Adsorption isotherms specific surface area calculations from

BET surface area m2/g ASTM D 3037 DIN 66131 DIN 66132 total specific surface area calculated from the nitrogen adsorption isotherm by using the BET equation... 

FIGURE 2.33 DTF IPSDs with respect to (a) the pore volume and (b) the specific surface area calculated on the basis of the water adsorption isotherms for nanooxides. (Adapted from Powder TechnoL, 195, Gun ko, V.M., Zarko, V.L, Turov, V.V. et al.. Morphological and structural features of individual and composite nanooxides with alumina, silica, and titania in powders and aqueous suspensions, 245-258, 2009g, Copyright 2009, with permission from Elsevier.)... 

The calculation of the specific surface area a ) from adsorption isotherms is based on the following relationship ... 

For adsorption on Spheron 6 from benzene-cyclohexane solutions, the plot of N N2/noAN2 versus N2 (cyclohexane being component 2) has a slope of 2.3 and an intercept of 0.4. (a) Calculate K. (b) Taking the area per molecule to be 40 A, calculate the specific surface area of the spheron 6. (c) Plot the isotherm of composition change. Note Assume that is in millimoles per gram. 

The physical adsorption of gases by non-porous solids, in the vast majority of cases, gives rise to a Type II isotherm. From the Type II isotherm of a given gas on a particular solid it is possible in principle to derive a value of the monolayer capacity of the solid, which in turn can be used to calculate the specific surface of the solid. The monolayer capacity is defined as the amount of adsorbate which can be accommodated in a completely filled, single molecular layer—a monolayer—on the surface of unit mass (1 g) of the solid. It is related to the specific surface area A, the surface area of 1 g of the solid, by the simple equation... 

BET method. The most commonly used method for determining the specific surface area is the so-called BET method, which obtained its name from three Nobel prize winners Brunauer, Emmett and Teller (1938). It is a modification of the Langmuir theory, which, besides monolayer adsorption, also considers multilayer adsorption. The equation allows easy calculation of the surface area, commonly referred to as the BET surface area ( bet). From the isotherms also pore-radii and pore-volumes can be calculated (from classical equation for condensation in the pores). 

Table 2. Characteristics of the silica templates and the corresponding carbon materials a unit cell parameter Sbet- specific surface area Vp total pore volume (at P/Po=0.95) Pore size determined according to the BJH method - Maximum value of the BJH pore size distribution peak calculated from the adsorption branch of the N2 isotherm.

Physical properties of calcined catalysts were investigated by N2 adsorption at 77 K with an AUTOSORB-l-C analyzer (Quantachrome Instruments). Before the measurements, the samples were degassed at 523 K for 5 h. Specific surface areas (,S BEX) of the samples were calculated by multiplot BET method. Total pore volume (Vtot) was calculated by the Barrett-Joyner-Halenda (BJH) method from the desorption isotherm. The average pore diameter (Dave) was then calculated by assuming cylindrical pore structure. Nonlocal density functional theory (NL-DFT) analysis was also carried out to evaluate the distribution of micro- and mesopores. 

Calculate C and the specific surface area As of a material from the nitrogen adsorption isotherm according to the BET equation from the data points given in the figure. Use the ideal gas equation to convert the adsorbed volumes into moles (STP indicates that the volumes adsorbed are given for standard temperature and pressure, i.e., 273 K and 101.3 kPa). 

Chemical composition of fresh HTs was determined in a Perkin Elmer Mod. OPTIMA 3200 Dual Vision by inductively coupled plasma atomic emission spectrometry (ICP-AES). The crystalline structure of the solids was studied by X-ray diffraction (XRD) using a Siemens D-500 diffractometer equipped with a CuKa radiation source. The average crystal sizes were calculated from the (003) and (110) reflections employing the Debye-Scherrer equation. Textural properties of calcined HTs (at 500°C/4h) were analyzed by N2 adsorption-desorption isotherms on an AUTOSORB-I, prior to analysis the samples were outgassed in vacuum (10 Torr) at 300°C for 5 h. The specific surface areas were calculated by using the Brunauer-... 

