Mesoporous solids adsorption, capillary condensation

The Horvath-Kawazoe (HK) method is capable of generating model isotherms more efficiently than either molecular simulation (MS) or density functional theory (DFT) to characterize the pore size distribution (PSD) of microporous solids. A two-stage HK method is introduced that accounts for monolayer adsorption in mesopores prior to capillary condensation. PSD analysis results from the original and two-stage HK models are evaluated. 

These sizes can be determined from the aspect of N, adsorption at 77 K, and hence molecules are adsorbed by different mechanisms -multilayer adsorption, capillary condensation, and micropore filling for macropores, mesopores, and micropores, respectively (Figure 3.16). The critical widths of 50 and 2 nm are chosen from empirical and physical reasons. The pore width of 50 nm corresponds to the relative pressure of 0.96 for the adsorption isotherm. Adsorption experiments above that are considerably difficult and applicability of the capillary condensation theory is not sufficiently examined. The smaller critical width of 2 nm corresponds to the relative pressure of 0.39 through the Kelvin equation, where an unstable behavior of the N, adsorbed layer (tensile strength effect) is observed. The capillary condensation theory cannot be applied to pores having a smaller width than 2 nm. The micropores have two subgroups, namely ultra-micropores (0.7 nm) and super-micropores (0.7 nm < w < 2 nm). The statistical thickness of the adsorbed N2 layer on solid surfaces is 0.354 nm. The maximum size of ultra-micropores corresponds to the bilayer thickness of nitrogen molecules, and the adsorbed N2 molecules near the entrance of the pores often block further adsorption. The ultra-micropore assessment by N2... 

The majority of physisorption isotherms (Fig. 1.14 Type I-VI) and hysteresis loops (Fig. 1.14 H1-H4) are classified by lUPAC [21]. Reversible Type 1 isotherms are given by microporous (see below) solids having relatively small external surface areas (e.g. activated carbon or zeolites). The sharp and steep initial rise is associated with capillary condensation in micropores which follow a different mechanism compared with mesopores. Reversible Type II isotherms are typical for non-porous or macroporous (see below) materials and represent unrestricted monolayer-multilayer adsorption. Point B indicates the stage at which multilayer adsorption starts and lies at the beginning of the almost linear middle section. Reversible Type III isotherms are not very common. They have an indistinct point B, since the adsorbent-adsorbate interactions are weak. An example for such a system is nitrogen on polyethylene. Type IV isotherms are very common and show characteristic hysteresis loops which arise from different adsorption and desorption mechanisms in mesopores (see below). Type V and Type VI isotherms are uncommon, and their interpretation is difficult. A Type VI isotherm can arise with stepwise multilayer adsorption on a uniform nonporous surface. 

The most reliable information about the mesoporous structure of solids comes from low-temperature nitrogen adsorption isotherms which enable the calculation of the specific surface area, pore volume, and pore size distribution Figure I shows the N2 adsorption isotherms of the purely siliceous MCM-41, niobium-containing MCM-41, and A1MCM-41 They are typical of reversible adsorption type IV and at relative low pressures (p/po < 0.3) are accounted for by monolayer adsorption of nitrogen on the walls of the mesopores. As the relative pressure increases (p/p0 > 0,3), the isotherm exhibits a sharp inflection, characteristic of the capillary condensation within uniform mesopores, where the p/po position of the inflection point is... 

Figure 7.42 Types of gas sorption isotherm - microporous solids are characterised by a type I isotherm. Type II corresponds to macroporous materials with point B being the point at which monolayer coverage is complete. Type III is similar to type II but with adsorbate-adsorbate interactions playing an important role. Type IV corresponds to mesoporous industrial materials with the hysteresis arising from capillary condensation. The limiting adsorption at high P/P0 is a characteristic feature. Type V is uncommon. It is related to type III with weak adsorbent-adsorbate interactions. Type VI represents multilayer adsorption onto a uniform, non-porous surface with each step size representing the layer capacity (reproduced by permission of IUPAC).

An upward deviation is an indication that capillary condensation takes place in mesopores at high relative pressures so, the adsorption increases more rapidly than that of the standard nonporous solid. A downward deviation indicates the presence of micropores in the solid. Because of its simplicity, the t-method has been widely used to analyze microporous carbons. The MPV, the external surface area, and the total surface area are the quantities often calculated by this method for activated carbons. 

The physisorption isotherm on a mesoporous or macroporous adsorbent follows the same monolayer-multilayer path as on the corresponding non-porous surface until the secondary process of capillary condensation occurs. In the case of a macro-porous solid, the deviation from the standard monolayer-multilayer isotherm does not take place until very high relative pressures are attained (with nitrogen adsorption at 77 K, this would be at p)p° > 0.99). 

The aim of this chapter is to discuss in general terms the use of adsorption measurements for the characterization of mesoporous solids (i.e. adsorbents having effective pore widths in the approximate range of 2-50 nm). Our approach here is mainly along classical lines and is based on the concept of capillary condensation and the application of the Kelvin equation. However it is appropriate to include a brief discussion of the relevant aspects of network percolation and density functional theory. 

