I personnally prefer incremental intrusion, as I feel that it is closer to reality and common sense. However some phenomena (such as smal intyrusion peaks) are far easier to see when using a logarithmic plot. So I would say that, depending on what you want to emphasize, you may prefer one representation or another. Provided that you clearly explain what you show, it doesn't matter how it is presented.

Alain

Hello Sam

I did not check your "conversion" equation, but usually the instrument provides you with the converted data and I would just use that.

The more important question is which graph you want to use.

I agree with Alain that the cumulative distribution curve makes more sense. The reason for that is the fact that the cumulative curve will not give you a different impression of the data when you are either using a linear size scale or when you are using a logarithmic scale. On the other hand using the "linear" differential curve together with a logarithmic scale will give a different impression of the data.

Take a bimodal distribution with an equal amount of pore volume associated with the small as well as with the larger pores.

The linear differential curve with show a higher peak for the small pores, whereas the log differential curve with show a higher peak for the larger pore (or correspondingly smaller peak for the small pores).

So, from my own point of view, I would recommend to use the cumulative curve, but if you want to show the differential curve, use the one, which fits with your choice of the X-axis (size scale).

Let me know if that helps.

I also prefer cumulative curves for exactly the reasons Herbert explained. Log size scales are useful for emphasizing certain features, but they are often misleading, particularly for differential curves. Logarithmic differential curves are even worse, because the dV/dlogD has no real, physical meaning; the area under such a graph is not the cumulative pore volume. Incremental distributions are better avoided because those depend on the spacing of the measurement points.

The issue of distributions is addressed in detail in this very nice paper:

Meyer, K., & Klobes, P. (1999). Comparison between different presentations of pore size distribution in porous materials. Fresenius' journal of analytical chemistry, 363(2), 174-178.

Pieter

If you have a bimodal distribution that is separated by orders or magnitude on the x axis you have to use the dV/dlogD or the distribution of the wider pores can disappear altogether. Personally I divide the x-axis into equal widths (normally ten divisions for each section, whether 10 to 100, or 100 to 1000 etc.) and draw the distribution scale on a percentage basis. With gas adsorption you only look at pores from about 1 nm up to 100 nm whereas with MIP you can be looking at pore widths from 4 nm up to 200 µm. This is imposible to represent on a linear scale unless you have a very wide graph. I combine the 2 measurements all on a logarithmic x. axis.

Yes, I agree that "usually" I also use a logarithmic scale for the pore size distribution, but keep in mind that there is also a reason for showing the data on a linear scale.

In case you want to show or detect compressibility a linear pressure (or pore size scale) is very useful. Having a linear relation on the cumulative curve will be a strong indicator of "compressibility" effects in your sample.

Thank you all for your valuable comments and suggestions. In my article I am planning to plot both the cumulative pore volume and another form of pore size distribution on a single graphs with two ordinates. I feel that the pore size distributions such as e.g. dV/dD provide a somewhat more tangible overview of the pore sizes present in a material, but I agree that the cumulative pore volume curve provides indispensible information. 

I did base myself on the article by Klobes mentioned here for the calculations I did. Indeed it provides a good overview of different representations. I agree that for MIP it makes sense to plot the pore sizes logarithmic with dV/dLogD given the severeal orders of magnitude scanned in such experiment. However, for the material I'm studying, I'm mainly interested in pores below 3000 nm, hence allowing to plot dV/dD as a function of pore size on a linear scale. And in this representation, the area under the curve in a specific range of pore diamaters does represent the volume attirbuted to this region. For this reason, Klobes also suggest that this representation is most correct/valuable. 

Just to confirm your argument:

Yes, in case you plot the data on a linear pore size scale, the dV/dD differential curve is the correct (better) way for your graph.

Dear Sam,

Both distributions are reasonable. I preffer to use only log differential distribution dV/log(D). This type of distribution shows equally well the distribution of large and small pore sizes, while in linear distribution (dV/dD) large pores are supressed.

Regards,

Alexander

I ended up doing it like this by the way: Article Comprehensive study of the macropore and mesopore size distr...

Dear scholars,

do we know any information from dV/dlogD?

In my pore size distributions, I just know the micropore, mesopore, or macropore from X axis. but I have no idea about Y axis (dV/dlogD)?

please let me know.

Thanks

QUI

As I pointed out earlier, I add my nitrogen desorption data to my mercury intrusion porosimetry data and plot the cumulative curve on a logarithmic scale from 1 nm up to 100µm to get the total pore volume curve. Since my brain does not understand the machines differential scale I recalculate with 10 columns for every log scale i.e. 10 groups between 1 and 10 nm, 10 more between 10 and 100 nm and so on. So on 1 scale it is pore volume in cm3/g and on the other y axis it is the differential pore volumes in %.

thanks for your explanation.

could you give me any papers as a reference?

Actually, both distribution method are important for pore size. However, based on the case itself, one distribution method may be preferable than the other. If the case involves wide range porosity log scale is the best, specially for comparison between many samples. Some times subtle differences between samples can not be recognised in the small range value (2-10 nm) of linear form. However, these small differences can be observed very clearly on the log scale.

thanks for your sharing