C. Nadir Kaplan

Theory and simulations of water flow through carbon nanotubes: prospects and pitfalls

We study water flow through carbon nanotubes using continuum theory and molecular dynamics simulations. The large slip length in carbon nanotubes greatly enhances the pumping and electrokinetic energy conversion efficiency. In the absence of mobile charges, however, the electro-osmotic flow vanishes. Uncharged nanotubes filled with pure water can therefore not be used as electric field-driven pumps, contrary to some recently ventured ideas. This is in agreement with results from a generalized hydrodynamic theory that includes the angular momentum of rotating dipolar molecules. The electro-osmotic flow observed in simulations of such carbon nanotubes is caused by an imprudent implementation of the Lennard-Jones cutoff. We also discuss the influence of other simulation parameters on the spurious electro-osmotic flow.

Evaporation-driven ring and film deposition from colloidal droplets

Evaporating suspensions of colloidal particles lead to the formation of a variety of patterns, ranging from a left-over ring of a dried coffee drop to uniformly distributed solid pigments left behind wet paint. To characterize the transition between single rings, multiple concentric rings, broad bands, and uniform deposits, we investigate the dynamics of a drying droplet via a multiphase model of colloidal particles in a solvent. Our theory couples the inhomogeneous evaporation at the evolving droplet interface to the dynamics inside the drop, i.e. the liquid flow, local variations of the particle concentration, and the propagation of the deposition front where the solute forms an incompressible porous medium at high concentrations. A dimensionless parameter combining the capillary number and the droplet aspect ratio captures the formation conditions of different pattern types.

Controlled growth and form of precipitating microsculptures

A geometrical theory explains the three-dimensional growth and complex form of carbonate-silica precipitates. Predicting the shape of crystals to come Coprecipitating carbonate and silica can form complex three-dimensional shapes. These range from flowers to trumpets, depending on the pH. Kaplan et al. developed a theoretical model to interpret the crystal growth shapes. The model predicts crystal growth shapes under varying experimental conditions and captures the geometrical aspects of morphological development. Science, this issue p. 1395 Controlled self-assembly of three-dimensional shapes holds great potential for fabrication of functional materials. Their practical realization requires a theoretical framework to quantify and guide the dynamic sculpting of the curved structures that often arise in accretive mineralization. Motivated by a variety of bioinspired coprecipitation patterns of carbonate and silica, we develop a geometrical theory for the kinetics of the growth front that leaves behind thin-walled complex structures. Our theory explains the range of previously observed experimental patterns and, in addition, predicts unexplored assembly pathways. This allows us to design a number of functional base shapes of optical microstructures, which we synthesize to demonstrate their light-guiding capabilities. Overall, our framework provides a way to understand and control the growth and form of functional precipitating microsculptures.

Imprintable membranes from incomplete chiral coalescence

Coalescence is an essential phenomenon that governs the equilibrium behaviour in a variety of systems from intercellular transport to planetary formation. In this report, we study coalescence pathways of circularly shaped two-dimensional colloidal membranes, which are one rod-length-thick liquid-like monolayers of aligned rods. The chirality of the constituent rods leads to three atypical coalescence pathways that are not found in other simple or complex fluids. In particular, we characterize two pathways that do not proceed to completion but instead produce partially joined membranes connected by line defects-π-wall defects or alternating arrays of twisted bridges and pores. We elucidate the structure and energetics of these defects and ascribe their stability to a geometrical frustration inherently present in chiral colloidal membranes. Furthermore, we induce the coalescence process with optical forces, leading to a robust on-demand method for imprinting networks of channels and pores into colloidal membranes.

