Article pubs.acs.org/JPCC
Influence of Solution Chemistry on the Dielectric Properties of TiO2 Thin-Film Porous Electrodes Yang Wang,†,‡ M. Isabel Tejedor-Tejedor,‡ Wei Tan,† and Marc A. Anderson*,‡,§ †
School of Chemical Engineering &Technology, Tianjin University, Tianjin 300072, P. R. China Environmental Chemistry and Technology Program, University of WisconsinMadison, Madison, Wisconsin 53706, United States § Madrid Institute for Advanced Studies, IMDEA Energy (Electrochemical Processes Unit), 28933 Móstoles, Madrid Spain ‡
ABSTRACT: The development of supercapacitors having enhanced energy is of technological importance. Since energy scales not only with the square of the voltage but also with capacitance, we have focused on the role of the dielectric constant in enhancing capacitance. TiO2 thin-films were deposited on Si wafers by dip-coating techniques. The inhomogeneity of TiO2 thin-film generated by dip-coating and changes in crystal structure with different firing temperature were shown to be important variables in this system. Using ellipsometry under controlled humidity, we were able to measure the refractive index of pore water. Surprisingly, the refractive index of pore water decreases with increasing ionic strength, which is the opposite case of bulk water as measured by the ellipsometer. Furthermore, we found that the surface potential also influences the refractive index of pore water. Electrophoretic mobility studies were used to show the role of surface potential at the pore wall influencing the properties of pore water. The higher the surface potential, the higher the refractive index, the lowest refractive index occurring close to the isoelectric pH. The presence of the specifically adsorbed phosphate ions on the pore walls increases the refractive index. Electrochemical charge−discharge measurements were performed using TiO2 thinfilms coated on platinized Ti coupons to obtain the capacitance of these TiO2 thin-film systems. The capacitance followed a similar trend as the zeta potential and can be improved by phosphate addition. It should be noted that refractive indices that we have obtained from measurements using the ellipsometer only qualitatively relate to capacitance since they were acquired at much higher frequency than those we normally used to measure capacitance. However, the combined value of these experiments should help add insight into the nature of structured water and fundamental electrochemistry inside biased nanoporous oxide thin-films. some of these carbon materials is their insufficient stability.9 The wettability of carbon might also be a problem in aqueous systems. In our research group, where we have concentrated on these aqueous systems, we have employed thin-film porous oxide coatings on carbon materials as a way to enhance hydrophilicity and physical−chemical stability.10 To date, we have employed porous silica11 and porous alumina thin-films12 as coatings which have been shown to significantly enhance capacitance particularly in low to moderate surface area carbon materials. Of interest in this paper, particularly with respect to improvements in capacitance, is to note that, according to eq 1, capacitance not only scales directly with surface area and inversely with the distance of accumulated charge at the interface but as well with the dielectric constant of the material. The distance of accumulated charge, in other words, the thickness of the electrical double layer (EDL), is a value that is often ignored by researchers, as it is experimentally difficult to obtain. For a given surface area in a porous thin-film
1. INTRODUCTION For the last couple of decades, supercapacitors have been intensively investigated as promising energy storage and conversion devices due mostly to their high power density.1 Supercapacitors utilize high surface area electrode materials and ions sequestered angstroms away from charged surfaces to achieve great capacitance.2 The capacitance of supercapacitors is governed by the same fundamental equation as conventional capacitors. C = ϵ0ϵr A /D
(1)
where C is the capacitance in farads F; A is the area of each plate in a traditional capacitor (usually metal) in square meters; ϵr is relative static permittivity (dielectric constant) of the material between the plates, ϵ0 is the permittivity of free space (8.854 × 10−12 F/m), and D is the separation between the plates, in meters.3 According to eq 1, large surface areas greatly enhance the capacitance of a supercapacitor. As such, numerous studies have been devoted to developing porous carbon materials that have high surface areas but also reasonable electrical conductivity.4,5 These include such materials as porous graphene,6 carbon nanotubes, carbon nanofibers,7 carbide-derived carbon,8 et al. One main disadvantage of © XXXX American Chemical Society
Received: July 14, 2016 Revised: September 2, 2016
A
DOI: 10.1021/acs.jpcc.6b07061 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry C
dynamic simulations.20,22 In this paper, we have applied ellipsometry measurements under controlled humidity to obtain the refractive index of pore water. In this fashion, we hope to see the influence of the solution properties such as the pH, phosphate concentration, and ionic strength, on the refractive index (square root of dielectric constant at high frequencies) of these pore waters. Subsequently, capacitance will be measured directly in electrochemical charge−discharge experiments. However, we remind the reader that refractive indices obtained from ellipsometer only qualitatively relate to capacitance since much higher frequencies are employed using this technique than those we normally utilize to measure capacitance, as will be illustrated in the following sections of our paper.
