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Register a new userThe effect of finite pore length on ion structure and charging
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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.
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The evolution of porous structure, potential energy and local density in binary glasses under oscillatory shear deformation is investigated using molecular dynamics simulations. The porous glasses were initially prepared via a rapid thermal quench from the liquid state across the glass transition and allowed to phase separate and solidify at constant volume, thus producing an extended porous network in an amorphous solid. We find that under periodic shear, the potential energy decreases over consecutive cycles due to gradual rearrangement of the glassy material, and the minimum of the potential energy after thousands of shear cycles is lower at larger strain amplitudes. Moreover, with increasing cycle number, the pore size distributions become more skewed toward larger length scales where a distinct peak is developed and the peak intensity is enhanced at larger strain amplitudes. The numerical analysis of the local density distribution functions demonstrates that cyclic loading leads to formation of higher density solid domains and homogenization of the glass phase with reduced density.
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.
Descriptors that characterize the geometry and topology of the pore space of porous media are intimately linked to their transport properties. We quantify such descriptors, including pore-size functions and the critical pore radius $delta_c$, for four different models: maximally random jammed sphere packings, overlapping spheres, equilibrium hard spheres, and inherent structures of the quantizer energy. For precise estimates of the percolation thresholds, we use a strict relation of the void percolation around sphere configurations to weighted bond percolation on the corresponding Voronoi networks. We use the Newman-Ziff algorithm to determine the percolation threshold using universal properties of the cluster size distribution. Often, $delta_c$ is used as the key characteristic length scale that determines the fluid permeability $k$. A recent study [Torquato. Adv. Wat. Resour. 140, 103565 (2020)] suggested for porous media with a well-connected pore space an alternative estimate of $k$ based on the second moment of the pore size $langledelta^2rangle$. Here, we confirm that, for all porosities and all models considered, $delta_c^2$ is to a good approximation proportional to $langledelta^2rangle$. However, unlike $langledelta^2rangle$, the permeability estimate based on $delta_c^2$ does not predict the correct ranking of $k$ for our models. Thus, we confirm $langledelta^2rangle$ to be a promising candidate for convenient and reliable estimates of $k$ for porous media with a well-connected pore space. Moreover, we compare the fluid permeability of our models with varying degrees of order, as measured by the $tau$ order metric. We find that (effectively) hyperuniform models tend to have lower values of $k$ than their nonhyperuniform counterparts. Our findings could facilitate the design of porous media with desirable transport properties via targeted pore statistics.
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