Research Article | Open Access
Ahmad Okhovat, Ali Ahmadpour, Farzaneh Ahmadpour, Zahra Khaki Yadegar, "Pore Size Distribution Analysis of Coal-Based Activated Carbons: Investigating the Effects of Activating Agent and Chemical Ratio", International Scholarly Research Notices, vol. 2012, Article ID 352574, 10 pages, 2012. https://doi.org/10.5402/2012/352574
Pore Size Distribution Analysis of Coal-Based Activated Carbons: Investigating the Effects of Activating Agent and Chemical Ratio
The present study attempts to investigate the effects of different chemical agents and chemical ratios on pore structure of coal-based activated carbons. The adsorption isotherm data of two series of activated carbons prepared from bituminous coal by chemical activation with potassium hydroxide and zinc chloride were used. Four well-known models of Dubinin-Stoeckli, Stoeckli, Horvath-Kawazoe, and improved Horvath-Kawazoe were applied for the characterization of these porous solids. Although the results showed some differences among the models that arise from their fundamental assumptions, in general they are found to be comparable. Results showed that samples activated by ZnCl2 provide higher-adsorption capacity than those from KOH. In each series, it was shown that the pore volume increases with increasing impregnation ratio, ranging from 50% to 200%. Activated carbons obtained at low chemical ratio in ZnCl2 series (up to 100%) showed microporous structure, while those with higher ratios became predominantly mesoporous. In the KOH series, increasing KOH created more micropores in the carbon structure in the whole range of studied chemical ratio.
Activated carbon (AC) is among the important carbon based materials that find widespread use in almost every industrial field. They are employed in different applications such as purification, recovery, decolorization, deodorization, separation, catalyst, catalytic support, and gas storage due to the large internal surface area and specific pore structure. On this basis, activated carbon adsorption is of interest to many economic sectors and areas such as chemical, food, pharmaceutical, automobile, petroleum, petrochemical, and gas industries [1–4].
Coals have become the main precursor for the production of activated carbons because of their inherent microstructure and surface chemical properties . Low cost of production and unlimited resources as well as specific beneficial properties, such as well-developed internal pore structure and high surface area, high mechanical and chemical resistance, ease of degradation, and good ion-exchange properties are main reasons for increasing interest in the use of activated carbons obtained from coals [6–8]. Furthermore, coal products are in greater demand since they have greater density and corrosion endurance than other carbons [9, 10].
Important parameters that greatly affect the adsorption performance of a porous carbonaceous adsorbent are porosity and pore structure. Consequently, the determination of pore size distribution (PSD) of coal-based adsorbents is of particular interest. For this purpose, various methods have been proposed to study the structure of porous adsorbents [11–41].
A direct but cumbersome experimental technique for the determination of PSD is to measure the saturated amount of adsorbed probe molecules which have different dimensions. However, there is uncertainty about this method because of networking effects of some adsorbents including activated carbons . Other experimental techniques that usually implement for characterizing the pore structure of porous materials are mercury porosimetry, X-ray diffraction (XRD) or small angle X-ray scattering (SAXS), and immersion calorimetry.
A large number of simple and sophisticated models have been presented to obtain a realistic estimation of PSD of porous adsorbents. Relatively simple but restricted applicable methods such as Barret, Joyner and Halenda (BJH), Dollimore and Heal (DH), Mikhail et al. (MP), Horvath and Kawazoe (HK), Jaroniec and Choma (JC), Wojsz and Rozwadowski (WR), Kruk-Jaroniec-Sayari (KJS), and Nguyen and Do (ND) were presented from 1951 to 1999 by various researchers for the prediction of PSD from the adsorption isotherms [12–19]. For example, the BJH method which is usually recommended for mesoporous materials is in error even in large pores with dimension of 20 nm . The main criticism of the MP method, in addition to the uncertainty regarding the multilayer adsorption mechanism in micropores, is that we should have a judicious choice of the reference isotherm . HK model  was developed for calculating micropore size distribution of slit-shaped pore; however, the HK method suffers from the idealization of the micropore filling process. Extension of this theory for cylindrical and spherical pores was made by Saito and Foley  and Cheng and Ralph . By applying some modifications on the HK theory, some improved models for calculating PSD of porous adsorbents have been presented [11, 23–25]. Gauden et al.  extended the Nguyen and Do method for the determination of the bimodal PSD of various carbonaceous materials from a variety of synthetic and experimental data. The pore range of applicability of this model besides other limitations of ND method is its main constraint.
