When waves propagate through a weak disordered potential with correlation length larger than the wavelength, they form channels (branches) of enhanced intensity that keep dividing as the waves propagate. This fundamental wave phenomenon is known as branched flow. It was first observed for electrons and for microwave cavities, and it is generally expected for waves with vastly different wavelengths, for example, branched flow has been suggested as a focusing mechanism for ocean waves, and was suggested to occur also in sound waves and ultrarelativistic electrons in graphene. Branched flow may act as a trigger for the formation of extreme nonlinear events and as a channel through which energy is transmitted in a scattering medium. Here we present the experimental observation of the branched flow of light. We show that, as light propagates inside a thin soap membrane, smooth thickness variations in the film act as a correlated disordered potential, focusing the light into filaments that display the features of branched flow: scaling of the distance to the first branching point and the probability distribution of the intensity. We find that, counterintuitively, despite the random variations in the medium and the linear nature of the effect, the filaments remain collimated throughout their paths. Bringing branched flow to the field of optics, with its full arsenal of tools, opens the door to the investigation of a plethora of new ideas such as branched flow in nonlinear media, in curved space or in active systems with gain. Furthermore, the labile nature of soap films leads to a regime in which the branched flow of light interacts and affects the underlying disorder through radiation pressure and gradient force.

While recent studies clarify the effect of osmolytes on Coulomb interaction at elevated concentrations of salt, little is known about the way osmolytes affect the same interaction in cryoprotection. In this Communication we explore the effect of cold on the interaction between two charged surfaces immersed in ternary solution containing salt and osmolyte and find that the effect of cold parallels that of excess salt, i.e., low temperatures increase adsorption of salt counterions to the surface, thus neutralizing it. Two osmolytes, proline and glycine-betaine, are then shown to recharge the surface by releasing the adsorbed counterions. The ability to counteract effects of both cold and excess salt on Coulomb interactions renders these known osmolytes cryoprotectants as well as osmoprotectants, explaining why plants, fish, insects and bacteria accumulate them in response to either drought or cold stress.

Many cells synthesize significant quantities of zwitterionic osmolytes to cope with the osmotic stress induced by excess salt. In addition to their primary role in balancing osmotic pressure, these osmolytes also help stabilize protein structure and restore enzymatic activity compromised by high ionic strength. This osmoprotective effect has been studied extensively, but its electrostatic aspects have somehow escaped the mainstream. Here, we report that, despite their overall neutrality, zwitterions may dramatically affect electrostatic interactions in saline solutions of biological relevance. Using atomic force microscopy, we study the combined effect of osmolytes and salts on electrostatic interactions between two negatively charged silica surfaces in mixtures of five salts (NaCl, KCl, CsCl, MgCl₂, and CaCl₂) and five zwitterionic osmolytes (betaine, proline, trimethylamine N-oxide, glycine, and sarcosine) as a function of solutes concentration and pH. All osmolytes are found to counteract the screening effect of salt on electrostatic repulsion, albeit to a different extent. They do so by both increasing the screening length shortened by added salts and by desorbing bound protons and cations, hence enhancing the negative surface charge. Both effects are traced to the osmolytes’ higher molecular polarizability compared with water. In addition to this direct effect on the solution’s dielectric constant, we identify an osmolytic Hofmeister effect with the more hydrophobic osmolytes more efficiently desorbing weakly hydrated cations from weakly hydrated silica and the less hydrophobic osmolytes better desorbing strongly hydrated cations from strongly hydrated silica. The combined results shed light on Coulomb interactions in a more realistic model of the cytosol, a relatively unexplored territory.

Understanding the solvation layer of hydrophobic surfaces is essential for elucidating the interaction between hydrophobic surfaces in aqueous solutions. Despite their importance, little is known on these layers due to the lack of lateral resolution in spectroscopic or scattering experiments and probe instability in the static scanning probe methods used in most experiments. Using a high-resolution FM-AFM with stiff cantilevers and hydrophilic tips, we overcome this instability to provide the first detailed 3d maps of the solvation/hydration layer of two archetypal hydrophobic surfaces: graphite (HOPG) and self-assembled fluoro-alkane monolayer (FDTS). In degassed solutions we find different tip–surface interactions for the two surfaces; hydration oscillations superimposed on van der Waals attraction with HOPG and electrostatic repulsion with FDTS. Both are similar to interactions observed with hydrophilic surfaces. In solutions equilibrated with atmospheric air or high-pressure nitrogen, the tip–surface interaction changes dramatically, disclosing the formation of a 2–5 nm thick layer of condensed gas molecules adsorbed to the hydrophobic surfaces. This layer leads to strikingly similar tip–surface interactions for HOPG and FDTS with only weak dependence upon the concentration of dissolved gas molecules, indicating universality in the way hydrophobic surfaces present themselves to nondegassed aqueous solutions. Measurements at low cantilever oscillation amplitudes reveal the inner structure of the layer of condensed gas molecules with an average distance between its constituents, 0.5–0.8 nm, agreeing with recent molecular dynamics calculations. In addition to the uniform condensed layers, we probe sparse nanobubbles found on the surface. Those show distinct interaction with the tip, different from that with the flat layer.

