Frequency domain description of Kohlrausch response through a pair of Havriliak-Negami-type functions: an analysis of functional proximity

Computational Modeling: Up-to-Date Approaches and Cutting-Edge Applications from Clusters, Nanostructures to Bulk Systems

The contributions in this special theme collection, in honor to Prof. P. Villarreal, cover a broad variety of computational methodologies and experimental techniques, containing studies on gas phase, clusters and condensed phase systems.

Stochastic tools hidden behind the empirical dielectric relaxation laws

The paper is devoted to recent advances in stochastic modeling of anomalous kinetic processes observed in dielectric materials which are prominent examples of disordered (complex) systems. Theoretical studies of dynamical properties of 'structures with variations' (Goldenfield and Kadanoff 1999 Science 284 87-9) require application of such mathematical tools-by means of which their random nature can be analyzed and, independently of the details distinguishing various systems (dipolar materials, glasses, semiconductors, liquid crystals, polymers, etc), the empirical universal kinetic patterns can be derived. We begin with a brief survey of the historical background of the dielectric relaxation study. After a short outline of the theoretical ideas providing the random tools applicable to modeling of relaxation phenomena, we present probabilistic implications for the study of the relaxation-rate distribution models. In the framework of the probability distribution of relaxation rates we consider description of complex systems, in which relaxing entities form random clusters interacting with each other and single entities. Then we focus on stochastic mechanisms of the relaxation phenomenon. We discuss the diffusion approach and its usefulness for understanding of anomalous dynamics of relaxing systems. We also discuss extensions of the diffusive approach to systems under tempered random processes. Useful relationships among different stochastic approaches to the anomalous dynamics of complex systems allow us to get a fresh look at this subject. The paper closes with a final discussion on achievements of stochastic tools describing the anomalous time evolution of complex systems.

Why the dipolar response in dielectrics and spin-glasses is unavoidably universal

Materials response to electric or magnetic fields is often dominated by the dynamics of dipoles in the system. This is for instance the case of polar dielectrics and many transition metal compounds. An essential and not yet well understood fact is that, despite their structural diversity, dielectric solids exhibit a striking universality of frequency and time responses, sharing many aspects with the behaviour of spin-glasses. In this article I propose a stochastic approach to dipole dynamics within which the “universal frequency response” derives naturally with Debye’s relaxation mechanism as a special case. This formulation reveals constraints to the form of the relaxation functions, which are essential for a consistent representation of the dynamical slowing-down at the spin-glass transition. Relaxation functions with algebraic-, and exponential-tails, as well as damped oscillations, are shown to have a unified representation in which the stable limit of the distribution of waiting-times between dipole flips determines the present type of dynamics.

The heterogeneous energy landscape expression of KWW relaxation

Here we show a heterogeneous energy landscape approach to describing the Kohlrausch-Williams-Watts (KWW) relaxation function. For a homogeneous dynamic process, the distribution of free energy landscape is first proposed, revealing the significance of rugged fluctuations. In view of the heterogeneous relaxation given in two dynamic phases and the transmission coefficient in a rate process, we obtain a general characteristic relaxation time distribution equation for the KWW function in a closed, analytic form. Analyses of numerical computation show excellent accuracy, both in time and frequency domains, in the convergent performance of the heterogeneous energy landscape expression and shunning the catastrophic truncations reported in the previous work. The stretched exponential β, closely associated to temperature and apparent correlation with one dynamic phase, reveals a threshold value of 1/2 defining different behavior of the probability density functions. Our work may contribute, for example, to in-depth comprehension of the dynamic mechanism of glass transition, which cannot be provided by existing approaches.

A physicochemical mechanism of chemical gas sensors using an AC analysis

Electrical modeling of the chemical gas sensors was successfully applied to TiO2 nanofiber gas sensors by developing an equivalent circuit model where the junction capacitance as well as the resistance can be separated from the comparable stray capacitance. The Schottky junction impedance exhibited a characteristic skewed arc described by a Cole-Davidson function, and the variation of the fit and derived parameters with temperature, bias, and NO2 gas concentration indicated definitely a physicochemical sensing mechanism based on the Pt|TiO2 Schottky junctions against the conventional supposition of the enhanced sensitivity in nanostructured gas sensors with high grain boundary/surface area. Analysis on a model Pt|TiO2|Pt structure also confirmed the characteristic impedance response of TiO2 nanofiber sensors.