Solid-body trajectoids shaped to roll along desired pathways.

In everyday life, rolling motion is typically associated with cylindrical (for example, car wheels) or spherical (for example, billiard balls) bodies tracing linear paths. However, mathematicians have, for decades, been interested in more exotically shaped solids such as the famous oloids1, sphericons2, polycons3, platonicons4 and two-circle rollers5 that roll downhill in curvilinear paths (in contrast to cylinders or spheres) yet indefinitely (in contrast to cones, Supplementary Video 1). The trajectories traced by such bodies have been studied in detail6-9, and can be useful in the context of efficient mixing10,11 and robotics, for example, in magnetically actuated, millimetre-sized sphericon-shaped robots12,13, or larger sphericon- and oloid-shaped robots translocating by shifting their centre of mass14,15. However, the rolling paths of these shapes are all sinusoid-like and their diversity ends there. Accordingly, we were intrigued whether a more general problem is solvable: given an infinite periodic trajectory, find the shape that would trace this trajectory when rolling down a slope. Here, we develop an algorithm to design such bodies-which we call 'trajectoids'-and then validate these designs experimentally by three-dimensionally printing the computed shapes and tracking their rolling paths, including those that close onto themselves such that the body's centre of mass moves intermittently uphill (Supplementary Video 2). Our study is motivated largely by fundamental curiosity, but the existence of trajectoids for most paths has unexpected implications for quantum and classical optics, as the dynamics of qubits, spins and light polarization can be exactly mapped to trajectoids and their paths16.

Enhancing crystal growth using polyelectrolyte solutions and shear flow.

The ability to grow properly sized and good quality crystals is one of the cornerstones of single-crystal diffraction, is advantageous in many industrial-scale chemical processes1-3, and is important for obtaining institutional approvals of new drugs for which high-quality crystallographic data are required4-7. Typically, single crystals suitable for such processes and analyses are grown for hours to days during which any mechanical disturbances-believed to be detrimental to the process-are carefully avoided. In particular, stirring and shear flows are known to cause secondary nucleation, which decreases the final size of the crystals (though shear can also increase their quantity8-14). Here we demonstrate that in the presence of polymers (preferably, polyionic liquids), crystals of various types grow in common solvents, at constant temperature, much bigger and much faster when stirred, rather than kept still. This conclusion is based on the study of approximately 20 diverse organic molecules, inorganic salts, metal-organic complexes, and even some proteins. On typical timescales of a few to tens of minutes, these molecules grow into regularly faceted crystals that are always larger (with longest linear dimension about 16 times larger) than those obtained in control experiments of the same duration but without stirring or without polymers. We attribute this enhancement to two synergistic effects. First, under shear, the polymers and their aggregates disentangle, compete for solvent molecules and thus effectively 'salt out' (that is, induce precipitation by decreasing solubility of) the crystallizing species. Second, the local shear rate is dependent on particle size, ultimately promoting the growth of larger crystals (but not via surface-energy effects as in classical Ostwald ripening). This closed-system, constant-temperature crystallization driven by shear could be a valuable addition to the repertoire of crystal growth techniques, enabling accelerated growth of crystals required by the materials and pharmaceutical industries.

Concentric liquid reactors for chemical synthesis and separation.

Recent years have witnessed increased interest in systems that are capable of supporting multistep chemical processes without the need for manual handling of intermediates. These systems have been based either on collections of batch reactors1 or on flow-chemistry designs2-4, both of which require considerable engineering effort to set up and control. Here we develop an out-of-equilibrium system in which different reaction zones self-organize into a geometry that can dictate the progress of an entire process sequence. Multiple (routinely around 10, and in some cases more than 20) immiscible or pairwise-immiscible liquids of different densities are placed into a rotating container, in which they experience a centrifugal force that dominates over surface tension. As a result, the liquids organize into concentric layers, with thicknesses as low as 150 micrometres and theoretically reaching tens of micrometres. The layers are robust, yet can be internally mixed by accelerating or decelerating the rotation, and each layer can be individually addressed, enabling the addition, sampling or even withdrawal of entire layers during rotation. These features are combined in proof-of-concept experiments that demonstrate, for example, multistep syntheses of small molecules of medicinal interest, simultaneous acid-base extractions, and selective separations from complex mixtures mediated by chemical shuttles. We propose that 'wall-less' concentric liquid reactors could become a useful addition to the toolbox of process chemistry at small to medium scales and, in a broader context, illustrate the advantages of transplanting material and/or chemical systems from traditional, static settings into a rotating frame of reference.

Author Correction: Systems of mechanized and reactive droplets powered by multi-responsive surfactants.

In this Letter, the top structure of the right panel of Fig. 1a should be that of cis-9-octadecenoic acid, not trans-9-octadecenoic acid. Please see the accompanying Author Correction. This error has not been corrected online.