In 1985, Bunke and Gelbin  determined the PSD of activated carbons based on liquid chromatography (LC). Choice of suitable solvent and pore range of applicability of this method are two main problems that restrict its general applicability.
More sophisticated methods such as molecular dynamics (MD), Monte Carlo simulation, Grand Canonical Monte Carlo simulations (GCMS), and density functional theory (DFT) are theoretically capable of describing adsorption in the pore system [28–32]. The advantages of these methods are that they can apply on wide range of pores width. But, they are relatively complicated and provide accurate PSD estimation based on just some adsorbates with specified shapes. Requiring extensive computation time and significantly different idealized conditions from a real situation are other drawbacks of such methods. In 2008, Do et al.  used a new approach based on Monte Carlo integration to derive pore size and its volume distribution for porous solids having known configuration of solid atoms. They applied the proposed method to a wide range of commonly used porous solids. However, this method also seems to have limitations of Monte Carlo simulation in addition to requiring the information of solid atomistic configuration. Recently, Sitprasert et al.  proposed a multiscale approach based on Grand Canonical Monte Carlo (GCMC) to predict the adsorption isotherms and PSD of porous solids. However, the proposed methodology needs further improvement to provide high-accuracy predictions besides mass of computations that is needed.
There is also a different approach based on a single adsorption isotherm. Here, total adsorption amount which is simply a summation of the adsorbed molecules on various adsorption sites is equal to an integral of the local adsorption on particular sites multiplied by a PSD function, integrated over all sizes: where is the local adsorption isotherm (kernel) evaluated at bulk pressure and local pore size , and denotes the PSD of the heterogeneous solid adsorbent. Solving for the PSD function is an ill-posed problem unless the form of function is defined. Various models by assuming different kernels (Langmuir, Freundlich, BET, DR, DA, Sips, Toth, Unilan, Jovanovich, Fowler and Harkins,…) and mathematical functions (Gaussian, Gamma,…) for PSD have been presented. For instance, the Dubinin-Stoeckli (DS) and Stoeckli models which have been proposed based on the Dubinin theory of volume filling of micropores (TVFM) implement gaussian and gamma type of mathematical function, respectively [35, 36]. The advantage of these models is that they are experimentally convenient and do not need complicated PSD calculations.
In 1998, Bhatia  successfully applied the combination of finite element collocation technique with regularization method to extract various double peak PSDs from synthetic isotherm data points contaminated with 1% normally distributed random errors using DR isotherm. They applied the constraint of nonnegativity of solutions by simply utilizing a Newton-Raphson technique. Although they reported that “the method is stable over a wide range of values of the regularization parameter,” the application of nonnegativity constraint usually provides unrealistic solutions .
Sun  proposed a new method based on the modification of DR equation by introducing adsorption density and correlating between the pore filling pressure and critical pore size for nitrogen adsorption at 77 K. The results are found comparable with other popular PSD methods such as MP, JC, HK, and DFT. In addition to uncertainty about the general performance of this model as a result of some assumptions in the model derivation, it is relatively complicated and the procedure for obtaining PSD is cumbersome.
The average diameter of the mesopores is usually calculated from the nitrogen adsorption data using Kelvin equation . Recently, Shahsavand and Shahrak [38, 41] proposed two new methods for reliable extraction of PSD from adsorption and condensation branch of isotherms. According to their results, it seems that these two methods have also some limitation similar to the other previous ones. The regularization technique that used for obtaining optimum value of regularization parameter is challengeable in these methods. In addition, the basis of these methods is Kelvin equation which unlikely provides reliable PSD for microporous solids.
Although much has been done to address the PSD of porous adsorbents, up to now, no general reliable theory is available leading to the conclusion that for microporous carbons the extensive investigation should still continue.
