Letter pubs.acs.org/Langmuir
Unified Method for the Total Pore Volume and Pore Size Distribution of Hierarchical Zeolites from Argon Adsorption and Mercury Intrusion Jeffrey Kenvin,*,† Jacek Jagiello,† Sharon Mitchell,‡ and Javier Pérez-Ramírez‡ †
Micromeritics Instrument Corporation, 4356 Communications Drive, Norcross, Georgia 30093, United States Institute for Chemical and Bioengineering, Department Biosciences, ETH Zürich, Vladimir Prelog Weg 1, CH 8093 Zurich, Switzerland
‡
ABSTRACT: A generalized approach to determine the complete distribution of macropores, mesopores, and micropores from argon adsorption and mercury porosimetry is developed and validated for advanced zeolite catalysts with hierarchically structured pore systems in powder and shaped forms. Rather than using a fragmented approach of simple overlays from individual techniques, a unified approach that utilizes a kernel constructed from model isotherms and model intrusion curves is used to calculate the complete pore size distribution and the total pore volume of the material. An added benefit of a single fullrange pore size distribution is that the cumulative pore area and the area distribution are also obtained without the need for additional modeling. The resulting complete pore size distribution and the kernel accurately model both the adsorption isotherm and the mercury porosimetry. By bridging the data analysis of two primary characterization tools, this methodology fills an existing gap in the library of familiar methods for porosity assessment in the design of materials with multilevel porosity for novel technological applications.
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INTRODUCTION
often used separately to assess the pore volume and pore size distribution. For example, it is quite common to use argon or nitrogen adsorption isotherms for the characterization of micropores and mesopores and complement those results with mercury intrusion to assess the mesopores and macropores independently.7,8 The routine use of adsorption and porosimetry for the characterization of porous materials9−18 has also included extensive discussions on the agreement between these two methods. Each technique provides a method to determine the pore volume and pore size distributions. Adsorption methods may be used to determine the micropore and mesopore volume whereas mercury intrusion provides the mesopore and macropore volume. The cumulative pore volume from mercury intrusion11,19 is often less than the absolute pore volume obtained from density measurements, and this limitation has required the absolute pore volume of a material to be determined from density measurements.19,20 This limitation was attributed to the maximum pressure that may be achieved during intrusion, and this restricts the accessibility of mercury to the entire pore structure and, in particular, micropores and mesopores less than 3 nm are not probed by mercury intrusion. However, capillary condensation10 during adsorption is often used to characterize pore sizes from 2 to 50 nm, and this restricts the pore volume determined by adsorption to the combined contributions of the micropores and mesopores.
The development of complex porous materials such as hierarchically-structured zeolites combining networks of macropores, mesopores, and micropores finds relevance in diverse technological applications,1−4 and an illustration of the multilevel porosity is given in Figure 1. Traditionally, the textural characterization employed during new material synthesis and, in particular, for porous materials has relied upon adsorption and mercury intrusion to determine parameters such as the surface area and porosity.5,6 These techniques are
Figure 1. Trimodal porosity of hierarchical zeolite extrudates; the micropores and intracrystalline mesopores originate within the desilicated ZSM-5 crystals, and the macropores originate from the interparticle space between zeolite and binder particles. © XXXX American Chemical Society
Received: November 24, 2014 Revised: January 9, 2015
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DOI: 10.1021/la504575s Langmuir XXXX, XXX, XXX−XXX
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Figure 2. Example model intrusion curves (M) for pore diameters in μm and model isotherms (A) for pore diameters in angstroms. NaOH (0.2 M, 338 K, 30 min, 30 cm3 gzeolite−1). The resulting solids (coded Z40-H1 and Z50-H1) were subsequently converted to the protonic form by three consecutive treatments in aqueous NH4NO3 (0.1 M, 338 K, 6 h, 100 cm3 gzeolite−1), followed by calcination at 823 K (5 K min−1) for 5 h. The hierarchical zeolite extrudates (Ex) were manufactured at Zeochem Ag by extrusion with a kaolin clay binder (zeolite/binder dry mass ratio = 4). Argon isotherms (87 K) were recorded using a Micromeritics ASAP 2020. Prior to the sorption measurements, the samples were outgassed at 573 K under a turbomolecular pump vacuum for 8 h. Mercury intrusion curves (293 K) were obtained using an AutoPore 9520 operated from vacuum to 418 MPa.7,22 Samples were degassed in situ prior to measurement. A contact angle of 140° for mercury and a pressure equilibration of 10 s were applied. The CPSD and TPV are calculated from a kernel composed of theoretical mercury intrusion curves and model isotherms. The kernel takes the basic form of
