Pore connectivity effects on the internal surface electric charge of mesoporous silica

  • Tumcan Sen
  • Murat BarisikEmail author
Original Contribution


Nano-scale confinements within mesoporous systems develop overlapping electric double layers (EDL) such that the existing theoretical models cannot predict the electric potential distributions and resulting surface charges. In addition, ionic conditions undergo local variation through connections between the pore voids and pore throats. For the first time in literature, we studied the charging behavior of mesoporous silica in terms of the pore to throat size ratio (Rpt) to characterize the pore connectivity effects, in addition to porosity (є) and pore size (H). Both local and average surface charge densities inside mesoporous silica were examined by varying these parameters systematically. Results showed that the magnitude of surface charge density decreased with increasing EDL overlap and decreasing connectivity effects. We formulized this behavior and developed an extended model to predict mesoporous silica’s internal charge as a function of porosity, pore size, and pore to throat size ratio.

Graphical abstract

The table of contents entry


Mesoporous silica Internal surface electric charge Poisson-Nernst-Planck equations Charge regulation model Porosity Pore to throat connectivity 



Electric double layer


Boltzmann distribution




Charge regulation


Representative elementary volume


Pore size


Pore to throat size ratio


Bulk concentration of H+


Bulk concentration of K+


Bulk concentration of Cl


Bulk concentration of OH




Debye length


Debye-Hückel parameter


Permitivity of vacuum


Dielectric constant


Boltzmann constant




Avagadro constant


Elementary charge


Local concentration of the ith ion


Valance of the ith ion


Electric potential


Flux density




Faraday constant


Universal gas constant


Site density


Equilibrium constants


Surface charge density


Aspect ratio of the solid parts



This work was supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK) under the Grant Number 118M710. Authors also would like to thank the Center for Scientific Computation at Southern Methodist University.

Funding information

This work was supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK) under the Grant Number 118M710

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringIzmir Institute of TechnologyIzmirTurkey

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