In the present study, we have tried as a novel work to extend the analysis on PSD of porous adsorbents by investigating the effects of different chemical agent and chemical ratios for two series of chemically coal-based activated carbons using KOH and ZnCl2. Two well-known models based on Dubinin’s TVFM, namely, Dubinin-Stoeckli (DS) and Stoeckli models were used to investigate the effects of these two chemical agents and impregnation ratio on the porosity of AC samples, and the results were compared with the two widely used methods of Horvath-Kawazoe (HK) and improved Horvath-Kawazoe (IHK) for the determination of PSD of microporous solids. The first two models were derived based on benzene as a reference adsorbate, because it provides more accurate estimations than other adsorbates. On this basis, adsorption isotherm data of benzene at 30°C were used to determine the PSD of each sample. Finally, comparison of the PSD results from each model is also made for KOH and ZnCl2-activated carbon series.
Finding a reliable, accurate, and flexible method for the determination of PSD of porous adsorbents still remains an important concern in the area of characterization of porous materials. Although a large number of researches have been done in this area, some constraints such as type of adsorbate, adsorbent characteristics, adsorption temperature, applicable range of pore size, and range of relative pressure limit the applicability of each model in all cases . The lack of such method is tangible by rapid development of new porous materials and their wide applications in various fields. In the present study, the following three well-known models were used in order to obtain PSD for two series of chemically activated carbons and the results are compared.
2.1. Dubinin-Stoeckli (DS) Model
Here, (mmol·g−1) represents the amount adsorbed at relative pressure , denotes the limiting amount of micropores filling, and is the differential molar work of adsorption defined as at temperature of . One may write that , where is the affinity coefficient depending on the adsorptive only, and it has been assumed that for benzene as a reference .
Which implies a normal half-width () distribution of micropore volume for the slit-like pores as: where, is the half-width of a slit shaped micropore which corresponds to the maximum of the distribution curve, and is the variance. The letter is a constant coefficient for a given vapor:
For benzene as the reference vapor, the constant equals to 12 kJ·nm·mole−1. Using (3) to fit the experimental data, three parameters of , and , can be extracted. Knowing these parameters, the micropore size distribution in terms of volume can be calculated from (4).
2.2. Stoeckli Model
Another approach for the determination of PSD of porous adsorbents which is also based on the Dubinin’s TVFM is Stoeckli method . It had been shown by Stoeckli et al. [36, 47] that for the ideal slit-shaped microporous materials, a good estimate of the adsorption isotherm can be obtained by:
The and are constant parameters that are related to the mean and width of the distribution, respectively. is calculated using (7). This is applicable over a range of pore size from 0.4 to 2.0 nm .
After obtaining the model parameters using (6), pore size distribution can be determined using the following gamma type distribution of the mean pore width :
2.3. Horvath-Kawazoe (HK) Method
Horvath and Kawazoe  developed a rather simple means of characterizing the pore structure of porous materials. This model provides a simple, one-to-one correspondence between the pore size and relative pressure at which the pore is filled. Using thermodynamic arguments and applying the potential obtained by Everett and Powl , Horvath and Kawazoe derived the following expression: where represents the micropore width (), denotes Avogadro’s number, and and are gas constant and temperature, respectively. and are dispersion constant characterizing adsorbate-adsorbent and adsorbate-adsorbate interactions, and are the number of atoms per unit area of adsorbent and the number of molecules per unit area of adsorbate, is the arithmetic mean of the adsorbate molecular diameter and the adsorbent atomic diameter, and is the distance between a gas molecule and an adsorbent atom at zero interaction energy at relative pressure of .
From the amount adsorbed at relative pressure of , (9) yields the corresponding slit-pore width, . Thus, a plot of adsorbed volume versus is a cumulative pore-volume curve, the slopes of which give the differential PSD.
2.4. Improved Horvath-Kawazoe (IHK) Method
The HK equation is widely used for calculating the micropore size distribution (MPSD) from a single adsorption isotherm measured at subcritical temperature (e.g., N2 at 77 K). In the HK model, the ideal Henry’s law (or linear behavior) is assumed for the isotherm.
