D4 Surface Area: BET Method

Topic

This model measures nitrogen adsorption on the surface of these nanoparticles at cryogenic temperatures and increasing pressures; the BET equation—in its linearized form—is used to fit the nitrogen adsorption data obtained across a range of relative pressures. The BET equation describes how nitrogen first adsorbs to form a single, complete layer on the surface (the monolayer) and subsequently adsorbs in additional layers atop that initial monolayer as the relative pressure continues to rise. The fact that the measured nitrogen adsorption fits well with this linearized form of the BET equation—within the relative pressure range where that form is valid—allows for the reliable determination of the exact amount of nitrogen corresponding to this complete monolayer from the fit.

Consequently, this model—based on nitrogen adsorption and the BET equation—uses the monolayer volume derived from the fit to directly determine the specific surface area of ​​the nanoparticles. By knowing the space occupied by each adsorbed nitrogen molecule and the number of molecules required to complete the monolayer across the entire sample, the model calculates the total area covered by that monolayer relative to the sample mass. A larger monolayer volume results in a correspondingly larger calculated specific surface area. Furthermore, the fact that this specific surface area—measured directly here via gas adsorption—aligns with the value predicted by another model in the set (which describes the surface-to-volume ratio of the nanoparticles) means that this model serves as a direct experimental verification of that surface-to-volume ratio.

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