I can't tell you the number of times I have been asked when the best time of day to post, tweet or email. The digital agency Raka is cited in this post at Ragan Communications regarding the best time to tweet:

If brands want their followers to click links shared in tweets (referred to as “click throughs”), they should post to Twitter early in the afternoon—1 p.m. to 3 p.m.—Monday through Thursday, according to a study by link shortening service Bitly. 

The study also stressed the two worst times to tweet for click throughs: After 8 p.m. any day of the week and after 3 p.m. on Friday. 

You can see the infographic they put together below: