Investigation of Network Connectivity in Activated Carbons by Liquid

Langmuir 2000, 16, 9303-9313

9303

Investigation of Network Connectivity in Activated Carbons by Liquid Phase Adsorption S. Ismadji and S. K. Bhatia* Department of Chemical Engineering, The University of Queensland, St. Lucia, Brisbane, QLD 4072, Australia Received April 18, 2000. In Final Form: August 31, 2000

The connectivity of the pore network is an important aspect of the structure of porous materials. In this paper we propose a simple percolation theory based method for the determination of pore network connectivity of microporous carbons, using liquid-phase adsorption isotherm data combined with a DFT based pore size distribution. Aqueous phase esters were used as model adsorptives in the experiments, and the isotherms interpreted by the pore filling approach. The Dubinin-Radushkevich equation was modified for nonideality of the bulk phase, which yielded improved correlation of the adsorption data. Based on the estimated saturation capacities, the network coordination number of the carbon adsorbent was determined by the proposed method. In addition, the critical molecular sizes of model esters used in this study, which are largely unknown, were also extracted, and the results quantitatively matched those obtained theoretically from simulation of the molecular structure of the esters.

1. Introduction Activated carbons are materials having complex porous structures with associated energetic as well chemical inhomogeneities. Their structural heterogeneity is a result of the existence of micropores, mesopores, and macropores of different sizes and shapes. The presence of micropores in these solids substantially increases their sorption capacities over those for nonporous and mesoporous materials, and micropore characterization is one of the key problems in understanding the structure of these adsorbents. The macropores and large mesopores play an important role in the molecular transport process, whereas the remaining smaller pores determine the sorption properties of a given carbon. The energetic and chemical heterogeneities are determined by the variety of surface functional groups, irregularities, and strongly bound impurities, as well as structural nonuniformity. This heterogeneity considerably influences the process of physical adsorption. Characterization of the pore structure of the activated carbons is crucially important to adsorption and separation processes. A variety of techniques such as adsorption, mercury porosimetry, high-resolution transmission electron microscopy, image analysis, and small-angle X-ray scattering1,2 have been applied to characterize the pore structure of carbons. The most commonly used technique employed for the characterization of the pore structure of activated carbons is the physical adsorption of gases and vapors. This technique is used because of its convenience and its ability to provide information over a wide range of pore sizes. The large amount of research activity in this area is a strong indicator of the importance of adsorption measurements for characterizing the structural and surface heterogeneity of the activated carbons.3,4 However, * Corresponding author. Fax: +61-7-3365 4199. Tel.: +61-73365 4263. Email: [email protected]. (1) Bhatia, S. K.; Shethna, H. K. Langmuir 1994, 10, 3230. (2) Byrne, J. F.; Marsh, H. In Porosity in Carbons: Characterization and Application; Patrick, J. W., Ed.; Edward Arnold: London, 1995; pp 2-46.

although potentially important5 and simpler than gas phase adsorption, liquid phase adsorption measurements, especially those involving dilute aqueous solutions, are seldom used for characterizing the pore structure of activated carbons. Characterization of the structural heterogeneity of activated carbon is generally made in terms of the pore size distribution. Quantification of the latter is most commonly performed by employing the generalized adsorption equation in conjunction with a local isotherm model. Among the various models for physical adsorption on microporous solids, the Dubinin theory of micropore filling is long established from the viewpoint of data correlation as well as for gaining physical insight. Although other models exist, the Dubinin model is among the most popular because of its simplicity, and because it provides a good description of the adsorption of a variety of vapors by microporous carbons.6-8 This Dubinin approach forms the basis for many adsorption equations that are currently employed for the description of equilibria in activated carbons, among the most widely used of which is the Dubinin-Radushkevich (DR) equation. The Dubinin-Radushkevich equation has a uniform form that is useful for all adsorbates. Another important characteristic of the structure of porous materials, which governs their reaction and transport properties is the connectivity of the pore network. The most common method of quantifying this is in the terms of a coordination number Z, defined as the number of pores intersecting at a junction or node. Different methods have been developed for determining (3) Jaroniec, M.; Madey R. Physical Adsorption on Heterogeneous Solid Surface; Elsevier: Amsterdam, 1988. (4) Rudzinski, W.; Everet, D. H. Adsorption of Gases on Heterogeneous Surfaces; Academic Press: New York, 1991. (5) Choma, J.; Mortka, W. B.; Jaroniec, M.; Gilpin, R. K. Langmuir 1993, 9, 2555. (6) Stoeckli, H. F. In Porosity in Carbons: Characterization and Application; Patrick, J. W., Ed.; Edward Arnold: London, 1995; pp 67-91. (7) Chen, S. G.; Yang, R. T. Langmuir 1994, 10, 4244. (8) Do, D. D. Adsorption Analysis: Equilibria and Kinetics; Imperial College Press: London, 1998.

