for intracellular organization, enabling the formation of membraneless compartments like nucleoli and stress granules through multivalent interactions of proteins and ; as of 2025, research continues to uncover its roles in stem cell biology, tumorigenesis, and metabolic regulation. These biomolecular condensates concentrate molecules to enhance reaction rates and signaling, with implications for cellular , development, and diseases such as neurodegeneration when dysregulated.

Fundamentals

Definition and Overview

Phase separation is the by which a previously homogeneous single-phase becomes unstable and spontaneously divides into multiple coexisting phases exhibiting distinct compositions, densities, or structures, typically induced by changes in external conditions such as , , or overall composition. This demixing occurs because the separated state possesses a lower compared to the uniform mixture, as the seeks to minimize its total free energy G=H−TSG = H - TS, where HH is the , TT is the absolute , and SS is the . The driving force stems from the competition between enthalpic contributions from intermolecular attractions or repulsions and entropic effects from molecular configurations, leading to macroscopic phase domains when the free energy curve for mixing develops regions of negative convexity. The conceptual origins of phase separation trace back to the late , with foundational theoretical advancements in the of fluids and heterogeneous systems. In 1873, introduced his , which incorporated corrections for molecular volume and attractive forces, enabling the first quantitative prediction of phase coexistence and the liquid-gas transition in real gases. Building on this, J. Willard Gibbs developed the in his landmark 1876–1878 publication On the Equilibrium of Heterogeneous Substances, providing a general framework for determining the conditions under which multiple phases can stably coexist in a . The Gibbs phase rule quantifies the variability of multiphase equilibria and is given by F=C−P+2F = C - P + 2, where FF represents the (the number of intensive variables, such as , , or composition, that can be independently varied without changing the number or nature of phases in equilibrium), CC is the number of independently variable components, and PP is the number of phases. This relation arises from balancing the total number of variables against the constraints imposed by equilibrium conditions. For a general multicomponent without chemical reactions, the intensive variables include TT, pp, and C−1C-1 independent composition variables (e.g., mole fractions) per phase, yielding a total of P(C+1)−P=PC+P−P=PCP(C + 1) - P = PC + P - P = PC independent variables across PP phases (accounting for the sum-to-unity constraint per phase). Equilibrium requires TT and pp to be uniform (imposing P−1P-1 constraints each), and the of each component to be equal across all phases (imposing C(P−1)C(P-1) constraints total), resulting in 2(P−1)+C(P−1)=(C+2)(P−1)2(P-1) + C(P-1) = (C + 2)(P - 1) constraints. Thus, F=PC−(C+2)(P−1)=PC−CP+C−2P+2=C−P+2F = PC - (C + 2)(P - 1) = PC - CP + C - 2P + 2 = C - P + 2. In a (C=2C = 2), this simplifies to F=4−PF = 4 - P; for example, with two phases (P=2P = 2), F=2F = 2, allowing independent specification of TT and one composition variable (e.g., at fixed pressure) to define the equilibrium state uniquely. Illustrative examples of phase separation abound in everyday and materials contexts. A classic case is the spontaneous separation of oil and water into immiscible layers, where hydrophobic effects drive the nonpolar oil molecules to aggregate, minimizing unfavorable water-oil contacts and thus the system's free energy. Similarly, in polymer blends, incompatible macromolecules like and phase separate into micron-scale domains upon cooling from a melt, as entropic mixing penalties outweigh weak intermolecular attractions, yielding materials with tailored mechanical properties. In phase diagrams, boundaries such as the and spinodal curves demarcate regions of thermodynamic stability from those prone to separation.

