Maxwell displacement current and nature of Jonsher’s “universal” dynamic response in nanoionics

Abstract

New notion -Maxwell displacement current on potential barrier -is introduced in the structuredynamic approach of nanoionics for description of collective phenomenon: coupled ion-transport and dielectric-polarization processes occurring during ionic space charge formation and relaxation in non-uniform potential relief. We simulate the processes: (i) in an electronic conductor/advanced superionic conductor (AdSIC) ideally polarizable coherent heterojunction, (ii) in a few strained monolayers of solid electrolyte (SE) located between two AdSICs forming coherent interfaces with SE. We prove the sum of ionic current over any barrier and Maxwell displacement current through the same barrier is equal to the current of current generator.-Universal‖ dynamic response, Re*()   n (n < 1), was found for frequency-dependent conductivity *() for case (ii) with an exponential distribution of potential barrier heights in SE. The nature of phenomenon is revealed. The amplitudes of non-equilibrium ion concentrations (and induced voltages) in space charge region of SE change approximately as   -1 . Amplitudes yield a main linear contribution to Re*(). The deviation from linearity is provided by the cosine of phase shift  between current and voltage in SE-space charge but cos depends relatively slightly on  (near constant loss effect) for coupled ion-transport and dielectric-polarization processes.The canonical physical-mathematical formalism for the description of ion transport in solids [1] is based on the concept of a regular crystalline potential relief, i.e. the heights  of potential barriers are const. As a consequence, ion-transport characteristics (mean-square displacement, diffusion coefficient, mobility, activation energy) have a clear physical meaning only at averaging in the scale much exceeding the length of an elementary ion jump. However, the variation of  with a space coordinate x can be considerable in objects of solid state ionics. For example, local regions with  variation about 1 eV/nm exist in disordered solid electrolytes (SE) [2][3][4] and in crystals of superionic conductors (SIC) [5]. Various degrees of ordering occur near surfaces and in the region of interphase and intercrystalline boundaries [6] where specific ion dynamics can arise on the nanoscale [7] due to a non-uniform potential relief. The interface structure exhibits itself in, e.g., frequency-capacitance characteristics of EC/SIC heterojunctions [8][9][10]. The classification of solid ionic conductors [8-10] distinguishes a class of advanced superionic conductors (AdSIC) among SE and SIC because AdSIC-crystal structure is close to optimal for fast ion transport (FIT). This crystal structure determines the record high level of iontransport characteristics. The FIT structure represents a rigid sub-lattice of immobile ions in which there are the crystallographic positions interconnected with each other by low potential barriers (conduction tunnels) for hopping mobile ions. The number of such positions is several times larger ...

Origin of the Curie-von Schweidler law and the fractional capacitor from time-varying capacitance

“…But it is impossible to study them at atomic and molecular levels because of the resulting mathematical complexities [1,16]. Also, the values of the density and the magnitude of the polarizing species are rarely available [17]. Some more attempts inspired from the common observation of self-similarity in power-laws and fractal geometry have been made [18][19][20][21][22].…”

“…The undeniable fact that the CvS law is ubiquitous indicates that a more fundamental yet a universal mechanism is at play. In fact, its theoretical description is considered as one of most fundamental problems in physics [11,17,[30][31][32]. Therefore, the quest for an encompassing interpretation becomes imperative and serves as a motivation for this Letter.…”

Fundamental and Applied Nanoionics in Imt Ras

“…A new theoretical approach [9] addresses to the logic of elementary ion-transport processes on a nanoscale and emphasizes that solid-state ionic conductors are dynamical non-local non-linear systems. In such systems, key parameters (heights of barriers in potential landscape) depend on external influences.…”

“…In SDA, several theoretical innovations were proposed: method of effective uniform electrostatic field; new dimensional ri-factor; new notion "Maxwell displacement current on a potential barrier"; laws of spatial averaging of potential differences in solid-state ionic conductors [9][10][11][12].…”

“…According to the authors, nanoionics is defined by: 1) objects, i.e., nanostructures and nanosystems with FIT, for example, optically active nano-physical-chemical systems Ag(or Cu)Hal -M created in high vacuum (M is a metal in which the first ionization potential is smaller than one of Ag(or Cu) [4,5]; 2) properties, phenomena, effects and mechanisms of processes connected with FIT on nanoscale; 3) methods: design of nanomaterials and nano-objects with FIT [6][7][8], new theoretical system for description of dynamical response of layered nanostructures with 1D FIT in non-uniform on a nanoscale potential landscape (structure-dynamic approach of nanoionics, SDA) [9][10][11][12]; 4) dimensionless criterion of nanoionics λ/L ~ 1 [1]; 5) dimensional ri-factor for solid state ionic systems [11]; and 6) perspective applications, e.g., nanoionic supercapacitors for deep-sub-voltage https://doi.org/10.37904/nanocon.2019.8498 nanoelectronics, nanoionic memristors (i.e., "memory resistors" -two-terminal functional nanostructures, where conjugate ionic/electronic processes and electrical resistance change significantly at a changing of the polarity of external electric influence), etc. [13].…”