Surface Potential and Interfacial Water Order at the Amorphous TiO₂ Nanoparticle/Aqueous Interface

Abstract

Colloidal nanoparticles exhibit unique size-dependent properties differing from their bulk counterpart, which can be particularly relevant for catalytic applications. To optimize surface-mediated chemical reactions, the understanding of the microscopic structure of the nanoparticle–liquid interface is of paramount importance. Here we use polarimetric angle-resolved second harmonic scattering (AR-SHS) to determine surface potential values as well as interfacial water orientation of ∼100 nm diameter amorphous TiO₂ nanoparticles dispersed in aqueous solutions, without any initial assumption on the distribution of interfacial charges. We find three regions of different behavior with increasing NaCl concentration. At very low ionic strengths (0–10 μM), the Na⁺ ions are preferentially adsorbed at the TiO₂ surface as inner-sphere complexes. At low ionic strengths (10–100 μM), a distribution of counterions equivalent to a diffuse layer is observed, while at higher ionic strengths (>100 μM), an additional layer of hydrated condensed ions is formed. We find a similar behavior for TiO₂ nanoparticles in solutions of different basic pH. Compared to identically sized SiO₂ nanoparticles, the TiO₂ interface has a higher affinity for Na⁺ ions, which we further confirm with molecular dynamics simulations. With its ability to monitor ion adsorption at the surface with micromolar sensitivity and changes in the surface potential, AR-SHS is a powerful tool to investigate interfacial properties in a variety of catalytic and photocatalytic applications.

Introduction

Titanium dioxide (TiO₂) is a semiconductor material with high physical and chemical stability,^1,2 which makes it particularly interesting for use in aqueous environments. Titania has a broad range of applications: It is widely used as white pigment in paints, in food coloring, and in cosmetics and personal care products, such as sunscreen and toothpaste.³⁻⁶ Furthermore, TiO₂ is a well-known photocatalyst, used among others in environmental remediation through photocatalytic wastewater treatment,⁶⁻⁹ as building material for self-cleaning glass,^7,10,11 and for energy applications, such as photocatalytic water splitting.¹²⁻¹⁴ The understanding of the surface chemical reactivity of TiO₂ is key to develop highly efficient, low-cost, and environmentally friendly photocatalytic devices. Thus, it is of fundamental interest to understand the microscopic structure of this semiconductor–liquid interface and how it is affected by the composition of the surrounding aqueous environment.

As colloidal nanoparticles possess a high surface to volume ratio, which is beneficial in order to enhance surface-mediated chemical reactions, they are an attractive and relevant system to study in this context. Colloids in water or another fluid are only stable in solution if they develop a charged layer at their surface so that the repulsive forces between the particles are strong enough to prevent aggregation or flocculation. The surface charge of the particles depends on the pH and ionic strength of the aqueous environment and is compensated by counterions in the surrounding solution.^15,16 This charged surface together with its counterions is called the “electrical double layer” (EDL). The EDL plays a fundamental role in driving physical and chemical processes at the interface. However, a complete picture of the EDL is still missing. Multiple models describing the EDL have been put forward, which usually simplify the complex structure of the interface by assuming a uniformly charged interface, by reducing the aqueous environment to a uniform dielectric, and by representing ions as point charges. A model frequently referred to is the Gouy–Chapman model in which the counterions are distributed in the fluid surrounding a charged surface in such a way that the potential inside the electrolyte decays exponentially.^2,16 This charge distribution inside the EDL is called the diffuse layer (DL). As this model fails for high charge densities of counterions near the interface, a modification was proposed by Stern, which involves the formation of a layer of hydrated counterions at the surface, the so-called “Stern layer”. This layer of countercharges close to the charged surface is expected to act like a parallel plate capacitor, causing a steep linear potential drop within the Stern layer.^2,16−19 Nevertheless, a complete realistic description of the EDL remains challenging, as the electrostatic environment of the interface depends on many factors, such as individual material properties comprising the local chemical nature of the surface, the amount and the type of ions as well as their solvation shells, and the behavior of the solvent, for example the orientation of water molecules at the interface.^2,16,19−25 Most of those parameters are difficult to access experimentally, especially without using the assumptions implied by the presented models.²⁰

The simplest approach to investigate the EDL is to use techniques measuring electrokinetic mobilities. The velocity of a suspension of particles in an applied electric field is measured and can be converted into zeta potential via the Hückel or Smoluchowski equation.^16,17,19,26 In a simplified picture,²⁷ the zeta potential is the potential at the boundary between the solvent shell of ions and water molecules moving with the particle when an electric field is applied and the rest of the static solution. This boundary is commonly termed the shear plane. However, as the shear plane is presumed to be situated 0.3 to 1 nm away from the charged particle surface,^16,17,19 the knowledge of the zeta potential alone does not provide a full picture of the electrostatic environment of the investigated sample. In order to have a more complete picture of the EDL, one can also measure the surface charge density of the particle, which can be obtained by potentiometric titrations.²⁸⁻³² Yet this technique requires larger quantities of sample (on the order of hundreds of milligrams) and assumes that ions only adsorb on the surface (i.e., the sample is nonporous)²⁸ therefore providing, at best, an upper limit for the surface charge density.

A more direct indicator of the electrostatic environment around a charged particle in solution is the surface potential. With current experimental methods, this is a rather complicated parameter to access. Kelvin probe force microscopy (KPFM) can probe surface potentials of semiconductor/air or semiconductor/vacuum interfaces on flat surfaces. In this case, the surface potential is defined as the work function difference of the semiconductor surface and the metal tip probing the surface.³³ However, applying this technique to solid/liquid interfaces brings up practical challenges^34,35 and is not to date applicable to particles in solution. So far, a method that has been proved to be suitable for the measurement of surface potential of particles in aqueous environments is X-ray photoelectron spectroscopy (XPS). XPS measurements were done on colloidal SiO₂ particles in a liquid microjet by Brown et al.,³⁶⁻³⁹ assigning the charge divided binding energy difference between the Si 2p photoelectrons in an environment containing salt and the Si 2p photoelectrons at the point of zero charge to the value of the surface potential. Nevertheless, this method requires small-sized colloidal nanoparticles (∼3–20 nm) and high salt concentrations of approximately >10 mM, in addition to synchrotron facilities. First ambient pressure XPS studies on anatase TiO₂ particles in a liquid jet were performed by Makowski et al.,⁴⁰ examining the role of surface charge in the electronic surface band bending of the semiconductor particles in contact with an electrolyte. Soft X-ray photoelectron spectroscopy measurements with a liquid microjet were also applied to anatase TiO₂ particles in another study by Ali et al. to investigate the interaction between specific surface sites and water molecules in the aqueous environment in different pH conditions.⁴¹ However, to the best of our knowledge no direct surface potential measurements have been performed on TiO₂ particle dispersions until now.

