Article pubs.acs.org/JPCC
Simple Method to Relate Experimental Pore Size Distribution and Discharge Capacity in Cathodes for Li/O2 Batteries Mara Olivares-Marín,† Pablo Palomino,‡,§ Eduardo Enciso,‡,§ and Dino Tonti*,†,∥ †
Institut de Ciència de Materials de Barcelona, Consejo Superior de Investigaciones Científicas (ICMAB-CSIC), Campus UAB, ES 08193 Bellaterra, Barcelona, Spain ‡ Departamento de Química Física I, Facultad de Ciencias Químicas, Universidad Complutense de Madrid (UCM), Avenida Complutense s/n, ES 28040, Madrid, Spain § Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Científicas (ICMM-CSIC), C/Sor Juana Inés de la Cruz, 3, ES 28049, Madrid, Spain ∥ MATGAS, Campus UAB, ES 08193 Bellaterra, Barcelona, Spain S Supporting Information *
ABSTRACT: We analyze in detail the relationship between pore size distribution and discharge capacity for cathodes in ionic liquid-based Li/O2 batteries at room temperature (RT) and 60 °C. We used several porous carbons with similar composition and apparent surface area but with pore distribution peaks in different points of the meso/macroporous region. The porous structure of carbons caused a significant influence on the discharge specific capacity. However, no obvious correlations between specific capacity and surface area or total pore volumes were observed. Carbons with high mesopore volumes and a predominant pore size of 20−40 nm exhibited the highest specific capacities. When temperature rises from room temperature to 60 °C, discharge capacity increases by a factor higher than two, with the smallest pores providing the highest increases. A model is introduced to empirically correlate capacity with pore size distribution. This model assumes that during electrochemical discharge the pore walls are uniformly coated in their thickness but that pores below a threshold size value do not participate at all to the capacity. Our model can account for the effects of pore size distribution using a discharge layer thickness of a few nanometers and with threshold values of excluded pore sizes, of 12 nm at RT and 10 nm at 60 °C. The model also allowed the estimation of the penetration depth of the discharge reaction on the electrode thickness and indicates that its increase is the main factor justifying the increase of capacity when temperature is increased.
1. INTRODUCTION
hierarchical porosity, where small pores are used to store discharge products, while large pores ensure electrolyte penetration and transport of electroactive species.3−7 Although theoretical capacities taking into account carbon and its porosity can be calculated,8 practical values must be necessarily much lower. A large number of different carbons have been tested in different conditions, and experimental data are available in the literature, expressed as capacity per gram of carbon (mAh/g). 2,9 However, we are not aware of comprehensive studies discussing the impact of the electrode architecture on experimental capacities, although several studies address some aspects of this problem.10−16 Most of these contributions coincide on the general empirical idea that discharge capacity increases with pore volume especially when pore sizes are within the mesoporous range.
In spite of their several challenges, Li/O2 batteries have recently attracted enormous interest because of their promise to multiply by a factor of 2 or 3 the specific energy provided by state-of-the-art Li-ion batteries.1,2 This is crucial for demanding applications, for instance, in electric vehicles, where the increased energy density directly translates into a driving range that could eventually satisfy the needs of most customers. Whereas the theoretical specific energy can be easily calculated from the specific capacity of the discharge product (typically Li2O2), the estimation of practical values is complex. In fact, this product is insulating and it requires to be supported by a nanostructured conductive substrate, typically a porous carbon. Carbons are lightweight, environmentally benign, and cost-effective materials that can easily provide the complex architectures required by the air cathodes. These have to ensure electron and electrolyte connectivity to the reaction sites, located on a continuously evolving electrochemical interface and in a variable porosity. A possible configuration is a © XXXX American Chemical Society
Received: May 30, 2014 Revised: August 4, 2014
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Table 1. Textural Data from N2 Adsorption Isotherms and MIP Cumulative Pore Volume of Porous Carbons MIPa
N2 adsorption sample
pH
SBET (m /g)
Vmi (cm /g)
Sext (m /g)
Dmax (nm)
VT (cm /g)
Vme (cm /g)
Vma (cm3/g)
V′T (cm3/g)
C233 C235 C250 C237
6.00 6.30 6.50 6.70
596 638 603 641
0.24 0.23 0.17 0.13
92 170 246 350
119 39 22 11
1.50 1.20 0.85 0.55
0.09 0.66 0.82 0.62
1.20 0.33 0.19 0.28
1.53 1.22 1.18 1.03
2
3
2
3
3
a Mercury porosimetry data: Vma, macropore volume (cumulative pore volume, Vcu, at r = 25 nm, r = pore radius); Vme, mesopore volume (Vcu at r < 2 nm − Vma).
