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

Isotropic-nematic transition in hard-rod fluids: relation between continuous and restricted-orientation models

We explore models of hard-rod fluids with a finite number of allowed orientations, and construct their bulk phase diagrams within Onsager's second virial theory. For a one-component fluid, we show that the discretization of the orientations leads to the existence of an artificial (almost) perfectly aligned nematic phase, which coexists with the (physical) nematic phase if the number of orientations is sufficiently large, or with the isotropic phase if the number of orientations is small. Its appearance correlates with the accuracy of sampling the nematic orientation distribution within its typical opening angle. For a binary mixture this artificial phase also exists, and a much larger number of orientations is required to shift it to such high densities that it does not interfere with the physical part of the phase diagram.Comment: 4 pages, 2 figures, submitted to PR

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

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

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

Free Minimization of the Fundamental Measure Theory Functional: Freezing of Parallel Hard Squares and Cubes

Due to remarkable advances in colloid synthesis techniques, systems of squares and cubes, once an academic abstraction for theorists and simulators, are nowadays an experimental reality. By means of a free minimization of the free-energy functional, we apply Fundamental Measure Theory to analyze the phase behavior of parallel hard squares and hard cubes. We compare our results with those obtained by the traditional approach based on the Gaussian parameterization, finding small deviations and good overall agreement between the two methods. For hard squares our predictions feature at intermediate packing fraction a smectic phase, which is however expected to be unstable due to thermal fluctuations. This implies that for hard squares the theory predicts either a vacancy-rich second-order transition or a vacancy-poor weakly first-order phase transition at higher density. In accordance with previous studies, a second-order transition with a high vacancy concentration is predicted for hard cubes