The Student Room Group
Reply 1
I think its because of the ester linkage as terylene consists of ester linkage and esters can be hydrolysed by adding sodium hydroxide. ( not really sure but dats wat i think)!!!!
Reply 2
poly(phenylethene) consists only of C-C and C-H bonds which are not affected by NaOH.
I don't know what Terylene is! ... but if it does contain ester links as enigma says, then NaOH will hydrolyse them as base catalyses the hydrolysis of esters to the alcohol and carboxylate.
On a related question to ester hydrolysis: OH- can be used as catalysts to hydrolyse esters, and my thinking for that reaction was that the OH- reacts with the (carboxylic) acid formed, which then shifts the equilibrium to the right hand side.

Is that right? And what's happening when you use a H+ catalyst instead?
Reply 4
H+ protonates the carbonyl oxygen which activates the ester link to attack from a nucleophile (eg Water) so it acts to initiate the process. This is necessary as a normal ester is not reactive enough to be attacked by water.