Why charged molecules move across a temperature gradient: the role of electric fields

Colloid thermophoresis in surfactant solutions: Probing colloid-solvent interactions through microscale experiments

Thermophoresis has emerged as a powerful tool for characterizing and manipulating colloids at the nano- and micro-scales due to its sensitivity to colloid-solvent interactions. The use of surfactants enables the tailoring of surface chemistry on colloidal particles and the tuning of interfacial interactions. However, the microscopic mechanisms underlying thermophoresis in surfactant solutions remain poorly understood due to the complexity of multiscale interaction coupling. To achieve a more fundamental understanding of the roles of surfactants, we investigated the thermophoretic behavior of silica beads in both ionic and nonionic surfactant solutions at various background temperatures. We provide a complete mechanistic picture of the effects of surfactants on interfacial interactions through mode-coupling analysis of both electrophoretic and thermophoretic experiments. Our results demonstrate that silica thermophoresis is predominantly governed by the dissociation of silanol functional groups at silica-water interfaces in nonionic surfactant solutions, while in ionic surfactant solutions, the primary mechanism driving silica thermophoresis is the adsorption of ionic surfactants onto the silica surface.

Thermophoresis-Induced Polymer-Driven Destabilization of Gold Nanoparticles for Optically Directed Assembly at Interfaces

The limitations of conventional template-based methods for the deposition of nanoparticle assemblies into defined patterns on solid substrates call for the development of techniques that do not require templates or lithographic masks. The use of optically-induced thermal gradients to drive the migration of colloids toward or away from a laser spot, known as opto-thermophoresis, has shown promise for the low-power trapping and optical manipulation of a variety of colloidal species. However, the printing of colloids using this technique has so far not been established. Herein, a method for the optically directed printing of noble metal nanoparticles, specifically gold nanospheres is reported. The thermophoresis of the polymer polyvinylpyrrolidone and gold nanospheres toward a laser spot led to the deposition of nanoparticle aggregates, capable of serving as surface-enhanced Raman scattering substrates. The influence of heating laser power and the concentrations of polymer, salt, and surfactant on the nanoparticle deposition rate and structure of the printed pattern are studied, showing that a variety of conditions can permit printing, suggesting facile generalization to different nanoparticle compositions, sizes, and shapes. These findings will greatly benefit future efforts for directed nanoparticle assembly, and drive applications in sensing, photothermal heating, and relevant applications in biomedicine and devices.

Heat flows enrich prebiotic building blocks and enhance their reactivity

The emergence of biopolymer building blocks is a crucial step during the origins of life1-6. However, all known formation pathways rely on rare pure feedstocks and demand successive purification and mixing steps to suppress unwanted side reactions and enable high product yields. Here we show that heat flows through thin, crack-like geo-compartments could have provided a widely available yet selective mechanism that separates more than 50 prebiotically relevant building blocks from complex mixtures of amino acids, nucleobases, nucleotides, polyphosphates and 2-aminoazoles. Using measured thermophoretic properties7,8, we numerically model and experimentally prove the advantageous effect of geological networks of interconnected cracks9,10 that purify the previously mixed compounds, boosting their concentration ratios by up to three orders of magnitude. The importance for prebiotic chemistry is shown by the dimerization of glycine11,12, in which the selective purification of trimetaphosphate (TMP)13,14 increased reaction yields by five orders of magnitude. The observed effect is robust under various crack sizes, pH values, solvents and temperatures. Our results demonstrate how geologically driven non-equilibria could have explored highly parallelized reaction conditions to foster prebiotic chemistry.

A Mode-Coupling Model of Colloid Thermophoresis in Aqueous Systems: Temperature and Size Dependencies of the Soret Coefficient

Thermophoresis allows for the manipulation of colloids in systems containing a temperature gradient. A deep understanding of the phenomena at the molecular level allows for increased control and manipulation strategies. We developed a microscopic model revealing different coupling mechanisms for colloid thermophoresis under local thermodynamic equilibrium conditions. The model has been verified through comparison with a variety of previously published experimental data and shows good agreement across significantly different systems. We found five different temperature-dependent contributions to the Soret coefficient, two from bulk properties and three from interfacial interactions between the fluid medium and the colloid. Our analysis shows that the Soret coefficient for nanosized particles is governed by the competition between the electrostatic and hydration interfacial interactions, while bulk contributions become more pronounced for protein systems. This theory can be used as a guide to design thermophoretic transport, which is relevant for sensing, focusing, and separation at the microscale.

Target-based drug discovery: Applications of fluorescence techniques in high throughput and fragment-based screening

Target-based discovery of first-in-class therapeutics demands an in-depth understanding of the molecular mechanisms underlying human diseases. Precise measurements of cellular and biochemical activities are critical to gain mechanistic knowledge of biomolecules and their altered function in disease conditions. Such measurements enable the development of intervention strategies for preventing or treating diseases by modulation of desired molecular processes. Fluorescence-based techniques are routinely employed for accurate and robust measurements of in-vitro activity of molecular targets and for discovering novel chemical molecules that modulate the activity of molecular targets. In the current review, the authors focus on the applications of fluorescence-based high throughput screening (HTS) and fragment-based ligand discovery (FBLD) techniques such as fluorescence polarization (FP), Förster resonance energy transfer (FRET), fluorescence thermal shift assay (FTSA) and microscale thermophoresis (MST) for the discovery of chemical probe to exploring target's role in disease biology and ultimately, serve as a foundation for drug discovery. Some recent advancements in these techniques for compound library screening against important classes of drug targets, such as G-protein-coupled receptors (GPCRs) and GTPases, as well as phosphorylation- and acetylation-mediated protein-protein interactions, are discussed. Overall, this review presents a landscape of how these techniques paved the way for the discovery of small-molecule modulators and biologics against these targets for therapeutic benefits.