Second-order nonlinear optical techniques are suitable to study processes at surfaces and interfaces of centrosymmetric systems as second harmonic generation (SHG) is forbidden in centrosymmetric and isotropic media and therefore the signal arises only from the noncentrosymmetric regions at the interface.⁴²⁻⁴⁵ Nonlinear second-order scattering was used to obtain information about the interfacial properties of particles in liquids by the Eisenthal group,⁴⁶ including TiO₂ particles.⁴⁷ A first attempt to measure the surface potential of particles in solution was done in the same group.⁴⁸ The authors collected SHG of polystyrene sulfate spheres with a wide collection angle in the forward scattering direction and extracted the surface potential by fitting their data to the Gouy–Chapman model. In a more recent work, Yang et al.⁴⁹ were the first to measure resonant angular-resolved second harmonic scattering (AR-SHS) patterns from polystyrene colloids with surface-adsorbed malachite green in water. The angular-dependent scattering pattern is strongly polarization-dependent and holds information about the size and shape of the particles.⁴⁹⁻⁵¹

We recently showed the universal applicability of polarimetric angle-resolved second harmonic scattering (AR-SHS) in nonresonant conditions to extract values for the surface potential Φ₀ of a particle with respect to bulk liquid,⁵²⁻⁵⁶ with no a priori theoretical treatment to model the distribution of charges in the electrical double layer. Furthermore, AR-SHS enables one to obtain absolute values for the surface susceptibility χ_S,2⁽²⁾, which contains information about the orientation of interfacial water molecules. This nonresonant SHS technique has the advantage of being noninvasive and performed at ambient pressure on particles of a broad size range that are directly dispersed in solution. In this work, we apply AR-SHS to semiconductor particles, showing how the surface potential and surface susceptibility of ∼100 nm diameter amorphous TiO₂ particles evolve as a function of NaCl and pH. Three different regions can be identified with increasing ionic strength. We compare the results to SiO₂ particles of the same size investigated in different ionic strength conditions. Our findings are further supported with molecular information gathered by molecular dynamics (MD) simulations. The knowledge of surface potential and surface susceptibilty, together with the zeta potential and MD simulations, allow us to get a deeper understanding of the microscopic structure of the EDL around colloidal TiO₂ and SiO₂ in different salt and pH conditions.

Materials and Methods

Chemicals

Sodium hydroxide, (NaOH, > 99.99% trace metals basis, Sigma-Aldrich) and sodium chloride (NaCl, > 99.999%, abcr GmbH) were used as received. TiO₂ colloids (∼100 nm diameter) were purchased already dispersed in solution from Corpuscular Microspheres Nanospheres (2.5% w/v). The purity of the sample and the absence of stabilizing surfactants was verified by elemental analysis (1.04% C, 0.31% H, and 0% N). The residual carbon is likely to be due to a small amount of dissolved CO₂ or residual impurities from the synthetic process. Furthermore, the elemental analysis results of the stock solution are similar to the ones obtained for a TiO₂ sample in powder form with 99.9% purity from a different manufacturer (US Research Nanomaterials, with elemental analysis 1.1% C, 0% H, and 0% N). This confirms that no sizable amount of surfactants is present in the as-received particle solution (before the washing process). SiO₂ microspheres of 100 nm diameter were purchased from Polysciences, Inc. (5.9% w/w). The SiO₂ and TiO₂ particles were washed as described in the sample preparation section.

Sample Preparation

All procedures described hereafter used ultrapure water (Milli-Q, Millipore, Inc., electrical resistance of 18.2 MΩ·cm). The 2.5% w/v stock solution of colloidal TiO₂ particles was sonicated for 30 min (35 kHz, 400 W, Bandelin) and vortexed 2 min prior to usage. The stock was then diluted in water to a 0.5% w/v solution, where the particles were stabilized by addition of NaOH up to a final concentration of 80 μM. The 0.5% w/v dilution was then further sonicated for 10 min and vortexed 2 min. In order to remove residual ions from the synthetic procedure, nanoparticles were then collected via centrifugation and resuspended in Milli-Q water at the same concentration of 0.5% w/v. The pellet was resuspended by vortexing 5 min and ultrasonicating for 10 min. The conductivity of the washed particles was measured as described in the section Sample Characterization to ensure that the initial ionic strength of the particle solution was as low as possible. The TiO₂ particles were further diluted to 0.05% w/v solutions (corresponding to approximately 4.3 × 10¹¹ particles/mL) containing the desired amount of NaOH or NaCl. The pH or ionic strength of the solutions was adjusted using 0.1 mM or 1 mM solutions of NaOH and NaCl. The 0.05% w/v solutions were vortexed 2 min and sonicated 10 min, then filtered using four 0.2 μm PES syringe filters (Filtropur Sarstedt) per 10 mL tube to remove particle aggregates. We quantified the percentage of aggregates in the 0.05% w/v dilution by dynamic light scattering experiments and find this number to be very small (0.3% of the total number of particles), indicating that only a small fraction of the sample is lost through the filtering process. After filtering, each sample was sonicated another 10 min and vortexed 2 min. The sample stability over time is dependent on the salt concentration and pH, usually with particles remaining in suspension for several days. However, in order to keep consistent experimental conditions, the TiO₂ solutions were always prepared and measured on the same day. Corresponding water references at the same pH and ionic strength were prepared for each TiO₂ sample. For SiO₂ particle solutions and references a similar preparation procedure was employed. The particles were washed twice, but no additional NaOH was added. The SiO₂ stock solution was diluted to a 0.06% w/v solution (corresponding to approximately 2.9 × 10¹¹ particles/mL) containing the desired amount of NaOH or NaCl. No filtering of the particles was necessary. All preparation steps and measurements were performed at room temperature.

Sample Characterization

The particle size distribution was determined by dynamic light scattering (DLS), and the zeta potential was measured by electrophoretic measurements (Zetasizer Nano ZS, Malvern). After the filtering process, the TiO₂ colloids had a mean hydrodynamic diameter of ∼120 nm with a uniform size distribution (for most samples, polydispersity index (PDI) ≈ 0.1). The SiO₂ particles had a mean hydrodynamic diameter of ∼125 nm with a uniform size distribution (polydispersity index (PDI) < 0.05). Average radii and zeta potentials are given as the average of 3 measurements. The pH of the samples was determined using a pH meter (HI 5522 pH/ISE/EC bench meter and HI 1330 pH electrode, Hanna Instruments) calibrated with the appropriate buffer solutions. In order to control the amount of salt added to the samples and the initial ionic strength of the washed TiO₂ particles in water, the conductivity was measured by two different means: first using a conductivity meter (HI 5522 pH/ISE/EC bench meter and HI 76312 conductivity electrode, Hanna Instruments) calibrated with the appropriate buffer solutions and second, using the conductivity obtained from the zeta potential measurements (Zetasizer Nano ZS, Malvern). Knowing the conductivity σ, the average ionic strength, represented by the concentration of ions in solution c, was calculated using the equivalent (molar) ionic conductivity Λ_m:⁵⁷

Here λ_i are the equivalent ionic conductivities of the cations and anions present in the electrolyte that were taken from ref (58), and υ_i refers to the number of moles of each ion. In cases where the theoretical salt concentration of the sample is below 0.5 mM, the ionic molar conductivity at infinite dilution Λ_m^° can be used, whereas for a theoretical concentration of above 0.5 mM, the ionic molar conductivity Λ_m should be calculated according to the Debye–Hückel–Onsager equation. For all the samples considered here with a salt concentration below 0.5 mM, the ionic molar conductivity at infinite dilution Λ_m was used.

