Elucidating the Importance of Pore Structure in Determining the

Article pubs.acs.org/JPCC

Elucidating the Importance of Pore Structure in Determining the Double-Layer Capacitance of Nanoporous Carbon Materials Jocelyn E. Zuliani, Charles Q. Jia, and Donald W. Kirk* Department of Chemical Engineering & Applied Chemistry, University of Toronto, 200 College Street, Toronto, Ontario, Canada M5S 3E5 S Supporting Information *

ABSTRACT: Porous carbon is a common electrode material used in electrochemical double-layer capacitors, in which energy is stored by physical adsorption of electrolyte ions on the carbon’s surface, forming an electrical double layer (EDL). However, due to the complex nanoporous network of carbon materials, it is difficult to characterize the EDL structure. This work demonstrates that the understanding of the EDL structure in nanoporous carbon materials can be improved by defining the pore shapes using ultrahigh resolution scanning electron microscopy (SEM). The SEM images reveal a continuous network of curved pores. This characterization, along with the experimentally determined surface areas and pore sizes, enabled the investigation of the applicability of various models describing the EDL configuration. This study found that, by using the microscopic information to characterize the 3-D nanostructure and select the appropriate models for the pore shape, it is possible to predict a porous carbon material’s experimental capacitance within ±8%. This updated approach may be used to identify ideal pore structures and top-performing carbon materials. It is clear that using ultrahigh resolution SEM images to understand the relationship between pore shape, EDL structure, and capacitance provides valuable insight into the complexity of energy storage in nanoporous carbon materials.

1. INTRODUCTION Supercapacitors are emerging energy storage devices that offer the benefits of high power density, rapid charging rates, long cycle life, and moderate energy density. Supercapacitors can be divided into three general categories, electrochemical doublelayer capacitors (EDLCs), pseudocapacitors, and asymmetric hybrid capacitors, taking advantage of both double-layer and pseudocapacitive energy storage mechanisms. This study will focus on EDLCs, which store energy by physical ion adsorption on the electrode surface in the electrical double layer (EDL).1−15 Electrochemical double-layer capacitors are governed by the nanoscale phenomena that occur in the EDL. The EDL is formed when a charged electrode is placed in an electrolyte, which causes the electrolyte ions to migrate toward the charged surface in order to balance the applied potential.1,3,4 The model for the EDL was originally proposed by Helmholtz, which consisted of a single layer of counterions adsorbed on the charged surface.16 However, as understanding of the electrode/ electrolyte interface advanced, it became apparent that this model did not apply to all cases. Stern developed a model, consisting of a single layer of ions adsorbed onto the surface of the electrode, the inner Helmholtz plane, with a diffuse double layer, as proposed by Gouy and Chapman, adjacent to the inner Helmholtz plane, which is composed of an exponentially decaying ion concentration until the concentration matches that of the bulk electrolyte.17 The EDL model was further © XXXX American Chemical Society

advanced by Bockris, Devanthan, and Mueller, in order to account for the dielectric effects of free solvent molecules.18 The general structure of the EDL on a flat plate is shown in Figure 1.

Figure 1. Diagram of the electrical double layer, highlighting the inner Helmholtz plane, the diffuse double layer, and the potential and concentration gradient. Received: March 28, 2017 Revised: June 29, 2017 Published: August 16, 2017 A

DOI: 10.1021/acs.jpcc.7b02944 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Figure 2. Diagram of the electrical double layer, in (a) a cylindrical pore with a distinct double layer, (b) electric wire-in-cylinder capacitor model for a pore that allows a fully hydrated ion adsorb, and (c) a pore that is smaller than the diameter of the hydrated ion, and causes solvation shell distortion or desolvation.

The EDL behaves like a plate capacitor, with two flat surfaces of opposite charge separated by a dielectric material. The capacitance of the EDL on a flat surface is described by eq 1, where capacitance is proportional to the vacuum permittivity, ε0, the relative dielectric constant of the electrolyte in the EDL, ε, and the accessible surface area for ion adsorption, A, and inversely proportional to the thickness of the EDL, d.16 Since capacitance would be maximized by having a thinner EDL, highly concentrated electrolyte solutions, of greater than 1 M, are typically used, resulting in an EDL thickness of less than 1 nm.19 εε A C= 0R d

of the EDL in pores that are able to accommodate a distinct double layer, or 2+ layers of ions. In KOH electrolyte, the diameter of the hydrated K+ ion is 0.662 nm and the diameter of the hydrated OH− ion is 0.600 nm. Therefore, the minimum pore size to form a distinct cylindrical layer is 1.24 and 1.20 nm for potassium and hydroxide ions, respectively. However, even these diameters are larger than the majority of the subnanometer pores in porous carbon materials. ε0εR C = R A R outer ln R outer− d

