Water, Not Salt, Causes Most of the Seebeck Effect of Nonisothermal Aqueous Electrolytes.

A temperature difference between two electrolyte-immersed electrodes often yields a voltage Δψ between them. This electrolyte Seebeck effect is usually explained by cations and anions flowing differently in thermal gradients. However, using molecular simulations, we found almost the same Δψ for cells filled with pure water as with aqueous alkali halides. Water layering and orientation near polarizable electrodes cause a large temperature-dependent potential drop χ there. The difference in χ of hot and cold electrodes captures most of the thermovoltage, Δψ≈χ_{hot}-χ_{cold}.

Crowding-Regulated Binding of Divalent Biomolecules.

Macromolecular crowding affects biophysical processes as diverse as diffusion, gene expression, cell growth, and senescence. Yet, there is no comprehensive understanding of how crowding affects reactions, particularly multivalent binding. Herein, we use scaled particle theory and develop a molecular simulation method to investigate the binding of monovalent to divalent biomolecules. We find that crowding can increase or reduce cooperativity-the extent to which the binding of a second molecule is enhanced after binding a first molecule-by orders of magnitude, depending on the sizes of the involved molecular complexes. Cooperativity generally increases when a divalent molecule swells and then shrinks upon binding two ligands. Our calculations also reveal that, in some cases, crowding enables binding that does not occur otherwise. As an immunological example, we consider immunoglobulin G-antigen binding and show that crowding enhances its cooperativity in bulk but reduces it when an immunoglobulin G binds antigens on a surface.

Simulating the charging of cylindrical electrolyte-filled pores with the modified Poisson-Nernst-Planck equations.

Understanding how electrolyte-filled porous electrodes respond to an applied potential is important to many electrochemical technologies. Here, we consider a model supercapacitor of two blocking cylindrical pores on either side of a cylindrical electrolyte reservoir. A stepwise potential difference 2Φ between the pores drives ionic fluxes in the setup, which we study through the modified Poisson-Nernst-Planck equations, solved with finite elements. We focus our discussion on the dominant timescales with which the pores charge and how these timescales depend on three dimensionless numbers. Next to the dimensionless applied potential Φ, we consider the ratio R/Rb of the pore's resistance R to the bulk reservoir resistance Rb and the ratio rp/λ of the pore radius rp to the Debye length λ. We compare our data to theoretical predictions by Aslyamov and Janssen (Φ), Posey and Morozumi (R/Rb), and Henrique, Zuk, and Gupta (rp/λ). Through our numerical approach, we delineate the validity of these theories and the assumptions on which they were based.

Dynamic density functional theory for the charging of electric double layer capacitors.

We consider the charging of a model capacitor comprised of two planar electrodes and an electrolyte. Upon switching on a voltage difference, electric double layers build up in this setup, which we characterize with a classical dynamic density functional theory (DDFT) that accounts for electrostatic correlations and for molecular excluded volume of finite-sized ions and solvent molecules. Our DDFT predicts the electrode charge Q(t) to form exponentially with two timescales: at early times, the system relaxes on the RC time, namely, λDL/[D(2 + σ/λD)], with λD being the Debye length, L being the electrode separation, σ being the ion diameter, and D being the ionic diffusivity. Contrasting an earlier DDFT study, this early-time response does not depend on the applied potential. At late times, the capacitor relaxes with a relaxation time proportional to the diffusion time L2/D.

ELECTRODE: An electrochemistry package for atomistic simulations.

Constant potential methods (CPMs) enable computationally efficient simulations of the solid-liquid interface at conducting electrodes in molecular dynamics. They have been successfully used, for example, to realistically model the behavior of ionic liquids or water-in-salt electrolytes in supercapacitors and batteries. CPMs model conductive electrodes by updating charges of individual electrode atoms according to the applied electric potential and the (time-dependent) local electrolyte structure. Here, we present a feature-rich CPM implementation, called ELECTRODE, for the Large-scale Atomic/Molecular Massively Parallel Simulator, which includes a constrained charge method and a thermo-potentiostat. The ELECTRODE package also contains a finite-field approach, multiple corrections for nonperiodic boundary conditions of the particle-particle particle-mesh solver, and a Thomas-Fermi model for using nonideal metals as electrodes. We demonstrate the capabilities of this implementation for a parallel-plate electrical double-layer capacitor, for which we have investigated the charging times with the different implemented methods and found an interesting relationship between water and ionic dipole relaxations. To prove the validity of the one-dimensional correction for the long-range electrostatics, we estimated the vacuum capacitance of two coaxial carbon nanotubes and compared it to structureless cylinders, for which an analytical expression exists. In summary, the ELECTRODE package enables efficient electrochemical simulations using state-of-the-art methods, allowing one to simulate even heterogeneous electrodes. Moreover, it allows unveiling more rigorously how electrode curvature affects the capacitance with the one-dimensional correction.

Transmission Line Circuit and Equation for an Electrolyte-Filled Pore of Finite Length.

