Probing the surface electrical properties of clay minerals with electrostatic force microscopy and kelvin probe force microscopy

Many surface processes of clay minerals require in-depth understanding of their surface electrical properties, such as surface charge density, surface potential distribution, etc In this paper, electrostatic force microscopy (EFM) and Kelvin probe force microscopy (KPFM) were used to study the surface charge densities, surface potentials, electric field intensities, and electric field force gradients of three common clay minerals: kaolinite, montmorillonite, and illite. The properties were directly imaged, and the average surface permanent charge densities of kaolinite, montmorillonite, and illite were obtained to be −0.0060, −2.136, and −5.456 μC m−2, respectively. In addition, a good linear relationship was found between the surface charge densities obtained by KPFM and the layer charges calculated from the mineral chemical formulas of three clay minerals.


Introduction
Clay minerals, which generally refer to layered silicate minerals (phyllosilicates), are the major mineral components of soil in the critical zones of the earth's surface.Common clay minerals include kaolinite, montmorillonite, and illite [1].
Due to the strong adsorption and/or ion exchange properties of clay minerals, they possess good removal capacities for various types of metal ions [2, 3], organic pollutants [4,5], bacteria [6,7], and viruses [8,9].They are widely used as environmentally friendly materials [10] and pharmaceuticals [11].Meanwhile, due to their excellent rheology and swelling properties, clay minerals are also applied for cosmetics [12], coatings [13], and drilling muds [14].These applications are closely related to the surface properties of clay minerals, especially surface charge properties.
The surface charge properties of clay minerals are closely related to their crystal structure, surface groups, and surrounding media.The permanent charge on the basal surface of clay minerals comes from the isomorphic substitution of the sheets.Clay minerals are usually connected by silicon-oxygen tetrahedral sheets and aluminum-oxygen octahedral sheets to form a basic unit layer.According to the number of tetrahedral sheets and octahedral sheets in the basic unit layer, they are divided into 1:1 type (such as kaolin) and 2:1 type (such as montmorillonite and illite) [15].If Si 4+ in the tetrahedral sheets is replaced by Al 3+ and/or Al 3+ in the octahedral sheets is replaced by Mg 2+ or Fe 2+ , the surface of the clay mineral will possess a permanent negative charge that does not change with the surrounding environment.The degree and location of isomorphic substitution determine the number and distribution of permanent negative charges on the surface.For example, kaolinite generally has a deficient degree of isomorphic substitution, and its permanent negative charge is close to zero [16].Another example of that is montmorillonite and illite.They are both 2:1 type clay minerals, but illite has a higher and more densely distributed surface charge than montmorillonite.This fact is because the isomorphic substitutions of tetrahedral and octahedral sheets both exist in illite, while only octahedral substitution occurs in montmorillonite [17,18].Different from the basal surface, there are variable charges at the edge surface of clay minerals, and their charge properties change with the surrounding environment (such as solution pH and ionic strength), e.g., positively charged at low pH and negatively charged at high pH.This pHdependent charging behavior is closely related to the amphoteric hydroxyl groups on the edge surface [19,20].
Presently, researches on the surface electrical properties of clay minerals mainly focus on the determination of surface charge.Research methods include calculation through mineral chemical formula, cation exchange capacity, zero charge point, and ζ potential.
The quantity of permanent negative charges on the basal surface can be calculated using a mineral chemical formula.However, the data obtained is the equivalent charge number in a half-unit cell, which is a statistical average.Since the exact location of isomorph substitution in clay minerals is difficult to determine, this method cannot obtain the actual charge distribution on the mineral surface [21,22].
The numbers obtained by the other three methods are relative to the joint effects of the permanent charges on the base surface and the variable charges on the end surface, and there are certain limitations in experimental methods or theoretical assumptions.
