I found the charge in my smartphone (Samsung Galaxy s2, if that matters) was insufficient to carry me through a day of constant usage, so I bought myself an external battery case (Lithium polymer, rated 2200mAh, 5V output, 750mAh output current). This case has a button on the back, such that until you push the button, it's sitting dormant; after you push it, it starts charging the phone.
I have no scientific evidence, just an "anecdotal" sense that when I start the day with the battery 100% full, and switch on the battery immediately, so that it sustains my battery at 100% until the external battery has fully discharged, it doesn't give me as long a lifespan as if I wait until the battery is down to about 40% and only then switch it on.
Is that correct? If so, what happens to the charge in the external battery while the phone is at 100%? Does it "leak" somewhere?