I discuss the strong link between the transmission line (TL) equation and the TL circuit model for the charging of an electrolyte-filled pore of finite length. In particular, I show how Robin and Neumann boundary conditions to the TL equation, proposed by others on physical grounds, also emerge in the TL circuit subject to a stepwise potential. The pore relaxes with a timescale τ, an expression for which consistently follows from the TL circuit, TL equation, and from the pore's known impedance. An approximation to τ explains the numerically determined relaxation time of the stack-electrode model of Lian et al. [Phys. Rev. Lett. 124, 076001 (2020)PRLTAO0031-900710.1103/PhysRevLett.124.076001].

Divalent ligand-monovalent molecule binding.

Simultaneous binding of a divalent ligand to two identical monovalent molecules is a widespread phenomenon in biology and chemistry. Here, we describe how two such monovalent molecules B bind to a divalent ligand AA to form the intermediate and final complexes AA·B and AA·B2. Cases wherein the total concentration [AA]T is either much larger or much smaller than the total concentration [B]T have been studied earlier, but a systematic description of comparable concentrations [AA]T and [B]T is missing. Here, we present numerical and analytical results for the concentrations [AA·B] and [AA·B2] for the entire range 0 < [B]T/[AA]T < ∞. Specifically, we theoretically study three types of experimental procedures: dilution of AA and B at fixed [B]T/[AA]T, addition of AA at fixed [B]T, and addition of B at fixed [AA]T. When [AA]T and [B]T are comparable, the concentrations of free ligands and molecules both decrease upon binding. Such depletion is expected to be important in cellular contexts, e.g., in antigen detection and in coincidence detection of proteins or lipids.

On the time-dependent electrolyte Seebeck effect.

Single-ion Soret coefficients αi characterize the tendency of ions in an electrolyte solution to move in a thermal gradient. When these coefficients differ between cations and anions, an electric field can be generated. For this so-called electrolyte Seebeck effect to occur, different thermodiffusive fluxes need to be blocked by boundaries-electrodes, for example. Local charge neutrality is then broken in the Debye-length vicinity of the electrodes. Confusingly, many authors point to these regions as the source of the thermoelectric field yet ignore them in derivations of the time-dependent Seebeck coefficient S(t), giving a false impression that the electrolyte Seebeck effect is purely a bulk phenomenon. Without enforcing local electroneutrality, we derive S(t) generated by a binary electrolyte with arbitrary ionic valencies subject to a time-dependent thermal gradient. Next, we experimentally measure S(t) for five acids, bases, and salts near titanium electrodes. For the steady state, we find S ≈ 2 mV K-1 for many electrolytes, roughly one order of magnitude larger than the predictions based on literature αi. We fit our expression for S(t) to the experimental data, treating the αi as fit parameters, and also find larger-than-literature values, accordingly.

Reversible heat production during electric double layer buildup depends sensitively on the electrolyte and its reservoir.

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 Qrev/Wel of reversible heat flowing into a supercapacitor during an isothermal charging process and the electric work applied therein. To rationalize that data, here, we determine Qrev/Wel within different models of the EDL using theoretical approaches such as 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 Qrev/Wel. Here, we identified the entropic contribution of certain DFT functionals, which grants direct access to the reversible heat. We further demonstrate how Qrev/Wel 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 Qrev/Wel significantly depends on parameters such as pore and ion size, salt concentration, and valencies of the cations 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.

Blessing and Curse: How a Supercapacitor's Large Capacitance Causes its Slow Charging.

The development of novel electrolytes and electrodes for supercapacitors is hindered by a gap of several orders of magnitude between experimentally measured and theoretically predicted charging time scales. Here, we propose an electrode model, containing many parallel stacked electrodes, that explains the slow charging dynamics of supercapacitors. At low applied potentials, the charging behavior of this model is described well by an equivalent circuit model. Conversely, at high potentials, charging dynamics slow down and evolve on two relaxation time scales: a generalized RC time and a diffusion time, which, interestingly, become similar for porous electrodes. The charging behavior of the stack-electrode model presented here helps to understand the charging dynamics of porous electrodes and qualitatively agrees with experimental time scales measured with porous electrodes.

Driving an electrolyte through a corrugated nanopore.

We characterize the dynamics of a z - z electrolyte embedded in a varying-section channel. In the linear response regime, by means of suitable approximations, we derive the Onsager matrix associated with externally enforced gradients in electrostatic potential, chemical potential, and pressure, for both dielectric and conducting channel walls. We show here that the linear transport coefficients are particularly sensitive to the geometry and the conductive properties of the channel walls when the Debye length is comparable to the channel width. In this regime, we found that one pair of off-diagonal Onsager matrix elements increases with the corrugation of the channel transport, in contrast to all other elements which are either unaffected by or decrease with increasing corrugation. Our results have a possible impact on the design of blue-energy devices as well as on the understanding of biological ion channels through membranes.

Reversible Heating in Electric Double Layer Capacitors.