supercapacitor system, if we keep ionic strength constant, the thickness of EDL should be a constant. Therefore, the only variable of this system would be the dielectric constant. Unfortunately, we have found that there is a paucity of studies that have been devoted to the role of the dielectric constant with respect to electrochemical capacitance. Materials having a high dielectric constant could hold more charge and therefore have higher capacitance.13,14 According to eq 1, as the dielectric constant for TiO2 is around 50 whereas SiO2 is close to 3 and Al2O3 around 10, in terms of capacitance, it would make sense to replace SiO2 or Al2O3 with TiO2 thereby improving the performance of oxide-based supercapacitors. However, Leonard et al. showed that electrodes coated with thin-films of these oxide materials have equivalent capacitance when the pH of the electrolyte is equidistant from their respective isoelectric pH (pHiep) values, |pH − pHiep|.15 That means the capacitance values of these oxide electrodes in equivalent electrolytes were similar despite these large differences in the dielectric constant of the bulk solid fraction of these films. This suggests that capacitance is rather independent of the dielectric constant of the bulk solid fraction of the porous electrode but is more likely influenced by the electrolyte in the pores of these materials. According to the literature, the variables affecting the properties of pore water are pore size, solute characteristics, surface potential of the pore wall, and specific adsorption.16−18 Several molecular dynamic simulations of water in narrow pores have predicted that the presence of the pore walls causes water structure to become more rigid, reducing polarizability significantly. The dielectric constant of water in pores is found to be significantly smaller than that of bulk water.19 The average behavior of pore water is sometimes represented with a “core−shell” model, by which pore water is conceptually divided into a core of free water with bulk-liquid-like properties and a shell of interfacial water having distinct properties.20 Furthermore, the ratio of interfacial water is smaller in larger pores than in smaller pores.21 Thus, pore size as well should play an important role in the properties of the pore water. The size and geometry of the pore in a given porous film are controlled by the size and packing of the particles as well by the temperature and time used in the sintering process, either by influencing the degree of sintering of the particles and/or by changing the crystal structure.22,23 For porous metal oxides, the potential of the pore surface can be changed by solution pH and other chemically adsorbed ions. This potential can be either positive, negative, or net neutral (pHiep) depending on the pH of the solution. The presence of a potential affects the distribution of ions adjacent to the surface, resulting in an increase in the concentration of counterions. This redistribution of ions is likely to affect the properties of pore water. In addition to the role of the proton, the chemiadsorption of potential determining ions such as phosphate will act in concert to affect surface potential and thereby control the distribution of charge inside the pores of these materials. Therefore, the surface chemistry of the materials, pore geometry, and size as well as solute composition all act together to determine the properties of water in the pore space.24 In summary, the dielectric constant of the water inside the pores might play an important role in determining electrochemical capacitance. Our interest is to investigate the properties of water in the pores. Unfortunately, until now, the dielectric properties of pore water have not been experimentally determined, but rather evaluated by molecular
2. THEORY 2.1. Dielectric Polarization of Water. The dielectric constant is related to polarization. As has been shown in Figure 1, dielectric constant changes at various frequencies produced
Figure 1. Schematic of dielectric constant as it varies with frequency.
