Homogeneous membranes are disclosed which are composed of acrylic copolymers and are capable of absorbing 10% to 50% of their dry weight of water. The copolymers include a hydrophilic component which comprises acrylic esters having a poly(ethylene oxide) substituent as part of the alcohol moiety. The copolymers further comprise methacrylate and/or acrylate monomer units. The membranes are useful in the fabrication of biosensors, e.g., a glucose sensor, intended for in vivo use. Variations in the ratios of the monomeric components make possible the fabrication of membranes which have varying permeabilities.