A charge-dependent long-ranged force drives tailored assembly of matter in solution.

The interaction between charged objects in solution is generally expected to recapitulate two central principles of electromagnetics: (1) like-charged objects repel, and (2) they do so regardless of the sign of their electrical charge. Here we demonstrate experimentally that the solvent plays a hitherto unforeseen but crucial role in interparticle interactions, and importantly, that interactions in the fluid phase can break charge-reversal symmetry. We show that in aqueous solution, negatively charged particles can attract at long range while positively charged particles repel. In solvents that exhibit an inversion of the net molecular dipole at an interface, such as alcohols, we find that the converse can be true: positively charged particles may attract whereas negatives repel. The observations hold across a wide variety of surface chemistries: from inorganic silica and polymeric particles to polyelectrolyte- and polypeptide-coated surfaces in aqueous solution. A theory of interparticle interactions that invokes solvent structuring at an interface captures the observations. Our study establishes a nanoscopic interfacial mechanism by which solvent molecules may give rise to a strong and long-ranged force in solution, with immediate ramifications for a range of particulate and molecular processes across length scales such as self-assembly, gelation and crystallization, biomolecular condensation, coacervation, and phase segregation.

Wide-field optical imaging of electrical charge and chemical reactions at the solid-liquid interface.

From molecules and particles to macroscopic surfaces immersed in fluids, chemical reactions often endow interfaces with electrical charge which in turn governs surface interactions and interfacial phenomena. The ability to measure the electrical properties of a material immersed in any solvent, as well as to monitor the spatial heterogeneity and temporal variation thereof, has been a long-standing challenge. Here, we describe an optical microscopy-based approach to probe the surface charge distribution of a range of materials, including inorganic oxide, polymer, and polyelectrolyte films, in contact with a fluid. The method relies on optical visualization of the electrical repulsion between diffusing charged probe molecules and the unknown surface to be characterized. Rapid image-based measurements enable us to further determine isoelectric points of the material as well as properties of its ionizable chemical groups. We further demonstrate the ability to optically monitor chemically triggered surface charge changes with millisecond time resolution. Finally, we present a scanning-surface probe technique capable of diffraction-limited imaging of spatial heterogeneities in chemical composition and charge over large areas. This technique will enable facile characterization of the solid-liquid interface with wide-ranging relevance across application areas from biology to engineering.

Single-Molecule Trapping and Measurement in a Nanostructured Lipid Bilayer System.

The repulsive electrostatic force between a biomolecule and a like-charged surface can be geometrically tailored to create spatial traps for charged molecules in solution. Using a parallel-plate system composed of silicon dioxide surfaces, we recently demonstrated single-molecule trapping and high precision molecular charge measurements in a nanostructured free energy landscape. Here we show that surfaces coated with charged lipid bilayers provide a system with tunable surface properties for molecular electrometry experiments. Working with molecular species whose effective charge and geometry are well-defined, we demonstrate the ability to quantitatively probe the electrical charge density of a supported lipid bilayer. Our findings indicate that the fraction of charged lipids in nanoslit lipid bilayers can be significantly different from that in the precursor lipid mixtures used to generate them. We also explore the temporal stability of bilayer properties in nanofluidic systems. Beyond their relevance in molecular measurement, such experimental systems offer the opportunity to examine lipid bilayer formation and wetting dynamics on nanostructured surfaces.

Far-Field Electrostatic Signatures of Macromolecular 3D Conformation.

In solution as in vacuum, the electrostatic field distribution in the vicinity of a charged object carries information on its three-dimensional geometry. We report on an experimental study exploring the effect of molecular shape on long-range electrostatic interactions in solution. Working with DNA nanostructures carrying approximately equal amounts of total charge but each in a different three-dimensional conformation, we demonstrate that the geometry of the distribution of charge in a molecule has substantial impact on its electrical interactions. For instance, a tetrahedral structure, which is the most compact distribution of charge we tested, can create a far-field effect that is effectively identical to that of a rod-shaped molecule carrying half the amount of total structural charge. Our experiments demonstrate that escape-time electrometry (ETe) furnishes a rapid and facile method to screen and identify 3D conformations of charged biomolecules or molecular complexes in solution.

