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I'm studying the article Synthesis of ordered mesoporous phenanthrenequinone-carbon via π-π interaction-dependent vapor pressure for rechargeable batteries, in which authors explain some properties of the resultant composite of phenanthrenequinone (PQ) and ordered mesoporous carbon CMK-3 by the $\pi-\pi$ stacking between these moieties.

While PQ obviously contains aromatic rings, does the ordered mesoporous carbon do? As far as I know, $\pi-\pi$ stacking is possible only between aromatic compounds.

UPD1: So I did several things to elaborate on this question.

First, I tried to figure out, how ordered mesoporous carbon is produced. In this article authors report on several ways therefor; most of those include pyrolysis of hydrocarbons. Well, in my non-professional opinion, this means, that the product will contain hydrogen in some form. Thus, there will be hydrocarbons, including, probably, cyclic and aromatic (for example, pyrene is often a product of burning, as far as I know). Is this right?

Second, I tried to figure out whether it is in general necessary for $\pi$-stacking to have both compounds aromatic. This answer suggests, that not, but that p-orbitals are needed. Can anyone confirm, please? Also, in this article (still to be read) there should be some insights.

Third, I decided to check on the question what is $\pi-\pi$ stacking in general, by reviewing this article. While I'm still in process of reading it, I've already understood, that there's a lot of confusion in this field since there is a variety of this interaction types; possibilities depend strongly on the molecules themselves and their surroundings. Am I wrong?

Fourth, I tried to track back one of the statements regarding multi-walled carbon nanotubes $\pi-\pi$-interacting with PQ from this article (nanotubes just seem to me somewhat more clear than CMK-3, the chemical formula of which I even don't know). This led to surprisingly branched and sad journey to several articles aged past to '70s, not in any of which the $\pi$-stacking was ever proven, but always assumed (I have a long report for myself on this journey, here it is, however, not the correct place to post it). Anyways, it's an ongoing literature research and I decided to make a pause when the amount of articles to check reached six.

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