The most commonly used method of measuring the surface area and pore size distribution of nanomaterials is the Brunnauer-Emmett-Teller

The most commonly used method of measuring the surface area and pore size distribution of nanomaterials is the Brunnauer-Emmett-Teller (BET) surface adsorption method. This information is used to predict the dissolution rate, as this rate is proportional to the specific surface area. This method is useful in the evaluation of product performance and manufacturing consistency. The specific surface determined by BET relates to the total surface area (reactive surface) as all porous structures adsorb the small gas molecules. The surface area determined by BET is thus normally than the surface area determined by air permeability.
In 1938, Stephen Brunauer, Paul Hugh Emmett, and Edward Teller published the first article about the BET theory. The BET theory applies to systems of multilayer adsorption and usually utilizes probing gases that do not chemically react with material surfaces as adsorbates to quantify specific surface area. Nitrogen is the most commonly employed gaseous adsorbate used for surface probing by BET methods. For this reason, standard BET analysis is most often conducted at the boiling temperature of N2 (77 K). Further probing adsorbates are also utilized, albeit with lower frequency allowing the measurement of surface area at different temperatures and measurement scales. These have included argon, carbon dioxide, and water. The specific surface area is a scale-dependent property, with no single true value of specific surface area definable, and thus quantities of the specific surface area determined through BET theory may depend on the adsorbate molecule utilized and its adsorption cross-section.

Fig 2.13 BET analysis 20
Samples are placed in glass cells to be degassed and analyzed by the BET machine. Glass rods are placed within the cell to minimize the dead space in the cell. Sample cells typically come in sizes of 6, 9 and 12 mm and come in different shapes. 6 mm cells are usually used for fine powders, 9 mm cells for larger particles and small pellets and 12 mm are used for large pieces that cannot be further reduced. The cells are placed into heating mantles and connected to the outgas port of the machine 20.
After the sample is degassed, the cell is moved to the analysis port. Liquid nitrogen is used to cool the sample and maintain it at a constant temperature. A low temperature must be maintained so that the interaction between the gas molecules and the surface of the sample will be strong enough for measurable amounts of adsorption to occur. The adsorbate, nitrogen gas, in this case, is injected into the sample cell with a calibrated piston. The dead volume in the sample cell must be calibrated before and after each measurement. To do that, helium gas is used for a blank run, because helium does not adsorb onto the sample.
The generalized BET equation for gas adsorption is,
V = (V_m CP)/((P_0-P)C-1P/P0) …………. (1)
Here Vis the adsorbed volume of gas, Vmis the adsorbed monolayer volume, pis the equilibrium gas pressure, P0 is the saturation pressure and cis the BET constant. This equation can then be rearranged as a linear function of p/p0 as follows:
1/(V(P/P_0 )-1) = (C-1)/(CV_m )( P/P_0 )+1/(CV_m ) …………. (2)
The y-intercept and slope of this function can then be used to solve for the constants c (=slope/intercept +1) and Vm(=1/ (slope + intercept). The specific surface area (S, the surface area per unit mass) can then be found by the equation:
S = (Vm NA)/(22400*m) ……………. (3)
The constant N is Avogadro’s number (# of molecules per mole), A is the cross-sectional surface area of a single adsorbed gas molecule, and ‘m’is the mass of nanomaterials used in the measurement and 22,400 represents the Standard Temperature and pressure (STP) volume of one mole of gas This surface area is given in units of area/mass (e.g., m2/g), which can be converted to a volume-specific surface area by multiplying by the material density.The raw data provided by the BET analyzer instrument is in the form of a table indicating the volume of gas (nitrogen) introduced per mass of sample (cc/g), along with the relative pressure (P/P0) during analysis. The data can be used to calculate the mass-specific surface area of the material measured according to equations 2 and 3 21, 22. Most instruments include this calculation automatically as a part of the software.

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