10.1021/la000578m CCC: $19.00 © 2000 American Chemical Society Published on Web 11/04/2000

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the network connectivity, and are most commonly based on the percolation theory interpretation of mercury intrusion9 or nitrogen adsorption data.10-14 These approaches generally utilize the property that in randomly connected pore networks, when pores larger than a critical size become available (such as during mercury intrusion or nitrogen desorption) only a certain fraction of these are actually accessible. This is because in such networks there is a finite probability that a supercritical pore is connected only through subcritical pores and is therefore not accessible. When the fraction of supercritical pores attains a sufficiently large value, known as the percolation threshold, breakthrough occurs and the mercury or nitrogen meniscus begins to percolate. This threshold is dependent on the coordination number Z and the morphology of the pore network, and measurement of breakthrough pressure is therefore often used to determine Z. Most recently Seaton and co-workers have determined network connectivity based on adsorption for different gases. Thereby, they have determined pore size distribution by studying the influence of pore exclusion due to finite molecular size.15 In this study simple gas molecules such as nitrogen, CH4, CF4, and SF6, whose theoretical isotherms can be conveniently analyzed by molecular simulations methods, have been used. The present work deals with the use of liquid-phase adsorption methods with more complex molecules to determine the network connectivity features. The adsorption of three different esters on three carbons is analyzed by the Dubinin-Radushkevich model, improved to include liquid-phase nonideality, to determine the capacity for each ester. This capacity is interpreted by means of percolation theory modeling to extract the connectivity features of the carbons, while utilizing the pore size distribution of the carbon based on density functional theory (DFT) characterization with a small adsorptive molecule such as argon. The technique also yields the critical molecular dimension of the liquid-phase adsorptive, which is found to compare well with the corresponding value obtained by geometry optimization of the potential energy surfaces of the molecules. 2. DR Equation and Effect of Nonideality In the present work liquid-phase adsorption by microporous carbons is described by the theory of volume filling of micropores developed by Dubinin and co-workers. The fundamental relation used is the Dubinin-Radushkevich (DR) equation that has been widely used for gas phase adsorption, especially for the calculation of the parameters of the porous structure of adsorbents,16-22 and (9) Larson, R. G.; Morrow, N. R. Powder Technol. 1981, 30, 123. (10) Zhdanov, V. P.; Fenelonov, V. B.; Efremov, D. K. J. Colloid Interface Sci. 1987, 120, 218. (11) Mason, G. Proc. R. Soc. London. 1988, A415, 453. (12) Seaton, N. A. Chem. Eng. Sci. 1991, 46, 1895. (13) Liu, H.; Seaton, N. A. Chem. Eng. Sci. 1994, 49, 1869. (14) Murray, K. L.; Seaton, N. A.; Day, M. A. Langmuir 1999, 15, 6728. (15) Lopez-Ramon, M. V.; Jagiello, J.; Bandosz, T. J.; Seaton, N. A. Langmuir 1997, 13, 4435. (16) Bradley, R. H. Carbon 1991, 29, 893. (17) Burevski, D. Carbon 1997, 35, 1001. (18) Rychicki, G.; Terzyk, A. P. Ads. Sci. Tech. 1998, 16, 641. (19) Mangun, C. L.; Daley, M. A.; Braatz, R. D.; Economy J. Carbon 1998, 36, 123. (20) Diaz, L.; Huesca, R. H.; Armenta, G. A. Ind. Eng. Chem. Res. 1999, 38, 1396. (21) Ehrburger, P.; Pusset, N.; Dziendzinl, P. Carbon 1992, 30, 1105. (22) Dobruskin, V. K. Langmuir 1996, 12, 987.

