The invention is directed to an apparatus and methods for electrospinning composite fibers including polymeric material and mesoporous molecular sieve material. The methods include in one aspect electrospinning fibers from a conducting solution to which a high voltage electric current is applied. The apparatus includes in one aspect one or more conducting solution introduction devices for providing a quantity of conducting solution, the conducting solution introduction devices being electrically charged thereby establishing an electric field between the conduction solution introduction devices and a target, and means for controlling the flow characteristics of conducting solution from the conducting solution introduction devices.