https://doi.org/10.1140/epje/s10189-023-00334-2
Regular Article - Soft Matter
Renormalized charge and dielectric effects in colloidal interactions: a numerical solution of the nonlinear Poisson–Boltzmann equation for unknown boundary conditions
1
Stuttgart Center for Simulation Science (SC SimTech), University of Stuttgart, 70569, Stuttgart, Germany
2
Institute for Computational Physics, University of Stuttgart, Allmandring 3, 70569, Stuttgart, Germany
3
, 2a Malzeard Road Surgery, LU3 1BD, Luton, UK
4
Forschungszentrum Jülich (FZJ), Jülich Supercomputing Centre, 52428, Jülich, Germany
5
Department of Chemical Engineering, University College London, WC1E 7JE, London, UK
Received:
2
June
2023
Accepted:
11
August
2023
Published online:
11
September
2023
The Derjaguin–Landau–Verwey–Overbeek (DLVO) theory, introduced more than 70 years ago, is a hallmark of colloidal particle modeling. For highly charged particles in the dilute regime, it is often supplemented by Alexander’s prescription (Alexander et al. in J Chem Phys 80:5776, 1984) for using a renormalized charge. Here, we solve the problem of the interaction between two charged colloids at finite ionic strength, including dielectric mismatch effects, using an efficient numerical scheme to solve the nonlinear Poisson–Boltzmann (NPB) equation with unknown boundary conditions. Our results perfectly match the analytical predictions for the renormalized charge by Trizac and coworkers (Aubouy et al. in J Phys A 36:5835, 2003). Moreover, they allow us to reinterpret previous molecular dynamics (MD) simulation results by Kreer et al. (Phys Rev E 74:021401, 2006), rendering them now in agreement with the expected behavior. We furthermore find that the influence of polarization becomes important only when the Debye layers overlap significantly.
© The Author(s) 2023. corrected publication 2023
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