Ismadji and Bhatia

has the following form

[(

nDR ) n∞ exp -

)]

RT ln(ps/p) βEo

2

(1)

Here n∞ is the maximum capacity of the micropores, n is the amount adsorbed, ps is the saturation pressure, β is an affinity coefficient of the characteristic curves, and Eo is the characteristic energy of adsorption. In utilizing the DR equation in the present work our principal aim is to determine the saturation capacity n∞ . The latter is subsequently used to extract the network connectivity parameter Z, by exploiting the relation between pore accessibility and n∞. Although the use of the Dubinin-Radushkevich equation for gas-phase adsorption is common, very little is reported on its application for the adsorption of organic compounds from dilute solutions on activated carbon.5 For adsorption from the liquid phase the DR equation is generally written as follows:

[(

nDR ) n∞ exp -

)]

RgT ln(Cs/Ce) βEo

2

(2)

where Cs is solute solubility at given temperature T, and Ce is equilibrium concentration. Equation 2 considers the liquid phase to be ideal, an assumption that can lead to inaccuracies with regard to the description of real system behavior. In this work therefore we have considered the nonideality of the liquid phase in applying the DR model. This nonideality can be incorporated by defining an activity coefficient for the liquid phase, following

γli(T,Ci,xi) ≡

ai fiL ) o xi x f

(3)

i i

where ai is the activity of component i, fil and fio are the fugacities of ester in liquid mixture and fugacity of pure species, respectively. The concentration dependence of γil is expressed through the UNIFAC activity coefficient model23 which is well-established and is only briefly described here. The model has the form: ad ad ln γad i ) ln γi (combinatorial) + ln γi (residual) (4)

The combinatorial term is evaluated using

ln γiad(combinatorial) ) Φi z Φi θi ln + qi ln + li xi 2 Φi xi

()

∑j xjlj

(5)

with li ) (ri - qi)z/2 - (ri - 1). Here z is the average coordination number, usually taken to be 10, while qi and ri are the surface area and size parameters of species i, respectively. Further, Φi and θi represent the volume and area fractions of species I, obtained from molar averages over ri and qi respectively. The residual term is evaluated by a group contribution method, so that the mixture is envisioned as being a mixture of functional groups, rather (23) Sandler, S. I. Chemical and Engineering Thermodynamics; Wiley: New York, 1999.

Network Connectivity in Activated Carbons by LPA

Langmuir, Vol. 16, No. 24, 2000 9305 Table 1. Structural Characteristics of Activated Carbons Used sorption characteristics

Filtrasorb400

Norit ROW 0.8

Norit ROX 0.8

BET surface area, m2/g micropore surface area, m2/g micropore volume, cm3/g total pore volume, cm3/g

877.82 761.8 0.343 0.468

849.39 718 0.314 0.443

978.85 847 0.365 0.467

Figure 1. Schematic illustration of the pore network accessibility. The empty pores are inaccessible.

than of molecules.

ln γad i (residual) )

∑k vk(i)[ln Γk - ln Γ(i)k ]

(6)

Here vk(I) is the number of k groups present in the species i, and Γk is the residual contribution to the activity coefficient of group k and can be defined as

[

ln Γk ) Qk 1 - ln(

∑ m

ΘmΨmk) -

ΘmΨkm

]

∑ m ∑n ΘnΨnm

(7)

where Θm is surface area fraction of group m, and Ψnm is equal to exp(-anm/T). Here anm is a binary parameter for each pair of functional groups, tabulated in Reid et al.24 In terms of the liquid-phase activities, eq 5 can be written in the following form:

[(

nDR ) n∞ exp -

)]

RgT ln(as/ae) βEo

2

(8)

where as and ae are the activity of the adsorptive in the bulk liquid at saturation and at equilibrium concentration, respectively. 3. Network Connectivity The behavior of transport and reaction properties on the porous materials is very strongly affected by the internal structure of porous materials. There are now many different technique available for characterizing the structure of porous materials. These techniques are based on direct measurement, such as xenon NMR and size exclusion chromatography, or indirect measurement, such as gas adsorption. To obtain structural information from indirect measurement experimental data, a model of the pore network is required. As previously indicated, the most common and simplest concept for characterizing the topology of porous materials based on percolation theory is the mean coordination number of the pore network, Z. (24) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids; McGraw-Hill: New York, 1987.

Figure 2. Adsorption isotherms of argon at 87 K on the three carbons used.

For the carbon materials to be investigated here it is assumed that the individual pores (or network elements) are slit-shaped, and that the length and breadth are uncorrelated with pore width. For a given network, the number fraction of the pores that can accommodate a given probe molecule can be written as:

f(H) dH H Φ) ∞f(H) dH 0 H

∫d∞

m

∫

(9)

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Ismadji and Bhatia

Figure 3. Pore size distributions of the activated carbons.

where dm is molecular size of the probe molecule, H is the slit-width of the pore, and f(H) is the pore volume distribution of the activated carbon. However, although large enough to accommodate the probe molecules, some of these pores will be connected only through smaller impenetrable pores and are not accessible to the probe molecules, as depicted in Figure 1. The fraction of the pores that are actually accessible to the probe molecules Φa is a function of the network topology and coordination number Z, as well as the fraction of available pores Φ. This accessible fraction Φa is generally obtained by computer simulation; however, the results may often be represented by correlations that are convenient to use. A simple expression obtained by Zhang and Seaton25 for cubic lattices (having Z ) 6) has been generalized by Lopez-Ramon et al.15 to an arbitrary Z coordinate lattice (25) Zhang, L.; Seaton, N. A. Chem. Eng. Sci. 1996, 51, 3257.

Figure 4. Plot of adsorption isotherm of ethyl propionate in the form of DR characteristic curve on (a) Filtrasorb 400, (b) Norit ROW 0.8, and (c) Norit ROX 0.8. The units of n are mg ester/g carbon.

as follows:

Φa ) 0, Φ e (1.494/Z)

(10)

Φa ) [1.314(ΦZ - 1.494)0.41 + 3.153(ΦZ - 1.494) 3.48(ΦZ - 1.494)2 + 1.433(ΦZ - 1.494)3]/Z, (1.494/Z) < Φ < (2.7/Z) (11) Φa ) Φ, Φ g (2.7/Z)

(12)

Based on the fraction of pores accessible to a given probe


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Figure 5. Variation of bulk liquid-phase activity with equilibrium concentration for (a) ethyl propionate, (b) ethyl butyrate, and (c) ethyl isovalerate. Table 2. Parameter Values Used in UNIFAC Model for Activity Coefficient Estimation compound UNIFAC parameter

ethyl propionate

ethyl butyrate

ethyl isovalerate

ri qi li

4.1530 3.6560 -0.6680

4.8274 4.1960 -0.6704

5.5010 4.7320 -0.6560

molecule, Φa, the accessible pore volume may be readily estimated as

Va )

a

Φ Φ

∫d f(H)dH ∞

m

(13)

which may be compared with that actually accessed Vexp a to obtain the coordination number Z by nonlinear leastis squares fitting. A reasonably good estimate of Vexp a obtained from n∞ by assuming that the density of the saturated adsorbate is that of the saturated pure liquid at ambient temperature. The pore volume distribution f(H) may be obtained by DFT characterization based on gas-phase adsorption data for a small molecule such as argon, to which the entire pore volume may be considered accessible. 4. Experimental Section 4.1. Materials and Characterization. Food grade industrial activated carbons were used as the adsorbents in this study.

