Structure factor of hard spheres near a wall

Comparative study of force-based classical density functional theory

We reexamine results obtained with the recently proposed density functional theory framework based on forces (force-DFT) [S. M. Tschopp et al., Phys. Rev. E 106, 014115 (2022)2470-004510.1103/PhysRevE.106.014115]. We compare inhomogeneous density profiles for hard sphere fluids to results from both standard density functional theory and from computer simulations. Test situations include the equilibrium hard sphere fluid adsorbed against a planar hard wall and the dynamical relaxation of hard spheres in a switched harmonic potential. The comparison to grand canonical Monte Carlo simulation profiles shows that equilibrium force-DFT alone does not improve upon results obtained with the standard Rosenfeld functional. Similar behavior holds for the relaxation dynamics, where we use our event-driven Brownian dynamics data as benchmark. Based on an appropriate linear combination of standard and force-DFT results, we investigate a simple hybrid scheme which rectifies these deficiencies in both the equilibrium and the dynamical case. We explicitly demonstrate that although the hybrid method is based on the original Rosenfeld fundamental measure functional, its performance is comparable to that of the more advanced White Bear theory.

Fundamental measure theory of inhomogeneous two-body correlation functions

For the three-dimensional hard-sphere model we investigate the inhomogeneous two-body correlations predicted by Rosenfeld's fundamental measure theory. For the special cases in which the density has either planar or spherical symmetry we provide analytic formulas for the Hankel and Legendre transforms, respectively, of the inhomogeneous two-body direct correlation function as explicit functionals of the density. When combined with the Ornstein-Zernike relation our analytical results allow for rapid calculation of inhomogeneous hard-sphere density correlations in real space. These not only provide information about the packing structures of the hard-sphere system but also form an essential building-block for constructing perturbation theories of more realistic models.

Evidence of electrostatic-enhanced depletion attraction in the structural properties and phase behavior of binary charged colloidal suspensions

In this paper we study the structure and phase behavior of binary mixtures of charged particles at low ionic strength. Due to the large size asymmetry between both species, light scattering measurements give us access only to the partial static structure factor that corresponds to the big particles. We observe that the addition of small charged colloids produces a decrease of the main peak of the measured static structure factor and a shift to larger scattering vector values. This finding is in agreement with theory based on integral equations with the Hypernetted-Chain Closure (HNC) relation. The effective interaction between two big particles due to the presence of small particles is obtained by a HNC inversion scheme and used in numerical simulations that adequately reproduce the experiments. We find that the presence of small particles induces an electrostatic depletion screening among the big colloids, creating around them an exclusion zone for the small charged colloids greater than that caused in the case of neutral small colloids, which in turn augments the depletion effect.

Classical density functional study of wetting transitions on nanopatterned surfaces

Even simple fluids on simple substrates can exhibit very rich surface phase behaviour. To illustrate this, we consider fluid adsorption on a planar wall chemically patterned with a deep stripe of a different material. In this system, two phase transitions compete: unbending and pre-wetting. Using microscopic density-functional theory, we show that, for thin stripes, the lines of these two phase transitions may merge, leading to a new two-dimensional-like wetting transition occurring along the walls. The influence of intermolecular forces and interfacial fluctuations on this phase transition and at complete pre-wetting are considered in detail.

Diffusive dynamics of polymer chains in an array of nanoposts

The diffusion of the head, side, and middle segments in confined polymer chains displays different dynamics in different directions.

Anisotropy and memory during cage breaking events close to a wall

The slow dynamics in a glassy hard-sphere system is dominated by cage breaking events, i.e. rearrangements where a particle escapes from the cage formed by its neighboring particles. We study such events for an overdamped colloidal system by the means of Brownian dynamics simulations. While it is difficult to relate cage breaking events to structural mean field results in bulk, we show that the microscopic dynamics of particles close to a wall can be related to the anisotropic two-particle density. In particular, we study cage-breaking trajectories, mean forces on a tracked particle, and the impact of the history of trajectories. Based on our simulation results, we further construct two different one-particle random-walk models-one without and one with memory incorporated-and find the local anisotropy and the history-dependence of particles as crucial ingredients to describe the escape from a cage. Finally, our detailed study of a rearrangement event close to a wall not only reveals the memory effect of cages, but leads to a deeper insight into the fundamental mechanisms of glassy dynamics.

