physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

and electrical engineering, the universal dielectric response, or UDR, refers to the observed emergent behaviour of the

dielectric In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the mate ...

properties exhibited by diverse solid state systems. In particular this widely observed response involves power law scaling of dielectric properties with

frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...

under conditions of

alternating current Alternating current (AC) is an electric current which periodically reverses direction and changes its magnitude continuously with time in contrast to direct current (DC) which flows only in one direction. Alternating current is the form in whic ...

, AC. First defined in a landmark article by A. K. Jonscher in ''

Nature Nature, in the broadest sense, is the physical world or universe. "Nature" can refer to the phenomena of the physical world, and also to life in general. The study of nature is a large, if not the only, part of science. Although humans are ...

'' published in 1977, the origins of the UDR were attributed to the dominance of many-body interactions in systems, and their analogous RC network equivalence. The universal dielectric response manifests in the variation of AC Conductivity with frequency and is most often observed in complex systems consisting of multiple phases of similar or dissimilar materials. Such systems, which can be called heterogenous or composite materials, can be described from a dielectric perspective as a large network consisting of resistor and capacitor elements, known also as an RC network. At low and high frequencies, the dielectric response of heterogeneous materials is governed by percolation pathways. If a heterogeneous material is represented by a network in which more than 50% of the elements are capacitors,

percolation Percolation (from Latin ''percolare'', "to filter" or "trickle through"), in physics, chemistry and materials science, refers to the movement and filtering of fluids through porous materials. It is described by Darcy's law. Broader applicatio ...

through capacitor elements will occur. This percolation results in conductivity at high and low frequencies that is directly proportional to frequency. Conversely, if the fraction of capacitor elements in the representative RC network (P_c) is lower than 0.5, dielectric behavior at low and high frequency regimes is independent of frequency. At intermediate frequencies, a very broad range of heterogeneous materials show a well-defined emergent region, in which power law correlation of

admittance In electrical engineering, admittance is a measure of how easily a circuit or device will allow a current to flow. It is defined as the reciprocal of impedance, analogous to how conductance & resistance are defined. The SI unit of admittan ...

to frequency is observed. The power law emergent region is the key feature of the UDR. In materials or systems exhibiting UDR, the overall dielectric response from high to low frequencies is symmetrical, being centered at the middle point of the emergent region, which occurs in equivalent RC networks at a frequency of :

\omega = (RC)^

. In the power law emergent region, the admittance of the overall system follows the general power law proportionality

Y\propto\omega^

, where the power law exponent α can be approximated to the fraction of capacitors in the equivalent RC network of the system α≅P_c.

Significance of the UDR

The power law scaling of dielectric properties with frequency is valuable in interpreting impedance spectroscopy data towards the characterisation of responses in emerging

ferroelectric Ferroelectricity is a characteristic of certain materials that have a spontaneous electric polarization that can be reversed by the application of an external electric field. All ferroelectrics are also piezoelectric and pyroelectric, with the ad ...

and multiferroic materials.

References

{{Reflist, 30em Dielectrics Electric and magnetic fields in matter Condensed matter physics Electrical engineering *