Figure 6. The characteristic DR equation plot for (a) ethyl propionate, (b) ethyl butyrate, and (c) ethyl isovalerate on activated carbon Filtrasorb 400. The units of n are mg ester/g carbon. Granular activated carbon, Filtrasorb 400, a commercially available coal based activated carbon, produced by Calgon Carbon, as well as Norit ROX 0.8 (acid washed) and its unwashed parent carbon Norit ROW 0.8 activated carbon pellets, were chosen as the adsorbents. Prior to each isotherm measurement, the activated carbons were repeatedly washed with RO water to remove fine particles and degassed under nitrogen at 250 °C for 16 h. Subsequently the following characteristics were determined for each carbon: BET surface area, micropore surface area, micropore volume, total pore volume and the pore size distribution. These were obtained on an automatic Micromeritics ASAP2010 volumetric sorption analyzer, using argon adsorption at 87.15 K, and are summarized in Table 1. The micropore surface area of the carbon was obtained based on argon adsorption at 87.15 K using Dubinin-Asthakov analysis, while the micropore

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Ismadji and Bhatia

Figure 7. The characteristic DR equation plot for (a) ethyl propionate, (b) ethyl butyrate, and (c) ethyl isovalerate on activated carbon Norit ROW 0.8. The units of n are mg ester/g carbon.

Figure 8. The characteristic DR equation plot for (a) ethyl propionate, (b) ethyl butyrate, and (c) ethyl isovalerate on activated carbon Norit ROX 0.8. The units of n are mg ester/g carbon.

volume and total pore volume were obtained by density functional theory (DFT) analysis of the isotherm. The micropore volumes that are shown in Table 1 correspond to those in pores smaller than 2.52 nm, while the total pore volume is that in pores smaller than 80 nm. The adsorbates investigated were ethyl propionate, ethyl butyrate, and ethyl isovalerate, obtained as analytical grade. The adsorbates were purchased from Sigma Aldrich Pty., LTD (NSW, Australia) with purity about 98-99%. The specific gravities for these were listed by the manufacturer as 0.891, 0.878, and 0.868, and refractive indices as 1.384, 1.392, and 1.396 for ethyl propionate, ethyl butyrate, and ethyl isovalerate, respectively.

4.2. Adsorption Procedure. In the adsorption experiment, the adsorbate solution was prepared by mixing a known amount of adsorbate with deionized water to yield various desired concentrations. The adsorption experiments were carried out isothermally in static mode at three different temperatures, 303.15, 308.15, and 313.15 K. The experiments were conducted by adding a fixed amount of activated carbon (0.2-0.7 g) to a series of 250 mL glass-stoppered flasks filled with 200 mL diluted solutions. The glass stoppered flask was then placed in a thermostatic shaker bath and shaken at 120 rpm for 2 days. Product analysis showed that the equilibrium condition was reached by about 24 h. The initial and equilibrium concentrations of all liquid samples were analyzed by means of a Shimadzu gas chromatograph (GC-


Langmuir, Vol. 16, No. 24, 2000 9309

Figure 9. Molecular structure of the esters. 17A) provided with a flame ionization detector. The amount adsorbed on the activated carbon was determined from the initial liquid-phase concentration of the adsorptive, and the concentration at equilibrium.

Table 3. Accessible Pore Volume of Activated Carbon Estimated from DR Plots accessible pore volume, cm3/g