On the basis of the limited ranges of porosity that may be characterized via adsorption or intrusion,11 the cumulative pore volume from intrusion versus the cumulative pore volume from adsorption10 should never be compared, and the results from both may be required to assess the absolute pore volume of the material. The inability of either method to obtain the absolute pore volume led Joyner et al.11 to propose using a portion of the cumulative pore volume from adsorption10 and a portion of the intrusion curve,9 and the two curves were joined at a diameter corresponding to 8 nm. In a similar manner, the range restricted the use of mercury intrusion (pore diameter >20 nm), and gas adsorption (pore diameters of between 1 and 30 nm) was also proposed by Davis15 to address the concerns and limitations of each technique. Previously, the pore size distribution from mercury intrusion17 has been used to calculate an equivalent adsorption isotherm, and molecular simulation21 has been used to model both adsorption and intrusion. These modeling approaches assume that a single pore size distribution exists that may then be used to predict the adsorption isotherm or mercury intrusion. In this work, we also consider that a single, complete pore size distribution (CPSD) and total pore volume (TPV) exist and may be calculated from a model that combines model adsorption isotherms and mercury intrusion curves. This approach is validated for an important class of hierarchically structured zeolites, integrating macropores and mesopores to facilitate access to the active sites within the micropores in powder and shaped form, allowing for the development of the catalyst while simultaneously addressing the future needs of scale-up to technical catalyst bodies. Simultaneous use of the mercury intrusion and adsorption isotherm is employed to calculate the CPSD and TPV, and this avoids the tedious multistep approach of calculating a pore size distribution from the adsorption isotherm and a pore size distribution from mercury intrusion and then subjectively constructing the pore size distribution of the material from a portion of the intrusionbased distribution and a portion of the isotherm-based distribution. The CPSD and TPV have the added benefit that a single pore size distribution may be used to model the measured adsorption isotherm and the mercury intrusion.
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M v A xd = n , xd ≥ 0 0 λL
(1)
where M is a matrix of model intrusion curves and v is the experimentally measured mercury intrusion, A is a matrix of model isotherms and n is the experimentally measured adsorption isotherm, and λL is used for regularization. The incremental pore volume (xd) is calculated using non-negative least squares (NNLS).23,24 The total pore volume is the cumulative sum of the incremental pore volumes (xd), and the complete pore size distribution may then be calculated by taking the derivative of the total pore volume with respect to the pore diameter.25 The matrix of model intrusion curves (M) is calculated using the Washburn equation.26 p=−
4γ cos θ d
(2)
The model intrusion curves have the form of pressure (p) versus cumulative intrusion volume (1 cm3) at a certain pore diameter (d), assuming a mercury surface tension (γ) of 486.5 dyn/cm and a contact angle (θ) of 140°. The Washburn equation continues to be recommended by IUPAC27 for the interpretation of mercury intrusion data. However, both semiempirical28,29 and more advanced alternatives such as mean field−density functional theory29 exist. The semiempirical alternative29 (Rigby equation) is given by
d=2×
EXPERIMENTAL SECTION
Materials, Models, and Methods. The preparation and characterization of the hierarchically structured zeolites have been previously reported.7,22 Briefly, the conventional ZSM-5 zeolites (CBV 8014 from Zeolyst International, nominal Si/Al = 40, and PZ-2/100 from Zeochem Ag, nominal Si/Al = 50) were treated in aqueous
302.533 +
91526.216 + 1.478p p
(3)
where the pressure (p) is in MPa and the diameter (d) is in nanometers, and this equation has been calibrated for silica in the range of 12 to 199.5 nm. This Washburn equation alternative is effective for the deconvolution of the contact angle component of the hysteresis from the structural component29 for controlled pore glass B
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Figure 3. Pore volume (blue lines, Washburn) and complete pore size distributions (red solid lines, Washburn; red dashed lines, Rigby) (UM40, UM50, and UMEX) for three hierarchically structured zeolites (Z40-H1, Z50-H1, and extrudate) are obtained from mercury intrusion and argon adsorption. The pore size and cumulative pore volumes from mercury porosimetry (Hg40, Hg50, and HgEX) and argon adsorption (Ar40, Ar50, and ArEX) are provided for comparison.
