Statistical thermodynamics of supercapacitors and blue engines

We study the thermodynamics of electrode-electrolyte systems, for instance supercapacitors filled with an ionic liquid or blue-energy devices filled with river- or sea water. By a suitable mapping of thermodynamic variables, we identify a strong analogy with classical heat engines. We introduce several Legendre transformations and Maxwell relations. We argue that one should distinguish between the differential capacity at constant ion number and at constant ion chemical potential, and derive a relation between them that resembles the standard relation between heat capacity at constant volume and constant pressure. Finally, we consider the probability distribution of the electrode charge at a given electrode potential, the standard deviation of which is given by the differential capacity.Comment: To be published in "New challenges in Electrostatics of Soft and Disordered Matter", Eds. J. Dobnikar, A. Naji, D.Dean and R. Podgornik, PanStanford Pub. Singapore (2012

Solvo-osmotic flow in electrolytic mixtures

We show that an electric field parallel to an electrically neutral surface can generate flow of electrolytic mixtures in small channels. We term this solvo-osmotic flow, since the flow is induced by the asymmetric preferential solvation of ions at the liquid-solid interface. The generated flow is comparable in magnitude to the ubiquitous electro-osmotic flow at charged surfaces, but for a fixed surface charge density, it differs qualitatively in its dependence on ionic strength. Solvo-osmotic flow can also be sensitively controlled with temperature. We derive a modified Helmholtz-Smoluchowski equation that accounts for these effects.Comment: 11 pages, 4 figure

Self-propulsion mechanism of active Janus particles in near-critical binary mixtures

Gold-capped Janus particles immersed in a near-critical binary mixture can be propelled using illumination. We employ a non-isothermal diffuse interface approach to investigate the self-propulsion mechanism of a single colloid. We attribute the motion to body forces at the edges of a micronsized droplet that nucleates around the particle. Thus, the often-used concept of a surface velocity cannot account for the self-propulsion. The particle's swimming velocity is related to the droplet shape and size, which is determined by a so-called critical isotherm. Two distinct swimming regimes exist, depending on whether the droplet partially or completely covers the particle. Interestingly, the dependence of the swimming velocity on temperature is non-monotonic in both regimes.Comment: 5 pages, 3 figure

Poisson-Boltzmann cell model for heterogeneously charged colloids

We introduce the Poisson-Boltzmann cell model for spherical colloidal particles with a heterogeneous surface charge distribution. This model is obtained by generalizing existing cell models for mixtures of homogeneously charged colloidal spheres. Our new model has similar features as Onsager's second-virial theory for liquid crystals, but it predicts no orientational ordering if there is no positional ordering. This implies that all phases of heterogeneously charged colloids that are liquid-like with respect to translational degrees of freedom are also isotropic with respect to particle orientation.Comment: 9 pages, 3 figure

The effect of flexibility and bend angle on the phase diagram of hard colloidal boomerangs

We study the effect of flexibility and bend angle on systems of hard semiflexible boomerangs. These are modelled as two rodlike segments joined at one end with an angle that can fluctuate about a preferred angle. We use a second-virial theory for semiflexible chains with two segments, and numerically solve for the full orientation distribution function as a function of the four angles that determine the boomerang's orientation. We plot the single segment distributions as a function of two angles as well as the interarm angle distribution. For stiff boomerangs, we find prolate, oblate, and biaxial nematic phases depending on the bend angle and density, in partial agreement with previous results on rigid boomerangs. For the case that the preferred interarm angle is $90^\circ$, however, we find that the biaxial nematic phase has four-fold rather than two-fold rotational symmetry, and thus requires fourth-rank order parameters to describe it. In addition, we find that flexibility drastically reduces the region of stability for the biaxial nematic phase, with the prolate nematic becoming more favourable.Comment: 14 pages, 7 figure

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 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

Tuning colloid-interface interactions by salt partitioning

We show that the interaction of an oil-dispersed colloidal particle with an oil-water interface is highly tunable from attractive to repulsive, either by varying the sign of the colloidal charge via charge regulation, or by varying the difference in hydrophilicity between the dissolved cations and anions. In addition, we investigate the yet unexplored interplay between the self-regulated colloidal surface charge distribution with the planar double layer across the oil-water interface and the spherical one around the colloid. Our findings explain recent experiments and have direct relevance for tunable Pickering emulsions.Comment: 5+4 pages, 3+4 figures, V2: improved text and figures, more detailed supplementar

Harvesting vibrational energy with liquid-bridged electrodes: thermodynamics in mechanically and electrically driven RC-circuits

We theoretically study a vibrating pair of parallel electrodes bridged by a (deformed) liquid droplet, which is a recently developed microfluidic device to harvest vibrational energy. The device can operate with various liquids, including liquid metals, electrolytes, as well as ionic liquids. We numerically solve the Young-Laplace equation for all droplet shapes during a vibration period, from which the time-dependent capacitance follows that serves as input for an equivalent circuit model. We first investigate two existing energy harvesters (with a constant and a vanishing bias potential), for which we explain an open issue related to their optimal electrode separations, which is as small as possible or as large as possible in the two cases, respectively. Then we propose a new engine with a time-dependent bias voltage, with which the harvested work and the power can be increased by orders of magnitude at low vibration frequencies and by factors 2-5 at high frequencies, where frequencies are to be compared to the inverse RC-time of the circuit.Comment: 9 pages, 6 figure

Connectedness percolation of hard convex polygonal rods and platelets

The properties of polymer composites with nanofiller particles change drastically above a critical filler density known as the percolation threshold. Real nanofillers, such as graphene flakes and cellulose nanocrystals, are not idealized disks and rods but are often modeled as such. Here we investigate the effect of the shape of the particle cross section on the geometric percolation threshold. Using connectedness percolation theory and the second-virial approximation, we analytically calculate the percolation threshold of hard convex particles in terms of three single-particle measures. We apply this method to polygonal rods and platelets and find that the universal scaling of the percolation threshold is lowered by decreasing the number of sides of the particle cross section. This is caused by the increase of the surface area to volume ratio with decreasing number of sides.Comment: 7 pages, 3 figures; added references, corrected typo, results unchange

Dynamic Stern layers in charge-regulating electrokinetic systems: three regimes from an analytical approach

We present analytical solutions for the electrokinetics at a charged surface with both non-zero Stern-layer conductance and finite chemical reaction rates. We have recently studied the same system numerically [Werkhoven {\em et al.}, Phys. Rev. Lett. {\bf 120}, 264502 (2018)], and have shown that an applied pressure drop across the surface leads to a non-trivial, laterally heterogeneous surface charge distribution at steady state. In this work, we linearise the governing electrokinetic equations to find closed expressions for the surface charge profile and the generated streaming electric field. The main results of our calculations are the identification of three important length and time scales that govern the charge distribution, and consequently the classification of electrokinetic systems into three distinct regimes. The three governing time scales can be associated to (i) the chemical reaction, (ii) diffusion in the Stern layer, and (iii) conduction in the Stern layer, where the dominating (smallest) time scale characterises the regime. In the reaction-dominated regime we find a constant surface charge with an edge effect, and recover the Helmholtz-Smoluchowski equation. In the other two regimes, we find that the surface charge heterogeneity extends over the entire surface, either linearly (diffusion-dominated regime) or nonlinearly (conduction-dominated regime).Comment: Accepted for publication in European Physical Journal: Special Topic