Pore size analysis

A detailed characterization of nanoporous carbons should include pore size analysis in the entire range of pores. In the case of active carbons this analysis should be focused on the micropore size distribution because these carbons are often microporous. 

The BJH, Cl and DH methods assume the same general picture of the adsorption-desorption process. Adsorption in mesopores of a given size is pictured as the multilayer adsorption followed by capillary condensation (filling of the pore core, i.e., the space that is unoccupied 1 the multilayer film on the pore walls) at a relative pressure determined by the pore diameter. The desorption is pictured as capillary evaporation (emptying of the pore core with retention of the multilayer film) at a relative pressure related to the pore diameter followed by thinning of the multilayer. 

Because the concept underlying the BJH, Cl, and DH algorithms appears to be coiTect, it is important to  

This would allow performing accurate PSD calculations using these simple algorithms. Theoretical considerations [13], nonlocal density functional theory (NLDFT) calculations [62, 146], computer simulations [147], and studies of the model adsorbents [63, 88] strongly suggested that the Kelvin equation commonly used to provide a relation between the capillary condensation or evaporation pressure and the pore size underestimates the pore size. 

Porosity of nanoporous carbonaceous materials is usually analyzed on the basis of nitrogen adsorption isotherms, which reflect the gradual formation of a multilayer film on the pore walls followed by capillary condensation in the unfilled pore interior. The pressure-dependence of the film thickness is affected by the adsorbent surface. Hence, an accurate estimation of the pore-size distribution (i.e., pore-size analysis) requires a correction for the thickness of the film formed on the pore walls. The latter (so-called t-curve) is determined on the basis of adsorption isotherms on non-porous or macroporous adsorbents of the surface properties analogous to those for the adsorbent studied. 

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Pore size plays a key role in determining permeability and permselectivity (or retention property) of a membrane. The structural stability of porous inorganic membranes under high pressures makes them amenable to conventional pore size analysis such as mercury porosimetry and nitrogen adsor-ption/desorption. In contrast, organic polymeric membranes often suffer from high-pressure pore compaction or collapse of the porous support structure which is typically spongy . 

Equation (8.7) is the working equation for pore size analysis by adsorption unless more specific information is available regarding pore geometry and the wetting angle. 

Since P < P it follows that < AGads- Therefore, the desorption value of relative pressure corresponds to the more stable adsorbate condition and the desorption isotherm should, with certain exceptions, be used for pore-size analysis. 

The ideas of Wheeler that condensation and evaporation occur within a center core during adsorption and desorption and that an adsorbed film is present on the pore wall has led to the proposal of various methods for pore size analysis. In addition to the methods of Pierce and the BJH technique, other schemes have been proposed, including those by Shull, Oulton, Roberts, Innes, and Cranston and Inkley. These ideas are all based upon some assumption regarding the pore shape. 

After attachment of surface ligands the pore size decreased as expected. In addition to small-angle X-ray scattering and transmission electron microscopy, which are used to obtain information about structural ordering, nitrogen adsorption provides important information about solids under study such as BET surface area, pore size, pore volume, microporosity and surface heterogeneity. Pore size analysis for OMMs is especially crucial and it was performed by the KJS method,48 which was elaborated especially for ordered mesostructures. Table 1 presents adsorption parameters for the materials under study and provides details about calculations. 

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 13, 6267-6273 (1997). 

We turn now to the question of validity of the Kelvin equation. Although the thermodynamic basis of the Kelvin equation is well established (Defay and Prigogine 1966), its reliability for pore size analysis is questionable. In this context, there are three related questions (1) What is the exact relation between the meniscus curvature and the pore size and shape (2) Is the Kelvin equation applicable in the range of narrow mesopores (say >vp < 5 nm) (3) Does the surface tension vary with pore width The answers to these questions are still elusive, but recent theoretical work has improved our understanding of mesopore filling and the nature of the condensate. 

It is still too early to give a definitive appraisal of the value of DFT for pore size analysis. Considerable progress has already been made in the theoretical treatment of... 

For the pore size analysis of microporous carbons, a series of liquids of different molecular size should be employed (see Section 8.3.1). The energy of immersion can be converted into an effective area, which is accessible to each liquid, and the micropore size distribution obtained from the plot of surface area versus molecular size (see Figure 8.5). 

A long-standing problem is the interpretation of the hysteresis loop. For many years the desorption branch was favoured for pore size analysis, but this practice is now considered to be unreliable. There are three related problems (a) network-percolation effects (b) delayed condensation and (c) instability of the condensate below a critical p/p°. 

As shown in Fig. 3, nitrogen adsorption isotherms of CMK-1 feature well-pronounced capillary condensation steps similar to those of ordered mesoporous silicas and indicative of high degree of mesopore size uniformity. The isotherms reveal that the CMK-1 carbon has high nitrogen BET specific surface area (1500-1800 m g ), and large total pore volume (0.9-1.2 cm g ) [14]. The adsorption capacity is comparable or larger than that of MCM-48 template. The pore-size analysis (calibrated BJH analysis) shows that typical CMK-1 has uniform mesopores about 3 nm in size, which is accompanied by a certain amount of micropores when sucrose is used as the carbon source. 

Choma J., Jaroniec M. and Kloske M., Improved pore-size analysis of carbonaceous adsorbents. Adsorption Sci. Technol. 20 (2002) pp. 307-315. 

