Different Approach to Estimation of Hydrogen-Binding Energy in

Article pubs.acs.org/JPCC

Different Approach to Estimation of Hydrogen-Binding Energy in Nanospace-Engineered Activated Carbons L. Firlej,*,†,‡ M. Beckner,† J. Romanos,† P. Pfeifer,† and B. Kuchta†,§ †

Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211, United States Laboratoire Charles Coulomb, Université Montpellier 2, 34095 Montpellier, France § Laboratoire MADIREL, Université Aix-Marseille, 13396 Marseille, France ‡

ABSTRACT: Binding energy between adsorbent and adsorbate strongly affects the mechanism of adsorption. Porous systems are usually characterized by a distribution of this energy, which is not easy to determine experimentally. A coupled experimentalsimulation procedure to estimate binding energy directly from experimental adsorption isotherms is proposed. This new approach combines experimental information (pore size distribution determined from nitrogen adsorption at 77 K) and numerical data (grand canonical Monte Carlo simulations of adsorption in pores) to explain an influence of binding energy on adsorption isotherms. The procedure has been validated by analysis of hydrogen adsorption in a series of carbons activated with KOH:C ratio varying from 3 to 6. These carbons show high capacity of hydrogen storage both at 80 and 303 K (115 gH2/kgC and 23 gH2/kgC at p = 100 bar, respectively, for carbon activated during 1 h at T = 790 C (T = 1361 K) with KOH:C ratio equal to 3, having the surface area above 2600 m2/g, 0.77 porosity, and large fraction (31%) of pores with average width below 1 nm). An additional energetic parameter has been introduced into the conventional fitting procedure to account for the distribution of adsorption energy in measured samples. The observed high consistency between experimental and simulated results validates/correlates the characterization procedures and proves the coherence and robustness of both the experimental results and the numerical simulations.

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kJ/mol),5−8 activated carbons with high specific surface area and increased binding energy should be prepared to achieve the required storage capacity. Obviously, the distribution of binding energy should be carefully monitored in the process of synthesis of new materials. In our previous10 paper, we showed that it is possible to control the formation of pore network in KOH activated carbons by an adequate choice of the mass ratio of activation agent to carbon (KOH:C ratio), activation temperature, and activation time. The formation of tunable distribution of pores was confirmed by subcritical nitrogen adsorption. We have also determined (using grand canonical Monte Carlo (GCMC) simulations of H2 adsorption in carbon slit pores) that the optimal pores’ widths to achieve high gravimetric and volumetric storage capacity are in the range 0.7−1.2 nm.11 In the present work, we apply the activation procedure described previously10 to develop new carbon adsorbent for H2 storage, showing high surface area (over 2600 m2/g) and pore size distribution (PSD) located mostly in the subnanometric regime with minimal volume of meso- and macropores. Additionally, we extend the characterization of these systems to estimate the average binding energy in the

INTRODUCTION Real adsorbents usually exhibit complex distributions of both pore sizes and energies of adsorption. Characterization of porous system is then required before any applications. Adsorption of gases (N2, Ar, and CO2) is the usual way to determine the most essential adsorbent parameters such as specific surface, pore size distribution, and porosity. However, the energy of adsorption which is essential for optimization of storage capacity of materials is not easily accessible from experimental data, although isosteric heat of adsorption can be directly evaluated from the Clausius−Clapeyron equation. In this paper, we propose and test a new methodology that combines both experiment and computer simulations to provide the energetic information from a numerical analysis of adsorption isotherms. To validate this procedure, we analyze quantitatively hydrogen adsorption in a series of new KOH activated carbons. Activated carbons constitute a large class of materials which porosity can be tailored to fit the requirements of any a priori application in the domain of adsorption. They are light, inexpensive, and nontoxic; therefore, they are widely used in industrial and biomedical processes of gas/liquid separation and sequestration.1−3 In recent decades, they were also intensely studied as the potential storage media for future ecologic energy vectors: natural gas and hydrogen.4−9 In particular, as the energy of H2 adsorption on carbon is relatively low (∼4−5 © 2013 American Chemical Society