Values of the total specific mesopore volume wp(mes) in Table 12.4 have been obtained from the amounts adsorbed at p/p° = 0.95, by making the usual assumption that the pores were filled with the condensed liquid adsorptive (i.e. assuming the validity of the Gurvich law). The fairly good agreement between the three values of vp(mes) is consistent with the assumption that the capillary condensed state of argon is the supercooled liquid rather than the solid. 

Pores with different sizes show characteristic physical adsorption effects as manifested in the isotherm. The isotherm shows the relationship between the amount of a given gas taken np or released by a solid as a function of the gas pressnre nnder a constant temperature. The type-I isotherm shows a steep increase at very low pressmes and a long satnration platean and is characteristic of microporous materials. The type-IV isotherm exhibits a steep iucrease at high relative pressme and, in many cases, a hysteresis loop, which is associated with capillary condensation in mesopores. 

Although the routine analytical method of porosity such as BET analysis is established for mesoporous and macroporous solids, nanoporosity evaluation method is not necessarily established. As the term of nanoporosity is not recommended by lUPAC, we need to define the nanoporosity here. The classical capillary condensation theory using the Kelvin relation has a catastrophe for the pores whose pore width w is less than about 4 nm in the N2 adsorption isotherm at 77 K N2 adsorption isotherms even on cylinderical mesopores of w < about 4 nm and open both ends at 77 K disappear, which cannot be described by the classical theory. [6,7] Hence, it is quite convenient to use the nanopores in this articles for the pores whose pore width is less than about 5 nm. 

The adsorption isotherm calculated is of type IV in lUPAC classification, showing a rapid increase at low pressure as expected for hydrophilic surfaces. The steep rise in adsorption arround P/P°=0.7 is due to capillary condensation in the mesoporous solid. The result is comparable to two available experimental adsorption isotherm of water measured by very different techniques (gravimetry and calorimetry). This result, and the good agreement of the simulated isosteric heat of adsorption at very low coverage (75 kJ/mol) with experimental data, show that the model presented is able to describe quantitatively the hydrophilicity of the vycor surface with no adjustable parameters. 

The type II isotherm is associated with solids with no apparent porosity or macropores (pore size > 50 nm). The adsorption phenomenon involved is interpreted in terms of single-layer adsorption up to an inversion point B, followed by a multi-layer type adsorption. The type IV isotherm is characteristic of solids with mesopores (2 nm < pore size < 50 nm). It has a hysteresis loop reflecting a capillary condensation type phenomenon. A phase transition occurs during which, under the eflcct of interactions with the surface of the solid, the gas phase abruptly condenses in the pore, accompanied by the formation of a meniscus at the liquid-gas interface. Modelling of this phenomenon, in the form of semi-empirical equations (BJH, Kelvin), can be used to ascertain the pore size distribution (cf. Paragr. 1.1.3.2). 

The problem of adsorption hysteresis remains enigmatic after more than fifty years of active use of adsorption method for pore size characterization in mesoporous solids [1-3]. Which branch of the hysteresis loop, adsorption or desorption, should be used for calculations This problem has two aspects. The first is practical pore size distributions calculated from the adsorption and desorption branches are substantially diflferent, and the users of adsorption instruments want to have clear instructions in which situations this or that branch of the isotherm must be employed. The second is fundamental as for now, no theory exists, which can provide a quantitatively accurate description of capillary condensation hysteresis in nanopores. A better understanding of this phenomenon would shed light on peculiarities of phase transitions in confined fluids. 

As a typical example of CEDFT calculations, we present in Fig. 1 the capillary condensation isotherm of N2 in a cylindrical pore mimicking the pore channel in MCM-41 mesoporous molecular sieves. The isotherm is presented in co-ordinates adsorption N versus chemical potential p Calculations were performed at 77 K for the internal diameter of 3.3 nm up to the saturation conditions, point H. We used Tarazona s representation of the Helmholtz free energy [6] with the parameters for fluid-fluid and solid-fluid interaction potentials, which were employed in our previous papers [7]. We distinguish three regions on the isotherm. The adsorption branch OC corresponds to consecutive formation of adsorption layers. Note that the sharp transitions between the consecutive layers are not observed in experiments. They are caused by a well-known shortcoming of the model employed, which ignores intrinsic to real... 

The non-local density functional theory (NLDFT) with properly chosen parameters of fluid-fluid and fluid-solid intermolecular interactions quantitatively predicts both adsorption and desorption branches of capillary condensation isotherms on MCM-41 materials with the pore sizes from 5 to 10 nm. Both experimental branches can be used for calculating the pore size distributions in this pore size range. However for the samples with smaller pores, the desorption branch has an advantage of being theoretically accurate. Thus, we recommend to use the desorption isotherms for estimating the pore size distributions in mesoporous materials of MCM-41 type, provided that the pore networking effects are absent. 

