Bruggeman Model For Concentration Dependent Dieletrics:Theory And Numerics

The structure of the electric double layer has long been described by the classi-cal Poisson-Boltzmann(PB)theory,in which a uniform dielectric coefficient is often assumed.Experimental data and molecular simulations evidence that the effective di-electric coefficient decreases as local ionic concentrations.In this work,we develop a modified PB theory with concentration-dependent dielectrics that are described by the Bruggeman equation,which defines an implicit function of the effective dielectric co-efficient on both the size and dielectric coefficients of hydrated ions.The Bruggeman equation,which takes into account contributions from both counterions and coions systematically,provides a closure to the modified PB theory,making the theory self-consistent.In addition to ionic size and valence,our theory introduces another source of ion-specificity,i.e.,the dielectric coefficient of hydrated ions,to the continuum mod-eling of electrostatics.Asymptotic analysis reveals the connection between the modified PB theory and previous linear decrement models,and derives a criterion for the pres-ence of counterion saturation.Robust numerical methods with efficient acceleration techniques are proposed to solve the resulting coupled equations.Dielectric coefficients predicted by our theory show good agreement with the experimental data for certain electrolytes.The dielectric decrement effect on the ionic structure of electric double layers is assessed in extensive numerical simulations.With ion-specific parameters,our theory predicts asymmetric camel-shape profiles of differential capacitance against ap-plied potentials for electrolytes with low salinity,and asymmetric bell-shape profiles for electrolytes with high salinity.The impact of counterion saturation,arising from the steric effects and dielectric decrement,on the shape of differential capacitance profiles is demonstrated through analysis and numerical investigations.To further understand the effect of concentration-dependent dielectrics,the modified PB theory is also ap-plied to study the distribution of counterions around charged cylinders with various dielectric coefficients.