Received: May 31, 2013 Revised: November 6, 2013 Published: December 6, 2013 955

dx.doi.org/10.1021/jp405375g | J. Phys. Chem. C 2014, 118, 955−961

The Journal of Physical Chemistry C

Article

Figure 1. Left: the effect of KOH:C ratio on the pore size distribution for R = 3−6. For comparison, PSD for MCS-30 activated carbon is also shown. Right: an example of multimodal PSD fit for sample 3K. The square symbols are the experimental data; the solid line (red) is the multiGaussian fit. The dotted lines (blue) are the Gaussian components of the fit: position (w) and statistical weight (α) of each component are given. The fitting errors are negligible except close to the PSD maxima, where the experimental form of the peaks is not always of Gaussian type.

(NLDFT) that takes into consideration an influence of surface roughness and heterogeneity on adsorption mechanism,14,15 making it suitable for characterization of heterogeneous materials. Experimental Setup for Hydrogen Adsorption. The hydrogen gravimetric excess adsorption isotherms (excess adsorption) were measured using the HTP-1 volumetric analyzer (Hiden Isochema, Warrington, U.K.), operating at pressures from 0.001 mbar to 200 bar. The sample temperature was controlled by a combined use of a heating element and a continuous flow of liquid nitrogen. This combination allows for variation of temperature between 77 and 773 K. The isotherms were measured according to the Sievert’s procedure16 on the preliminary outgassed samples (outgassing for 2 h at 200 °C to a pressure of approximately 10−6 mbar using the built-in Pfeiffer Vacuum turbomolecular pump). The calibration of the experimental setup was validated at 77 and 303 K by measuring hydrogen excess adsorption on the standard carbon reference sample MSC-30.17 The results agree with published data obtained on samples from the same commercial product line (Maxsorb MSC-30, manufactured by Kansai Coke and Chemical Co., Ltd., Japan).18,19 Gravimetric and volumetric storage capacities were calculated from measured excess adsorption using eqs 2 and 3, respectively.

measured samples. This estimation is performed as a part of the isotherm fitting procedure.

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EXPERIMENTAL METHODS Sample Preparation. The nanoporous activated carbons were prepared from the corncob waste following the general activation procedure described in our previous paper.10 The optimized activation temperature was T = 790 °C (T = 1361 K), and the activation time was kept constant (1 h) to avoid an excessive carbon consumption during activation process and to limit the formation of supra-nanometer pores, nonsuitable for hydrogen storage. Therefore, the only variable which differentiates samples from different activation batches is KOH:C weight ratio (R). Later in the paper, we name the samples 3K, 4K, 5K, and 6K, where the numbers indicate the ratio R and where K stands for activation with KOH. The samples with lower values of R have not been analyzed; they show small specific surface areas, and they are not interesting from the point of view of hydrogen storage.10 Specific surface area (SSA) and pore size distribution (PSD) were determined from nitrogen adsorption isotherms measured at subcritical conditions (T = 77 K) using Autosorb-1-C (Quantachrome Instruments). The device was calibrated with Quantachrome SARM 2012 reference material (SSA = 768 m2/ g). The samples’ specific areas were determined from the pressure range 0.01−0.03 P/P0, using Brunauer−Emett−Teller (BET) procedure. P0 is the saturation pressure of nitrogen at T = 77 K. Surface areas were rounded to the nearest hundred. The total open pore volume Vtot was determined at a relative pressure of 0.995 P/P0. The porosity ϕ, defined as a ratio of the open-pore volume to the apparent sample volume, was calculated using the equation −1⎤−1 ⎡ ⎛ Vtot ⎞ ⎥ ⎢ ϕ = 1 + ⎜ρskel ⎟ ⎢⎣ ms ⎠ ⎥⎦ ⎝

ρH (p , T ) mstored m 2 = excess + ((1 − ϕ)−1 − 1) ρskel ms ms

(2)

mstored m = stored (1 − ϕ)ρskel Vs ms

(3)

