Measurement of the Curvature-Dependent Surface Tension in Nucleating Colloidal Liquids

Measuring the Surface Tension of Atmospheric Particles and Relevant Mixtures to Better Understand Key Atmospheric Processes

Aerosol and aqueous particles are ubiquitous in Earth's atmosphere and play key roles in geochemical processes such as natural chemical cycles, cloud and fog formation, air pollution, visibility, climate forcing, etc. The surface tension of atmospheric particles can affect their size distribution, condensational growth, evaporation, and exchange of chemicals with the atmosphere, which, in turn, are important in the above-mentioned geochemical processes. However, because measuring this quantity is challenging, its role in atmospheric processes was dismissed for decades. Over the last 15 years, this field of research has seen some tremendous developments and is rapidly evolving. This review presents the state-of-the-art of this subject focusing on the experimental approaches. It also presents a unique inventory of experimental adsorption isotherms for over 130 mixtures of organic compounds in water of relevance for model development and validation. Potential future areas of research seeking to better determine the surface tension of atmospheric particles, better constrain laboratory investigations, or better understand the role of surface tension in various atmospheric processes, are discussed. We hope that this review appeals not only to atmospheric scientists but also to researchers from other fields, who could help identify new approaches and solutions to the current challenges.

Superheating of grain boundaries within bulk colloidal crystals

Whether grain boundaries (GBs) premelt is a longstanding question, because of the difficulty of direct experimental tests. Here, we focused an optical beam to locally heat single GBs within bulk hard-sphere colloidal crystals, observing the melting dynamics at single-particle resolution by video microscopy. The melting point is determined by analysing both the Lindemann parameter and the critical nucleus size for homogeneous nucleation. We found that all the GBs, including the high-energy GBs, can be superheated and melt via a heterogeneous nucleation mechanism. Based on the classical nucleation theory of GBs, we measured the incubation time and contact angle of the critical nucleus to compute all relevant kinetic factors, as well as the energy barrier, nucleation rate and the diffusion coefficient at the solid–liquid interface under weak superheating. The superheat limits of GBs with various misorientations have also been measured to further explore the instability mechanism. Under traditional uniform heating, premelting occurs only at triple junctions, whereas GBs retain their original structures up to the melting point. The premelted regions at triple junctions further interrupt high-energy GBs from superheating, through intrusion by uniform liquid layers. Overall, our experiments confirm the existence of superheating of GBs.

Understanding the dynamics of grain boundaries and their melting behaviour is important for controlling the mechanical properties of materials. Now, experiments show that grain boundaries can be superheated, and that they melt via a nucleation mechanism.

Extension of Kelvin's equation to dipolar colloids

Suspensions of colloids driven out-of-equilibrium demonstrate interesting collective behavior, such as organized and directed clustering and swarming. These systems require continuous energy input, yet some of the dynamics of these driven systems resemble the equilibrium-phase behavior of molecular fluids, such as crystallization, condensation, and phase separation. Consequently, there has been significant interest in exploring the applicability of thermodynamic concepts, such as pressure and surface tension, to describe nonequilibrium phenomena. Here, we show how rotating magnetic fields can drive superparamagnetic particles to form steady-state vapor–liquid coexistence that can be analyzed with Kelvin’s equation to determine an “effective vapor pressure” for this active colloidal system. These results illustrate the convergence of statistical physics of simple liquids to nonequilibrium colloidal fluids.

Vapor pressure refers to the pressure exerted by the vapor phase in thermodynamic equilibrium with either its liquid or solid phase. An important class of active matter is field-driven colloids. A suspension of dipolar colloids placed in a high-frequency rotating magnetic field undergoes a nonequilibrium phase transition into a dilute and dense phase, akin to liquid–vapor coexistence in a simple fluid. Here, we compute the vapor pressure of this colloidal fluid. The number of particles that exist as the dilute bulk phase versus condensed cluster phases can be directly visualized. An exponential relationship between vapor pressure and effective temperature is determined as a function of applied field strength, analogous to the thermodynamic expression between vapor pressure and temperature found for pure liquids. Additionally, we demonstrate the applicability of Kelvin’s equation to this field-driven system. In principle, this appears to be in conflict with macroscopic thermodynamic assumptions due to the nonequilibrium and discrete nature of this colloidal system. However, the curvature of the vapor–liquid interface provides a mechanical equilibrium characterized by interfacial tension that connects the condensed clusters observed with these active fluids to classical colligative fluid properties.

