The present invention relates to a compound of formula (I):

##STR00001##

in which: the R.sub.1 and R.sub.2 groups, which may be identical or different, are, independently of one another, a saturated or unsaturated, linear, branched or cyclic hydrocarbon group having from 1 to 15 carbon atoms, preferably from 1 to 10 carbon atoms; the R.sub.3 and R.sub.4 groups, which may be identical or different, are selected, independently of one another, from a hydrogen atom, a methyl group or an ethyl group; the R, R.sub.6 and R.sub.7 groups, which may be identical or different, are selected, independently of one another, from a hydrogen atom or an alkyl group comprising from 1 to 6 carbon atoms; n is an integer of 0 to 20; and m is an integer of 1 to 6.

A multi-arm polyethylene glycol derivative having a narrow molecular weight distribution represented by the formula (1): ##STR00001##
wherein, L represents a group selected from a linear or branched alkylene, arylene, or cycloalkylene group having two or more carbon atoms and combinations thereof, which may have an ether bond in a chain; X represents a dehydroxylation residue of a linear sugar alcohol having 5 or 7 carbon atoms; m is the number of polyethylene glycol chains bonded to X and represents 4 or 6; n is the average addition molar number of oxyethylene groups and represents an integer of 3 to 600; Y represents a single bond or an alkylene group as further defined herein; and Z represents a chemically reactive functional group.

Provided herein is a class of reversible thermal gel polymers, formulations thereof, methods for using, and methods for making said reversible thermal gel polymers. Reversible thermal gel polymers and formulations are provided having versatile chemical, physical, mechanical and/or optical properties beneficial for a range of applications including medical treatment. In some embodiments, the architecture and composition of the polymer allows for tunable selection of one or more physical properties supporting a particular application.