Probe-free optical chromatin deformation and measurement of differential mechanical properties in the nucleus

The nucleus is highly organized to facilitate coordinated gene transcription. Measuring the rheological properties of the nucleus and its sub-compartments will be crucial to understand the principles underlying nuclear organization. Here, we show that strongly localized temperature gradients (approaching 1°C/µm) can lead to substantial intra-nuclear chromatin displacements (>1 µm), while nuclear area and lamina shape remain unaffected. Using particle image velocimetry (PIV), intra-nuclear displacement fields can be calculated and converted into spatio-temporally resolved maps of various strain components. Using this approach, we show that chromatin displacements are highly reversible, indicating that elastic contributions are dominant in maintaining nuclear organization on the time scale of seconds. In genetically inverted nuclei, centrally compacted heterochromatin displays high resistance to deformation, giving a rigid, solid-like appearance. Correlating spatially resolved strain maps with fluorescent reporters in conventional interphase nuclei reveals that various nuclear compartments possess distinct mechanical identities. Surprisingly, both densely and loosely packed chromatin showed high resistance to deformation, compared to medium dense chromatin. Equally, nucleoli display particularly high resistance and strong local anchoring to heterochromatin. Our results establish how localized temperature gradients can be used to drive nuclear compartments out of mechanical equilibrium to obtain spatial maps of their material responses.

The Soret coefficient of human low-density lipoprotein in solution: a thermophilic behavior

Thermodiffusion, or Soret effect, is the physical phenomenon of matter gradients originated by the migration of chemical species induced by thermal gradients. Thermodiffusion has been widely applied in the study of colloidal suspensions. In this study, we investigate the termodiffusion behavior of low-density lipoprotein (LDL) particles, by the Soret coefficient measurement. It is a new approach to studies of plasma lipoproteins. The experimental work was based on thermal- and Soret-lens effects. These effects were induced by laser irradiation of the samples, at two different time scales, in a Z-scan setup. LDL samples were analyzed under physiological conditions, notedly, ionic strength and pH, and at different temperatures. Temperature dependence of Soret coefficient showed a slight decrease in the absolute value of this coefficient, as a function of temperature increasing. However, its sign does not change at the temperatures investigated (15, 22.5 and 37.5 °C). The results show that LDL particles exhibit thermophilic behavior. The origin of this thermophilic behavior is not yet completely understood. We discuss some aspects that can be related with the Soret effect in LDL samples.

3D printing of inorganic nanomaterials by photochemically bonding colloidal nanocrystals

3D printing of inorganic materials with nanoscale resolution offers a different materials processing pathway to explore devices with emergent functionalities. However, existing technologies typically involve photocurable resins that reduce material purity and degrade properties. We develop a general strategy for laser direct printing of inorganic nanomaterials, as exemplified by more than 10 semiconductors, metal oxides, metals, and their mixtures. Colloidal nanocrystals are used as building blocks and photochemically bonded through their native ligands. Without resins, this bonding process produces arbitrary three-dimensional (3D) structures with a large inorganic mass fraction (~90%) and high mechanical strength. The printed materials preserve the intrinsic properties of constituent nanocrystals and create structure-dictated functionalities, such as the broadband chiroptical responses with an anisotropic factor of ~0.24 for semiconducting cadmium chalcogenide nanohelical arrays.

Tunable Self-Thermophoretic Nanomotors with Polymeric Coating

Thermophoretic micro/nanomotors (MNMs) generate self-propulsion without a chemical reaction. Intrinsically, this promises excellent biocompatibility and is thus suitable for biomedical applications. However, their propulsion efficiency is severely limited due to the poor understanding of the thermophoretic process, which dominates the conversion from thermal energy into mechanical movement. We here developed a series of self-thermophoresis light-powered MNMs with variable surface coatings and discovered obvious self-thermophoresis propulsion enhancement of the polymeric layer. An intrinsically negative self-thermophoretic movement is also observed for the first time in the MNM system. We propose that enthalpic contributions from polymer-solvent interactions should play a fundamental role in the self-thermophoretic MNMs. Quantitative microcalorimetry and molecular dynamics simulations are performed to support our hypothesis. The polymer solvation enthalpy and coating thickness influences on self-thermophoresis are investigated, further highlighting the essential enthalpy contributions to thermophoresis. Our work indicates that surface grafting would be important in designing high-efficiency thermally driven nanorobotic systems for biomedical applications.

Multimodal Optothermal Manipulations along Various Surfaces

Optical tweezers have provided tremendous opportunities for fundamental studies and applications in the life sciences, chemistry, and physics by offering contact-free manipulation of small objects. However, it requires sophisticated real-time imaging and feedback systems for conventional optical tweezers to achieve controlled motion of micro/nanoparticles along textured surfaces, which are required for such applications as high-resolution near-field characterizations of cell membranes with nanoparticles as probes. In addition, most optical tweezers systems are limited to single manipulation modes, restricting their broader applications. Herein, we develop an optothermal platform that enables the multimodal manipulation of micro/nanoparticles along various surfaces. Specifically, we achieve the manipulation of micro/nanoparticles through the synergy between the optical and thermal forces, which arise due to the temperature gradient self-generated by the particles absorbing the light. With a simple control of the laser beam, we achieve five switchable working modes [i.e., tweezing, rotating, rolling (toward), rolling (away), and shooting] for the versatile manipulation of both synthesized particles and biological cells along various substrates. More interestingly, we realize the manipulation of micro/nanoparticles on rough surfaces of live worms and their embryos for localized control of biological functions. By enabling the three-dimensional control of micro/nano-objects along various surfaces, including topologically uneven biological tissues, our multimodal optothermal platform will become a powerful tool in life sciences, nanotechnology, and colloidal sciences.

Thermophoretic motion of a charged single colloidal particle

We calculate the thermophoretic drift of a charged single colloidal particle with hydrodynamically slipping surface immersed in an electrolyte solution in response to a small temperature gradient. Here we rely on a linearized hydrodynamic approach for the fluid flow and the motion of the electrolyte ions while keeping the full nonlinearity of the Poisson-Boltzmann equation of the unperturbed system to account for possible large surface charging. The partial differential equations are transformed into a coupled set of ordinary differential equations in linear response. Numerical solutions are elaborated for parameter regimes of small and large Debye shielding and different hydrodynamic boundary conditions encoded in a varying slip length. Our results are in good agreement with predictions from recent theoretical work and successfully describe experimental observations on thermophoresis of DNA. We also compare our numerical results with experimental data on polystyrene beads.

