Density of a microporous solid

How can I obtain the envelope density for a microporous solid, knowing solid density and porosity?

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Use Achemedies principle to determine both true and bulk density. Now here is a crude method that will get you into the ball park ( within a 0.1% or so - depending on your sample):

  1. Weigh the sample dry
  2. infiltrate the sample with a fluid (ie. water) a) place the sample in water and boil for an hour or so....... - to remove air from the pores OR.... b) place the sample in a vacuum chamber (desiccator) - pull a vacuum and then suck in enough water to cover the sample and let soak - add a wetting agent to the water to aid infiltration.
  3. weigh the sample while suspended in water.
  4. carefully blot away surface water without sucking water from the pores and weigh the wet (infiltrated) sample

You now have all the information you need to determine bulk density (envelope density), true density and % porosity - if your pores are continuous:

  1. The the difference in weight between the dry sample and the suspended sample can be used to determine true volume (volume of the material used to make the part): - True volume = (weight dry sample - weight suspended sample)/ liquid density
  2. find the volume of the pores: (weight of saturated sample - weight of dry sample)/ density of liquid = pore volume
  3. total volume = pore volume + true volume
  4. bulk density = dry weight/ total volume
  5. true density = dry weight/ true volume
6 % porosity = (pore volume/total volume) * 100

There are corrections you can apply for barometric pressure and surface tension effects on the suspension rig used to measure submerged weight - if you want very - very precise numbers.

This method works well on materials that are wetted by the fluid being used. I've used this method on materials ranging in mean pore sizes from 1-2mm to .05 microns. boiling water is a pain - so I typically use vacuum infiltration.

Good Luck


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If you have the time and interest, some discussion of "closed porosity" and how it cannot be measured by ordinary immersion techniques is potentially useful.

However, the original poster gave you no clues as to the nature of his solid, or of the potential "open" vs "closed" porosity that he may encounter.

So, you had to shoot in the dark to give an answer, and you gave a good answer for the easier case of open porosity.

On the other hand, the answer to his exact question might be as easy as:

"Envelope Density" = Solid Density * (1.0 - Porosity).

I would never question how the OP managed to get the actual porosity, and simply take his or her word for it.

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Your point is well taken - It's not always wise to shoot in the dark......

I've run into the problem of measuring density on materials with closed porosity. I would be very interested in any ideas on the subject. I've used porosity estimations from SEM photos and topology analysis, He picnometry on the starting powders (assuming the density of the material does not change after forming) to assuming true density based on XRD (phase analysis). I don't feel these techniques are adequate - especially using theoretical true densities of phases determined from XRD. .........And If you're measuring a component with glass phase..................... Perhaps measuring radiation attenuation though the sample? (assuming you know the composition)


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I'm sorry, but I don't understand what you mean by "envelope density".

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Olin Perry Norton

Hi Gregg,

I'm retired from materials science now.

For three widely spaced periods in my life, I was interested in porosity

- and specifically the effects of porosity on materials.

After a while, I decided that people actually know relatively little about porosity, even though the first book "The Nature of Porous Bodies" or similar title was published in about the 1700's by a prominent chemist.

Even now, people appear to know relatively little about porosity. And porosity effects.

Your suggestion for the use of X-Ray attenuation is a reasonable one. To estimate the percentage of solid material in the sample. And thus infer something about the total volume of the pores in the sample.

One could make reference standards out of stepped thickness bars of the pore free bulk metal, if available.

But for understanding the actual nature of porosity, and trying to predict effects of porosity on properties, the X-Ray attenuation route offers no physical details.

A structural mechanic type would ask a question of the nature "What is (are) the load path(s) in your solid structure?" And generally, you and I might have absolutely no idea of the answer.

What seems needed is the microscopic equivalent of a CT scan. To reveal in three dimensions and two dimensional slices the distribution of solid and pore phases in a material.

Serial 2D optical microscopy is pretty tedious, and nobody will advocate it as a cost effective way to characterize pore geomentry.

The chemists are near useless in this area. They defined microporosity about a century ago in terms of chemical reaction parameters - access to the solid surface from the exterior reactive gases.

