Death of the phalanx

So when is an approximate time phalanx armies ceased to exist?

In the broadest sense, the Napoleonic Wars perhaps?
But if you mean in the classical world, I guess you could say they took an extended break with Rome’s final defeat of eastern powers like Pontus that still deployed some Macedonian style units.

But even Imperial Rome had some Phalanx like Auxiliaries, and the very late legions seem to have moved back to a spear and shield armament.

In terms of the mass use of pikes, probably about 1660-1690, when bayonets began to emerge

Back in the Ancient period it's probably fairly safe to say the phalanx didn't survive contact with the Romans, who (after their initial troubles with Carthage) mopped the floor with it on a fairly reliable basis. And the Parthians with their horse-archers and cataphracts had apparently all but eaten up the Seleucids by the time the Romans got that far.

It is true that late Roman infantry fought with long swords and spears in a shieldwall, and this would be something of an European infantry standard until around the High Middle Ages, but the shieldwall and the phalanx are two quite different albeit related animals.

Pikemen were reintroduced by the Swiss during the Late Middle Ages with a drill markedly improved from the old phalanx. Naturally enough, as the Swiss didn't have enough cavalry around to leave smashing the opponent to bits to that arm and had to use their pikes for the job instead, which required a fair bit more maneuverability and a generally more aggressive stance. Huge square and rectangular blocks of pikemen supported by musketeers were the infantry backbone until around the middle of the Thirty Years' War (ie. about the point the Swedes butted in, 1632), when it was proven rather harshly that the huge massed tercios were too vulnerable to the increasingly more effective field artillery and had no genuine advantage over shallower, more flexible pike-and-shot formations.

By that point the main killing power of the infantry came from the musketeers anyway. The pikemen were there primarily to keep enemy cavalry and pikemen from trampling the lightly armed musketeers flat in head-on clashes - the heavy cavalry in particular could be quite inconveniently bulletproof.

During the course of that troubled century the relative number of pikemen became ever smaller, especially after the invention of the bayonet towards the fin de siecle which gave the musketeers a decent close-combat and anti-cavalry weapon - nevermind once the improved socket bayonet was introduced. Both the Russian and Swedish infantry still had pikeman contignents during the Great Northern War at the beginning of the 18th century partly to counter each others' cavalry forces (the highly aggressive and rightly feared Swedish cavalry was a particular headache for the Russians, whereas there was a whole lot of the less illustrious but still competent Russian dragoons) and because the Swedish tactical doctrine of the time emphasized shock charge with cold arms, but this was apparently considered rather quaint and old-fashioned by other armies of the time. Poltava, 1712, may well have been the last major battle where a meaningful number of pikemen were present.