Sorption Analysis. Specific surface areas and porosity can be calculated from the adsorption isotherm of nitrogen at — 196 °C. The method of Brunauer, Emmett, and Teller [4.29] is generally accepted for the evaluation of specific surface areas (BET surface area in square meters per gram). The two-parameter equation is applicable to carbon black. The BET surface area comprises the outer surface area as well as the surface area of the pores. 

The nitrogen adsorption-desorption isotherms were obtained at 77K by AutoSorb-1 -C (Quantachrome). Prior to measurement, the samples were outgassed at 300°C for 3 h. The specific surface areas of the samples were determined from the linear portion of the BET plots. Pore size distribution was calculated from the desorption branch of N2 desorption isotherm using the conventional Barrett-Joyner-Halenda (BJH) method, as suggested by Tanev and Vlaev [15], because the desorption branch can provide more information about the degree of blocking than the adsorption branch. 

Specific surface areas of the materials under study were calculated using the BET method [22, 23]. Their pore size distributions were evaluated from adsorption branches of nitrogen isotherms using the BJH method [24] with the corrected form of the Kelvin equation for capillary condensation in cylindrical pores [25, 26]. In addition, adsorption energy distributions (AED) were evaluated from submonolayer parts of nitrogen adsorption isotherms using the algorithm reported in Ref. [27],... 

Specific surface areas and micropore volumes were obtained from nitrogen adsorption - desorption isotherms at -196°C using Micromeritics ASAP 2010. Prior to the measurements all powdered samples were degassed at 175 °C under vacuum 10 6 Torr for 6 hours. The total surface area was calculated using BET equation. The method of Horvath and Kawazoe was used to determine the pore size diameters of the product. 

The BET specific surface area [28] was calculated in the relative pressure range between 0.04 and 0.2. The total pore volume was determined from the amount adsorbed at a relative pressure of 0.99 [28], The primary mesopore volume and external surface area were evaluated using the as-plot method [24, 28, 29] with the reference adsorption isotherm for macroporous silica [29], The pore size distributions were determined using the Kruk-Jaroniec-Sayari (KJS) equation [30] and the calculation procedure proposed by Barrett, Joyner and Halenda (BJH) [31]. 

Silica MCM-41 was synthesized hydrothermally at 373 K for 7 days by using water glass and n-hexadecyltrimethylammonium bromide in a manner similar to that reported by Beck et al. [2]. The quality of MCM-41 prepared here was examined by the measurements of XRD, specific surface area and pore size distribution (calculated from N2 adsorption isotherm), and TEM. 

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... 

The volumetric method is mainly used for the purpose of determining specific surface areas of solids from gas (particularly nitrogen) adsorption measurements (see page 134). The gas is contained in a gas burette, and its pressure is measured with a manometer (see Figure 5.4). All of the volumes in the apparatus are calibrated so that when the gas is admitted to the adsorbent sample the amount adsorbed can be calculated from the equilibrium pressure reading. The adsorption isotherm is obtained from a series of measurements at different pressures. 

Most commercial instruments using gas adsorption for surface area and porosity determination are based on the BET isotherm. In Eq. (1.45), the monolayer capacity Vm can be used to calculate the surface area on the basis of the area occupied by each adsorbed gas molecule. According to Eq. (1.45), a plot of p/[Va(p0 - p)] versus p/po is linear. From the slope and the intercept, Vm can be obtained. Thus, the specific surface area S can be obtained as... 

Parameters of the porous structure of titania samples (pores volume Vs, specific surface area Ssp) were calculated using BET theory [34] from the adsorption isotherms of methanol. The average pore diameter (Dp) values were estimated from the differential curves of pore size distribution. 

Nitrogen adsorption isotherms for the OMMs studied were recorded at 77K using a Micromeritics ASAP 2010 adsorption analyzer. All samples prior to adsorption analysis were degassed at 120°C for 2h under vacuum. The BET specific surface area was calculated from the adsorption data in the range of the relative pressure from 0.04 to 0.2 according to the BET method.46 The total pore volume was estimated from the amount adsorbed taken at the relative pressure about 0.99.47 The pore width was estimated at the pore size distribution maximum obtained by the KJS method.48... 

