Bulk dynamics of Brownian hard disks: Dynamical density functional theory versus experiments on two-dimensional colloidal hard spheres

Using dynamical density functional theory (DDFT), we theoretically study Brownian self-diffusion and structural relaxation of hard disks and compare to experimental results on quasi two-dimensional colloidal hard spheres. To this end, we calculate the self and distinct van Hove correlation functions by extending a recently proposed DDFT-approach for three-dimensional systems to two dimensions. We find that the theoretical results for both self- and distinct part of the van Hove function are in very good quantitative agreement with the experiments up to relatively high fluid packing fractions of roughly 0.60. However, at even higher densities, deviations between experiment and the theoretical approach become clearly visible. Upon increasing packing fraction, in experiments the short-time self diffusive behavior is strongly affected by hydrodynamic effects and leads to a significant decrease in the respective mean-squared displacement. In contrast, and in accordance with previous simulation studies, the present DDFT which neglects hydrodynamic effects, shows no dependence on the particle density for this quantity

3D Flow Field Measurements Outside Nanopores

We demonstrate a non-stereoscopic, video-based particle tracking system with optical tweezers to study fluid flow in 3D in the vicinity of glass nanopores. In particular, we used the Quadrant Interpolation algorithm to extend our video-based particle tracking to displacements out of the trapping plane of the tweezers. This permitted the study of flow from nanopores oriented at an angle to the trapping plane, enabling the mounting of nanopores on a micromanipulator with which it was then possible to automate the mapping procedure. Mapping of voltage driven flow in 3D volumes outside nanopores revealed polarity dependent flow fields. This is in agreement with the model of voltage driven flow in conical nanopores depending on the interaction of distinct flows within the nanopore and along the outer walls.Comment: 3 pages, 3 figure

Direct detection of molecular intermediates from first-passage times

All natural phenomena are governed by energy landscapes. However, the direct measurement of this fundamen-tal quantity remains challenging, particularly in complex systems involving intermediate states. Here, we uncover key details of the energy landscapes that underpin a range of experimental systems through quantitative analysis of first-passage time distributions. By combined study of colloidal dynamics in confinement, transport through a biological pore, and the folding kinetics of DNA hairpins, we demonstrate conclusively how a short-time, power-law regime of the first-passage time distribution reflects the number of intermediate states associated with each of these processes, despite their differing length scales, time scales, and interactions. We thereby establish a powerful method for investigating the underlying mechanisms of complex molecular processes

Tunable Anion-Selective Transport through Monolayer Graphene and Hexagonal Boron Nitride.

Membranes that selectively filter for both anions and cations are central to technological applications from clean energy generation to desalination devices. 2D materials have immense potential as these ion-selective membranes due to their thinness, mechanical strength, and tunable surface chemistry; however, currently, only cation-selective membranes have been reported. Here we demonstrate the controllable cation and anion selectivity of both monolayer graphene and hexagonal boron nitride. In particular, we measure the ionic current through membranes grown by chemical vapor deposition containing well-known defects inherent to scalably produced and wet-transferred 2D materials. We observe a striking change from cation selectivity with monovalent ions to anion selectivity by controlling the concentration of multivalent ions and inducing charge inversion on the 2D membrane. Furthermore, we find good agreement between our experimental data and theoretical predictions from the Goldman-Hodgkin-Katz equation and use this model to extract selectivity ratios. These tunable selective membranes conduct up to 500 anions for each cation and thus show potential for osmotic power generation

Structure and dynamics of two-dimensional colloidal hard spheres

The structural and dynamic behaviour of quasi-two-dimensional monodisperse and bidisperse colloidal hard spheres are studied by optical microscopy. Firstly, a full characterisation of the equilibrium structure is presented through a consideration of structural correlation functions and number fluctuations. Comparison to fundamental measure theory and Monte Carlo simulations confirms both the behaviour of the system as a model for hard disks and the equation of state. The differing structural behaviour of binary systems at different size ratios is also discussed in relation to the nonadditivity. Next, the short- and long-time self-diffusion of particles is considered. Results for the long-time diffusion coefficient are again compared to Monte Carlo simulations, which demonstrates that at long times the dynamic behaviour is effectively not affected by hydrodynamic interactions. Additionally, simple theoretical expressions for the area fraction dependence of the short- and long-time diffusion coefficients are discussed. The selfdynamic properties of particles are probed further using the self-intermediate scattering function and the self-van Hove correlation function. In particular, the extent to which these quantities may be described by the Gaussian approximation is considered in relation to the relevant hydrodynamic limits for colloidal systems. A scaling relation to describe the crossover between these limits at short and long times is also developed. The consideration of dynamic behaviour is then extended to collective phenomena and, in particular, to the process of interdiffusion. Here, the thermodynamic and kinetic drives for this process are explored for binary systems at two different size ratios. The differing interdiffusive effects seen in the two systems are considered in light of the predictions of the Darken equation. Finally, the melting of quasi-two-dimensional colloidal hard spheres is studied by considering a monolayer of particles in sedimentation-diffusion equilibrium. Density profiles and the equation of state are used to characterise the system. These quantities display a discontinuity, indicating a coexistence gap and hence an interface. This interface is located and analysed using capillary wave theory, from which both the size of the coexistence gap and the anisotropic stiffness of the interface are determined.</p

