1 Introduction

The surface area of porous materials is one of the significant properties because it significantly influences the performance of porous adsorbents in many applications including gas adsorption capacity [1,2,3,4], catalysis [5,6,7], and gas separations [8,9,10,11]. Brunauer–Emmett–Teller (BET) [12, 13] technique is one of the most prominent analyses based on argon or nitrogen gas adsorption–desorption isotherms to determine the surface of microporous materials [14], such as zeolites [15], metal–organic frameworks (MOFs) [16], and covalent organic polymers (COPs).

Most of the porous materials have pore texture properties generated from their specific synthesis methods such as (1) precursor particles originated from a solution that produces agglomeration and results a porous structure, (2) synthesis of crystalline compounds such as zeolites or other through hydrothermal crystallization, where the particular arrangement of building blocks yields intra-crystalline pores of molecular size, (3) the thermal treatments including burning or evaporation which may eliminate the volatile compounds or impurities and produce pores as a result of both exist ways of eliminated materials and solid rearrangements, and (4) the selective dissolution of some components that can produce molecular size cavities [17, 18]. Therefore, most of the porous materials are classified into four major groups based on their pore size including micropores (< 2 nm), ultra-micropores (< 0.7 nm), mesopores (2 nm < pore size < 50 nm), and macropores (> 50 nm) [19, 20].

Some of the researchers have questioned the applications of BET theory to the microporous materials because the origin of this theory is based on the gas adsorption–desorption on flat surfaces of adsorbent materials. From a simulation study carried out by Walton et al. [21], they proposed that BET theory can be applied for the determination of the surface area of porous materials containing micropores with a size in the range of (7–20 × 10−10 m) [22, 23]. Hence, this work aims to investigate the application of BET theory on CO2 adsorption–desorption isotherms for the surface area determination for covalent organic polymers (COPs) containing ultra-micropores.

2 Materials and methods

Nitrogen-rich porous covalent triazine-based organic polymer has been used in the work for surface area determination through nitrogen as well as CO2 adsorption–desorption isotherms via BET analysis. The surface area was determined using N2 adsorption–desorption isotherms at 77 K and CO2 adsorption–desorption isotherms at 273 K. The sample is outgassed at 393 K for 3 h to remove moisture contents.

3 Results and discussions

The N2 and CO2 adsorption–desorption isotherms obtained were further subjected to the BET analysis as shown in Fig. 1. The results show that according to the IUPAC classification of adsorption isotherms [24], the N2 isotherm resembles the type III having sharp adsorption capacity while indicating the presence of broader pore size distributions, narrower mesopores, and wider micropores. The small hysteresis present in the N2 adsorption–desorption isotherm is an indication of the capillary condensation phenomenon indicating the mesoporous nature [25]. There is no significant hysteresis observed in the CO2 adsorption–desorption isotherms which is an indication of easy desorption of the CO2 molecules because of thermal vibrations of molecules that are in agreement with the reported studies [26, 27].

Fig. 1
figure 1

N2 and CO2 adsorption–desorption isotherms at 77 K and 273 K, respectively

Full size image

To investigate the application of BET theory for surface area determination using CO2 adsorption isotherms, we followed a method reported by Walton and Bae [21, 28]. The BET theory was applied to CO2 adsorption isotherm by plotting a graph between x as a function of the x axis and x/q(1 − x) as a function of the y-axis, where x is P/Po for CO2 at 273 K and q is the adsorption capacity of CO2 over COP. The intercept of the plot yields [c − 1/q], while the slope yields [1/qc] in the linear region of the plot. To satisfy these criteria of calculating surface area, two conditions must be fulfilled: (1) the value of q(P − Po) should be increased with increasing x, and (2) the y intercept in the linear region of the graph must yield a positive value, which must be greater than zero to get the meaningful value of c. Finally, the surface can be calculated using Eq. 1:

$$ A = q \times \sigma_{{\text{o}}} \times N_{{{\text{AV}}}} $$
(1)

where q is the adsorption capacity of CO2 at 273 K, σo is the cross-sectional area of CO2 at 273 K, which is 21.8 × 10−10 m, and NAV is the Avogadro’s number, which is 6.022 × 1023 mol−1.

The graphical representation of this method is presented in Fig. 2. The surface area from CO2 adsorption isotherm is calculated using Eq. (1) at 273 K and from N2 adsorption isotherm at 77 K which is tabulated in Table 1. We now investigate the surface area determination using CO2 adsorption isotherms only in the linear region because the linearity of the BET plot is a key factor for the determination of the accurate specific surface area of porous materials. Since the selection of a linear region in the convex or concave-shaped plot is not difficult, it can be identified easily. However, in the selection of the linear region, it must be considered that the linear range should be in the low pressure range and there should not be any overshooting in CO2 adsorption capacity. The results clearly show that the surface area calculated from CO2 adsorption isotherms at 273 K is higher than the surface area calculated using N2 adsorption isotherm at 77 K. It can be considered that surface area calculated by CO2 adsorption isotherm may be accounted for the ultra-microporosity because of its small kinetic diameter than N2 molecules. However, the diffusional resistances due to the temperature of the adsorption process are one of the significant parameters which affect the reach of adsorbate molecules into the ultra-micropores. The results are in agreement with the previously reported studies [21]. In comparison with the reported literature, Sami et al. [29] and his coworkers reported the experimental investigation of the ultra-microporosity determination in a metal–organic framework (MOF-177) by employing the CO2 adsorption for BET technique. The results revealed that the absence of any ultra-micropores in the MOF-177 as the specific surface area of the MOF-177 was reduced from 1721.09 to 47.4739 m2/g when N2 and CO2 gases were used for BET technique, respectively. Similarly, in another work, Sami et al. [30] and his coworkers reported the ultra-microporosity analysis of the two metal–organic frameworks: one was unfunctionalized (MOF-200) and one was functionalized with the graphene oxide (MOF-200/GO). The results again demonstrated the loss of the specific surface areas of both metal and organic frameworks, i.e., MOF-200 (1265 m2/g) and MOF-200/GO (167 m2/g) from MOF-200 (3624 m2/g) and MOF-200/GO (3359 m2/g). This was an indication of the absence of any ultra-micropores in the MOF-177 as the surface area of the MOF-177 was reduced from 1721.09 to 47.4739 m2/g when N2 and CO2 gases were used for BET technique, respectively. However, both reported studies revealed that the reported method can be employed for the ultra-microporosity analysis.

Fig. 2
figure 2

Application of BET theory on CO2 adsorption isotherms at 273 K

Full size image
Table 1 BET surface area calculated by applying BET theory on N2 and CO2 adsorption isotherms
Full size table

4 Conclusion

In this study, a porous covalent organic polymer (COP) was subjected to the BET analysis to investigate the application of BET theory for specific surface area determination using N2 adsorption isotherm at 77 K and CO2 adsorption isotherm at 273 K. The results showed that the surface area determined by using the CO2 adsorption isotherms was higher than the surface area determined by using the N2 adsorption isotherms. The results provided a clear indication of the presence of an ultra-microporous region in the microporous structure. The results recommend the meaningfulness of CO2 adsorption isotherms for the surface area determination in the ultra-microporosity using BET theory. Future research can be carried out to investigate the comparative effect of the kinetic diameter of the adsorbate molecule and diffusive resistance due to the temperature of the adsorption process on the ultra-microporosity.