Hydration interaction shapes biomolecules and is a dominant intermolecular force. Mapping the hydration patterns of biomolecules is therefore essential for understanding molecular processes in biology. Numerous studies have been devoted to this challenge, but current methods cannot map the hydration of single biomolecules, let alone do so under physiological conditions. Here, we show that frequency-modulation atomic force microscopy (FM-AFM) can fill this gap and generate 3D hydration maps of single DNA molecules under near-physiological conditions. Additionally, we present real-space images of DNA in which the double helix is resolved with unprecedented resolution, clearly revealing individual phosphate groups along the DNA backbone. FM-AFM therefore emerges as a powerful enabling tool in the study of individual biomolecules and their hydration under physiological conditions.

Osmolytes, small molecules synthesized by all organisms, play a crucial role in tuning protein stability and function under variable external conditions. Despite their electrical neutrality, osmolyte action is entwined with that of cellular salts and protons in a mechanism only partially understood. To elucidate this mechanism, we utilize an ultrahigh-resolution frequency modulation-AFM for measuring the effect of two biological osmolytes, urea and glycerol, on the surface charge of silica, an archetype protic surface with a pK value similar to that of acidic amino acids. We find that addition of urea, a known protein destabilizer, enhances silica's surface charge by more than 50%, an effect equivalent to a 4-unit increase of pH. Conversely, addition of glycerol, a protein stabilizer, practically neutralizes the silica surface, an effect equivalent to 2-units' reduction of pH. Simultaneous measurements of the interfacial liquid viscosity indicate that urea accumulates extensively near the silica surface, while glycerol depletes there. Comparison between the measured surface charge and Gouy-Chapman-Stern model for the silica surface shows that the modification of surface charge is 4 times too large to be explained by the change in dielectric constant upon addition of urea or glycerol. The model hence leads to the conclusion that surface charge is chiefly governed by the effect of osmolytes on the surface reaction constants, namely, on silanol deprotonation and on cation binding. These findings highlight the unexpectedly large effect that neutral osmolytes may have on surface charging and Coulomb interactions.

Using ultrahigh resolution atomic force microscopy (AFM) operated in frequency modulation mode, we extend existing measurements of the force acting between hydrophobic surfaces immersed in water in three essential ways. (1) The measurement range, which was previously limited to distances longer than 2–3 nm, is extended to cover all distances, down to contact. The measurements disclose that the long-range attraction observed also by conventional techniques, turns at distances shorter than 1–2 nm into pronounced repulsion. (2) Simultaneous measurements of the dissipative component of the tip–surface interaction reveal an anomalously large dissipation commencing abruptly at the point where attraction begins. The dissipation is more than 2 orders of magnitude larger than expected from bulk water viscosity or from similar measurements between hydrophilic surfaces. (3) The short-range repulsion is oscillatory, indicating molecular ordering of the medium as the hydrophobic surfaces approach each other. The oscillation period, ∼0.5 nm, is larger than the ∼0.3 nm period observed with hydrophilic surfaces. Their range, ∼1.5 nm, is longer as well. These observations are consistent with a conspicuous change in the properties of the surrounding medium, taking place simultaneously with the onset of attraction as the two surfaces approach each other.

Over recent years, the supposedly universal Hofmeister series has been replaced by a diverse spectrum of direct, partially altered and reversed series. This review aims to provide a detailed understanding of the full spectrum by combining results from molecular dynamics simulations, Poisson–Boltzmann theory and AFM experiments. Primary insight into the origin of the Hofmeister series and its reversal is gained from simulation-derived ion–surface interaction potentials at surfaces containing non-polar, polar and charged functional groups for halide anions and alkali cations. In a second step, the detailed microscopic interactions of ions, water and functional surface groups are incorporated into Poisson–Boltzmann theory. This allows us to quantify ion-specific binding affinities to surface groups of varying polarity and charge, and to provide a connection to the experimentally measured long-ranged electrostatic forces that stabilize colloids, proteins and other particles against precipitation. Based on the stabilizing efficiency, the direct Hofmeister series is obtained for negatively charged hydrophobic surfaces. Hofmeister series reversal is induced by changing the sign of the surface charge from negative to positive, by changing the nature of the functional surface groups from hydrophobic to hydrophilic, by increasing the salt concentration, or by changing the pH. The resulting diverse spectrum reflects that alterations of Hofmeister series are the rule rather than the exception and originate from the variation of ion-surface interactions upon changing surface properties.