Structure and dynamics of two-dimensional colloidal hard spheres

The structural and dynamic behaviour of quasi-two-dimensional monodisperse and bidisperse colloidal hard spheres are studied by optical microscopy. Firstly, a full characterisation of the equilibrium structure is presented through a consideration of structural correlation functions and number fluctuations. Comparison to fundamental measure theory and Monte Carlo simulations confirms both the behaviour of the system as a model for hard disks and the equation of state. The differing structural behaviour of binary systems at different size ratios is also discussed in relation to the nonadditivity. Next, the short- and long-time self-diffusion of particles is considered. Results for the long-time diffusion coefficient are again compared to Monte Carlo simulations, which demonstrates that at long times the dynamic behaviour is effectively not affected by hydrodynamic interactions. Additionally, simple theoretical expressions for the area fraction dependence of the short- and long-time diffusion coefficients are discussed. The selfdynamic properties of particles are probed further using the self-intermediate scattering function and the self-van Hove correlation function. In particular, the extent to which these quantities may be described by the Gaussian approximation is considered in relation to the relevant hydrodynamic limits for colloidal systems. A scaling relation to describe the crossover between these limits at short and long times is also developed. The consideration of dynamic behaviour is then extended to collective phenomena and, in particular, to the process of interdiffusion. Here, the thermodynamic and kinetic drives for this process are explored for binary systems at two different size ratios. The differing interdiffusive effects seen in the two systems are considered in light of the predictions of the Darken equation. Finally, the melting of quasi-two-dimensional colloidal hard spheres is studied by considering a monolayer of particles in sedimentation-diffusion equilibrium. Density profiles and the equation of state are used to characterise the system. These quantities display a discontinuity, indicating a coexistence gap and hence an interface. This interface is located and analysed using capillary wave theory, from which both the size of the coexistence gap and the anisotropic stiffness of the interface are determined.</p

Generalized network theory of physical two-dimensional systems

The properties of a wide range of two-dimensional network materials are investigated by developing a generalized network theory. The methods developed are shown to be applicable to a wide range of systems generated from both computation and experiment; incorporating atomistic materials, foams, fullerenes, colloidal monolayers, and geopolitical regions. The ring structure in physical networks is described in terms of the node degree distribution and the assortativity. These quantities are linked to previous empirical measures such as Lemaître's law and the Aboav-Weaire law. The effect on these network properties is explored by systematically changing the coordination environments, topologies, and underlying potential model of the physical system

Long-time self-diffusion in quasi-two-dimensional colloidal fluids of paramagnetic particles

The effect of hydrodynamic interactions (HI) on the long-time self-diffusion in quasi-two-dimensional fluids of paramagnetic colloidal particles is investigated using a combination of experiments and Brownian dynamics (BD) simulations. In the BD simulations, the direct interactions (DI) between the particles consist of a short-ranged repulsive part and a long-ranged part that is proportional to 1/r3, with r the interparticle distance. By studying the equation of state, the simulations allow for the identification of the regime where the properties of the fluid are fully controlled by the long-ranged interactions, and the thermodynamic state solely depends on the dimensionless interaction strength Γ. In this regime, the radial distribution functions from the simulations are in quantitative agreement with those from the experiments for different fluid area fractions. This agreement confirms that the DI in the experiments and simulations are identical, which thus allows us to isolate the role of HI, as these are not taken into account in the BD simulations. Experiment and simulation fall onto a master curve with respect to the Γ dependence of D★L=DL/(D0Γ1/2), with D0 the self-diffusion coefficient at infinite dilution and DL the long-time self-diffusion coefficient. Our results thus show that, although HI affect the short-time self-diffusion, for a quasi-two-dimensional system with 1/r3 long-ranged DI, the reduced quantity D★L is effectively not affected by HI. Interestingly, this is in agreement with prior work on quasi-two-dimensional colloidal hard spheres