presence of unused regions of the electrode and how effectively each pore size contributes to discharge capacity. It allows one to prove the discharge mechanism and understand the capacity limitation while optimizing electrodes for given operating conditions.
Some modeling has been reported on idealized monodisperse porous systems. Porosity, pore size, and their variation during discharge have been taken into account to calculate capacities17 or discharge profiles18−21 as a function of operating conditions such as current densities. The actual pore size distribution (PSD) of an electrode has instead been taken into account in two recent publications. Nimon et al. could reproduce the experimental discharge profile22 taking into account the experimental PSD of the same electrode. The focus of that work was mainly the mechanism of discharge, while the effect of different distributions was not addressed in detail. The effect of PSD comparing shapes typical of Super P and Ketjen Black has been discussed in modeling by Franco et al., who also identified different types of discharge profiles depending on the pore distribution.9,23 In this work, we present an alternative approach, by applying a simple model with two adjustable parameters to find the best match between the experimental PSD and discharge capacity for a series of four similar resorcinol formaldehyde-based carbons with controlled porous structure used in a Li/O2 battery with an ionic liquid electrolyte. Hierarchical porous carbon derived from resorcinol−formaldehyde (RF) gels have attracted interest as material candidates for different electrochemical energy storage applications such as electrodes for lithium-ion batteries,24 supercapacitors,25−28 or lithium/oxygen batteries.11,16,29−32 That is mainly because they allow easy control of final porous structure and form giving, under relatively low production costs, rise to unique properties such as low mass densities, welldeveloped pore texture, large surface area, continuous porosities, large mesopore volume, or high electrical conductivity. We have also used RF gels to prepare carbon inverse opals as model systems to test the effects of cathode architecture in Li/O2 cells.33 Room-temperature ionic liquids (RTILs) such as those based on quaternary ammonium cations have shown a high stability toward superoxide radicals34−39 and lower oxidation voltages for the lithiated discharge products.32,40,41 In addition, these RTILs are nonflammable and thermally stable, and their nearly zero vapor pressure makes them very attractive for this solid− liquid−gas system, which in practical applications could be open to ambient air.42 Their use in lithium/oxygen batteries has been limited because of their rather low oxygen solubility and a high viscosity, which leads to poor O2 mass transport.2,41 However, Monaco et al. have recently shown that it is possible to remove this limitation by appropriate design of the cell configuration and achieve remarkable electrochemical performance.40 The method presented here can also be applied to other systems, where a conformal layer is electrochemically deposited over a porous structure. It provides valuable information such as the thickness of the discharged layer and quantifies the
2. MATERIAL AND METHODS 2.1. Synthesis of Mesoporous Carbons. Porous carbons were prepared by using a mixture of resorcinol (R, SigmaAldrich 99%), formaldehyde (F, Panreac 37% in water), and sodium hydroxide (Sigma-Aldrich 97%) according with the original procedure described by Pekala43 followed by carbonization at 900 °C under N2 flow. First of all, R was diluted with deionized water (W) maintaining always a molar ratio R/W of 0.04, and then, a sodium hydroxide solution was added as catalyst (C) varying the R/C molar ratio between 750 and 150. The mixture was stirred for 30 min. F was then added at a molar ratio R/F = 0.5, and 10 min after stirring, the samples were sealed and introduced in an oven at 84 °C for 3 days. The resulting wet resins were dried for 2 days at 80 °C at ambient pressure and then carbonized to obtain the porous carbon. Carbonization was carried out in a horizontal tubular furnace at 900 °C for 1 h at a rate of 3 °C/min under an inert atmosphere of N2. The samples were then allowed to cool down to room temperature under a constant N2 flow rate. The final porous structure of the carbons was controlled by modifying the pH of the initial mixture from 6.00 to 6.70. Table 1 indicates pH levels used during synthesis and nomenclature of porous carbons. 