to a diverse array of interfacial systems, detailed at the beginning of section 1.5, has led to the development of an equally diverse set of techniques used to measure that charge. No single technique is applicable to every system, with some being more suitable for the study of particulate (colloidal) systems, while others are best used on extended substrates. This section aims to summarise the techniques that have historically been used to measure surface charge, and motivate the opportunities for SICM as an alternative method for spatially resolved charge mapping on extended substrates. Studies of surface charge via electrocapillary phenomena at a dropping mercury electrode were essential to many of the foundational studies of surface charge, but are not included here as they have been reviewed extensively and are far
removed from the applications for which SICM is used in this thesis.150,153
1.4.2.1 Zeta-potential Measurements: One of the most common ways to
investigate surface charge in colloidal systems is to measure it indirectly using a
concept known as the zeta (ζ) potential.155,156
For a NP in solution, the ζ-potential is
defined as the difference in electric potential between the ‘slipping plane’ of the NP and the bulk solution (Figure 1.9). When in solution, a charged NP will form an EDL of counterions, as described in section 1.4.1. The EDL can be separated into the compact Stern later, comprised of ions that are either adsorbed on the surface or at the point of closest approach, and the diffuse layer. When considering charged particles under an external electric field, the diffuse layer around a NP can be further subdivided into those ions that are sufficiently close to the NP that they keep their position as the NP moves through solution, and those that are distant from the NP such that the electrostatic forces are too weak to hold them next to the particle (Figure 1.9a). The boundary between these two regions is known as the slipping
plane, and it is at this point that the definition of the ζ-potential is taken (Figure 1.9b). When the surface of the NP is charged, that charge can be related to the
surface potential, !!, by a relation such as that in equation 1.1. The presence of both
the Stern layer and the diffuse layer lead to a decrease in the electric potential further from the surface of the NP, and as these layers are ‘attached’ to the NP it is not possible to measure the surface potential directly.
Figure 1.9. Defining the ζ-potential at a charged NP. (a) Schematic of a negatively
charged NP, surrounded by a compact Stern layer of cations and a diffuse layer held
within the slipping plane. (b) The ζ-potential of the NP is taken at the slipping plane,
and is of a lower magnitude than the Stern and surface potentials.
As the ζ-potential cannot be directly measured, it has to be deduced by
subjecting particles to an external electric field and tracking their movement in
solution, known as their electrophoretic mobility. The theory that relates ζ-potential
to electrophoretic mobility was developed by Smoluchowski in the early 20th
Century and makes several assumptions such as the EDL thickness being significantly smaller that the particle radius. If this is not the case (as in very low
electrolyte concentrations), then an alternative theory is used. ζ-potentials are
measured in millivolts, and particles with a higher magnitude ζ-potential are more
stable and less prone to aggregation.157,158
The measurement of the ζ-potential of
1.4.2.2 Electrostatic Force Microscopy: Electrostatic force microscopy (EFM) is one of several techniques that are capable of creating spatially resolved images of the
charge on a surface.159
In EFM, a cantilever analogous to that used in AFM is oscillated at some separation (at least tens of nanometres) from the surface. A potential difference of known magnitude is applied between the cantilever and the surface, and the work functions of both the probe and the substrate must be known to make an accurate measurement. As the probe is scanned over the surface, long-range electrostatic forces can affect both the resonant frequency and amplitude of the cantilever oscillation, and it is these variables that are the measurable quantities in an EFM. In order to probe electrostatic forces at a large separation from the surface, an EFM typically operates under vacuum or in a non-conductive solution. If the substrate and cantilever were under electrolyte solution, the formation of EDLs would hinder the required potential difference between the probe and surface. Despite this drawback, EFM has been used to investigate many systems, including
graphene surfaces in a water environment,160
the reduction of graphene oxide,161
single triglycine sulfate crystals,162
and proteins via both imaging163
and approach
curves.164
The interpretation of electrostatic forces in force microscopy remains a
challenge,165 particularly when imaging under electrolytic conditions.166,167 In order to
measure electrostatic forces, the probe itself must be charged. While this charge may be known at the beginning of an experiment, it is liable to change throughout the course of a scan, making the extraction of reliable charge data extremely challenging. Despite these difficulties, there have been multiple studies using AFM
in a non-conventional mode to measure charge density on an extended substrate.168–
172
Despite the success of some of these new imaging modes, force microscopy remains unable to probe the surface charge density on living cells, as they require a high concentration of electrolyte to maintain realistic physiological conditions. Under this setup, the EDL is compressed to less than 10 angstroms and thus probing it directly with force microscopy would likely lead to the damage of the cell. It is in these biological systems that SICM has been shown to be able to resolve surface
1.4.2.3 Additional Methods: A further scanning probe technique that has been used
to investigate surface charge is Kelvin probe force microscopy (KPFM).174–177
KPFM uses a conducting tip with an applied AC voltage to form a capacitor between the probe and the surface. When a direct current flows between the tip and the surface, the cantilever vibrates, and the magnitude of that oscillation is then translated into the local potential difference between the tip and the surface, and thus the surface potential. KPFM has largely been applied to either conducting or semiconducting
materials,177
with a handful of studies investigating biological substrates.178,179
While KPFM has been used to successfully map surface potential on the nanoscale, it requires significant knowledge about the physical properties of the probe in order to
correctly infer information about the surface,177
and has thus not been as widely used as it may otherwise have been.
Surface plasmon resonance (SPR) is a technique in which a surface is
irradiated in order to study the interaction of electrons at the interface.180
As SPR is highly sensitive to the environment directly adjacent to the irradiated surface, it is possible to study interactions on the same length scale as the EDL. It has traditionally been used the study the adsorption of molecules onto a surface, but has
also found application in the measurement of surface charge.181
In the first study to use SPR for the investigation of surface charge, the charge on silica NPs was shown to influence the point of closest approach to a surface coated with a charged layer of
the same parity.181
Combining the experimental observations with a theoretical consideration of the system, it was possible to simultaneously study both the
topography and charge of individual particles using SPR.181
Further to that initial study, SPR has been used to detect small molecules in a surface charge based
regime,182
and to track the charge-dependent swelling of nanocrystalline films.183
However, SPR still suffers from a topography-charge convolution that is common to many of the above techniques, which often means that one of the two factors needs to be either known or assumed before the experiment can begin. The deconvolution of charge and topography has been an important aspect of surface charge mapping
with SICM,60
and is discussed in more detail in Chapter 3.