The association between carbon nanotubes (CNTs) and polymers to afford functional composites has been attributed to enthalpic interactions, neglecting the entropic depletion effect, in which bound solvents are released during the association process. Here, we show that association between multiwalled CNTs and common polymers is governed by the depletion effect, generating a corresponding entropic free energy up to ca. 13 kJ mol(-1) at room temperature, while the enthalpic contribution is insignificant or even negative. Notably, association between the polymers and the CNTs takes place preferentially at the highly stacked CNT junctions, leading to mechanical reinforcement without impacting conductivity. Consequently, high-performance composite membranes were fabricated from inexpensive multiwalled CNTs and polyacrylonitrile (PAN) and were used as electrode supports for platinum (Pt) nanoparticles, affording specific currents 6-7-fold higher than that of Pt foil in the hydrogen evolution reaction and displaying outstanding stability.