Influence of confinement on the vibrational density of states and the Boson peak in a polymer glass

Abstract

We have performed a normal-mode analysis on a glass forming polymer system for bulk and free-standing film geometries prepared under identical conditions. It is found that for free-standing film glasses, the normal-mode spectrum exhibits significant differences from the bulk glass with the appearance of an additional low-frequency peak and a higher intensity at the Boson peak frequency. A detailed eigenvector analysis shows that the low-frequency peak corresponds to a shear-horizontal mode which is predicted by continuum theory. The peak at higher frequency ͑Boson peak͒ corresponds to motions that are correlated over a length scale of approximately twice the interaction site diameter. These observations shed some light on the microscopic dynamics of glass formers, and help explain decreasing fragility that arises with decreasing thickness in thin films.

Local dynamic mechanical properties in model free-standing polymer thin films

“…Meanwhile, the shoulder slope of GЈ * ͑z * ͒ becomes milder at higher temperatures ͑i.e., T * = 0.3, 0.4͒, and several of the surface underlying layers exhibit a GЈ * ͑z * ͒ below the bulk value, even if a bulk density has been attained ͑see, for example, z * = 4.0-6.0 and z * = 25.5-24.0 at T * = 0.3, z * = 3.5-6.5, and z * = 25.0-22.0 at T * = 0.4͒. This decrease of the stiffness at bulk-like densities is consistent with observations that the motion of polymer segments near interfaces is highly cooperative, 9 and that the activation energy for segmental motions near free surfaces is much lower. 24 Faster segmental motions near the free surfaces can initiate a global rotational motion that includes many segments, 9 and the mobility of polymer segments in the film can be enhanced even under bulk-like conditions.…”

“…This decrease of the stiffness at bulk-like densities is consistent with observations that the motion of polymer segments near interfaces is highly cooperative, 9 and that the activation energy for segmental motions near free surfaces is much lower. 24 Faster segmental motions near the free surfaces can initiate a global rotational motion that includes many segments, 9 and the mobility of polymer segments in the film can be enhanced even under bulk-like conditions. 24 Above the bulk T g * , we could not find a clear relationship between * ͑z * ͒ and GЈ * ͑z * ͒ or between * ͑z * ͒ and GЉ * ͑z * ͒, mainly as a result of relatively large fluctuations.…”

“…9 Each polymer chain consists of 32 interactive sites ͑i.e., monomer particles͒. The interaction energy function u͑r͒ between nonbonded monomers is given by a shifted Lennard-Jones ͑LJ͒ potential, 17…”

“…Such a choice of parameters inhibits crystallization and facilitates the formation of an amorphous material. 9 In what follows, all quantities are reported in reduced units, 17 e.g., distance r * = r / , number density * = 3 , temperature T * = k B T / ⑀, where k B is the Boltzmann constant, and stress * = 3 / ⑀. The bulk system contains 22 polymer chains under periodic boundary conditions in all three directions.…”

“…1,2 The glass transition temperature T g of chemically amplified photoresist thin films is also a key parameter for optimization of lithographic processes. 3 A number of experimental [4][5][6][7] and theoretical 8,9 studies have shown that T g of thin polymer films can change with thickness h. Mattsson, Forrest, and Börjesson, for example, report that the T g of free-standing polystyrene ͑PS͒ thin films decreases monotonically below thicknesses of 100 nm. 4 In contrast, past work by our group suggests that the T g of supported PS thin films can be either larger or lower than the bulk T g for h Ͻ 100 nm, depending on the chemical interactions between the substrate and the polymer matrix.…”