arXiv subjects
Publications and source records attributed to Andreas Härtel.
This paper constitutes a presentation of work in progress at a discussion session of the conference Dense ionic fluids Faraday Discussion, 8-10 July 2024, London, and is published on pages 293-295 in Ref. [Faraday Discuss. 2024, volume 253, page 289].
The electric double layer (EDL) has a pivotal role in screening charges on surfaces as in supercapacitor electrodes or colloidal and polymer solutions. Its structure is determined by correlations between the finite-sized ionic charge carriers of the underlying electrolyte and, this way, these correlations affect the properties of the EDL and of applications utilizing EDLs. We study the structure of EDLs within classical density functional theory (DFT) in order to uncover whether a structural transition in the first layer of the EDL that is driven by changes in the surface potential depends on specific particle interactions or has a general footing. This transition has been found in full-atom simulations. Thus far, investigating the in-plane structure of the EDL for the primitive model (PM) using DFT proved a challenge. We show here that the use of an appropriate functional predicts the in-plane structure of EDLs in excellent agreement with molecular dynamics (MD) simulations. This provides the playground to investigate how the structure factor within a layer parallel to a charged surface changes as function of both the applied surface potential and its separation from the surface. We discuss pitfalls in properly defining an in-plane structure factor and fully map out the structure of the EDL within the PM for a wide range of electrostatic electrode potentials. However, we do not find any signature of a structural crossover and conclude that the previously reported effect is not fundamental but rather occurs due to the specific force field of ions used in the simulations.
Underscreening is a collective term for charge correlations in electrolytes decaying slower than the Debye length. Anomalous underscreening refers to phenomenology that cannot be attributed alone to steric interactions. Experiments with concentrated electrolytes and ionic fluids report anomalous underscreening, which so far has not been observed in simulation. We present Molecular Dynamics simulation results exhibiting anomalous underscreening that can be connected to cluster formation. A theory that accounts for ion pairing confirms the trend. Our results challenge the classic understanding of dense electrolytes impacting the design of technologies for energy storage and conversion.
The primitive model describes ions by point charges with an additional hard-core interaction. In classical density-functional theory the mean-field electrostatic contribution can be obtained from the first order of a functional perturbation of the pair potential for an uncharged reference system of hard spheres. This mean-field electrostatic term particularly contributes at particle separations that are forbidden due to hard-core overlap. In this work we modify the mean-field contribution such that the pair potential is constant for distances smaller than the contact distance of the ions. We motivate our modification by the underlying splitting of the potential, which is similar to the splitting of the Weeks-Chandler-Andersen potential and leads to higher-order terms in the respective expansion of the functional around the reference system. The resulting formalism involves weighted densities similar to the ones found in fundamental measure theory. To test our modifications, we analyze and compare density profiles, direct and total correlation functions, and the thermodynamic consistency of the functional via a widely established sum rule and the virial pressure formula for our modified functional, for established functionals, and for data from computer simulations. We found that our modifications clearly show improvements compared to the standard mean-field functional, especially when predicting layering effects and direct correlation functions in high concentration scenarios; for the latter we also find improved consistency when calculated via different thermodynamic routes. In conclusion, we demonstrate how modifications towards higher order corrections beyond mean-field functionals can be made and how they perform, by this providing a basis for systematic future improvements in classical density-functional theory for the description of electrostatic interactions.
Recently the reversible heat production during the electric double layer (EDL) buildup in a sodium chloride solution was measured experimentally [Janssen et al., Phys. Rev. Lett. 119, 166002 (2017)] and matched with theoretical predictions from density functional theory and molecular dynamics simulations [Glatzel et al., J. Chem. Phys. 154, 064901 (2021)]. In the latter, it was found that steric interactions of ions with the electrode's walls, which result in the so-called Stern layer, are sufficient to explain the experimental results. As only symmetric ion sizes in a restricted primitive model were examined, it is instructive to investigate systems of unequal ion sizes that lead to modified Stern layers. In this work, we explore the impact of ion asymmetry on the reversible heat production for each electrode separately. In this context, we further study an extension of the primitive model where hydration shells of ions can evade in the vicinity of electrode's walls. We find a strong dependence on system parameters such as the particle sizes and the total volume taken by particles. Here, we even found situations where one electrode was heated and the other electrode was cooled at the same time during charging, while, in sum, both electrodes together behaved very similarly to the already mentioned experimental results. Thus, heat production should also be measured in experiments for each electrode separately. By this, the importance of certain ingredients that we proposed to model electrolytes could be confirmed or ruled out experimentally, finally leading to a deeper understanding of the physics of EDLs.
