Apostrophe interrupts the discussion or discourse and addresses directly a person or personified thing, either present or absent. Its most common purpose in prose is to give vent to or display intense emotion, which can no longer be held back:

• O value of wisdom that fadeth not away with time, virtue ever flourishing, that cleanseth its possessor from all venom! O heavenly gift of the divine bounty, descending from the Father of lights, that thou mayest exalt the rational soul to the very heavens! Thou art the celestial nourishment of the intellect . . . . --Richard de Bury
• O books who alone are liberal and free, who give to all who ask of you and enfranchise all who serve you faithfully! -- Richard de Bury
• O Jerusalem, Jerusalem, the city that kills the prophets and stones those sent to her! How often I wanted to gather your children together, just as a hen gathers her brood under her wings, and you would not have it! --Luke 13:34 (NASB)

Apostrophe does not appear very often in argumentative writing because formal argument is by its nature fairly restrained and intellectual rather than emotional; but under the right circumstances an apostrophe could be useful:

• But all such reasons notwithstanding, dear reader, does not the cost in lives persuade you by itself that we must do something immediately about the situation?