Analytic solution of the Ornstein-Zernike relation for inhomogeneous liquids

The properties of a classical simple liquid are strongly affected by the application of an external potential that supports inhomogeneity. To understand the nature of these property changes, the equilibrium particle distribution functions of the liquid have, typically, been calculated directly using either integral equation or density functional based analyses. In this study, we develop a different approach with a focus on two distribution functions that characterize the inhomogeneous liquid: the pair direct correlation function c(r₁,r₂) and the pair correlation function g(r₁,r₂). With g(r₁,r₂) considered to be an experimental observable, we solve the Ornstein-Zernike equation for the inhomogeneous liquid to obtain c(r₁,r₂), using information about the well studied and resolved g⁽⁰⁾(r₁,r₂) and c⁽⁰⁾(r₁,r₂) for the parent homogeneous (⁽⁰⁾) system. In practical cases, where g(r₁,r₂) is available from experimental data in a discrete form, the resulting c(r₁,r₂) is expressed as an explicit function of g(r₁,r₂) in a discrete form. A weaker continuous form of solution is also obtained, in the form of an integral equation with finite integration limits. The result obtained with our formulation is tested against the exact solutions for the correlation and distribution functions of a one-dimensional inhomogeneous hard rod liquid. Following the success of that test, the formalism is extended to higher dimensional systems with explicit consideration of the two-dimensional liquid.

Approach to approximating the pair distribution function of inhomogeneous hard-sphere fluids

We introduce an approximation for the pair distribution function of the inhomogeneous hard sphere fluid. Our approximation makes use of our recently published averaged pair distribution function at contact, which has been shown to accurately reproduce the averaged pair distribution function at contact for inhomogeneous density distributions. This approach achieves greater computational efficiency than previous approaches by enabling the use of exclusively fixed-kernel convolutions and thus allowing an implementation using fast Fourier transforms. We compare results for our pair distribution approximation with two previously published works and Monte Carlo simulation, showing favorable results.

Dynamical density functional theory for colloidal dispersions including hydrodynamic interactions

A dynamical density functional theory (DDFT) for translational Brownian dynamics is derived which includes hydrodynamic interactions. The theory reduces to the simple Brownian DDFT proposed by Marconi and Tarazona (U. Marini Bettolo Marconi and P. Tarazona, J. Chem. Phys. 110, 8032 (1999); J. Phys.: Condens. Matter 12, A413 (2000)) when hydrodynamic interactions are neglected. The derivation is based on Smoluchowski's equation for the time evolution of the probability density with pairwise hydrodynamic interactions. The theory is applied to hard-sphere colloids in an oscillating spherical optical trap which switches periodically in time from a stable confining to an unstable potential. Rosenfeld's fundamental measure theory for the equilibrium density functional is used and hydrodynamics are incorporated on the Rotne-Prager level. The results for the time-dependent density profiles are compared to extensive Brownian dynamics simulations which are performed on the same Rotne-Prager level and excellent agreement is obtained. It is further found that hydrodynamic interactions damp and slow the dynamics of the confined colloid cluster in comparison to the same situation with neglected hydrodynamic interactions.

Dynamical density functional theory with hydrodynamic interactions and colloids in unstable traps

A density functional theory for colloidal dynamics is presented which includes hydrodynamic interactions between the colloidal particles. The theory is applied to the dynamics of colloidal particles in an optical trap which switches periodically in time from a stable to an unstable confining potential. In the absence of hydrodynamic interactions, the resulting density breathing mode exhibits huge single peaked oscillations in the trap center which become double peaked and damped by hydrodynamic interactions. The predicted dynamical density fields are in good agreement with Brownian dynamics computer simulations.