Optothermal rotation of micro-/nano-objects

Due to its contactless and fuel-free operation, optical rotation of micro-/nano-objects provides tremendous opportunities for cellular biology, three-dimensional (3D) imaging, and micro/nanorobotics. However, complex optics, extremely high operational power, and the applicability to limited objects restrict the broader use of optical rotation techniques. This Feature Article focuses on a rapidly emerging class of optical rotation techniques, termed optothermal rotation. Based on light-mediated thermal phenomena, optothermal rotation techniques overcome the bottlenecks of conventional optical rotation by enabling versatile rotary control of arbitrary objects with simpler optics using lower powers. We start with the fundamental thermal phenomena and concepts: thermophoresis, thermoelectricity, thermo-electrokinetics, thermo-osmosis, thermal convection, thermo-capillarity, and photophoresis. Then, we highlight various optothermal rotation techniques, categorizing them based on their rotation modes (i.e., in-plane and out-of-plane rotation) and the thermal phenomena involved. Next, we explore the potential applications of these optothermal manipulation techniques in areas such as single-cell mechanics, 3D bio-imaging, and micro/nanomotors. We conclude the Feature Article with our insights on the operating guidelines, existing challenges, and future directions of optothermal rotation.

A heated rock crack captures and polymerizes primordial DNA and RNA

Life is based on informational polymers such as DNA or RNA. For their polymerization, high concentrations of complex monomer building blocks are required. Therefore, the dilution by diffusion poses a major problem before early life could establish a non-equilibrium of compartmentalization. Here, we explored a natural non-equilibrium habitat to polymerize RNA and DNA. A heat flux across thin rock cracks is shown to accumulate and maintain nucleotides. This boosts the polymerization to RNA and DNA inside the crack. Moreover, the polymers remain localized, aiding both the creation of longer polymers and fostering downstream evolutionary steps. In a closed system, we found single nucleotides concentrate 10⁴-fold at the bottom of the crack compared to the top after 24 hours. We detected enhanced polymerization for 2 different activation chemistries: aminoimidazole-activated DNA nucleotides and 2',3'-cyclic RNA nucleotides. The copolymerization of 2',3'-cGMP and 2',3'-cCMP in the thermal pore showed an increased heterogeneity in sequence composition compared to isothermal drying. Finite element models unravelled the combined polymerization and accumulation kinetics and indicated that the escape of the nucleotides from such a crack is negligible over a time span of years. The thermal non-equilibrium habitat establishes a cell-like compartment that actively accumulates nucleotides for polymerization and traps the resulting oligomers. We argue that the setting creates a pre-cellular non-equilibrium steady state for the first steps of molecular evolution.

Plasmonic-Thermoelectric Nanotweezers for Immersive SERS Mapping

Surface-enhanced Raman spectroscopy (SERS) technology usually uses metallic nanoparticles to enhance Raman scattering signals, thereby significantly adding to molecule-level recognition and detection. However, realization of nanometer-scaled SERS imaging in liquid environments is extremely difficult due to the requirements of both precise scanning of single metallic nanoparticle and high enhancement field and thus has never been achieved before. To overcome this obstacle, we demonstrate an immersive nanometer-scaled SERS mapping technology, based on dynamic scanning of a single metallic nanoparticle with a plasmonic-thermoelectric nanotweezers system. The technology offers greater stability in the plasmonic trapping of gold nanoparticles at relative low power, as well as generating higher electric fields in the gap region. Through its dynamics, two-dimensional nanometer-scaled SERS imaging is achieved successfully. In regard to in liquid environments, this technology provides a mapping method for label-free imaging of ultrathin materials, structures, and biological samples.

Complementary Experimental Methods to Obtain Thermodynamic Parameters of Protein Ligand Systems

In recent years, thermophoresis has emerged as a promising tool for quantifying biomolecular interactions. The underlying microscopic physical effect is still not understood, but often attributed to changes in the hydration layer once the binding occurs. To gain deeper insight, we investigate whether non-equilibrium coefficients can be related to equilibrium properties. Therefore, we compare thermophoretic data measured by thermal diffusion forced Rayleigh scattering (TDFRS) (which is a non-equilibrium process) with thermodynamic data obtained by isothermal titration calorimetry (ITC) (which is an equilibrium process). As a reference system, we studied the chelation reaction between ethylenediaminetetraacetic acid (EDTA) and calcium chloride (CaCl2) to relate the thermophoretic behavior quantified by the Soret coefficient ST to the Gibb's free energy ΔG determined in the ITC experiment using an expression proposed by Eastman. Finally, we have studied the binding of the protein Bovine Carbonic Anhydrase I (BCA I) to two different benzenesulfonamide derivatives: 4-fluorobenzenesulfonamide (4FBS) and pentafluorobenzenesulfonamide (PFBS). For all three systems, we find that the Gibb's free energies calculated from ST agree with ΔG from the ITC experiment. In addition, we also investigate the influence of fluorescent labeling, which allows measurements in a thermophoretic microfluidic cell. Re-examination of the fluorescently labeled system using ITC showed a strong influence of the dye on the binding behavior.

Heat-Mediated Optical Manipulation

Progress in optical manipulation has stimulated remarkable advances in a wide range of fields, including materials science, robotics, medical engineering, and nanotechnology. This Review focuses on an emerging class of optical manipulation techniques, termed heat-mediated optical manipulation. In comparison to conventional optical tweezers that rely on a tightly focused laser beam to trap objects, heat-mediated optical manipulation techniques exploit tailorable optothermo-matter interactions and rich mass transport dynamics to enable versatile control of matter of various compositions, shapes, and sizes. In addition to conventional tweezing, more distinct manipulation modes, including optothermal pulling, nudging, rotating, swimming, oscillating, and walking, have been demonstrated to enhance the functionalities using simple and low-power optics. We start with an introduction to basic physics involved in heat-mediated optical manipulation, highlighting major working mechanisms underpinning a variety of manipulation techniques. Next, we categorize the heat-mediated optical manipulation techniques based on different working mechanisms and discuss working modes, capabilities, and applications for each technique. We conclude this Review with our outlook on current challenges and future opportunities in this rapidly evolving field of heat-mediated optical manipulation.

The Acid-Base/Deprotonation Equilibrium Can Be Studied with a MicroScale Thermophoresis (MST)

MicroScale thermophoresis (MST) is a rapidly developing bioanalytical technique used routinely for the examination of ligand-target affinity. It has never been used so far for the analysis of acid-base dissociation and the determination of pK_a constant. This work is the-proof-of-concept of this new idea. It demonstrates that the pK_a values obtained from the thermophoretic data are consistent with the reference methods. As a result, the analytical potential and utility of the MST technology can become even greater, especially if the new detection system of thermophoretic movement will be developed in the future. Even now, taking into account the necessity to use fluorescence, the proposed method may be useful in many respects.