by different mechanisms. Viewed from a microscopic perspective, we know that the molecular polarizability is also frequency dependent. Electronic polarizability is present in all molecules and has a response time that is rapid (>1014 s−1). The high frequency response can follow the undulations of electromagnetic radiation in the visible region, and hence this response gives rise to refraction of light. This contribution is the high frequency or optical dielectric constant. In liquid water, polar molecules possess a distribution of permanent dipole moments due to an asymmetric arrangement of hydrogen and oxygen atoms. There is an orientation polarizability in polar molecules due to their tendency to align in an applied electric field due to the torque of the applied field in the frequency range from 10 6 to 1010 s−1. These motions give rise to absorption and dispersion in the microwave region. They also contribute to the low frequency or static dielectric constant. The static dielectric constant is not really static but rather is due to changes in the electrical response due to dipolar reorientation. The larger the dipole moment, the greater the tendency of the solvent to respond to an applied field by reorientation of the microscopic dipoles.25 2.2. Refractive Index Measured from Ellipsometer. As known, light has the character of waves. When light enters a B
DOI: 10.1021/acs.jpcc.6b07061 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry C
3. EXPERIMENTAL SECTION 3.1. Materials. TiO2 Sol. The TiO2 sol was synthesized by acidic hydrolysis of titanium isopropoxide and additional dialysis following the procedure of Xu and Anderson.29 The sol had a final density of 20.0 g·L−1 with a pH of 3.6. Substrates. In this paper, we used two different substrates: silicon wafers and platinized Ti plates. Silicon wafers manufactured by Virginia Semiconductor, Inc. with 500 μm thick, 2.54 cm diameter and 2−3 nm native SiO2 were used for ellipsometry analysis as the optical properties of the Si−SiO2 system have been extensively studied using ellipsometry.30 For Ti plates, following the procedure of Voort,31 Ti coupons (75 mm*25 mm*1 mm) were ground and polished with a Buehler Ecomet 4 until the surface roughness was less than 40 nm. The polished Ti coupons were sputtered with Pt to eliminate the effect of passivating (oxidizing) the Ti surface. This might interfere with characterizing the TiO2 film by ellipsometry. Furthermore, these sputtered Ti coupons, due to their good conductivity, permitted their use as electrodes in electrochemical measurements. Sol−gel dip-coating methods were utilized for depositing TiO2 porous films on Si wafers and Ti coupons. The substrates were heated at 300 °C to increase their hydrophilicity (wettability) before dip-coating. The substrates were then withdrawn from the TiO2 sol at a controlled speed of 3 mm/s and subsequently allowed to dry in air. This procedure was repeated three times. The samples were then fired at a desired temperature to sinter the TiO2 porous thin-films. 3.2. Methods. Zeta Potential. Zeta potentials were determined by electrophoretic mobility of a TiO2 monolith ground to a fine powder and measured using a Malvern Zetasizer 3000HSA. Measurements were performed at room temperature, and each data value was an average of five measurements. To prepare samples for electrophoretic mobility, a concentrated stock suspension of powdered TiO2 in a 0.1 M NaNO3 solution was made. Next, a small amount of the concentrated suspension NaNO3 was diluted with either a 0.1 M NaNO3 solution or a 0.1 M NaNO3 and 1 mM phosphate solution. The pH of these solutions was then adjusted by adding HNO3 or NaOH. Ellipsometry. Previous to any ellipsometry measurements, the TiO2 coated supports were immersed in the desired solution and let to equilibrate for 12 h. In this study, samples were equilibrated in aqueous 0.01 M NaNO3 solutions having different phosphate concentrations and different pH values. Spectroscopic ellipsometry, which is known to be a very useful and nondestructive technique with which to investigate the optical properties of thin-films, has been employed to