Depletion potentials induced by charged colloidal rods

We present direct depletion potential measurements for a single colloidal sphere close to a wall in suspensions of charged colloidal rods. In contrast to earlier studies of purely entropic systems (Helden et al. Phys. Rev. Lett. 2003, 90, 048301), here electrostatic interactions are important. These enhance the depletion attraction and lead to repulsive parts in the interaction potentials, indicating correlation effects between the rods.

Variational methods for the solution of the Ornstein-Zernicke equation in inhomogeneous systems

We show that the Ornstein-Zernicke equation and other equations of similar form obey a variational principle that can be used to derive approximate solutions. This method requires the use of an initial trial solution where the variational solution possesses a stationary "point" with respect to the trial solution when the latter is equal to the exact solution. We show that with even a very simple form of the trial solution the results are quite reasonable. Furthermore, we have demonstrated that by combining the variational method with an iterative expansion of the Ornstein-Zernicke equation it is possible to develop a self-consistent method of writing the direct correlation function.

Freezing transition of hard hyperspheres

We investigate the system of D-dimensional hard spheres in D-dimensional space, where D>3. For the fluid phase of these hyperspheres, we generalize scaled-particle theory to arbitrary D and furthermore use the virial expansion and the Percus-Yevick integral equation. For the crystalline phase, we adopt cell theory based on elementary geometrical assumptions about close-packed lattices. Regardless of the approximation applied, and for dimensions as high as D=50, we find a first-order freezing transition, which preempts the Kirkwood second-order instability of the fluid. The relative density jump increases with D, and a generalized Lindemann rule of melting holds. We have also used ideas from fundamental-measure theory to obtain a free energy density functional for hard hyperspheres. Finally, we have calculated the surface tension of a hypersphere fluid near a hard smooth (hyper-)wall within scaled-particle theory.

Three-dimensional confocal microscopy of colloids

Confocal microscopy is used in the study of colloidal gels, glasses, and binary fluids. We measure the three-dimensional positions of colloidal particles with a precision of approximately 50 nm (a small fraction of each particle's radius) and with a time resolution sufficient for tracking the thermal motions of several thousand particles at once. This information allows us to characterize the structure and the dynamics of these materials in qualitatively new ways, for example, by quantifying the topology of chains and clusters of particles as well as by measuring the spatial correlations between particles with high mobilities. We describe our experimental technique and describe measurements that complement the results of light scattering.

Binary hard-sphere fluids near a hard wall

By using the Rosenfeld density functional, we determine the number density profiles of both components of binary hard-sphere fluids close to a planar hard wall as well as the corresponding excess coverage and surface tension. The comparison with published simulation data demonstrates that the Rosenfeld functional, both its original version and sophistications thereof, is superior to previous approaches, and exhibits the same excellent accuracy as known from studies of the corresponding one-component system.

Density correlations in lattice gases in contact with a confining wall

A discrete version of classical density functional theory applicable to lattice gases or Ising spin systems is proposed, which accounts for the requirement of particle-hole symmetry in the presence of pairwise forces. Results of our theory for density profiles and two-particle correlation functions in two-dimensional strip geometries compare favorably with Monte Carlo simulations. Some problems with standard "weighted-density" approximation schemes, when applied to lattice gases, are pointed out.

Interfacial free energy of hard-sphere fluids and solids near a hard wall

A hard-sphere system near a planar structureless hard wall is considered in thermodynamic equilibrium. The associated interfacial free energies are calculated both for a bulk fluid and a bulk face-centered-cubic crystal along (111), (110), and (100) orientation. Combining Monte Carlo simulations and thermodynamic integration, we obtain the wall-fluid and the wall-solid interfacial free energy over the whole range of possible bulk densities. The "exact" computer simulation data are compared to theoretical approximations. For moderate bulk densities, the wall-fluid interfacial free energies compare reasonably well with scaled-particle theory and density functional results. For the wall-crystal interface, we propose a simple analytical cell theory which yields good agreement with our simulation data over the whole range of bulk crystal densities.