nitrogen adsorption data analysis for metal&#45;organic framework &#40;mof&#41; pore space characterization

Using Nitrogen Porosimetry to Characterize Metal-Organic Frameworks

Relevance of surface area and pore volume 
The accurate characterization of porous materials is imperative to understanding their potential applications. Surface area and pore volume are important quantitative metrics that provide insight into metal-organic framework (MOF) performance in a variety of applications, including gas adsorption, separation, catalysis, and sensing1.
The surface area of a MOF is a parameter that quantifies the amount of surface available for interactions with guest molecules and can affect its performance in various applications2,3. In gas adsorption applications, the surface area of a MOF reflects binding site availability and affinity, which is directly related to its separation performance4. In catalysis applications, MOF surface area can affect the number of active sites and their accessibility to reactant molecules and, thus, their catalytic activity5. The quantity and accessibility of active sites are also relevant in sensing applications, as more guest interactions with active sites lead to improved sensitivity (and potentially selectivity)6. The surface area can also affect the stability of the MOF under extreme conditions, as a larger surface area can indicate a higher number of surface defects7.
The pore volume of a MOF is a parameter that quantifies the amount of void space within the porous structure. It is defined as the total volume of the pores in the MOF, which includes both the open (accessible) and closed (inaccessible) pores. The pore volume of a MOF can affect its performance in various applications, including gas adsorption, separation, and catalysis. Like surface area, the pore volume of a MOF is directly related to its capacity for gas uptake and storage and its ability to allow guest molecules to reach adsorptive or catalytic sites8.
Using nitrogen sorption to determine surface area and pore volume 
Both surface area and pore volume are typically measured using gas adsorption techniques, most commonly nitrogen sorption. Nitrogen is chosen as the adsorbate in Brunauer-Emmett-Teller (BET) analysis due to its quadrupole moment, where the orientation of the nitrogen molecule is dependent on the surface chemistry of the adsorbent, allowing for the formation of a monolayer. The plot of nitrogen uptake as a function of pressure can be used to obtain information about the surface and pore sizes of the MOF. The material surface area and total pore volume can be calculated using the sorption data9. The overall goal of the method detailed here is to obtain nitrogen sorption data and use that data to calculate MOF surface area and pore volume.
The BET method10 is a widely used technique for determining the specific surface area of a porous material, based on the principle that the adsorption of a gas onto a solid surface is a function of the surface area, the properties of the gas molecule, and the system. A known amount of an adsorbate gas (such as nitrogen) is introduced to the sample material over a given pressure range, and the amount of gas adsorbed onto the surface is measured at each pressure increment. The data is used to calculate the specific surface area by relating the adsorbate uptake, pressure, and monolayer capacity, which is represented by the BET equation9:
<img alt="Equation 1" src="/files/ftp_upload/65716/65716eq01.jpg" style="margin: auto;" /> (equation 1; eq. 1)
where: 
p = equilibrium pressure of adsorbate (Pa) 
p0 = adsorbate saturation pressure (Pa) 
n = adsorbate uptake amount (m3/g) 
nm = monolayer capacity (m3/g) 
C = BET constant (unitless)
The monolayer capacity is related to the total surface area by the following equation:
<img alt="Equation 2" src="/files/ftp_upload/65716/65716eq02.jpg" style="margin: auto;" /> (equation 2; eq. 2)
where: 
St = total MOF surface area (m2) 
nm = monolayer capacity (m3/g) 
NAv = Avogadro&#39;s number (molecule/mol) 
scs = cross sectional area of adsorbate molecule (m2/molecule) 
Vmolar = adsorbate molar volume (m3/mol)
The Barrett-Joyner-Halenda (BJH) method11 is a common procedure that utilizes desorption data to calculate the total pore volume. Like the BET method, a known amount of adsorbate gas (often nitrogen) is introduced to the sample. The partial pressure of the adsorbate is then incrementally decreased, and the volume of gas desorbed at each step is measured. Under the assumption that desorption in each pore first occurs in the capillary volume, followed by a reduction in adsorbed layer thickness, the BJH equation relates the volume desorbed to the adsorbed layer thickness, pore radius, and pore volume. This relationship can be represented with a BJH pore size distribution plot, which plots pore radius against pore volume. The distribution is integrated with respect to pore size to determine the total pore volume. The BJH equation12 is written as:
<img alt="Equation 3" src="/files/ftp_upload/65716/65716eq03.jpg" style="margin: auto;" /> (equation 3; eq. 3)
where: 
n = desorption step (unitless) 
vn = volume of pores emptied of capillary condensate (m3) 
&#916;Vn = volume of adsorbate removed from pores (m3) 
&#916;tn = change in adsorbed layer thickness (m) 
A = surface area of pores involved in desorption (m2) 
Rn = BJH constant dependent on average pore size (unitless) 
c = BJH constant, dependent on average adsorbed layer thickness (unitless)

Author Spotlight: Characterizing Porous Materials for Aiding the Development of Robust Metal-Organic Frameworks with Adsorption Behavior 

Determining Surface Areas and Pore Volumes of Metal-Organic Frameworks

Our group focuses on synthesizing and characterizing porous materials for applications like water harvesting, air purification, and capturing carbon dioxide. What we're really interested in, is understanding how the size, volume, connectivity, and chemistry of the pores, impact the absorption performance, and then using those insights to inform our work on materials design. So robust characterization techniques are essential.Characterization is an essential aspect of any porous material research. X-ray diffraction, gas absorption techniques, and thermal analysis techniques are among the top methods for characterization. These can also be used to study structural stability, which is a crucial feature of any material used for real world applications.Surface area and pore volume are two of the most important properties of porous materials. These properties can be measured using commercially available instruments that operate with established methods and software. Nitrogen as an absorbate is inexpensive, readily available, and safe.The measurements are quick and reliable.

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Nitrogen Adsorption Data Analysis for Metal-Organic Framework (MOF) Pore Space Characterization  

Nitrogen Adsorption Data Analysis for Metal&#45;Organic Framework &#40;MOF&#41; Pore Space Characterization

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