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The pursuit of chemically-powered colloidal machines requires individual components that perform different motions within a common environment. Such motions can be tailored by controlling the shape and/or composition of catalytic microparticles; however, the ability to design particle motions remains limited by incomplete understanding of the relevant propulsion mechanism(s). Here, we demonstrate that platinum microparticles move spontaneously in solutions of hydrogen peroxide and that their motions can be rationally designed by controlling particle shape. Nanofabricated particles with n -fold rotational symmetry rotate steadily with speed and direction specified by the type and extent of shape asymmetry. The observed relationships between particle shape and motion provide evidence for a self-electrophoretic propulsion mechanism, whereby anodic oxidation and cathodic reduction occur at different rates at different locations on the particle surface. We develop a mathematical model that explains how particle shape impacts the relevant electrocatalytic reactions and the resulting electrokinetic flows that drive particle motion. Self-propelled motors operating at the micro- or nanoscale can be powered by catalytic reactions and show appealing potential in robotic applications. Brooks et al. describe how the motions of platinum spinners in hydrogen peroxide solutions can be rationally designed by controlling particle shape.

Active colloids are a class of microparticles that ‘swim’ through fluids by breaking the symmetry of the force distribution on their surfaces. Our ability to direct these particles along complex trajectories in three-dimensional (3D) space requires strategies to encode the desired forces and torques at the single particle level. Here, we show that spherical colloids with metal patches of low symmetry self-propel along non-linear 3D trajectories when powered remotely by an alternating current (AC) electric field. In particular, particles with triangular patches of approximate mirror symmetry trace helical paths along the axis of the field. We demonstrate that the speed and shape of the particle’s trajectory can be tuned by the applied field strength and the patch geometry. We show that helical motion can enhance particle transport through porous materials with implications for the design of microrobots that can navigate complex environments. The development of functional microrobots calls for new strategies to design locomotion facilitating navigation through complex environments. Here, Lee et al. show how to realize and program helical motion in three dimensions using patchy microspheres under an alternating current electric field.

Self-assembly of charged, equally sized metal nanoparticles of two types (gold and silver) leads to the formation of large, sphalerite (diamond-like) crystals, in which each nanoparticle has four oppositely charged neighbors. Formation of these non-close-packed structures is a consequence of electrostatic effects specific to the nanoscale, where the thickness of the screening layer is commensurate with the dimensions of the assembling objects. Because of electrostatic stabilization of larger crystallizing particles by smaller ones, better-quality crystals can be obtained from more polydisperse nanoparticle solutions.

Deformable, spherical aggregates of metal nanoparticles connected by long-chain dithiol ligands self-assemble into nanostructured materials of macroscopic dimensions. These materials are plastic and moldable against arbitrarily shaped masters and can be thermally hardened into polycrystalline metal structures of controllable porosity. In addition, in both plastic and hardened states, the assemblies are electrically conductive and exhibit Ohmic characteristics down to ~20 volts per meter. The self-assembly method leading to such materials is applicable both to pure metals and to bimetallic structures of various elemental compositions.

The purpose of this article is to analyze a sequence of independent bets by modeling it with a convective-diffusion equation (CDE). The approach follows the derivation of the Kelly Criterion (i.e., with a binomial distribution for the numbers of wins and losses in a sequence of bets) and reframes it as a CDE in the limit of many bets. The use of the CDE clarifies the role of steady growth (characterized by a velocity U) and random fluctuations (characterized by a diffusion coefficient D) to predict a probability distribution for the remaining bankroll as a function of time. Whereas the Kelly Criterion selects the investment fraction that maximizes the median bankroll (0.50 quantile), we show that the CDE formulation can readily find an optimum betting fraction f for any quantile. We also consider the effects of “ruin” using an absorbing boundary condition, which describes the termination of the betting sequence when the bankroll becomes too small. We show that the probability of ruin can be expressed by a dimensionless Péclet number characterizing the relative rates of convection and diffusion. Finally, the fractional Kelly heuristic is analyzed to show how it impacts returns and ruin. The reframing of the Kelly approach with the CDE opens new possibilities to use known results from the chemico-physical literature to address sequential betting problems.