For TiO₂ samples diluted in ultrapure water where no salt was added, the average conductivity was assumed to be due to residual Na⁺ and OH^– ions from the preparation process. The measured conductivity values of washed and filtered samples at pH 7 without additional salt of the same particle batch varied from 9.7 to 11.3 μS/cm (corresponding to an ionic strength of 3.9 × 10^–5 and 4.6 × 10^–5 mol/L). This conductivity, attributed to residual Na⁺ and OH^– ions in solution, was subtracted from the conductivity measured for TiO₂ samples where salt was added in order to calculate the pure contribution of Na⁺ and Cl^– ions to the ionic strength of the solution. The total ionic strength value of the samples used in the fitting procedure includes the ionic strength originating from the Na⁺ and Cl^– ions, as well as the residual Na⁺ and OH^– ions.

AR-SHS Model and Theory

In the following, we want to briefly summarize some of the important aspects of the AR-SHS model and the nonlinear optics theory that are relevant for the fitting procedure. A more detailed description can be found elsewhere.^{52−54,59,60} In a nonresonant AR-SHS experiment, the fundamental frequency of a high energy femtosecond laser pulse interacts with an aqueous solution that contains particles. The intense femtosecond laser pulses distort the electron clouds of all noncentrosymmetric molecules, which causes a displacement of charge with a frequency component of 2ω. These induced charge oscillations are, to leading order, the origin of molecular dipole moments. The sum of the molecular SH dipoles results in a macroscopic polarization P⁽²⁾. This polarization P⁽²⁾ is defined as

1

where ε₀ is the permittivity of free space, χ⁽²⁾ is the second-order susceptibility, which describes the local second harmonic response of the medium, and E(ω) is the incoming electromagnetic field for SHS. The generated electromagnetic wave has double the frequency (2ω) of the incoming light. In the electric dipole approximation, the emission of SH light is forbidden in the bulk of centrosymmetric media as they possess inversion symmetry. Considering a spherical particle with an isotropic amorphous interior and water as an isotropic liquid, the SH signal originates specifically from the noncentrosymmetric regions at the interface. Under nonresonant conditions, the second-order polarization P⁽²⁾ depends on the molecular electron density in the interfacial region. Therefore, every noncentrosymmetric molecule in the noncentrosymmetric region around the particle contributes equally to the SH polarization. However, since the SH intensity scales quadratically with the number density of molecules, the majority of the SH signal intensity originates from water molecules at the interface, as the number of noncentrosymmetrically distributed surface groups of the particle is much smaller than the number of oriented water molecules at the interface. The SHS signal then arises from the net orientational order of water molecules along the surface normal. Besides the χ⁽²⁾ contribution to the SHS signal that describes the orientational order induced by all (chemical) interactions confined to the particle surface plane, the electrostatic field, E_DC, generated between the counterions and the charged surface affects the SHS signal. The effective third-order susceptibility tensor, χ^(3)′ represents all processes that lead to the emission of SH light and require an interaction with E_DC. This includes the reorientation of water molecules in the interfacial region and in the bulk solution (main χ^(3)′ contributions), as well as a pure third-order interaction that arises from the isotropic third-order susceptibility of bulk water. The resulting effective third-order polarization P^(3)′ is defined as

2

with being the surface potential. We then obtain for the total SHS intensity . Thus, within the Rayleigh–Gans–Debye (RGB) approximation, which assumes no reflection nor absorption by the scatterer, the SHS intensity can be given as

3

where R is the particle radius, θ is the scattering angle, and κ^–1 is the Debye length (directly correlated to the ionic strength of the solution). The Debye length is defined as and takes into account the vacuum and relative permittivity ε₀ and ε_r, respectively, the Boltzmann constant k_B, the temperature T, the elementary charge e, the valency z, Avogadro’s number N_A, and the ionic concentration c. Γ⁽²⁾ and Γ^(3)′ are, respectively, the effective second- and third-order susceptibilities that are connected to the two SHS contributions χ⁽²⁾ and χ^(3)′ through multiplication of geometrical form factors that are specific to the geometry of the scatterer and the geometry of the incoming and outgoing electromagnetic fields. The geometrical form factors for spheres are shown in the Supporting Information. In the experimental geometry that we use, we obtain nonzero normalized SHS signal in two independent polarization combinations of light: PPP and PSS = SSP = SPS. Here the first letter refers to the polarization state of the SH beam and the second and third letter refer to that of the fundamental incoming beam. P polarized light is parallel and S polarized light is perpendicular to the scattering plane. Within the aforementioned RGD approximation, the scattered intensity from a sphere or shell in the two independent polarization combinations normalized by the bulk water signal can analytically be expressed as

4

5

where μ̅ = β̅_H2O⁽²⁾E(ω)² is the averaged induced second-order dipole moment with β̅_H2O being the averaged hyperpolarizability of water. N_p is the number of particles and N_b is the density of bulk water (3.34 × 10²⁸ molecules/m³), so that N_b/N_p is the number of bulk water molecules per particle. A summary of all the relevant constants and analytical expressions used can be found in Tables S1 and S2 in the Supporting Information for completeness. Note that the effective third-order susceptibility Γ^(3)′ is directly related to the surface potential Φ₀, and the effective second-order susceptibility Γ⁽²⁾ is related to the orientation of water molecules at the interface given by χ⁽²⁾ as described in eq 3. By fitting of the measured and normalized AR-SHS patterns in two different polarization combinations according to eqs 4 and 5, absolute values for the surface potential and the orientation of water molecules at the surface can be extracted. More information about the measurements and the normalization procedure can be found in the next section.

AR-SHS Measurements

The second harmonic scattering measurements were performed on the same SHS setup previously described in detail in refs (54, 56, and 61). To measure AR-SHS, a pulsed 190 fs Yb:KGW laser (Pharos-SP system) with a center wavelength of 1028 nm, a repetition rate of 200 kHz and an average power of 80 mW was focused into a cylindrical glass sample cell (4.2 mm inner diameter, high precision cylindrical glass cuvettes, LS instruments). The input and output polarization was controlled by a Glan-Taylor polarizer (GT10-B, Thorlabs) and a zero-order half wave plate (WPH05M-1030) and another Glan Taylor polarizer (GT10-A, Thorlabs), respectively. The beam waist was about 2w₀ ≈ 36 μm; the corresponding Rayleigh length was ∼0.94 mm. The scattered SH light was collected, collimated with a plano-convex lens (f = 5 cm), polarization analyzed, and filtered (ET525/10, Chroma) before being focused into a gated photomultiplier tube (H7421-40, Hamamatsu). The acceptance angle was set to 3.4° for scattering patterns. Patterns were obtained in steps of 5° from θ = −90° to θ = 90° with 0° being the forward direction of the fundamental beam. Data points were acquired using 20 × 1.5 s acquisition time with a gate width of 10 ns. To correct for incoherent hyper-Rayleigh scattering (HRS) from the solvent phase, both the SHS response from the sample solution I(θ)_SHS,sample and the HRS response from a solution of identical ionic strength and pH but without nanoparticles I(θ)_HRS,solution are collected. The HRS is subtracted from the SHS signal of the sample, and the obtained difference is then normalized to the isotropic SSS signal of pure water I(θ)_{HRS,water,SSS} to correct for differences in the beam profile on a day-to-day basis:

