What could be the most efficient fan blade design? There are three main factors for a good fan: one is speed at which air is circulated; second,the volume of air it can circulate; and the third is providing maximum work for minimum power. Combining these three which would be the most efficient fan blade design.
Just as the most efficient wings are long, narrow, and run at slow speed, propellers that waste the least energy are long, narrow, and turn at slow speed.
Given all that, the helix angle of the blade (as a function of radius) should be adjusted so that it makes a good angle of attack against the air moving past it. Not too low, and not too high. Not more than about 15 degrees.
Also, the shape of the tip can be adjusted so as to minimize the energy in the wingtip vortex, by making the vortex as large and slow-turning as possible.
And the cost of the material and manufacture.
Each of this differ depending on the application. The most efficent shape for a wind turbine is not the most efficent for a jet engine.
There is an overall most 'efficient' in terms of maximum amount of energy transferred to/from the air-flow, but it would only be valid for a particular speed assumption. IIRC these are used in a class of model aircraft where you have to fly the furthest on least power - these use a single blade design with a fan blade on one side and a counterweight on the other.