study our films. The measurements were performed on a J. A. Woollam Spectroscopic Ellipsometer under a controlled humidity environment. The refractive index, thickness, and porosity of TiO2 thin-films on Ti coupons and Si wafers were determined simultaneously within the wavelength range of 400−1000 nm at an angle of incidence of 70°. We used the data points at the wavelength of 500 nm for all of the following analysis. The ellipsometry data was fit with a Cauchy film model to yield the refractive index of the film and its thickness. An effective medium approximation (EMA) model was employed to obtain the porosity of the film. It should be noted that, because of the small sampling area, this technique
media, it shows a rather complicated behavior due to its refraction or absorption. The propagation of light in media can be expressed by the complex refractive index, which is defined through the equation n ̃ = n + iκ
(2)
where n is the real part of ñ, same as the normal refractive index, and κ is the imaginary part, called extinction coefficient. κ is directly related to the absorption coefficient of the medium. On the other hand, the refractive index of a material is a physical parameter that shows the effect of the electric field component of the light wave on the distribution around each atom in the crystal structure. The refractive index (n) is defined as the ratio of velocity of light in free space (c) to the velocity in the medium (v):
n = c /v
(3)
Materials with highly polarizable electrons give rise to a high value of the refractive index and vice versa.26 Accordingly, there is a close relation between the dielectric constant and the refractive index. From Maxwell’s electromagnetic field theory, the velocity of light in a medium is given by
1/v 2 = μ0 μr ϵ0ϵr
(4)
where μ0 is permeability of material in vacuum, μr is relative permeability of material, ϵ0 is permittivity of material in vacuum, and ϵr is relative permittivity of material. In free space, μr = ϵr = 1 and the velocity of the light is c, so we have
v = c/ ϵrμr
(5)
At optical frequencies, we can set μr = 1 for most naturally occurring materials and thus conclude n=
ϵr
(6)
Here we obtain an equation directly linking refractive index and dielectric constant. In this paper, using porous instead of bulk materials, we study the variation of refractive index as a function of porous structure as well as solution chemistries. Realizing we have an aqueous electrolyte inside a porous material, we can return to the discussion above concerning the measurement of refractive index. The refractive indices of these thin-films depend on the related values of bulk material, material filling the void, in this case, air or water, and the void fraction. A procedure to interpret these parameters for a twophase mixture has been already developed based on Bruggeman’s effective-medium approximation and also consistent with the Clausius−Mosotti relation27 ⎛ n2 − n 2 ⎞⎛ n2 + 2n 2 ⎞ q1 2 1 ⎟= ⎟⎜ 2 ⎜ 2 2 2 ⎝ n + 2n2 ⎠⎝ n1 − n ⎠ 1 − q1
(7)
where n1 is the refractive index of phase 1 with volume fraction q1 and n2 is the refractive index of phase 2 with volume fraction 1 − q1. In this paper, we try to evaluate the refractive index of water (away from the well-known value of 1.33 at 589 nm, 20 °C28) inside pores with respect to pore structure and surface chemistry as influenced by ionic strength, pH, and phosphate concentration. We expect these variables to impact the dielectric constant of our porous thin-film TiO2 electrodes. C
DOI: 10.1021/acs.jpcc.6b07061 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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Figure 2. Measurements of TiO2 thin-film at different locations under dry conditions. (A) Schematic of Si wafer coated with TiO2 thin-film. (B) Film thickness as a function of measured spot locations (vertical from B to T, horizontal from H1 to H2). (C) Refractive index and porosity of film as a function of spots measured (locations inside dash line-horizontal from H1 to H2). (D) Refractive index and porosity of film as a function of spots measured (locations inside dash line-vertical from B to T).
