Mechanical properties of thin confined polymer films close to the glass transition in the linear regime of deformation: Theory and simulations

Abstract

Over the past twenty years experiments performed on thin polymer films deposited on substrates have shown that the glass transition temperature T(g) can either decrease or increase depending on the strength of the interactions. Over the same period, experiments have also demonstrated that the dynamics in liquids close to the glass transition temperature is strongly heterogeneous, on the scale of a few nanometers. A model for the dynamics of non-polar polymers, based on percolation of slow subunits, has been proposed and developed over the past ten years. It proposes a unified mechanism regarding these two features. By extending this model, we have developed a 3D model, solved by numerical simulations, in order to describe and calculate the mechanical properties of polymers close to the glass transition in the linear regime of deformation, with a spatial resolution corresponding to the subunit size. We focus on the case of polymers confined between two substrates with non-negligible interactions between the polymer and the substrates, a situation which may be compared to filled elastomers. We calculate the evolution of the elastic modulus as a function of temperature, for different film thicknesses and polymer-substrate interactions. In particular, this allows to calculate the corresponding increase of glass transition temperature, up to 20 K in the considered situations. Moreover, between the bulk T(g) and T(g) + 50 K the modulus of the confined layers is found to decrease very slowly in some cases, with moduli more than ten times larger than that of the pure matrix at temperatures up to T(g) + 50 K. This is consistent with what is observed in reinforced elastomers. This slow decrease of the modulus is accompanied by huge fluctuations of the stress at the scale of a few tens of nanometers that may even be negative as compared to the solicitation, in a way that may be analogous to mechanical heterogeneities observed recently in molecular dynamics simulations. As a consequence, confinement may result not only in an increase of the glass transition temperature, but in a huge broadening of the glass transition.

Mechanical and viscoelastic properties of confined amorphous polymers

“…This crudely leads to a film with some fraction of glassy segments that can effectively pin the polymer chains on the time scale of the measurements . This explanation is similar to the arguments from Dequidt et al where their model uses the broadening of T g on confinement to predict as much as an order of magnitude increase in the modulus between bulk T g and T g + 50 K in comparison to the bulk polymer . Recently, Priestley and coworkers elegantly demonstrated that there is a gradient in viscosity through polymer thin films when probed with non‐contact shear, which is consistent with the distribution of properties explanation of Mirigian and Schweizer.…”

Confinement-Induced Stiffening of Thin Elastomer Films: Linear and Nonlinear Mechanics vs Local Dynamics

“…52 Changes in the Young modulus upon confinement have also been reported in other studies. 52−56 Recently, Dequidt et al 57 made DPD simulations of the reinforcement of polymer films confined under strongly attractive substrates. They found thickness-dependent peaks in the plots of reinforcement vs temperature at temperatures above the bulk T g , which were attributed to the increased T g of the films due to the presence of the attractive surfaces.…”

Concurrent two-scale model for the viscoelastic behavior of elastomers filled with hard nanoparticles

“…Based on the relation for T g (z), the thickness of the glassy layer z th at temperature T can be estimated by T g (z th ) = T , i.e., z th = βT g,b / T − T g,b . The divergence in T g (z) is purely formal, since the physics which lead to this relation [50,51] has a natural cutoff at short distance of about 2 nm. The corresponding increase in the glass transition temperature, about 100 K at 2 nm in their system, corresponds to the increase of T g measured in [7], either in mechanical experiments or by using NMR.…”

“…In particular, the value we chose for the parameter β = 0.8 nm, which sets the amplitude of the T g -shift in the vicinity of the fillers, has been considered in [18], and corresponds to that measured experimentally in [6,7]. The only parameter that is slightly adapted from the many-particle simulations in [18][19][20] to our two-particle model is the stress sensitivity K in (51). In [18], K is determined such that, when imposing an oscillatory strain with amplitude 0.1 and rate 0.1 s −1 , the stress-induced shift of the glass transition temperature is 100 K at the maximum strain, which would result in K = 1.2 · 10 −20 J K −1 .…”

“…However, in order to get better agreement between our model and the results in [20] (see further below), it was advantageous to choose the value K = 2 · 10 −20 J K −1 . In the simulations, the stress-induced shift in the glass transition temperature (51) has been limited to ≤200 K, since above that value the system is already plasticized (see also [19]). Finally, for numerical reasons, the range of the relaxation time (52) has been limited to 0.01 s ≤ τ α ≤ 100 s [20].…”