A method of obtaining a purified regenerated diacid from a depolymerization of a polyester in a waste material wherein the depolymerization provides a depolymerized mixture comprising a regenerated diol, a regenerated diacid, and a catalyst is disclosed. The method comprises: separating a regenerated composition including the regenerated acid and the catalyst from the regenerated diol; providing the regenerated composition in a liquid medium to form a pre-aged mixture; subjecting the pre-aged mixture to thermal cycling wherein the cycling occurs within 25° C. and within a temperature range of from 150° C. or more to 300° C. or less to form an aged mixture; and separating the regenerated composition from the liquid medium in the aged mixture.