Porosity determination by physisorption analysis
The nature of the treatment depends on :
- the shapes of the pores
- cylindrical, slit-shaped
- inter-particular voids
- the range of sizes
- micropores, mesopores, macropores
- Is there a single size of pores, or several families of different scales ?
- connectivity of the pores
- nature of the chemical/physical interactions
- Both on the surface and inside the pores
- sorptive - sample interaction
- sorptive - sorptive interaction
There is a wide range of methods, using models ranging from the very simple, requiring a single measurement point on the isotherm curve, to sophisticated simulations, which need detailed measurements.
Gurvitsch’s Rule : Total pore volume
Assume :
- at some pressure, all the pores of interest are filled
- For micropores, a value of \(P/P_0 = 0.1\) is sometimes used
- For full micro- and meso-porosity, \(P/P_0 = 0.995\) or \(0.998\) are typical
- the adsorbate density is equal to the liquid density
Measure :
- isothermal sorption up to the pressure where the pores are all filled
Calculation:
- Use the liquid density of the adsorbate at the isotherm temperature
- Calculate the liquid phase volume of the amount of adsorbed gas at that pressure
Notes :
- It is very important to specify the values of \(P/P_0\) and of \(\rho_l\) used.
- for micropores, the density of the adsorbed phase is unlikely to be equal to the liquid density
- for large values of \(P/P_0\), a large gradient on the isotherm curve can lead to corresponding uncertainty in the amount of adsorption. Accurate determination of \(P_0\) is important.
Planar surface models - independent adsorption sites
Assume :
a simple model treating the adsorption as a surface interaction. Often this is based on determination of gas interaction with fixed density of adsorption sites per unit area. Typical models are :
- Langmuir
- BET
- BET 3 parameter
a determination of the pore volume, using the Gurvitsch Rule
a model pore shape - typically planar slits, or cylindrical - which relates a nominal pore size with an amount of surface area.
Measure :
- A full isotherm covering the BET or Langmuir range, and the required pressure for the pore volume determination.
Calculate :
- the nominal pore size - a diameter or width - which would give the calculated volume and surface area
Planar surfaces - multilayer thickness models
- t-plot
- alpha-s
Kelvin model
Kelvin + thickness model
- BJH
The physisorption measurement
Instruments like the BELSORP mini X BET analyser, and the BELSORP MAX II sorption analyser, can easily measure the adsorption isotherm of gases such as Nitrogen, Argon, Krypton, often at cryogenic temperatures.
Adsorption of Water and other volatile substances is often performed by Dynamic Vapour Sorption instruments, such as the IGAsorp from Hiden Isochema, and the multisample SPS from ProUmid.