Conductivity Sigma Dc Research Articles

On the nonlinear variation of dc conductivity with dielectric relaxation time

The long-known observations that dc conductivity sigma(dc) of an ultraviscous liquid varies nonlinearly with the dielectric relaxation time tau, and the slope of the log sigma(dc) against log tau plot deviates from -1 are currently seen as two of the violations of the Debye-Stokes-Einstein equation. Here we provide a formalism using a zeroth order Bjerrum description for ion association to show that in addition to its variation with temperature T and pressure P, impurity ion population varies with a liquid's equilibrium dielectric permittivity. Inclusion of this electrostatic effect modifies the Debye-Stokes-Einstein equation to log(sigma(dc)tau)=constant+log alpha, where alpha is the T and P-dependent degree of ionic dissociation of an electrolytic impurity. Variation of a liquid's shear modulus with T and P would add to the nonlinearity of sigma(dc)-tau relation, as would a nonequivalence of the shear and dielectric relaxation times, proton transfer along the hydrogen bonds, or occurrence of another chemical process. This is illustrated by using the data for ultraviscous acetaminophen-aspirin liquid.

Structure and relaxation dynamics of poly(amide urethane)s with bioactive transition metal acetyl acetonates in hard blocks

Structural characteristics, thermal transitions and molecular dynamics of selected poly(amide urethane)s with transition metal acetyl acetonates Me(AcAc)(2) (Me = Sn(4+), Zn(2+), Cu(2+), Pb(2+)) as chain extenders, were comparatively investigated using small- and wide-angle X-ray scattering (SAXS, WAXS), differential scanning calorimetry (DSC), and dielectric techniques (dielectric relaxation spectroscopy, DRS; thermally stimulated currents, TSC). We studied the influence of metal chelates on the mixing of the soft-segment (SS) and hard-segment (HS) domains and the related degree of microphase separation (DMS). The reactivity of Me(AcAc)(2) with macrodiisocyanate was found to decrease in the order Sn(AcAc)(2)Cl(2) > Cu(AcAc)(2) > Zn(AcAc)(2) > Pb(AcAc)(2). While Pb(AcAc)(2) shows a higher tendency for crystallisation, both the dielectric and calorimetric results suggest that the corresponding polyurethane has comparatively low DMS. The type of the transition metal has moderate effect on the glass transition temperature and no influence on the shape of the dielectric alpha relaxation signal, indicating weak interactions between metal ions and SS domains. In contrast, structural parameters and the dielectric behaviour of the beta relaxation suggest preference for hydrogen-bonding interactions between Sn(4+) and Cu(2+) metal-chelates and HS domains. The temperature dependence of dc conductivity sigma(dc) is described by the Vogel-Tammann-Fulcher equation and signifies the coupling between the mobility of polymeric chains and charges' motion. It may be expected that the present combination of techniques and particular results with respect to DMS will contribute to the development and testing of novel biodegradation-resistant and antibacterial metal-polyurethanes for biotechnological and industrial applications.

Changes in dynamic crossover with temperature and pressure in glass-forming diethyl phthalate.

Dielectric relaxation measurements have been used to study the crossover in dynamics with temperature and pressure, onset of breakdown of the Debye-Stokes-Einstein law, and the relation between the alpha and the beta relaxations in diethyl phthalate. The measurements made over 10 decades in frequency and a broad range of temperature and pressure enable the dc conductivity and the alpha- and the beta-relaxations to be studied altogether. The isobaric data show that the alpha-relaxation time tau(alpha) has temperature dependence that crosses over from one Vogel-Fulcher-Tammann-Hesse form to another at T(B) approximately 227 K and tau(alpha) approximately 10(-2) s. The dc conductivity sigma exhibits similar crossover at the same T(B). At temperatures above T(B), tau(alpha) and sigma have the same temperature dependence, but below T(B) they become different and the Debye-Stokes-Einstein law breaks down. The breadth of the alpha relaxation is nearly constant for T<T(B), but decreases with increasing temperature for T>T(B). The time dependence of tau(beta) is Arrhenius, which when extrapolated to higher temperatures intersects tau(alpha) at T(beta) nearly coincident with T(B). Isothermal measurements at various applied pressures when compared with isobaric data show that the shape of the alpha-relaxation depends only on tau(alpha), and not on the T and P combinations. At a constant temperature, while tau(alpha) increases rapidly with pressure, the beta-relaxation time tau(beta) is insensitive to applied pressure. This behavior is exactly the same as found in 1,1(')-bis (p-methoxyphenyl) cyclohexane. The findings are discussed in the framework of the coupling model.