Achiral symmetry breaking and positive Gaussian modulus lead to scalloped colloidal membranes

Significance A number of essential processes in biology and materials science, such as vesicle fusion and fission as well as pore formation, change the membrane topology and require formation of saddle surfaces. The energetic cost associated with such deformations is described by the Gaussian curvature modulus. We show that flat 2D colloidal membranes composed of achiral rods are unstable and spontaneously form scalloped edges. Quantitative analysis of such instability estimates the Gaussian curvature modulus of colloidal membranes. The measured sign and magnitude of the modulus can be explained by a simple excluded volume argument that was originally developed for polymeric surfactants. In the presence of a nonadsorbing polymer, monodisperse rod-like particles assemble into colloidal membranes, which are one-rod-length–thick liquid-like monolayers of aligned rods. Unlike 3D edgeless bilayer vesicles, colloidal monolayer membranes form open structures with an exposed edge, thus presenting an opportunity to study elasticity of fluid sheets. Membranes assembled from single-component chiral rods form flat disks with uniform edge twist. In comparison, membranes composed of a mixture of rods with opposite chiralities can have the edge twist of either handedness. In this limit, disk-shaped membranes become unstable, instead forming structures with scalloped edges, where two adjacent lobes with opposite handedness are separated by a cusp-shaped point defect. Such membranes adopt a 3D configuration, with cusp defects alternatively located above and below the membrane plane. In the achiral regime, the cusp defects have repulsive interactions, but away from this limit we measure effective long-ranged attractive binding. A phenomenological model shows that the increase in the edge energy of scalloped membranes is compensated by concomitant decrease in the deformation energy due to Gaussian curvature associated with scalloped edges, demonstrating that colloidal membranes have positive Gaussian modulus. A simple excluded volume argument predicts the sign and magnitude of the Gaussian curvature modulus that is in agreement with experimental measurements. Our results provide insight into how the interplay between membrane elasticity, geometrical frustration, and achiral symmetry breaking can be used to fold colloidal membranes into 3D shapes.

Infinitely robust order and local order-parameter tulips in Apollonian networks with quenched disorder.

For a variety of quenched random spin systems on an Apollonian network, including ferromagnetic and antiferromagnetic bond percolation and the Ising spin glass, we find the persistence of ordered phases up to infinite temperature over the entire range of disorder. We develop a renormalization-group technique that yields highly detailed information, including the exact distributions of local magnetizations and local spin-glass order parameters, which turn out to exhibit, as function of temperature, complex and distinctive tulip patterns.

Intrinsic curvature determines the crinkled edges of “crenellated disks”

Elastic curvature constants determine many structural and functional properties of fluid membranes. Methods to measure the mean curvature modulus have proved to be robust. In contrast, Gaussian curvature is an intrinsic property of a surface. Thus, measuring the relevant modulus in fluid membranes remains a challenging task. Inspired from colloidal “crenellated disks” observed in a model system composed of hard rods, we propose a concise relation between the two curvature moduli and the parameters associated with the free, crinkled edges. Our approach offers a straightforward way to determine of these reconfigurable membranes, where various complex topologies can be nanosculpted. Further, we reveal the structure and stability of the “crenellated disks.”

Quantum-mechanically induced asymmetry in the phase diagrams of spin-glass systems.

The spin-1/2 quantum Heisenberg spin-glass system is studied in all spatial dimensions d by renormalization-group theory. Strongly asymmetric phase diagrams in temperature and antiferromagnetic bond probability p are obtained in dimensions d>or=3. The asymmetry at high temperatures approaching the pure ferromagnetic and antiferromagnetic systems disappears as d is increased. However, the asymmetry at low but finite temperatures remains in all dimensions, with the antiferromagnetic phase receding from the ferromagnetic phase. A finite-temperature second-order phase boundary directly between the ferromagnetic and antiferromagnetic phases occurs in d>or=6, resulting in a new multicritical point. In d=3, 4, 5, a paramagnetic phase reaching zero temperature intervenes asymmetrically between the ferromagnetic and reentrant antiferromagnetic phases. There is no spin-glass phase in any dimension.

Frustrated further-neighbor antiferromagnetic and electron-hopping interactions in the d=3 t−J model: Finite-temperature global phase diagrams from renormalization group theory

The renormalization-group theory of the d = 3 tJ model is extended to further-neighbor an-tiferromagnetic or electron-hopping interactions, including the ranges of frustration. The global phase diagram of each model is calculated for the entire ranges of temperatures, electron densities, further first-neighbor interaction-strength ratios. With the inclusion of further-neighbor interactions, an extremely rich phase diagram structure is found and is explained by competing and frustrated interactions. In addition to the ?tJ phase seen in earlier studies of the nearest-neighbor d = 3tJ model, the ?Hb phase seen before in the d = 3 Hubbard model appears both near and away from half-filling.