# Is “density per unit volume” something?

I was reading articles on the preparation of shellac-based composites when I encountered the following statement (in ref. 1):

Wood flour and fibres are interesting because of their low cost, good specific strength, low density per unit volume, along with their renewable and degradable features. The drawbacks of natural organic fillers include poor adhesion between the filler and the polymer matrix, and poor thermal and water resistance (Saba et al. 2014).

Note the same phrase is used in the reference cited in the passage quoted above (Saba et al. 2014) but then the trail goes dead.

Is "density per unit volume" a typo or other error that's been propagated during citation or a real concept of concern for material scientists? If it is, what is the meaning of this concept?

References

1. Obradovic et al. (2017). “Cellulose-shellac composites,”BioResources12(1), 1943-1959.
• I suppose it is a common error, when a writer thinks about 2 related things or sentence variants, ending up somehow with their hybrid, that does not make sense. I do such errors quite often.:-) – Poutnik Sep 30 '19 at 10:35
• Unless it is a measure of density variability across the bulk object volume. – Poutnik Sep 30 '19 at 10:37
• @Poutnik I don't know either way. I make such mistakes myself often enough, but this article is very clearly written otherwise, so it makes me wonder... – Buck Thorn Sep 30 '19 at 11:58
• If you can, you should call the vendor and ask them to connect you with a technical support person who can answer this question. I assume the vendor literature is correct and ask them to clarify. Vendor literature is not always written to be easily understood by people outside their market. – J. Ari Sep 30 '19 at 12:10
• @J.Ari Thanks? The article I reference is academic, but I suppose I could contact one of the authors. – Buck Thorn Sep 30 '19 at 13:51

## 2 Answers

Here, "density per unit volume" implicitly indicates that the densities of the substances being compared have been normalized.

It is redundant but safe - it rules out the possibility of having compared the density of one pound of something with that of a kilogram of another, for example.

The authors probably should have used the phrase "specific density" instead, although, as seen below, "specific density" is equated with "density."

From the Grundfos company website:

The specific density of a material or liquid is the term used to describe the unit mass of a material or liquid.

The technical term for specific density, also referred to as density, is $$\rho$$ and is measured in $$\mathrm{kg\cdot m^{-3}}$$.

The specific heat capacity is dependent on the temperature of the medium. The specific density of water in a heating system at a temperature of between 20–90$$^\circ$$C is 1,000 $$\mathrm{kg\cdot m^{-3}}$$.

In the case above, specific density appears to always reference the mass (in kilograms) of one cubic meter of a substance (here, water in a certain temperature range).

In the literature, the phrase "density per unit volume" appears to be used when describing bulk properties of materials which consist of a wide range of particle sizes (as in your case, wood flour and fiber).

I note that the widely-used phrase "energy density per unit volume" and other variants such as "energy density of states per unit volume" are not included in my explanation here, but do apply to the field of materials science and many others when describing systems of interest.

See here, in reference to different particle sizes of wood contributing to "density per unit volume" when looking at bulk properties of adsorbates; and here for dry-matter "density per unit volume" of forest biomass.

• Have you seen usage of this specific term "density per unit volume" anywhere else? Any references? Your explanation is reasonable otherwise. – Buck Thorn Sep 30 '19 at 19:46
• I've added my own interpretation as an answer. I think your own is interesting but not quite right. – Buck Thorn Oct 1 '19 at 6:59
• It is a kind of average density, is this that you mean? Still I don't see why it should be called something else that simply density. I am not convinced, but it is just an opinion. I see density per unit volume as redundant while in some cases, I see the use proposed by @Buck Thorn as common, though mass density require a very special contest to be meaningfull, eg the amount of mass ablate off a thin layer on a surface. – Alchimista Oct 1 '19 at 11:53
• I have to ask: is my interpretation different from yours, and do you have an opinion either way who is (more) right? – Buck Thorn Oct 1 '19 at 15:30

Density usually specifies a ratio (or equivalent derivative) of the type "amount/unit dimension" where dimension is usually one of (distance, area, volume, hypervolume). Based on further examples of usage (see links in Todd Minehardt's answer) of the expression "density per unit dimension" where "dimension" might be "distance", "area", "volume" or other spatial dimension, the point with writing "density per unit volume" seems to be an attempt to be explicit about the dimension in the divisor (denominator). For instance, when writing "density per unit dimension" it is meant that "density=amount/dimension". Thus "density per unit volume" means "density=amount/volume". One could equally well say "volume density" or "area density" to be specific, but there might be ambiguity there as well, as one might confuse usage with expressions such as "number density" or "energy density" where the property in the numerator is being specified. Then "volume density" might be interpreted as meaning "density of volume", even if farfetched. One could specify dimensions by placing the units in parentheses, for instance, as density (per unit volume) or density (per unit area) etc.