A detailed comparison is made between different viewpoints on reversible heating in electric double layer capacitors. We show in the limit of slow charging that a combined Poisson-Nernst-Planck and heat equation, first studied by d'Entremont and Pilon [J. Power Sources 246, 887 (2014)JPSODZ0378-775310.1016/j.jpowsour.2013.08.024], recovers the temperature changes as predicted by the thermodynamic identity of Janssen et al. [Phys. Rev. Lett. 113, 268501 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.268501], and disagrees with the approximative model of Schiffer et al. [J. Power Sources 160, 765 (2006)JPSODZ0378-775310.1016/j.jpowsour.2005.12.070] that predominates the literature. The thermal response to the adiabatic charging of supercapacitors contains information on electric double layer formation that has remained largely unexplored.

Coulometry and Calorimetry of Electric Double Layer Formation in Porous Electrodes.

Coulometric measurements on salt-water-immersed nanoporous carbon electrodes reveal, at a fixed voltage, a charge decrease with increasing temperature. During far-out-of-equilibrium charging of these electrodes, calorimetry indicates the production of both irreversible Joule heat and reversible heat, the latter being associated with entropy changes during electric double layer (EDL) formation in the nanopores. These measurements grant experimental access-for the first time-to the entropic contribution of the grand potential; for our electrodes, this amounts to roughly 25% of the total grand potential energy cost of EDL formation at large applied potentials, in contrast with point-charge model calculations that predict 100%. The coulometric and calorimetric experiments show a consistent picture of the role of heat and temperature in EDL formation and provide hitherto unused information to test against EDL models.

Boosting capacitive blue-energy and desalination devices with waste heat.

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 2 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.

Stability of a biomembrane tube covered with proteins.

Membrane tubes are essential structural features in cells that facilitate biomaterial transport and inter- and intracellular signaling. The shape of these tubes can be regulated by the proteins that surround and adhere to them. We study the stability of a biomembrane tube coated with proteins by combining linear stability analysis, out-of-equilibrium hydrodynamic calculations, and numerical solutions of a Helfrich-like membrane model. Our analysis demonstrates that both long- and short-wavelength perturbations can destabilize the tubes. Numerical simulations confirm the derived linear stability criteria and yield the nonlinearly perturbed vesicle shapes. Our study highlights the interplay between membrane shape and protein density, where the shape instability concurs with a redistribution of proteins into a banded pattern.

From Frequency Domain to Time Transient Methods for Halide Perovskite Solar Cells: The Connections of IMPS, IMVS, TPC, and TPV.

The correlation of different methods of measurement can become an important tool to identify the dominant physical elements that govern the electronic and ionic dynamics in perovskite solar cells. The diverse phenomena underlying the response of halide perovskite materials to different stimuli are reflected in time-domain measurements, where transients appear with time scales spanning orders of magnitude, from nanoseconds to hours. We discuss the connection between different frequency- and time-domain methods to probe the voltage and current response of halide perovskite solar cells to different small perturbations. To solve the frequency-to-time transformation, we start from models of the transfer function of intensity-modulated photocurrent spectroscopy (IMPS) and derive the associated impulse response function, the transient photocurrent (TPC), in response to a short light pulse. Similarly, we determine the transient photovoltage (TPV) starting from the intensity-modulated photovoltage spectroscopy (IMVS) transfer function. We also discuss the open-circuit voltage decays (OCVD). We first show the response of simple equivalent circuit models, and then we treat the full model for generation-diffusion-recombination of electrons that shows a spiraling loop in IMPS. This model gives rise to overshoots in the time domain.

How to speed up ion transport in nanopores.

Electrolyte-filled subnanometre pores exhibit exciting physics and play an increasingly important role in science and technology. In supercapacitors, for instance, ultranarrow pores provide excellent capacitive characteristics. However, ions experience difficulties in entering and leaving such pores, which slows down charging and discharging processes. In an earlier work we showed for a simple model that a slow voltage sweep charges ultranarrow pores quicker than an abrupt voltage step. A slowly applied voltage avoids ionic clogging and co-ion trapping-a problem known to occur when the applied potential is varied too quickly-causing sluggish dynamics. Herein, we verify this finding experimentally. Guided by theoretical considerations, we also develop a non-linear voltage sweep and demonstrate, with molecular dynamics simulations, that it can charge a nanopore even faster than the corresponding optimized linear sweep. For discharging we find, with simulations and in experiments, that if we reverse the applied potential and then sweep it to zero, the pores lose their charge much quicker than they do for a short-circuited discharge over their internal resistance. Our findings open up opportunities to greatly accelerate charging and discharging of subnanometre pores without compromising the capacitive characteristics, improving their importance for energy storage, capacitive deionization, and electrochemical heat harvesting.

Curvature affects electrolyte relaxation: Studies of spherical and cylindrical electrodes.

With two minimal models, I study how electrode curvature affects the response of electrolytes to applied electrostatic potentials. For flat electrodes, Bazant et al. [Phys. Rev. E 70, 021506 (2004)PLEEE81539-375510.1103/PhysRevE.70.021506] popularized the RC timescale λ_{D}L/D, with λ_{D} being the Debye length, 2L the electrode separation, and D the ionic diffusivity. For thin electric double layers near concentric spherical and coaxial cylindrical electrodes, I show here that equivalent circuit models again predict the correct ionic relaxation timescales. Importantly, these timescales explicitly depend on both electrode radii, not simply on their difference.