Cheng and Yang (1994) modified the HK formulation by assuming the nonlinearity of the isotherm equation. This has improved the HK model significantly with the advantage of maintaining the PSD calculation simple . The nonlinearity assumption also results in sharpening PSD . Considering the mentioned nonlinearity correction, Cheng and Yang (1995) derived the improved HK equation (IHK) for three different pore geometries. For the slit-shaped pores, the IHK equation is derived as 
The influence of this term and thus depends on where the adsorption occurs and also the shape of the isotherm. In the initial part of the adsorption isotherm, where is small and -dependent term (second term in LHS of IHK equation) approaches zero, the IHK model approaches HK. By increasing , the pore filling term becomes more negative. In the meantime, as the relative pressure is increased, the free energy term increases . The increase in free energy term is partly offset by the pore filling term. So, the LHS of the IHK equation is increased at a slower rate as compared with the original HK equation. Consequently, the calculated pore size is increased at a slower rate, resulting in sharpening the pore size distribution . In the present study, has been calculated from the following DR equation.
A bituminous coal with medium ash content was used as a precursor for the preparation of chemically activated carbons with KOH and ZnCl2. The influence of different chemical natures, a strong base (KOH) and a Lewis acid (ZnCl2), on the structure of the prepared activated carbons were investigated. The characteristics of precursor and detailed experimental procedure were described in our previous work . In brief, 10 g of dried coal (212–250 μm) was well mixed with a concentrated solution of KOH or ZnCl2 with the chemical ratio ranging from 50 to 200% (mass basis) for about 5 min, and then the resulting homogeneous slurry was dried at 110°C for 14 hrs. The resulting chemical loaded samples were heated (5°C/min) to the final carbonization temperature in nitrogen flow of 150 cm3/min. Samples were held at the final temperature for carbonization times of 1 hr, in ZnCl2 series and in KOH series, before cooling down under nitrogen. The products were washed sequentially with 0.5 N HCl, hot water and finally cold distilled water to remove residual organic and mineral matters, and then dried at 110°C. In all runs of chemical activation, heating rate and nitrogen flow were kept constant and nitrogen was passed through a copper turning bed at 480°C as well as a molecular sieve bed to remove the trace of oxygen and water content in the gases before entering the reactor.
After preparing samples, adsorption of benzene at 30°C and nitrogen at −196°C were performed to evaluate the adsorptive properties of the activated carbons. The benzene adsorption isotherms were determined in a conventional high accuracy volumetric adsorption rig and the nitrogen isotherms were obtained using Autosorb-1, Quantachrome.
4. Results and Discussion
Two series of activated carbons with different chemical ratios of 50, 75, 100 and 200 were prepared by chemical activation of a bituminous coal with potassium hydroxide and zinc chloride. Figure 1 shows benzene adsorption isotherms of the prepared samples with different chemical ratios at 30°C.
Nitrogen isotherms of both carbon series at −196°C are also presented in Figure 2. The shape of adsorption isotherm can provide preliminary qualitative information about the adsorption mechanism as well as the pore structure of activated carbons. These isotherms clearly show that the KOH mainly created microporosity in the carbon samples for the whole range of chemical to coal ratio studied here. Zinc chloride, on the other hand, produced a wide range of porosity and high ratio of this chemical changed the form of isotherm from type I to type II which is an indication of mesoporous carbon [42, 50, 51].
To clarify the differences between the mechanism of KOH and ZnCl2 on pore evolution, mesopore volumes and pore half-width of the carbons have been plotted versus chemical ratio in Figure 3. The mesopore volumes are calculated by subtracting the micropore volumes (deduced from the DR equation) from the amount adsorbed at of N2 isotherm at 77 K and pore half-widths are obtained using DS equation. This figure shows that the high ratio of ZnCl2 increases mesoporosity in the resulting carbon, while KOH creates more micropore and the mesopore contribution in this series is almost constant.
The pore width and pore volume were increased steadily and samples became mesoporous with increasing ZnCl2 ratio, while mesopores volumes are almost constant in the case of KOH. It is evident from Figure 3 that ZnCl2 is not only responsible for the development of new micropores, but also for the enlargement of existing micropores to mesopores, while in the case of KOH activation, the micropore creation still plays an important role in the entire range of chemical ratio studied here.
