Bone-crack detection, targeting, and repair using ion gradients

Diffusiophoresis of Weakly Charged Fluid Droplets in a General Electrolyte Solution: An Analytical Theory

Owing to the importance of analytical results for electrokinetics of colloidal entities, we performed a mathematical analysis to determine the closed form analytical results for the diffusiophoretic velocity of a hydrophobic and polarizable fluid droplet. A comprehensive mathematical model is developed for diffusiophoresis, considering the background aqueous medium as general electrolytes (e.g., binary valence-symmetric/asymmetric electrolytes and a mixed solution of binary electrolytes). We performed our analysis under a weak concentration gradient, and the analytical results for diffusiophoretic velocity are calculated within the Debye-Hückel electrostatic framework. The exact form of the diffusiophoretic velocity is further approximated with negligible error, and the approximate form is found to be free from any of the cumbersome exponential integrals and thus very convenient for practical use. The present theory also covers the diffusiophoresis of perfectly dielectric as well as perfectly conducting droplets as its limiting case. In addition, we have further derived a number of closed form expressions for diffusiophoretic velocity pertaining to several particular cases, and we observed that the derived limit correctly recovers the available existing analytical results for diffusiophoretic velocity. Thus, the present analytical theory for diffusiophoresis can be applied to a wide class of fluidic droplets, e.g., hydrophobic and dielectric oil/conducting mercury droplets, air bubbles, nanoemulsions, as well as any polarizable and hydrophobic fluidic droplet suspended in a solution of general electrolytes.

Diffusiophoresis of a Weakly Charged Liquid Metal Droplet

Diffusiophoresis of a weakly charged liquid metal droplet (LMD) is investigated theoretically, motivated by its potential application in drug delivery. A general analytical formula valid for weakly charged condition is adopted to explore the droplet phoretic behavior. We determined that a liquid metal droplet, which is a special category of the conducting droplet in general, always moves up along the chemical gradient in sole chemiphoresis, contrary to a dielectric droplet where the droplet tends to move down the chemical gradient most of the time. This suggests a therapeutic nanomedicine such as a gallium LMD is inherently superior to a corresponding dielectric liposome droplet in drug delivery in terms of self-guiding to its desired destination. The droplet moving direction can still be manipulated via the polarity dependence; however, there should be an induced diffusion potential present in the electrolyte solution under consideration, which spontaneously generates an extra electrophoresis component. Moreover, the smaller the conducting liquid metal droplet is, the faster it moves in general, which means a smaller LMD nanomedicine is preferred. These findings demonstrate the superior features of an LMD nanomedicine in drug delivery.

Analytical solution to dielectric droplet diffusiophoresis under Debye-Hückel approximation

A simple analytical formula is obtained for the diffusiophoresis of a dielectric fluid droplet in symmetric binary electrolyte solutions under Debye-Hückel approximation valid for weakly charged droplets. The chemiphoresis is found to yield negative mobilities most of the time for droplets of constant surface charge density, which implies that the droplets tend to move away from the source releasing ionic chemicals. This is undesirable in some practical applications like drug delivery with liposomes in terms of conveying the drug-carrying liposomes to the desired area in the human body releasing specific ionic chemicals utilizing the self-guiding nature of diffusiophoresis. The further involvement of the electrophoresis component, however, may change the scenario via the oriented electric field generated by the induced diffusion potential. The lesson here is that while the impact of the chemiphoresis component is determined by nature and uncontrollable, the electrophoresis component serves as an artificially adjustable factor via choosing droplets with the surface charge of appropriate sign in practical applications. The results here have potential use in practical applications such as drug delivery. The portable simple analytical formula is a powerful asset to experimental researchers and design engineers in colloid science and technology to facilitate their works.

Confinement-Dependent Diffusiophoretic Transport of Nanoparticles in Collagen Hydrogels

The transport of nanoparticles in biological hydrogels is often hindered by the strong confinement of the media, thus limiting important applications such as drug delivery and disinfection. Here, we investigate nanoparticle transport in collagen hydrogels driven by diffusiophoresis. Contrary to common expectations for boundary confinement effects where the confinement hinders diffusiophoresis, we observe a nonmonotonic behavior in which maximum diffusiophoretic mobility is observed at intermediate confinement. We find that such behavior is a consequence of the interplay between multiple size-dependent effects. Our results display the utility of diffusiophoresis for enhanced nanoparticle transport in physiologically relevant conditions under tight confinement, suggesting a potential strategy for drug delivery in compressed tissues.

