what is the name for the space between the leaves of a tree
The empty space is called "OTIOSE".   Pronounced "oh-she-ohs"

otiosity

Synonyms &amp; Antonyms for otiose 
Synonyms
abortive, barren, bootless, empty, fruitless, futile, ineffective, ineffectual, inefficacious, profitless, unavailing, unproductive, unprofitable, unsuccessful, useless, vain