It depends on the type of metal ions and the type of polymer (the presence and strength of the polymer-metal complex, etc.)

Dear Rashid Thanks for your answer.

So if we have a complex in solution we can't separate solutes without chemical method is it true?

I don't want use chemical method.:-) 

I am afraid,  the use of chemical reagents is inevitable

precipitate the polymer in excess of a nonsolvent that has some solubility for the metal ion

If you know a non-solvent of the polymer that is miscible with water, slowly add that solvent to water till a cloudiness forms and then use a centrifuge to precipitate the polymer. Otherwise you can try dialysis. But these methods work only if the polymer and metal are not linked by any type of bonds.

you can perform an anion resin column. i have used this method to remove Cu2+ from polymer. wishes.

If this solution consist of dissolved polymer and the colloids of the metal ions you can try to centrifuge this solution directly, if you see a sediment that means it is done. 

Is a precipitation possible?

it's very good if we can precipitate metal ions.

is precipitation related to Gibbs free energy? How?

thanks for your idea dear Thomas

Dear all,

I think the use of membrane dialysis is the best choice according to your requirements. Just look for a membrane with molecular cut-off with respect to the molecular weight of your polymer. Other possibility is to work under polyelectrolyte salting-out conditions. Finally, ion-exchange chromatography is also possible to use. This question is strongly covered in the field of polymer-metal complexes sorption and disorption. Regards

Dear Afshin, you have to reduction it by acidic solution accordance to the pKa of the polymer