Autonomous Low-Reynolds-Number Soft Robots with Structurally Encoded Motion and Their Thermodynamic Efficiency

Soft low-Reynolds-number robotics hold the potential to significantly impact numerous fields including drug delivery, sensing, and diagnostics. Realizing this potential is predicated upon the ability to design soft robots tailored to their intended function. In this work, we identify the effect of different geometric and symmetry parameters on the motion of soft, autonomous robots that operate in the low-Reynolds-number regime and use organic fuel. The ability to power low-Reynolds-number soft robots using an organic fuel would provide a new avenue for their potential use in biomedical applications, as is the use of a polymeric biocompatible material as is done here. We introduce a simple and cost-effective 3D-printer-assisted method to fabricate robots of different shapes that is scalable and widely applicable for a variety of materials. The efficiency of chemical energy to mechanical energy conversion is measured in soft low-Reynolds-number robots for the first time, and their mechanism of motion is assessed. Motion is a result of a periodic and oscillatory change in the charge state of the gel. This work lays the groundwork for the structure-function design of soft, chemically operated, and autonomous low-Reynolds-number robots.

Diffusiophoresis of a highly charged soft particle normal to a conducting plane

Diffusiophoresis of a soft particle in electrolyte solutions normal to a conducting solid plane is investigated theoretically in this study, focusing on the highly charged particle in particular. A pseudo-spectral method based on Chebyshev polynomial is adopted to solve the resultant governing electrokinetic equations. It was found, among other things, that the closer the soft particle is to the plane, the faster it moves in general, provided only the chemiphoresis component of the diffusiophoresis is involved, i.e., no diffusion potential is present. The presence of the conducting plane is found to have three effects upon the particle motion nearby: the geometric boundary confinement effect, the electrostatic mirror-image force analog effect, and the hydrodynamic retarding effect. The enhancement of the double layer polarization by the first two effects leads to the seeming intriguing observation mentioned above. The particle always moves away from the plane in chemiphoresis. If a diffusion potential is present, however, then it is possible to drive the particle toward the plane. The results have potential applications in drug delivery.

Diffusiophoresis of a Highly Charged Soft Particle in Electrolyte Solutions

Diffusiophoresis of a soft particle suspended in an infinite medium of symmetric binary electrolyte solution is investigated theoretically in this study, focusing on the chemiphoresis component when there is no global diffusion potential in the bulk solution. The general governing electrokinetic equations are solved with a pseudo-spectral method based on Chebyshev polynomials, and particle mobility, defined as the particle velocity per unit concentration gradient, is calculated. Parameters of electrokinetic interest are examined, in general, to explore their respective impact upon particle motion, such as the fixed charge density and permeability in the outer porous layer, the surface charge density and size of the inner rigid core, and the electrolyte strength in the solution. Nonlinear phenomena such as the motion-deterring double-layer polarization and the counterion condensation effects are scrutinized, in particular, for highly charged soft particles. Mobility reversal is observed in some range of electrolyte strength for highly charged particles. The generation of an axisymmetric counterclockwise vortex flow across the porous layer is found to be responsible for it. The onset of the mobility reversal is synchronized with the appearance or disappearance of this vortex flow. Mobility reversal may happen more than once, with particle moving toward or away from the region of higher solute concentration. The latter is undesirable in the application of drug delivery and thus should be avoided by delicate control of the electrokinetic environment. A local micro diffusion potential is discovered, which always speeds up the migration of coions and slows down that of counterions to guarantee that there is no net electric current across the double layer. Moreover, multilayer structure of the double-layer polarization is discovered when the electrolyte strength is high. The study presented here provides insight and crucial information for practical applications of soft particles, such as drug delivery.

Colloid Separation by CO2-Induced Diffusiophoresis

We present a microfluidic crossflow separation of colloids enabled by the dissolution of CO₂ gas in aqueous suspensions. The dissolved CO₂ dissociates into H⁺ and HCO₃^- ions, which are efficient candidates for electrolytic diffusiophoresis, because of the fast diffusion of protons. By exposing CO₂ gas to one side of a microfluidic flow channel, a crossflow gradient can be created, enabling the crossflow diffusiophoresis of suspended particles. We develop a simple two-dimensional model to describe the coupled transport dynamics that is due to the competition of advection and diffusiophoresis. Furthermore, we show that oil nanoemulsions can be effectively separated by utilizing highly charged particles as a carrier vehicle, which is otherwise difficult to achieve. These results demonstrate a portable, versatile method for separating particles in broad applications including oil extraction, drug delivery, and bioseparation.

