We have used photolithography to make barrier membranes containing titanium flakes in a polydimethylsiloxane matrix. The flakes, which are shaped as ribbons, squares or hexagons, retard the diffusion of helium across the membranes. The retardation is due to the tortuous diffusion through the composite. The tortuosity can be due to diffusion from the bulk to a permeable gap between flakes or "necking"; to diffusion through the gaps between flakes; to diffusion back and forth between layers of flakes, or "wiggling". The results for necking into a single layer of flakes do not agree with previously published theories and simulations. The results are not limited by diffusion through the gaps between flakes. The results for multiple layers of flakes are close to those predicted by earlier theories which consider wiggling. All the results provide a benchmark for further theoretical development. (c) 2006 Elsevier B.V. All rights reserved.