The surface area of Adsorbent (carbon, agriculture waste)
Measured in some article by
1. Adsorption of iodine
2. Adsorption of Methylene Blue
3.Adsorption of EGME
4. Adsorption of nitrogen gas
and so on
What is the best method and why
The best method could be chosen according to the physiochemical characteristic of the material/sample.
If the sample is a rigid solid (by drying the structure does not change or collapse, like silica particles), you can use BET, Mercury intrusion ..., Take cares in interpretation of the adsorption-desorption isotherms for micro/meso/ macropores.
If the sample is going to be used in liquid media and swells in the liquid, it is better to use iodine, Methylene Blue, or EGME.
The choice between the aforementioned chemicals depends on their adsorption property on the sample's surface.
So, you should use a chemical that makes a monolayer on the sample surface upon the adsorption. To determine whether the adsorption is monolayer or multilayer either look in the papers or perform adsorption isotherm experiment. The isotherm should obey the Langmuir isotherm formula.
Instead of adsorption experiment you can use Thermoporometry in liquid medium as well.
Please see the following paper for the adsorption isotherm:
Article Catecholamine coated maghemite nanoparticles for the environ...
The commonly used procedure is the Nitrogen adsorption. In other cases there is the chance of water adsorption as well.
I agree with Ghazaleh Chegini, however, if You would like to study sorption of some pollutant, the Methylene blue is criticized in many papers as "standard" substance for sorption test. Because of it "stick" even to glass surface! I've used dye [10.1007/s13762-018-1647-5] - easy to determine by UV or visible light spectroscopy. But first of all , You have find a isosbestic point and best pH. For chemical activity, our colleagues used NH3 [10.2174/1874070701509010076] (ammonia water) sorption from water, because of it easy to measure.
For surface area - BET (CO2 or N2).
BET is the best method as N2 has a smaller size and inert as well, in other methods like methylene blue adsorption there is a chance for water adsorption as well.