You should find the answer in the t-plot transformation using linear regression between 3.5 and 5.0 Å (some softwares do the calculations using points below 3.5 Å). These thicknesses correspond approximately to a pressure range between 0.10 and 0.30 using the transformation t = [ 13.99 / ( 0.034 - log(P/Po) ) ] ^ 0.5 (for N2 at 77K). The intercept will give you the micropore volume (cm3/g STP converted into cm3/g).

 What is the reason behind considering the thickness between 3.5 and 5 Å which lies almost in the pressure range of 0.1-0.3? While analysing BET area the pressure range was 0.02-0.1, so can't we consider the same pressure range for analysing micropore volume.

Theoretically you could take pressures as low as 0.02, as I said some softwares use pressures lower than 0.1 to calculate the regression. I think it also depends on the method used for the calculations on the t-plot, e.g. Harkins & Jura. I cannot tell you the theoretical reasons for considering these points, it is just an observation I made and saw several times in the literature.

 Thankyou for your reply

From 0.0001 to 0.1relative pressure

If you use the Quantachrome equipment, then is better to use more advanced methods for micropore characterization such as NLDFT or (even better) QSDFT. Should be included with your apparatus.

I don't think you'll get better results with DFT methods on this sort of material. 'Argicultural waste' sounds like something with heterogeneous surface chemistry and pore geometries to me. DFT methods are brilliant for the systems they were developed for, so basically if you know the sorbent and its pore geometry and have the right kernel for it, but for heterogeneous materials they will give non-unique and unrealistic results, though the fit of the model to your measured data will probably be perfect.

The reason for taking the thickness range from 3.5-5Å is that this is where multilayer sorption is normally taking place. What you are basically doing in a t-plot is plotting your isotherm vs a reference isotherm of a non-porous material, which is supposed to have the same surface chemistry as the measured material. The Harkins and Jura t-curve for example, was measured on corundum I think. Such a non-porous material sorbs by (multi-)layer formation, and not by volume filling of micropores or capillary condensation. This plot of your measured data against the reference isotherm will be linear in the p/p° range, or thickness range, where multilayer sorption is the dominant mechanism, and it will deviate from that linear trend where micropore filling or capillary condensation take place. Where micropores are being filled, i.e. at low p/p° or low t, the curve on the t-plot is typically steeper than the linear range, same for capillary condensation at high p/p°. The problem with t-plots of complex materials is that they often don't really show a single linear range, different linear regressions can be fitted to different t-ranges.

You write that the BET-regression was fitted in a very low pressure range. I suppose that range is based on a Rouquerol plot? It confirms that your material is strongly microporous, which means that the BET monolayer capacity is more like a 'capacity of strong N2-retention' than a monolayer. And that means that the BET model is fitted in the relative pressure range where volume filling of micropores dominates over multilayer sorption (See Rouquerol's book or papers for more info).

So it seems you should be looking for the linear range in your t-plot at higher p/p° or t, and not let that low BET-range mislead you. I also don't really know how reliable (physically correct) the 'internal-external' areas are you get from a t-plot in this case. For the micropore volume in this case, I'd personally use on of the volume filling theory (Dubinin) models.

Pieter

You can use DR equation in the relative pressure range of 0.0001 to 0.1

Thankyou all for your replies.

By applying DR equation in the relative pressure range of 0.0001 to 0.1