Volumetric method

Figure 1 Schematic structure of a volumetric setup

Volumetric method was used in the early days of adsorption studies by Langmuir, Dubinin and others. It basically comprises a gas expansion process from a storage vessel (reference cell) to an adsorption chamber including adsorbent (adsorption cell) through a controlling valve C, as schematically shown in Figure 1. The reference cell with volume ${\displaystyle V_{ref}}$ is kept at a constant temperature ${\displaystyle T_{ref}}$. The value of ${\displaystyle V_{ref}}$ includes the volume of the tube between the reference cell and valve C. The adsorption cell is kept at the specified equilibrium temperature ${\displaystyle T_{ad}}$. The volume of the connecting tube between the adsorption cell and valve is divided into two parts: one part with volume ${\displaystyle V_{t}}$ with same temperature as the reference cell. The other part is buried in an atmosphere of temperature ${\displaystyle T_{ad}}$. Its volume is added to the volume of adsorption cell ${\displaystyle V_{ad}}$.

Figure 2 Adsorption/desorption isotherms of ${\displaystyle H_{2}}$ on activated carbon

Figure 3 Adsorption isotherms of ${\displaystyle CH_{4}}$ on activated carbon

Figure 4 Adsorption isotherms of ${\displaystyle N_{2}}$ on activated carbon

Figure 5 Adsorption isotherms of ${\displaystyle N_{2}}$ on silica gel on activated carbon

Figure 6 Adsorption isotherms of ${\displaystyle CH_{4}}$ on silica gel on activated carbon

The amount adsorbed can be calculated from the pressure readings before and after opening valve C based on the p-V-T relationship of real gases. A dry and degassed adsorbent sample of known weight was enclosed in the adsorption cell. An amount of gas is let into ${\displaystyle V_{ref}}$ to maintain a pressure ${\displaystyle p_{1}}$. The moles of gas confined in ${\displaystyle V_{ref}}$ are calculated as:

${\displaystyle n_{1}={\frac {p_{1}V_{ref}}{z_{f1}RT_{ref}}}}$

The pressure drops to ${\displaystyle p_{2}}$ after opening valve C. The amount of gas maintained in ${\displaystyle V_{ref}}$, ${\displaystyle V_{t}}$, and ${\displaystyle V_{ad}}$ are respectively:

${\displaystyle n_{2}={\frac {p_{2}V_{ref}}{z_{f2}RT_{ref}}}}$

${\displaystyle n_{3}={\frac {p_{2}V_{t}}{z_{f2}RT_{ref}}}}$

${\displaystyle n_{4}={\frac {p_{2}V_{ad}}{z_{d2}RT_{ad}}}}$

The amount adsorbed or the excess adsorption N is then obtained:

${\displaystyle N=n_{1}+n_{3}'+n_{4}'-n_{2}-n_{3}-n_{4}}$

where ${\displaystyle n_{3}'}$ and ${\displaystyle n_{4}'}$ are the moles of the gas remaining in ${\displaystyle V_{t}}$ and ${\displaystyle V_{ad}}$ before opening valve C. All of the compressibility factor values are calculated by a proper equation of state, which can generate appropriate z values for temperatures not close to the critical zone.

The main advantages of this method are simplicity in procedure, commercial availability of instruments, and the large ranges of pressure and temperature in which this method can be realized. The disadvantage of volumetric measurements is the considerable amount of adsorbent sample needed to overcome adsorption effects on the walls of the vessels. However, this may be a positive aspect if the sample is adequate. A larger amount of sample results in considerable adsorption and usually provides a larger void space in the adsorption cell, rendering the effect of uncertainty in “dead space” to a minimum.

Gravimetric method

In gravimetric method, the weight change of the adsorbent sample in the gravity field due to adsorption from the gas phase is recorded. Various types of sensitive microbalance have been developed for this purpose. A continuous-flow gravimetric technique coupled with wavelet rectification allows for higher precision, especially in the near-critical region.

Major advantages of gravimetric method include sensitivity, accuracy, and the possibility of checking the state of activation of an adsorbent sample. However, consideration must be given to buoyancy correction in gravimetric measurement. A counterpart is used for this purpose. The solid sample is placed in a sample holder on one arm of the microbalance while the counterpart is loaded on the other arm. Care must be taken to keep the volume of the sample and the counterpart as close as possible to reduce the buoyancy effect. The system is vacuumed and the balance is zeroed before starting experiments. Buoyancy is measured by introducing helium and pressurizing up to the highest pressure of the experiment. It is assumed that helium does not adsorb and any weight change (ΔW) is due to buoyancy. Knowing the density of helium (${\displaystyle \rho _{He}}$), one can determine the difference in volume (ΔV) between the sample and the counterpart:

${\displaystyle \Delta V={\frac {\Delta W}{\rho _{He}(p,T)}}}$

The measured weight can be corrected for the buoyancy effect at a specified temperature and pressure:

${\displaystyle W=W_{exp}-\Delta V\rho _{b}(p,T)}$

${\displaystyle W_{exp}}$ is the weight reading before correction.