6

Here, the normalized signal of the sample I^norm(θ) is given for SHS in PPP polarization combination. The normalization procedure was applied in the same way for SHS measured in PSS polarization combination. In order to obtain absolute values for the surface potential Φ₀ and the surface susceptibility χ_S,2⁽²⁾ as a measure of surface molecular orientation of water molecules, the relative measured SHS signal needs to be related to absolute quantities. Here we use the fact that the second-order hyperpolarizability β⁽²⁾ and the third-order hyperpolarizability β⁽³⁾ of uncorrelated water are known, so that through normalization by I(θ)_{HRS,water,SSS}, the measured SHS response can directly be linked to an absolute value of the β⁽²⁾ component of the particle solution. The second-order hyperpolarizability β⁽²⁾ is connected to the second-order susceptibility χ⁽²⁾, which than can be used to determine the orientation of water molecules at the interface. The particle interface of a spherical scatterer can be considered as isotropic in the interfacial plane (tangential coordinates are degenerate). This reduces the 27 possible χ⁽²⁾ tensor elements to only 4 nonzero χ⁽²⁾ elements (χ_S,1, χ_S,2⁽²⁾, χ_S,3, χ_S,4⁽²⁾). Considering a lossless medium (appropriate for nonresonant SHG) and Kleinman symmetry, 3 of the 4 remaining elements are degenerate (χ_S,2 = χ_S,3⁽²⁾ = χ_S,4). Assuming that the orientational distribution of water molecules at the interface is broad, χ_S,1⁽²⁾ can be neglected. Knowing χ_S,2 is therefore sufficient to describe the molecular ordering at the surface. As a sign convention for χ_S,2⁽²⁾ we use the following: negative values for water molecules with O atoms pointing toward the surface (dipole moment pointing away from the surface) and positive values for water molecules with H atoms pointing toward the surface (dipole moment pointing in direction of the surface). This sign convention arises from a comparison to values obtained from sum-frequency generation studies.⁶²

The fitting procedure using the AR-SHS model that allows us to determine Φ₀ and χ_S,2⁽²⁾ is described in detail elsewhere.⁵⁴⁻⁵⁶ It uses the analytical eqs 4 and 5 and takes into consideration the particle radius R, as measured by dynamic light scattering (DLS), the ionic strength, as determined from conductivity measurements, the refractive indices of water (1.33)⁶³ and TiO₂ (2.61)⁶⁴ or SiO₂ (1.46),⁶⁵ the SH wavelength λ = 514 nm, the temperature T, and the number of particles per milliliter.

We note that the errors that we report for Φ₀ and χ_S,2⁽²⁾ are based on the statistical errors of the measured AR-SHS patterns prior to normalization. The errors on Φ₀ and χ_S,2 are numerical errors on the fitting procedure. Other sources of error may contribute to the total error, such as the variations in the experimentally determined parameters (i.e., the particle radius, the number of particles, or the ionic strength). An estimation of the influence of those uncertainties on the surface potential Φ₀ and the surface susceptibility χ_S,2⁽²⁾ was done for oil droplets in water and can be found in ref (54).

Molecular Dynamics Simulations

TiO₂ was modeled as a negatively charged (−0.104 C/m²) hydroxylated rutile (110) surface,⁶⁶ because dissociative adsorption of water dominates at high pH with estimated 65% ± 15% first-layer water dissociation in rutile–RbCl solution at pH 12.⁶⁷ At the rutile–deionized water interface, this fraction was estimated as 30% ± 15%;⁶⁷ however, the realistic scenario even for neutral surfaces is that adsorbed cations promote deprotonation of surface groups. A recent STM study found that the dissociative form of water is more stable than associated water molecules.⁶⁸ SiO₂ was modeled as a negatively charged (−0.12 C/m²) quartz (101) surface with singly coordinated silanol groups.⁶⁹

Water was modeled as rigid SPC/E,⁷⁰ whereas parameters for Na⁺ ions were taken from the literature.⁷¹ All employed models utilize the electronic continuum correction (ECC) theory,⁷² which in a mean-field way incorporates electronic polarization effects into classical, nonpolarizable MD simulations. Other technical details of the simulations are the same or similar to those in our previous works.^56,66,69

Results and Discussion

Surface Potential and Water Order under Different Ionic Strength Conditions

Part A of Figure 1 shows AR-SHS patterns of colloidal ∼100 nm diameter amorphous TiO₂ particles in two different polarization combinations (PPP and PSS). The scattering patterns were measured for different concentrations of NaCl ranging from 0 to 300 μM.

Figure 1.

(A) AR-SHS patterns of amorphous ∼100 nm diameter TiO₂ particles as a function of ionic strength in PPP polarization combination (top) and PSS polarization combination (bottom). Plain data points of different colors represent different salt concentrations of the aqueous environment. The ionic strength was adjusted through NaCl addition. The particle density was kept constant for each sample and equal to 4.3 × 10¹¹ particles/mL. All measurements were performed at T = 296.15 K. Solid lines represent the fits to the corresponding data points using the AR-SHS model. A summary of all the parameters used for the fits can be found in Tables S3 and S5. (B) Surface potential Φ₀ (dark red diamonds), and surface susceptibility χ_S,2⁽²⁾ (gray triangles) as a function of ionic strength. Φ₀ and χ_S,2 were obtained by fitting the corresponding AR-SHS patterns of ∼100 nm diameter amorphous TiO₂ particles in solution in PPP and PSS polarization combination (see panel A). The light red squares represent the zeta potential values ζ, measured for the different ionic strength conditions using electrophoretic mobility measurements.

Both PPP and PSS AR-SHS patterns show a decrease of the normalized SHS intensity with increasing salt concentration. At a higher ionic strength, more counterions will be situated in proximity of the charged interface of the particle, leading to a reduced penetration of the electrostatic field E_DC in the electrolyte solution. As a consequence, the volume of the overall probed water shell around the particles is reduced, resulting in a lower SHS intensity with increasing ionic strength. The solid lines represent the fit of the corresponding data points using the AR-SHS model described in the section AR-SHS Model and Theory. The results of the fits for the surface potential Φ₀ and the surface susceptibility χ_S,2⁽²⁾ as a function of added NaCl are shown graphically in Figure 1B and are given in Table 1. Tables S3 and S5 (Supporting Information) summarize all the parameters used for the fitting. Note that the radius obtained through DLS measurements indicated in Table 1 is slightly larger than the nominal radius of the particles.

Table 1. Surface Potential Φ₀ and Surface Susceptibility χ _S,2⁽²⁾ Values That Were Obtained by Fitting the AR-SHS Patterns of ∼100 nm Diameter Amorphous TiO₂ Nanoparticles in Aqueous Solutions for Different NaCl Concentrations^a.

added NaCl [μM]	R [nm]	ζ [mV]	Φ0 [mV]	χ S,2(2) [10–24 m2 V–1]
0	59 ± 21	–24 ± 21	–182 ± 13	–8.1 ± 0.4
10	60 ± 19	–27 ± 20	–57 ± 23	–39.6 ± 0.5
50	60 ± 19	–25 ± 17	–12 ± 19	46.1 ± 2.7
100	60 ± 15	–26 ± 20	–57 ± 40	45.3 ± 6.9
300	59 ± 28	–30 ± 22	–326 ± 163	94.1 ± 16.3

^aThe radius R was measured by DLS, and the zeta potential ζ was obtained from electrophoretic mobility measurements.