Thermodynamic Principles

Phase separation in mixtures is governed by the principles of , particularly the minimization of the GG. At equilibrium, the chemical potentials μi\mu_i of each component ii must be equal across coexisting phases, ensuring that the system achieves the lowest possible free energy state. This condition arises from the fundamental relation dG=−SdT+VdP+∑μidnidG = -SdT + VdP + \sum \mu_i dn_i, where for a at constant and , the equilibrium requires μiα=μiβ\mu_i^\alpha = \mu_i^\beta for phases α\alpha and β\beta. For binary mixtures, the common tangent construction on the free energy-composition curve illustrates this: the tangent line connecting the free energy curves of two phases touches them at points of equal chemical potential (slopes ∂G/∂x=μ1−μ2\partial G / \partial x = \mu_1 - \mu_2), defining the compositions of the equilibrium phases. Binary temperature-composition phase diagrams map the equilibrium conditions for phase separation, with the x-axis representing composition (e.g., mole fraction xx) and the y-axis temperature at constant pressure. The binodal curve separates single-phase and two-phase regions, constructed by identifying common tangents on the Gibbs free energy curves at varying temperatures; tie lines connect the equilibrium compositions of coexisting phases at a given temperature. Within the two-phase region, the lever rule determines the relative phase fractions: for an overall composition xx, the fraction of phase α\alpha is fα=(xβ−x)/(xβ−xα)f_\alpha = (x_\beta - x)/(x_\beta - x_\alpha), and fβ=1−fαf_\beta = 1 - f_\alpha, reflecting the conservation of mass and minimization of total free energy along the tie line. A key model for phase separation in polymer systems is the Flory-Huggins theory, which provides the molar free energy of mixing as ΔGmixNkT=ϕNln⁡ϕ+(1−ϕ)ln⁡(1−ϕ)+χϕ(1−ϕ),\frac{\Delta G_\text{mix}}{NkT} = \frac{\phi}{N} \ln \phi + (1 - \phi) \ln (1 - \phi) + \chi \phi (1 - \phi), where ϕ\phi is the volume fraction of polymer, NN is the degree of polymerization, kk is Boltzmann's constant, TT is temperature, and χ\chi is the Flory interaction parameter capturing enthalpic contributions. Phase separation occurs when χ>2/N\chi > 2/N for large NN, leading to a miscibility gap; the entropy term favors mixing, while the χ\chi term promotes demixing for poor solvents (χ>0.5\chi > 0.5). The critical point marks the temperature and composition where the two phases become indistinguishable, located at the top of the miscibility gap where the binodal and spinodal curves meet. At this point, the third and fourth derivatives of the free energy with respect to composition vanish, signaling the onset of phase separation. Universality near the critical point is described using reduced variables, such as reduced temperature t=(Tc−T)/Tct = (T_c - T)/T_c and order parameter, allowing critical exponents to be independent of microscopic details across systems. Regions of the are classified by the curvature of the free energy: the single-phase region is stable where ∂2G/∂x2>0\partial^2 G / \partial x^2 > 0, the metastable region (between and spinodal) has ∂2G/∂x2>0\partial^2 G / \partial x^2 > 0 but allows , and the unstable region (inside the spinodal) has ∂2G/∂x2<0\partial^2 G / \partial x^2 < 0, where small fluctuations spontaneously amplify.

Mechanisms

Binodal Decomposition

Binodal decomposition refers to the process of phase separation that occurs in the metastable region of a binary mixture, where the system is located between the binodal curve and the spinodal boundary in the phase diagram. In this regime, phase separation proceeds through a nucleation and growth mechanism, requiring the system to overcome a free energy barrier to form stable nuclei of the new phase, in contrast to the barrierless process within the spinodal region. The binodal curve represents the locus of points in the phase diagram where two phases coexist in thermodynamic equilibrium, delineating the boundary between the single-phase region and the two-phase coexistence region. For compositions inside the binodal but outside the spinodal, the homogeneous mixture is metastable, meaning it is locally stable but not at the global minimum free energy, thus necessitating an activation process for decomposition. This curve is determined by the equality of chemical potentials and pressures between the coexisting phases, as derived from the common tangent construction on the free energy curve. The kinetics of binodal decomposition are described by classical nucleation theory (CNT), which posits that the formation of a new phase begins with the creation of small clusters or embryos whose size must exceed a critical radius to grow stably. The free energy change associated with forming a spherical nucleus of radius rr is given by ΔG(r)=43πr3Δμ+4πr2σ,\Delta G(r) = \frac{4}{3} \pi r^3 \Delta \mu + 4 \pi r^2 \sigma, where Δμ\Delta \mu is the chemical potential difference driving the phase change (related to supersaturation) and σ\sigma is the interfacial tension between phases. The maximum free energy barrier ΔG∗\Delta G^* occurs at the critical radius r∗=−2σΔμr^* = -\frac{2\sigma}{\Delta \mu}, with ΔG∗=16πσ33(Δμ)2.\Delta G^* = \frac{16 \pi \sigma^3}{3 (\Delta \mu)^2}. This barrier height decreases with increasing supersaturation (larger ∣Δμ∣|\Delta \mu|), making nucleation more probable deeper in the metastable region. The nucleation rate is then exponentially sensitive to ΔG∗\Delta G^*, as J∝exp⁡(−ΔG∗kT)J \propto \exp\left( -\frac{\Delta G^*}{kT} \right), where kk is Boltzmann's constant and TT is temperature. Following nucleation, the subsequent growth of domains occurs through diffusion-limited attachment of material to the nuclei, leading to a coarsening process where larger domains grow at the expense of smaller ones to minimize interfacial energy. This late-stage coarsening is governed by the Lifshitz-Slyozov-Wagner (LSW) theory, which predicts that the average domain size RR scales as R∼t1/3R \sim t^{1/3} in three dimensions for diffusion-controlled , assuming a dilute dispersion of spherical precipitates. The theory, developed independently by Lifshitz and Slyozov in 1958 and Wagner in 1961, derives this scaling from the continuity equation for solute concentration and the Gibbs-Thomson effect, which relates solubility to curvature. Key factors influencing binodal decomposition include the depth of undercooling or supersaturation, which controls the nucleation barrier and rate, and the minimization of interfacial energy, which drives the coarsening dynamics. Greater undercooling reduces ΔG∗\Delta G^*, accelerating the process, while lower interfacial tension facilitates both nucleation and growth. A representative example of binodal decomposition is the nucleation of liquid droplets from a supersaturated vapor, such as water vapor in air, where clusters form and grow into fog or cloud droplets once exceeding the critical size determined by CNT. In such systems, experiments with argon vapor at elevated supersaturations have confirmed the liquid-like nature of critical nuclei and the subsequent diffusion-limited growth.