Opto-Electrostatic Determination of Nucleic Acid Double-Helix Dimensions and the Structure of the Molecule-Solvent Interface.

A DNA molecule is highly electrically charged in solution. The electrical potential at the molecular surface is known to vary strongly with the local geometry of the double helix and plays a pivotal role in DNA-protein interactions. Further out from the molecular surface, the electrical field propagating into the surrounding electrolyte bears fingerprints of the three-dimensional arrangement of the charged atoms in the molecule. However, precise extraction of the structural information encoded in the electrostatic "far field" has remained experimentally challenging. Here, we report an optical microscopy-based approach that detects the field distribution surrounding a charged molecule in solution, revealing geometric features such as the radius and the average rise per basepair of the double helix with up to sub-Angstrom precision, comparable with traditional molecular structure determination techniques like X-ray crystallography and nuclear magnetic resonance. Moreover, measurement of the helical radius furnishes an unprecedented view of both hydration and the arrangement of cations at the molecule-solvent interface. We demonstrate that a probe in the electrostatic far field delivers structural and chemical information on macromolecules, opening up a new dimension in the study of charged molecules and interfaces in solution.

The Role of Surface Chemistry in the Orientational Behavior of Water at an Interface.

Molecular dynamics studies have demonstrated that molecular water at an interface, with either a gas or a solid, displays anisotropic orientational behavior in contrast to its bulk counterpart. This effect has been recently implicated in the like-charge attraction problem for colloidal particles in solution. Here, negatively charged particles in solution display a long-ranged attraction where continuum electrostatic theory predicts monotonically repulsive interactions, particularly in solutions with monovalent salt ions at low ionic strength. Anisotropic orientational behavior of solvent molecules at an interface gives rise to an excess interfacial electrical potential which we suggest generates an additional solvation contribution to the total free energy that is traditionally overlooked in continuum descriptions of interparticle interactions in solution. In the present investigation we perform molecular dynamics simulation based calculations of the interfacial potential using realistic surface models representing various chemistries as well as different solvents. Similar to previous work that focused on simple model surfaces constructed by using oxygen atoms, we find that solvents at more realistic model surfaces exhibit substantial anisotropic orientational behavior. We explore the dependence of the interfacial solvation potential on surface properties such as surface group chemistry and group density at silica and carboxylated polystyrene interfaces. For water, we note surprisingly good agreement between results obtained for a simple O-atom wall and more complex surface models, suggesting a general qualitative consistency of the interfacial solvation effect for surfaces in contact with water. In contrast, for an aprotic solvent such as DMSO, surface chemistry appears to exert a stronger influence on the sign and magnitude of the interfacial solvation potential. The study carries broad implications for molecular-scale interactions and may find relevance in explaining a range of phenomena in soft-matter physics and cell biology.

Electrostatic free energies carry structural information on nucleic acid molecules in solution.

Over the last several decades, a range of experimental techniques from x-ray crystallography and atomic force microscopy to nuclear magnetic resonance and small angle x-ray scattering have probed nucleic acid structure and conformation with high resolution both in the condensed state and in solution. We present a computational study that examines the prospect of using electrostatic free energy measurements to detect 3D conformational properties of nucleic acid molecules in solution. As an example, we consider the conformational difference between A- and B-form double helices whose structures differ in the values of two key parameters-the helical radius and rise per basepair. Mapping the double helix onto a smooth charged cylinder reveals that electrostatic free energies for molecular helices can, indeed, be described by two parameters: the axial charge spacing and the radius of a corresponding equivalent cylinder. We show that electrostatic free energies are also sensitive to the local structure of the molecular interface with the surrounding electrolyte. A free energy measurement accuracy of 1%, achievable using the escape time electrometry (ETe) technique, could be expected to offer a measurement precision on the radius of the double helix of approximately 1 Å. Electrostatic free energy measurements may, therefore, not only provide information on the structure and conformation of biomolecules but could also shed light on the interfacial hydration layer and the size and arrangement of counterions at the molecular interface in solution.

