scholarly journals Entropic origin of dielectric relaxation universalities in heterogeneous materials (polymers, glasses, aerogel catalysts)

2005 ◽  
Vol 2 (10) ◽  
pp. 3529-3531 ◽  
Author(s):  
F. Brouers ◽  
O. Sotolongo-Costa ◽  
A. Gonzalez ◽  
J. P. Pirard
Keyword(s):  
Dielectric Relaxation ◽  
Heterogeneous Materials

The “Fractional” Kinetic Equations and General Theory of Dielectric Relaxation

2005 ◽  
Author(s):  
Raoul R. Nigmatullin
Keyword(s):  
General Theory ◽  
Dielectric Relaxation ◽  
Collective Motion ◽  
Kinetic Equations ◽  
Heterogeneous Materials ◽  
Complex Conjugate ◽  
Electric Circuits ◽  
Self Similar ◽  
Fractional Kinetic Equations ◽  
Frequency Temperature

Based on the Mori-Zwanzig formalism it becomes possible to suggest a general decoupling procedure, which reduces a wide set of various micromotions distributed over a self-similar structure to a few collective/reduced motions describing the relaxation/exchange behavior of a complex system in the mesoscale region. The frequency dependence of the reduced collective motion contains real and pair of complex-conjugate power-law exponents in the frequency domain and explains naturally the “universal response” (UR) phenomenon discovered by A. Jonscher in a wide class of heterogeneous materials. This strict mathematical result allows in developing a consistent and general theory of dielectric relaxation that can describe wide set of dielectric spectroscopy (DS) data measured in some frequency/temperature range in many heterogeneous materials. Based on this result it becomes possible also to suggest a new set of two-pole elements, which generalizes the conventional RLC-elements and can constitute the basis of new theory of the linear electric circuits.

Dielectric Relaxation Studies of Silver Nanoparticles dispersed Liquid Crystal

2015 ◽  
Vol 8 (3) ◽  
pp. 2176-2188 ◽  
Author(s):  
Keisham Nanao Singh
Keyword(s):  
Activation Energy ◽  
Silver Nanoparticles ◽  
Liquid Crystal ◽  
Dielectric Relaxation ◽  
Relaxation Process ◽  
Relaxation Times ◽  
Low Frequency ◽  
Bulk Liquid ◽  
Molecular Rearrangement ◽  
Relaxation Studies

This article reports on the Dielectric Relaxation Studies of two Liquid Crystalline compounds - 7O.4 and 7O.6 - doped with dodecanethiol capped Silver Nanoparticles. The liquid crystal molecules are aligned homeotropically using CTAB. The low frequency relaxation process occurring above 1 MHz is fitted to Cole-Cole formula using the software Dielectric Spectra fit. The effect of the Silver Nanoparticles on the molecular dipole dynamics are discussed in terms of the fitted relaxation times, Cole-Cole distribution parameter and activation energy. The study indicate a local molecular rearrangement of the liquid crystal molecules without affecting the order of the bulk liquid crystal molecules but these local molecules surrounding the Silver Nanoparticles do not contribute to the relaxation process in the studied frequency range. The observed effect on activation energy suggests a change in interaction between the nanoparticles/liquid crystal molecules.

Probabilistic multiscale modeling of fracture in heterogeneous materials and structures

2020 ◽  
Vol 86 (7) ◽  
pp. 45-54
Author(s):  
A. M. Lepikhin ◽  
N. A. Makhutov ◽  
Yu. I. Shokin
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Fracture Mechanics ◽  
Multiscale Modeling ◽  
Virtual Work ◽  
Numerical Models ◽  
Heterogeneous Materials ◽  
Heterogeneous Structure ◽  
Generalized Coordinates ◽  
Heterogeneous Structures

The probabilistic aspects of multiscale modeling of the fracture of heterogeneous structures are considered. An approach combining homogenization methods with phenomenological and numerical models of fracture mechanics is proposed to solve the problems of assessing the probabilities of destruction of structurally heterogeneous materials. A model of a generalized heterogeneous structure consisting of heterogeneous materials and regions of different scales containing cracks and crack-like defects is formulated. Linking of scales is carried out using kinematic conditions and multiscale principle of virtual forces. The probability of destruction is formulated as the conditional probability of successive nested fracture events of different scales. Cracks and crack-like defects are considered the main sources of fracture. The distribution of defects is represented in the form of Poisson ensembles. Critical stresses at the tops of cracks are described by the Weibull model. Analytical expressions for the fracture probabilities of multiscale heterogeneous structures with multilevel limit states are obtained. An approach based on a modified Monte Carlo method of statistical modeling is proposed to assess the fracture probabilities taking into account the real morphology of heterogeneous structures. A feature of the proposed method is the use of a three-level fracture scheme with numerical solution of the problems at the micro, meso and macro scales. The main variables are generalized forces of the crack propagation and crack growth resistance. Crack sizes are considered generalized coordinates. To reduce the dimensionality, the problem of fracture mechanics is reformulated into the problem of stability of a heterogeneous structure under load with variations of generalized coordinates and analysis of the virtual work of generalized forces. Expressions for estimating the fracture probabilities using a modified Monte Carlo method for multiscale heterogeneous structures are obtained. The prospects of using the developed approaches to assess the fracture probabilities and address the problems of risk analysis of heterogeneous structures are shown.

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