Extending the diffuse layer model of surface acidity constant behaviour: IV. Diffuse layer charge/potential relationships

Abstract

Most current electrostatic surface complexation models describing ionic binding at the particle/water interface rely on the use of Poisson–Boltzmann (PB) theory for relating diffuse layer charge densities to diffuse layer electrostatic potentials. PB theory is known to contain a number of implicit assumptions whose significance in environmental applications is largely unknown. This study seeks to better quantify the impact of these assumptions by: (1) comparing potentials obtained from planar analytical solutions to the PB with those obtained from Hypernetted Chain (HNC) theory (Attard, 2006), (2) assessing the accuracy of the Ohshima et al. (1982) spherical approximate analytical solution to the PB equation by comparison with published numerical values (Loeb et al., 1961), and (3) comparing interfacial potential estimates obtained from the spherical approximate analytical solution to the PB equation at and adjacent to the particle surface with potential estimates obtained from the Entropic Balanced Surface Potential (EB) model (Loux, 1985; Loux and Anderson, 2001) and published potential estimates obtained from the Hypernetted Chain/Mean Spherical Approximation procedure (HNC/MSA; Gonzalez-Tovar and Lozada-Cassou, 1989). EB potential estimates were obtained assuming a surface volume thickness equal to the Bjerrum length (0.357 nm in a room temperature monovalent electrolyte solution). Findings from the study included: (1) the planar, surficial HNC estimates compared favourably with planar surficial PB relationships at charge densities equal to or less than 0.05 C m−2, (2) the Ohshima et al. (1982) approximate spherical analytical solution to the PB equation replicated the numerical charge density estimates required to obtain 72 datapoints over an e<img>/kT range of one to four with a maximum error of 3.37% and a coefficient of variation of 0.92%, (3) for a 0.1 μm radius particle in a room temperature 0.01 M (1 : 1) ionic strength solution, potential estimates over a surface charge density range of 0 to 0.3C m−2 occurred in the following order: ψHNC/MSA,R >ψPB,R >ψHNC/MSA,R+0.2125nm >ψPB,R+0.2nm ~ ψEB >ψHNC/MSA,R+0.425nm ~ ψPB,R+0.4nm and (4) with 45 datapoints including both 1 μm and 10 nm radius particles over an ionic strength range of 1.0 to 0.001 M, the PB potential estimates 0.2 nm from the particle surface (ψPBR+02nm) closely tracked the corresponding EB estimates (ψEB) with a 5.3% coefficient of variation. If one assumes that interfacial potential values adjacent to the particle surface are most relevant for describing environmental phenomena and that a 10% coefficient of variation in potential estimates is acceptable, then presumably any of the non-surficial charge/potential relationships would be useful below an absolute charge density of 0.125 C m −2 (with monovalent electrolyte solutions).