Nonmonotonic Pair Potentials in the Interaction of Like-Charged Objects in Solution.

We consider the long-standing like-charge attraction problem, wherein under certain conditions, similarly charged spheres suspended in aqueous electrolyte have been observed to display a minimum in their interaction potential, contrary to the intuitively expected monotonically varying repulsion. Recently, we described an interfacial mechanism invoking the molecular nature of the solvent that explains this anomalous experimental observation. In our model for the interaction of negatively charged particles in water, the minimum in the pair potential results from the superposition of competing contributions to the total free energy. One of these contributions is the canonical repulsive electrostatic term, whereas the other is a solvation-induced attractive contribution. We find that whereas both contributions grow approximately exponentially with decreasing interparticle separation, the occurrence of a stable, long-ranged minimum in the pair potential arises from differences in the precise interparticle separation dependence of the two terms. Specifically, the interfacial solvation term exhibits a more gradual decay with distance than the electrostatic repulsion, permitting the attractive contribution to dominate the interaction at large distances. Importantly, these disparities become evident in quantities calculated from exact numerical solutions to the governing nonlinear Poisson-Boltzmann (PB) equation for the spatial electrical potential distribution in the system. In marked contrast, we find that the linearized PB equation, applicable in the regime of low surface electrical potentials, does not support nonmonotonic trends in the total interaction free energy within the present model. Our results point to the importance of exact descriptions of electrostatic interactions in real systems that most often do not subscribe to particular mathematical limits where analytical approximations may provide a sufficiently accurate description of the problem.

Electroviscous effect for a confined nanosphere in solution.

A charged colloidal particle suspended in an electrolyte experiences electroviscous stresses arising from motion-driven electrohydrodynamic phenomena. Under certain conditions, the additional contribution from electroviscous drag forces to the total drag experienced by the moving particle can lead to measurable deviations of particle diffusion coefficients from values predicted by the well known Stokes-Einstein relation that describes diffusive behavior of small particles in an unbounded charge-free fluid. In this study, we investigate the role of electroviscous stresses on nanoparticle diffusion in confined geometries using both simulations and experiment. We compare our experimental measurements with the results of a numerically solved continuum model based on the Poisson-Nernst-Planck-Stokes system of equations and find good agreement between experiment and theory. Depending on the radius of the counterion species in solution and the degree of confinement, we find that the viscous drag on polystyrene nanoparticles can be augmented by approximately 10-25% compared to the values predicted by pure hydrodynamic models in the absence of free charge in the fluid. This enhancement corresponds approximately to a 5-10% increase compared to the electroviscous contribution for a charged particle in an unbounded fluid. Contrary to recent reports in the experimental literature, we find neither experimental nor theoretical evidence of an anomalously large enhancement of electroviscous forces on a confined charged nanoparticle in solution.

Interfacial solvation can explain attraction between like-charged objects in aqueous solution.

Over the past few decades, the experimental literature has consistently reported observations of attraction between like-charged colloidal particles and macromolecules in aqueous solution. Examples include nucleic acids and colloidal particles in the bulk solution and under confinement, and biological liquid-liquid phase separation. This observation is at odds with the intuitive expectation of an interparticle repulsion that decays monotonically with distance. Although attraction between like-charged particles can be rationalized theoretically in the strong-coupling regime, e.g., in the presence of multivalent counterions, recurring accounts of long-range attraction in aqueous solution containing monovalent ions at low ionic strength have posed an open conundrum. Here, we show that the behavior of molecular water at an interface-traditionally disregarded in the continuum electrostatics picture-provides a mechanism to explain the attraction between like-charged objects in a broad spectrum of experiments. This basic principle will have important ramifications in the ongoing quest to better understand intermolecular interactions in solution.

Single-molecule trapping and measurement in solution.

Trapping of a single molecule in the fluid phase was realized decades following developments in the gas-phase, because in some ways the solution phase posed a greater challenge. The key issues have since been addressed by several different means; techniques to confine nanometer scale entities in solution now abound and are gaining traction in a variety of single molecule studies. Available methods range from pure physical entrapment of a molecule on the one hand to electrokinetic and optical techniques, and approaches that exploit thermodynamic principles on the other. Some trapping techniques have also opened up new avenues to highly precise, accurate measurements of molecular physical properties in solution.

