Determination of Surface Potential and Electrical Double-Layer Structure at the Aqueous Electrolyte-Nanoparticle Interface

The structure of the electrical double layer has been debated for well over a century, since it mediates colloidal interactions, regulates surface structure, controls reactivity, sets capacitance, and represents the central element of electrochemical supercapacitors. The surface potential of such surfaces generally exceeds the electrokinetic potential, often substantially. Traditionally, a Stern layer of nonspecifically adsorbed ions has been invoked to rationalize the difference between these two potentials; however, the inability to directly measure the surface potential of dispersed systems has rendered quantitative measurements of the Stern layer potential, and other quantities associated with the outer Helmholtz plane, impossible. Here, we use x-ray photoelectron spectroscopy from a liquid microjet to measure the absolute surface potentials of silica nanoparticles dispersed in aqueous electrolytes. We quantitatively determine the impact of specific cations (${\mathrm{Li}}^{+}$, ${\mathrm{Na}}^{+}$, ${\mathrm{K}}^{+}$, and ${\mathrm{Cs}}^{+}$) in chloride electrolytes on the surface potential, the location of the shear plane, and the capacitance of the Stern layer. We find that the magnitude of the surface potential increases linearly with the hydrated-cation radius. Interpreting our data using the simplest assumptions and most straightforward understanding of Gouy-Chapman-Stern theory reveals a Stern layer whose thickness corresponds to a single layer of water molecules hydrating the silica surface, plus the radius of the hydrated cation. These results subject electrical double-layer theories to direct and falsifiable tests to reveal a physically intuitive and quantitatively verified picture of the Stern layer that is consistent across multiple electrolytes and solution conditions.

Popular Summary

A solid-liquid boundary is characterized by an electrical double layer in which charge builds up both on the solid surface and on the adjacent aqueous layer.

The structure of this electrical double layer mediates colloidal interactions, regulates surface structure, controls reactivity, sets capacitance, and represents the central element of electrochemical supercapacitors, but the local ion arrangement near the charged surface remains poorly understood. Traditionally, a layer of nonspecifically adsorbed ions has been invoked to rationalize the difference between the surface and electrokinetic potentials. However, the inability to directly measure the absolute surface potential of dispersed systems prohibits a quantitative determination of electrical double-layer structure. Here, we use x-ray photoelectron spectroscopy from a liquid microjet to measure, for the first time, the absolute surface potentials of silica nanoparticles dispersed in aqueous electrolytes.

We employ a liquid microjet that permits the passage of a colloidal solution. The sample is only exposed to x-ray radiation for approximately $20\mu s$, so we anticipate that x-ray-induced damage is minimal. We quantitatively determine the impact of specific ion effects on the surface potential of silica nanoparticles. Using 420- and 840-eV synchrotron radiation, we ionize the sample, and we find that the magnitude of the surface potential increases linearly with the hydrated cation radius. We also determine that the thickness of the Stern layer—the charge-free region directly above the surface—corresponds to a single layer of water molecules hydrating the silica surface, plus the radius of the hydrated cation. Our findings are consistent with a simple hydration-modified Poisson-Boltzmann model.

We anticipate that our results will be applicable to a wide range of colloidal and quantum dot suspensions.

Figure 1

Surface potential measurements by XPS. (a) Energy level diagram for the photoelectron process from an unbiased sample (blue) and from a sample under positive external potential (red). $E_F$, Fermi level; $E_V$, vacuum level; $\mathrm{\Phi }$, work function; sam, sample; ana, hemispherical energy analyzer; eKE, photoelectron kinetic energy; BE, binding energy; CL, core level; V, applied potential. A positive bias shifts all of the sample levels down with respect to those of the analyzer, having the effect of decreasing the kinetic energy of the outgoing photoelectron. (b) Si $2p$ spectra from a ${\mathrm{SiO}}_2/\mathrm{Si}$ (100) substrate. Blue, grounded; red, positive (1 V) bias; black, negative ($-1\mathrm{V}$) bias. (c) Si $2p$ BE as a function of applied potential.

