Role of neutral and non-hard sphere interaction in differential capacitance of electrical double-layer

Abstract

Classical density functional theory is combined with the extended primitive model and solvent primitive model to investigate how differential capacitance Cd of electrical double-layer formed inside cylindrical pore is influenced by solvent granularity, bulk concentration, counter-ion diameter, and neutral and non-hard sphere (HS) potential utail_αβ(r) between ion species, between solvent and counter-ion (and co-ion). Several main conclusions are drawn. (i) The Cd−surface charge strength (|σ|) curve generally rises as a result of consideration of the solvent granularity. (ii) An interionic attractive utail_αβ(r) helps in raising the Cd curve whereas a repulsive utail_αβ(r) tends to lower the Cd curve. Moreover, a secondary Cd peak appears when |σ| increases to an appropriately large value, and becomes increasingly evident with the strength of the attractive utail_αβ(r) and eventually disappears as the attractive utail_αβ(r)reduces in attraction or changes into repulsion at all. (iii) The Cd − |σ| curve is raised by increasing the repulsion between the solvent and counter-ion; however, both counter-ion diameter and bulk concentration cause obvious changes of the Cd − |σ∗| curve morphology. Concretely speaking, the Cd peak height and the peak position rise with the counter-ion size decreasing. Moreover, changing the utail_αβ(r) between solvent and counter-ion from attraction to repulsion facilitates a transition from bell-shaped curve to camel-shaped curve. (iv) Effects of all of the factors considered in influencing the Cd curve diminish increasingly with |σ|. All of the above observations can be explained by considering the interionic depletion potential induced by the solvent and its changes with the system parameters.