Comparing Fractal Dims by Hg & Profilometry

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The discussion centers on the differences between fractal dimensions obtained from surface profilometry and mercury (Hg) porosimetry. Hg porosimetry measures the internal structure and surface area of materials, resulting in an increasing fractal dimension from 2.5 to 3 across samples, indicating higher percolation fractality. In contrast, surface profilometry, which analyzes a 2D surface with a third dimension for height, shows a decreasing fractal dimension from 3 to 2.5, suggesting a different perspective on surface characteristics. The key point is that these methods measure different aspects of material structure: profilometry provides an external view while porosimetry reveals internal features. This fundamental difference explains the inverse relationship between the results of the two techniques, highlighting that combining both datasets offers a more comprehensive understanding of material geometry.
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What is the difference between fractal dimension determined by surface profilometry and Hg porosimetry?
For example, for a given dataset, say samples 1-5, the backbone fractal dimension determined by Hg porosimetry increases from 2.5 to 3 (the percolation fractality is 3 for all samples).
For Surface profilometry determined on a 2D surface (not a line!) with z as the third dimension, the data is exactly inversed, it decreases from 3 to 2.5
(see example data below)
Why?

What is the difference between the two methods?

thanks.

Data# Hg Profilom.
1 2.5 3
2 2.6 2.9
3 2.7 2.8
4 2.8 2.7
5 2.9 2.5
 
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Perhaps I am missing something...but those experiments don't measure the same thing. Profilometry will give you a wet blanket approximation of the surface. It has no information about the internal structure or surface area under the measured hyperplane. Porosimetry basically gives the opposite result in high surface area materials...it gives most of the internal surfaces but no relational geometry...the total geometry is realized by putting Both of the datasets together.
 


Thanks for your reply.

Thant might be it.
I also thought that one output is the outer blanket, and the other the internal structure, but outer or inner surface would have the same characteristics, no?
Anyways, your explanation might explain why they don't correlate linearly, but with inversely.

Thx.
 
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