Different metrics for connecting mobility and glassiness in thin films

DeFelice, Jeffrey; Lipson, Jane E. G.

doi:10.1039/c8sm02355g

Cited by 4 publications

(1 citation statement)

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“…At the same time, simulations are generally limited to relatively small timescales, so assumptions need to be made if one were to describe the truly glassy dynamics. There are currently multiple theories that capture the T g -reduction in free-standing thin filmsthe “Elastically Cooperative Nonlinear Langevin Equation” (ECNLE) of Schweizer and co-workers, , the combined “Locally Correlated Cluster” (LCL) – “Cooperative Free Volume” (CFV) approach of Lipson and White, − the “slow-domain percolation” theory of Long and co-workers, − the “string model” of Douglas and co-workers, − and many others.…”

Section: Introductionmentioning

confidence: 99%

Modeling the Glass Transition of Free-Standing Polymer Thin Films Using the “SL-TS2” Mean-Field Approach

Ginzburg

2022

Macromolecules

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In free-standing polymer thin films, the glass-transition temperature decreases as the film thickness is reduced. This behavior is ascribed to the formation of mobile layers near the two film/air interfaces (“free surfaces”). Here, we propose to describe this phenomenon using our recently developed “SL-TS2” mean-field theory, in which the phenomenological “two-state, two-(time)scale” (TS2) approach for the relaxation time is coupled to the Sanchez–Lacombe equation of state (SL-EoS). Here, we first recap our SL-TS2 approach for bulk materials and demonstrate that the model correctly describes both pressure–volume–temperature (PVT) and relaxation time data for polystyrene (PS) and poly(methyl methacrylate) (PMMA) polymers both above and below their glass-transition temperatures (T g). Next, we formulate a simple density-gradient version of SL-TS2 to describe the density and relaxation time dependence of the spatial position in the film near the free surface. By minimizing the free-energy functional, we obtain a simple partial differential equation for the equilibrium density profile and the relaxation time profile. Solving this equation and utilizing a simple logarithmic mixing rule, we can compute the relaxation time dependence on temperature as a function of film thickness. The results are compared with experimental data for free-standing films of PS and PMMA, and a good semiquantitative agreement is found. The approach can be generalized in a straightforward fashion to supported (instead of free-standing) thin films.

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