The zeta potential ζ of the TiO₂ samples in different ionic strength conditions is presented in Figure 1B for comparison to the surface potential. The zeta potential is a common measure for the stability of a particle suspension, and values around ±30 mV are generally indicative of stable suspensions.⁷³ The isoelectric point (ζ = 0) was determined through electrophoretic mobility measurements and is close to pH 4 for the here used colloidal ∼100 nm diameter amorphous TiO₂ particles. It can be seen that the zeta potential does not change in magnitude and remains between −24 mV and −30 mV, whereas the surface potential varies from −12 mV to −326 mV in the investigated ionic strength range. For the behavior of the surface potential, three different regions can be identified: (i) 0–10 μM NaCl, where |Φ₀| > |ζ|, (ii) 10–100 μM NaCl, where |Φ₀| ≈ |ζ|, and (iii) above 100 μM NaCl where |Φ₀| ≫ |ζ|. At the same time, the surface susceptibility shown in the bottom part of Figure 1B changes in sign between 10 and 50 μM NaCl. Negative values of χ_S,2⁽²⁾ indicate that the net dipole moment of water molecules points away from the surface (oxygens toward the surface), while positive values of χ_S,2 indicate that the average orientation of water molecules is with their dipole moment facing the surface (hydrogens toward the surface).

As all the ionic strength measurements were carried out at pH 7, above the isoelectric point of the TiO₂ particles, some surface groups are deprotonated in an amount corresponding to the surface charge density.^17,74 We estimate the deprotonation to be between 1% and 8% at pH 7 using surface charge density values from the literature (see Supporting Information). This estimation is only meant as a guidance as very different surface charge density values have been reported by different groups.²⁹⁻³² These values can greatly differ depending on the size,^29,75,76 the surface roughness,⁷⁷ and the crystal phase of the particles,¹ as well as the synthetic procedure. For the less known amorphous phase, no record of surface charge density values could be found so far. Our results show negative values of zeta potentials, as anticipated for a negatively charged surface. In the very low ionic strength range (0–10 μM NaCl), where |Φ₀| > |ζ|, we observe that the magnitude of the surface potential decreases until a value of the same magnitude of the zeta potential is reached (see Figure 2A,B). We assign this behavior as arising from positively charged Na⁺ ions that directly adsorb at the deprotonated Ti–O^– surface groups of the colloids (inner-sphere complex), as illustrated in Figure 2B. Because of the reduction of the effective negative surface charge by the adsorbed counterions, the magnitude of the surface potential will decrease accordingly. Additionally, in this ionic strength region, the surface susceptibility is negative, which indicates that the interfacial water molecules are oriented with their net dipole moment away from the surface (oxygens toward the surface). This behavior can be explained by hydrogen bonding between the oxygen atoms of the water molecules and the hydroxyl surface groups of the TiO₂ particles. Note that we chose a hydroxylated model of the TiO₂ surface as illustrated in Figure 2; however our conclusions would remain the same for a nonhydroxylated surface, where the oxygen atom of a water molecule could interact with an undercoordinated Ti surface site. While the surface structure and adsorption of the first monolayer of water has been the object of many debates,⁷⁸⁻⁸⁰ it is beyond the scope of this study to clarify the exact configuration of the first layer of water molecules at the surface, which is furthermore very dependent on the crystal structure, the presence of surface defects, the sample preparation procedure, and the experimental conditions. Here, the main contribution to the measured surface susceptibility is due to the average dipole of all the water molecules that have a chemical type of interaction with the surface (i.e., not induced by the electric field), with the advantage of easily distinguishing changes in average water orientation as a function of ionic strength, as further detailed hereafter.

Figure 2.

EDL around a TiO₂ particle surface and the corresponding surface potential Φ₀ and zeta potential ζ over the distance to the surface (A) with no added salt and under (B) very low ionic strength, (C) low ionic strength and (D) high ionic strength conditions. The particle surface is approximated to a flat surface for clarity, and no anions are displayed. The mean orientation of water molecules in direct proximity of the slightly deprotonated surface is given by the net dipole moment pointing away or toward the surface, reflecting average water orientation with the hydrogens away (A, B) or toward (C, D) the surface. Scheme B displays the direction of the net dipole moment before the sign of the surface susceptibility χ_S,2⁽²⁾ flips to positive values, while scheme C shows the net dipole moment after the χ_S,2 flip. The surface potential Φ₀ is the potential difference between the potential at the surface of the particle Φ_S and the potential of the bulk solution Φ_b. Note that this schematic illustration shows the magnitudes of the previously mentioned potentials. ζ is the potential at the shear plane. In this simplistic scheme, the Stern plane is approximated to be equal to the shear plane in the high ionic strength situation where a condensed layer of counterions is formed in panel D.

In the low ionic strength region (10–100 μM NaCl), the surface potential reaches a minimum in magnitude and is close to zero. This suggests that once all the favorable sites have been occupied by direct adsorption of the counterions, further addition of salt does not affect the surface potential and thus the surface charge density in this concentration range. Our experiment cannot provide insights on the nature of these favorable sites. However, it evidences that only a fraction of the deprotonated hydroxyls is occupied by direct adsorption of Na⁺, as complete coverage would result in a neutral particle (Φ₀ = 0), which could not be stable in solution and would precipitate. Furthermore, the surface potential remains very close to the zeta potential up to 100 μM NaCl. As the zeta potential is considered to be located a few water layers away from the surface,^16,17,19 a value of surface potential close to the zeta potential suggests that there are no mobile counterions accumulated between the shear plane and the surface but that they are rather distributed in solution. In the Gouy–Chapman model, this would be equivalent to a diffuse layer forming around the TiO₂ particles, which is illustrated in Figure 2C. At the same time, we observe a change in sign of the surface susceptibility between 10 μM and 50 μM of added NaCl. This reflects a change in orientation of the water molecules situated directly at the interface, as the surface susceptibility describes the orientational order induced by all (chemical) interactions confined to the particle surface plane (see Materials and Methods). The average surface molecular directionality changes from the net dipole moment pointing away from the surface (oxygens toward the surface) to the net dipole moment pointing toward the surface (hydrogens toward the surface). Therefore, it can be argued that, above a certain threshold, the presence of Na⁺ near the interface is responsible for the change in directionality of interfacial water. This phenomenon can be rationalized by the rearrangement of the H-bonding network between the Ti–OH groups and the surface water molecules caused by the Na⁺ ions.