As discussed elsewhere [10, 52], in carbonization of bituminous coals with ZnCl2, by increasing chemical ratio the mechanism of pore evolution is changed and the dependence of pore evolution on the chemical ratio can be divided into three different zones. In the first zone with < 50%, microporosity creation is predominant which is reflected by the sharp rise in the micropore volume versus chemical ratio. For the range of 50% < < 100% there is competition between the microporosity creation and the widening of microporosity into the range of mesoporosity (Figure 3). Benzene and nitrogen isotherms of these carbons with chemical ratio less than 100% show that the resulting carbons are mainly microporous (Figures 1 and 2). In the third zone where the chemical ratio is greater than 100%, larger widening of porosity, mainly in mesopore range, increases the pore volume to some extent. In the case of KOH, the mechanism of pore creation is different . Here, micropore and mesopore contribution that is almost constant and chemical to precursor ratio does not seem to have significant effect on the average pore size (Figure 3).
Undoubtedly, pore size distribution is one of the most important aspects for characterization of structural heterogeneity of porous materials employed in industrial application. Based on the results of benzene adsorption isotherms, the PSD of prepared samples chemically activated with KOH and ZnCl2 at different chemical ratios were calculated using four well-known models, and the results are presented in Figures 4 and 5, respectively. In these figures, a comparison can also be made among different models in characterizing the AC porous structures.
By fitting the experimental adsorption isotherms to the DS and Stoeckli models, the parameters were obtained using a nonlinear optimization technique and presented in Table 1. Parameters of the HK and IHK models for benzene adsorption were taken from Terzyk and Gauden .
With regard to the values presented in Table 1, the DS model shows higher limits for micropore filling than that of Stoeckli model. Also, increasing the chemical ratio enhanced the adsorption limit of the prepared ACs. It is obvious that chemical ratio plays an important role on the pore structure of chemically activated carbons.
Pore size distribution of the prepared samples chemically activated by KOH obtained from DS, Stoeckli, HK and IHK models is presented in Figure 4. As expected from benzene and N2 adsorption isotherms (Figures 1(a) and 2(a)), all samples in the KOH series showed microporous structure. Moreover, by increasing impregnation ratio the pore volumes were also increased. However, there is a difference between the PSDs calculated using DS, Stoeckli, HK and IHK models which are related to their fundamental assumptions on describing the porous structure and/or mechanism of adsorption.
The PSDs calculated from the Stoeckli model shift slightly to larger pore diameters in comparison to the DS model but with a similar trend. Furthermore, one can notice that the method proposed by Horvath-Kawazoe shows slightly lower pore diameters in comparison to the DS results (Figure 3). As mentioned above, the fundamental assumptions of each model are responsible for the differences in the results. Although DS and Stoeckli models are both based on the TVFM, implementing different mathematical functions and local isotherms, as mentioned before, causes the differences. The idealization of the micropore filling process of HK method in addition to completely different approach for characterizing porous solids is the main reasons for differences among the PSDs predicted by HK and IHK methods compared to those of DS and Stoeckli models. However, the differences are not so significant, and the results are comparable. Malformed predicted PSDs by HK and IHK methods are due to lack of experimental data especially in low range of relative pressure. Although the HK and IHK methods showed some different pore volumes, they provided similar mean pore size predictions for all the investigated adsorbents.
The PSD of samples activated with ZnCl2 is depicted in Figure 5. As it can be clearly seen in the figure, ZnCl2 provides larger pores than KOH, which leads to pore widening and mesoporous structure at higher chemical ratio. Similar to the results of KOH activated samples, the DS model indicates larger pore diameters in comparison with the Stoeckli model and HK and IHK methods.
As seen in Figure 5, with increasing the chemical to coal ratio (up to 100%) in the ZnCl2 series, the micropores are widened with a very fast rate, and further increase of ZnCl2 changes the micropores to mesopores. However, this behaviour is not seen in the results of Stoeckli model (Figure 5(b)). This model is recommended for characterization of microporous materials, and it does not provide good PSD estimation of mesoporous solids [42, 47].
