The Elastic Mechanical Response of Nanoscale Thin Films of Miscible Polymer/Polymer Blends

Abstract

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 ...

Role of “Hard” and “Soft” Confinement on Polymer Dynamics at the Nanoscale

“…In other words, the effective modulus of the PS layer increases with decreasing L . Nanoindentation measurements show that the effective modulus of a thin polymer film supported by a hard substrate increases with decreasing film thickness; this is known as the “substrate effect”. − The length scales of this enhancement of the effective modulus with decreasing film thickness can be from hundreds to tens of nanometers, depending on the polymer. ,, Incoherent neutron scattering measurements of supported polymer thin films show that the vibrational spring constants (extracted from the Debye–Waller factor) increase with decreasing film thickness, consistent with the increasing effective modulus with decreasing film thickness . Note that our dynamics observations are not directly associated with the change in the average T g of the confining film with film thicknessthere are significant shifts in the PVA dynamics even with changing PS film thicknesses (∼50 nm to ∼195 nm) in which the literature reports no or minimal changes in PS film T g . , If the changing PS T g was causing the shift in PVA dynamics, we would not expect to see a change here, yet this is where we see the biggest change in PVA relaxation rates.…”

“…44−46 The length scales of this enhancement of the effective modulus with decreasing film thickness can be from hundreds to tens of nanometers, depending on the polymer. 44,47,48 Incoherent neutron scattering measurements of supported polymer thin films show that the vibrational spring constants (extracted from the Debye− Waller factor) increase with decreasing film thickness, consistent with the increasing effective modulus with decreasing film thickness. 49 Note that our dynamics observations are not directly associated with the change in the average T g of the confining film with film thicknessthere are significant shifts in the PVA dynamics even with changing PS film thicknesses (∼50 nm to ∼195 nm) in which the literature reports no or minimal changes in PS film T g .…”

Mechanical Coupling in Gold Nanoparticles Supermolecules Revealed by Plasmon-Enhanced Ultralow Frequency Raman Spectroscopy

“…43 Moreover, this model only provides a rough approximation of the dimer nano-contact as it does not allow taking into account subtle effects such as the elastic stiffening of the surrounding medium due to the interaction with the NP surface. [47][48][49][50] More importantly, the spring model assumes a purely stretching motion of rigid spheres, while the actual rattling motion involves a dipolar-type deformation of the nanospheres.…”

“…However, the spring model cannot be expected to provide a good description of the observed low-frequency mode as the nonzero frequency of the NP rattling mode was shown to be a consequence of the full embedding of the NPs . Moreover, this model only provides a rough approximation of the dimer nanocontact as it does not allow taking into account subtle effects such as the elastic stiffening of the surrounding medium due to the interaction with the NP surface. − More importantly, the spring model assumes a purely stretching motion of rigid spheres, while the actual rattling motion involves a dipolar-type deformation of the nanospheres.…”

Elastic Mechanical Response of Thin Supported Star-Shaped Polymer Films

“…Nanoindentation measurements of polymer thin films supported by stiff (noncompliant) substrates, performed using and atomic force microscope (AFM), reveal that the effective out-of-plane modulus E ( h ) increases with decreasing h , for film thickness h smaller than a threshold film thickness h t . − This enhancement of E ( h < h th ) is due to the propagation of the indentation-induced stress field, from the free surface of the polymer in the direction normal to the polymer/substrate interface, throughout the entire polymer film and interacting with the underlying substrate. , This is the so-called substrate effect . Nanoindentation stress fields, even for indentations of a few nanometers, extend hundreds of nanometers throughout a film.…”