2.2. Characterization of Mesoporous Carbons. Texture and porosity of mesoporous carbons were analyzed by scanning electron microscopy (SEM), transmission electron microscopy (TEM), N2 adsorption/desorption, and mercury porosimetry (MIP). SEM images were collected on a SEM FEI Quanta 200 FEG-ESEM instrument. TEM studies were performed with a JEOL (JEM1210) instrument, operating at 100 keV. Before examination, the samples were dispersed in anhydrous ethanol and deposited on a holey carbon film on a copper grid. N2 adsorption/desorption experiments were performed at −196 °C using Micromeritics ASAP 2020 equipment. Apparent surface areas, SBET, were determined by the BET equation.44 Micropore volumes (Vmi) and external surface areas (Sext) were determined by the t-plot method.45 Total pore volume (VT) was obtained by Gurvitsch’s rule (P/P0 = 0.99).45 Pore size distributions (PSDs) were estimated by the Barrett−Joyner− Halenda (BJH) method.46 The predominant pore size (Dmax) has been taken as the pore size corresponding to the maximum of the N2 adsorption PSD. Mercury intrusion porosimetry was performed using a Quantachrome porosimeter, Autoscan-60. From the values of MIP, the macropore volume, Vma, and the mesopore volume, Vme, were estimated as indicated elsewhere.47 Total pore volume (VT′ ) was also calculated by making use of the expression: VT′ = Vmi (N2) + Vme (MIP) + Vma B
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(MIP). Table 1 summarizes the main textural data obtained from N2 adsorption/desorption isotherms and MIP. 2.3. Electrode Preparation. As carbon powders, the different porous carbons synthesized here were used, after grinding in a mortar and sieving through a 180-mesh per inch mesh. The method used for the preparation of carbon−binder composite electrodes was based on the common procedure in which a carbon powder (80 wt %) was mixed with 10 wt % of polyvinylidene fluoride (PVDF) as a binder and 10 wt % of carbon black (Super P, M.M.M. Carbon) in N-methylpyrrolidone (NMP). The slurry obtained was used to impregnate a stainless steel mesh (AISI316, 180 meshes per inch, Advent Research Materials Ltd.) and finally dried at 100 °C for 12 h. The electrode loading was of the order of 1 mg/cm2. 2.4. Electrochemical Tests. The electrochemical cell was described in detail elsewhere.33 It is based on ISO-KF standard stainless steel high-vacuum components supplied from ITL (UK). The electroactive components of the cell were placed in the volume existing between the steel hose nozzle connector and the centering ring. A nickel foil soldered to a copper wire was used as a current collector. The electrolyte was lithium bis(trifluoromethanesulfonyl)-imide (LiTFSI, 99.95%, SigmaAldrich) in 1-butyl-1-methylpyrrolidinium bis(trifluoromethanesulfonyl)-imide (PYR14TFSI, 99.5%, Solvionic) in a 11:1 molar ratio. PYR14TFSI was stored in a drybox and used as received, and LiTFSI was dried at 120 °C under vacuum for 48 h before use. The water content of the electrolyte was below 20 ppm, as checked with a Metrohm KFC 899 Coulometric Karl Fischer titrator. The separator was a glass fiber filter (filterLab MFV1, 260 μm thick) soaked with ∼100 μL of electrolyte; the anode was a Li metal foil (SigmaAldrich, 0.4 mm thick, cut to approximately 0.8 cm2). All cells were assembled in an Ar-filled glovebox. The electrochemical response was tested by galvanostatic discharge/charge at 0.1 mA/cm2 at room temperature (RT) and 60 °C in a Bio-Logic VMP3 multichannel potentiostat. For tests at 60 °C, cells were placed in a small thermostated chamber designed specifically for this purpose. Pure O2 flow was forced to pass continuously through the cell during measurements at constant flow (5 mL/min) and for at least 20 min always before starting the electrochemical measurements. Capacities are normalized by the total carbon weight (synthesized carbon + super P). As shown in the Results and Discussion, the super P discharge capacity in our conditions is lower than for the synthesized carbons. This may lead to slight underestimation (less than 10%; see Supporting Information) of the “intrinsic” capacities of the mesocarbons, without significantly affecting our conclusions. 2.5. Analysis of Discharge Capacity vs Pore Size Distribution. Scheme 1 reports a flow diagram of the analysis method used in this work. Linear fits of experimental capacity vs calculated filled volumes are iteratively executed as a function of two weight parameters used to calculate the filled volumes. 2D maps of the resulting fit parameters are then built as a function of the weight parameters used. Calculation of the effectively filled pore volume Veff is made by integrating a weighted PSD. By definition, the total pore volume V is given by V=
