There are first mentioned in Fantastic Four (Volume 1) #6.
In Earth-616, Reed Richards invents the unstable molecules by configurating unknown atomic nuclei and electrons synthesizing them into a useable material.
This material is seen in the Fantastic Four's blue uniforms allowing them to be highly resilient to extremely high or low changes in heat, cold, pressure, weight, and so on. This made them great for use as superhero costumes for both the Fantastic Four, and the Future Foundation which Reed Richards founded and made costumes for.
Costumes with Unstable Molecules are also noted as being made to withstand the extreme conditions of space, requiring only the addition of a space helmet, as seen in Fantastic Four (Volume 1) 6, the first mentioning of them.
The third generation of unstable molecules, also created by Reed, was able to allow Peter Parker change his original Spider-Man costume back and forth, allowing him to switch between his Future Foundation costume and his red and blue costume.
- In issue #34 of the comic book series, What If? there is an alternate reality that explores the possibility of Reed Richards not inventing unstable molecules for the Fantastic Four's costumes. This reality is designated as Earth-24883.