The isotherms and corresponding as-plots in Figures 10.8 and 10.9 are for the adsorption of nitrogen on representative mesoporous and microporous silica gels (Bhambhani et al., 1972). The derived values of the specific surface area are given in Table 10.8. The values of the BET nitrogen area, a(BET), in Table 10.8 are based on the usual assumption that the adsorbed molecules were close-packed in the completed monolayer (i.e. a(N2) 0.162 nm2). The corresponding values of a(S, N2) were calculated from the initial slope of the as-plots by die relation... 

Nitrogen adsorption/condensation is used for the determination of specific surface areas (relative pressure < 0.3) and pore size distributions in the pore size range of 1 to 100 nm (relative pressure > 0.3). As with mercury porosimetry, surface area and PSD information are obtained from the same instrument. Typically, the desorption branch of the isotherm is used (which corresponds to the porosimetry intrusion curve). However, if the isotherm does not plateau at high relative pressure, the calculated PSD will be in error. For PSD s, nitrogen condensation suffers from many of the same disadvantages as porosimetry such as network/percolation effects and pore shape effects. In addition, adsorption/condensation analysis can be quite time consuming with analysis times greater than 1 day for PSD s with reasonable resolution. 

The measurements of external and internal specific surface area have already been discussed in Chapter 1, Section 1.1.3. The principles and the isotherm equation of the BET method to measure external specific surface area, including macro- and mesopores, have been presented in Chapter 1, Section 1.3.4.1.5. The external specific surface area is usually determined by nitrogen gas adsorption at the temperature of liquid nitrogen. Both static (one-point) and dynamic (five-point) methods are applied. The calculations are made by Equation 1.75 (Chapter 1), using one or five different pressure values. The external specific surface area is calculated from the maximum number of surface sites, that is, monolayer and the cross-sectional area of nitrogen molecules. 

Nitrogen adsorption isotherms were measured using an ASAP 2010 analyzer (Micromeritics, Norcross, GA, USA) at -196 °C. Before the experiment the samples were degassed at 120 C to constant pressure of 10 torr. The isotherms were used to calculate the specific surface area, S j.-, micropore volume, average size of micropores, L j, and pore size distribution using Density Functional Theory (DFT) [16, 17]. The total pore volume, V, was evaluated from the last point of the isotherm. 

For the pure alumina sample the chosen model for computing cumulative surface area. SedB, cumulative volume Fedn and surface area and volume distribution as a function of pore size is a cylinder closed at one end. This choice is motivated by the type IV shape of the isotherm and by the E type hysteresis. In the case of the cylinder model closed at one end, the relevant branch of the isotherm is the adsorption. The calculation is carried out from the saturation pressure down to the pressure corresponding to the hysteresis loop s closing. The cumulative specific surface area, SadB, is close to both 5bet and St values for the pure mesoporous material, X(0) (Table 1). 

Textural characterization was performed by N2 adsorption-desorption at 77 K using a Micromeritics ASAP 2010 analyzer. The samples were preheated under vacuum in three steps of Ih at 423 K, Ih at 513 K, and finally 4 h at 623 K. BET specific surface area, Sbet, was calculated using adsorption data in the relative pressure range, P/Po, from 0.05 to 0.2. Total pore volume, Vp , was estimated by Gurvitsch rule on the basis of the amount adsorbed at P/Po of about 0.95. The primary mesopore diameter, Dp, was evaluated using the BJH method from the desorption data of the isotherm. The primary mesopore volume, Vp, and the external surface area, Sext were determined using the t-plot method with the statistical film thickness curve of a macroporous silica gel [5]. 

Textural Parameters. Adsorption-desorption isotherms of N2 at 77K were determined in a Micromeritics ASAP 2010 with a micropore system. Prior to measurement, the samples were outgassed at 140 C for at least 16 h. The specific surface area was determined by the BET method, assuming that the area of a nitrogen molecule is 0.162 nm [12]. Micropore volume was calculated by the t-plot method using the Harkins and Jura [13] thickness. We used model isotherms calculated from density functional theory (DFT) to determine the pore size distributions and cumulative pore volume of the pillared samples by taking the adsorption branch of the experimental nitrogen isotherm, assuming slit-like pores [14]. 

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