I've had this idea for some time now. If a smartphone were populated with low-power components, and an E-ink display, the energy consumption could really be stretched out. The goal would be to have something that, even when being used, could last a week at minimum.
Think about those old hand-held LCD games. They didn't have much to them, but one or two AA batteries could power them for months of use.
If we could build a phone that utilized the lowest power components, and work out a new OS from the ground up for that device, long life could be achieved. Instead, most energy efficient smartphones we have today, are not very efficient. They all use some sort of high resolution color LCD (or LED screen) that drains most of the battery life. An E-ink display with a toggle for the backlight would really save battery life.
Depending on the thickness of the device, it could even have a 9V battery connector embedded on the back for a little extra juice if no power is available.