Several modern technologies for energy storage and conversion are based on the screening of electric charge on the surface of porous electrodes by ions in an adjacent electrolyte. This so-called electric double layer (EDL) exhibits an intricate interplay with the electrolyte's temperature that was the focus of several recent studies. In one of them, Janssen et al. [Phys. Rev. Lett. 119, 166002 (2017)] experimentally determined the ratio $\mathcal{Q}_\text{rev}/W_\text{el}$ of reversible eat flowing into a supercapacitor during an isothermal charging process and the electric work applied therein. To rationalize that data, here, we determine $\mathcal{Q}_\text{rev}/W_\text{el}$ within different models of the EDL using theoretical approaches like density functional theory (DFT) as well as molecular dynamics simulations. Applying mainly the restricted primitive model, we find quantitative support for a speculation of Janssen et al. that steric ion interactions are key to the ratio $\mathcal{Q}_\text{rev}/W_\text{el}$. Here, we identified the entropic contribution of certain DFT functionals, which grants direct access to the reversible heat. We further demonstrate how $\mathcal{Q}_\text{rev}/W_\text{el}$ changes when calculated in different thermodynamic ensembles and processes. We show that the experiments of Janssen et al. are explained best by a charging process at fixed bulk density, or in a "semi-canonical" system. Finally, we find that $\mathcal{Q}_\text{rev}/W_\text{el}$ significantly depends on parameters as pore and ion size, salt concentration, and valencies of the cat- and anions of the electrolyte. Our findings can guide further heat production measurements and can be applied in studies on, for instance, nervous conduction, where reversible heat is a key element.
Electrolytes play an important role in a plethora of applications ranging from energy storage to biomaterials. Notwithstanding this, the structure of concentrated electrolytes remains enigmatic. Many theoretical approaches attempt to model the concentrated electrolytes by introducing the idea of ion pairs, with ions either being tightly `paired' with a counter-ion, or `free' to screen charge. In this study we reframe the problem into the language of computational statistics, and test the null hypothesis that all ions share the same local environment. Applying the framework to molecular dynamics simulations, we show that this null hypothesis is not supported by data. Our statistical technique suggests the presence of distinct local ionic environments; surprisingly, these differences arise in like charge correlations rather than unlike charge attraction. The resulting fraction of particles in non-aggregated environments shows a universal scaling behaviour across different background dielectric constants and ionic concentrations.
We present a new approach to derive the connectivity properties of pairwise interacting n-body systems in thermal equilibrium. We formulate an integral equation that relates the pair connectedness to the distribution of nearest neighbors. For one-dimensional systems with nearest-neighbor interactions, the nearest-neighbor distribution is, in turn, related to the pair correlation function g through a simple integral equation. As a consequence, for those systems, we arrive at an integral equation relating g to the pair connectedness, which is readily solved even analytically if g is specified analytically. We demonstrate the procedure for a variety of pair-potentials including fully penetrable spheres as well as impenetrable spheres, the only two systems for which analytical results for the pair connectedness exist. However, the approach is not limited to nearest-neighbor interactions in one dimension. Hence, we also outline the treatment of external fields and long-ranged interactions, and we illustrate how the formalism can applied to higher-dimensional systems using the three-dimensional ideal gas as an example.
The decay of correlations in ionic fluids is a classical problem in soft matter physics that underpins applications ranging from controlling colloidal self-assembly to batteries and supercapacitors. The conventional wisdom, based on analyzing a solvent-free electrolyte model, suggests that all correlation functions between species decay with a common decay length in the asymptotic far field limit. Nonetheless, a solvent is present in many electrolyte systems. We show using an analytical theory and molecular dynamics simulations that multiple decay lengths can coexist in the asymptotic limit as well as at intermediate distances once a hard sphere solvent is considered. Our analysis provides an explanation for the recently observed discontinuous change in the structural force across a thin film of ionic liquid-solvent mixtures as the composition is varied, as well as reframes recent debates in the literature about the screening length in concentrated electrolytes.
Self-propelled Brownian particles show rich out-of-equilibrium physics, for instance, the motility-induced phase separation (MIPS). While decades of studying the structure of liquids have established a deep understanding of passive systems, not much is known about correlations in active suspensions. In this work we derive an approximate analytic theory for three-body correlations and forces in systems of active Brownian disks starting from the many-body Smoluchowski equation. We use our theory to predict the conditional forces that act on a tagged particle and their dependence on the propulsion speed of self-propelled disks. We identify preferred directions of these forces in relation to the direction of propulsion and the positions of the surrounding particles. We further relate our theory to the effective swimming speed of the active disks, which is relevant for the physics of MIPS. To test and validate our theory, we additionally run particle-resolved computer simulations, for which we explicitly calculate the three-body forces. In this context, we discuss the modeling of active Brownian swimmers with nearly hard interaction potentials. We find very good agreement between our simulations and numerical solutions of our theory, especially for the nonequilibrium pair-distribution function. For our analytical results, we carefully discuss their range of validity in the context of the different levels of approximation we applied. This discussion allows us to study the individual contribution of particles to three-body forces and to the emerging structure. Thus, our work sheds light on the collective behavior, provides the basis for further studies of correlations in active suspensions, sheds new light onto the collective behavior, and makes a step towards an emerging liquid state theory.
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.
