A membrane structure is provided. The membrane structure includes a first layer having a plurality of pores; and a second layer disposed on the first layer. The second layer has a plurality of unconnected pores. At least a portion of the plurality of unconnected pores of the second layer is at least partially filled with a filler such that the first layer is substantially free of the filler. At least a portion of the plurality of unconnected pores of the second layer is in fluid communication with at least one of the pores of the first layer. A method of making a membrane structure is provided. The method includes the steps of providing a first layer having a plurality of interconnected pores; disposing a second layer on the first layer, and filling at least a portion of the unconnected pores of the second layer with a filler such that the first layer is substantially free of the filler. Disposing a second layer includes depositing a metal layer on the first layer; and anodizing the metal layer to convert the metal layer into porous oxide layer.