The value of cation exchange capacity (CEC) is closely related to the structure of clay minerals.Many clay minerals possess interlayer cations, which are used to balance the negative charges of the structure sheets, and the exchangeability of interlayer cations significantly impacts the determination of CEC.For example, the binding force of montmorillonite to interlayer Ca 2+ and Na + is small, and the interlayer ions make a more significant contribution to the CEC value.At the same time, illite has a greater binding force to interlayer K + , and the interlayer ions make a much smaller contribution to the CEC value.In addition, the degree of exchange will also affect the result of CEC determination, thereby affecting the accuracy of calculating the number of surface charges [22,23].
Point of zero charge (PZC) is usually calculated based on potentiometric titration results [24,25].However, since clay minerals usually have both permanent and variable charges and may also contain interlayer cations, clay minerals have various types of points of zero charge [26][27][28][29].The results measured using different methods contain different meanings, and it is necessary to analyze the corresponding charge types and causes specifically.Furthermore, the PZC determination of clay minerals requires specific skills and experiments that need to be designed according to specific conditions.Kraepiel et al discussed the surface acid-base properties of minerals with permanent charges and theoretically explained why the PZC values of such minerals cannot be measured through potentiometric titration by changing the ionic strength of suspension [30].
The ζ potential is usually determined by electrophoresis and then calculated through a mathematical model after measuring the electrophoretic mobility.In most electrophoretic measurements, highly dilute colloidal dispersions are required.However, the mathematical models that convert electrophoretic mobility into ζ potential are based on spherical particles and assume that the charges are uniformly distributed on the particles [31,32].Therefore, the ζ potentials of clay minerals (usually plate-shaped) measured by electrophoresis are likely to have significant errors.In addition, the electroacoustic method can also be used to measure the dynamic mobility of kaolinite and montmorillonite colloidal dispersion systems with higher concentrations, thereby obtaining the ζ potential.However, its background theory needs to be further improved [33,34].
There are currently limited methods to obtain the quantity of surface permanent charges directly.Meanwhile, due to the diversity and heterogeneity of the structure and surface properties of clay minerals, the explanation of the microscopic mechanism of many application scenarios of clay minerals requires not only data about the number of surface charges but also the distribution of surface charge, field intensity, and potential.
Scanning probe microscopy (SPM) is a method for the characterization of the sample surface that uses a physical probe rather than light, including scanning tunneling microscope, atomic force microscope, electrostatic force microscope, Kelvin probe force microscope, etc It has many applications in the surface and interface structures, properties, and chemical reactions of minerals [35].Some researchers have also used it to study the surface electrical properties of clay minerals.For example, Gupta and Miller used an atomic force microscope to measure the changes in the surface force of kaolinite under different solution pH [36].Yan et al used an atomic force microscope to measure the force curve of talc and then calculated the surface potential and surface energy of silicate with different solution pH based on DLVO theory [37].Shao et al used atomic force microscopy to measure the interaction between the tip and illite surface under different solution pH and obtained the surface potential of illite based on the DLVO theory [38].The current relevant researches mainly focus on the aqueous solution system, especially the solution conditions that affect the surface interaction forces.However, little attention has been paid to quantitative analysis of the number and distribution of surface charges [39].
In this study, electrostatic force microscopy and Kelvin probe force microscopy were used to quantitatively analyze the distribution and changes of permanent negative charges, electric fields, and potentials on the surfaces of kaolinite, montmorillonite, and illite in air, which will provide relevant information for in-depth understanding and quantitative description of the surface and interface processes of clay minerals.