5. Results and Discussion

esters

Filtrasorb400

Norit ROW 0.8

Norit ROX 0.8

5.1. Characterization of Activated Carbons. The adsorption isotherms of argon on Filtrasorb 400, Norit ROW 0.8, and Norit ROX 0.8 activated carbons are shown in Figure 2. These isotherms clearly show the largely microporous nature of the carbons, with some mesopores leading to a gradual increase in adsorption after the initial filling of the micropores, followed by a more rapid increase near saturation. From analyzing the values of parameters characterizing argon adsorption on the studied carbon (see Table 1) it is evident that the values of BET surface area, micropore surface area, micropore volume, and total pore volume are the highest for the carbon Norit ROX 0.8, and they are the lowest for the activated carbon ROW 0.8. When the activated carbon is washed with acid (Norit ROX 0.8), the micropore volume and total pore volume of the carbon increase. The pore size distribution of Filtrasorb-400, Norit ROW 0.8, and Norit ROX 0.8 obtained based on argon adsorption, using the Micromeritics package implementing DFT with

ethyl propionate ethyl butyrate ethyl isovalerate

0.310 0.327 0.275

0.269 0.259 0.228

0.426 0.343 0.254

regularization, are depicted in Figure 3. The regularization-based distribution is clearly bimodal in each case, with peaks around 0.45-0.55 nm and 1.4-1.6 nm. 5.2. Effect of Nonideality. Figure 4 presents the plot of adsorption isotherm of ethyl propionate on the different carbons in the form of ln(n) versus ln[RgTln(Cs/Ce)]2. It can be seen that substantial linearity was observed for all the carbons, supporting the choice of the DubininRadushkevich (DR) model for correlating the data. In a recent article26 we have compared the fits of a number of traditional isotherms (Unilan, Toth, Sips, and DubininRadushkevich) to the data for adsorption of the esters on Filtrasorb F-400, and found only the DR model to yield physically realistic and consistent parameters. (26) Ismadji, S.; Bhatia, S. K. Can. J. Chem. Eng. 2000, accepted.

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Figure 10. Molecular structure of ethyl propionate viewed in different configuration in a carbon slit pore. (a) Critical configuration, and (b) configuration requiring larger pore size.

The significance of the liquid phase activities can be most simply visualized by means of Figure 5 which depicts the variation of relative activity with relative concentration at the three experimental temperatures for each of the adsorptives. Table 2 lists the values of the UNIFAC parameters ri, qi, and li that were used, determined from group volume and surface area parameters listed by Sandler.23 The calculated results obtained from the UNIFAC model are represented by the symbols and cover the range of values pertinent to the experiments. At low relative concentrations the deviation of ae/as from Ce/Cs is small, but increases with increase in Ce/Cs. Clearly, over the range of the current data the deviation of activity ratio from concentration ratio is most significant for ethyl propionate, where the activity ratio is larger by as much as 25-30% at the higher concentrations used. For the other esters deviations of up to 10-15% are evident. As a result of these deviations further correlation of the data was performed using the activity ratio in place of the concentration ratio, yielding somewhat better conformity with the expected behavior on the characteristic linear plots as in Figure 4. The characteristic plots for adsoprtion of ethyl propionate, ethyl butyrate, and ethyl isovalerate on Filtrasorb 400, Norit ROW 0.8, and Norit ROX 0.8 in the form of ln(n) versus ln[RTln(ae/as)]2 are shown in Figures 6-8. The intersection of the characteristic lines with the ordinate gives the maximum amounts of esters adsorbed on each carbon, and thereby the accessible volumes. The results are summarized in Table 3. These values were subsequently used for the determination of the connectivity parameter of the carbon as discussed in the next section. 5.3. Determination of Pore Network Connectivity. Determination of the mean coordination number, Z, was performed by means of eqs 9-13 using two different

Ismadji and Bhatia

Figure 11. Critical molecular size and configuration of (a) ethyl butyrate, and (b) ethyl isovalerate in carbon slit pore.