Single Molecule Surface Enhanced Raman Scattering in a Single Gold Nanoparticle-Driven Thermoplasmonic Tweezer

Surface enhanced Raman scattering (SERS) is optically sensitive and chemically specific to detect single-molecule spectroscopic signatures. Facilitating this capability in optically trapped nanoparticles at low laser power remains a significant challenge. In this letter, we show single molecule SERS signatures in reversible assemblies of trapped plasmonic nanoparticles using a single laser excitation (633 nm). Importantly, this trap is facilitated by the thermoplasmonic field of a single gold nanoparticle dropcasted on a glass surface. We employ the bianalyte SERS technique to ascertain the single molecule statistical signatures and identify the critical parameters of the thermoplasmonic tweezer that provide this sensitivity. Furthermore, we show the utility of this low power (≈ 0.1 mW/μm²) tweezer platform to trap a single gold nanoparticle and transport assembly of nanoparticles. Given that our configuration is based on a dropcasted gold nanoparticle, we envisage its utility to create reconfigurable plasmonic metafluids in physiological and catalytic environments and to be potentially adapted as an in vivo plasmonic tweezer.

Optothermal pulling, trapping, and assembly of colloids using nanowire plasmons

Optical excitation of colloids can be harnessed to realize soft matter systems that are out of equilibrium. In this paper, we present our experimental studies on the dynamics of silica colloids in the vicinity of a silver nanowire propagating surface plasmon polaritons (SPPs). Due to the optothermal interaction, the colloids are directionally pulled towards the excitation point of the nanowire. Having reached this point, they are spatio-temporally trapped around the excitation location. By increasing the concentration of colloids in the system, we observe multi-particle assembly around the nanowire. This process is thermophoretically driven and assisted by the SPPs. Furthermore, we find such an assembly to be sensitive to the excitation polarization at the input of the nanowire. Numerically-simulated temperature distribution around an illuminated nanowire corroborates sensitivity to the excitation polarization. Our study will find relevance in exploration of SPP-assisted optothermal pulling, trapping and assembly of colloids, and can serve as a test-bed of plasmon-driven active matter.

Plasmon-Directed On-Wire Growth of Branched Silver Nanowires with Chiroptic Activity

Silver nanowires (Ag NWs) present prominent waveguiding properties of subwavelength light due to their nanoconfinement with propagating surface plasmons, which is of great importance for on-chip integration of nanophotonic devices and optical computation. Such propagating plasmons also exert plasmonic forces, which can be utilized to manipulate nanoparticles (NPs) beyond the diffraction limit. However, such controllability is spatially limited to the near fields, whereas a large portion of uncontrolled particles are randomly deposited on the chips, which could be detrimental to the integrated optical devices. Herein we shine continuous wave laser at one end of the Ag NW immersed in AgNO₃ solution to launch the propagating surface plasmons. The laser irradiation also induces the photoreduction of Ag⁺ ions to locally generate tiny Ag NPs, which evolve into large Ag flake branches closer to the other end of the Ag NW. Such a peculiar growth is due to the synergistic effect of plasmonic forces and the thermophoretic/thermo-osmosis forces induced by temperature gradient. These branched Ag NWs with sharp angles are intrinsically chiral, which can be partially controlled by changing the irradiation location, forming plasmonic chiral enantiomers. The circular differential scattering (CDS) response of these branched Ag NWs can be as large as 40%, which can be used for chiral enantiomer sensing with spectral dissymmetric factor up to 4 nm induced by phenylalanine. This plasmon-directed on-wire growth not only offers a facile approach for generating plasmonic chiral nanostructures with remote controllability, but also provides significant insights on the synergistic effect of plasmonic forces and thermal-induced forces, which has great implications for self-assembly and integration of on-chip optics.

Heat flows in rock cracks naturally optimize salt compositions for ribozymes

Catalytic nucleic acids, such as ribozymes, are central to a variety of origin-of-life scenarios. Typically, they require elevated magnesium concentrations for folding and activity, but their function can be inhibited by high concentrations of monovalent salts. Here we show that geologically plausible high-sodium, low-magnesium solutions derived from leaching basalt (rock and remelted glass) inhibit ribozyme catalysis, but that this activity can be rescued by selective magnesium up-concentration by heat flow across rock fissures. In contrast to up-concentration by dehydration or freezing, this system is so far from equilibrium that it can actively alter the Mg:Na salt ratio to an extent that enables key ribozyme activities, such as self-replication and RNA extension, in otherwise challenging solution conditions. The principle demonstrated here is applicable to a broad range of salt concentrations and compositions, and, as such, highly relevant to various origin-of-life scenarios.

Analytical analysis of anisotropic thermophoresis of a charged spheroidal colloid in aqueous media for extremely thin EDL cases

Thermophoresis of charged spheroids has been widely applied in biology and medical science. In this work, we report an analysis of the anisotropic thermophoresis of diluted spheroidal colloids in aqueous media for extremely thin EDL cases. Under the boundary layer approximation, we formulate the thermophoretic velocity, the thermophoretic force, and the thermodiffusion coefficient of a randomly dispersed spheroid. The parametric studies show that under the aforementioned conditions, the thermophoresis is anisotropic and its thermodiffusion coefficient should be considered as a vector, D_T . The thermodiffusion coefficient values and directions of D_T are strongly related to the aspect ratio and the angle θ between the externally applied temperature gradient and the particle's axis of revolution: The increasing aspect ratio enlarges the thermodiffusion coefficient value D_T of prolate (oblate) spheroids to a constant value when θ < 60° (θ > 45°), and it reduces D_T of prolate (oblate) spheroids to a constant value when θ > 60° (θ < 45°). The thermodiffusion coefficient direction of both prolate and oblate spheroids deviates slightly from -∇T_∞ for a small aspect ratio, and such deviation becomes serious for a large aspect ratio.