In the higher ionic strength region above 100 μM NaCl, where |Φ₀| ≫ |ζ|, we observe a strong increase in magnitude of the surface potential with salt concentration. This large deviation from the zeta potential suggests the formation of a condensed layer of ions at the interface, which is further supported by the observation of the drastic reduction in the SHS intensity. This charge condensation layer is also predicted by the Gouy–Chapman–Stern model, where the steep potential drop in the very first interfacial layers is approximated to the linear potential drop in a parallel plate capacitor. Taking the distance between the surface and the zeta potential plane to be between 0.3 and 0.9 nm (1–3 water molecules),^16,17,19 the electric field can be estimated here to be ∼3 × 10⁸ to 1 × 10⁹ V/m for an ionic strength of 300 μM NaCl. This large value of the electric field in the interfacial region provides additional evidence of the presence of a condensed layer of ions. The latter is schematically illustrated in Figure 2D. Note that in this case the ions cannot be directly adsorbed at the TiO₂ surface. The absence of water molecules between the negatively charged surface and the counterions would lead to charge neutralization and a consequent decrease in surface potential, as already observed for the very low ionic strength case. As such, the ions are present as outer-sphere complexes and likely have one or more layers of water between them and the surface.

The surface susceptibility has a positive sign in this higher ionic strength region. As a consequence, the net dipole moment of the interfacial water is oriented toward the surface with the hydrogen atoms facing the surface. This behavior further confirms the presence of a condensed layer of positively charged ions at the interface. Analogously to the previous case, we expect the net dipole moment to be influenced by the rearrangement of the H-bonding network between the surface hydroxyl groups and the interfacial water molecules, caused by Na⁺ ions, as well as by the presence of additional oriented water molecules belonging to the Na⁺ hydration shell.

Both the diffuse region and the condensed layer region have been previously experimentally determined by our group for 300 nm diameter SiO₂ particles,⁵⁶ exhibiting a similar increase in the surface potential magnitude for NaCl concentrations between 0.1 and 10 mM.⁵⁶ However, the direct counterion adsorption was not observed in that case, most likely because the initial ionic strength of the nanoparticles was higher (0.1 mM vs tens of micromolar here). We further speculate that a similar trend in surface potential versus ionic strength would be observed for smaller nanoparticles. In this case, it is reasonable to expect the minimum in the magnitude of the surface potential to be shifted to higher ionic strengths, as surface charge densities have been shown to be size-dependent for TiO₂ particles below 25 nm, with the magnitude of the surface charge density increasing with decreasing size.²⁹ Interestingly, Brown et al.³⁷ reported values for surface potential and Stern layer thicknesses for 9 nm SiO₂ particles for higher salt concentrations (≥0.01 M NaCl), showing that surface potential values decrease with increasing salt concentration. This opposite behavior with respect to our observation of increasing surface potential in the 100–300 μM range is related to different relative variations of the surface charge density and of the condensed layer region thickness and has been discussed in detail in our previous work.⁵⁶

Surface Potential and Water Order in Different pH Conditions

In order to investigate the influence of different surface charge densities on the molecular water order and the surface potential, similar AR-SHS measurements were performed as a function of pH. The initial TiO₂ dispersion in water prior to pH adjustment had a pH = 7, and no additional salt was added. The sample pH was varied by addition of NaOH. Addition of NaOH to the particle suspension results in a more negatively charged surface. In our experiment, the pH range was limited to 7 ≤ pH ≤ 10.7 because the signal-to-noise ratio of the SHS patterns was too low for pH > 10.7 (see Supporting Information for more details about the investigated pH range). The results for the AR-SHS patterns of colloidal ∼100 nm diameter amorphous TiO₂ at different basic pH are shown in part A of Figure 3. It can be seen that the normalized SHS signal decreases with increasing pH for both polarization combinations, as also observed for increasing salt concentrations in Figure 1A, which reflects a smaller number of oriented water molecules. Figure 3B shows the surface potential Φ₀ and the surface susceptibility χ_S,2⁽²⁾ as a function of the pH of the aqueous environment. A list of the exact values can be found in Table 2. A summary of all the parameters used for the fitting is given in Tables S3 and S6 (Supporting Information). Despite our limited pH range, the three behaviors found in Figure 1 are also seen here: Close to pH 7, the magnitude of the surface potential Φ₀ is larger than the zeta potential. For more basic pH (9.5), the surface potential decreases in magnitude and becomes comparable to the zeta potential. For the highest pH investigated here the surface potential increases again in magnitude. A change of sign in the surface susceptibility is observed between pH 9.5 and pH 10.7, indicative of the reorientation of the net dipole moment of interfacial water molecules from oxygens facing the surface to hydrogens facing the surface.

Figure 3.

(A) AR-SHS patterns of amorphous 100 nm diameter TiO₂ particles in solutions of different pH in PPP polarization combination (top) and PSS polarization combination (bottom). Plain data points of different colors represent different pH conditions of the aqueous environment. For pH values above 7, the pH was adjusted through NaOH addition. The particle density was kept constant for each sample and equal to 4.3 × 10¹¹ particles/mL. All measurements were performed at T = 296.15 K. Solid lines represent fits to the corresponding data points using the AR-SHS model. A summary of all the parameters used for the fits can be found in Tables S3 and S6. (B) Surface potential Φ₀ (dark red diamonds), and surface susceptibility χ_S,2⁽²⁾ (gray triangles) as a function of pH as they were obtained by fitting the corresponding AR-SHS patterns of 100 nm diameter amorphous TiO₂ particles in solution in PPP and PSS polarization combination (see panel A). The light red squares represent the zeta potential values ζ that were measured for the different pH conditions of the aqueous environment using electrophoretic mobility measurements.

Table 2. Surface Potential Φ₀ and Surface Susceptibility χ _S,2⁽²⁾ Values Obtained from Fitting the AR-SHS Patterns of 100 nm Diameter Amorphous TiO₂ Nanoparticles in Aqueous Solutions of Different pH^a.

pH	R [nm]	ζ [mV]	Φ0 [mV]	χ S,2(2) [10–24 m2 V–1]
7	63 ± 17	–27 ± 19	–138 ± 15	–18.1 ± 0.5
9.5	63 ± 14	–32 ± 19	–47 ± 48	–32.3 ± 4.6
10.7	59 ± 19	–34 ± 22	–137 ± 91	66.2 ± 31.9

^aThe pH was adjusted through NaOH addition. The radius R was measured by DLS, and the zeta potential ζ was obtained from electrophoretic mobility measurements.

Between pH 7 and pH 11, the surface charge of the colloids is expected to be increasingly negative due to deprotonation of hydroxyl groups at the surface, while the same counterion (Na⁺) is expected to interact with the negatively charged groups. As for the neutral pH case, we can estimate the approximate percentage of deprotonation at pH = 9.5 using surface charge density values from the literature (see Supporting Information) and find it to be between 10% and 35%. This indicates that while the surface is approximately three to ten times more charged than at pH = 7, the majority of the surface groups remain protonated. Given the similarities with the results as a function of ionic strength, we assign these findings to the same mechanisms of counterion adsorption (for pH 7 to pH 9.5), the creation of a diffuse layer (around pH 9.5), and the creation of a layer of condensed ions (for pH > 9.5) as was discussed in detail above. The change in orientation of the interfacial water molecules from the net dipole moment pointing away from the surface to the net dipole moment pointing toward the surface occurs here between pH 9.5 and pH 10.7. Converting these pH values to the corresponding ionic strength values, we find that the change in sign occurs above 30 μM added NaOH, which is in good agreement with the change in sign observed for the NaCl case (between 10 and 50 μM added NaCl). The fact that the surface potential values are similar and that the change in water orientation occurs in the same ionic strength region in both the salt and pH cases shows that the surface charge densities for a given ionic strength are comparable and do not depend on the use of a salt (NaCl) or a base (NaOH). Note that this is observed in the here investigated range of salt concentration and pH, as well as in our previous study of SiO₂ particles;⁵⁶ however it might not be the case for higher salt concentrations (>300 μM) or higher pH values (pH > 10.7). Furthermore, our results suggest that at pH 7, at which the AR-SHS patterns as a function of salt are recorded, the surface charge density is already negative enough to permit the formation of a layer of condensed counterions.