(

outer

)

(2)

In order to predict the capacitance in subnanometer pores, Huang et al.38,39 proposed a model to represent pores where a distinct double layer cannot be formed, as displayed in Figure 2b and c and eq 3.38,39 This configuration is known as the electric wire-in-cylinder capacitor model. This model accounts for a single string of ions in a narrow cylindrical pore.

(1)

The electrolyte affects the double-layer thickness, and the electrode material affects the total accessible area for ion adsorption. Also, in subnanometer micropores, it has been suggested that the electrolyte ion solvation shell may be distorted to allow the ions to penetrate these pores, which causes the thickness of the double-layer to be reduced. As such, highly porous materials, with specific surface area (SSA) values above 1000 m2 g−1, are desirable for EDLC applications.1−4,20 The effects of pore size and shape on EDL structure in porous carbon have been the topic of significant debate in the research community. There have been competing theories presented on the effects and EDL structure in subnanometer pores, and there remains an ongoing debate as to the origin of enhanced capacitance in subnanometer pores.7,21−36 1.1. Geometric Adaptations to the Helmholtz Model. The Helmholtz model applies to a flat plate configuration; however, the Helmholtz model does not adequately describe the curved and highly nanoporous carbon network in porous carbons, which is an interconnected network of macropores (diameter: >50 nm), mesopores (diameter: 2−50 nm), and micropores (diameter: 90 wt %) and a low impurities content. Additionally, the samples have a high total surface area and moderate to high microporosity. The pore size distributions of the four samples are presented in Figure 5, showing that all four samples have differences in D


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Figure 5. Pore size distributions (PSD) of the activated fluid coke (AFC) and activated delayed coke (ADC) samples. Analysis was performed using density function models and CO2 and N2 isothermal adsorption data.

3.2. Analysis of Model and Physical Parameter Applicability. The results presented in this section represent a test of the EDL models in order to determine if the models can be applied with an assumed pore shape. The models are applied to the pore size distributions of the four porous carbon materials under investigation assuming one pore shape for micropores and one pore shape for mesopores. This strategy will be used to determine if pore shape is important for calculating capacitance, as well as to identify if a model with a single pore shape for micropores and a single pore shape for mesopores can be used to accurately calculate the capacitance. The first set of parameters, presented by Huang et al.,39 generates the results in Table 4, which show a significant overestimation of the capacitance associated with subnanometer pores, with the predicted capacitance values by 20+%. There are several possible sources of error with these results. First, the relative dielectric constant may be less in these subnanometer pores; this would result in an overestimation of the SSA-normalized capacitance. Second, it is possible that ions do not penetrate the pores of diameter 0.53 nm, which would result in a more reasonable prediction of the capacitance. The second set of parameters is a combination of several sources; the micropore data is predicted by Feng et al.,41 the relative dielectric constant for mesopores is predicted by Conway,1 and the EDL thickness in the mesopores is predicted by Huang et al.39 The predicted gravimetric capacitance from these parameters is presented in Table 5, which shows a significant underestimation of the experimental data. The predicted ion radius in the subnanometer pores is significantly larger than the ion radius of 0.133 nm, and is approaching the fully hydrated ion radius of 0.33 nm.46 These parameters result in the model predicting that the ions are unable to penetrate

the pore sizes, especially in the mesopore range. These pore size distributions will be used in combination with the above structural models to predict the measured capacitance of each material. This will be outlined in the model data analysis. The isothermal data for the samples collected using nitrogen gas and carbon dioxide gas is presented in the Supporting Information, Figure S-1. The electrochemical characteristics of the activated petroleum coke samples are displayed in Table 3. The results show Table 3. Total Specific Surface Area and Gravimetric Capacitance Values for the Activated Fluid Coke (AFC) and Activated Delayed Coke (ADC) Samplesa parameter

specific surface area (m2 g−1)

gravimetric capacitance (F g−1)

AFC-2.5:1 AFC-3.5:1 ADC-2.5:1 ADC-3.5:1

1995 2150 2095 2455

333 333 375 413

Capacitance was measured with a current density of 25 mA g−1 and a voltage window of 1 V, and normalized to the mass of active material in a single electrode.

a

that the activated coke samples have high capacitance values, greater than 300 F g−1, which is consistent with the high total SSA values. However, there is no direct link between capacitance and total measured specific surface area. The galvanostatic cycle curves for each sample are presented in the Supporting Information, Figure S-2. Therefore, given the similar chemical composition, skeletal density, but differing electrochemical behavior and pore size distributions, these four samples are excellent candidates to investigate the EDL models based on pore size.

