Although techniques such as X-ray photoelectron spectroscopy (XPS) have provided in-
formation on ion stucture at the aqueous silica interface,58, 59, 60 experimental methods
that allow the direct observation of the interfacial ion distribution with subnanometer resolution, as demonstrated in a recent high resolution atomic force microscopy (AFM)
study, have not yet been well-established generally.61 Thus, theoretical models dat-
ing back to the early 20th century are still routinely used to describe the interface and
interpret experimental data.62
The majority of materials will experience surface charging when placed in con- tact with an aqueous solution. For the natively oxidised silicon surface, this charging is
due to deprotonation/protonation of silanol groups (giving SiO−, SiOH and SiOH2+), a
pH and salt concentration dependent process. Electrostatic attraction results in a higher concentration of counterions near the surface compared to the concentration in bulk so-
lution, whilst repulsion means co-ions (ions of the same charge as the surface) will be more concentrated in the bulk. The net charge in a solution volume near the surface balances the surface charge. This liquid region and the charged surface is defined as the electrical double layer (EDL). Different affinities between the ions and the surface
may also lead to the formation of an EDL.63, 64, 65, 66Indeed, the existence of an EDL at
charge-neutral surfaces has been confirmed experimentally.67
The EDL can be further characterised and various models have been developed.
The Helmholtz68 -Gouy64-Chapman65 -Stern66 -Grahame69 model, commonly termed
the Gouy-Chapman-Stern (GCS) model, has been frequently employed, even in recent years, and was shown to quantitatively explain most experimental results within the low
to moderate surface charge regime.70, 71 The model is shown schematically in Figure
1.6. In this model, an EDL formed as result of electrostatic interactions between the charged surface and ions in solution, with counterions being more concentrated near
the surface compared to bulk and a higher concentration of co-ions in the bulk.62 The
EDL was classed into two distinct regions: the Stern layer, composed of the inner Helmholtz plane where counterions specifically adsorbed to the surface and the outer Helmholtz plane where hydrated ions were adsorbed; and a diffuse outer layer with a net charge that gradually decayed to zero as bulk solution was approached (the lower the ionic strength of solution, the wider this layer will be). The classical GCS model has been criticized for several reasons and many variants of the classical GCS model have
been developed.61 Dukhinet. al. presented experimental evidence that indicated EDL
formation could occur at charge-neutral surfaces and suggested that interfacial water
structure should be considered as a governing influence.67 The importance of solvent
structure was also emphasized by Wu and co-workers.71 Cardenas attributed the success
of the model to its ability to describe experimental results from the classical mercury- solution interface and other Nernstian systems, arguing that the model broke down for
non-Nernstian systems, such as oxides.58 Experimental data at the subnanometer scale
is limited and despite its widespread use, the GCS model may not be applicable to oxide systems. Furthermore, interfacial solvent structure could be more important than accounted for in the model.
Figure 1.6: Schematic of the Gouy-Chapman-Stern layer. The inner Helmholtz plane (IHP), outer Helmholtz plane (OHP) and Stern layer have been labelled.
There was a dynamic aspect to the GCS model. In standard models, the fluid within the Stern layer was considered immobile and a plane of shear - where the viscos- ity changed sharply from an infinite value to the bulk solution viscosity - was located
at the boundary between this immobile region and the diffuse layer.72 This concept
has been well-accepted and used in the physics, electrochemistry and colloidal science communities. Indeed, the zeta potential, an experimentally accessible parameter com- monly used as a measure of surface charge, was defined as the electrostatic potential at the slipping plane. Crucially, however, surface conduction measurements higher than
could be produced solely from ions outside of the Stern layer have been recorded.73
Furthermore, there are many cases where zeta potentials obtained by different experi- mental techniques varied unless a contribution to surface conductivity from ions in the Stern layer was included; the Helmholtz-Smoluchowski (H-S) equation, often used in the interpretation of electrokinetic data and zeta potential calculation, did not account
for it.74, 75, 73, 76 A ’dynamic Stern layer’, in which ions with near bulk mobility migrate
through immobile water, was proposed.74, 75, 73, 77 Lyklema proposed that ions were able
to move through the regions located at the distances of the solvent density minima.73
Some, however, did not interpret the ’dynamic Stern layer’ model in a literal way. In- deed, Saville and Zukoski, who derived such a model, viewed it as ’one that allows
the introduction of certain functional relationships which reproduce the experimental
results’.74 An alternative model, where water was also mobile within the Stern layer,
was suggested.78 Although variants of the traditional model have been developed to ra-
tionalize higher than expected surface conduction measurements, experimental support at the atomic scale is limited and this area, as with that of interfacial ion structure, has particularly benefited from the insight of atomistic simulations.
Most attempts to locate the slipping plane using atomistic simulation have fo- cussed on determining the ’sharp’ boundary between the mobile and immobile layers through calculation of dynamic properties, such as velocities, viscosities and diffusion constants. This method directly probes hypotheses based on a mobile Stern layer. The ultimate aim of some attempts to locate the slipping plane is to calculate the zeta poten- tial.
The validity of the traditional GCS model and ’dynamic Stern layer’ at the aqueous electrolyte-amorphous silica interface was specifically addressed in a non-
equilibrium molecular dynamics (NEMD) study of Singer et. al. in 2011.72 Ion and
water surface parallel velocities were calculated as a function of distance from the sur- face and found to be qualitatively the same for the interface with NaCl solution at three different concentrations, 0 M, 0.30 M and 0.55 M. Though water mobility gradually re-
duced in a region 3 ˚A from the surface and approached zero, it was not immobile. Fur-
thermore, ion mobility followed the same trend and was not enhanced compared to that of the solvent. Indeed, solvent immobility was only observed when the surface charge was increased to an extremely high value and coincided with a region of immobilized cations. Surface conductivity calculations from the simulation were, however, similar to the corresponding experimental values. The absence of quiescent layers of water at
typical surface charge densities was supported by a simulation study of Lorenz et. al
featuring the calculation of electro-osmotic velocities of 0.4 M NaCl and 0.2 M CaCl2
solutions in an amorphous silica nanopore of width 7.5 nm.79 Classical simulation stud-
ies of the charge-neutral quartz/pure water interface also reported a region of reduced
solvent mobility close to the surface.80, 3 Joseph and Aluru calculated surface parallel
ion and water diffusion coefficients from an NEMD simulation of a flat, neutral, crys-
talline α-quartz surface in 1 M KCl solution.81 Close to the surface, in the first layer
of water molecules, water diffusion coefficients had reduced to 38% of the bulk value. Although the observance of a region of immobile water or ions was not commented
on, in a 2014 study of amorphous silica nanoparticles, Heinzet. al. did note a correla- tion between the amount of higher mobility, free cations and experimentally determined
values of the zeta potential as a function of pH and particle size.82 Computed interfa-
cial ion and solvent dynamics did not support the ’dynamic Stern layer’ concept of the traditional and widely-applied GCS model and provided insight that could inform the development of future theoretical models.