Table 1. Pore Volume and Area for the Unified Method and Individual Techniquesa pore area, m2/g
pore volume, mL/g sample
method
Vmicro
Vmeso
Vmacro
total
Amicro
Ameso
Amacro
Z40-H1
UM Hg Ar UM Hg Ar UM Hg Ar
0.18
0.33 0.37 0.28 0.29 0.28 0.16 0.26 0.28 0.19
0.37 0.38
0.88 0.74 0.45 1.10 0.96 0.34 0.73 0.58 0.37
1346
106 119 122 94 135 145 87 99 62
7 7
Z50-H1
extrudate
0.18 0.18 0.18 0.17 0.17
0.63 0.68 0.30 0.31
1125 1308 1475 1296 918
18 19 7 8
a
The pore volume and area are distributed among the microregion, mesoregion, and macroregion as designated by IUPAC:27 the microregion is 0.3−2 nm, the mesoregion is 2−50 nm, and the macroregion is >50 nm. previously calculated dM values, and the overlapping diameters (dO) are recorded. These overlapping diameters, dO, identify the region of porosity that is probed by both mercury intrusion and argon adsorption. Mercury intrusion subkernel M is calculated for pores dO (from the NLDFT kernel), and diameters greater than dO are calculated from the set dM. This provides a subkernel that has theoretical intrusion curves at the same diameter as the NLDFT kernel for the overlapping region plus additional intrusion curves for the mercury exclusive region. The overlapping region may be considered to be primarily mesopores whereas the mercury exclusive region is composed of macropores. Mercury subkernel M also requires compensation for pores smaller than dO, and this may be accomplished by zero padding the mercury subkernel for micropores. Adsorption subkernel A is constructed by zero padding the NLDFT kernel for pore sizes greater than dO (i.e., the macropores). Mercury subkernel M and adsorption subkernel A have the same number of columns, and each column corresponds to the theoretical intrusion or adsorption density for a given pore diameter. The same diameters are used for both subkernels, but the zero padding minimizes the influence of the mercury intrusion data in microporous regions and similarly the influence of the argon adsorption data in the macroporous region. The full kernel also requires a subkernel for regularization, and this matrix λL is a square matrix with the same number of columns as M and A. The entries for L may be as simple as a tridiagonal of [1, −2, 1], and all other values are zero. The value of λ is adjustable and is used to
and makes the semiempirical alternative suitable for use with siliceous materials. Gas adsorption methods based on the nonlocal density functional theory (NLDFT) have been well developed and used to determine the pore size distributions (PSD) of zeolites.30,31 The underlying challenge in modeling the PSD of a zeolite is the fact that the adsorption potential field inside a zeolite pore depends on the pore width and the type and number of charge-compensating cations or, in more general terms, on the chemical structure of the zeolite. These properties are reflected by gas adsorption isotherms measured on zeolite materials. The model isotherms for the kernel are calculated using NLDFT.32 Ω[ρ(r)] = F[ρ(r )] −
∫
dr ρ(r )[μ − Vext(r )]
(4)
The grand potential Ω is a function of the free-energy functional to describe the fluid−fluid interactions (F), the local density (ρ), the chemical potential (μ), and the external potential (Vext) to describe the solid−fluid interactions. Examples of the model intrusion curves calculated from the Washburn equation and model argon adsorption isotherms are given in Figure 2. Extended Description of the Unified Kernel. Kernel matrices M, A, and λL are constructed in the following manner. The Washburn equation (or alternative) is used to convert the pressures from mercury intrusion data to a set of pore diameters (dM). The pore diameters (dA) from the NLDFT argon adsorption kernel are then compared to C
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Figure 4. Mercury intrusion (vHg) and argon adsorption isotherms (nAr) for three hierarchically structured zeolites (Z40-H1, Z50-H1, and extrudate) are compared to the model fit obtained by the simultaneous deconvolution of the experimental isotherm and intrusion curve.
Figure 5. Cumulative intrusion and mesopore surface area distribution (inset) for three hierarchically structured zeolites may be obtained from the unified approach to modeling complex porous materials. reduce the roughness (increase the smoothing) of the resulting pore size distribution. This provides a regularization matrix that uses finite differences to calculate the second derivative of the pore size distribution. Matrices M, A, and λL are then stacked to form the full kernel. Non-negative least squares (NNLS)23 is then used to solve eq 1 for the pore size distribution.