could be used to measure the properties of these films at different locations on the substrates. Using the ellipsometer, measurements were performed with the thin-films under two conditions: dry and at a relative humidity (RH) > 85%. Dry N2 was flowing over the wafers for measurements under dry conditions. At RH levels >85%, capillary condensation for the pore size of our materials results in pore filling.32 To control the RH of the environment, the entire measurement process was conducted in a closed chamber with humid N2 flowing inside the chamber. Humid N2 was produced by flowing N2 through two consecutive gas-scrubbing bottles filled with water. RH was measured by a Vaisala HMI 36 Humidity Data Processor connected to a HMP 36B Probe and controlled to be greater than 85% throughout the measurement. Electrochemical Measurements. Galvanostatic charge− discharge tests were conducted to acquire the capacitance values on a Princeton Applied Research VMP2 potentiostat using a three-electrode electrochemical cell at room temperature. Pt sputtered Ti coupons coated with a film of porous TiO2 were employed as the working electrodes, a Pt sputtered Ti coupon was used as a counter electrode, and a saturated calomel electrode as a reference electrode. As in ellipsometry measurements, platinized Ti coupons with TiO2 coatings were equilibrated with aqueous 0.1 M NaNO3 solutions at different phosphate concentrations and different pH values for 12 h before electrochemical measurements.
4. RESULTS AND DISCUSSION 4.1. TiO2 Thin-Film Properties. Pore Structure. Nitrogen adsorption measurements on surrogate TiO2 xerogels synthesized by same procedure have been performed to determine specific surface areas and pore size distributions by former researchers in our group. The specific surface area of a TiO2 xerogel fired at 300 °C is around 155 m2/g. The average pore radius at this condition is close to 20 Å obtained from the desorption branch of the isotherm.33 An average porosity of the TiO2 xerogel from nitrogen adsorption is 34%.34 It should be noted that we obtained a porosity of 35% using ellipsometry employing an EMA model. These numbers are close, but it is not unreasonable to expect that ellipsometry measurements might yield a higher porosity due to the presence of closed pores which may not be accessible by nitrogen.35 Film Thickness and Substrate Effects. To measure the thickness and refractive index of the TiO2 films deposited on a Si wafer, the INTR-JAW Oxide Layer model was used. We found that the average of 10 randomly picked points on the film of these parameters that best fit this model are 121.67 ± 3.20 nm, 1.785 ± 0.008, respectively. Films coated on platinized Ti coupons were measured using a Ti substrate model adapted from a Ti Lorentz model provided by the instrument. The average best fit for the thickness of these films was 124.50 ± 4.79 nm and for the refractive index 1.799 ± 0.012, again determined at 10 randomly picked points on the film. These results seem quite close to each other since the difference between these two substrates is only 2%. However, we know D
DOI: 10.1021/acs.jpcc.6b07061 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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Figure 3. Measurements of TiO2 thin-films fired at different temperatures under dry conditions. (A) Refractive index and thickness as a function of temperature. (B) Porosity calculated from refractive index and thickness as a function of temperature.
probably associated with the lack of small enough pores to close by the surface diffusion sintering mechanism. Above 350 °C, the transformation of the TiO2 particles from amorphous TiO2 to anatase involving bulk diffusion is able to further densify the film. In the meantime, refractive index varies as the firing temperature increases. The refractive index is directly correlated with porosity and the crystal structure of TiO2. In Figure 3A, the almost linear increase of refractive index below 300 °C suggests that the film is undergoing densification which is only related to porosity. This is consistent with the measurements of thickness. Above 300 °C, the change of refractive index is a mixture of porosity variation and crystal structure transformation. The reason why the refractive index decreases between 300 and 400 °C is still unknown. Therefore, our research has focused for the most part on the system at 300 °C. After 400 °C, one expects a linear increase again as the TiO2 coatings are now all anatase at these temperatures.40 Using refractive indices or thickness values, porosity of the thin-films could be calculated through eq 7. Here, we applied the refractive index of amorphous TiO2 (n = 2.35)41 for our calculations. These two approaches produced almost the same porosity that decreases with increasing temperature (