Zero bias anomaly in the density of states of low-dimensional metals

We consider the effect of Coulomb interactions on the average density of states (DOS) of disordered low-dimensional metals for temperatures T and frequencies omega smaller than the inverse elastic life-time. Using the fact that long-range Coulomb interactions in two dimensions (2d) generate ln^2-singularities in the DOS nu (omega) but only ln-singularities in the conductivity sigma(omega), we can re-sum the most singular contributions to the average DOS via a simple gauge-transformation. If lim_{omega -> 0} sigma (omega) > 0, then a metallic Coulomb gap nu(omega) propto |omega|/e^4 appears in the DOS at T=0 for frequencies below a certain crossover frequency Omega_2 which depends on the value of the DC conductivity sigma(0). Here, -e is the charge of the electron. Naively adopting the same procedure to calculate the DOS in quasi 1d metals, we find nu(omega) propto (|omega|/Omega_1)^{1/2} exp(-Omega_1/|omega|) at T = 0, where Omega_1 is some interaction-dependent frequency scale. However, we argue that in quasi 1d the above gauge-transformation method is on less firm grounds than in 2d. We also discuss the behavior of the DOS at finite temperatures and give numerical results for the expected tunneling conductance that can be compared with experiments.

Thermopower sign reversal versus temperature and DC conductivity in polyaniline derivatives

The DC conductivity and thermopower of polyaniline derivatives were measured for temperatures ranging from 80 to 345 K. The samples were oxidized to different degrees, fully protonated and further doped with -SO3H, -COOH and phosphorylated polystyrene additives to concentrations varying from 0 to 100 mol.% of functional group per mole of aniline. The DC conductivity sigma (300 K) ranges from 0.01 to 16 S cm-1, depending on the degree of oxidation and dopant concentration, while sigma (T)= sigma 0 exp(-(T0/T)0.5), where T0 is mainly determined by the degree of oxidation. The thermopower, which is of the order of -15 mu V K-1 at 300 K, changes sign from n to p with increasing temperature at Tr, which varies between 290 and 325 K. This change in sign, which is reversed during cooling, is attributed to the existence of a half-filled polaronic band situated deep in the energy gap of polyaniline.

Frequency-dependent conductivity in glasses

The Barton-Nakajima-Namikawa relationship between the static dielectric constant epsilon (0), and the DC conductivity sigma (0), observed in many glasses, sigma (0) varies as omega c epsilon (0), with omega c the loss peak frequency, has been generally assumed to signify a connection between the low frequency AC and the DC conduction processes. The author argues that the connection is that both are due to non-local relaxation processes, the relaxation time of the DC process being effectively infinite. Above the loss peak, the relation sigma ( omega ) varies as omega s is compatible with the pair approximation, i.e. a local relaxation theory. Below the loss peak, the role of Coulomb interactions is critical. If the effects of Coulomb interactions may be neglected, or treated perturbatively, the relaxation time of a process spanning a linear dimension x is proportional to x2. But if Coulomb interactions dominate, the relaxation time may be proportional to x. Only the latter condition is compatible with the BNN relation, and is believed to be one of the most important distinctions between the ionic glasses and the Fermi (electronic) glass.

Electron transport in NiCr-O thin films at low temperatures

Starting from measurements of the DC conductivity sigma (T) in the temperature range from 0.05 to 300 K, the authors can qualitatively describe the electron transport in NiCr-O thin films at low temperatures by its dependence on the atomic oxygen concentration cO. At a critical value of cO a metal-insulator transition occurs near T=0. In the metallic region the electrical behaviour can be interpreted in terms of weakly localised electrons including electron correlation. In the non-metallic region an activated temperature dependence is found which is due to variable-range hopping of strongly localised electrons.

A new percolation theory for many-electron excitations at low temperatures

A new percolation theory for n-electron hopping in the low-temperature (large-n) limit is presented. Applied to the DC conductivity sigma the theory yields sigma varies as TP. While p can vary from system to system, it is typically large, of the order of 20. In another application the glass temperature, Te, of the electron glass is calculated. Here Te is the minimum temperature for which the ergodic hypothesis may be satisfied within reasonable experimental times. For the specific case of impurity conduction systems in germanium (concentration 1016 cm-3, compensation 1/2) Te=0.6 K. A related calculation of the entropy yields a low-temperature behaviour S varies as T2, and shows that the time evolution of the entropy is smooth.

Quantum tunnelling and the temperature dependent DC conduction in low-conductivity semiconductors

Conventional models of electronic conduction through localised states lead to a simply activated temperature dependence, log sigma varies as T-1, for the DC conductivity sigma . But this behaviour is not always followed over the whole experimental range, and in some instances log sigma varies as T appears to be a better description. The authors show some examples of this behaviour, and point out that it is a characteristic that was anticipated more than 20 years ago by a model of quantum tunnelling through a vibrating potential barrier. They show how this model can be incorporated into the small-polaron picture of electron transport to explain qualitatively a wider range of experimental behaviours.