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In Figure 3, the results from a kernel constructed using the Rigby equation, an alternative to the Washburn equation, are also provided so that a more modern approach to the treatment of the mercury intrusion data may be compared to the IUPAC27-recommended technique. The results of the two treatments are quite similar; however, a systematic shift to smaller pore sizes is observed when the Rigby equation is used, and this may be directly attributable to the different functionality of the explicit contact angle in the Washburn equation versus the embedded contact angle function in the semiempirical alternative. The total pore volume from the unified method for UM40, UM50, and UMEX in Figure 3 exceeds the cumulative pore volume obtained from mercury porosimetry, and this observation is consistent with previous reports.10,15,19,20 However, the previous reports required the selective use of the results from adsorption and mercury intrusion and the pore size at which the two distributions are joined is selected from an overlay plot, and the junction of methods must be located in a nonporous region. Use of the unified method provides the total pore volume of micropores, mesopores, and macropores without the arbitrary nature of trying to identify a nonporous region. Results from the deconvolution, eq 1, provides the incremental pore volume (xd) at each pore diameter. This is a convenient result that allows us to calculate an adsorption isotherm and the mercury intrusion for the unified method. The argon isotherm and mercury intrusion are compared to the predicted isotherm and intrusion in Figure 4. Predicted
RESULTS AND DISCUSSION
The pore volume, pore size distribution, cumulative surface area, and surface area distribution were calculated for three hierarchically structured zeolites in the form of powders or extrudates. The total pore volume and pore size distribution are given in Figure 3 and Table 1, and a trimodal pore size distribution was obtained for each zeolite. Pore size distributions from the individual measurements are also shown so that they may be readily compared to the unified method. For each zeolite, the results from the unified method, UM40, UM50, and UMEX demonstrate pore size distributions that are a combination of the individual techniques, and no new or unusual artifacts are evidenced when compared to the results from mercury porosimetry (Hg40, Hg50, and HgEX) and argon adsorption (Ar40, Ar50, and ArEX). Artifacts that are typically observed in the pore size distribution from NLDFT using an argon adsorption isotherm are not corrected by the unified method. In fact, we can see that the peak in the pore size distribution at around 1 nm, which is associated with the monoclinic−orthorhombic transition, remains present in the data attained by the unified model. D
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isotherms nAr and intrusions vHg are in good agreement with the experimentally measured isotherms and intrusions. A complete pore size distribution obtained from the unified method (Figure 3) may also be used to calculate the pore area and pore area distribution. The pore volume and pore size distribution may be converted to pore area and pore area distribution using the simple volume to surface area ratio of a cylinder, Ap = 4Vp/dp, in which Ap is the pore area at pore diameter dp with pore volume Vp. The total pore area and mesopore area distributions for Z40-H1, Z50-H1, and the extrudate are presented in Figure 5. Calculating the area from the unified method is advantageous over traditional techniques that may require the use of a t-plot and the BET surface area. These traditional techniques require a thickness curve for argon adsorption on an alumino-silicate surface, and the results from this analysis could provide an estimate of the mesopore plus macropore (external surface) area. Use of the t-plot has been recently questioned because of the validity of the basic assumption inherent in the t plot that adsorption on a flat surface may be used to characterize hierarchically structured porous materials.33 The BET area could then be calculated and assumed to represent the total area. However, this further fragmented approach requires assumptions about the area an argon atom occupies on an alumino-silicate surface in addition to the validity of the BET surface area to model the total surface area of a zeolite accurately. Using the t-plot and BET results could provide estimates of the micropore and mesopore plus macropore areas. The use of multiple methods and the subsequent ambiguity as to the appropriateness of their application and interpretation are avoided by the use of the unified method. Utilization of the data obtained from two independent techniques and the resulting pore size distribution, pore volume, pore area, and pore area distribution satisfy both the mercury intrusion and gas adsorption.
Letter
AUTHOR INFORMATION
Corresponding Author
*E-mail: jeff
[email protected]. Author Contributions
The manuscript was written through the contributions of all authors. All authors have given approval to the final version of the manuscript. Notes
The authors declare no competing financial interest.
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REFERENCES
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OUTLOOK A method to attain the unified pore size distribution, total pore volume, complete pore size distribution, cumulative pore area, and pore area distribution by combining the information from adsorption and mercury porosimetry has been demonstrated, enabling the characterization of hierarchically structured porous materials from angstroms to micrometers. A general technique such as the one presented requires only a theoretical basis relating the pore size to a theoretical response. In this work, we have demonstrated that model isotherms calculated from NLDFT and model mercury intrusion curves obtained from the Washburn equation and variants thereof could be combined to calculate the complete pore size distribution and total pore volume of complex porous materials. In addition to the pore volume and size distribution, we also obtained the cumulative area and pore area distribution without the use of additional techniques. The unified method will be available in MicroActive software from Micromeritics and will allow all users of adsorption and mercury porosimetry to benefit from this approach to modeling pore size distributions. The direct assessment of these parameters offered by the unified method greatly facilitates the analysis of advanced hierarchically organized systems such as the zeolites studied. Given the exponential growth in the technological relevance of such materials, the applications of this methodology are expected to grow rapidly. E
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