Spinodal Decomposition

Spinodal decomposition represents a barrierless mechanism of phase separation that occurs within the spinodal region of the phase diagram, where the homogeneous mixture is thermodynamically unstable, allowing infinitesimal composition fluctuations to grow spontaneously through diffusion without an energy barrier. This process contrasts with nucleation outside the spinodal, as it involves no critical nucleus formation and leads to the development of interconnected domains rather than isolated droplets. The spinodal curve delineates the boundary of this unstable region and is defined as the locus of points where the second derivative of the GG with respect to the composition xx vanishes, i.e., ∂2G/∂x2=0\partial^2 G / \partial x^2 = 0. Inside the spinodal, the negative curvature of the free energy surface (∂2G/∂x2<0\partial^2 G / \partial x^2 < 0) renders the system susceptible to phase separation, with thermal fluctuations amplifying into macroscopic domains over time. The dynamics of spinodal decomposition are governed by the Cahn-Hilliard equation, a conserved order parameter model that describes diffusive transport driven by chemical potential gradients: ∂ϕ∂t=∇⋅[M∇δFδϕ],\frac{\partial \phi}{\partial t} = \nabla \cdot \left[ M \nabla \frac{\delta F}{\delta \phi} \right], where ϕ\phi is the concentration field serving as the order parameter, MM is the mobility (assumed constant), and F[ϕ]F[\phi] is the Ginzburg-Landau free energy functional incorporating both bulk and gradient contributions: F[ϕ]=∫[f(ϕ)+κ2∣∇ϕ∣2]dr.F[\phi] = \int \left[ f(\phi) + \frac{\kappa}{2} |\nabla \phi|^2 \right] d\mathbf{r}. Here, f(ϕ)f(\phi) is the local homogeneous free energy density (often modeled as a double-well potential), and κ>0\kappa > 0 is the gradient energy coefficient that penalizes sharp interfaces. Linear stability analysis of the uniform state reveals the growth rate ω(k)\omega(\mathbf{k}) of Fourier modes with wavenumber k=∣k∣k = |\mathbf{k}|: ω(k)=−Mk2(∂2f∂ϕ2+κk2).\omega(k) = -M k^2 \left( \frac{\partial^2 f}{\partial \phi^2} + \kappa k^2 \right). Within the spinodal, ∂2f/∂ϕ2<0\partial^2 f / \partial \phi^2 < 0, so long-wavelength modes (kk small) exhibit positive growth rates (ω>0\omega > 0), leading to exponential amplification of fluctuations. The dominant mode occurs at the maximum growth rate kmax⁡=−12κ∂2f∂ϕ2k_{\max} = \sqrt{ - \frac{1}{2\kappa} \frac{\partial^2 f}{\partial \phi^2} }
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