Future progress in materials for tissue engineering and 3D cell cultures applications requires control of two key physical properties: nanoscale mechanical properties and mass transport. These requirements remain uncontrolled partly due to a lack of physical parameters and quantitative measurements. Using chitosan scaffolds as a model system in close-to-physiological conditions and a combination of experimental techniques and theory, we link structure with local nanomechanical properties. Additionally we introduce a parameter, the free volume, to predict variations in transport properties. By fabricating nanocomposites with single walled carbon nanotubes (SWNTs) we are able to test our approach: incorporation of acid-treated, soluble, ∼80 nm SWNTs in a chitosan matrix leads to a 2 fold increase in mean local elastic modulus and a decrease of 3% of the free volume available for oxygen diffusion. Inclusion of hydrophobic, ∼800 nm SWNTs leads to a 100 fold increase of elastic modulus and doubles the voids percentage available for the transport of glucose.