Table 4. Predicted Gravimetric Capacitance and Percentage Difference Compared to Experimental Values for the Activated Fluid Coke (AFC) and Activated Delayed Coke (ADC) Samplesa AFC-2.5:1 experimental capacitance (F g−1) electrical wire (d < 2 nm) + cylinder (d > 2 nm) (F g−1) electrical wire (d < 2 nm) + spherical (d > 2 nm) (F g−1) slit pore (d < 2 nm) + cylinder (d > 2 nm) (F g−1) slit pore (d < 2 nm) + spherical (d > 2 nm) (F g−1) a

333 508 488 648 628

(+53%) (+46%) (+95%) (+88%)

AFC-3.5:1 333 470 435 578 543

(+41%) (+31%) (+73%) (+63%)

ADC-2.5:1

ADC-3.5:1

375 492 462 619 589

413 461 410 572 520

(+31%) (+23%) (+65%) (+57%)

(+12%) (−1%) (+38%) (+26%)

Excludes subnanometer pores less than 0.42 nm in diameter. Model Parameters εR,micro = 7.76, εR,meso = 13.4, a0 = 0.164 nm, and d = 0.672 nm.39 E


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Table 5. Predicted Gravimetric Capacitance and Percentage Difference Compared to Experimental Values for the Activated Fluid Coke (AFC) and Activated Delayed Coke (ADC) Samplesa AFC-2.5:1 −1

experimental capacitance (F g ) electrical wire (d < 2 nm) + cylinder (d > 2 nm) (F g−1) electrical wire (d < 2 nm) + spherical (d > 2 nm) (F g−1) slit pore (d < 2 nm) + cylinder (d > 2 nm) (F g−1) slit pore (d < 2 nm) + spherical (d > 2 nm) (F g−1) a

333 132 120 154 142

(−60%) (−64%) (−54%) (−57%)

AFC-3.5:1 333 150 130 167 147

(−55%) (−61%) (−50%) (−56%)

ADC-2.5:1 375 146 129 166 149

(−61%) (−66%) (−56%) (−60%)

ADC-3.5:1 413 154 124 173 143

(−63%) (−70%) (−58%) (−65%)

Excludes subnanometer pores less than 0.66 nm in diameter. Model Parameters εR,micro = 3.33,41 εR,meso = 7.8,1 a0 = 0.265 nm,41 and d = 0.672 nm.39

Table 6. Predicted Gravimetric Capacitance and Percentage Difference Compared to Experimental Values for the Activated Fluid Coke (AFC) and Activated Delayed Coke (ADC) Samplesa AFC-2.5:1 −1

experimental capacitance (F g ) electrical wire (d < 2 nm) + cylinder (d > 2 nm) (F g−1) electrical wire (d < 2 nm) + spherical (d > 2 nm) (F g−1) slit pore (d < 2 nm) + cylinder (d > 2 nm) (F g−1) slit pore (d < 2 nm) + spherical (d > 2 nm) (F g−1) a

333 253 240 314 302

(−24%) (−28%) (−6%) (−9%)

AFC-3.5:1 333 312 291 360 338

(−6%) (−13%) (+8%) (+2%)

ADC-2.5:1 375 284 265 340 321

(−24%) (−29%) (−9%) (−14%)

ADC-3.5:1 413 342 308 390 357

(−17%) (−25%) (−6%) (−14%)

Excludes pores less than 0.42 nm in diameter. Model Parameters εR,micro = 3.33,41 εR,meso = 7.8,1 a0 = 0.138 nm, and d = 0.33 nm.46