Here, Vs is the sample volume and ρH2 is the hydrogen gas density calculated by Leachman et al.20 at the experimental pressure and temperature (p, T). We recall that the excess gravimetric adsorption (mexcess/ms) is defined by the equation mexcess = mstored − ρH2(p, T)Vpore, where Vpore is the volume of pores accessible for H2 adsorption and mstored is the total mass of H2 adsorbed in the pores. Numerical Methods. Our procedure of modeling the experimental isotherms uses a set of simulated isotherms, calculated for adsorption of hydrogen molecules in slit-shaped pores delimited by graphene walls. The pore walls are considered as infinite. The atomic corrugation of the graphitic wall is not explicitly treated in this paper as it represents a small perturbation of the H2−wall interaction energy (2000 m2/g) are between 1.8 and 2.1 g/cm312). The pore size distributions have been calculated using the QSDFT (quenched solid density functional theory) data reduction software provided by Quantachrome.13 The pores were assumed to be infinite and slit shaped. QSDFT is a modified version of the nonlocal density functional theory 956



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RESULTS AND DISCUSSION Sample Characterization. Table 1 gives structural characteristics of activated carbons prepared using different

and its influence on the total storage capacity is negligible. Moreover, the hydrogen layer is incommensurate with the graphene structure, and the average influence of the corrugation is equal to zero. The effective pore width w is defined as a distance between the positions of centers of mass of carbons in the opposite pore walls reduced by Δ = 0.35 nm, the carbon atom diameter. In other words, Δ defines the dead volume of the pore. The isotherms have been calculated for pore sizes w + Δ in the range from 0.6 to 3.0 nm. The detailed description of the interaction model and the methodology of grand canonical Monte Carlo (GCMC) simulations were given in previous papers.11 The Monte Carlo box has been defined as a slit pore with graphene walls separated by distance w + Δ in the zdirection. The periodic boundary conditions have been used in the xy directions (parallel to the pore walls) to model infinite pores. The main set of isotherm has been calculated assuming the characteristic value of binding energy of hydrogen on graphene layer (E = 4.5 kJ/mol).11 This basic set of isotherms has been supplemented by additional calculations performed using lower adsorption energy, down to 3 kJ/mol. These isotherms have been used to account for energetic heterogeneity of surface in the real samples. The proposed procedure of modeling the experimental isotherms uses the simulated ones and the experimental pore size distributions measured by nitrogen adsorption. We have proceeded as follows: First, the experimental PSD has been deconvoluted into a small number (n) of Gaussian contributions (usually n = 2−4 has given an excellent fit, see Figure 1a and b). The maxima of the Gaussian contributions have defined the theoretical, discrete PSD. The final model isotherms have been calculated as linear combinations of isotherms simulated for the slit pores sizes defined by the theoretical PSD. The surface areas under the Gaussian peaks have determined the statistical weight αi(wi) of each contribution in the theoretical isotherms. The numerical fitting has been carried out using the following formula: n

Itheor(T ) =

Table 1. Specific Surface Area, Open Pores’ Volume, Porosity (eq 1), Ultramicropore Fraction, and Energy Factor A (eq 4, See the Text) for KOH Activated Carbonsa

∑ αi(wi) = 1

i=1

i=1

sample

SSA [m2/g]

Vtot [cm3/g]

ϕ porosity

ultramicropore fraction

A

3K 4K 5K 6K MCS-30

2600 2600 2500 2700 2600

1.7 1.6 1.7 2.1 1.9

0.77 0.76 0.77 0.81 0.79

0.31 0.18 0.14 0.26 0.23

1 0.9 0.72 0.85 0.9

a

Ultramicropore fraction has been determined from multimodal Gaussian fit of experimental PSD (from nitrogen adsorption, see Figure 1b). It is calculated as a fraction of surface of PSD components located below 1 nm. The reference MSC-30 porous carbon is shown for comparison.

