Chemical composition from photos: Dried solution drops reveal a morphogenetic tree.

Under nonequilibrium conditions, inorganic systems can produce a wealth of life-like shapes and patterns which, compared to well-formed crystalline materials, remain widely unexplored. A seemingly simple example is the formation of salt deposits during the evaporation of sessile droplets. These evaporites show great variations in their specific patterns including single rings, creep, small crystals, fractals, and featureless disks. We have explored the patterns of 42 different salts at otherwise constant conditions. Based on 7,500 images, we show that distinct pattern families can be identified and that some salts (e.g., Na2SO4 and NH4NO3) are bifurcated creating two distinct motifs. Family affiliations cannot be predicted a priori from composition alone but rather emerge from the complex interplay of evaporation, crystallization, thermodynamics, capillarity, and fluid flow. Nonetheless, chemical composition can be predicted from the deposit pattern with surprisingly high accuracy even if the set of reference images is small. These findings suggest possible applications including smartphone-based analyses and lightweight tools for space missions.

Exploring the Synthesis of Self-Organization and Active Motion.

Proteins, genetic material, and membranes are fundamental to all known organisms, yet these components alone do not constitute life. Life emerges from the dynamic processes of self-organization, assembly, and active motion, suggesting the existence of similar artificial systems. Against this backdrop, our Perspective explores a variety of chemical phenomena illustrating how nonequilibrium self-organization and micromotors contribute to life-like behavior and functionalities. After explaining key terms, we discuss specific examples including enzymatic motion, diffusiophoretic and bubble-driven self-propulsion, pattern-forming reaction-diffusion systems, self-assembling inorganic aggregates, and hierarchically emergent phenomena. We also provide a roadmap for combining self-organization and active motion and discuss possible outcomes through biological analogs. We suggest that this research direction, deeply rooted in physical chemistry, offers opportunities for further development with broad impacts on related sciences and technologies.

A minimal physical model for curvotaxis driven by curved protein complexes at the cell's leading edge.

Cells often migrate on curved surfaces inside the body, such as curved tissues, blood vessels, or highly curved protrusions of other cells. Recent in vitro experiments provide clear evidence that motile cells are affected by the curvature of the substrate on which they migrate, preferring certain curvatures to others, termed "curvotaxis." The origin and underlying mechanism that gives rise to this curvature sensitivity are not well understood. Here, we employ a "minimal cell" model which is composed of a vesicle that contains curved membrane protein complexes, that exert protrusive forces on the membrane (representing the pressure due to actin polymerization). This minimal-cell model gives rise to spontaneous emergence of a motile phenotype, driven by a lamellipodia-like leading edge. By systematically screening the behavior of this model on different types of curved substrates (sinusoidal, cylinder, and tube), we show that minimal ingredients and energy terms capture the experimental data. The model recovers the observed migration on the sinusoidal substrate, where cells move along the grooves (minima), while avoiding motion along the ridges. In addition, the model predicts the tendency of cells to migrate circumferentially on convex substrates and axially on concave ones. Both of these predictions are verified experimentally, on several cell types. Altogether, our results identify the minimization of membrane-substrate adhesion energy and binding energy between the membrane protein complexes as key players of curvotaxis in cell migration.

Coiling of Secondary Tubes Formed from the Colloidal Exhaust of Primary Chemical Gardens.

Chemical gardens are self-organized precipitate structures such as thin-walled tubes and membrane-bound cells reminiscent of biological shapes. These usually inorganic precipitates compartmentalize the reaction system and allow the study of materials synthesis in very steep concentration gradients. We create such tubes by steadily injecting a mixture of MnCl2 and CuSO4 solutions into a large reservoir of sodium silicate solution. The growing tube is open at its tip and ejects a stream of colloidal particles that aggregate to form a secondary tube above the original one. This secondary tube can coil into a tightly wound nest-like structure, freely suspended underneath the solution-air interface. Using three-dimensional image reconstruction, we analyze the onset of coiling and show that the structure is helical with a helix radius that increases in the vertical direction. The height at which the coiling begins is lowered with each successive repeat of the growth experiment, suggesting that coiling is induced by small variations in the density of the silicate solution.

Patterns Lead the Way to Far-from-Equilibrium Materials.