Figure 6. Comparison of calculated and experimentally measured capacitance. Model parameters: εR,micro = 3.33,41 εR,meso = 7.8,1 a0 = 0.138 nm, d = 0.33 nm,46. (a) Full scale; (b) magnified scale. Legend: black line, measured capacitance = calculated capacitance. Models: electrical wire micropore + cylindrical mesopore, diamonds; electrical wire micropore + spherical mesopore, squares; slit micropore + cylindrical mesopore, triangles; slit micropore + spherical mesopore, circles; carbon materials, AFC-2.5:1: gray points, AFC-3.5:1: white points, ADC-2.5:1: black points, ADC-3.5:1: diagonal pattern points.

dielectric behavior in the EDL in mesopores and micropores. Additionally, Figure 6a demonstrates that there is a reasonable fit for all models. Therefore, these parameters appear to be reasonable estimates of the relative dielectric constant in both micropores and mesopores, and using a physical estimate of the hydrated and ionic ion radius, for the mesopore and micropore EDL thickness calculations, provides a reasonable estimate. However, the models do not show a clear differentiation in electrochemical performance of different carbon materials of similar surface area but different pore size distribution. Also, upon magnification of the axes, in Figure 6b, it is clear there remains some discrepancy in the model predictions. The results presented in Figure 6 show that assuming one pore shape for mesopores and one pore shape for micropores, without evidence that these shapes exist in the material, does not result in an accurate prediction of the material’s capacitance. Suggesting that in broad pore size distribution activated carbon materials, the complex pore shapes and sizes cannot be represented by assuming a single structure for mesopores and one for micropores. In order to further investigate the structure of the EDL in the pores of the porous

and adsorb in the pores of diameter 0.35 or 0.53 nm. On the basis of the significant underestimation of the experimental data using these model parameters, it is clear that pores between 0.42 and 0.66 nm must be accessible. This leads to the conclusion that ion solvation shell distortion occurs to allow ions to penetrate the subnanometer diameter pores in aqueous solutions. This result is similar to the conclusions drawn by Jäckel et al., who demonstrated that the surface area of subnanometer pores must be accessible to ions in order to explain the materials measured capacitance.21 Table 6 provides a closer approximation of the capacitance compared to the experimental data. The parameters selected for this analysis were εR,micro = 3.33, predicted by Feng et al.,41 εR,meso = 7.8, predicted by Conway,1 and the radius of the ion (0.138 nm) and hydrated ion (0.33 nm)46 for the a0 and d values, respectively. A comparison of the four possible configurations is presented in parts a and b of Figure 6, with the experimentally measured data. The predicted gravimetric capacitance for the activated coke samples is between 29% below and 8% above the experimental values. This suggests that these parameters provide a reasonable prediction of the F


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Figure 7. SEM images of activated fluid coke (AFC-2.5:1) samples, using electron deceleration analysis, for nominal SEM instrument magnifications of (a) 200,000× and (b) 400,000×. Images show the porous structure of activated fluid coke at nanometer scale, demonstrating a continuous carbon structure with curved pores of various shapes and sizes.

Figure 8. SEM images of activated fluid coke (AFC-3.5:1) samples, using electron deceleration analysis, for nominal SEM instrument magnifications of (a) 200,000× and (b) 400,000×. Images show the porous structure of activated fluid coke at nanometer scale, demonstrating a continuous carbon structure with curved pores of various shapes and sizes.

Figure 9. SEM images of activated delayed coke (ADC-2.5:1) samples, using electron deceleration analysis, for nominal SEM instrument magnifications of (a) 200,000× and (b) 400,000×. Images show the porous structure of activated delayed coke at nanometer scale, demonstrating a continuous carbon structure with curved pores of various shapes and sizes.

smoothing of the carbon surface due to electron penetration of the carbon sample and backscattering detection. In order to improve the resolution of the SEM analysis, electron deceleration will be used, which involves applying a bias across the sample, as outlined in the Methods section. The ultrahigh resolution SEM images of the AFC-2.5:1 sample are displayed in Figure 7, the AFC-3.5:1 sample is displayed in Figure 8, the ADC-2.5:1 sample in Figure 9, and the ADC-3.5:1 sample in Figure 10, which show magnifications of 200,000 and 400,000 times. At this high magnification, it is possible to visualize the 3-D pore structure, for pores up to 1.5−2 nm in diameter. On the basis of these images, it is

carbon samples, electron microscopy imaging will be used in order to visualize the 3-D structure of the pores. 3.3. Electron Microscopy Imaging of the Porous Carbon Structure. In order to assess the applicability of the structural models to the porous carbon samples used in EDLCs, the true carbon structure must be characterized. As such, high resolution, high magnification images of the 3-D pores in the carbon surface would provide further insight. However, due to the low molecular weight of porous carbon samples, the resolution of traditional electron microscopy techniques is limited. Additionally, the high accelerating voltages used to increase magnification and resolution may lead to artificial G