concentrations of activation agent (R ≥ 3). In general, specific surface area and its fluctuations (±100 m2/g) are almost Rindependent from the point of view of storage capacity. The total pore volume Vtot and, in consequence, sample porosity show a tendency to increase with increasing R. However, the nonmonotonic variation of ultramicropore fraction and specific surface areas (see Table 1) disturb this tendency. The principal mechanism seems to be a competition between increasing suprananometer volume (supermicropores according to IUPAC classification, w > 1 nm, and small mesopores w > 2 nm) and decreasing subnanometer volume (ultramicropores, w < 1 nm) (Figure 1a shows the general tendency). These results are consistent with our previous observation10 that increasing the KOH:C ratio above 3 at the constant activation temperature results in a progressive expansion of the carbon matrix, consumption of carbon from the pore walls, and transformation of subnanometer pores into suprananometer pores without affecting the surface area in a significant way. They also confirm that the engineering of nanospace in activated carbons is possible and can be controlled by appropriate choice of activation parameters. The samples activated at R = 3 show the fraction of subnanometer pore volume that exceeds the corresponding values of the MSC-30 carbon which we consider as a reference material in this paper. At the same time, both samples have similar porosity. Hydrogen Adsorption at T = 80 K. Figure 2 shows the comparison of gravimetric excess adsorption and storage capacity of the carbon samples activated at different KOH:C ratios at T = 80 K. The presented isotherms are averaged over repeated measurements; the experimental errors are less than 5% at pressures below 40 bar and less than 7% above. All storage characteristics indicate that carbons activated at R = 3 perform the best, better than MSC-30 reference carbon. For R = 4 and 5, the storage capacity progressively decreases and increases again for R = 6. This evolution can be partially explained by a variation of fraction of subnanometer pores (optimal for hydrogen storage) in different carbons (see Table 1); the larger the KOH:C activation ratio, the larger the fraction of subnanometer pores in the resulting carbon and the better it performs. However, an additional factor must affect the results as the difference between the 6K and the MCS-30 storage capacity does not follow this rule.

n

∑ Aiαi(wi)Isim(wi , T )

Article

(4)

where Isim(wi, T) is the adsorption isotherm in infinite slit pore of the effective width wi, simulated at temperature T. Equation 4 is a discrete variation of the standard adsorption integral used to determine pore size distribution in real samples21 from experimental nitrogen adsorption isotherms and a large kernel of adsorption isotherms precalculated for model pores of width w. In our case, the pore size distribution is represented by the coefficients αi(w), and the kernel is represented by Isim(w, T). The additional coefficients Ai are energy factors. The value Ai = 1 indicates that the binding energy of hydrogen is the same as on ideal, infinite graphene plane (4.5 kJ/mol). If the energy is lower, then Ai < 1 and the adsorption within the porous structure is reduced. The energy factor is absent in the standard kernel-based procedures of PSD determination. It means that any existing heterogeneity of the adsorption energy distribution is effectively included in the resulting pore size distribution. Our procedure avoids such an approximation and extracts the binding energy information directly from the isotherms’ fit. 957



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Figure 2. Gravimetric excess adsorption (left) and gravimetric storage capacity (right) of samples 3K, 4K, 5K, and 6K at T = 80 K. For comparison, the results for MCS-30 activated carbon are also shown.

Figure 3. Total (black squares) and excess (red circles) gravimetric hydrogen adsorption at T = 80 K in carbons activated at different KOH:C ratios. Open symbols are the experimental data; closed symbols are numerical fits calculated assuming a linear combination of simulated isotherms for pore sizes defined by theoretical (fitted) PSD. The pore sizes and the weight of their contribution to each model isotherm are given on the graphs.

number (2−4) of main contributions, the same (discrete) pore size distribution reproduces both experimental excess and total adsorption isotherms. The residual differences are within the experimental errors and may result from (1) discrete model of sample porosity and (2) additional heterogeneity of the adsorption energy, not taken into account here, resulting from finite lateral dimensions of the adsorbing surface.21−23 The 3K carbon is the only one in which the hydrogen adsorption could be modeled using the isotherms calculated for the binding energy E = 4.5 kJ/mol (A = 1). This suggests that the pore walls can be fairly well approximated by ideal, infinite

To get more physical insight that could explain this behavior, we performed numerical modeling discussed below. The simulations allowed accounting separately for the geometric and energetic aspects of interaction between hydrogen molecules and activated carbon. Figure 3 compares the experimental isotherms shown in Figure 2 (total and excess gravimetric adsorption) to their numerical fits Itheor calculated using eq 4. All experimental isotherms are reproduced by calculated ones with great accuracy. This proves that our initial fit of PSD is robust: although it reduces the experimental PSD to a very limited 958



