Holding aloft the Phial Frodo looked and before him he saw a greyness which the radiance of the star-glass did not pierce and did not illuminate, as if it were a shadow that being cast by no light, no light could dissipate.
There are no more uses of "dissipate" in the book.
Show samples from other sources
Airborne radiation dissipates over time and distance.
Everyone is frightened right now, but the fear will eventually dissipate.