In general, the comparison of the data of two activated carbon series (Figures 1 to 5) revealed that, at the same chemical ratio, samples activated by ZnCl2 have more adsorption capacity than those from KOH.
Activated carbons were prepared from bituminous coal by KOH and ZnCl2 chemical activation at different chemical ratios. From Benzene and nitrogen adsorption data, the KOH series showed similar behavior to type I isotherms in the whole range of chemical to precursor ratio studied here, while activated carbons in the ZnCl2 series illustrated the combination of types I and II isotherms. Pore characteristics of the prepared porous samples in terms of PSD were determined using four well-known models of DS, Stoeckli, HK, and IHK. The effect of different chemical activating agents and ratio of chemical to coal precursor on PSD of the prepared samples were also investigated. Increasing impregnation ratio increases the pore volume of activated samples, and ZnCl2 resulted in ACs with more adsorption capacities than those of KOH. This increase for KOH chemical agent will create more micropores with insignificant variations of average pore size, while in the case of ZnCl2 it creates wider pores, and after a specific impregnation ratio (100%) it begins to create mesopores in the carbonaceous structure.
- A. Ahmadpour and D. D. Do, “Characterization of modified activated carbons: equilibria and dynamics studies,” Carbon, vol. 33, no. 10, pp. 1393–1398, 1995.
- R. C. Bansal and M. Goyal, Activated Carbon Adsorption, CRC Press, 2005.
- N. Quirke, Adsorption and Transport at the Nanoscale, CRC Press, 2006.
- R. M. A. Roque-Malherbe, Adsorption and Diffusion in Nanoporous Materials, CRC Press, 2007.
- G. Gryglewicz and E. Lorenc-Grabowska, “Mesoporous activated carbons from Ca and Fe exchanged sub-bituminous and bituminous coals,” Carbon, vol. 42, no. 3, pp. 688–691, 2004.
- H. H. Schobert and C. Song, “Chemicals and materials from coal in the 21st century,” Fuel, vol. 81, no. 1, pp. 15–32, 2002.
- R. Pietrzak, H. Wachowska, P. Nowicki, and K. Babeł, “Preparation of modified active carbon from brown coal by ammoxidation,” Fuel Processing Technology, vol. 88, no. 4, pp. 409–415, 2007.
- T. Kopac and A. Toprak, “Preparation of activated carbons from Zonguldak region coals by physical and chemical activations for hydrogen sorption,” International Journal of Hydrogen Energy, vol. 32, no. 18, pp. 5005–5014, 2007.
- M. Greenbank and S. Spotts, “six criteria for coal-based carbons,” Water Technology, vol. 16, p. 56, 1993.
- A. Ahmadpour and D. D. Do, “The preparation of active carbons from coal by chemical and physical activation,” Carbon, vol. 34, no. 4, pp. 471–479, 1996.
- L. S. Cheng and Y. Ralph T, “Improved Horvath-Kawazoe equations including spherical pore models for calculating micropore size distribution,” Chemical Engineering Science, vol. 49, no. 16, pp. 2599–2609, 1994.
- E. P. Barrett, L. G. Joyner, and P. P. Halenda, “The determination of pore volume and area distributions in porous substances. I. Computations from nitrogen isotherms,” Journal of the American Chemical Society, vol. 73, no. 1, pp. 373–380, 1951.
- D. Dollimore and G. R. Heal, “An improved method for the calculation of pore size distribution from adsorption data,” Journal of Applied Chemistry, vol. 14, no. 3, pp. 109–114, 1964.
- R. S. Mikhail, S. Brunauer, and E. E. Bodor, “Investigations of a complete pore structure analysis. I. Analysis of micropores,” Journal of Colloid And Interface Science, vol. 26, no. 1, pp. 45–53, 1968.
- G. Horvath and K. Kawazoe, “Method for the calculation of effective pore size distribution in molecular sieve carbon,” Journal of Chemical Engineering of Japan, vol. 16, no. 6, pp. 470–475, 1983.
- M. Jaroniec and J. Choma, “Characterization of heterogeneity of activated carbons by utilizing the benzene adsorption data,” Materials Chemistry and Physics, vol. 15, no. 6, pp. 521–536, 1986.
