Reincarnations of the phase separation problem

Phase separation is familiar and useful, yet opportunities to manipulate it are surprisingly subtle and complex.

enter the statement of the problem 3 . Yet the paper by Tateno and Tanaka 1 demonstrates unconventional t 1/2 power-law growth of time (t)-dependent structure in liquid-liquid phase separation, shockingly faster than the t 1/3 dependence that normally follows from conventional analysis for the Lifshitz-Slyozov-Wagner mechanism, Brownian coagulation mechanism, and even nonequilibrium thermodynamics when energy-dissipating systems are mapped onto a formalism of equivalent free energy 6 . The engineering-oriented paper by Xi et al. likewise demonstrates findings contrary to textbook expectations. Adding nanoparticles designed to be miscible in only one phase of a phase-separating system, the authors assert that their tiny particles avoid the interface because their small size and high charge avoid the traditional rule of thumb that particles and nanoparticles ubiquitously segregate to interfaces. 7 Instead, the authors report that nanoparticles stabilize the phase-separated structure because they jam one of the liquid phases. If substantiated by direct test, this would provide an interesting extension to the traditional Pickering emulsion concept. Freezing bicontinuous structures into place using this strategy, Xi et al. 2 argue that their process to accomplish this may be useful from technology and materials processing standpoints.
Phase separation modulated by mismatched time scales, a process conceived decades ago by Tanaka 8 , has come of age after a long childhood. Seeds planted by the early concepts 8,9 are likewise sprouting in other laboratories. For example, the group of E. Dufresne at the ETH Zürich investigates Ostwald ripening, finding provocative differences from classical expectations when this happens within a polymer network such that droplet growth comes at the cost of elastic stiffening in the surrounding medium 10 . The toggled interactions proposed as a concept by the group of J. Swan at Massachusetts Institute of Technology 11 could evidently also be extended to become an additional control variable. The concept of using nanoparticles to jam interfaces, thereby bypassing the conventional temperature or pressure quench, has been used in multiple systems by the group of T.P. Russell, with an impact that extends to the patent literature 12 . Independently in multiple laboratories, the view is gelling that beyond conventional thermodynamic variables, the time variable belongs as an axis on phase diagrams, not literally, but when one thinks about the problem conceptually.
Materials physicists and engineers previously were (of course) aware from experience that time matters. But this was regarded chiefly as a nuisance, something akin to trying to play sports during bad weather. These new papers show beautiful conceptual novelty 1 and practical utility 2 . When one speculates how these ideas may spread in the future, the latter is especially notable when one considers the high value that the era in which we live gives to having technology impact. It is natural to anticipate further advances when, in further studies the time variable, according to which interactions are toggled, is made syncopated and enriched with rhythm and tempo, as outlined speculatively in Fig. 1.
Out-of-equilibrium self-organization is interesting even more generally. Going even farther beyond the standard view of phase separation, the new field of active matter considers "phases" and "phase diagrams" under conditions where motility ("selfpropulsion"), is the heart of the problem 13,14 . In this view, phase separation is induced by motility itself-not enthalpy and entropy. Moving objects, individually self-propelled by consumption of energy, tend to accumulate where they move more slowly. The resulting phase-separated structures often look c Other modern work toggles molecular interactions themselves during the course of phase separation, shown here schematically as modulation in time. d Out-of-equilibrium active matter systems present radically different situations. These active, motile particles have directional motion because they consume energy, shown here schematically as arrows on the moving particles. e States of motility-induced phase separation, controlled by differential motility of individual active particles, can result. The regions of high-density form because moving objects tend to accumulate where they move more slowly. Here the differential arrow lengths denote differential motility.
visually like nucleated or spinodal structures known from thermal phase separation. At a deep level, that they are so similar to the casual eye is not coincidental-elegant theory shows that the situations can be mapped onto one another conceptually, so similar geometrical patterns of phase separation follow naturally from equations whose structure is similar 6 .
However, most current experiments in this field still struggle with the challenge of how to produce active matter systems with controllable mutual interactions in the laboratory 13 . Despite experimental tours de force, and provocative analogies to living systems of animals, fish, and bird, it remains easier to do so on the computer than in the laboratory 14 . The concept of effective temperature remains ambiguous 15 . Details of this correspondence are, at the time of this writing, too little explored experimentally. The search for practical applications is, at present, mostly limited; known examples include the construction of membrane-less organelles with possible biophysical action 16 , the speculative use of isolated active particles in medicine 17 , and the construction of robot swarms of various kinds 18 . Regarding these examples of applications, a survey of the experimental literature shows too little data about phase diagrams. The laboratory studies of phase separation in the active matter are mostly in two-dimensional systems, but experimental studies of thermal phase separation are usually three-dimensional. Experiments with active matter are (so far) geared toward understanding individual clusters, swarms, or organelles, not yet system-spanning such as bicontinuous structures that are standard to find in thermal phase separation, and not yet in the presence of viscoelastic 1 or jammed 2 background. To bridge the obvious gaps in this long list will be a significant agenda for the future. Now in the second quintile of the 21st century, we are at a tipping point. The study of classical thermal phase separation is being enriched intellectually by relaxing the previously-strict injunction that thermodynamics and kinetics are distinct subjects. Independently, out-of-equilibrium systems draw massive attention. It is fascinating to observe the evolution of science in a microcosm. Each chapter of progress is accompanied by a new generation of young scientists. In the field of phase separation, as in so many others, science often advances one funeral at a time 19 .