Fluorescence Detection of Bone Microcracks Using Monophosphonated Carbon Dots

Phosphonated compounds, in particular, bisanalogs are widely applied in clinical settings for the treatment of severe bone turnovers and recently as imaging probes when conjugated with organic fluorophores. Herein, we introduce a bone seeking luminescent probe that shows a high binding affinity toward bone minerals based on monophosphonated carbon dots (CDs). Spheroidal CDs tethered with PEG monophosphates are synthesized in a one-pot hydrothermal method and are physicochemically characterized, where the retention of phosphonates is confirmed by ¹³P NMR and X-ray photoelectron spectroscopy. Interestingly, the high abundance of multiple monodentate phosphonates exhibited strong binding to hydroxyapatite, the main bone mineral constituent. The remarkable optophysical properties of monophosphonated CDs were confirmed in an ex vivo model of the bovine cortical bone where the imaging feasibility of microcracks, which are calcium-rich regions, was demonstrated. The in vivo studies specified the potential application of monophosphonated CDs for imaging when injected intramuscularly. The biodigestible nature and cytocompatibility of the probe presented here obviate the demand for a secondary fluorophore, while offering a nanoscale strategy for bone targeting and can eventually be employed for potential bone therapy in the future.

Aggregation-Induced Emission Probe for Light-Up and in Situ Detection of Calcium Ions at High Concentration

The fluorescent probe for the detection of calcium ions is an indispensable tool in the biomedical field. The millimolar order of Ca(II) ions is associated with many physiological processes and diseases, such as hypercalcemia, soft tissue calcification, and bone microcracks. However, the conventional fluorescent probes are only suitable for imaging Ca(II) ions in the nanomolar to micromolar range, which can be because of their high affinities toward Ca(II) ions and aggregation-caused quenching drawbacks. To tackle this challenge, we herein develop an aggregation-induced emission (AIE) probe SA-4CO₂Na for selective and light-up detection of Ca(II) ions in the millimolar range (0.6-3.0 mM), which can efficiently distinguish between hypercalcemic (1.4-3.0 mM) and normal (1.0-1.4 mM) Ca²⁺ ion levels. The formation of fibrillar aggregates between SA-4CO₂Na and Ca(II) ions was clearly verified by fluorescence, scanning electron microscopy, and transmission electron analysis. Moreover, this AIE-active probe can be used for wash-free and light-up imaging of a high concentration of Ca(II) ions even in the solid analytes, including calcium deposits in psammomatous meningioma slice, microcracks on bovine bone surface, and microdefects on hydroxyapatite-based scaffold. It is thus expected that this AIE-active probe would have broad biomedical applications through light-up imaging and sensing of Ca(II) ions at the millimolar level.

Micro/nanomotors towards in vivo application: cell, tissue and biofluid

Inspired by highly efficient natural motors, synthetic micro/nanomotors are self-propelled machines capable of converting the supplied fuel into mechanical motion. A significant advance has been made in the construction of diverse motors over the last decade. These synthetic motor systems, with rapid transporting and efficient cargo towing abilities, are expected to open up new horizons for various applications. Utilizing emergent motor platforms for in vivo applications is one important aspect receiving growing interest as conventional therapeutic methodology still remains limited for cancer, heart, or vasculature diseases. In this review we will highlight the recent efforts towards realistic in vivo application of various motor systems. With ever booming research enthusiasm in this field and increasing multidisciplinary cooperation, micro/nanomotors with integrated multifunctionality and selectivity are on their way to revolutionize clinical practice.

Light-Controlled Swarming and Assembly of Colloidal Particles

Swarms and assemblies are ubiquitous in nature and they can perform complex collective behaviors and cooperative functions that they cannot accomplish individually. In response to light, some colloidal particles (CPs), including light active and passive CPs, can mimic their counterparts in nature and organize into complex structures that exhibit collective functions with remote controllability and high temporospatial precision. In this review, we firstly analyze the structural characteristics of swarms and assemblies of CPs and point out that light-controlled swarming and assembly of CPs are generally achieved by constructing light-responsive interactions between CPs. Then, we summarize in detail the recent advances in light-controlled swarming and assembly of CPs based on the interactions arisen from optical forces, photochemical reactions, photothermal effects, and photoisomerizations, as well as their potential applications. In the end, we also envision some challenges and future prospects of light-controlled swarming and assembly of CPs. With the increasing innovations in mechanisms and control strategies with easy operation, low cost, and arbitrary applicability, light-controlled swarming and assembly of CPs may be employed to manufacture programmable materials and reconfigurable robots for cooperative grasping, collective cargo transportation, and micro- and nanoengineering.