The universe is a complex fabric of repeating patterns that unfold their beauty in system-specific diversity. The periodic table, crystallography, and the genetic code are classic examples that illustrate how even a small number of rules generate a vast range of shapes and structures. Today, we are on the brink of an AI-driven revolution that will reveal an unprecedented number of novel patterns, many of which will escape human intuition and expertise. We suggest that in the second half of the 21st century, the challenge for Physical Chemistry will be to guide and interpret these advances in the broader context of physical sciences and materials-related engineering. If we succeed in this role, Physical Chemistry will be able to extend to new horizons. In this article, we will discuss examples that strike us as particularly promising, specifically the discovery of high-entropy and far-from-equilibrium materials as well as applications to origins-of-life research and the search for life on other planets.

Nonclassical Crystallization Causes Dendritic and Band-Like Microscale Patterns in Inorganic Precipitates.

The self-organization of complex solids can create patterns extending hierarchically from the atomic to the macroscopic scale. A frequently studied model is the chemical garden system which consists of life-like precipitate shapes. In this study, we examine the thin walls of chemical gardens using microfluidic devices that yield linear Ni(OH)2 precipitate membranes. We observe distinct light-scattering patterns within the compositionally pure membranes, including disorganized spots, dendrites, and parallel bands. The bands are tilted with respect to the membrane axis and their spacing (20-100 µm) increases with increasing flow rates. Scanning electron microscopy reveals that the bands consist of submicron particles embedded in a denser material and these particles are also found in the reactant stream. We propose that dendrites and bands arise from the attachment of solution-borne nanoparticles. The bands are generated by particle-aggregation zones moving upstream along the slowly advancing membrane surface. The speed of the aggregation zones is proportional to the band distance and defines the system's dispersion relation. This speed-wavelength dependence and the flow-opposing motion of the aggregation zones are likely caused by low particle concentrations in the wake of the zones that only slowly recover due to Brownian motion and particle nucleation.

Pattern selection by material aging: Modeling chemical gardens in two and three dimensions.

Chemical gardens are complex, often macroscopic, structures formed by precipitation reactions. Their thin walls compartmentalize the system and adjust in size and shape if the volume of the interior reactant solution is increased by osmosis or active injection. Spatial confinement to a thin layer is known to result in various patterns including self-extending filaments and flower-like patterns organized around a continuous, expanding front. Here, we describe a cellular automaton model for this type of self-organization, in which each lattice site is occupied by one of the two reactants or the precipitate. Reactant injection causes the random replacement of precipitate and generates an expanding near-circular precipitate front. If this process includes an age bias favoring the replacement of fresh precipitate, thin-walled filaments arise and grow-like in the experiments-at the leading tip. In addition, the inclusion of a buoyancy effect allows the model to capture various branched and unbranched chemical garden shapes in two and three dimensions. Our results provide a model of chemical garden structures and highlight the importance of temporal changes in the self-healing membrane material.

Characteristic growth of chemical gardens from mixtures of two salts.

Chemical gardens formed from two metal salts (MCl2 or MSO4) have been investigated to understand the effects of mixing on the growth of precipitate tubes. The growth of tubes can be classified into three types, i.e., collaborative, inhibited, and individual growth, depending on the combination of the two metal salts. Characteristic features of tube growth are discussed in relation to the flow near the tip of the tube controlled by osmotic pressure and the solubility product, Ksp, for M(OH)2. The present study can be interpreted as an inanimate model system of symbiosis among different species, such as mixed cropping systems and survival among different kinds of microbial cells.

Bobbing chemical garden tubes: oscillatory self-motion from buoyancy and catalytic gas production.

Chemical reactions can induce self-propulsion by the production and ejection of gas bubbles from micro-rocket like cylindrical units. We describe related micro-submarines that change their depth in response to catalytic gas production. The structures consist of silica-supported CuO and are produced by utilizing the self-assembly rules of chemical gardens. In H2O2 solution, the tube cavity produces O2(g) and the resulting buoyancy lifts the tube to the air-solution interface, where it releases oxygen and sinks back down to the bottom of the container. In 5 cm deep solutions, the resulting bobbing cycles have a period of 20-30 s and repeat for several hours. The ascent is characterized by a vertical orientation of the tube and a constant acceleration. During the descent, the tubes are oriented horizontally and sink at a nearly constant speed. These striking features are quantitatively captured by an analysis of the involved mechanical forces and chemical kinetics. The results show that ascending tubes increase their oxygen-production rate by the motion-induced injection of fresh solution into the tube cavity.