Figure 2

XPS at the water-silica nanoparticle interface. (a) A liquid microjet delivers a stable free-flowing suspension of colloidal silica inside the measurement chamber of an XPS spectrometer. (b) O $1s$ and Si $2p$ spectra for 5.0 wt % ${\mathrm{SiO}}_2$ in 50-mM LiCl, NaCl, KCl, and CsCl electrolytes at $p\mathrm{H}$ 10. (c) Measured Si $2p$ BE, relative to the vacuum level, as a function of hydrated cation radius [37]. The change in surface potential relative to that in NaCl electrolyte is shown on the right-hand axis. Error bars represent the standard deviation of four repeat measurements.

Figure 3

$p\mathrm{H}$-dependent absolute surface potential at the silica-electrolyte interface. Si $2p$ binding energy (left-hand axis) and absolute surface potential (right-hand axis) at the water-silica interface for 9-nm ${\mathrm{SiO}}_2$ in 50-mM NaCl electrolyte (open black markers) as a function of bulk suspension $p\mathrm{H}$. Open markers: Surface potentials at $p\mathrm{H}$ 10.0 in 50-mM LiCl (green), KCl (blue), and CsCl (red). Error bars represent the standard deviation of two measurements (four at $p\mathrm{H}$ 10.0). Solid markers: Surface potentials for various extended ${\mathrm{SiO}}_2$ surfaces as reported in the literature: SHG [38], ISFET [39], EOS [40], and Impedance [41].

Figure 4

$p\mathrm{H}$-dependent surface charge density of colloidal silica in (a) 50-mM LiCl, (b) 50-mM NaCl, (c) 50-mM KCl, and (d) 50-mM CsCl. Markers: Experimental results from three repeat measurements. Solid lines: Fits from surface complexation modeling using the basic Stern model and $4.75\mathrm{OH}\text{sites}/\mathrm{nm}$. The point of zero charge is set at $p\mathrm{H}$ 3.0 in all electrolytes [33, 34].

Figure 5

Gouy-Chapman-Stern model of the electrical double layer. (a) The structure of the electrical double layer takes the form of a charged silanol plane and an outer Helmholtz plane (OHP), which represents the distance of closest approach of ions [17]. A diffuse layer of hydrated ions sits outside the OHP, screening the net surface charge over a characteristic Debye length. (b) The surface potential is given by the potential drop across the Stern layer (bounded by the OHP) and the potential across the diffuse layer, the latter being given by the zeta potential. (c) Thickness of the Stern layer [$d_{\text{Stern}}$, from Eq. (5)] as a function of hydrated cation radius, taking the reference potential ${\mathrm{\Phi }}_0^{\mathrm{NaCl}}$ to be $-385\pm 20\mathrm{mV}$, as determined from Fig. 3. The linear fit has a $y$ intercept at $1.4\pm 0.6\AA$.

Figure 6

Surface potentials at the silica NP-electrolyte interface. Red, solid circles: Results from XPS measurements. The solid line is a linear fit to the experimental data. Black, open squares: Prediction from the hydration-modified PB model. Black, open circles: Prediction from the Grahame equation based on the classic PB model.

Figure 7

Counterion concentration profiles in the electrical double layer. Cation concentration profiles as predicted by the hydration-modified PB model (solid lines) for 50-mM electrolyte: black, CsCl; red, KCl; green, NaCl; blue LiCl. Inset: Stern layer thicknesses calculated from experiments (red, closed symbols) and predicted by the hydration-modified PB model (black, open symbols).

Figure 8

Reference O $1s$ spectrum in the absence of nanoparticles. Spectrum of 50-mM NaCl solution (no silica NPs) under identical conditions to those presented in Fig. 2. The region between 310 and 314 eV is flat in the absence of the nanoparticles.