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Figure 10. SEM images of activated delayed coke (ADC-3.5:1) samples, using electron deceleration analysis, for nominal SEM instrument magnifications of (a) 200,000× and (b) 400,000×. Images show the porous structure of activated delayed coke at nanometer scale, demonstrating a continuous carbon structure with curved pores of various shapes and sizes.

possible to understand the porous structure of the activated carbon materials. The SEM images are a selection of representative images from a suite of images that were collected for many particles of each sample. The same observations of pore structure and shapes were made for all of the SEM images of the different particles within each sample. The porous structure of carbon materials is highly variable, and does not show a clear pore shape. The structure has a continuous carbon network, containing combined shallow and deep holes with curved pore walls. Quite often, the larger pores are composed of a nonsymmetric curved shape. The AFC-2.5:1 sample has a finer pore structure compared to the other samples, having smaller pore diameters and less clear curved structures. This observation is consistent with the high microporosity of the AFC-2.5:1 sample and the high abundance of subnanometer pores. Additionally, the chemical KOH activation of these particles included a room temperature soaking step and a 400 °C melting step in order to ensure the KOH fully penetrates the petroleum coke particles. Therefore, the chemical KOH activation results in activation of both the internal and surface of the particles. Also, this activation technique results in cracking and fracturing of the petroleum coke particles. Therefore, these images are representative of the bulk structure of the activated petroleum coke materials. On the basis of these images, it is clear that there is not a single pore structure that can represent the EDL formation in mesopores or micropores for these broad pore size distribution activated carbon samples. However, it is also clear that using KOH activation has led to the formation of curved pore walls. The curved pore shape is consistent with observations made by Guo et al. using transmission electron microscopy (TEM) imaging. Guo et al. observed that porous carbon prepared using potassium hydroxide activation is composed of several slitshaped subnanometer pores, which have curves associated with the KOH activation.49,50 Therefore, the 3-D SEM results in this manuscript provide further confirmation that the curved pores observed in the 2-D TEM imaging are consistent with the 3-D structure of the KOH activated porous carbon materials. 3.4. Interpretation of EDL Models Based on SEM Images of the Porous Carbon. The SEM images provide significant insight into the porous carbon structure in the mesoporous and larger diameter microporous range. On the basis of the curvature of the pore walls in the KOH activated samples, both the spherical and cylindrical models are important for predicting the structure of the EDL in the

mesopores. In the SEM images, the smaller mesopores show a dark background, which is indicative of a pore that is deeper than it is wide. These pores may be approximated by the cylindrical pore. The larger pores visible in the images, which are on the order of tens to hundreds of nanometers in diameter, are more spherical in shape, with the diameter being similar or larger than the depth of the pore. Additionally, these larger pores have several smaller pores found inside their surface. Interpretation of the micropores presents a greater challenge, since the SEM imaging resolution shows pores approximately 1.5−2 nm in diameter. On the basis of the model calculations, the slit micropore model provides an estimate closer to the measured capacitance. However, using the SEM images, the pores appear to have a curved wall structure. Finally, consideration must be given to the amount of solvation shell distortion that is required for the ions to adsorb in the micropores based on their diameter. By assuming that the curved pore wall continues into a portion of the micropores, and by using the highest resolution SEM images, it is reasonable to assume that the micropores between 1 and 2 nm in diameter are a curved wall shape, and may be represented either by the cylindrical model, for pores, where a distinct double layer may be formed (d > 1.4 nm in diameter) or the electrical wire micropore model, since only a single hydrated ion may fit in these pores (1 nm < d < 1.4 nm). Since these pores are larger than the hydrated ion diameter, (K+, d = 0.662 nm; OH−, d = 0.600 nm), there will likely be some water molecules present around the ions. Therefore, a larger relative dielectric constant compared to the subnanometer pores is required to account for water’s dielectric properties. As an estimate, assuming a partial desolvation of the ions in the micropores, the relative dielectric constant and the ion radius were approximated as the average of the values for ions that have no solvation shell, and fully solvated ions, where a0, average = 0.236 nm and εR,micro = 5.57. For the subnanometer pores, on the basis of the model results presented above, slit pores appear to provide a closer approximation of the capacitance. Additionally, these pores of 0.4−1 nm in diameter are likely to have more of a slit pore shape, as they may be caused by delamination of carbon graphite layers. Therefore, it will be assumed that the subnanometer pores may be approximated by a slit shape. This is consistent with observations made by Guo et al. using TEM analysis, showing KOH activated carbon materials are composed of curved and defected graphene-type layers.49 Finally, for the relative dielectric constant, due to the small H