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graphene layers and that the contribution of the adsorption on surface defects or pore edges is negligible. The presence of a large number of subnanometer pores agrees with current understanding of the activation process:10 at small activation ratio R, only a limited number of carbon layers are removed from graphite-like structures, leaving narrow, subnanometer pores. This pore size is optimal for hydrogen adsorption (the effective energy of adsorption is much larger than 4.5 kJ/mol because of the strong overlapping of interaction potential from both pore walls, up to two molecular layers can be accommodated within the pore, and there is no space for molecules in the gas state).11 In consequence, the capacity of storage of these pores is the largest. The MSC-30 and 3K carbons show similar storage characteristics. Gravimetric storage capacity is practically the same. However, the excess adsorption is larger in the 3K carbon (Figure 3) because of the larger fraction of subnanometer pores in 3K than in the MSC-30 carbon (Figure 1a). This difference in PSD affects mainly the excess adsorption. The value of energy factor in numerical fit of MCS-30 isotherms A = 0.9 corresponds to average adsorption energy of ∼4.1 kJ/mol. It indicates that the pores in the MCS-30 carbon cannot be approximated by infinite slits. Their lateral dimension should be smaller than in the 3K sample. As the energy of adsorption at the pore edges is lower than in infinite pores,22 the excess adsorption decreases. When the activation ratio increases (R = 4 and R = 5), the fraction of subnanometer pores in the resulting carbon decreases (Table 1). The average binding energy used in simulations to reproduce adsorption isotherms also decreases (A = 0.9 and 0.72, corresponding to ∼4.1 and 3.2 kJ/mol, respectively). Both results are consistent with our previous hypothesis of a progressive transformation of subnanometer pores into suprananometer pores when the activation ratio increases. This process potentially can also produce an increasing number of defects and fragmentation of the pore walls. In consequence, the average energy of hydrogen adsorption in the material (and the A-factor) decreases.22 In general, in activated carbons, the hydrogen storage capacity follows the variation of the fraction of subnanometer pores: in 6K carbon, it is higher than in 4K and 5K but remains lower than for 3K. We suppose that at higher KOH concentrations the increased consumption of carbon may lead to a creation of additional subnanometer pores with thinner pore walls or additional edge surface. In consequence, the specific surface area and the porosity of 6K carbons also increase. As the effective binding energy in narrow pores is larger than in large pores, the energy factor A to fit experimental isotherms increases. Hydrogen Adsorption at T = 303 K. Figure 4 compares room temperature (T = 303 K) gravimetric excess adsorption and gravimetric storage capacity of the carbons activated at different KOH:C ratios. The quantities of stored hydrogen decrease (by a factor of 6) with respect to adsorption at 80 K. The differences between samples prepared at different KOH concentrations described in the previous section are preserved, although they are less pronounced than at low temperature. Figure 5 compares the experimental isotherms (total and excess gravimetric adsorption) and their numerical fits. The fit parameters (the position and weight of each component and the energetic factor A) are the same at T = 80 K and T = 303 K. This confirms again the robustness of the discrete fit of PSD and the accuracy of the estimation of energetic factor A.

Figure 4. Gravimetric total (open symbols) and excess adsorption(closed symbols) of samples 3K, 4K, 5K, and 6K at T = 303 K.

The fact that not all experimental isotherms have been reproduced perfectly (although all differences are smaller than the experimental errors) does not constitute the weakness of our analysis. More important is the fact that the theoretical curves have been modeled without any fitting parameters, except the energy factor A, which adjusts the calculated isotherms to the variations of the binding energy in the real samples. The calculated kernel isotherms are routinely prepared for a constant binding energy. At the same time, the real samples are very often heterogeneous, and their mean energy may be different from the theoretical one. In this way, our fitting procedure provides additional characterization of the measured samples, complementary to the direct determination of the isosteric heat using the Clapeyron−Clausius approach or from the calorimetric measurements.