Comparison to acidic pH values was not possible due to particle instability close to the isoelectric point and the low signal-to-noise ratio of the SHS patterns below pH 3 (see Supporting Information). However, we would expect different surface potential and water orientation behavior as the particle surface is positively charged at pH values below the isoelectric point (as a first approximation, here the isoelectric point can be considered equal to the point of zero charge) and therefore not directly comparable to the NaOH and NaCl case.

Comparison of SiO₂ and TiO₂ Interfacial Properties

In order to determine if the evolution of the surface potential and the water orientation with increasing ionic strength and pH is specific to the nature of the investigated surface, we performed AR-SHS on SiO₂ particles of the same size (∼100 nm diameter). SiO₂ was chosen in order to have a comparison with another metal oxide surface bearing the same potential determining ions (H⁺ and OH^–). The SiO₂ colloids were found to have a stronger SHS signal than the amorphous TiO₂ particles (both relative to neat water, ∼10 times higher, see Figure S1 in Supporting Information) even though the particle density of the two particle suspensions was on the same order of magnitude (2.9 × 10¹¹ particles/mL in the case of SiO₂ and 4.3 × 10¹¹ particles/mL for TiO₂). Figure 4A shows the surface potential Φ₀ of 100 nm diameter SiO₂ particles in different NaCl concentrations compared to 100 nm diameter amorphous TiO₂ particles. Three regions of surface potential behavior can also be distinguished for SiO₂ particles. (i) It can be seen that the surface potential of the SiO₂ particles decreases in magnitude with increasing salt concentration for low ionic strength (<300 μM). (ii) At 300 μM NaCl concentration, the surface potential value is similar to the zeta potential, which is not shown here for clarity but lies in the range of −32 to −48 mV (See Table 3). (iii) For ionic strength >300 μM, the magnitude of the surface potential rises again to values of |Φ₀| > |ζ|. Compared to TiO₂, the increase in magnitude of the surface potential in region (iii) occurs at a higher ionic strength for SiO₂. Likewise, the decay in magnitude of the surface potential in region (i) until the surface potential |Φ₀| ≈ |ζ| in region (ii) spans over a wider ionic strength range for SiO₂ compared to TiO₂.

Figure 4.

(A) Surface potential Φ₀ and (B) surface susceptibility χ_S,2⁽²⁾ of ∼100 nm diameter SiO₂ particles and ∼100 nm diameter amorphous TiO₂ particles as a function of ionic strength. The ionic strength was adjusted through NaCl addition. The particle density was kept constant and equal to 2.9 × 10¹¹ particles/mL for the SiO₂ and equal to 4.3 × 10¹¹ particles/mL for the TiO₂ samples. All measurements were performed at T = 296.15 K and pH = 7. Dark blue open diamonds and triangles represent the SiO₂ samples, and dark green diamonds and triangles represent the TiO₂ particles in aqueous environment. A summary of all the parameters used for the fits through which Φ₀ and χ_S,2 were extracted can be found in Tables S3, S4, S5, and S7.

Table 3. Surface Potential Φ₀ and Surface Susceptibility χ _S,2⁽²⁾ Values Obtained from Fitting the AR-SHS Patterns of ∼100 nm Diameter SiO₂ Nanoparticles in Aqueous Solutions of Different NaCl Concentrations^a.

added NaCl [μM]	R [nm]	ζ [mV]	Φ0 [mV]	χ S,2(2) [10–22 m2 V–1]
0	65 ± 12	–48 ± 31	–163 ± 5	–2.2 ± 0.1
10	64 ± 11	–41 ± 22	–130 ± 5	–2.8 ± 0.08
50	62 ± 7	–36 ± 24	–92 ± 7	–3.2 ± 0.08
100	61 ± 7	–35 ± 23	–54 ± 15	–3.4 ± 0.01
300	60 ± 5	–32 ± 23	–19 ± 50	3.9 ± 0.7
600	58 ± 5	–34 ± 26	–430 ± 90	9.1 ± 0.7

^aThe radius R was measured by DLS, and the zeta potential ζ was obtained from electrophoretic mobility measurements.

In Figure 4B, the surface susceptibility χ_S,2⁽²⁾ of SiO₂ and TiO₂ can be seen. A change in sign of χ_S,2 from negative values to positive values happens at NaCl concentration between 100 μM and 300 μM. This indicates that the reorientation of the net dipole moment of the water molecules from oxygens facing the surface to hydrogens facing the surface happens at higher ionic strength for SiO₂ than for TiO₂. The surface susceptibility of SiO₂ is one order of magnitude higher than the surface susceptibility of TiO₂, which implies a larger net dipole moment of the interfacial water molecules near the SiO₂ surface compared to the water molecules close to the TiO₂ surface. This larger net dipole moment translates into a stronger ordering of the interfacial water molecules that contributes to the higher SHS intensity observed in the SiO₂ case. Such an effect could be caused by the different molecular surface groups (e.g., bridging or terminal hydroxyls for TiO₂ vs different siloxane and silanol groups for SiO₂) and their different occurrences, with consequential influence on the interfacial H-bonding network.

The same mechanisms of ion adsorption, formation of a diffuse layer, and creation of a layer of condensed charges, which were discussed in detail for the ionic strength dependency of TiO₂ particles and further confirmed in the case of pH variation, can explain the three regions of surface potential and surface susceptibility behavior for the SiO₂ particles. Even though the general behavior is similar for both surfaces, the onset of the three regions as a function of ionic strength is clearly different in the case of SiO₂ particles. Counterion adsorption is more gradual and requires up to 300 μM to reach a minimum in the surface potential magnitude, indicative of a saturation of all the favorable deprotonated hydroxyls. Analogously to the TiO₂, we note here that all the deprotonated hydroxyls cannot be occupied, as this would result in a neutral, unstable particle. It is interesting to see that for both materials the change in sign of χ_S,2⁽²⁾ occurs just before the minimum in the surface potential magnitude is reached. This result suggests that the hypothesized rearrangement of the H-bonding network at the surface by the counterions is already significant enough before the favorable deprotonated hydroxyls are saturated with Na⁺ ions. Furthermore, the increase of surface potential magnitudes, which implies the formation of a layer of condensed charges, occurs at ionic strengths above 300 μM in the case of the SiO₂ particles, compared to above 100 μM in the case of TiO₂ particles. Knowing that the density of OH groups per surface area is similar for both surfaces (4.8 OH/nm² for TiO₂⁸¹ and 4.9 OH/nm² for SiO₂⁸²), this implies that the TiO₂ surface has a higher affinity for Na⁺ ions than SiO₂, which has been already observed by our simulations comparing the amount of adsorbed cations at negatively charged (and even neutral) rutile and quartz surfaces.⁶⁹

In order to decipher the molecular origin of our experimental results, we performed molecular dynamics (MD) calculations following the same strategy as in our previous study.⁵⁶ We adopted our molecular dynamics models of TiO₂ and SiO₂ to investigate and compare the effect of ionic concentration on the orientation of water molecules at these interfaces. TiO₂ was modeled as a negatively charged (−0.104 C/m²) hydroxylated rutile (110) surface, while as a SiO₂ model, we used a negatively charged (−0.12 C/m²) quartz (101) surface, as described in the Materials and Methods section. A similar negative surface charge density, which is constant in a single simulation, was chosen to fairly compare properties above the point of zero charge for both TiO₂ and SiO₂, when a portion of surface hydroxyls is deprotonated, corresponding to neutral or slightly basic pH.