Optothermally Assembled Nanostructures

Nanofabrication is one of the core techniques in rapidly evolving nanoscience and nanotechnology. Conventional top-down nanofabrication approaches such as photolithography and electron beam lithography can produce high-resolution nanostructures in a robust way. However, these methods usually involve multistep processing and sophisticated instruments and have difficulty in fabricating three-dimensional complex structures of multiple materials and reconfigurability. Recently, bottom-up techniques have emerged as promising alternatives to fabricating nanostructures via the assembly of individual building blocks. In comparison to top-down lithographical methods, bottom-up assembly features the on-demand construction of superstructures with controllable configurations at single-particle resolution. The size, shape, and composition of chemically synthesized building blocks can also be precisely tailored down to the atomic scale to fabricate multimaterial architectural structures of high flexibility. Many techniques have been reported to assemble individual nanoparticles into complex structures, such as self-assembly, DNA nanotechnology, patchy colloids, and optically controlled assembly. Among them, the optically controlled assembly has the advantages of remote control, site-specific manipulation of single components, applicability to a wide range of building blocks, and arbitrary configurations of the assembled structures. In this Account, we provide a concise review of our contributions to the optical assembly of architectural materials and structures using discrete nanoparticles as the building blocks. By exploiting entropically favorable optothermal conversion and controlling optothermal-matter interactions, we have developed optothermal assembly techniques to manipulate and assemble individual nanoparticles. Our techniques can be operated both in solution and on solid substrates. First, we discuss the opto-thermoelectric assembly (OTA) of colloidal particles into superstructures by coordinating thermophoresis and interparticle depletion bonding in the solution. Localized laser heating generates a temperature gradient field, where the thermal migration of ions creates a thermoelectric field to trap charged particles. The depletion of ion species at the gap between closely positioned particles under optical heating provides strong interparticle bonding to stabilize colloidal superstructures with precisely controlled configurations and interparticle distances. Second, we discuss bubble-pen lithography (BPL) for the rapid printing of nanoparticles using an optothermal microbubble. The long-range convection flow induced by the optothermal bubble drags the colloidal particles to the substrate with a high velocity. BPL represents a general method for printing all kinds of building blocks into desired patterns in a high-resolution and high-throughput way. Third, we present the optothermally-gated photon nudging (OPN) technique, which manipulates and assembles particles on a solid substrate. Our solid-phase optical control of particles synergizes the modulation of particle-substrate interactions by optothermal effects and photon nudging of the particles by optical scattering forces. Operated on the solid surfaces without liquid media, OPN can avoid the undesired Brownian motion of nanoparticles in solutions to manipulate individual particles with high accuracy. In addition, the assembled structures can be actively reassembled into new configurations for the fabrication of tunable functional devices. Next, we discuss applications of the optothermally assembled nanostructures in surface-enhanced Raman spectroscopy, color displays, biomolecule sensing, and fundamental research. Finally, we conclude this Account with our perspectives on the challenges, opportunities, and future directions in the development and application of optothermal assembly.

Non-associative phase separation in an evaporating droplet as a model for prebiotic compartmentalization

The synthetic pathways of life’s building blocks are envisaged to be through a series of complex prebiotic reactions and processes. However, the strategy to compartmentalize and concentrate biopolymers under prebiotic conditions remains elusive. Liquid-liquid phase separation is a mechanism by which membraneless organelles form inside cells, and has been hypothesized as a potential mechanism for prebiotic compartmentalization. Associative phase separation of oppositely charged species has been shown to partition RNA, but the strongly negative charge exhibited by RNA suggests that RNA-polycation interactions could inhibit RNA folding and its functioning inside the coacervates. Here, we present a prebiotically plausible pathway for non-associative phase separation within an evaporating all-aqueous sessile droplet. We quantitatively investigate the kinetic pathway of phase separation triggered by the non-uniform evaporation rate, together with the Marangoni flow-driven hydrodynamics inside the sessile droplet. With the ability to undergo liquid-liquid phase separation, the drying droplets provide a robust mechanism for formation of prebiotic membraneless compartments, as demonstrated by localization and storage of nucleic acids, in vitro transcription, as well as a three-fold enhancement of ribozyme activity. The compartmentalization mechanism illustrated in this model system is feasible on wet organophilic silica-rich surfaces during early molecular evolution.

Prebiotic compartmentalization could prove essential for the evolution of life. Guo et al. show that liquid-liquid separation in an aqueous two-phase system driven by evaporation may already suffice to facilitate chemical processes required for the RNA world hypothesis.

Molecular Dynamics Approach to Calculate the Thermodiffusion (Soret and Seebeck) Coefficients of Salts in Aqueous Solutions

An approach to investigate the physical parameters related to ion thermodiffusion in aqueous solutions is proposed herein by calculating the equilibrium hydration free energy and the self-diffusion coefficient as a function of temperature, ranging from 293 to 353 K, using molecular dynamics simulations of infinitely diluted ions in aqueous solutions. Several ion force field parameters are used in the simulations, and new parameters are proposed for some ions to better describe their hydration free energy. Such a theoretical framework enables the calculation of some single-ion properties, such as heat of transport, Soret coefficient, and mass current density, as well as properties of salts, such as effective mass and thermal diffusion, Soret and Seebeck, coefficients. These calculated properties are compared with experimental data available from optical measurements and showed good agreement revealing an excellent theoretical predictability of salt thermodiffusion properties. Differences in single-ion Soret and self-diffusion coefficients of anions and cations give rise to a thermoelectric field, which affects the system response that is quantified by the Seebeck coefficient. The fast and slow Seebeck coefficients are calculated and discussed, resulting in values with mV/K order of magnitude, as observed in experiments involving several salts, such as K⁺Cl^-, Na⁺Cl^-, H⁺Cl^-, Na⁺OH^-, TMA⁺OH^-, and TBA⁺OH^-. The present approach can be adopted for any ion or charged particle dispersed in water with the aim of predicting the thermoelectric field induced through the fluid. It has potential applications in designing electrolytes for ionic thermoelectric devices in order to harvest energy and thermoelectricity in biological nanofluids.

On the time-dependent electrolyte Seebeck effect

Single-ion Soret coefficients α_i characterize the tendency of ions in an electrolyte solution to move in a thermal gradient. When these coefficients differ between cations and anions, an electric field can be generated. For this so-called electrolyte Seebeck effect to occur, different thermodiffusive fluxes need to be blocked by boundaries-electrodes, for example. Local charge neutrality is then broken in the Debye-length vicinity of the electrodes. Confusingly, many authors point to these regions as the source of the thermoelectric field yet ignore them in derivations of the time-dependent Seebeck coefficient S(t), giving a false impression that the electrolyte Seebeck effect is purely a bulk phenomenon. Without enforcing local electroneutrality, we derive S(t) generated by a binary electrolyte with arbitrary ionic valencies subject to a time-dependent thermal gradient. Next, we experimentally measure S(t) for five acids, bases, and salts near titanium electrodes. For the steady state, we find S ≈ 2 mV K^-1 for many electrolytes, roughly one order of magnitude larger than the predictions based on literature α_i. We fit our expression for S(t) to the experimental data, treating the α_i as fit parameters, and also find larger-than-literature values, accordingly.

