Self-energy Modified Poisson Nernst Planck Model And Relative Dielectric Effect

The interaction between charged objects in solution is strongly affected by the presence of an electrolyte.One of the most widely used analytical method to describe electrolyte solution is the Poisson-Boltzmann(PB)approach.The PB theory has been successfully used in predicting ionic profiles close to planar and curved surfaces,as well as resultant of system.The description of ion structure and transport in double layer often uses Poisson-Nernst-Planck(PNP)equation.Classical PNP equation neglects ion-ion correlation in double layer just like PB theory.A useful approach of remedying the PB and PNP theory is to add the effect of self energy of mobile ions.There are five parts of this paper.The first part is the introduction of this topic.In the second part we introduce the PB theory and its applications.In the third part,we introduce the self-energy modified PNP equation,to solved Debye-Hückel(DH)equation,we uses Green's function and developed finite difference method as well as WKB method.In the fourth part,we get the expression of relative dielectric permittivity ? by Dipolar-Poisson-Boltzmann(DBP)model.In the last part,we show the result of numerical method and analysis of property.We draw a conclusion that the applied electric field will be weaken due to the effect of hydration shell,which meet result of the DBP we considered.As a result,the effect of polarization in electrolyte solution was weaken.