Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Zakat is not to be paid except to the poor and the kinds of people mentioned in the verse. Hence, one is not allowed to pay Zakat to his son's children; whether for their livelihood or education, for they are either supported enough by their father or their father is poor, in which case the grandfather will be responsible for their livelihood.
So, he (the grandfather) should not pay Zakat to them since he is sponsoring them and responsible for their expenditure. Hence, the questioner is to know that a grandfather is not allowed, in any case, to pay Zakat for his grandsons' study or livelihood, whether their father is rich or poor or not available for any reason (death or otherwise).
He is not allowed to pay Zakat to his son's wife to spend it on herself, for her expenditure is the responsibility of her husband.
Allah knows best.