Good question. I'm not aware of any major peaks other than what is probably "normal" for most big airports (the morning rush of business travelers, for example).

There are a couple of "waves" of international departures: the European directs (CDG, AMS, the first LHR flight) all seem to leave around 4pm, FRA and the later LHR flight depart around 6 or 7pm, while the South American departures are much later in the evening (~9pm or later). The European flights tend to leave out of Terminal E; there may be a corresponding spike in security there a few hours beforehand (say, 2pm and 4pm). I generally prefer the later LHR flight, but haven't noticed anything specific. The one time I took the earlier LHR departure, the President's Club at E was packed out until Paris and Amsterdam got on their way; after that it was much calmer.