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CONCLUSIONS We have proposed a simple procedure of experimental isotherms analysis on the basis of correlated analysis of experimental pore size distribution (from nitrogen adsorption) and simulated isotherms of gas (hydrogen) adsorption in slitshaped pores with infinite walls (grand canonical Monte Carlo simulations). We have applied this procedure to analyze adsorption of hydrogen in a series of activated carbons. The method consists of two steps. First, the experimental (continuous) PSD is modeled by a small number of Gaussian peaks. It reduces the continuous PSD to a discrete (multipeak) theoretical PSD. In the second step, the experimental gas adsorption isotherm is modeled by a linear combination of isotherms simulated for single pores, each representing one peak in discrete PSD distribution. This approach allows us to reproduce both total and excess gas uptake with very good accuracy. The residual differences between calculated and experimental curves may depend on experimental errors (the accuracy of the measured isotherms and of the determination of pore size distributions) and on the quality of the Gaussian decomposition (in particular, on the number of Gaussian components). The applied procedure shows that experimental isotherms can be modeled without the direct fitting procedure if the reliable PSD is available. This approach presents several advantages with respect to the direct fit. First, it verifies the quality of measurements by comparing two quantities that are measured independently: PSD and adsorption isotherm. Second, it requires simulations of only a few isotherms, contrary to the direct fitting procedure where a very large 959



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Figure 5. Total (black squares) and excess (red circles) gravimetric hydrogen adsorption at T = 303 K in carbons activated at different KOH:C ratios. Open symbols are the experimental data; closed symbols are numerical fits calculated assuming a linear combination of simulated isotherms for pore sizes defined by theoretical (fitted) PSD. The pore sizes and the weight of their contribution to each model isotherm are the same as in Figure 3.

interpretation of an activation process which assumes a progressive consumption of carbon from the pore walls at high activation ratios R. This process transforms subnanometer pores into suprananometer pores22 but may also create an increased number of defects and cause fragmentation of the pore walls. Both processes may be responsible for a slightly larger adsorption surface experimentally observed for 6K samples. Moreover, the increased heterogeneity of 6K samples is consistent with lower energy factor A in the fitting procedure. The presented results suggest that the energy factors should be introduced into standard fitting procedures used to calculate the pore size distributions23 assuming that different energies correspond to different contributions found from PSD analysis. Having binding energy as an additional fitting parameter should lead to more refined and correct PSD.

number of model isotherms (a kernel) are necessary to make the fitting procedure efficient. The most important benefit of our procedure is to provide information about the average binding energy in real samples and, indirectly, additional structural information complementing conventional characterization of the adsorbent via the value of the fitting parameter A. This information is not available from the standard isotherm fitting methods. The energy factor A represents the average interaction energy between the adsorbed molecules and a surface. We defined A = 1 for adsorption in ideal, defect-free, and infinite slit shape pores built from graphene layers. In activated carbons, in absence of heteroatoms (that could be introduced by substitution, intercalation, or doping), there are no sites with higher energy than the one corresponding to the perfect graphene surface. The structural heterogeneity of the adsorbent (presence of surface defects or finite size of the pore walls21) leads then to energetic heterogeneity and, on average, to lower adsorption energy. In consequence, in real samples, the value of energetic factor will always be 0 ≤ A ≤ 1 and directly measures the difference between the real structure and the ideal slit model. The highest hydrogen uptake was observed in carbons activated at the KOH:C ratio R = 3, containing the highest fraction of subnanometer pores. From our fitting procedure, we have concluded that only these carbons have the geometry which can be approximated by a model of slit pores with infinite walls and graphene-like energy of adsorption. Higher activation ratios always produce carbons with lower (on average) adsorption energy. This is consistent with our

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AUTHOR INFORMATION

Corresponding Author

*Phone: (33) 4 67 14 47 49; fax: (33) 4 67 14 46 37; e-mail: lucyna.fi[email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

This material is based upon work supported by the Department of Energy Grant under award No. DE-FG02-07ER46411. 960



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Different Approach to Estimation of Hydrogen-Binding Energy in

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