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Register a new userCharging Dynamics of Electrical Double Layers Inside Porous Electrodes: Predicting the Effect of Pore-Size Distribution
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Porous electrodes are found in energy storage devices such as supercapacitors and pseudo-capacitors. However, the effect of electrode-pore-size distribution over their energy storage properties remains unclear. Here, we develop a model for the charging of electrical double layers inside a cylindrical pore for arbitrary pore size. We assume small applied potentials and perform a regular perturbation analysis to predict the evolution of electrical potential and ion concentrations in both the radial and axial directions. We validate our perturbation model with direct numerical simulations of the Poisson-Nernst-Planck equations, and obtain quantitative agreement between the two approaches for small and moderate potentials. Our analysis yields two main characteristic features of arbitrary pore size: i) a monotonic decrease of the charging timescale with an increase in relative pore size (pore size relative to Debye length); ii) a region of large potential gradients at the mouth of the pore due to charge conservation. We develop a modified transmission circuit model that captures the effect of arbitrary pore sizes and demonstrate that a time-dependent interfacial capacitance needs to be included in the circuit. We also derive expressions for effective capacitance and charging timescale as a function of pore-size distribution, and show that the capacitance and charging timescale increase for narrower and less polydisperse distributions, resulting in a gain of energy density at a constant power density. Overall, our results advance the fundamental understanding of electrical-double-layer charging and will be useful for the electrode design of energy storage devices.
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Surface analyses inside the nanopore, micropore, and a very narrow pipe are important topics for development of the chemical engineering. Here, we propose a measuring method which evaluates the surface coverage of the chemically modified pore surface and the corrosion rate of the inner surface of the narrow pipe, etc. The method uses Kelvins equation that expresses saturated vapor pressure of a liquid in the pore (pipe). The surface coverage and the corrosion rate are calculated by measuring saturated vapor pressure of the liquid in the pore and the pipe, respectively. In this letter, we explain the concept of the method briefly.
Nanoporous supercapacitors play an important role in modern energy storage systems, and their modeling is essential to predict and optimize the charging behaviour. Two classes of models have been developed that consist of finite and infinitely long pores. Here, we show that although both types of models predict qualitatively consistent results, there are important differences emerging due to the finite pore length. In particular, we find that the ion density inside a finite pore is not constant but increases linearly from the pore entrance to the pore end, where the ions form a strongly layered structure. This hinders a direct quantitative comparison between the two models. In addition, we show that although the ion density between the electrodes changes appreciably with the applied potential, this change has a minor effect on charging. Our simulations also reveal a complex charging behaviour, which is adsorption-driven at high voltages, but it is dominated either by co-ion desorption or by adsorption of both types of ions at low voltages, depending on the ion concentration.
In order to characterize the geometrical mesh size $xi$, we simulate a solution of coarse-grained polymers with densities ranging from the dilute to the concentrated regime and for different chain lengths. Conventional ways to estimate $xi$ rely either on scaling assumptions which give $xi$ only up to an unknown multiplicative factor, or on measurements of the monomer density fluctuation correlation length $xi_c$. We determine $xi_c$ from the monomer structure factor and from the radial distribution function, and find that the identification $xi=xi_c$ is not justified outside of the semidilute regime. In order to better characterize $xi$, we compute the pore size distribution (PSD) following two different definitions, one by Torquato et al. (Ref.1) and one by Gubbins et al. (Ref.2). We show that the mean values of the two distributions, $langle r rangle_T$ and $langle r rangle_G$, both display the behavior predicted for $xi$ by scaling theory, and argue that $xi$ can be identified with either one of these quantities. This identification allows to interpret the PSD as the distribution of mesh sizes, a quantity which conventional methods cannot access. Finally, we show that it is possible to map a polymer solution on a system of hard or overlapping spheres, for which Torquatos PSD can be computed analytically and reproduces accurately the PSD of the solution. We give an expression that allows $langle r rangle_T$ to be estimated with great accuracy in the semidilute regime by knowing only the radius of gyration and the density of the polymers.
Biased electrodes are common components of plasma sources and diagnostics. The plasma-electrode interaction is mediated by an intervening sheath structure that influences properties of the electrons and ions contacting the electrode surface, as well as how the electrode influences properties of the bulk plasma. A rich variety of sheath structures have been observed, including ion sheaths, electron sheaths, double sheaths, double layers, anode glow, and fireballs. These represent complex self-organized responses of the plasma that depend not only on the local influence of the electrode, but also on the global properties of the plasma and the other boundaries that it is in contact with. This review summarizes recent advances in understanding the conditions under which each type of sheath forms, what the basic stability criteria and steady-state properties of each are, and the ways in which each can influence plasma-boundary interactions and bulk plasma properties. These results may be of interest to a number of application areas where biased electrodes are used, including diagnostics, plasma modification of materials, plasma sources, electric propulsion, and the interaction of plasmas with objects in space.
Molecular dynamics simulations are carried out to investigate mechanical properties and porous structure of binary glasses subjected to steady shear. The model vitreous systems were prepared via thermal quench at constant volume to a temperature well below the glass transition. The quiescent samples are characterized by a relatively narrow pore size distribution whose mean size is larger at lower glass densities. We find that in the linear regime of deformation, the shear modulus is a strong function of porosity, and the individual pores become slightly stretched while their structural topology remains unaffected. By contrast, with further increasing strain, the shear stress saturates to a density-dependent plateau value, which is accompanied by pore coalescence and a gradual development of a broader pore size distribution with a discrete set of peaks at large length scales.
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