Determination of the Micropore Volume

Determination of the Micropore Volume 6.7.3.1 Dubinin Adsorption Isotherm Equation... 

One more isotherm equation that could be helpful for the determination of the micropore volume is the osmotic isotherm of adsorption. Within the framework of the osmotic theory of adsorption, the adsorption process in a microporous adsorbent is regarded as the osmotic equilibrium between two solutions (vacancy plus molecules) of different concentrations. One of these solutions is generated in the micropores, and the other in the gas phase, and the function of the solvent is carried out by the vacancies that is, by vacuum [26], Subsequently, if we suppose that adsorption in a micropore system could be described as an osmotic process, where vacuum, that is, the vacancies are the solvent, and the adsorbed molecules the solute, it is possible then, by applying the methods of thermodynamics to the above described model, to obtain the so-called osmotic isotherm adsorption equation [55] ... 

Figure 1.8 Adsorption isotherm for a Y zeolite (A) and determination of the microporous volume using the Dubinin method (B>.

The evolution of N2 and CO2 adsorption with pore size is related to diffusional problems of the N2 molecules at temperatures close to the boiling point in solids with narrow microporosity [4,8-13]. It must be remembered that pore size in zeolite NaA is close to 0.4nm (Table 2) and N2 cannot enter into the porosity but it can go into the pores of silicalite which are approximately 0.5 nm (Table 2). The results obtained with these zeolites are additional examples which confirm the interest of CO2 adsorption at 273K at subatmospheric pressures to characterise the narrow microporosity (pore size lower than 0.7 nm). Additionally, this study demonstrates that the characterisation of microporous materials through, exclusively, N2 adsorption at 77K may lead to a wrong determination of the micropore volume. 

It was only the application of a comparative method [17] (a modification of as method by Sing [18]) which allowed a reliable determination of the micropore volume. In Fig. S, C7H16 adsorption isotherm plots are compared with the adsorption isotherm of carbon black (calculated from the above equation) used as a standard reference. These curves look like those typical for microporous systems the linear fragment slope corresponds to the mesopore surface Aa, and the intercept of the ordinate axis, to the micropore volume V. ... 

Frere, M. Jadot, R., and Bougard, J., Determination of the micropore volume distribution function of activated carbons by gas adsorption. Adsorption, 3(1), 55-66 (1997). 

No current theory is capable of providing a general mathematical description of micropore fiUirig and caution should be exercised in the interpretation of values derived from simple equations. Apart from the empirical methods described above for the assessment of the micropore volume, semi-empirical methods exist for the determination of the pore size distributions for micropores. Common approaches are the Dubinin-Radushkevich method, the Dubinin-Astakhov analysis and the Horvath-Kawazoe equation [79]. 

As explained in Chapter 7, since the multilayer isotherm path is rather insensitive to differences in surface chemistry, for routine mesopore analysis it is possible to make use of a universal form of nitrogen isotherm. However, most activated carbons are highly microporous and the determination of the micropore size distribution remains a more difficult problem. Indeed, as discussed in Chapter 8, even the assessment of the total micropore volume presents conceptual difficulties. We should therefore regard the measurement of a nitrogen adsorption isotherm as only the first stage in the characterization of a microporous carbon. 

The diameter and volume of the micropores were also determined by the measurement of the density using as displacement molecules with different sizes, e g., helium, water, benzene, decaline. It was found that in the case of CMS-Kl and CMS-K2 sieves, the micropores with the pore size within the range 0.255-0.528 are dominated and that the used measurements enable characterisation of the structure of carbon molecular sieves. For equilibrium sieve the analysis of the micropores volume with the use of the pycnometric technique does not give proper results. 

The BET surface areas of the zeolite samples were determined by N2 adsorption-desorption at -196 C in a Micromeritics ASAP 2010 equipment. Prior to the determination of the adsorption isotherm, the calcined sample (0.5 g) was outgassed at 400 C under a residual pressure of 1 Pa in order to remove moisture. The adsorption data were treated with the full BET equation. The t-plot method using the universal t-curve was applied in order to obtain an estimation of the micropore volume, microporous surface and external surface area [7]. 

According to the XRD pattern all samples are well crystallized and show the typical feature of the MFI structure. Its largely pure formation is confirmed by the results of n-hexane adsorption. The values of the micropore volume (at p/ps = 0.5) are fairly close to the theoretical ones calculated for an ideal MFI-structure (0.19 cm /g, see Table 1). Table 1 gives the Si/Me ratios of the fnunework as further characteristic data. An equal concentration of Me in the lattice have been strived for. However, the results of the chemically determined Me concentration and the ammonium ion exchange capacity disagree especially for the In-Sil. It is less pronounced for Fe-Sil. Therefore the creation of extra-framework species in In-Sil and Fe-Sil has to be considered which do not contribute to the Bronsted acidity but to other kinds of acidic sites. This is in agreement with the results of the TPD measurements. 

Table 1 presents the textural parameters of the different materials studied using adsorption/ desorption isotherms before and after modifications or catalytic testing, corresponding to BET surface area, the total pore volume and the proportion of the micropore volume. The adsorption isotherm was found to be in agreement with the ones reported for MCM-41 materials with similar pore sizes [5]. Pore condensation of N, signified by a steep increase in the adsorbed volume in the N2 adsorption isotherm, was observed at a relative pressure (P/Po) of 0.26. Using Kelvin s equation, compensating for the multilayer adsorption the pore size was determined to be 2.5 nm. 