The ongoing scientific interest in the properties and structure of electric double layers (EDLs) stems from their pivotal role in (super)capacitive energy storage, energy harvesting, and water treatment technologies. Classical density functional theory (DFT) is a promising framework for the study of the in- and out-of-plane structural properties of double layers. Supported by molecular dynamics simulations, we demonstrate the adequate performance of DFT for analyzing charge layering in the EDL perpendicular to the electrodes. We discuss charge storage and capacitance of the EDL and the impact of screening due to dielectric solvents. We further calculate, for the first time, the in-plane structure of the EDL within the framework of DFT. While our out-of-plane results already hint at structural in-plane transitions inside the EDL, which have been observed recently in simulations and experiments, our DFT approach performs poorly in predicting in-plane structure in comparison to simulations. However, our findings isolate fundamental issues in the theoretical description of the EDL within the primitive model and point towards limitations in the performance of DFT in describing the out-of-plane structure of the EDL at high concentrations and potentials.
The fundamental measure approach to classical density functional theory has been shown to be a powerful tool to predict various thermodynamic properties of hard-sphere systems. We employ this approach to determine not only one-particle densities but also two-particle correlations in binary and six-component mixtures of hard spheres in the vicinity of a hard wall. The broken isotropy enables us to carefully test a large variety of theoretically predicted two-particle features by quantitatively comparing them to the results of Brownian dynamics simulations. Specifically, we determine and compare the one-particle density, the total correlation functions, their contact values, and the force distributions acting on a particle. For this purpose, we follow the compressibility route and theoretically calculate the direct correlation functions by taking functional derivatives. We usually observe an excellent agreement between theory and simulations, except for small deviations in cases where local crystal-like order sets in. Our results set the course for further investigations on the consistency of functionals as well as for structural analysis on, e.g., the primitive model. In addition, we demonstrate that due to the suppression of local crystallization, the predictions of six-component mixtures are better than those in bidisperse or monodisperse systems. Finally, we are confident that our results of the structural modulations induced by the wall lead to a deeper understanding of ordering in anisotropic systems in general, the onset of heterogeneous crystallization, caging effects, and glassy dynamics close to a wall, as well as structural properties in systems with confinement.
Capacitive mixing (CAPMIX) and capacitive deionization (CDI) are promising candidates for harvesting clean, renewable energy and for the energy efficient production of potable water, respectively. Both CAPMIX and CDI involve water-immersed porous carbon (supercapacitors) electrodes at voltages of the order of hundreds of millivolts, such that counter-ionic packing is important for the electric double layer (EDL) which forms near the surface of these porous materials. Thus, we propose a density functional theory (DFT) to model the EDL, where the White-Bear mark II fundamental measure theory functional is combined with a mean-field Coulombic and a mean spherical approximation-type correction to describe the interplay between dense packing and electrostatics, in good agreement with molecular dynamics simulations. We discuss the concentration-dependent potential rise due to changes in the chemical potential in capacitors in the context of an over-ideal theoretical description and its impact on energy harvesting and water desalination. Compared to less elaborate mean-field models our DFT calculations reveal a higher work output for blue-energy cycles and a higher energy demand for desalination cycles.
We show that sustainably harvesting 'blue' energy from the spontaneous mixing process of fresh and salty water can be boosted by varying the water temperature during a capacitive mixing process. Our modified Poisson-Boltzmann calculations predict a strong temperature dependence of the electrostatic potential of a charged electrode in contact with an adjacent aqueous 1:1 electrolyte. We propose to exploit this dependence to boost the efficiency of capacitive blue engines, which are based on cyclically charging and discharging nanoporous supercapacitors immersed in salty and fresh water, respectively [D. Brogioli, Phys. Rev. Lett. 103, 058501 (2009)]. We show that the energy output of blue engines can be increased by a factor of order two if warm (waste-heated) fresh water is mixed with cold sea water. Moreover, the underlying physics can also be used to optimize the reverse process of capacitive desalination of water.
We review recent progress in the theoretical description of anisotropic hard colloidal particles. The shapes considered range from rods and dumbbells to rounded cubes, polyhedra and to biaxial particles with arbitrary shape. Our focus is on both static and dynamical density functional theory and on computer simulations. We describe recent results for the structure, dynamics and phase behaviour in the bulk and in various confining geometries, e.g. established by two parallel walls which reduce the dimensionality of the system to two dimensions. We also include recent theoretical modelling for active particles, which are autonomously driven by some intrinsic motor, and highlight their fascinating nonequilibrium dynamics and collective behaviour.
A combination of fundamental measure density functional theory and Monte Carlo computer simulation is used to determine the orientation-resolved interfacial tension and stiffness for the equilibrium hard-sphere crystal-fluid interface. Microscopic density functional theory is in quantitative agreement with simulations and predicts a tension of 0.66 kT/σ^2 with a small anisotropy of about 0.025 kT and stiffnesses with e.g. 0.53 kT/σ^2 for the (001) orientation and 1.03 kT/σ^2 for the (111) orientation. Here kT is denoting the thermal energy and σthe hard sphere diameter. We compare our results with existing experimental findings.