Opto-Thermophoretic Manipulation

The optical manipulation of tiny objects is significant to understand and to explore the unknown in the microworld, which has found many applications in materials science and life science. Physically speaking, these technologies arise from direct or indirect optomechanical coupling to convert incident optical energy to mechanical energy of target objects, while their efficiency and functionalities are determined by the coupling behavior. Traditional optical tweezers stem from direct light-to-matter momentum transfer, and the generation of an optical gradient force requires high optical power and rigorous optics. As a comparison, the opto-thermophoretic manipulation techniques proposed recently originate from high-efficiency opto-thermomechanical coupling and feature low optical power. Through rational design of the light-generated temperature gradient and exploring the mechanical response of diverse targets to the temperature gradient, a variety of opto-thermophoretic techniques were developed, which exhibit broad applicability to a wide range of target objects from colloid materials to biological cells to biomolecules. In this review, we will discuss the underlying mechanism of thermophoresis in different liquid environments, the cutting-edge technological innovation, and their applications in colloidal science and life science. We also provide a brief outlook on the existing challenges and anticipate their future development.

Numerical Analysis of Thermophoresis of a Charged Spheroidal Colloid in Aqueous Media

Thermophoresis of charged colloids in aqueous media has wide applications in biology. Most existing studies of thermophoresis focused on spherical particles, but biological compounds are usually non-spherical. The present paper reports a numerical analysis of the thermophoresis of a charged spheroidal colloid in aqueous media. The model accounts for the strongly coupled temperature field, the flow field, the electric potential field, and the ion concentration field. Numerical simulations revealed that prolate spheroids move faster than spherical particles, and oblate spheroids move slower than spherical particles. For the arbitrary electric double layer (EDL) thickness, the thermodiffusion coefficient of prolate (oblate) spheroids increases (decreases) with the increasing particle’s dimension ratio between the major and minor semiaxes. For the extremely thin EDL case, the hydrodynamic effect is significant, and the thermodiffusion coefficient for prolate (oblate) spheroids converges to a fixed value with the increasing particle’s dimension ratio. For the extremely thick EDL case, the particle curvature’s effect also becomes important, and the increasing (decreasing) rate of thermodiffusion coefficient for prolate (oblate) spheroids is reduced slightly.

Liquid Optothermoelectrics: Fundamentals and Applications

Liquid thermoelectricity describes the redistribution of ions in an electrolytic solution under the influence of temperature gradients, which leads to the formation of electric fields. The thermoelectric field is effective in driving the thermophoretic migration of charged colloidal particles for versatile manipulation. However, traditional macroscopic thermoelectric fields are not suitable for particle manipulations at high spatial resolution. Inspired by optical tweezers and relevant optical manipulation techniques, we employ laser interaction with light-absorbing nanostructures to achieve subtle heat management on the micro- and nanoscales. The resulting thermoelectric fields are exploited to develop new optical technologies, leading to a research field known as liquid optothermoelectrics. This Invited Feature Article highlights our recent works on advancing fundamentals, technologies, and applications of optothermoelectrics in colloidal solutions. The effects of light irradiation, substrates, electrolytes, and particles on the optothermoelectric manipulations of colloidal particles along with their theoretical limitations are discussed in detail. Our optothermoelectric technologies with the versatile capabilities of trapping, manipulating, and pulling colloidal particles at low optical power are finding applications in microswimmers and nanoscience. With its intricate interfacial processes and tremendous technological promise, optothermoelectrics in colloidal solutions will remain relevant for the foreseeable future.

Thermodiffusion: The physico-chemical mechanics view

Thermodiffusion in liquids (the Soret effect) has several unusual properties. In particular, transport can occur with or against a temperature gradient depending on the case. Numerous empirical correlations have been proposed with mixed success or range of applicability. Here, we show that physicochemical mechanics, derived from the Smoluchowski equation as a description of diffusive transport phenomena, is in accord with the experimental and simulated thermodiffusion data from colloidal beads and biomacromolecules to ionic solutions and ultracold fluid mixtures. It yields a simple formula for the Soret coefficient S_T based on the reference molar entropy including non-ideality. Hydrodynamic and local non-equilibrium effects are discussed but not included as these are apparently not a major contribution for the wide range of solutes under the near-equilibrium experimental conditions considered here.

Atomistic modeling and rational design of optothermal tweezers for targeted applications

Optical manipulation of micro/nanoscale objects is of importance in life sciences, colloidal science, and nanotechnology. Optothermal tweezers exhibit superior manipulation capability at low optical intensity. However, our implicit understanding of the working mechanism has limited the further applications and innovations of optothermal tweezers. Herein, we present an atomistic view of opto-thermo-electro-mechanic coupling in optothermal tweezers, which enables us to rationally design the tweezers for optimum performance in targeted applications. Specifically, we have revealed that the non-uniform temperature distribution induces water polarization and charge separation, which creates the thermoelectric field dominating the optothermal trapping. We further design experiments to systematically verify our atomistic simulations. Guided by our new model, we develop new types of optothermal tweezers of high performance using low-concentrated electrolytes. Moreover, we demonstrate the use of new tweezers in opto-thermophoretic separation of colloidal particles of the same size based on the difference in their surface charge, which has been challenging for conventional optical tweezers. With the atomistic understanding that enables the performance optimization and function expansion, optothermal tweezers will further their impacts.

Anomalous Thermodiffusion of Electrons in Graphene

We reveal a dramatic departure of electron thermodiffusion in solids relative to the commonly accepted picture of the ideal free-electron gas model. In particular, we show that the interaction with the lattice and impurities, combined with a strong material dependence of the electron dispersion relation, leads to counterintuitive diffusion behavior, which we identify by comparing a two-dimensional electron gas (2DEG) and single-layer graphene. When subject to a temperature gradient ∇T, thermodiffusion of massless Dirac fermions in graphene exhibits an anomalous behavior with electrons moving along ∇T and accumulating in hot regions, in contrast to normal electron diffusion in a 2DEG with parabolic dispersion, where net motion against ∇T is observed, accompanied by electron depletion in hot regions. These findings bear fundamental importance for the understanding of the spatial electron dynamics in emerging materials, establishing close relations with other branches of physics dealing with electron systems under nonuniform temperature conditions.