Source of clay mineral samples
The kaolinite sample came from Suzhou City, Jiangsu Province, China; the montmorillonite sample came from Chifeng City, Inner Mongolia, China; and the illite sample came from Bijie City, Guizhou Province, China.The samples were washed, crushed, ground, and gravity-settled for characterization and subsequent experiments.

Characterization of mineral phases
The phases of the samples were determined by a powder crystal x-ray diffraction (XRD) method.Use an agate mortar to grind the sample to about 40 μm.Add the powder sample into the middle of the cavity of the sample holder so that the loose sample powder is slightly higher than the plane of the sample holder.Then, take a glass slide and gently press the surface of the sample to make the surface of the powder sample flat and consistent with the plane of the sample holder, and finally, scrape off the excess powder that is not in the cavity.
The XRD testing was performed on a PANalytical Empyream x-ray powder crystal diffractometer with a copper target (Kα = 1.5418Å).The tube volt is 40 kV, and the tube current is 40 mA.The 2θ angle of the scanning range is from 4°to 60°.The signal was collected with a PIXcel3D detector.The width of the divergence slit and anti-scatter slit are 2°and 4°, respectively.The scanning time is 100 s.

Characterization of chemical composition
The samples were prepared using the fusion bead method and tested using the x-ray fluorescence (XRF) method for the major elements content.The sample was ball-milled to about 75 μm.Then, 0.7 g sample, 5.2 g anhydrous lithium tetraborate, 0.4 g lithium fluoride, and 0.3 g ammonium nitrate were mixed evenly in a 25 ml magnetic crucible.Move the mixed sample into a platinum-gold alloy crucible and add 1 ml of 15 g l −1 lithium bromide solution.Place the alloy crucible on the automatic melting machine, melt it at 1200 °C for 10 min, and then pour the melt into the casting mold.After cooling, the glass discs are separated from the mold.
Testing was performed on a Thermo Scientific™ X-RARL Perform' X 4200 x-ray fluorescence spectrometer.The x-ray tube voltage is 50 kV, and the tube current is 50 mA.The field aperture diameter is 30 mm.The relative standard deviation of the repeatability test is better than 0.1%.

Determination of the cantilever spring constant 2.4.1. Deflection sensitivity calibration
Scans were performed with contact mode on the sapphire surface using a Bruker Multimode 8 scanning probe microscope mounted with an antimony-doped silicon probe with a cobalt-chromium coating (model: Bruker MESP).The ramp size is 10 V, the ramp rate is 1 Hz, the sample Poisson's ratio is 0.3, and the tip half angle is 18°.The force curve is obtained through relative trigger mode, and the difference between the ordinate reading and the baseline of the force curve is used as the controlling parameter.The trigger threshold is 0.3 V. Through linear fitting of the straight line part at the right end of the force curve, the derived slope is the deflection sensitivity of the probe cantilever.

Determination of the cantilever size
The cantilever was observed directly by an optical microscope using a standard grating (VGRP-15M, period length 10 μm) as a ruler.The size of the cantilever can be acquired by calculating the number of periods occupied by the length and width of the cantilever beam.

Determination of quality factor
The thermal tune method is used to analyze the power spectral density (PSD) of the cantilever beam's thermal vibration [40,41], and the quality factor Q is calculated using least squares fitting according to the following equation: where A(ν) is the amplitude as a function of frequency, ν.A 0 is the baseline amplitude.A DC is the amplitude at DC (zero frequency).ν 0 is the center resonant frequency of the resonant peak.

Calculation of cantilever spring constant
The normal spring constant of the probe cantilever is calculated according to the following formula using Sader method [42,43]: where L and b are the length and width of the cantilever, respectively, ρ is the density of the dielectric medium, ν 0 and Q are the center resonant frequency and quality factor of the resonance peak, respectively, and Γ(ν) is the imaginary part of the hydrodynamic function.

Electrostatic force microscopy and Kelvin probe microscopy of clay samples
The dilute suspensions of mineral powders were dripped on the iron disc holders which were washed with 0.01 wt% (weight percentage) sulfuric acid solution and deionized water (18.2MΩ cm).Then, the sample was dry at 50 °C.
Testing was performed on a Bruker Multimode 8 scanning probe microscope.EFM and KPFM tests were both conducted in tapping mode.The probe is an antimony-doped silicon probe with a cobalt-chromium coating (model: Bruker MESP).The tip and sample biases were set to 3 V and 0 V in the EFM test, respectively.The potential offset holds at 0 V during the KPFM scanning.The scanning range is 1 × 1 μm, and the scan rate is 1 Hz.

Mineral phases of samples
From the x-ray diffraction (XRD) peaks shown in figure 1 and comparison with the ICDD's Powder Diffraction File (PDF), it can be seen that the samples are kaolinite (PDF no.14-0164), montmorillonite (PDF no.13-0135) and illite.(PDF no.43-0685), and these samples all possess high purity and well crystallinity.
According to the Bragg's law: 2 d sinθ = n λ (where d is the crystal plane spacing, θ is the angle between the incident ray and the diffracting plane, λ is the x-ray wavelength, and n is the order of the diffraction), the crystal plane spacings of three minerals can be calculated.The basal spacings are 0.722 nm for kaolinite, 1.515 nm for montmorillonite, and 1.022 nm for illite, respectively.

