DIELECTRIC PROPERTIES : COMPUTER SIMULATION

Alioune Aidara Diouf and Bassirou Lo Faculty of Sciences &Techniques, Cheikh Anta Diop University, Dakar, Senegal. ...................................................................................................................... Manuscript Info Abstract ......................... ........................................................................ Manuscript History Received: 10 April 2020 Final Accepted: 12 May 2020 Published: June 2020


Model and Formalism:
To investigate the dielectric environment, Lorentz considered atoms as weakened oscillators bound between them by springs. By applying a variable electric field, Lorentz had noted the appearance of a polarization. By making an assessment of strengths, he defined the following strengths: With f e : Electric force.
By considering the displacement "r" of an electron with regard to the core, which it is elastically connected. Such an electron obeys the equation of the movement given by the Newton's Law [16], so we defined the radius (r) by: The polarization is thus defined from the position r r of the electrons reason why we have:  reprents the susceptibility of the dielectric environment [11].
So from the susceptibility one can define the permittivity [12][13][14][15][16] of the dielectric environment defines by thefollowing relation: By posing We obtain:

Results and Discussions: -
To investigate the dielectric properties in the dense environment, wechoose to look at the behavior of the susceptibilities as well as the refractive index by making a variation of the spectral width, the specific pulsation (ω 0 ) and the number of particle (N). The spectral width allows us to understand the complex aspect of the amortization in the dielectric environment. So, in the figure 1 we observe that for values of 0   , which represent the normal dispersion, the growth of the susceptibility is a function of the increase of the spectral width Г. For values 0   , the susceptibility decrease rapidly, this phenomenon corresponds to an abnormal dispersion with positive and negative values of the susceptibility. Reason why, the growth of the spectral width influences the width of the peaks in the real susceptibility. Otherwise, more the spectral width is important more the real susceptibility increase. In the figure 2, with the imaginary susceptibility, the variation of the spectral width (  ) influences the absorption of the dielectric environment. So for values of 3   and 5   the imaginary susceptibility is null for various values of Г. For 35  , the imaginary susceptibility presents a peak which increases with the spectral width. Reason why, to make more absorption in materials with dense properties, the augmentation of the spectral width (  ) on the imaginary susceptibility is better. The investigation of the reflective constant is very important in the dielectric materials because it allows the understanding of the optical behavior in the dielectric environment.Reason why, the figure3 represents the influence of the spectral width (  )on the reflective index. So we note that the spectral width (  ) increases the capacity of the environment to be reflective. Moreover, certain authors [18, 19and 20] have already used this parameter for the investigation of certain materials such as ZnO, CdS etc.Besides, the vibrational character of the materials plays an important role in the investigation of the structural properties of the physical systems, so one of the parameters responsible for this phenomenon is the specific pulsation ω 0 . The figures 4, 5 and 6shows the influence of the pulsation ω 0 on the dielectric properties of the materials. The variation of ω 0 reveals that the susceptibilities and the reflective index decrease with the increase of the specific pulsation (ω 0 ). This is due to the fact that the specific pulsation is inversely proportional to the susceptibilities and the refractive index. Reason why an increase of the specific pulsation creates a change of the curves from the reflective index but decrease the maximal values of the peaks of refraction and susceptibility. In the dense dielectric material, the investigation of the statistical physic is mandatory. With the physic of particles, the large number of particle is closely linked to the strength of oscillator in the dielectric materials reason why its influence is noted in the dielectricproperties. So the figures 7, 8 and 9, display the influence of the number of particle on the dielectric materials. Unlike figures 1, 2 and 3, the curves of the susceptibilities and the reflective index increase with the augmentation of the number of particle. As result, we observe an importance of the refraction as well as the absorption. The Lorentz model is an good model for investigating the dense dielectric properties but also it is very used to study the behavior of phonons and transitions inter-bands. Reason why, certain authors have already used it to investigate the reflectivity of certain materials such as YMnO 3 [21].

Conclusion:-
The present paper was dedicated to model and investigate the physical dielectric properties of the dense dielectric environment. The work led during this study brought numerous answers on the influences of the number of particle, the spectral width and the pulsation in the dielectric properties. However, several studies deserve to be pursued. In particular, the study of the dielectric properties in the artificial fibers and also the importance of its applications the industry and new technology. Several investigators have already implanted a model to investigate the properties of materials according to their membership [22][23]. But in our case one of the perspectives is to implement a model which allows to investigate any type of materials.