methods. For the first method the critical molecular size of each ester was first estimated using a molecular structure simulation method, implemented in the Cambridge Soft Chem3D software package, and the mean coordination number of each activated carbon was chosen as the fitted parameter. A nonlinear least squares procedure was used to minimize the error between the experimental and predicted accessible pore volumes. The latter is estimated from eqs 9-13 using the DFT based pore size distribution. The molecular size calculations by the molecular structure simulation are based on geometry optimization of the potential energy surfaces of the molecules. In the geometry optimization, the atomic coordinates in the compound are systematically modified in the model to identify a local energy minimum. In the first step the structural model of the molecule is created through the geometry optimization and then the model of the molecule is rotated in different angles and axes until the critical size of the molecule is found. These processes are iterative and begin at some starting geometry and continue until convergence is achieved, at which point the minimization process terminates. The ability of this technique to converge to a minimum strongly depends on the starting geometry that we create, the potential energy function used, and the convergence criteria.27 The molecular sizes of ethyl propionate, ethyl butyrate, and ethyl isovalerate obtained by this molecular simulation procedure are 0.5089, 0.5299, and 0.5815 nm respectively. Diagrams of the flavor esters model molecules and their structure are shown in Figures 9-11. In Figures 10 and 11 the carbon atoms are shown in black, hydrogen in yellow, and oxygen in red. In this method of determining (27) User’s Guide. Chem3D Molecular Modeling and Analysis; Cambridge Soft: Cambridge, MA, 1997.


Langmuir, Vol. 16, No. 24, 2000 9311 Table 4. Fitted Values of Molecular Size and Mean Coordination Number molecular size of ethyl propionate (DEP) molecular size of ethyl butyrate (DEB) molecular size of ethyl isovalerate (DEI) mean coordination number of F-400 (ZF) mean coordination number of Norit ROW 0.8 (ZW) mean coordination number of Norit ROX 0.8 (Zx)

0.512 nm 0.537 nm 0.577 nm 2.97 4.00 4.06

Figure 12. Correlation between accessible pore volume and fitted molecular size. (a) Filtrasorb-400, (b) Norit ROW 0.8, and (c) Norit ROX 0.8.

the coordination number Z the fitting for each carbon could be done individually. The fitted mean coordination number of Filtrasorb 400, Norit ROW 0.8, and Norit ROX 0.8 are 2.91, 4.16, and 4.07, respectively. The correlations of accessible pore volume with the molecular size obtained from molecular simulation are shown in Figure 12 for the experimental data, as well as percolation theory based fitted values. For the second method the molecular sizes of the esters (dEP, dEB, and dEI, for ethyl propionate, ethyl butyrate, and ethyl isovalerate, respectively) and the mean coordination number of each carbon (ZF, ZW, and ZX, for Filtrasorb 400, Norit ROW 0.8, and Norit ROX 0.8, respectively) were chosen as the fitting parameters. The accessible pore volumes of each adsorbate-adsorbent system obtained through the DR plots were then jointly

Figure 13. Correlation between accessible pore volume and molecular size obtained from simulation. (a) Filtrasorb 400, (b) Norit ROW 0.8, and (c) Norit ROX 0.8.

fitted using the nonlinear least-squares approach to determine the fitting parameters. The fitted values of molecular size of each ester and the mean coordination number of each carbon are given in Table 4. The variation of accessible pore volume with fitted molecular size is depicted for each carbon in Figure 13. Good agreement between the experimental and theoretical pore volume can be observed from this figure. From Table 4 it can be

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Figure 15. Effect of molecular size on actual accessible (a) pore number fraction, and (b) pore volume.

Figure 14. Correlation between fitted molecular size and that from (a) molecular simulation, and (b) critical volume.

seen that fitted value of Z obtained by this second method is in excellent agreement with the first method. This evidence supports the validity of the second method for determination of the mean coordination number. While comparing the fitted molecular sizes and those obtained from molecular simulation, the effective molecular sizes of the esters were also estimated using a wellknown correlation recommended by Reid et al.24