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SEM images, a closer approximation of the carbon’s porous structure can be made, which allows for a more accurate model. 3.5.1. Sensitivity Analysis. In order to investigate the robustness of the model, particularly relating to the gas physisorption model selection and the calculated pore sizes, a sensitivity analysis was performed. Puziy et al. previously investigated the scientific differences between the two common density functional theory models used to calculate the pore size distribution (quenched solid density functional theory (QSDFT) and 2-D nonlocal density functional theory (2DNLDFT)). This study showed that, in spite of different mathematical approaches, both the QSDFT and 2D-NLDFT models resulted in nearly identical pore size distributions, with slight variation in the average pore size.51 Therefore, to test the effect of pore size, a sensitivity analysis on the effect of pore size on calculated capacitance was performed. For pores above 1 nm in diameter, which are calculated by the QSDFT model, the pore size was varied by ±0.13 nm, which is the roughness parameter used in the QSDFT model. These results, presented in Table 8, demonstrate no scientifically relevant differences, with a maximum variation between calculated capacitance and measured capacitance of ±9%. Therefore, the sensitivity analysis demonstrates that the proposed model is robust and accurate, in spite of slight variations associated with calculated pore size due to the two commonly used DFT models. 3.5.2. Discussion of Model Results and Impact. The combined model presented in this paper demonstrates the importance of determining pore size and shape in order to predict a porous material’s capacitance. A new technique is introduced using ultrahigh resolution SEM imaging to characterize the nanoporous structure, which can improve the understanding of the EDL and the appropriate selection of EDL capacitance models. One further consideration to the EDL model that should be discussed is the effect of atomic level surface roughness. Using ionic liquid electrolytes, Vatamanu et al. and Xing et al. showed that nanopore surface roughness increases the capacitance of the porous carbon materials, compared to atomically flat carbon materials. This increase was attributed to the denser packing of the ions on atomically rough surfaces (on the order of 3−10 Å) which is caused by enhanced ion shielding at high voltages (ΔV ≥ 3 V). Also, it was demonstrated that surface roughness results in faster double layer formation during charging.52−55 The current model investigates a wider pore size range (d = 0.3−33 nm), using aqueous electrolytes. There are significant differences between the aqueous electrolytes and ionic liquid electrolytes. First, with an aqueous electrolyte, the distortion of the ion solvation shell must be accounted for, which allows the consideration of variable double-layer thicknesses and dielectric constants in the model. Second, the applied voltage in the

diameter of these pores, hydration shell distortion will be required. Therefore, the relative dielectric constant prediction will be lower than that of the 1−1.4 nm micropores. 3.5. Model Results Based on Updated Pore Shapes. The results of the combined model are displayed in Table 7 and Table 7. Comparison of Calculated and Experimentally Measured Capacitance for Activated Fluid Coke (AFC) and Activated Delayed Coke (ADC) Samples and Percentage Differencea AFC-2.5:1

AFC-3.5:1

ADC-2.5:1

ADC-3.5:1

333

333

375

413

313

358

346

393

−6%

+7%

−8%

−5%

experimental capacitance (F g−1) calculated capacitance with combined model (F g−1) percentage difference

Combined model, based on SEM images, parameters: εR,micro,slit = 3.33,41 εR,meso = 7.8,1 a0 = 0.138 nm, d = 0.33 nm,46 εR,wire = 5.56, a0,wire = 0.236 nm (average). a

Figure 11. Comparison of calculated and experimentally measured capacitance of the activated fluid coke (AFC) and activated delayed coke (ADC) samples, using the combined model, based on SEM images and the following parameters: εR,micro,slit = 3.33,41 εR,meso = 7.8,1 a0 = 0.138 nm, d = 0.33 nm,46 εR,wire = 5.56, a0,wire = 0.236 nm (average).