A new method for the accurate pore size analysis of MCM-41 and other silica based mesoporous materials... 

The novel approach for calculation of pore size distributions, which is reported in the current study is based on recent developments in the materials science and in the theory of inhomogeneous fluids. First, an application of experimental adsorption data for well-characterized MCM-41 silicas enabled proper calibration of the pore size analysis. Second, an application of a modem theory to describe the behavior of inhomogeneous fluids in confined spaces, that is the non-local density functional theory [6], allowed the numerical calculation of model isotherms for various pore sizes. In addition, a practical numerical deconvolution method that provides a "best fit" solution representing the pore distribution of the sample was implemented [7, 8]. In this paper we describe a deconvolution method for estimating mesopore size distribution that explicitly allows for unfilled large pores, and a method for creating composite, or hybrid, models that incorporate both theoretical calculations and experimental observations. Moreover, we showed the applicability of the new approach in characterization of MCM-41 and related materials. 

Figure 4. Pore size distributions for 2.8 nm MCM-41 [12], 4.2 ran MCM-41 [15], 5.5 nm MCM-41 [4], and microporous-mesoporous MCM-41 [18] calculated using the new method for the pore size analysis proposed in the current work.

A series of good quality MCM-41 samples of known pore sizes was used to examine the applicability of the Horvath-Kawazoe (HK) method for the pore size analysis of mesoporous silicas. It is shown that the HK-type equation, which relates the pore width with the condensation pressure for cylindrical oxide-type pores, underestimates their size by about 20-40%. The replacement of this equation by the relation established experimentally for a series of well-defined MCM-41 samples allows for a correct prediction of the pore size of siliceous materials but does not improve the shape of the pore size distribution (PSD). Both these versions of the HK method significantly underestimate the height of PSD. In addition, PSD exhibits an artificial tail in direction of fine pores, ended with a small peak, which may be interpreted as indicator of non-existing microporosity. 

The applicability of the HK method for the pore size analysis of active carbons was questioned on the basis of adsorption isotherms obtained via density functional theory [19,20] as well as computer simulations [21,22]. The crudest assumption in this method is the use of the condensation approximation to represent the micropore filling, which in fact has a... 

Since the HK method has been used by prominent researchers for the pore size analysis of the MCM-41 and related solids [12-18], it would be desirable to discuss its applicability for characterization of ordered mesoporous materials. The aim of the current work is to examine the HK method for a series of good quality MCM-41 samples of known pore sizes and discuss its usefulness for characterization of ordered mesoporous structures. 

Figure 4 represents the evolution of the EoWo/EorcfWo ref ratio for the different carbon molecular sieves of the two series, as a function of the molecular size of the immersion liquid, and using CH2CI2 as a reference. A decrease of this ratio as the size of the immersion liquid increases indicates that the accessibility of the porosity is limited. It can be seen that the pore size distributions obtained by this method are comparable to those shown in Figure 3, corresponding to the surface area accessible to the different immersion liquids. In conclusion of this pore-size analysis, a variety of CMS with different pore size distribution, but always smaller than 0.7 nm, have been obtained. CMS with the narrowest pore diameter are prepared from the acid-washed precursors, i.e., without ashes able to catalyse the gasification reaction. 

Although DFT is now rapidly replacing the HK method, there remain a number of fundamental problems to overcome. For example, energetic heterogeneity and hysteresis phenomena are generally not taken into account in the application of DFT for pore size analysis. On the other hand, in principle DFT should be applicable to both microporous and mesoporous solids. The derived pore size distributions are shown in Figure 3. It is of interest that the results of the DFT analysis and the Os-plots are at least consistent, but further progress will depend on the application of DFT to a number of well-defined pore structures. 

The more general technique for window-size analysis is based on the study of adsorption isotherms. The conventional methods of pore-size analysis assuming cylindrical pore channels, such as the Barret-Joyner-Halenda (BJH) method, were shown not to be appropriate for cage-type structures. 

In membrane filtration, water-filled pores are frequently encountered and consequently the liquid-solid transition of water is often used for membrane pore size analysis. Other condensates can however also be used such as benzene, hexane, decane or potassium nitrate [68]. Due to the marked curvature of the solid-liquid interface within pores, a freezing (or melting) point depression of the water (or ice) occurs. Figure 4.9a illustrates schematically the freezing of a liquid (water) in a porous medium as a fimction of the pore size. Solidification within a capillary pore can occur either by a mechanism of nucleation or by a progressive penetration of the liquid-solid meniscus formed at the entrance of the pore (Figure 4.9b). 

Fig. 18. PSDsfor model porous silica glasses [25]. A, B, C, and D are sample glasses prepared by quench MD the samples differ in mean pore size and porosity. The solid curves are exact geometric PSD results for the model adsorbents the dashed lines are the PSDs predicted from BJH pore size analysis of simulated nitrogen isotherms for the model porous glasses.

Neimark, A.V., Ravikovitch, P.I., Griin, M., et al. (1998). Pore size analysis of MCM-41 type adsorbents by means of nitrogen and argon adsorption. J. Colloid Interface Sci., 207, 159-69. 

Jaroniec, M., Kmk, M., Olivier, J.P., and Koch, S. (2000). A new method for the accurate pore size analysis of MCM-41 and other sflica based mesoporous materials. COPS V. In Studies in Surface Science and Catalysis 128 (K.K. Unger et al., eds). Tkmsterdam Elsevier, pp. 71-80. 

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