σ ) 0.809Vc1/3

(14)

where σ is the effective Lennard-Jones size parameter in A, and Vc is the critical volume in cm3/gmol. The values of σ for the three esters were obtained as 0.567 nm for ethyl propionate, 0.606 nm for ethyl butyrate, and 0.642 nm for ethyl isovalerate. Figure 14 depicts the correlation of fitted molecular size with that obtained from simulation as well as that calculated by eq 14. Clearly, excellent correlation between fitted and theoretical critical molecular size is evident, supporting the procedure of the second method, in spite of the larger number of fitting parameters. In addition, a large difference between the fitted critical molecular size and that estimated by eq 14 is observed, with the theoretical critical sizes being significantly

smaller. This is clearly due to the asymmetry of the ester molecules, as seen in Figures 10 and 11 with the lateral dimension being significantly larger than the minimal dimension in the critical orientation. A good indication of the validity of the method is obtained not only from the values of fitted critical molecular sizes, which are only slightly different from those obtained by molecular simulation, but also from the fact that the mean coordination number obtained from both methods is also substantially the same. Examination of Z values of Norit ROW 0.8 and Norit ROX 0.8 shows that the acid washing increases the connectivity of the pore network only marginally, from about 4.07 to 4.16. Figures 15A and B depict the theoretical decrease in accessible number fraction and pore volume with increase of the molecular size, using Norit ROX 0.8 as an example (Z ) 4.06). From this figure it can be seen that the pore network becomes more accessible as the size of probe molecule decreases. In heterogeneous materials such as activated carbon, the pores are connected randomly and the probe molecule will penetrate and fill only those pores that are connected through pores larger than its critical dimension. However, pores connected only through those that are too small to accommodate the probe molecule cannot be penetrated, and are shielded by the small pores. All of the three carbons were more accessible to ethyl propionate since this ester has the smallest molecular size of three esters used. This is indicated by the higher accessible pore volume of ethyl propionate in comparison to that of the other esters.


Langmuir, Vol. 16, No. 24, 2000 9313

Table 5. Accessible Surface Area of Activated Carbons compounds

F-400, m2/g

Norit ROW 0.8, m2/g

Norit ROX 0.8, m2/g


631.15 597.52 554.48

532.89 490.31 425.39

662.24 639.49 555.78

The accessible surface areas of the carbons were also calculated by the following equation

Sacc )

Φa Φ

∫d∞ H2 f(H)dH m

(15)

and the results are summarized in Table 5. Here we did not estimate surface areas using slope of DubininRadushkevich characteristic curve because the usual form of of βEo ) (βk/H) in the DR equation does not include repulsive interactions that are important at molecular scales, and is therefore inaccurate. By knowing the accessible surface area and assuming that the adsorption takes place predominantly in a monolayer near each pore wall, the effective molecular area of the ester can be calculated by

am ) Sacc/(n∞No)

(16)

where No is Avogadro’s number, and n∞ is the maximum amount of ester adsorbed. The effective molecular areas obtained from eqs 15 and 16 may be compared with those from

A ) 1.091

( ) M NoF

2/3

(17)

where M is the molecular weight and F is the liquid density.

Table 6. Effective Molecular Areas of the Esters Calculated from Theoretical Correlation and from Monolayer Assumption

compounds

theoretical correlation, nm2/molecule


0.361 0.4 0.432

monolayer assumption, nm2/molecule Norit Norit F-400 ROW 0.8 ROX 0.8 0.363 0.427 0.533

0.331 0.421 0.512

0.325 0.392 0.511

These values are summarized in Table 6, showing substantial agreement. Nevertheless, the molecular effective area of ethyl isovalerate calculated from eq 16 is about 20% higher than that predicted by eq 17. This is most likely due to the inaccuracy of eq 17 for compounds that have branches in the primary chain, and the complex effect of molecular orientation in these cases. 6. Conclusions The present work indicates that liquid phase adsorption can be reliably used to determined the pore network connectivity of activated carbons. Two different methods were used to determine the mean coordination number, Z, with good agreement between these two methods. In one of these the molecular size of the adsorbates used was determined by molecular simulation, while in the other it was obtained by parameter fitting, and excellent agreement between the two values was obtained. The effect of nonideality in the liquid phase on the DubininRadushkevich equation is also discussed in this paper, and an improvement of the model for applications to liquidphase adsorption is presented. LA000578M

Investigation of Network Connectivity in Activated Carbons by Liquid

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