Figure 11. The results show that the capacitance has been predicted within 8% of the measured value, indicating that the model has a good fit with the experimental data. By combining the different structural models with the ultrahigh resolution

Table 8. Sensitivity Analysis Results for Deviation of ±0.13 nm in Pore Size for Pores Calculated Using the QSDFT model (Pore Diameter > 1 nm)a deviation in pore size: −0.13 nm

deviation in pore size: +0.13 nm

AFC-2.5:1 AFC-3.5:1 ADC-2.5:1 ADC-3.5:1 a

experimental capacitance (F g−1)

calculated capacitance with combined model (F g−1)

percentage difference

calculated capacitance with combined model (F g−1)

percentage difference

333 333 375 413

306 357 342 394

−8% 7% −8% −5%

331 362 359 395

−1% 9% −4% −4%

Parameters: εR,micro,slit = 3.33,41 εR,meso = 7.8,1 a0 = 0.138 nm, d = 0.33 nm,46 εR,wire = 5.56, a0,wire = 0.236 nm (average). I


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The Journal of Physical Chemistry C aqueous electrolyte is 1 V, which is less than the 3 V used to induce the ion shielding. Also, the current model investigates pores of 0.3 nm and greater in diameter. Therefore, the surface roughness under consideration would have dimensions less than 0.3 nm, and as such, the ions would have to be completely desolvated and intercalate in order to penetrate these features. As discussed above, this is not possible at the 1 V applied potential. Third, the diffusivity and mobility of aqueous ions are much higher than those of ionic liquids, likely leading to differing behavior during charging and discharging processes. Therefore, it is expected that the atomic surface roughness would have less of an effect on maximum capacitance in aqueous electrolyte systems compared to ionic liquid ones. Further work is needed to verify this hypothesis. The combined model approach presented above represents a scientific advancement in the techniques to predict a material’s capacitance. By using the ultrahigh resolution SEM images, a rational approach to selecting the appropriate models for the various sized pores can be made. The SEM images offer insights into the nanoporous structure of carbon materials, providing detailed information on the structure of the micropores and mesopores and allowing for a better understanding of the EDL structure in these pores. Therefore, with this knowledge of the pore structure at various pore sizes, it is possible to more accurately predict the capacitance as a function of surface area and pore size distribution.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +1 416 978 7409. Fax: +1 416 978 8605. E-mail: don. [email protected]. ORCID

Donald W. Kirk: 0000-0002-9469-3500 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to acknowledge the Natural Science and Engineering Research Council (NSERC), the Consortium on Sustainable Materials (COSM-Japan), and the Chinese-NSF for funding for this project. The authors would like to thank S. Boccia and J. Tam at the Ontario Centre for the Characterization of Advanced Materials for training and help with the scanning electron microscope analysis. Also, the authors would like to thank the Canadian Oil Sands industry for supply of raw petroleum coke.

4. CONCLUSIONS The ability to predict a material’s capacitance based on its pore size and shape is highly beneficial in order to determine the ideal porous structures to maximize energy density. In order to improve the accuracy of the predicted capacitance for a porous carbon material, the appropriate models must be selected on the basis of both the pore shape and the pore size, which can be defined by ultrahigh resolution SEM images of the nanoporous carbon structure. On the basis of SEM characterization, it was found that potassium hydroxide activated carbon materials had curved mesopores. By using this information, it is possible to have a more accurate description of the pore structure and thus a more accurate description of the EDL structure. Also, the relative dielectric constant and ion size can be adjusted depending on the predicted ion solvation. Using these strategies, the capacitance of porous carbon materials in this study was predicted within ±8% of the maximum measured capacitance value. These results identify the importance of characterizing the nanoporous structure of carbon materials using ultrahigh resolution imaging. Additionally, the combined models and SEM characterization can be used to identify potential top performing carbon materials for EDLCs. Finally, these results demonstrate the complexity of the EDL structure in nanoporous carbon materials, as well as the challenges associated with predicting the capacitance of these materials. It is clear that characterization of the pore shape using ultrahigh resolution SEM imaging can provide valuable information to describe the structure of the EDL in these confined nanoporous spaces.

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The raw adsorption isotherms for the four porous carbon samples, collected using nitrogen gas at 77 K and carbon dioxide gas at 273 K; the raw capacitance data, for constant current cycling, of each of the carbon samples; and detailed tables for each carbon sample, which include the pore size distribution breakdowns, contributions to total surface area, and SSA-normalized and gravimetric contributions from each pore size (PDF)

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REFERENCES

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The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b02944. J


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