- R. Wojsz and M. Rozwadowski, “The micropore structure analysis of active carbons,” Carbon, vol. 27, no. 1, pp. 135–139, 1989.
- M. Kruk, M. Jaroniec, and A. Sayari, “Application of large pore MCM-41 molecular sieves to improve pore size analysis using nitrogen adsorption measurements,” Langmuir, vol. 13, no. 23, pp. 6267–6273, 1997.
- C. Nguyen and D. D. Do, “New method for the characterization of porous materials,” Langmuir, vol. 15, no. 10, pp. 3608–3615, 1999.
- A. V. Neimark and P. I. Ravikovitch, “Capillary condensation in MMS and pore structure characterization,” Microporous and Mesoporous Materials, vol. 44-45, pp. 697–707, 2001.
- B. P. Russell and M. D. Levan, “Pore size distribution of BPL activated carbon determined by different methods,” Carbon, vol. 32, no. 5, pp. 845–855, 1994.
- A. Saito and H. C. Foley, “Curvature and parametric sensitivity in models for adsorption in micropores,” AIChE Journal, vol. 37, no. 3, pp. 429–436, 1991.
- L. S. Cheng and R. T. Yang, “Predicting isotherms in micropores for different molecules and temperatures from a known isotherm by improved Horvath-Kawazoe equations,” Adsorption, vol. 1, no. 3, pp. 187–196, 1995.
- E. A. Ustinov and D. D. Do, “Adsorption in slit-like pores of activated carbons: improvement of the Horvath and Kawazoe method,” Langmuir, vol. 18, no. 12, pp. 4637–4647, 2002.
- P. Kowalczyk, E. A. Ustinov, A. P. Terzyk, P. A. Gauden, K. Kaneko, and G. Rychlicki, “Description of benzene adsorption in slit-like pores. Theoretical foundations of the improved Horvath-Kawazoe method,” Carbon, vol. 42, no. 4, pp. 851–864, 2004.
- P. A. Gauden, A. P. Terzyk, M. Jaroniec, and P. Kowalczyk, “Bimodal pore size distributions for carbons: experimental results and computational studies,” Journal of Colloid and Interface Science, vol. 310, no. 1, pp. 205–216, 2007.
- G. Bunke and D. Gelbin, “Determining pore-size distribution of activated carbons by liquid chromatography,” Chemical Engineering Science, vol. 40, no. 11, pp. 2079–2085, 1985.
- J. P. Olivier, W. B. Conklin, and M. v. Szombathely, “Determination of pore size distribution from density functional theory: a comparison of nitrogen and argon results,” Studies in Surface Science and Catalysis, vol. 87, pp. 81–89, 1994.
- J. P. Olivier, “Modeling physical adsorption on porous and nonporous solids using density functional theory,” Journal of Porous Materials, vol. 2, no. 1, pp. 9–17, 1995.
- C. M. Lastoskie, N. Quirke, and K. E. Gubbins, in Equilibria and Dynamics of Gas Adsorption on Heterogeneous Solid Surfaces, W. Rudzinski, W. A. Steele, and G. Zgrablich, Eds., Studies in Surface Science and Catalysis, p. 745, Elsevier, Amsterdam, The Netherlands, 1997.
- V. Yu. Gusev and J. A. O'Brien, “Can molecular simulations Be used to predict adsorption on activated carbons?” Langmuir, vol. 13, no. 10, pp. 2822–2824, 1997.
- P. I. Ravikovitch, A. Vishnyakov, R. Russo, and A. V. Neimark, “Unified approach to pore size characterization of microporous carbonaceous materials from N2, Ar, and CO2 adsorption isotherms,” Langmuir, vol. 16, no. 5, pp. 2311–2320, 2000.
- D. D. Do, L. F. Herrera, and H. D. Do, “A new method to determine pore size and its volume distribution of porous solids having known atomistic configuration,” Journal of Colloid and Interface Science, vol. 328, no. 1, pp. 110–119, 2008.
