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Estimation of zeta potentials of titania nanoparticles by molecular simulation
Niall J. English a,∗ , William F. Long b
The SEC Strategic Research Cluster and the Centre for Synthesis and Chemical Biology, Conway Institute of Biomolecular andBiomedical Research, School of Chemical and Bioprocess Engineering, University College Dublin, Belfield, Dublin 4, Ireland
Chemical Computing Group Inc., 1010 Sherbrooke Street W., Suite 910, Montréal, Québec, Canada H3A 2R7
Non-equilibrium molecular dynamics (NEMD) simulations have been performed for static electric fields for a range of positively charged sphericalrutile–titania nanoparticles with radii of 1.5 to 2.9 nm for two different salt concentrations in water, in order to simulate electrophoresis directly. Using the observed limiting drag velocities, Helmholtz–Smoluchowski (HS) theory was used to estimate their ζ potentials. These estimates were compared to values from numerical solution of the non-linear Poisson–Boltzmann (PB) equation forrepresentative configurations of the nanoparticles, in addition to idealised analytic and Debye–Hückel (DH) solutions about spherical particles of the same geometry and charge state, for the given salt concentrations. It was found that reasonable agreement was obtained between the various approaches, with the NEMD-HS results some 15%–15% smaller than the numerical PB results for more highly chargednanoparticles. © 2009 Elsevier B.V. All rights reserved.
Article history: Received 15 April 2009 Available online 23 June 2009 Keywords: Nanoparticles Titania Zeta potential Electrostatic potential Molecular dynamics Poisson–Boltzmann Electrophoresis Electric field
1. Introduction Zeta potentials are important for characterising the interactions of a wide variety of charged particles, from colloidsto nanoparticles, with their environment. They are measured directly from experiments performing electrophoresis, and have important ramifications in processes employing electrophoretic deposition (EPD) [1,2]. In electrolyte solutions, the electrostatic interactions between charged particles and their surrounding electric double layer determine the kinetics of aggregation, flocculation,coalescence, coagulation, as well as interactions with surfaces which may lead to deposition or adsorption. Titania is an important technological material, and studies of the interaction of titania nanoparticles with biological systems and the environment are of increasing interest . The electrostatic properties of the double layer are highly influential in these interactions, for instance indetermining the ‘biological identity’ of nanoparticles through the protein ‘corona’ adsorbed on their surfaces . The possibility of using computational methods to estimate electrostatic properties of nanoparticles, in particular the ζ potential and the electrostatic potential (ESP) distribution, is clearly attractive. The motivation of this study is to use a variety of methods to estimate the ζ potentialand ESP distribution of a variety of representative titania nanoparticles. One of the main topics in the physics of charged particles relates to charge screening, which affects the ESP directly. The numerical solution of the non-linear Poisson–Boltzmann equation generates the ESP about particles directly, and this may be gauged as the ‘definitive’ solution, but useful analytic approaches areavailable for ESP distributions, via solution of either the linear PB equation, e.g. in Debye–Hückel, Derjaguin–Landau  or Verwey–Overbeek  approaches, or the non-linear form for spherical geometries given by Wang et al. [7–10] and D’yachkov . The Gouy–Chapman–Stern model may then be used to estimate the ζ potential at the Debye length, κ −1 .
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