Mesoscale perspective on the Tolman length

We demonstrate that the multiphase Shan-Chen lattice Boltzmann method (LBM) yields a curvature dependent surface tension σ as computed from three-dimensional hydrostatic droplets and bubbles simulations. Such curvature dependence is routinely characterized, at first order, by the so-called Tolman length δ. LBM allows one to precisely compute σ at the surface of tension R_{s} and determine the Tolman length from the coefficient of the first order correction. The corresponding values of δ display universality for different equations of state, following a power-law scaling near the critical temperature. The Tolman length has been studied so far mainly via computationally demanding Molecular Dynamics simulations or by means of Density Functional Theory approaches playing a pivotal role in extending Classical Nucleation Theory. The present results open a hydrodynamic-compliant mesoscale arena, in which the fundamental role of the Tolman length, alongside real-world applications to cavitation phenomena, can be effectively tackled. All the results can be independently reproduced through the "idea.deploy" framework.

Direct measurement of curvature-dependent surface tension of an alcohol nanomeniscus

Surface tension is a key parameter for understanding nucleation in the very initial stage of phase transformation. Although surface tension has been predicted to vary with the curvature of the liquid-vapor interface, particularly at the large curvature of, e.g., the subnanometric critical nucleus, experimental study still remains challenging due to inaccessibility to such a small cluster. Here, by directly measuring the critical size of a single capillary-condensed nanomeniscus using atomic force microscopy, we address the curvature dependence of surface tension of alcohols and observe that the surface tension is doubled for ethanol and n-propanol with a radius-of-curvature of ∼-0.46 nm. We also find that the interface of larger negative (positive) curvature exhibits larger (smaller) surface tension, which evidently governs nucleation at the ∼1 nm scale and below, indicating more facilitated nucleation than normally expected. Such well characterized curvature effects contribute to better understanding and accurate analysis of nucleation occurring in various fields including materials science and atmospheric science.

A framework for understanding the functions of biomolecular condensates across scales

Biomolecular condensates are found throughout eukaryotic cells, including in the nucleus, in the cytoplasm and on membranes. They are also implicated in a wide range of cellular functions, organizing molecules that act in processes ranging from RNA metabolism to signalling to gene regulation. Early work in the field focused on identifying condensates and understanding how their physical properties and regulation arise from molecular constituents. Recent years have brought a focus on understanding condensate functions. Studies have revealed functions that span different length scales: from molecular (modulating the rates of chemical reactions) to mesoscale (organizing large structures within cells) to cellular (facilitating localization of cellular materials and homeostatic responses). In this Roadmap, we discuss representative examples of biochemical and cellular functions of biomolecular condensates from the recent literature and organize these functions into a series of non-exclusive classes across the different length scales. We conclude with a discussion of areas of current interest and challenges in the field, and thoughts about how progress may be made to further our understanding of the widespread roles of condensates in cell biology.

Nonequilibrium continuous phase transition in colloidal gelation with short-range attraction

The dynamical arrest of attractive colloidal particles into out-of-equilibrium structures, known as gelation, is central to biophysics, materials science, nanotechnology, and food and cosmetic applications, but a complete understanding is lacking. In particular, for intermediate particle density and attraction, the structure formation process remains unclear. Here, we show that the gelation of short-range attractive particles is governed by a nonequilibrium percolation process. We combine experiments on critical Casimir colloidal suspensions, numerical simulations, and analytical modeling with a master kinetic equation to show that cluster sizes and correlation lengths diverge with exponents  ~1.6 and 0.8, respectively, consistent with percolation theory, while detailed balance in the particle attachment and detachment processes is broken. Cluster masses exhibit power-law distributions with exponents  -3/2 and  -5/2 before and after percolation, as predicted by solutions to the master kinetic equation. These results revealing a nonequilibrium continuous phase transition unify the structural arrest and yielding into related frameworks.

Curvature Corrections Remove the Inconsistencies of Binary Classical Nucleation Theory

The study of nucleation in fluid mixtures exposes challenges beyond those of pure systems. A striking example is homogeneous condensation in highly surface-active water-alcohol mixtures, where classical nucleation theory yields an unphysical, negative number of water molecules in the critical embryo. This flaw has rendered multicomponent nucleation theory useless for many industrial and scientific applications. Here, we show that this inconsistency is removed by properly incorporating the curvature dependence of the surface tension of the mixture into classical nucleation theory for multicomponent systems. The Gibbs adsorption equation is used to explain the origin of the inconsistency by linking the molecules adsorbed at the interface to the curvature corrections of the surface tension. The Tolman length and rigidity constant are determined for several water-alcohol mixtures and used to show that the corrected theory is free of physical inconsistencies and provides accurate predictions of the nucleation rates. In particular, for the ethanol-water and propanol-water mixtures, the average error in the predicted nucleation rates is reduced from 11-15 orders of magnitude to below 1.5. The curvature-corrected nucleation theory opens the door to reliable predictions of nucleation rates in multicomponent systems, which are crucial for applications ranging from atmospheric science to research on volcanos.