Revisiting the Curie-Von Schweidler Law for Dielectric Relaxation and Derivation of Distribution Function for Relaxation Rates as Zipf’s Power Law and Manifestation of Fractional Differential Equation for Capacitor

The classical power law relaxation, i.e. relaxation of current with inverse of power of time for a step-voltage excitation to dielectric—as popularly known as Curie-von Schweidler law is empirically derived and is observed in several relaxation experiments on various dielectrics studies since late 19th Century. This relaxation law is also regarded as “universal-law” for dielectric relaxations;and is also termed as power law. This empirical Curie-von Schewidler relaxation law is then used to derive fractional differential equations describing constituent expression for capacitor. In this paper, we give simple mathematical treatment to derive the distribution of relaxation rates of this Curie-von Schweidler law, and show that the relaxation rate follows Zipf’s power law distribution. We also show the method developed here give Zipfian power law distribution for relaxing time constants. Then we will show however mathematically correct this may be, but physical interpretation from the obtained time constants distribution are contradictory to the Zipfian rate relaxation distribution. In this paper, we develop possible explanation that as to why Zipfian distribution of relaxation rates appears for Curie-von Schweidler Law, and relate this law to time variant rate of relaxation. In this paper, we derive appearance of fractional derivative while using Zipfian power law distribution that gives notion of scale dependent relaxation rate function for Curie-von Schweidler relaxation phenomena. This paper gives analytical approach to get insight of a non-Debye relaxation and gives a new treatment to especially much used empirical Curie-von Schweidler (universal) relaxation law.

Influence of Organoclay Structure on Nanostructured Materials Based on Eva

This article reports the preparation of a series of EVA nanocomposites employing solution casting methods using different types of organo-modified montmorillonite clay. The effect of the organoclay type on the structural organization and thermal behavior of EVA nanostructured materials were systematically investigated. Regarding thermal behavior, the thermogravimetric analysis showed that the nanocomposites presented a slight decrease in thermal degradation temperature compared to EVA, while differential scanning calorimetry, in general, did not show a significant change in the thermal transition temperatures such as glass transition, melting temperature and crystallization temperature of the nanocomposites, regardless of the type and proportion of organoclay in the systems. With respect to structural aspect, the X-ray diffractograms showed that all systems presented a heterogeneous distribution of the nanoparticles, containing part intercalated. Nuclear magnetic resonance relaxometry data provided complementary information for the X-ray results, showing that the EVA systems containing 5 wt% of both studied organoclays presented a mixture of intercalated and exfoliated structures, evidencing that there was a surface interaction between polymer chains and clay lamellae.

Effect of single walled carbon nanotubes on series resistance of Rose Bengal and Methyl Red dye-based organic photovoltaic device

The influence of single walled carbon nanotube（SWCNT）on the series resistanceof Rose Bengal（RB）and Methyl Red（MR）dye-based organic diodes has been studied.It has been revealed from experimental results that SWCNT has a significant effect on Rs.The values of Rs are measured from current–voltage（I–V）characteristics and also by utilizing the Cheung method.Obtained values from the Cheung method have been verified using H（I）–I plots for all dye-based devices.The extracted values using these two processes show a good consistency with each other.It is observed that Rs is reduced significantly by incorporating SWCNT for both dyes.The estimated amounts of reduction of Rs using SWCNT are 76.08%and 64.23%obtained from the I–V relationship whereas the value of Rs shows a reduction of 83.5%and 67.1%when measured by using the Cheung method for RB and MR dyes respectively.The ideality factor and barrier height of the diodes have also been extracted.The ideality factor has decreased with incorporation of SWCNT.A reduction in barrier height for the devices has also been observed in the presence of SWCNT.