Negative photoconductance A photoconductor is a material whose electrical conductivity changes when illuminated — invariably increasing in response to the incident light. Now Nakanishi et al . show how nanoparticle-based materials can be engineered, through careful choice of the molecules used to stabilize the nanoparticles, to exhibit negative (or 'inverse') photoconductance — thin films of these materials become less conducting in the presence of light. Nanoparticle-based photoconductors based on the principles underlying these observations could find use as chemical sensors. A photoconductor is a material in which electrical conductivity changes when it is illuminated — invariably increasing in response to impinging light. However, here it is shown that nanoparticle-based materials can be engineered, through the careful choice of the molecules used to stabilize the nanoparticles, to exhibit negative photoconductance: conductivity in these materials decreases in the presence of light. In traditional photoconductors 1 , 2 , 3 , the impinging light generates mobile charge carriers in the valence and/or conduction bands, causing the material’s conductivity to increase 4 . Such positive photoconductance is observed in both bulk and nanostructured 5 , 6 photoconductors. Here we describe a class of nanoparticle-based materials whose conductivity can either increase or decrease on irradiation with visible light of wavelengths close to the particles’ surface plasmon resonance. The remarkable feature of these plasmonic materials is that the sign of the conductivity change and the nature of the electron transport between the nanoparticles depend on the molecules comprising the self-assembled monolayers (SAMs) 7 , 8 stabilizing the nanoparticles. For SAMs made of electrically neutral (polar and non-polar) molecules, conductivity increases on irradiation. If, however, the SAMs contain electrically charged (either negatively or positively) groups, conductivity decreases. The optical and electrical characteristics of these previously undescribed inverse photoconductors can be engineered flexibly by adjusting the material properties of the nanoparticles and of the coating SAMs. In particular, in films comprising mixtures of different nanoparticles or nanoparticles coated with mixed SAMs, the overall photoconductance is a weighted average of the changes induced by the individual components. These and other observations can be rationalized in terms of light-induced creation of mobile charge carriers whose transport through the charged SAMs is inhibited by carrier trapping in transient polaron-like states 9 , 10 . The nanoparticle-based photoconductors we describe could have uses in chemical sensors and/or in conjunction with flexible substrates.

Coupling between nanoscale self-assembly and capillary pattern formation leads to ordered thin films with multiscale structure spanning six orders of magnitude.

Nanoparticles (NPs) decorated with ligands combining photoswitchable dipoles and covalent cross-linkers can be assembled by light into organized, three-dimensional suprastructures of various types and sizes. NPs covered with only few photoactive ligands form metastable crystals that can be assembled and disassembled \"on demand\" by using light of different wavelengths. For higher surface concentrations, self-assembly is irreversible, and the NPs organize into permanently cross-linked structures including robust supracrystals and plastic spherical aggregates.

Small autonomous machines like biological cells or soft robots can convert energy input into control of function and form. It is desired that this behavior emerges spontaneously and can be easily switched over time. For this purpose we introduce an active matter system that is loosely inspired by biology and which we term an active colloidal cell. The active colloidal cell consists of a boundary and a fluid interior, both of which are built from identical rotating spinners whose activity creates convective flows. Similarly to biological cell motility, which is driven by cytoskeletal components spread throughout the entire volume of the cell, active colloidal cells are characterized by highly distributed energy conversion. We demonstrate that we can control the shape of the active colloidal cell and drive compartmentalization by varying the details of the boundary (hard vs. flexible) and the character of the spinners (passive vs. active). We report buckling of the boundary controlled by the pattern of boundary activity, as well as formation of core–shell and inverted Janus phase-separated configurations within the active cell interior. As the cell size is increased, the inverted Janus configuration spontaneously breaks its mirror symmetry. The result is a bubble–crescent configuration, which alternates between two degenerate states over time and exhibits collective migration of the fluid along the boundary. Our results are obtained using microscopic, non–momentum-conserving Langevin dynamics simulations and verified via a phase-field continuum model coupled to a Navier–Stokes equation.

Cell motility is a process deriving from the synchronized dynamics of the cytoskeleton. In several important physiological processes—notably, cancer metastasis—the randomly moving cells can acquire a directional motility phenotype and bias their motions in response to environmental cues. Despite intense research, however, the current understanding of directional cell migration is incomplete and there is a growing need to develop systems that would enable the study and control of this process. This article demonstrates that random motions of motile cells can be rectified by asymmetric (‘ratchet’) microgeometries. Interactions between the cells and the imposed geometrical cues guide cell polarization and give rise to directional motility. Depending on the ratchet design, cells of different types can move either in the same or in opposite directions on the same imposed pattern. In the latter case, it is possible to partially sort mixed cell populations into different collecting reservoirs. It is not surprising that a microfluidic channel whose walls have a ratchet-like structure can preferentially direct the flow of large particles in one direction. But a study of the movement of living cells through such channels provides the remarkable observation that the direction of preferred motion can be different for different species of cell.