Shape Evolution of Precipitate Membranes in Flow Systems.

Chemical gardens are macroscopic structures that form when a salt seed is submerged in an alkaline solution. Their thin precipitate membranes separate the reactant partners and slow down the approach toward equilibrium. During this stage, a gradual thickening occurs, which is driven by steep cross-membrane gradients and governed by selective ion transport. We study these growth dynamics in microfluidic channels for the case of Ni(OH)2 membranes. Fast flowing reactant solutions create thickening membranes of a nearly constant width along the channel, whereas slow flows produce wedge-shaped structures that fail to grow along their downstream end. The overall dynamics and shapes are caused by the competition of reactant consumption and transport replenishment. They are reproduced quantitatively by a two-variable reaction-diffusion-advection model which provides kinetic insights into the growth of precipitate membranes.

Perovskite chemical gardens: highly fluorescent microtubes from self-assembly and ion exchange.

We report the shape-preserving conversion of self-assembled CaCO3 microtubes to PbCO3 and MAPbBr3 perovskite. The first step induces the growth of cerussite needles on the outer surface. When further converted, these hedgehog-like structures become fluorescent. Additional spatial control of the process yields Janus tubes of CaCO3 and perovskite segments.

Coexistence of oscillatory and reduced states on a spherical field controlled by electrical potential.

The Belousov-Zhabotinsky (BZ) reaction was investigated to elucidate features of oscillations depending on the applied electrical potential, E. A cation-exchange resin bead loaded with the catalyst of the BZ reaction was placed on a platinum plate as a working electrode and then E was applied. We found that global oscillations (GO) and a reduced state coexisted on the bead at a negative value of E and that the source point of GO changed depending on E. The thickness of the reduced state was determined by a yellow colored region which corresponded to the distribution of Br2. The present studies suggest that the distribution of the inhibitor, Br-, which is produced from Br2, plays an important role in the existence of the reduced state and GO, and the source point of GO.

Shape-preserving conversion of calcium carbonate tubes to self-propelled micromotors.

The self-assembly of inorganic structures beyond the euhedral shape repertoire is a powerful approach to grow hierarchically ordered materials and mesoscopic devices. The hollow precipitate tubes in chemical gardens are a classic example, which we produce on Nafion membranes separating a CaCl2-containing gel from a Na2CO3 solution. The resulting CaCO3 microtubes are conical and consist of either pure vaterite or calcite. The process also forms branched T- and Y-shaped structures. The metastable vaterite polymorph can be converted to Mn-based structures without loss of the macroscopic shape. In H2O2 solution, the resulting tubes self-propel by the release of O2 bubbles, which for branched structures causes rotation. The tubes can contain multiple bubbles which are ejected in a quasi-periodic fashion (e.g. in groups of four). The addition of surfactants causes the accumulation of bubble trails and bubble rafts that interact with the moving tubes and give rise to distinct motion patterns.

Front-like expansion and arrest of programmed cell death in brown banana spots.

The spot patterns on bananas are a striking case of biological pattern formation and-as a qualitative ripeness indicator-linked to 50 million tons of wasted food per year. Ripening bananas develop these senescent spots as phenolic compounds are enzymatically oxidized and cellular integrity is lost. We characterize the dynamics of the spot expansion and their nucleation rates based on time-lapse movies. Spots nucleate for about 2 days yielding a typical density of 8 spots/cm2. The expansion is initially diffusion controlled and the effective diffusion coefficient decreases with nucleation time from 1.3 to 0.4 mm2d-1. During and after expansion, the browning fronts maintain a steep and constant intensity gradient. We quantitatively reproduce these features by a reaction-diffusion model that considers the local oxygen concentration and browning degree of the peel. All model parameters are based on measurements and front stalling is explained by decreasing oxygen levels in the nucleation sites.

Collective motion of self-propelled chemical garden tubes.