Two kinds of pitch-based ACFs (P5 and P20 Osaka Gas Co.) were used. The microporous structure was determined by high-resolution N, adsorption isotherms at 77 K using a gravimetric method. The micropore structual parameters were obtained from high-resolution a, -plot analysis with subtracting pore effect (SPE) method. The average slit pore width w was determined from the micropore volume and the surface area. The adsorption isotherms of methanol and ethanol on carbon samples were gravimetrically measured at 303 K. The sample was preevacuated at 10 mPa and 383 K for 2h. 

The density of confined methanol and ethanol can be determined using the micropore volume from the N, adsorption at 77 K and the. saturated amount of adsorbed methanol and ethanol which was obtained from the Dubinin-Radushkevich (DR) plots. Table 2 shows the adsorbed density of methanol and ethanol on ACF. The solid density at 113 K and liquid density at 303 K of bulk methanol are 0.98 and 0.79 g/cm, respectively. On the other hand, the solid density at 87 K " and liquid density at 303 K of bulk ethanol are 1.025 and 0.7868 g /cm respectively. The adsorbed density values indicate that methanol and ethanol confined in P20 have their solid-like structures and those of P5 have less-packed structures. 

The difficulty in the case of microporous materials stems from the porefilling mechanism. For this reason, the surface area of such materials is often determined by other methods than BET, which is based on layer formation. From the Dubinin equation the micropore volume Wo can be converted to the surface area. The as isotherm comparison method is an independent method for estimating the micropore volume and the surface area (20). The reference isotherm is a plot of the measured isotherm normalized by the amount of gas adsorbed at a fixed relative pressure, typically at p/po = 0.4. High resolution as analysis (21) yields more information about the characteristic texture of the adsorbent. Further methods (MP (22), -plot (23), Dubinin-Astakhov (11), Dubinin-Stockli (12), and so on) are also available for more reliable estimates of the micropore volume and surface area. 

The volume of the solid phase Vp is usually measured by a pycnometric technique, which measures the excluded volume of a pycnometric fluid, whose molecules cannot penetrate the solid phase of PS. A simple example of a pycnometric fluid is helium [55], The pycnometric fluid fill in all void space (pores) accessible to it, and presumably do not adsorb on the surface of PS. In the case of microporous PSs, measurement of the volume accessible for guests with various sizes allows the determination of a distribution of micropores volume vs. the characteristic size of guest molecules. This approach lays the basis of the method of molecular probes. The essence of this method is in the following we have a series of probe molecules with different mean sizes (dl>d2>d3>---). The pycnometric measurements of the excluded volume will give a series The difference A V=Vpi-Vpi(i>j) corresponds to the volume of micropores with pycnometric sizes of d in a range dt[Pg.283]

Porous texture characterization of all the samples was performed by physical adsorption of N2 at 77K. and CO2 at 273K, using an automatic adsorption system (Autosorb-6, Quantachrome). The micropore volume, Vpp (N2), was determined by application of Dubinin-Radushkevich equation to the N2 adsorption isotherm at 77K up to P/Po< 0.1. The volume of narrow micropores, Vnpp (DR,C02>, (mean pore size lower than 0.7 nm) was calculated from CO2 adsorption at 273 K. 

The amount of water, which is sorbed on zeolites, can be very significant, up to 25 wt% for Na and H-FAU samples with low Si/Al ratios. This amount depends on the partial pressure of water and on various characteristics of the zeolite, such as the pore system, which determines the micropore volume accessible to water, the framework Si/Al ratio, the nature of the cations and the crystallite size. Thus, a linear decrease was found in the amount of water adsorbed at low pressure (that is, strongly adsorbed) over various protonic high silica zeolite materials MOR,[28] bea[29] or MFI,[30] with a decrease in the framework A1 content. This can be attributed to the decrease in the number of partially ionic, hydrophilic centres associated with the tetrahedrally coordinated A1 atoms at the profit of nearly homopolar (hydrophobic) =Si-0-Si= bonds. A stoichiometry of four water molecules per H(A1) was found, suggesting the formation of H9O4 species. 

The micropore volume is defined as the pore volume of the pores < 2 nm. Microporous volumes calculated from the application of the Dubinin-Radushkevich equation to the N2 adsorption isotherms at 77 K. The mean pore size of each sample obtained from N2 adsorption was determined by applying Dubinin-Radushkevich equation. The hydrogen sorption isotherms were measured with the High Speed Gas Sorption Analyser NOVA 1200 at 77 K in the pressure range 0-0.1 MPa. 

The calculation of the volume of molecules is fundamental not only for the study of packing, but also in the computer simulation of the dynamics and fundamental physical properties of macromolecules such as proteins and nucleic acids [23], Likewise, the determination of the void space within any microporous material is of interest in sorption applications [28],... 

Helium is often used in adsorption manometry for the determination of the dead space volume (see Chapter 3), but this procedure is based on the presupposition that the gas is not adsorbed at ambient temperature and that it does not penetrate into regions of the adsorbent structure which are inaccessible to the adsorptive molecules. In fact, with some microporous adsorbents, significant amounts of helium adsorption can be detected at temperatures well above the normal boiling point (4.2 K). For this reason, the apparent density (or so-called true density ) determined by helium pycnometry (Rouquerol et al., 1994) is sometimes dependent on the operational temperature and pressure (Fulconis, 1996). 

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