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How to measure the microscopic surface area of something like a piece of cloth?

By microscopic, I mean on the level of fiber surface, not the area that would be measured by using a ruler on the piece.

For special cases, there are some estimates possible:

  • A piece of straight foil.

    • The ruler based area, which is a lower bound in general
  • A woven material made of a fiber with a known diameter and density and length of fiber

    • The surface area of a cylinder of the fiber diameter plus the expected area of the end surfaces, circles of the fiber diameter (Length of fiber from mass and density)
  • Material consisting of fibers of consistent shape

    • Sum of fiber surface based on empirically measured fiber examples

There are also the questions of measuring rough surfaces in general, surfaces not exposed by contacting fibers, straight versus crumbled fibers.

But if it is a textile consisting of unknown fibers: Is it possible to measure this kind of surface area?

An approach that could work in principle is to wet the textile in a way that covers the surfaces, but does not otherwise stay in the intermediate spaces. The wetting cover thickness, liquid density and mass increase would give a result. That would even work for a woven material of water pipes and using paint, but for water and a cotton bed sheet it would not.

It would be interesting to know if there is a measuring method for this, even if it works only in special cases.

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Fabric surface area can be measured using gas adsorption (https://wiki.anton-paar.com/en/bet-theory/)

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