The mass of material can be easily determined to varying accuracy by a balance. Structural density can be measured via a pycnometer, which uses gas pressure, typically helium, in a defined cell volume to determine the sample's skeletal volume of given mass.
Envelope density can be more difficult to measure due errors from the shape your material. Ideally you could use an intact monolith with a dimensions that are easily measurable with a micrometer for calculating the volume.
In order to get the skeletal density, you could use helium pycnometry.. Refer to the following:
http://link.springer.com/article/10.1007%2FBF01142014
In order to measure the envelope density, amongst the literature I have read, in recent times they use the envelope density analyzer by Micromeritics GeoPyc 1360..
Good luck!
that's right, the best way how get the envelope density is to prepare well-shaped monoliths. Often it's problematic. Geopyc 1360 from Micromeritics is another possible solution.
If you need just a tendency across several samples and do not care much about the accuracy, I would take a graduated cylinder and fill it with a powder (NaCl, sugar...) up to some volume without any tapping or compression and measure the weight of the powder. The weight-to-volume ratio gives you the tap density. Then place your aerogel into emptied cylinder and do the same. You know the aerogel weight and the total weight (aerogel + powder). So you you can get the weight of the powder. Using the tap density measured right before, you get the volume of the powder and hence the volume of the aerogel. Geopyc works on the same principle. Good luck!
which density do you want to measure, bulk density or skeletal density?
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