∫0
∞
dV dD = dD
∫0
Scheme 1. Flow Diagram of the Analysis Method Used to Correlate Discharge Capacities with Carbon PSDs
Veff =
∞
W × PSD dD
(2)
where W is a weighting function composed by two terms, Wsp excluding contribution of small pores and Wf providing the fraction of the pore volume that may be filled with the discharged layer:
W = Wsp × Wf
(3)
Wsp = [1 + e α(D0 − D)]−1
(4)
2 ⎛ d⎞ Wf = {π[r 2 − (r − d)2 ]}/{πr 2} = 1 − ⎜1 − 2 ⎟ ⎝ D⎠
(5)
where r and D are, respectively, the pore radius and diameter, D0 is the maximum excluded pore size, d is the limit thickness of the discharged layer, and α is a constant. Wsp is a sigmoidal function centered at D0, tending to 0 for smaller D and to 1 for larger D. It has been used to give a physically more acceptable aspect to the assumption made that small pores do not contribute. The Wf factor is the volume fraction of a pore (assumed cylindrical, with radius r = D/2) that can be filled by a uniform layer of thickness d. For d ≥ r the constant value Wf = 1 is assumed. When we introduce the full expression of W(D) into eq 2, we obtain ∞
Veff =
∫0
2d
1 1 + e α(D0 − D)
× PSD dD +
∫
(
d 2
1 − 1 − 2D
)
1 + e α(D0 − D)
2d
× PSD dD
(6)
Processing of data has been performed with the IgorPro software (version 6.2, Wavemetrics). The experimental BJH cumulative pore volume curves were determined by the ASAP software from N2 adsorption isotherms. Depending on the sample, they consisted of 20−23 points of volume (cm3/g) vs pore size, in the range of 1.5−120 nm. Each curve was interpolated to 256 points with a cubic spline method,
∞
PSD dD
∫0
(1)
In analogy with this expression, we define Veff as C
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Vmi (0.13−0.24 cm3/g) were very similar for all the materials, being almost independent of the initial pH of the RF solution. Conversely, the pH noticeably played an important role in the development of meso/macroporosity in the samples (see Vme and Vma in Table 1). Specifically, Sext values preferentially increased with pH, with the contribution of macropores to the total pore volume at the lowest pH being rather significant. When pH was increased, carbons showed an important development of mesoporosity, with pores becoming progressively narrower. The fact that pore volume was larger at low pH can be related to less cross-linked resorcinol polymerization, which leads to the growth of large resin nano/microparticles, and the formation of large voids between particle aggregates. In particular, the PSD curve (Figure 2a) of sample C233, which was prepared at the lowest pH, depicted a very broad peak centered at around 119 nm denoting that a wide range of macropore sizes predominates in this carbon. Furthermore, the PSD curve given by the desorption branch (Figure 2b) showed a main peak centered at pore sizes lower than 100 nm (∼74 nm), which can suggest the presence of bottleneck pores defined by voids between particles which hinder the access to the largest pores. TEM and SEM images in Figure 3a−d,e−h, respectively, give more information about the progression of the average pore diameter in the samples. In general, all carbons exhibited the typical morphology of gels composed of interconnected particles of nearly spherical shapes which appeared more or less fused with each other. However, several differences in geometry, particle size, and coalescence level can be observed. Samples C233 (Figure 3a,e), C235 (Figure 3b,f), and C250 (Figure 3c,g) showed similar geometry but a progressive particle size decrease as the pH rises from 6.00 to 6.50. At the highest pH (sample C237, Figure 3d,h), the geometry changed significantly giving a higher degree of coalescence (fused particles) and, therefore, more compaction. This resulted in a porous carbon with larger particle sizes and smaller average pore diameter, making C237 (Figure 3d,h) a more dense carbon. These results show that the use of different initial pH (6.00− 6.70) of the RF solution allowed a controlled sol−gel chemistry, giving place to resins and eventually carbons with a tailored and progressive mesopore size. This tendency is consistent with previous studies on analogous materials.49−52 3.2. Electrochemical Tests. Figure 4a,b compares voltage profiles upon galvanostatic discharge of porous carbon electrodes at 0.1 mA/cm2 and in PYR14TFSI:LiTFSI (11:1) at (a) room temperature (RT) and (b) 60 °C, respectively.