- C. Sitprasert, Z. H. Zhu, F. Y. Wang, and V. Rudolph, “A multi-scale approach to the physical adsorption in slit pores,” Chemical Engineering Science, vol. 66, no. 22, pp. 5447–5458, 2011.
- M. M. Dubinin and O. Kadlec, “Novel ideas in the theory of the physical adsorption of vapors on micropore adsorbents,” Carbon, vol. 25, no. 3, pp. 321–324, 1987.
- F. Stoeckli, in Porosity in Carbon Characterization and Applications, J. Patrick, Ed., pp. 67–92, Arnold, London, UK, 1995.
- S. K. Bhatia, “Determination of pore size distributions by regularization and finite element collocation,” Chemical Engineering Science, vol. 53, no. 18, pp. 3239–3249, 1998.
- A. Shahsavand and M. N. Shahrak, “Reliable prediction of pore size distribution for nano-sized adsorbents with minimum information requirements,” Chemical Engineering Journal, vol. 171, no. 1, pp. 69–80, 2011.
- J. Sun, “Pore size distribution model derived from a modified DR equation and simulated pore filling for nitrogen adsorption at 77 K,” Carbon, vol. 40, no. 7, pp. 1051–1062, 2002.
- D. D. Do, C. Nguyen, and H. D. Do, “Characterization of micro-mesoporous carbon media,” Colloids and Surfaces A, vol. 187-188, pp. 51–71, 2001.
- A. Shahsavand and M. N. Shahrak, “Direct pore size distribution estimation of heterogeneous nano-structured solid adsorbents from condensation data: condensation with no prior adsorption,” Colloids and Surfaces A, vol. 378, no. 1–3, pp. 1–13, 2011.
- A. Okhovat and A. Ahmadpour, “A comparative study of the effects of different chemical agents on the pore-size distributions of macadamia nutshell-based activated carbons using different models,” Adsorption Science and Technology, vol. 30, no. 2, pp. 159–169, 2012.
- R. C. Bansal, J. B. Donnet, and F. Stoeckli, Active Carbon, Marcel Dekker, New York, NY, USA, 1988.
- M. M. Dubinin, in Progress in Surface and Membrane Science, D. A. Cadenhead, Ed., Academic Press, New York, NY, USA, 1975.
- M. M. Dubinin, “Generalization of the theory of volume filling of micropores to nonhomogeneous microporous structures,” Carbon, vol. 23, no. 4, pp. 373–380, 1985.
- M. M. Dubinin and O. Keldec, “Microporous adsorbents with limiting developments of micropores,” Adsorpt. Sci. Technol, vol. 4, p. 45, 1987.
- F. Stoeckli, A. Guillot, A. M. Slasli, and D. Hugi-Cleary, “The comparison of experimental and calculated pore size distributions of activated carbons,” Carbon, vol. 40, no. 3, pp. 383–388, 2002.
- P. J. M. Carrott and M. M. L. Ribeiro Carrott, “Evaluation of the Stoeckli method for the estimation of micropore size distributions of activated charcoal cloths,” Carbon, vol. 37, no. 4, pp. 647–656, 1999.
- D. H. Everett and J. C. Powl, “Adsorption in slit-like and cylindrical micropores in the henry's law region, a model for the microporosity of carbons,” Journal of the Chemical Society, Faraday Transactions, vol. 72, p. 619, 1976.
- A. Ahmadpour and D. D. Do, “The preparation of activated carbon from macadamia nutshell by chemical activation,” Carbon, vol. 35, no. 12, pp. 1723–1732, 1997.
- S. J. Gregg and K. S. W. Sing, Adsorption, Surface Area and Porosity, Academic Press, London, UK, 1982.
- A. Ahmadpour, Fundamental studies on preparation and characterization of carbonaceous adsorbents for natural gas storage [Ph.D. thesis], University of Queensland, Queensland, Australia, 1997.
- A. P. Terzyk and P. A. Gauden, “New relationships between the characteristic energy of adsorption and the average effective diameter of carbon slit-like micropores—the dependence on the type of an adsorbate,” Colloids and Surfaces A, vol. 177, no. 1, pp. 57–68, 2001.
Copyright © 2012 Ahmad Okhovat et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.