Crossover to surface flow in supercooled unentangled polymer films

We study the driven flow of an unentangled glassy polymer film with a free upper surface and supported below by a substrate using nonequilibrium molecular dynamics simulations based on a bead-spring model. Above the glass transition temperature $T_g$, simple Poiseuille laminar flow is observed with the film mobility defined as the flow current density per unit pressure gradient scaling as $h^3$ with the film thickness $h$. Below $T_g$, the film mobility becomes independent of $h$, signifying surface transport. This is in full agreement with recent experiments on the time evolution of capillary waves in polystyrene films supported by silica. A mobile layer is found responsible for the surface transport, as previously conjectured. Our result also shows that it has a velocity profile decaying exponentially into the bulk.

Figure 1

A film of 900 chains (randomly colored) of length $N=10$ on a substrate shaded in yellow (bottom) at $T=0.36$. Note that periodic boundary conditions are applied in the lateral directions.

Figure 2

Plot of density $\rho$ against $z$ for a film with 1800 chains at $T=0.36$. The solid lines show fits to a constant and the cumulative normal distribution function for the inner and surface regions, respectively.

Figure 3

Plot of film mobility $M$ against film thickness $h$. The solid and dashed lines show fits to $M\propto h^3$ and a constant, respectively.

Figure 4

Plot of thin-film viscosity $\eta$ against thickness $h$. The solid and the dashed lines show fits to a constant and $\eta \propto h^3$, respectively.

Figure 5

Plots of force-normalized particle velocity $v_x/f_e$ against distance $z$ from the substrate at $T$ $=$ 0.50 (a), 0.40 (b), and 0.36 (c).

Figure 6

Plot of $v_x/h^2{f}_e$ against $z/h$ for $T=0.50$. The solid line shows a fit based on Poiseuille flow with a homogeneous viscosity [Eq. (7)].

Figure 7

Plot of $v_x/f_e$ against distance $h-z$ from the free surface. The solid line shows a fit to an exponential function.