Model nitrogen adsorption isotherms

Construction of model nitrogen adsorption isotherms for MCM-41 silicas... 

MCM-41 samples usually exhibit certain external surface area, so the amount adsorbed on the external surface also needs to be accounted for. This amount can be described as the amount adsorbed on the macroporous reference adsorbent, vref(p/po), multiplied by the MCM-41 external surface area, Sex, divided by the specific surface area, Srer, of the reference adsorbent used to evaluate Sex. Therefore, the model nitrogen adsorption isotherm for the MCM-41 sample with the capillary condensation pressure of pc/po, primary mesopore adsorption capacity of vp>max and external surface area of Sex is described by the following equation ... 

Fig. 20. (a) Model nitrogen adsorption isotherms at 77 K calculated using a modified Kelvin-BET method for carbon slit pores of physical width (reading from left to right) 10.0,11.4,14.3, 21.4 and 42.9 A [138]. (b) Comparison of pore filling pressure correlations for DFT (points) and the MK-BET method (line) for nitrogen adsorption in carbon slit pores at 77 K [139]. 

Equation 3 can be rearranged to obtain the adsorption isotherm for pressures below those of the capillary condensation pressure, and for pressures above this limit, the pores can be considered as completely filled with the adsorbate. This leads to the following model MCM-41 nitrogen adsorption isotherm for pores with the capillary condensation pressure pc/po ... 

Figure 2. Results of fitting of nitrogen adsorption isotherm for the hexagonal-lamellar HL3 sample with the model MCM-41 isotherm and experimental lamellar phase isotherm.

Figure 5. Nitrogen adsorption isotherms at 77 K obtained from GCMC simulations in the resulting models of CS400 (squares) and CSIOOO (circles).

Figure 8 PSDs for model porous silica glasses [10]. A, B, C, D are sample glasses prepared by Quench Molecular Dynamics, and differ in mean pore size and porosity. The solid curves are the exact geometric PSDs for the models the dashed lines are PSDs predicted by analyzing simulated nitrogen adsorption isotherms for these materials using the BJH method (a form of the modified Kelvin equation). The BJH method gives mean pore sizes that are too small by about I nm in each case.

Canonical ensemble density functional theory (CEDFT) has been employed for predicting hysteretic adsorption/desorption isotherms in nanopores of different geometries in the wide range of pore sizes (1 - 12 nm). It is shown that the CEDFT model qualitatively describes equilibrium and spinodal transitions and is in a reasonable quantitative agreement with experiments on well-characterized MCM-41 samples. A DFT-based method for calculating pore size distributions from the adsorption and desorption branches of nitrogen adsorption isotherms has been elaborated and tested against literature data on capillary condensation in MCM-41 samples with pores from 5 to 10 nm. 

Figure 5.8 Nitrogen adsorption isotherms at 77 K in an assembly of independent graphitic slit pores with a pore size distribution equal to that shown in Fig. 5.7(a) (solid line), and in two reahstic models of porous carbon CS400 (squares) and CSIOOO (circles). Fractional filling is shown as a function of relative pressure. (Adapted from Ref. [68].)...

Choma, J. and Jaroniec, M. (2001). A model-independent analysis of nitrogen adsorption isotherms on oxidized active carbons. Colloids Surf. A Physicochem. Eng. Asp., 189, 103-11. 

In this contribution we report on the incorporation of tin into the mesoporous molecular sieves MCM-41 and MCM-48 comparing traditional hydrothermal approach with microwave synthesis of these materials. X-ray powder diffraction, nitrogen adsorption isotherms, scanning electron microscopy and FUR of probe molecules were employed to characterize these molecular sieves. Oxidation of adamantanone with hydrogen peroxide was used as model reaction. 

With respect to the values of the apparent specific surfiice area, we have to note here that modem instmmentation permitting the measurement of nitrogen adsorption isotherms is usually provided with software permitting surface area calculation according to several mathematical models, including the BJH (corresponding to the names of Barrett, Joyner, Halenda) method, Langmuir adsorption isotherms, and the BET theory these methods may provide for the same sample of a porous material, values that may differ by as much as 30%. 

Figure 11.5. (a) Nitrogen adsorption isotherms and (b) pore size distributions of LP-FDU-12 silica (calcined at 450 °C) before and after surface modification with trimethylsilyl (TMS) and butyldimethylsilyl (BDMS) groups. The pictures of models of the TMS and BDMS groups are included to illustrate the relative size of these two kinds of surface groups. The adsorption data for unmodified LP-FDU-12 were taken from our earlier publication. ... 

Nanosilica A-400 (S BKr=409 mVg and bulk density Pb=0.061 g/cm ) was selected as a material with small nanoparticles (d, =6J nm) relatively strongly aggregated (pore volume 1 =0.86 cmVg) and having a broad PSD calculated using the nitrogen adsorption isotherm with the model of a... 

FIGURE 1.206 Comparison of the pore (voids between nanoparticles) size distributions calculated using four methods (1) NMR cryoporometry and (2) NMR relaxometry, (3) and (4) TSDC cryoporometry (aqueous suspensions at Cj, qq=3-1 wt%), and (5) PSD calculated using the nitrogen adsorption isotherm (SCV/SCR model, see Section 1.1.1). 

FIGURE 4.33 Nitrogen adsorption isotherms for nanosilica (curve 1), AC (curve 2), silica/AC (2 1) (curve 3) and a model isotherm for silica/AC estimated as the sum of the weighted terms of silica and AC (curve 4) for nanosilicas (a) A-300 and (b) A-500. (Adapted from Appl. Surf. Sci., 258, Gun ko, V.M., Zaulychnyy, Ya.V., llkiv, B.l. et al., Textural and electronic characteristics of mechanochemically activated composites with nanosilica and activated carbon, 1115-1125, 2011f, Copyright 2011, with permission from Elsevier.)... 

Additionally,/s(i ) was used to estimate the deviation (Aw) of the pore shape from the model using a self-consistent (to better fit the nitrogen adsorption isotherms) regularization in the case of the use of a complex model of the pore shape (Gun ko and Mikhalovsky 2004) ... 

Figure 3.16. (a) The model of glassy carbon as an assembly of threads of carbon atoms, so creating porosity (adapted from Pikunic et al, 2001). (b) Nitrogen adsorption isotherms at 77 K obtained from GCMC simulations of models for saccharose-based carbons, HTT 400, 1000 and 2800 °C (Pikunic et al., 2002). 

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