Origins of concentration gradients for diffusiophoresis

Fluid transport that is driven by gradients of pressure, gravity, or electro-magnetic potential is well-known and studied in many fields. A subtler type of transport, called diffusiophoresis, occurs in a gradient of chemical concentration, either electrolyte or non-electrolyte. Diffusiophoresis works by driving a slip velocity at the fluid-solid interface. Although the mechanism is well-known, the diffusiophoresis mechanism is often considered to be an esoteric laboratory phenomenon. However, in this article we show that concentration gradients can develop in a surprisingly wide variety of physical phenomena - imposed gradients, asymmetric reactions, dissolution, crystallization, evaporation, mixing, sedimentation, and others - so that diffusiophoresis is in fact a very common transport mechanism, in both natural and artificial systems. We anticipate that in georeservoir extractions, physiological systems, drying operations, laboratory and industrial separations, crystallization operations, membrane processes, and many other situations, diffusiophoresis is already occurring - often without being recognized - and that opportunities exist for designing this transport to great advantage.

Targeted Imaging of Damaged Bone in Vivo with Gemstone Spectral Computed Tomography

Achieving high-resolution imaging of bone-cracks and even monitoring them in live organisms are of great significance for understanding their extreme biological effects but remain quite challenging, especially for adopting commercial imaging systems. Herein, we explore the use of the clinical gemstone spectral computed tomography (GSCT) technique as a powerful tool for targeted imaging of bone-cracks in rats via intramuscularly administrating crack-targeted ytterbium-based contrast agents (CAs). Material density images of GSCT reveal that bone-cracks targeted with CAs can be successfully differentiated from healthy bone based on their different X-ray attenuation characteristics, giving GSCT a distinct advantage over conventional CT. More importantly, the superior imaging capability of GSCT allows us to real-time monitor the targeting and accumulation of CAs toward bone-crack in vivo. These results highlight that clinical GSCT, combined with ytterbium-based CAs, provides a promising opportunity for understanding bone-related diseases in the future.

Self-Propelled Nanomotors Autonomously Seek and Repair Cracks

Biological self-healing involves the autonomous localization of healing agents at the site of damage. Herein, we design and characterize a synthetic repair system where self-propelled nanomotors autonomously seek and localize at microscopic cracks and thus mimic salient features of biological wound healing. We demonstrate that these chemically powered catalytic nanomotors, composed of conductive Au/Pt spherical Janus particles, can autonomously detect and repair microscopic mechanical defects to restore the electrical conductivity of broken electronic pathways. This repair mechanism capitalizes on energetic wells and obstacles formed by surface cracks, which dramatically alter the nanomotor dynamics and trigger their localization at the defects. By developing models for self-propelled Janus nanomotors on a cracked surface, we simulate the systems' dynamics over a range of particle speeds and densities to verify the process by which the nanomotors autonomously localize and accumulate at the cracks. We take advantage of this localization to demonstrate that the nanomotors can form conductive "patches" to repair scratched electrodes and restore the conductive pathway. Such a nanomotor-based repair system represents an important step toward the realization of biomimetic nanosystems that can autonomously sense and respond to environmental changes, a development that potentially can be expanded to a wide range of applications, from self-healing electronics to targeted drug delivery.