The present contribution offers a unified explanation to three central phenomena in physical chemistry of interfaces in contact with aqueous solution: (1) Accumulation of large anions at the air/water interface. (2) Accumulation of neutral gas molecules near hydrophobic surfaces and the resulting hydrophobic interaction between two such surfaces, and (3) The Hofmeister effect, namely, the enhanced propensity of small ions to hydrophilic surfaces and large ions to hydrophobic surfaces. The common thread linking these phenomena is the free energy balance between ion or molecule hydration in solution and the cost of localizing these objects at the water-surface interface. Comparing the results of an abstract lattice-gas model to force spectroscopy data collected by AFM we reveal the underlying principles and demonstrate their universality.

AFM measurements of the force acting between silica surfaces in the presence of varied alkali chloride salts and pH’s elucidate the origin of the Hofmeister adsorption series and its reversal. At low pH, electrostatics is shown to be insignificant. The preferential adsorption of Cs+ to the silica surface is traced to the weak hydration of neutral silanols and the resulting hydrophobic expulsion of weakly hydrated ions from bulk solution to the interface. The same interactions keep the strongly hydrated Na+ and Li+ in solution. As pH is increased, a tightly bound hydration layer forms on deprotonating silanols. Cs+ is correspondingly expelled from the surface, and adsorption of small ions is encouraged. The deduced role of surface hydration is corroborated by hydration repulsion observed at high pH, surface overcharging at low pH, and data in other oxides.

We present a novel hollow nanoneedle array (NNA) device capable of simultaneously delivering diverse cargo into a group of cells in a culture over prolonged periods. The silica needles are fed by a common reservoir whose content can be replenished and modified in real time while maintaining contact with the same cells. The NNA, albeit its submicrometer features, is fabricated in a silicon-on-insulator wafer using conventional, large scale, silicon technology. 3T3-NIH fibroblast cells and HEK293 human embryonic kidney cells are shown to grow and proliferate successfully on the NNAs. Cargo delivery from the reservoir through the needles to a group of HEK293 cells in the culture is demonstrated by repeated administration of fluorescently labeled dextran to the same cells and transfection with DNA coding for red fluorescent protein. The capabilities demonstrated by the NNA device open the door to large scale studies of the effect of selected cells on their environment as encountered, for instance, in the study of cell-fate decisions, the role of cell-autonomous versus nonautonomous mechanisms in developmental biology, and in the study of excitable cell-networks.

The force between silica surfaces in NaCl, KCl and CsCl aqueous solutions is studied at pH 5.5 using an atomic force microscope (AFM). As ion concentration is increased, more cations adsorb to the negatively charged silica, gradually neutralizing the surface charge, hence, suppressing the electrostatic double layer repulsion and revealing van der Waals attraction. At even higher salt concentrations, repulsion reemerges due to surface charge reversal by excess adsorbed cations. Adsorption grows monotonically with cation radius. At pH 5.5 the smallest ion, Na⁺, neutralizes the surface at 0.5−1 M, K⁺ at 0.2−0.5 M, and Cs⁺ at ∼0.1 M. Titration with HCl to pH 4.0 shifts surface neutralization and charge reversal to lower salt concentrations compared with pH 5.5. When attraction dominates, the force curves are practically identical for the three salts, independent of their concentration.

Inspired by biology where pathways are triggered and suppressed by specific binding of two molecules, we realize a functional interface between electronics and biology by replacing one of the pair molecules with a two-state "electronic antigen" device comprising a hydroquinone monolayer assembled on gold, and choosing for the pair molecule an antibody that discriminates between the two electrically selected redox states of the monolayer. Application of an oxidative +0.6 V pulse to the antigen switches it to its benzoquinone state where antibodies bind the layer. A subsequent -0.6 V pulse reduces the monolayer back to the unbinding hydroquinone state, releases the specifically bound antibody molecules, and prevents further binding.

Seamless integration of biomolecules with manmade materials will most likely rely on molecular recognition and specific binding. In the following we show that combinatorial antibody libraries, based on the vast repertoire of the human immune system, can be harnessed to generate such binders. As a demonstration, we isolate antibody fragments that discriminate and bind selectively GaAs (111A) facets as opposed to GaAs (100). The isolated antibodies are utilized for exclusive localization of a fluorescent dye on (111A) surfaces in a structure comprising a mixture of (100) and (111A) surfaces. The potential importance of structure rigidity to facet recognition is suggested vis-a-vis published experiments with short and longer peptides.

Using an atomic force microscope we measure the interaction between two identically charged silica surfaces in the presence of a saline solution. For pure NaCl the interaction is always repulsive. Upon addition of cobalt hexamine ions, Co(NH₃)₆⁺³, the repulsion is gradually suppressed and a pronounced attraction develops at distances much shorter than the screening length. Higher concentrations of cobalt hexamine turn the attraction back into repulsion. Measurements of surface charge renormalization by the trivalent cations provide their surface density and their association constant to the negatively charged silica surface. These estimates tend to exclude interaction between two condensed Wigner crystals as an explanation for the attraction.