Chemical composition of minerals
The chemical formulas of three clay minerals are calculated [44]

Deflection sensitivity calibration
Deflection sensitivity is the conversion coefficient from volts measured on the photodetector to the nanometers of the piezo motion.The calibration is usually performed by measuring a force curve on the sapphire surface such that the cantilever does not indent the surface during the measurement.
Figure 2 shows the force curves of the sapphire standard sample.The red dotted one is the extend curve, which indicates that the tip approaches the sample, and the black solid one is the retrace curve, which indicates that the tip leaves the sample.The trigger threshold used in the test is 0.3 V; that is when the ordinate deflection error reading reaches 0.3V, the probe is closest to the sample, and at this time, the cantilever beam reaches the maximum bending amount during the force curve test.The abscissa of the acquired force curve is the distance between the tip and the sample surface, and the ordinate is the deflection error.The deflection sensitivity of the probe (59.05nm V −1 ) can be calculated from the slope by linear fitting based on the sloped part of the right end of the retrace curve (the range of Z is 24-25 V).

Length and width of the cantilever
Figure 3 is an optical microscope image of the probe cantilever.It can be seen that the shape of the probe (Bruker MESP) cantilever is rectangular.The cantilever size is measured using the standard grating VGRP-15M (period length is 10 μm) as a ruler.The length of the probe cantilever can be obtained to be approximately 210 μm, and the width is approximately 40 μm.

Quality factor of the cantilever
The quality factor is a parameter that describes the energy loss rate of the micro-cantilever in tapping mode.It is obtained by fitting the power spectral density (PSD) of the free thermal vibration of the probe cantilever and can be used to calculate the cantilever's spring constant.
Figure 4 is a power spectral density graph of the probe cantilever's thermal vibration in the frequency range of 1-100 kHz.The peak frequency (72.5 kHz) is the micro-cantilever's center resonant frequency (ν0).According to the fitting result of equation (1), the quality factor of the micro-cantilever is 200.2.

The spring constant of the probe cantilever
The probe cantilever's spring constant (k) calculated through Sader method is 2.84 N m −1 .

Electrostatic force microscopy of clay minerals
EFM mainly detects changes in probe amplitude, frequency, or phase caused by the electric field force on the sample surface.The small surface charge of the clay mineral results in a weak electric field force between the surface and the probe, which appears as a small phase shift (Δj).Figure 5 is an image of the surface morphologies of three clay minerals and the phase shifts caused by the surface electric field.It shows that the three clay minerals are all lamellar structures, among which kaolinite and montmorillonite have smoother surfaces, indicating that these two minerals have a higher degree of crystallization and a more intact lamellar structure; the surface of illite is relatively rough, suggesting that its particles are relatively broken.This phenomenon is consistent with the x-ray diffraction results.Kaolinite and montmorillonite have higher intensity diffraction peaks, while illite has a weaker overall peak intensity and a lower signal-to-noise ratio.Relatively flat areas on the surfaces (basal surfaces) of the three clay minerals are selected, and the average phase shifts (Δj) in the calculated areas are listed in table 2. The values in the sequence from smallest to largest are Δj(kaolinite) < Δj(montmorillonite ) < Δj(illite).
According to the equation dF/dz = −4kΔj/(πQ), the electrostatic force gradient dF/dz of the mineral surface can be obtained [45] (The vibration amplitudes of the cantilevers are approximately 0.04, 0.09, and  0.06 mV for kaolinite, montmorillonite and illite, respectively), the phase shift images of the three clay minerals can be transformed into those of the surface electric field force gradient distribution (figure 5).Moreover, the average value of the electric field force gradient in the relatively flat areas (basal surfaces) of the three clay mineral surfaces are calculated (table 2).It suggests that: |dF/dz|(kaolinite) < |dF/dz|(montmorillonite) < |dF/dz|(illite), which is consistent with the sequential increase in surface charge of kaolinite, montmorillonite and illite.

