Nanoindentation measurements of the elastic moduli E r of thin polymer films supported by stiff substrates with moduli E s ≫ E r show an increase of E r with decreasing h, for h less than a threshold thickness h t . In the thickness range h < h t , the value of the modulus manifests the influence of various interactions associated with the "stiff" substrate. We show that h t is a function of composition for the miscible blend of polystyrene (PS) and tetramethyl bisphenol-A polycarbonate (TMPC). The modulus E r,TMPC of TMPC films supported by SiO x increases for h < h t (TMPC) ∼ 300 nm while h t (PS) ∼ 450 nm for the modulus E r,PS of PS films, supported by the same substrate. The threshold thicknesses of the blends and the moduli of the blends appear to be reasonably described by an effective medium approximation. This behavior is rationalized in terms of the vibrational force constants f, determined using incoherent neutron scattering experiments, of the materials.
■ INTRODUCTIONThe mechanical properties of thin polymer films are of critical importance in diverse applications, from coatings and nanoimprint lithography to functional applications that include organic electronics and energy conversion. Molecular dynamics (MD) simulations, 1,2 finite element analysis (FEA), 3,4 thin film buckling experiments, 5,6 Brillouin light scattering (BLS), 7,8 and nanoindentation measurements 9−17 have provided valuable insights into the mechanical behavior of polymer films in the nanoscale thickness range (from tens of nanometers to hundreds of nanometers). BLS experiments indicate that the highfrequency elastic properties of supported polystyrene (PS) and poly(methyl methacrylate) (PMMA) films are independent of film thickness, for films as thin as h ∼ 40 nm. 7,8 Thin film buckling studies of the elastic moduli of PS and of a range of methacrylate based polymeric thin films, each supported on soft poly(dimethylsiloxane) substrates, reveal that the apparent moduli deviate from the bulk, decreasing with decreasing film thickness, for thicknesses less than approximately 40−80 nm. 5,6 MD simulations corroborate these observations, indicating that when the polymer film is sufficiently thin the elastic modulus, or stiffness, decreases with decreasing film thickness. 1,2 This behavior is associated with the fact that the monomer segments at the free surface of a linear-chain polymer system possess enhanced configurational freedom (enhanced mobility) in comparison to the bulk. Therefore, when h is sufficiently small, the average modulus of the film becomes smaller than the bulk. The exact thickness h at which the deviation occurs depends on the difference between the temperature of the measurement T and the glass transition temperature T g of the polymer (T < T g ).In this paper we are interested in the elastic mechanical moduli of polymer films with thicknesses on the order of hundreds of nanometers. Specifically of interest here is the general finding by nanoindentation measurements of polymer films supported by stiff substrates ...