The combination of their electronic properties and dimensions makes carbon nanotubes ideal building blocks for molecular electronics. However, the advancement of carbon nanotube-based electronics requires assembly strategies that allow their precise localization and interconnection. Using a scheme based on recognition between molecular building blocks, we report the realization of a self-assembled carbon nanotube field-effect transistor operating at room temperature. A DNA scaffold molecule provides the address for precise localization of a semiconducting single-wall carbon nanotube as well as the template for the extended metallic wires contacting it.

Recent advances in the realization of individual molecular-scale electronic devices emphasize the need for novel tools and concepts capable of assembling such devices into large-scale functional circuits. We demonstrated sequence-specific molecular lithography on substrate DNA molecules by harnessing homologous recombination by RecA protein. In a sequence-specific manner, we patterned the coating of DNA with metal, localized labeled molecular objects and grew metal islands on specific sites along the DNA substrate, and generated molecularly accurate stable DNA junctions for patterning the DNA substrate connectivity. In our molecular lithography, the information encoded in the DNA molecules replaces the masks used in conventional microelectronics, and the RecA protein serves as the resist. The molecular lithography works with high resolution over a broad range of length scales from nanometers to many micrometers.

Recent research in the field of nanometre-scale electronics has focused on two fundamental issues: the operating principles of small-scale devices, and schemes that lead to their realization and eventual integration into useful circuits. Experimental studies on molecular to submicrometre quantum dots and on the electrical transport in carbon nanotubes have confirmed theoretical predictions of an increasing role for charging effects as the device size diminishes. Nevertheless, the construction of nanometre-scale circuits from such devices remains problematic, largely owing to the difficulties of achieving inter-element wiring and electrical interfacing to macroscopic electrodes. The use of molecular recognition processes and the self-assembly of molecules into supramolecular structures might help overcome these difficulties. In this context, DNA has the appropriate molecular-recognition and mechanical properties, but poor electrical characteristics prevent its direct use in electrical circuits. Here we describe a two-step procedure that may allow the application of DNA to the construction of functional circuits. In our scheme, hybridization of the DNA molecule with surface-bound oligonucleotides is first used to stretch it between two gold electrodes; the DNA molecule is then used as a template for the vectorial growth of a 12 µm long, 100 nm wide conductive silver wire. The experiment confirms that the recognition capabilities of DNA can be exploited for the targeted attachment of functional wires.

The ground state energy of disordered quantum dots is studied experimentally as a function of dot population. The fluctuations are found to be considerably larger than those predicted by random matrix theory and to display different statistics. Exact diagonalization of the Hamiltonian pertaining to small clusters shows, indeed, that the random matrix statistics holds only for weak Coulomb interactions. As the interaction is made realistic, a crossover to a different statistics, similar to the experimental one, is observed. The statistics crossover is accompanied by appearance of short range spatial correlations in the electron density.

We report on transport measurements in a novel system composed of two parallel 2D electron and hole gases separated by a barrier which is high enough to prevent tunneling and recombination while thin enough to allow for strong interlayer Coulomb interaction. Separate electrical contacts to each layer and independent control of both carrier densities facilitate a detailed study of the electron-hole interaction. Current driven in one layer is found to induce opposite current in the other layer. The measured electron-hole momentum-transfer rate is a factor of 5 to an order of magnitude larger than in previous experiments on electron-electron scattering and calculations based on Coulomb scattering theory.

A modified Young's double-slit experiment is realized for electrons in a high-mobility two-dimensional electron gas (2DEG). The observed quantum interference is employed to study dephasing by electron-electron interaction on length scales shorter than the elastic mean free path. It is found that the measured phase-breaking length agrees very well with theoretical calculations of the e-e mean free path in an ideal 2DEG. In contrast to the diffusive regime, dephasing occurs via e-e scattering events with an energy exchange on the order of the carrier excess energy.

Various thermoelectric linear transport coefficients are defined and calculated for two reservoirs connected with ideal multichannel leads and a segment of an arbitrary disordered system. The reservoirs have different temperatures and chemical potentials. All of the inelastic scattering (and, thus, the dissipation) is assumed to occur only in the reservoirs. The definitions of the chemical potentials and temperature differences across the sample itself (mostly due to elastic scattering) are presented. Subtleties of the thermoelectric effects across the sample are discussed. The associated transport coefficients display deviations from the Onsager relations and from the Cutler-Mott formula for the thermopower (although the deviations vanish for a large number of channels and/or high resistance). The expression obtained is used to predict the critical behavior of the electronic thermopower near the mobility edge. It is shown to satisfy a scaling form in the temperature and separation from the mobility edge.