Entropic Trapping of a Singly Charged Molecule in Solution.

We demonstrate the ability to confine a single molecule in solution by spatial modulation of its local configurational entropy. Previously we established electrostatic trapping of a charged macromolecule by geometric tailoring of a repulsive electrical interaction potential in a parallel plate system. However, since the lifetime of the trapped state depends exponentially on the electrical charge of the molecule, the electrostatic interaction alone is often insufficient in magnitude to stably confine molecules carrying a net charge of magnitude ≤5 e. Here we show that the configurational entropy of a thermally fluctuating molecule in a geometrically modulated system can be exploited to spatially confine weakly charged molecules in solution. Measurement of the configurational entropy contribution reveals good agreement with theoretical expectations. This additional translational contribution to the total free energy facilitates direct optical imaging and measurement of the effective charge of molecules on the size scale of ∼1 nm and a charge as low as 1 e, physical properties comparable with those of a monovalent ion in solution.

Single-molecule electrometry.

Mass and electrical charge are fundamental properties of biological macromolecules. Although molecular mass has long been determined with atomic precision, a direct and precise determination of molecular charge remains an outstanding challenge. Here we report high-precision (<1e) measurements of the electrical charge of molecules such as nucleic acids, and globular and disordered proteins in solution. The measurement is based on parallel external field-free trapping of single macromolecules, permits the estimation of a dielectric coefficient of the molecular interior and can be performed in real time. Further, we demonstrate the direct detection of single amino acid substitution and chemical modifications in proteins. As the electrical charge of a macromolecule strongly depends on its three-dimensional conformation, this kind of high-precision electrometry offers an approach to probe the structure, fluctuations and interactions of a single molecule in solution.

Lattice diffusion of a single molecule in solution.

The ability to trap a single molecule in an electrostatic potential well in solution has opened up new possibilities for the use of molecular electrical charge to study macromolecular conformation and dynamics at the level of the single entity. Here we study the diffusion of a single macromolecule in a two-dimensional lattice of electrostatic traps in solution. We report the ability to measure both the size and effective electrical charge of a macromolecule by observing single-molecule transport trajectories, typically a few seconds in length, using fluorescence microscopy. While, as shown previously, the time spent by the molecule in a trap is a strong function of its effective charge, we demonstrate here that the average travel time between traps in the landscape yields its hydrodynamic radius. Tailoring the pitch of the lattice thus yields two different experimentally measurable time scales that together uniquely determine both the size and charge of the molecule. Since no information is required on the location of the molecule between consecutive departure and arrival events at lattice sites, the technique is ideally suited to measurements on weakly emitting entities such as single molecules.

Information storage and retrieval in a single levitating colloidal particle.

The binary switch is a basic component of digital information. From phase-change alloys to nanomechanical beams, molecules and atoms, new strategies for controlled bistability hold great interest for emerging technologies. We present a generic methodology for precise and parallel spatiotemporal control of nanometre-scale matter in a fluid, and demonstrate the ability to attain digital functionalities such as switching, gating and data storage in a single colloid, with further implications for signal amplification and logic operations. This fluid-phase bit can be arrayed at high densities, manipulated by either electrical or optical fields, supports low-energy, high-speed operation and marks a first step toward 'colloidal information'. The principle generalizes to any system where spatial perturbation of a particle elicits a differential response amenable to readout.

Measuring three-dimensional interaction potentials using optical interference.

We describe the application of three-dimensional (3D) scattering interferometric (iSCAT) imaging to the measurement of spatial interaction potentials for nano-objects in solution. We study electrostatically trapped gold particles in a nanofluidic device and present details on axial particle localization in the presence of a strongly reflecting interface. Our results demonstrate high-speed (~kHz) particle tracking with subnanometer localization precision in the axial and average 2.5 nm in the lateral dimension. A comparison of the measured levitation heights of trapped particles with the calculated values for traps of various geometries reveals good agreement. Our work demonstrates that iSCAT imaging delivers label-free, high-speed and accurate 3D tracking of nano-objects conducive to probing weak and long-range interaction potentials in solution.