This has nothing to do with mechanical properties such as stiffness or strength. On the other hand the average chemist is aware of the importance of stiffness and strength, but cannot keep straight which is which.

About 12 years ago, I heard a talk by Dr. Edward Teller who predicted that 3-D X-Ray microscopy would be practical in just a few years. He was a bug on X-Ray stuff, having devoted some years of his life towards the weapons effects of X-Rays. He argued that work was beginning on the detector chips in weapons programs.

In short, how can we understand the effects of the porosity microstructure when we don't know much about what it is, or what to measure even if we had the full 3-D microstructure sitting in front of us in digital form.

A long time ago, one of the technical guys from Leitz told me that one of the limitations of quantitative microscopy instruments was the USER. He said that technically they can probably figure out how to measure definite things that the USER wants, but actually the USER can usually only describe in quantitative non-mathematical terms what he wants. I saw that clearly over 20 years ago. Probably things haven't changed that much.

"Open" and "Closed" porosity are terms over 100 years old by now, and we don't know how to go much beyond gross characterization.

As a field of materials specialists, we should be ashamed of ourselves for our lack of attention to the fundamentals of porosity.


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Hi Jim,

You maybe retired in body, but it sounds like your mind is still wrapped around the subject matter.

My previous job was the development of porous bodies mainly for filtration and diffusion. I was surprised at the lack of understanding in the field. When we worked with hot gas filters, we supplied a lot of samples for testing (through another company) and creep was a big issue. A couple of manufactures (including the company I worked for) supplied filters which were a granular SiC bonded with multiple crystalline phases. We could see that the creep was anisotropic from the deformation patterns that occurred. (tensile vs compressive between grains). Amazenly, no one would here of it - It would screw up their models and probably their funding. I don't see any significant progress being made in the near future.

I completely agree with the point - if we could represent porosity digitally - it doesn't mean we'd understand it. One could hope that the complete digital representation of a porous body would allow it to be modeled - and the proper fudge factors could be used to extrapolate real properties. - maybe someone could make sense of the fudge factors in the future?


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Sounds as if we have encountered similar people and similar thinking, or the lack of it.

The thinking that needs to be done is to change from "What can we measure?" to "What should we measure?"

About 25 years ago, I did a technical report on a theoretical approach to understanding the effect of pore shape on the elastic modulus. It required introducing simplified ideas of pore geometry - such as isolated ellipsoids of revolution.

The theory could be made to predict exponential decay of modulus with increases of porosity, and the more eccentric ( or non-spherical ) the ellipsoid of revolution, the higher was the exponential constant ( the modulus was increasingly sensitive to porosity ).

The automated quantitative microscopy equipment the company owned gave some pretty odd looking results when pore shape was output - it could only attempt to approximate some kind of minimum to maximum diameter ratio.

When I gave it synthetic images based on known circles, ellipses, rectangles, .... it virtually never produced results compatible with the known images.

It was hard to get a technician to sit down and make minimum and maximum diameter measurements from the SEM images. Nobody had ever actually asked them to make many measurements from photographs in their experience.

I finally wrote the experimental part off as a bad deal.

I have a talk I sometimes give :

"POROSITY : Much Ado About Nothing and Why We Still Fail To Understand It"


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Hi Jim, It sounds like an interesting talk - I'd like to hear it. I'd also like to read the technical report if it's available.

With the software available today - and with the help of some very patient technicians or gradual students ;-), it would not be a terrible task to map out an entire body. Using gage wedges in the epoxy mount and subsequent polish - image steps can be combined into a 3D image using free software (Image J). I don't think it would happen in industry (at least in the places I worked) - it's university work............. It's a measurement I've wanted to do for years.

I have a friend who is making porous bodies (both open and closed) and he's noted the lack of information out there. As soon as his company grows big enough - so he can have a free moment - I suspect he'll pursue some characterization. He's noted some oddities concerning pore size and thermal conductivity in highly porous bodies (qualitative measurements). I think he's a ways from understanding it - but at least he's trying. (and he's good at asking the right questions) I should see if you two would would like to chat and exchange notes.


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