providing equal spacing on the logarithmic horizontal axis (corresponding to pore sizes). The curve is then differentiated to provide the PSD function. The sigmoid smoothness, controlled by the α constant, has not been optimized for the best final results and was left fixed to the value α = 10 nm−1. 128 × 128 values of D0 and d were chosen stepwise logarithmically within the 1.8−60 nm range. For each pair, the program calculates numerically Veff and then linearly fits experimental capacities vs Veff. Finally, as a function of D0 and d, it builds 2D plots of the parameters determined at each fit: intercept, slope, and coefficient of determination (R2).
3. RESULTS AND DISCUSSION 3.1. Porous Carbon Materials Characterization. Figure 1 compares N2 adsorption and desorption isotherms at −196
Figure 1. N2 adsorption/desorption isotherms of porous carbons.
°C of the RF-based mesoporous carbons. Textural properties (apparent surface areas, pore volumes, and predominant pore size) of the synthesized porous carbon calculated from isotherms are reported in Table 1. The corresponding pore size distributions (BJH) are shown in Figure 2. In general, porous carbons exhibited type-IV isotherms with hysteresis loops which seem to be intermediate between types H2 and H1, denoting that mesoporosity is dominant in their structures. Also from the amount of N2 adsorbed at the initial region of isotherms at very low P/P0 values, certain microporosity can be appreciated that could be related to the intraparticle structure.48 From Table 1, it can be seen that SBET (590−645 m2/g) and
Figure 2. BJH-pore distribution of porous carbons: (a) from N2 adsorption branch and (b) from N2 desorption branch. D
dx.doi.org/10.1021/jp5053453 | J. Phys. Chem. C XXXX, XXX, XXX−XXX
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Figure 4. Galvanostatic measurements of porous carbon−binder composite electrodes at RT (a) and 60 °C (b) at 0.1 mA/cm2.
However, the particle size and shape has been found to be very sensitive to the applied current.63,64 In particular, Adams et al. recently demonstrated that by increasing the applied current a transition from 3D (large particles) to 2D (layer by layer) growth of Li2O2 is observed. The growth of a compact film is self-limited to a thickness of a few nanometers because of the high resistivity of Li2O2.64 SEM inspection of our discharged electrodes (see Figure S1 in the Supporting Information) did not reveal the presence of large particles typical of low current/ high capacity discharges. We therefore infer that in our conditions Li2O2 is discharged as a thin layer on the carbon surface. From the galvanostatic results in Figure 4, we can point out that the difference in the pore structure of the carbon materials, at both temperatures, had a significant influence on the discharge capacity. However, we could not establish a simple correlation between specific discharge capacities and SBET or total pore volumes (VT, VT′ ). C250 and C235 carbons, which exhibited the largest mesopore volume (Vme) with predominant pore diameters (Dmax) ranging from 20 to 40 nm, provided the highest specific capacities at both RT and 60 °C. In particular, sample C250 with the largest Vme, 0.82 cm3/g, and Dmax of 22 nm showed the largest specific capacity of about 850 mAh/g. This is in agreement with the literature, which suggests pore sizes within the mesoporosity range to be the most effectively used by discharge products.10−15 Table 2 compares the discharge capacities obtained at 60 °C with the theoretical specific capacity expected for different portions of the available volume filled by Li2O2 products, assuming a volumetric capacity of 2700 mAh/cm3.1,2 The following pore volumes are considered: VT (pores