From one to many: dynamic assembly and collective behavior of self-propelled colloidal motors

The assembly of complex structures from simpler, individual units is a hallmark of biology. Examples include the pairing of DNA strands, the assembly of protein chains into quaternary structures, the formation of tissues and organs from cells, and the self-organization of bacterial colonies, flocks of birds, and human beings in cities. While the individual behaviors of biomolecules, bacteria, birds, and humans are governed by relatively simple rules, groups assembled from many individuals exhibit complex collective behaviors and functions that do not exist in the absence of the hierarchically organized structure. Self-assembly is a familiar concept to chemists who study the formation and properties of monolayers, crystals, and supramolecular structures. In chemical self-assembly, disorder evolves to order as the system approaches equilibrium. In contrast, living assemblies are typically characterized by two additional features: (1) the system constantly dissipates energy and is not at thermodynamic equilibrium; (2) the structure is dynamic and can transform or disassemble in response to stimuli or changing conditions. To distinguish them from equilibrium self-assembled structures, living (or nonliving) assemblies of objects with these characteristics are referred to as active matter. In this Account, we focus on the powered assembly and collective behavior of self-propelled colloids. These nano- and microparticles, also called nano- and micromotors or microswimmers, autonomously convert energy available in the environment (in the form of chemical, electromagnetic, acoustic, or thermal energy) into mechanical motion. Collections of these colloids are a form of synthetic active matter. Because of the analogy to living swimmers of similar size such as bacteria, the dynamic interactions and collective behavior of self-propelled colloids are interesting in the context of understanding biological active matter and in the development of new applications. The progression from individual particle motion to pairwise interactions, and then to multiparticle behavior, can be studied systematically with colloidal particles. Colloidal particles are also amenable to designs (in terms of materials, shapes, and sizes) that are not readily available in, for example, microbial systems. We review here our efforts and those of other groups in studying these fundamental interactions and the collective behavior that emerges from them. Although this field is still very new, there are already unique and interesting applications in analysis, diagnostics, separations, and materials science that derive from our understanding of how powered colloids interact and assemble.

Synthetic Nano- and Micromachines in Analytical Chemistry: Sensing, Migration, Capture, Delivery, and Separation

Synthetic nano- and microscale machines move autonomously in solution or drive fluid flows by converting sources of energy into mechanical work. Their sizes are comparable to analytes (sub-nano- to microscale), and they respond to signals from each other and their surroundings, leading to emergent collective behavior. These machines can potentially enable hitherto difficult analytical applications. In this article, we review the development of different classes of synthetic nano- and micromotors and pumps and indicate their possible applications in real-time in situ chemical sensing, on-demand directional transport, cargo capture and delivery, as well as analyte isolation and separation.

Anatomy of Nanoscale Propulsion

Nature supports multifaceted forms of life. Despite the variety and complexity of these forms, motility remains the epicenter of life. The applicable laws of physics change upon going from macroscales to microscales and nanoscales, which are characterized by low Reynolds number (Re). We discuss motion at low Re in natural and synthetic systems, along with various propulsion mechanisms, including electrophoresis, electrolyte diffusiophoresis, and nonelectrolyte diffusiophoresis. We also describe the newly uncovered phenomena of motility in non-ATP-driven self-powered enzymes and the directional movement of these enzymes in response to substrate gradients. These enzymes can also be immobilized to function as fluid pumps in response to the presence of their substrates. Finally, we review emergent collective behavior arising from interacting motile species, and we discuss the possible biomedical applications of the synthetic nanobots and microbots.

A tale of two forces: simultaneous chemical and acoustic propulsion of bimetallic micromotors

Bimetallic gold–ruthenium microrods are propelled in opposite directions in water by ultrasound and by catalytic decomposition of hydrogen peroxide.

Chemically powered micro- and nanomotors

Chemically powered micro- and nanomotors are small devices that are self-propelled by catalytic reactions in fluids. Taking inspiration from biomotors, scientists are aiming to find the best architecture for self-propulsion, understand the mechanisms of motion, and develop accurate control over the motion. Remotely guided nanomotors can transport cargo to desired targets, drill into biomaterials, sense their environment, mix or pump fluids, and clean polluted water. This Review summarizes the major advances in the growing field of catalytic nanomotors, which started ten years ago.

Stability of liquid films covered by a carpet of self-propelled surfactant particles

We consider a carpet of self-propelled particles at the liquid-gas interface of a liquid film on a solid substrate. The particles exert an excess pressure on the interface and also move along the interface while the swimming direction changes due to rotational diffusion. We study the intricate influence of these self-propelled insoluble surfactants on the stability of the film surface and show that depending on the strength of in-surface rotational diffusion and the absolute value of the in-surface swimming velocity, several characteristic instability modes can occur. In particular, rotational diffusion can either stabilize the film or induce instabilities of different character.

Functionalized carbon dots enable simultaneous bone crack detection and drug deposition

Decorated carbon dots enable simultaneous bone crack viewing and drug deposition.