Kelvin probe microscopy of clay minerals
The probe tip-sample surface system is treated as a plate capacitor during the measurement of Kelvin probe microscopy, and the potential distribution on the sample surface is obtained by controlling the alternating potential applied to the probe and adjusting the compensation potential.
Figure 6 shows the surface micro-area morphology of three clay minerals and their corresponding surface potential distributions.Three clay minerals in figures 6 and 5 possess similar morphological characteristics, and prominent lamellar structures can be observed in all of them.Since the bias voltage is applied to the tip, the potential difference (ΔV) measured by KPFM is equal to the difference between the potential of the sample (Ψ sample ) and the potential of the tip (Ψ tip ), that is, ΔV = Ψ sample -Ψ tip .When the tip potential is 0, the sample potential Ψ sample = ΔV can be derived.The surface potentials of the three minerals were statistically calculated by selecting relatively flat surface areas (basal surfaces).The results are shown in table 3. It suggests that the absolute values of the surface potentials increase in the order of kaolinite, montmorillonite, and illite.It is worth noting that the dielectric constants of clay minerals are usually between 5 and 6 [46], so the Ψ sample measured by KPFM is due to the permanent surface charge induced by the isomorphic substitution in the silicon-oxygen tetrahedral sheets and aluminum-oxygen octahedral sheets of clay minerals [15,47].In addition, the surface electric field intensity (E = ΔV/d) can be calculated based on the tip-sample distance (d, set to 80 nm during testing) and the potential difference (ΔV) measured by KPFM when the tip voltage is 0 [45].Thus, the surface electric field intensity distributions of the three minerals (figure 7) and the average electric field intensities of the flat surface areas (table 3) are obtained.
Moreover, the surface charge density (σ, C m −2 ) can also be calculated based on the potential difference (ΔV) and tip-sample distance (d) measured by KPFM: σ = Q/A = ε•ε 0 •ΔV/d, where Q is the surface charge (C), A is the surface area (m 2 ), ε is the relative dielectric constant of air (1 C 2 N −1 •m −2 ), and ε 0 is the vacuum dielectric permittivity (8.854187817 × 10 −12 F m −1 ) [45].The surface charge density distribution of the three clay minerals and the corresponding average charge densities of the flat surface areas (basal surfaces) are shown in figure 8 and table 3, respectively.The results show that the absolute values of the average charge density also increase in the order of kaolinite, montmorillonite, and illite.These average values have a consistent changing trend with the layer charges of the three clay minerals, and a good linear correlation is found between them (figure 9).
For well-crystallized pure minerals, we can calculate the mineral chemical formula by determining the chemical composition and then obtain the statistical average of the surface charge, however, this method cannot obtain the actual distribution of the surface charge [21,22], and cannot provide persuasive and direct evidence  for the description of the microscopic mechanisms of the numerous surface charge-related physicochemical processes on the surface of minerals (e.g., adsorption, catalysis, redox).Through the aforementioned experimental results, we found that there is a linear relationship between the layer charges obtained through the chemical formula of minerals and the surface charge densities obtained by KPFM, indicating that KPFM can reliably characterize the charge property of the surface.Not only the amount but also the distribution of surface charge can be obtained by this method.In addition, whether involved in natural processes or used as a material,  the structure of clay minerals will be changed due to natural weathering [48] or artificial modification [49], which makes it impossible to calculate the surface charge from the theoretical mineral chemical formula, but the determination using KPFM will not be affected by this.Scanning probe microscopy will therefore provide information to explain the various surface natural processes in which clay minerals are involved and to expand the applications of clay minerals.

Conclusions
Electrostatic force microscopy and Kelvin probe force microscopy are used to study kaolinite, montmorillonite, and illite in this paper.Besides obtaining the morphologies of clay minerals, the surface electric field force gradients, surface potentials, electric field intensities, and surface charge densities are also measured and imaged.By selecting relatively flat areas on the surfaces (i.e., the basal surfaces), the average surface permanent charge densities of kaolinite, montmorillonite, and illite were obtained to be −0.006,−2.136, and −5.456 μC m −2 , respectively.A good linear relationship exists between the surface charge densities of the three clay minerals obtained using KPFM and the layer charges calculated from the mineral chemical formulas.This study provides a method for describing the heterogeneous distribution of surface charges of clay minerals, and it will provide relevant information for explaining the surface processes of clay minerals from a microscopic perspective.

Figure 2 .
Figure 2. Force curves of sapphire standard sample.(The red dotted curve indicates that the tip approaches the sample, and the black solid curve indicates that the tip leaves the sample).

Figure 4 .
Figure 4. Power spectral density (PSD) graph of the probe cantilever.

Figure 9 .
Figure 9. Relationship between layer charges (χ) and surface charge densities (σ) of three clay minerals.(The red solid line is a linear fitting line).

Table 1 .
Chemical composition of major elements of clay minerals (wt%).
a L.O.I.: Loss on ignition.

Table 2 .
Statistical values of EFM phase shifts and surface electrostatic force gradients of the clay minerals a .
a Averages of more than 10,000 data points.