The Analysis of Physical and Chemical Adsorption of Dysprosium Ions as Functions of the Temperature and Time in Terms of Boubaker Polynomials

In the present work, analytical solutions to the differential equation systems governing the kinetics of dysprosium adsorption within particular hosting edifices are presented. The chemical adsorption kinetics of rare earth elements inside regular crystalline materials such as ZnO are discussed. An approximate analytical expression of the non-steady-state doping concentrations is deduced by using the Boubaker polynomial expansion scheme (BPES). The results concerning the particular case of the dysprosium ion Dy3+ are discussed and evaluated in terms of temperature and time. In addition to an exponential parabolic time-dependent behavior, a notable temperature gradient is noted. Above a certain temperature limit, the reaction starts to occur and pertains to the energy needed to promote a 4f electron to the valence band.