Ladder Mechanisms of Ion Transport in Prussian Blue Analogues

Abstract

Prussian blue (PB) and its analogues (PBAs) are drawing attention as promising materials for sodium-ion batteries and other applications, such as desalination of water. Because of the possibilities to explore many analogous materials with engineered, defect-rich environments, computational optimization of ion-transport mechanisms that are key to the device performance could facilitate real-world applications. In this work, we have applied a multiscale approach involving quantum chemistry, self-consistent mean-field theory, and finite-element modeling to investigate ion transport in PBAs. We identify a cyanide-mediated ladder mechanism as the primary process of ion transport. Defects are found to be impermissible to diffusion, and a random distribution model accurately predicts the impact of defect concentrations. Notably, the inclusion of intermediary local minima in the models is key for predicting a realistic diffusion constant. Furthermore, the intermediary landscape is found to be an essential difference between both the intercalating species and the type of cation doping in PBAs. We also show that the ladder mechanism, when employed in multiscale computations, properly predicts the macroscopic charging performance based on atomistic results. In conclusion, the findings in this work may suggest the guiding principles for the design of new and effective PBAs for different applications.

Sodium to cesium ions: a general ladder mechanism of ion diffusion in prussian blue analogs

“…In recent work, we have defined this concept as a ladder mechanism. 36 In analogy, a ladder is broken if either a step or side rail is missing.…”

“…Recently, we proposed a ladder mechanism to describe how Na + diffuses through PBAs by climbing inner structural frames formed by oriented cyanide interactions. 36 That study also included simulations of analogous cations, such as Li + . That work also shows that such a model can be combined with macroscopic, [37][38][39] finite-element (FEM) 16,[40][41][42] simulations to successfully predict device-level performance.…”

Pairing of Aqueous and Nonaqueous Electrosynthetic Reactions Enabled by a Redox Reservoir Electrode

“…For further support that protons are the ions that are intercalated into the NiHCF RR, we conducted operando electrochemical quartz crystal microbalance (EQCM) measurements during cyclic voltammetry (Figure c,d) to monitor the electrode mass change (see details in the Supporting Information). In PBAs, cation (de)intercalation must be charge balancing the redox process . The EQCM results (Figure c, red trace) show that during reduction (protonation) the electrode experiences a frequency increase indicating a mass loss according to the Sauerbrey equation: Δ f s = − 2 · f 0 2 · Δ m · n ( μ q ρ q ) 1 / 2 which simplifies to normalΔ f = prefix− C f · normalΔ m where ρ q is the density of the quartz crystal (2.648 g/cm 3 ), μ q is the shear modulus of quartz (2.947 × 10 11 g/cm s 2 ), f 0 is the resonant frequency of the fundamental mode of the crystal in Hz, C f is the sensitivity factor, n is the overtone, and Δ m and Δ f are the mass change and frequency change, respectively.…”

Electrostatic interactions and physisorption: mechanisms of passive cesium adsorption on Prussian blue

“…Multiple studies have investigated the diffusion and replacement mechanisms to better understand this process. 2,34 However, PB can also adsorb cesium ions passively. 35 Passive adsorption of cesium ions is commonly described using a Langmuir isotherm, which works reasonably well.…”

“…Multiple studies have investigated the diffusion and replacement mechanisms to better understand this process. 2,34 However, PB can also adsorb cesium ions passively. 35…”