Systems of mechanized and reactive droplets powered by multi-responsive surfactants.

Although 'active' surfactants, which are responsive to individual external stimuli such as temperature, electric or magnetic fields, light, redox processes or chemical agents, are well known, it would be interesting to combine several of these properties within one surfactant species. Such multi-responsive surfactants could provide ways of manipulating individual droplets and possibly assembling them into larger systems of dynamic reactors. Here we describe surfactants based on functionalized nanoparticle dimers that combine all of these and several other characteristics. These surfactants and therefore the droplets that they cover are simultaneously addressable by magnetic, optical and electric fields. As a result, the surfactant-covered droplets can be assembled into various hierarchical structures, including dynamic ones, in which light powers the rapid rotation of the droplets. Such rotating droplets can transfer mechanical torques to their non-nearest neighbours, thus acting like systems of mechanical gears. Furthermore, droplets of different types can be merged by applying electric fields and, owing to interfacial jamming, can form complex, non-spherical, 'patchy' structures with different surface regions covered with different surfactants. In systems of droplets that carry different chemicals, combinations of multiple stimuli can be used to control the orientations of the droplets, inter-droplet transport, mixing of contents and, ultimately, sequences of chemical reactions. Overall, the multi-responsive active surfactants that we describe provide an unprecedented level of flexibility with which liquid droplets can be manipulated, assembled and reacted.

Aerodynamically Levitated Droplets as Small-Scale Chemical Reactors and Liquid Microprinters.

A thin liquid film spread over the inner surface of a rapidly rotating vial creates an aerodynamic cushion on which one or multiple droplets of various liquids can levitate stably for days or even weeks. These levitating droplets can serve as wall-less ("airware") chemical reactors that can be merged without touching-by remote impulses-to initiate reactions or sequences of reactions at scales down to hundreds of nanomoles. Moreover, under external electric fields, the droplets can act as the world's smallest chemical printers, shedding regular trains of pL or even fL microdrops. In one modality, the levitating droplets operate as completely wireless aliquoting/titrating systems delivering pg quantities of reagents into the liquid in the rotating vial; in another modality, they print microdroplet arrays onto target surfaces. The "airware", levitated reactors are inexpensive to set up, remarkably stable to external disturbances and, for printing applications, require operating voltages much lower than in electrospray, electrowetting, or ink jet systems.

Proving Cooperativity of a Catalytic Reaction by Means of Nanoscale Geometry: The Case of Click Reaction.

Establishing whether a reaction is catalyzed by a single-metal catalytic center or cooperatively by a fleeting complex encompassing two such centers may be an arduous pursuit requiring detailed kinetic, isotopic, and other types of studies─as illustrated, for instance, by over a decade-long work on single-copper versus di-copper mechanisms of the popular "click" reaction. This paper describes a method to interrogate such cooperative mechanisms by a nanoparticle-based platform in which the probabilities of catalytic units being proximal can be varied systematically and, more importantly, independently of their volume concentration. The method relies on geometrical considerations rather than a detailed knowledge of kinetic equations, yet the scaling trends it yield can distinguish between cooperative and non-cooperative mechanisms.

On-Nanoparticle Gating Units Render an Ordinary Catalyst Substrate- and Site-Selective.

When an organometallic catalyst is tethered onto a nanoparticle and is embedded in a monolayer of longer ligands terminated in "gating" end-groups, these groups can control the access and orientation of the incoming substrates. In this way, a nonspecific catalyst can become enzyme-like: it can select only certain substrates from substrate mixtures and, quite remarkably, can also preorganize these substrates such that only some of their otherwise equivalent sites react. For a simple, copper-based click reaction catalyst and for gating ligands terminated in charged groups, both substrate- and site-selectivities are on the order of 100, which is all the more notable given the relative simplicity of the on-particle monolayers compared to the intricacy of enzymes' active sites. The strategy of self-assembling macromolecular, on-nanoparticle environments to enhance selectivities of "ordinary" catalysts presented here is extendable to other types of catalysts and gating based on electrostatics, hydrophobicity, and chirality, or the combinations of these effects. Rational design of such systems should be guided by theoretical models we also describe.

Stimuli-responsive granular crystals assembled by dipolar and multipolar interactions.

This work describes granular crystals held together by unusual, multipolar interactions and, under the application of an external bias, undergoing reversible structural transitions between closed and open forms. The system comprises two types of polymeric beads agitated on one or between two conductive plates and gradually acquiring charges by contact electrification. The charges thus developed induce a series of electrostatic images in the conductive supports and, in effect, the beads interact via dipolar or multipolar interactions, enabling the stabilization of non-electroneutral crystals. Furthermore, under an applied bias, the beads become polarized and their complex interactions (due to the series of image charges as well as series of image dipoles) result in open-pore crystals which return to compact forms upon bias removal. These effects are rationalized by analytical calculations, and the crystal structures observed in the experiments are reproduced by molecular dynamics simulations.