Opto-Thermoelectric Tweezers: Principles and Applications

Opto-thermoelectric tweezers (OTET), which exploit the thermophoretic matter migration under a light-directed temperature field, present a new platform for manipulating colloidal particles with a wide range of materials, sizes, and shapes. Taking advantage of the entropically favorable photon-phonon conversion in light-absorbing materials and spatial separation of dissolved ions in electrolytes, OTET can manipulate the particles in a low-power and high-resolution fashion. In this mini-review, we summarize the concept, working principles, and applications of OTET. Recent developments of OTET in three-dimensional manipulation and parallel trapping of particles are discussed thoroughly. We further present their initial applications in particle filtration and biological studies. With their future development, OTET are expected to find a wide range of applications in life sciences, nanomedicine, colloidal sciences, photonics, and materials sciences.

Thermophoretic Micron-Scale Devices: Practical Approach and Review

In recent years, there has been increasing interest in the development of micron-scale devices utilizing thermal gradients to manipulate molecules and colloids, and to measure their thermophoretic properties quantitatively. Various devices have been realized, such as on-chip implements, micro-thermogravitational columns and other micron-scale thermophoretic cells. The advantage of the miniaturized devices lies in the reduced sample volume. Often, a direct observation of particles using various microscopic techniques is possible. On the other hand, the small dimensions lead to some technical problems, such as a precise temperature measurement on small length scale with high spatial resolution. In this review, we will focus on the "state of the art" thermophoretic micron-scale devices, covering various aspects such as generating temperature gradients, temperature measurement, and the analysis of the current micron-scale devices. We want to give researchers an orientation for their development of thermophoretic micron-scale devices for biological, chemical, analytical, and medical applications.

Thermal Habitat for RNA Amplification and Accumulation

The RNA world scenario posits replication by RNA polymerases. On early Earth, a geophysical setting is required to separate hybridized strands after their replication and to localize them against diffusion. We present a pointed heat source that drives exponential, RNA-catalyzed amplification of short RNA with high efficiency in a confined chamber. While shorter strands were periodically melted by laminar convection, the temperature gradient caused aggregated polymerase molecules to accumulate, protecting them from degradation in hot regions of the chamber. These findings demonstrate a size-selective pathway for autonomous RNA-based replication in natural nonequilibrium conditions.

Opto-thermoelectric speckle tweezers

Opto-thermoelectric tweezers present a new paradigm for optical trapping and manipulation of particles using low-power and simple optics. New real-life applications of opto-thermoelectric tweezers in areas such as biophysics, microfluidics, and nanomanufacturing will require them to have large-scale and high-throughput manipulation capabilities in complex environments. Here, we present opto-thermoelectric speckle tweezers, which use speckle field consisting of many randomly distributed thermal hotspots that arise from an optical speckle pattern to trap multiple particles over large areas. By further integrating the speckle tweezers with a microfluidic system, we experimentally demonstrate their application for size-based nanoparticle filtration. With their low-power operation, simplicity, and versatility, opto-thermoelectric speckle tweezers will broaden the applications of optical manipulation techniques.

Opto-thermoelectric pulling of light-absorbing particles

Optomechanics arises from the photon momentum and its exchange with low-dimensional objects. It is well known that optical radiation exerts pressure on objects, pushing them along the light path. However, optical pulling of an object against the light path is still a counter-intuitive phenomenon. Herein, we present a general concept of optical pulling-opto-thermoelectric pulling (OTEP)-where the optical heating of a light-absorbing particle using a simple plane wave can pull the particle itself against the light path. This irradiation orientation-directed pulling force imparts self-restoring behaviour to the particles, and three-dimensional (3D) trapping of single particles is achieved at an extremely low optical intensity of 10-2 mW μm-2. Moreover, the OTEP force can overcome the short trapping range of conventional optical tweezers and optically drive the particle flow up to a macroscopic distance. The concept of self-induced opto-thermomechanical coupling is paving the way towards freeform optofluidic technology and lab-on-a-chip devices.

Thermophoresis of colloids in nematic liquid crystal

Thermophoresis, or the directional motion of colloidal particles in liquids driven by a temperature gradient, is of both fundamental interest and practical use. In this work we explore the thermophoresis of colloids suspended in nematic liquid crystals (LCs). We observe that the motion of these colloids is fundamentally different from that in isotropic systems as a result of elastic distortions in the director fields caused by the colloidal inclusions. In the case of a sufficiently large local temperature and gradient, the elastic energy drives negative thermophoresis of immersed particles, which has a strongly nonlinear dependence on temperature. We develop a theory that incorporates elastic energy minimization into the traditional thermophoretic formulation and demonstrated a good agreement with experimental observations. We also examine the temperature dependence of the effective viscosity of the colloids and highlight the large magnitude of the Soret coefficient (|ST| > 5000), which results from the inherent enhancement in thermophoresis due to elastophoretic considerations and suppression of Brownian diffusion in LC media.

Thermophoretic tweezers for single nanoparticle manipulation

We present the trapping and manipulation of a single nano-object in an aqueous medium by optically induced temporally varying temperature gradients. By real-time object tracking and control of the position of the heating laser focus, we can precisely employ thermophoretic drift to oppose the random diffusive motion. As a result, a nano-object is confined in a micrometer-sized trap. Numerical modeling gives a quantitative prediction of the effect. Traps can be dynamically created and relocated, which we demonstrate by the controlled independent manipulation of two nanoparticles.

Thermophoresis of biological and biocompatible compounds in aqueous solution

With rising popularity of microscale thermophoresis for the characterisation of protein-ligand binding reactions and possible applications in microfluidic devices, there is a growing interest in considering thermodiffusion in the context of life sciences. But although the understanding of thermodiffusion in non-polar mixtures has grown rapidly in recent years, predictions for associated mixtures like aqueous solutions remain challenging. This review aims to give an overview of the literature on thermodiffusion in aqueous systems, show the difficulties in theoretical description that arise from the non-ideal behaviour of water-mixtures, and highlight the relevance of thermodiffusion in a biological context. We find that the thermodiffusion in aqueous systems is dominated by contributions from heat of transfer, hydrogen bond interactions and charge effects. However, the separation of these effects is often difficult, especially in case of biological systems where a systematic exclusion of contributions may not be feasible.

