Models for Calculation of Surface Area and Pore Sizes

2 Models for Calculation of Surface Area and Pore Sizes BET Theory for the determination of surface area 

This acronym is derived from the names of its originators Brunauer, Emmett and Teller [83]. A major advance relative to the monolayer approach of Langmuir [84] is the incorporation of multilayer adsorption. The BET equation can be written as follows [79], 

this theory is over-simplified, and holds only for a limited part of the sorption isotherm, which is usually the case for relative pressures between 0.05-0.30, and the presence of point B (Fig. 1.14). Thus, isotherms of Types II (macroporous polymer supports) and IV (mesoporous polymer supports), but not Type I and III, are those amenable to BET analysis [21, 80]. Attention should also be paid to the constant C, which is exponentially related to the enthalpy of adsorption of the first layer. A negative or high value of C exceeding 200-300, is likely to indicate the presence of micropores and the calculated surface area should be questioned since the BFT theory would not be applicable [79, 80]. 

Fmpirical methods can be applied in order to determine the validity of the BFT surface area. The derived standard isotherms can be obtained by normalization of the y-axis (volume adsorbed) of adsorption isotherms. It is strongly recommended that data should always be derived from standard isotherms related to a nonpor-ous sample of the same type of material. Various methods have been established like the as-method where the quantity of gas adsorbed V], is related to the value at a relative pressure of 0.4. In the t-plot, the vertical axis is normalized in relation to the average thickness of the adsorbed layer. The shape of the constructed reduced isotherms reveal the presence or absence of micropores and allows the determination of their volume [79, 80]. 

As discussed in Section 1.4.2.1, the critical condensation pressure in mesopores as a function of pore radius is described by the Kelvin equation. Capillary condensation always follows after multilayer adsorption, and is therefore responsible for the second upwards trend in the S-shaped Type II or IV isotherms (Fig. 1.14). If it can be completed, i.e. all pores are filled below a relative pressure of 1, the isotherm reaches a plateau as in Type IV (mesoporous polymer support). Incomplete filling occurs with macroporous materials containing even larger pores, resulting in a Type II isotherm (macroporous polymer support), usually accompanied by a H3 hysteresis loop. Thus, the upper limit of pore size where capillary condensation can occur is determined by the vapor pressure of the adsorptive. Above this pressure, complete bulk condensation would occur. Pores greater than about 50-100 nm in diameter (macropores) cannot be measured by nitrogen adsorption. 

---