The Influence of Distant Substrates on the Outcome of Contact Electrification.

The magnitudes of the charges developed on contact-electrified polymers depend on not only the properties of these materials but also the nature of distant substrates on which the polymers are supported. In particular, image charges induced in conductive substrates can decrease charges on the polymers by arc discharge through the surrounding gas. This mode of charge dissipation occurs on timescales of milliseconds and can be prevented by insulating the sharp edges of the conductive supports.

Fluorescence microscopy and spectroscopy of subsurface layer dynamics of polymers with nanometer resolution in the axial direction.

We studied the dynamics in ultrathin subsurface layers of an amorphous polymer by the spectra of single fluorescent molecules embedded into the layer by vapor deposition and subsequent controlled diffusion to the desired depth in ≈0.5 nm steps. The spectral trails of single molecules were recorded at 4.5 K as a function of diffusion depth. In depths shallower than 20 nm, the spectral dynamics deviate from those deep in the bulk. Less than 5 nm deep, the linewidths increase rapidly, whereas the number of detected molecules decreases. No zero-phonon lines were observed closer than 0.5 nm to the polymer surface. Possible physical reasons of the observed phenomena are discussed.

Low temperature spectral dynamics of single molecules in ultrathin polymer films.

We studied the spectral dynamics of single fluorescent dye molecules embedded in ultrathin films (5 - 100 nm) of the amorphous polymer polyisobutylene at cryogenic temperatures and its variation with film thickness. Noticeable portion of molecules in the ensemble shows a behavior which is inconsistent with the standard tunneling model: Their spectral lines are subject to irreversible spectral jumps, continuous shifting, and abrupt chaotic changes of the linewidth or jumping rate. In films thinner than 100 nm, the occurrence of "non-standard" spectral behavior increases with decreasing sample thickness at fixed excitation intensity. In addition, it also increases with laser intensity.

On-nanoparticle monolayers as a solute-specific, solvent-like phase.

In addition to modifying surface properties, self-assembled monolayers, SAMs, on nanoparticles can selectively incorporate small molecules from the surrounding solution. This selectivity has been used in the design of substrate-specific catalytic systems but its degree has not been quantified. This work uses catalytic centers embedded in on-nanoparticle hydrophobic SAMs to monitor and quantify the partitioning of molecules between the bulk solvent and these monolayers. A combination of experiments and theory allows us to relate the logarithm of the incorporation-into-SAM constant to the "bulk" log P values, characterizing the incoming substrates. These results are in line with classic, semi-empirical linear free energy relationships between partitioning solvent systems; in this way, they substantiate the view of nanoscopic on-particle SAMs acting akin to a bulk solvent phase.

Targeted crystallization of mixed-charge nanoparticles in lysosomes induces selective death of cancer cells.

Lysosomes have become an important target for anticancer therapeutics because lysosomal cell death bypasses the classical caspase-dependent apoptosis pathway, enabling the targeting of apoptosis- and drug-resistant cancers. However, only a few small molecules-mostly repurposed drugs-have been tested so far, and these typically exhibit low cancer selectivity, making them suitable only for combination therapies. Here, we show that mixed-charge nanoparticles covered with certain ratios of positively and negatively charged ligands can selectively target lysosomes in cancerous cells while exhibiting only marginal cytotoxicity towards normal cells. This selectivity results from distinct pH-dependent aggregation events, starting from the formation of small, endocytosis-prone clusters at cell surfaces and ending with the formation of large and well-ordered nanoparticle assemblies and crystals inside cancer lysosomes. These assemblies cannot be cleared by exocytosis and cause lysosome swelling, which gradually disrupts the integrity of lysosomal membranes, ultimately impairing lysosomal functions and triggering cell death.

Dynamic Assembly of Small Parts in Vortex-Vortex Traps Established within a Rotating Fluid.

Stable, purely fluidic particle traps established by vortex flows induced within a rotating fluid are described. The traps can manipulate various types of small parts, dynamically assembling them into high-symmetry clusters, cages, interlocked architectures, jammed colloidal monoliths, or colloidal formations on gas bubbles. The strength and the shape of the trapping region can be controlled by the strengths of one or both vortices and/or by the system's global angular velocity. The system exhibits a range of interesting dynamical behaviors including a Hopf-bifurcation transition between equilibrium-point trapping and the so-called limit cycle in which the particles are confined to circular orbits. Theoretical considerations indicate that these vortex-vortex traps can be further miniaturized to manipulate objects with sizes down to ≈10 µm.