Digital Assembly of Colloidal Particles for Nanoscale Manufacturing

From unravelling the most fundamental phenomena to enabling applications that impact our everyday lives, the nanoscale world holds great promise for science, technology and medicine. However, the extent of its practical realization would rely on manufacturing at the nanoscale. Among the various nanomanufacturing approaches being investigated, the bottom-up approach involving assembly of colloidal nanoparticles as building blocks is promising. Compared to a top-down lithographic approach, particle assembly exhibits advantages such as smaller feature size, finer control of chemical composition, less defects, lower material wastage, and higher scalability. The capability to assemble colloidal particles one by one or "digitally" has been heavily sought as it mimics the natural way of making matter and enables construction of nanomaterials with sophisticated architectures. This progress report provides an insight into the tools and techniques for digital assembly of particles, including their working mechanisms and demonstrated particle assemblies. Examples of nanomaterials and nanodevices are presented to demonstrate the strength of digital assembly in nanomanufacturing.

Optical Tweezers: Phototoxicity and Thermal Stress in Cells and Biomolecules

For several decades optical tweezers have proven to be an invaluable tool in the study and analysis of myriad biological responses and applications. However, as with every tool, they can have undesirable or damaging effects upon the very sample they are helping to study. In this review the main negative effects of optical tweezers upon biostructures and living systems will be presented. There are three main areas on which the review will focus: linear optical excitation within the tweezers, non-linear photonic effects, and thermal load upon the sampled volume. Additional information is provided on negative mechanical effects of optical traps on biological structures. Strategies to avoid or, at least, minimize these negative effects will be introduced. Finally, all these effects, undesirable for the most, can have positive applications under the right conditions. Some hints in this direction will also be discussed.

Inversion of thermodiffusive properties of ionic colloidal dispersions in water-DMSO mixtures probed by forced Rayleigh scattering

Thermodiffusion properties at room temperature of colloidal dispersions of hydroxyl-coated nanoparticles (NPs) are probed in water, in dimethyl sulfoxide (DMSO) and in mixtures of water and DMSO at various proportions of water, [Formula: see text]. In these polar solvents, the positive NPs superficial charge imparts the systems with a strong electrostatic interparticle repulsion, slightly decreasing from water to DMSO, which is here probed by Small Angle Neutron Scattering and Dynamic Light Scattering. However if submitted to a gradient of temperature, the NPs dispersed in water with ClO₄^- counterions present a thermophilic behavior, the same NPs dispersed in DMSO with the same counterions present a thermophobic behavior. Mass diffusion coefficient [Formula: see text] and Ludwig-Soret coefficient [Formula: see text] are measured as a function of NP volume fraction [Formula: see text] at various [Formula: see text]. The [Formula: see text]-dependence of [Formula: see text] is analyzed in terms of thermoelectric and thermophoretic contributions as a function of [Formula: see text]. Using two different models for evaluating the Eastman entropy of transfer of the co- and counterions in the mixtures, the single-particle thermophoretic contribution (the NP's Eastman entropy of transfer) is deduced. It is found to evolve from negative in water to positive in DMSO. It is close to zero on a large range of [Formula: see text] values, meaning that in this [Formula: see text]-range [Formula: see text] largely depends on the thermoelectric effect of free co- and counterions.

Optical Nanoprinting of Colloidal Particles and Functional Structures

Recent advances in chemical sciences have enabled the tailorable synthesis of colloidal particles with variable composition, size, shape, and properties. Building superstructures with colloidal particles as building blocks is appealing for the fabrication of functional metamaterials and nanodevices. Optical nanoprinting provides a versatile platform to print various particles into arbitrary configurations with nanometric precision. In this review, we summarize recent progress in optical nanoprinting of colloidal particles and its related applications. Diverse techniques based on different physical mechanisms, including optical forces, light-controlled electric fields, optothermal effects, laser-directed thermocapillary flows, and photochemical reactions, are discussed in detail. With its flexible and versatile capabilities, optical nanoprinting will find promising applications in numerous fields such as nanophotonics, energy, microelectronics, and nanomedicine.

Opto-thermophoretic fiber tweezers

Recent advances in opto-thermophoretic tweezers open new avenues for low-power trapping and manipulation of nanoparticles with potential applications in colloidal assembly, nanomanufacturing, life sciences, and nanomedicine. However, to fully exploit the opto-thermophoretic tweezers for widespread applications, the enhancement of their versatility in nanoparticle manipulations is pivotal. For this purpose, we translate our newly developed opto-thermophoretic tweezers onto an optical fiber platform known as opto-thermophoretic fiber tweezers (OTFT). We have demonstrated the applications of OTFT as a nanoparticle concentrator, as a nanopipette for single particle delivery, and as a nanoprobe. The simple setup and functional versatility of OTFT would encourage its use in various fields such as additive manufacturing, single nanoparticle-cell interactions, and biosensing.

Thermodiffusion of citrate-coated γ-Fe2O3 nanoparticles in aqueous dispersions with tuned counter-ions - anisotropy of the Soret coefficient under a magnetic field

Under a temperature gradient, the direction of thermodiffusion of charged γ-Fe2O3 nanoparticles (NPs) depends on the nature of the counter-ions present in the dispersion, resulting in either a positive or negative Soret coefficient. Various counter-ions are probed in finely tuned and well characterized dispersions of citrate-coated NPs at comparable concentrations of free ionic species. The Soret coefficient ST is measured in stationary conditions together with the mass-diffusion coefficient Dm using a forced Rayleigh scattering method. The strong interparticle repulsion, determined by SAXS, is also attested by the increase of Dm with NP volume fraction Φ. The Φ-dependence of ST is analyzed in terms of thermophoretic and thermoelectric contributions of the various ionic species. The obtained single-particle thermophoretic contribution of the NPs (the Eastman entropy of transfer ŝNP) varies linearly with the entropy of transfer of the counter-ions. This is understood in terms of electrostatic contribution and of hydration of the ionic shell surrounding the NPs. Two aqueous dispersions, respectively, with ST > 0 and with ST < 0 are then probed under an applied field H[combining right harpoon above], and an anisotropy of Dm and of ST is induced while the in-field system remains monophasic. Whatever the H[combining right harpoon above]-direction (parallel or perpendicular to the gradients and ), the Soret coefficient is modulated keeping the same sign as in zero applied field. In-field experimental determinations are well described using a mean field model of the interparticle magnetic interaction.