Electrostatic free energy for a confined nanoscale object in a fluid.

We present numerical calculations of electrostatic free energies, based on the nonlinear Poisson-Boltzmann (PB) equation, for the case of an isolated spherical nano-object in an aqueous suspension, interacting with charged bounding walls. We focus on systems with a low concentration of monovalent ions (≲10(-4) M), where the range of electrostatic interactions is long (~30 nm) and comparable to the system and object dimensions (~100 nm). Locally tailoring the geometry of the boundaries creates a modulation in the object-wall interaction, which for appropriately chosen system dimensions can be strong enough to result in stable spatial trapping of a nanoscale entity. A detailed view of the underlying mechanism of the trap shows that the physics depends predominantly on counterion entropy and the depth of the potential well is effectively independent of the object's dielectric function; we further note an appreciable trap depth even for an uncharged object in the fluid. These calculations not only provide a quantitative framework for understanding geometry-driven electrostatic effects at the nanoscale, but will also aid in identifying contributions from phenomena beyond mean field PB electrostatics, e.g., Casimir and other fluctuation-driven forces.

Angular trapping of anisometric nano-objects in a fluid.

We demonstrate the ability to trap, levitate, and orient single anisometric nanoscale objects with high angular precision in a fluid. An electrostatic fluidic trap confines a spherical object at a spatial location defined by the minimum of the electrostatic system free energy. For an anisometric object and a potential well lacking angular symmetry, the system free energy can further strongly depend on the object's orientation in the trap. Engineering the morphology of the trap thus enables precise spatial and angular confinement of a single levitating nano-object, and the process can be massively parallelized. Since the physics of the trap depends strongly on the surface charge of the object, the method is insensitive to the object's dielectric function. Furthermore, levitation of the assembled objects renders them amenable to individual manipulation using externally applied optical, electrical, or hydrodynamic fields, raising prospects for reconfigurable chip-based nano-object assemblies.

Measuring the size and charge of single nanoscale objects in solution using an electrostatic fluidic trap.

Measuring the size and charge of objects suspended in solution, such as dispersions of colloids or macromolecules, is a significant challenge. Measurements based on light scattering are inherently biased to larger entities, such as aggregates in the sample, because the intensity of light scattered by a small object scales as the sixth power of its size. Techniques that rely on the collective migration of species in response to external fields (electric or hydrodynamic, for example) are beset with difficulties including low accuracy and dispersion-limited resolution. Here, we show that the size and charge of single nanoscale objects can be directly measured with high throughput by analysing their thermal motion in an array of electrostatic traps. The approach, which is analogous to Millikan's oil drop experiment, could in future be used to detect molecular binding events with high sensitivity or carry out dynamic single-charge resolved measurements at the solid/liquid interface.

Geometry-induced electrostatic trapping of nanometric objects in a fluid.

The ability to trap an object-whether a single atom or a macroscopic entity-affects fields as diverse as quantum optics, soft condensed-matter physics, biophysics and clinical medicine. Many sophisticated methodologies have been developed to counter the randomizing effect of Brownian motion in solution, but stable trapping of nanometre-sized objects remains challenging. Optical tweezers are widely used traps, but require sufficiently polarizable objects and thus are unable to manipulate small macromolecules. Confinement of single molecules has been achieved using electrokinetic feedback guided by tracking of a fluorescent label, but photophysical constraints limit the trap stiffness and lifetime. Here we show that a fluidic slit with appropriately tailored topography has a spatially modulated electrostatic potential that can trap and levitate charged objects in solution for up to several hours. We illustrate this principle with gold particles, polymer beads and lipid vesicles with diameters of tens of nanometres, which are all trapped without external intervention and independently of their mass and dielectric function. The stiffness and stability of our electrostatic trap is easily tuned by adjusting the system geometry and the ionic strength of the solution, and it lends itself to integration with other manipulation mechanisms. We anticipate that these features will allow its use for contact-free confinement of single proteins and macromolecules, and the sorting and fractionation of nanometre-sized objects or their assembly into high-density arrays.