Despite the fact that the behavior of amorphous solids used in our SHS experiments and of crystalline solids used in our simulations may differ, the comparison to the crystalline form still can provide valuable information on the sorption properties of both materials. To probe concentration effects, we prepared a set of three systems for each modeled surface. To mimic extremely low concentrations studied in the experiments (micromolar concentrations) that are not directly accessible in simulations, the number of Na⁺ ions in the system was set to be equal to the amount of negative surface charges (and there were no anions). However, the number of ions allowed in the vicinity of the negative surface up to 10 Å varied from 0% compensation (i.e., all the counterions were forced to be further away from the surface) to 50% compensation (only half of the ions were allowed in the region up to 10 Å) and 100% compensation (no restriction on the position of ions, that is, a surface charge could be fully compensated). In the latter case, the surface charge could be fully (100%) compensated up to 10 Å. However, due to the equilibrium between the distribution of ions at regions closest to the surface and further away (including the bulk region), in conjunction with the low total number of ions allowed in the simulation, even in this 100% case, part of the surface charge remains uncompensated up to 10 Å. This situation resembles our experimental low ionic concentration conditions when, even in the presence of a sufficient number of cations to compensate the surface charge, the particles remain negatively charged and stable.

The measure that can be compared to the experimental data is the integral of the “dipole concentration”, which is a product of the average number density of water molecules and the perpendicular component of the water dipole moment with respect to the surface (with positive values indicating hydrogens facing the surface, that is, as in the experiment). The running integral of the dipole concentration provides an indicator for the buildup of the SHS intensity as a function of distance. The SHS intensity is proportional to the square of this running integral along the z-axis perpendicular to the surface.⁵⁶ The plane at z = 0 corresponds to the average position of the last TiO layer. Figure 5 shows the running integrals of dipoles as a function of distance for TiO₂ and SiO₂ surfaces. Both surfaces exhibit similar behavior as a function of sodium concentration as observed in region (i) of SHS experiments: addition of ions to the interface, resulting in inner-sphere complexes (or outer-sphere complexes adsorbed at the surface), shifts the signal toward negative values, that is, fewer water molecules are oriented, which is consistent with the effect of adsorbed Na⁺ compensating a negative surface charge. Moreover, the rate of change in the interfacial region (up to ∼10 Å from the surface) is more drastic for TiO₂. At 50% compensation, the integrated dipole value at 10 Å is 0.094 D/Ų for TiO₂ and 0.130 D/Ų for SiO₂. At 100% compensation, the integrated dipole value at 10 Å decreases to 0.026 D/Ų for TiO₂ and to 0.096 D/Ų for SiO₂. This steeper decrease of the integrated dipole moment with the amount of counterions indicates that the surface charge of TiO₂ is more efficiently screened by Na⁺ counterions. In other words, fewer ions are required at the TiO₂ surface to result in similar changes as in the case of SiO₂. This observation is also in line with the SHS experiments, where a minimum in the surface potential magnitude is reached at lower ionic strengths for TiO₂ than for SiO₂. Note also the flat profile of the curve allowing 100% compensation of the TiO₂ surface, compared to the same curve for SiO₂, which is still growing, that is, gaining further contributions to the SHS signal, with increasing distance from the surface. That clearly documents that while in both cases the ions can fully compensate the surface charge (and eventually do so at large distances), for TiO₂ nearly all the compensation occurs in the nearest vicinity of the surface, while for SiO₂, we observe a wide diffuse layer.

Figure 5.

Integrated dipole as a function of distance from negatively charged (A) (110) rutile (−0.104 C/m²) and (B) (101) quartz (−0.12 C/m²) surfaces. The brown line represents simulations allowing 0% compensation of the surface charge (i.e., all the counterions were forced to be at least 10 Å away from the surface), the turquois line represents 50% compensation (only half of the ions were allowed in the region up to 10 Å from the surface), and the purple line is from simulations allowing 100% compensation (no restriction on the positions of ions).

Conclusions

In summary, nonresonant polarimetric AR-SHS was applied for the first time to semiconductor nanoparticles in aqueous environments. By collection of two different polarization combinations of light from a colloidal suspension, the two analytical expressions from nonlinear optical theory containing Φ₀ and χ_S,2⁽²⁾ can be solved without assuming any model for the distribution of the ions at the interface. The surface potential and molecular orientation of interfacial water molecules of ∼100 nm diameter spherical TiO₂ particles in different NaCl and pH conditions are reported and compared to the results for insulating SiO₂ particles as a function of NaCl concentration. By comparison of the surface potential to the zeta potential, three different regions can be identified for TiO₂: At very low ionic strengths (0–10 μM), Na⁺ ions preferentially adsorb as inner-sphere complexes. At low ionic strengths (10–100 μM), we observe the presence of a distribution of counterions equivalent to a diffuse layer in the GC model, while at higher ionic strengths (>100 μM), the presence of an additional layer of condensed charges, similar to a Stern layer in the GCS model, is detected. Changes in interfacial water orientation as a consequence of counterions accumulating in proximity of the charged surface further support this picture and indicate a rearrangement of the water H-bond network caused by the Na⁺ ions. This rearrangement occurs already for small amounts of counterions present in solution (below 50 μM added Na⁺). Regions of equivalent behavior are observed for TiO₂ particles in varying basic pH conditions. Comparing TiO₂ and SiO₂ particles as a function of NaCl concentration shows that the TiO₂ surface has a higher affinity for Na⁺ ions than SiO₂. These findings are in line with data obtained by MD simulations of the rutile and quartz surfaces interacting with aqueous solutions, where the rate of change of the integrated dipole with increasing Na⁺ adsorption at the surface is faster for TiO₂ than for SiO₂.

Overall, these results pave the way to a better understanding of processes taking place at the surface of semiconductor nanoparticles in solution. In particular, they highlight the potential of AR-SHS to monitor ion adsorption at the surface, changes in the surface effective charge, and general interfacial properties in a variety of (photo)catalytic applications.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpcc.0c01158.

• AR-SHS model and theory, relevant constants, analytical expressions, and assumptions, experimental parameters used for fitting the AR-SHS patterns, surface charge densities and deprotonation, AR-SHS below pH 7, AR-SHS patterns of 100 nm diameter SiO₂ particles as a function of NaCl concentration (PDF)

The authors declare no competing financial interest.