For real density: open your fibrous structure as much as possible and use helium pycnometry. For apparent density, you can do an estimation of the volume, for example by considering a cylindrical shape for bast fibres. If not possible, or too inaccurate, use either enveloppe density measurement of mercury displacement at room pressure (the latter can be done in a mercury porosimeter).

Alain

Thank you for your answer, Alain.

The ideal solution would be to calculate the apparent density for each of my tested fibres : I can have the volume because I measure the length and the diameter but the weight of one fibre is too small (a few mg or tenth of a mg) to get an accurate measure (besides, our fibres need to be glued and we can't know exactly the amount of glue). The mercury displacement needs to be tried on a bunch of fibers but I have very low amounts of fibres so I'm not really sure it will work well...

I made a test by mercury porosimetry (I attached the xcl file of the data). First of all, I would like to know if my material (sorghum fibres) is compressed during the test and if it does affect the  reliability of the obtained data. Some compressibility values are displayed in the data but I can't figure out if it's high or not. What do you think ?

Although the calculated bulk density seems not too odd, I think that there is some compression of the sample, based on the general shape of the curve and the high hysteresis.  You can look at the attached file and see how this problem can be solved, doing a few hypotheses. But you really need more fibres for getting more accurate results.

Alain 

For the experimental density measurement we can use dimensional method (M/V) and Archimedes method. Both methods are suitable for the all crystal structure because here we use the ceramics sample. Theoretical density can be used by calculating unit cell parameters for example by rietveld refinement. The difference between theoretical and experimental density is termed as porosity. There are many types of porosity so many methods are available to calculate them.

  Depending on the method used to synthesize them, many powders may consist of agglomerates of primary particles which are highly porous. Commonly, it is necessary to quantitativly characterize the porosity and pore size distribution of the agglomerates. For pores that are accessible (i.e., pores that are not completely isolated from the external surface), two methods have been used: gas adsorption (sometimes referred to as capillary condensation) and mercury intrusion porosimetry (referred to simply as mercury porosimetry). The characteristic pore feature of interest is the size, taken as the diameter, radius, or width. Although there is considerable overlap in the range of applicability, gas condensation is applicable to pore size measurement in the mesopore range, while mercury porosimetry is better applied to the macropore range.

For more details please check section 3.2.6 chapter-3

M.N. Rahaman, Ceramic Processing and Sintering, CRC Press, 1995, p. 149 (Chapter 3).

It looks like you have pores below 100nm in size.

You can confirm that size distribution by N2 adsorption measurements.

The amount of sample should be sufficient and your sample can be comes out of the analysis unchanged. So, you can perform the N2 adsorption analysis first then then run the Hg-porosimetry on the exact same sample.

Otherwise, I would guess that a lot of your measured porosity is caused by the packing between the fibers. You could use SEM to see how large your fibers are and if they show any specific pores in the walls of those fibers.

I attached two SEM pictures of Maple (wood), which we calcined and measured the pore size.

Thank you, Alain. I read your paper. If I understand well, you stated that compression occurs at pressure below Pc (critical pressure) whereas Hg intrusion only occurs after Pc. How can you be sure that these mechanisms don't occur simultaneously or in the inverse way ? I thought that compression should occur only at high pressures...

Thank you Ajeet and Herbert for your contributions. I will take a look at N2 adsorption method.

Compression occurs when the pores are too small for being intruded by mercury at a given pressure, but when such pressure is enough for squeezing the material. For such materials, when you stop the Hg mercury intrusin experiment, you indeed see that it was compresses but no mercury was introduced inside. As soon as mercury is inside, the pression is hydrostatic, i.e., is the same inside and outside so no compression occurs.

Alain