Contact condition for the density profiles in spherical and cylindrical double layers

Optimising nanoporous supercapacitors for heat-to-electricity conversion

“…Challenging in experiments, this search can be aided by theoretical models. Many supercapacitors models, including those by Douglas Henderson and his collaborators [24][25][26][27][28], focused on the charging of narrow cylindrical pores [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. The behaviour of ions in such pores can be captured by onedimensional models that have analytically-tractable solutions [29,30,[32][33][34].…”

On the contact conditions for the density and charge profiles in the theory of electrical double layer: From planar to spherical and cylindrical geometry

“…The exact formulation of the CT for the TDP for the electric double layers in spherical and cylindrical geometries was obtained by Silvestre-Alcantara, Henderson and Bhuiyan [28]. According to their results, the CT for the TDP for the surface with nonplanar geometry can be presented in the form…”

“…( 24) for the density profile is identical to Eq. (11) obtained by Silvester-Alcantara, Henderson and Bhuiyan [28].…”

“…In the limit R s → ∞ for the spherical surface or in the limit R c → ∞ for the cylindrical surface, the CTs for the TDP and for the CDP reduce to the planar case. In particular in [28], it was shown that due to the local electroneutrality condition…”

“…In Ref. [28], this result was explained by the fact that in the case of a planar symmetry, one must assume the existence of a second electrode of opposite charge at infinite separation from the first electrode which contributes the identical additional electric field εE/(8π). In order to obtain the similar result from Eq.…”