In H2O2 solutions, manganese-containing chemical garden tubes can self-propel due to the catalytic production and ejection of oxygen bubbles. Here, we investigate the collective behavior of these self-assembled precipitate tubes. In thin solution layers, the tubes show definite autonomous dynamics with only weak interactions that result from fluid motion around the moving units and directional changes during collisions. In thick solution layers with convex menisci forcing spatial confinement, the tubes undergo cycles of self-assembly and dispersion. This collective motion results from the rhythmic creation of a large master bubble around which the tubes align tangentially.

Self-Propelled Chemical Garden Tubes.

Synthetic autonomous locomotion shows great promise in many research fields, including biomedicine and environmental science, because it can allow targeted drug/cargo delivery and the circumvention of kinetic and thermodynamic limitations. Creating such self-moving objects often requires advanced production techniques as exemplified by catalytic, gas-forming microrockets. Here, we grow such structures via the self-organization of precipitate tubes in chemical gardens by simply injecting metal salts into silicate solutions. This method generates hollow, cylindrical objects rich in catalytic manganese oxide that also feature a partially insulating outer layer of inert silica. In dilute H2O2 solution, these structures undergo self-propulsion by ejecting streams of oxygen bubbles. Each emission event pushes the tube forward by 1-2 tube radii. The ejection frequency depends linearly on the peroxide concentration as quantified by acoustic measurements of bursting bubbles. We expect our facile method and key results to be applicable to a diverse range of materials and reactions.

Hyperscroll dynamics: Vortices in four-dimensional networks.

We investigate a network of excitable nodes diffusively coupled to their neighbors along four orthogonal directions. This regular network effectively forms a four-dimensional reaction-diffusion system and has rotating wave solutions. We analyze some of the general features of these hyperscroll waves, which rotate around surfaces such as planes, spheres, or tori. The surfaces evolve according to local curvatures and a system-specific surface tension. They have associated local phases and phase gradients tend to decrease over time. We also discuss the robustness of these network states against the removal of random node connections and report an example of hyperscroll turbulence.

Dubiofossils from a Mars-analogue subsurface palaeoenvironment: The limits of biogenicity criteria.

The search for a fossil record of Earth's deep biosphere, partly motivated by potential analogies with subsurface habitats on Mars, has uncovered numerous assemblages of inorganic microfilaments and tubules inside ancient pores and fractures. Although these enigmatic objects are morphologically similar to mineralized microorganisms (and some contain organic carbon), they also resemble some abiotic structures. Palaeobiologists have responded to this ambiguity by evaluating problematic filaments against checklists of "biogenicity criteria". Here, we describe material that tests the limits of this approach. We sampled Jurassic calcite veins formed through subseafloor serpentinization, a water-rock reaction that can fuel the deep biosphere and is known to have occurred widely on Mars. At two localities ~4 km apart, veins contained curving, branched microfilaments composed of Mg-silicate and Fe-oxide minerals. Using a wide range of analytical techniques including synchrotron X-ray microtomography and scanning transmission electron microscopy, we show that these features meet many published criteria for biogenicity and are comparable to fossilized cryptoendolithic fungi or bacteria. However, we argue that abiotic processes driven by serpentinization could account for the same set of lifelike features, and report a chemical garden experiment that supports this view. These filaments are, therefore, most objectively described as dubiofossils, a designation we here defend from criticism and recommend over alternative approaches, but which nevertheless signifies an impasse. Similar impasses can be anticipated in the future exploration of subsurface palaeo-habitats on Earth and Mars. To avoid them, further studies are required in biomimetic geochemical self-organization, microbial taphonomy and micro-analytical techniques, with a focus on subsurface habitats.

Switching between Two Oscillatory States Depending on the Electrical Potential.

Various spatiotemporal patterns were created on the surface or in the body of cation-exchange resin beads which were loaded with the catalyst of the Belousov-Zhabotinsky (BZ) reaction. Either global oscillations (GO) or traveling waves (TW) and the switching between them were observed in the previous papers, but it was not clear how chemicals contribute to the reaction inside/around the BZ bead. In this paper, we scanned the electrical potential, E, from +1 to -1 V (negative scan) and then turned from -1 to +1 V (positive scan) to control the switching between GO and TW. We found that the electrical switching potential from TW to GO, ETG, and from GO to TW, EGT, depended on the scanning direction of E and the diameter of the bead, d. The present study suggests that the electrode-induced increase of the inhibitor, Br-, and the activator, HBrO2, around the BZ bead plays an important role in determining ETG and EGT.