Firstly: 

No, I don't own any "wrinkle-free" articles of clothing. So I haven't been able to observe first-hand if "wrinkle-free" clothing *is* totally "wrinkle- free" (if it isn't... then perhaps "wrinkle-resistant" might be an appropriate term?).

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Back to question:

**At the molecular level, what is it that makes cotton "wrinkle-free"? What chemo-physical process(es) is cotton subjected to, here?**

I ran a cursory Google-search, and [this was the best article that I could find][1], albeit, it's sorely lacking in information on the *actual* processes involved in the production of "wrinkle-free" cotton.

[1]: http://www.businessinsider.in/How-a-brilliant-female-chemist-who-owns-55-patents-re-invented-cotton-and-made-it-the-fabric-of-our-lives/articleshow/48993164.cms