Porous solids having a regular pore structure have gathered much attention in the fields of chemistry and physics[l-7]. Those solids are expected to elucidate the interaction of gas with pores from the microscopic level. lUPAC classified pores into micropores, mesopores, and macropores using pore width w ( micropores w< 2nm, mesopores 2 nm < w< 50 nm, and macropores w> 50 nm)[8]. Physical adsorption occurs by the mechanism inherent to the pore width. Vapor is adsorbed on the mesopore wall by multilayer adsorption in the low pressure range and then vapor is condensed in the mesopore space below the saturated vapor pressure P . This is so called capillary condensation. Capillary condensation has been explained by the Kelvin equation given by eq. (1). 

Isotherm I is typical of adsorption in micropores, e.g., adsorption on molecular sieves and activated carbons. Isotherm II represents multilayer physisorption on a flat surface (valid for many nonporous substances). Isotherms III and V are characteristics of weak gas-solid interactions, e.g., water adsorption on gold. Isotherm IV is frequently observed in the study of practical heterogeneous catalysts. Its shape is characteristic of multilayer adsorption accompanied by capillary condensation in mesopores. When the surface of a nonporous adsorbent is energetically uniform the isotherm may have a step-like shape (Isotherm VI). A good example of such behaviour is the adsorption isotherm of Rr at 90 K on graphite [5]. 

Specific surface areas and pore size distributions of mesoporous materials are best probed by nitrogen/argon adsorption and capillary condensation which will be outlined in detail below. It should be emphasized that the concept of specific surface area is not applicable when the size of the sorbed molecules approaches the diameter of the pore. Thus, for microporous substances values for specific surface areas have no physical meaning, but are rather characteristic of the volume of gas adsorbed. Nevertheless, these values are frequently used as practical numbers to compare the quality and porosity of microporous materials. The average pore size of microporous materials has to be probed by size exclusion measurements. For this purpose the uptake of a series of sorbates with increasing minimal kinetic diameter on a solid are explored. The drop in the adsorbed amount with increasing size of the sorbate defines the minimum pore diameter of the tested solid. The method will be described in detail below. 

The method devised by Barrett, Joyner, and Halenda (BJH) [35] is one of the earhest methods developed to address the pore size distribution of mesoporous sohds. This method assumes that adsorption in mesoporous solid (cylindrical pore is assumed) follows two sequential processes — building up of adsorbed layer on the surface followed by a capillary condensation process. Karnaukhov and Kiselev [45] accounted for the curvature in the first process, but Bonnetain et al. [46] found that this improvement has httle influence on the determination of pore size distribution. The second process is described by either the Cohan equation (for adsorption branch) or the Kelvin equation (for desorption branch). 

Figure 5 The six types of International Union for Physical and Applied Chemistry isotherms. The type I isotherm is typical of microporous solids and chemisorption isotherms. Type II is shown by finely divided nonporous solids. Types III and V are typical of vapor adsorption (i.e., water vapor on hydrophobic materials). Types V and VI feature a hysteresis loop generated by the capillary condensation of the adsorbate in the mesopores of the solid. The rare type VI, the step-like isotherm, is shown by nitrogen adsorbed on special carbon.

Another problem is related to the fact that Nj, is ill defined and it can be difficult to evaluate from experimental data. In particular, if the liquid adsorbate wets the adsorbent, then adsorption diverges as the pressure approaches the saturated vapor pressure. This divergence is due to the growth of a film at the solid surface. In the case of mesoporous adsorbents, the value of Nj, is usually assumed to be equal to the amount of adsorbate at the end of the capillary condensation loop [7,8]. 

Type I isotherm is the Langmuir isotherm type (monolayer coverage), typical of adsorption in microporous solids, such as adsorption of oxygen in charcoal. Type II typifies the BET adsorption mechanism. Type III is the type typical of water adsorption on charcoal where the adsorption is not favorable at low pressure because of the nonpolar (hydrophobic) nature of the charcoal surface. At sufficiently high pressures, the adsorption is due to the capillary condensation in mesopores. Type IV and type V are the same as types II and III with the exception that they have finite limit as P Pq due to the finite pore volume of porous solids. 

We have presented in previous sections the analysis of the intermolecular interaction, from which the interaction energy is derived in terms of the size of the pore. The method is particularly applicable to micropore. In the next section we shall consider a mesoporous solid where pore volume is distributed. The mechanism of adsorption is the surface adsorption and when the gas pressure is sufficiently high, capillary condensation will occur. The analysis presented below is basically the synthesis of those adsorption mechanisms, and this was done by Sircar and we will present the theory below. 

The last section presents the analysis of the capillary condensation and surface adsorption in mesoporous solids. This analysis can be easily extended to the class of microporous solids, where micropores exist. The pore size distribution of this class of solid contains micropores (less than 20A) and mesopores and macropores (greater than 20A). In micropore, the micropore filling is the main adsorption mechanism. The mechanisms for adsorption in meso- and macropores are those discussed in the last section. Readers are referred to Sircar (1991) for further exposition of the analysis of this microporous solid class. 

---