Relationship between induced fluid structure and boundary slip in nanoscale polymer films

The molecular mechanism of slip at the interface between polymer melts and weakly attractive smooth surfaces is investigated using molecular dynamics simulations. In agreement with our previous studies on slip flow of shear-thinning fluids, it is shown that the slip length passes through a local minimum at low shear rates and then increases rapidly at higher shear rates. We found that at sufficiently high shear rates, the slip flow over atomically flat crystalline surfaces is anisotropic. It is demonstrated numerically that the friction coefficient at the liquid-solid interface (the ratio of viscosity and slip length) undergoes a transition from a constant value to the power-law decay as a function of the slip velocity. The characteristic velocity of the transition correlates well with the diffusion velocity of fluid monomers in the first fluid layer near the solid wall at equilibrium. We also show that in the linear regime, the friction coefficient is well described by a function of a single variable, which is a product of the magnitude of surface-induced peak in the structure factor and the contact density of the adjacent fluid layer. The universal relationship between the friction coefficient and induced fluid structure holds for a number of material parameters of the interface: fluid density, chain length, wall-fluid interaction energy, wall density, lattice type and orientation, thermal or solid walls.

Figure 1

(Color online) A schematic of the flow with slip boundary conditions at the lower and upper walls. Shear flow is induced by the upper wall moving with a constant speed $U$ in the $\widehat{x}$ direction. The slip velocity and slip length $L_s$ are related via $V_s=\dot{\gamma }{L}_s$, where $\dot{\gamma }$ is the shear rate computed from the slope of the velocity profile.

Figure 2

(Color online) A snapshot of fluid monomers (open blue circles) and wall atoms (filled gray circles) positions. Five polymer chains are marked by solid lines and filled black circles. The black arrow indicates the direction of the upper wall velocity $U=0.5\sigma /\tau$. The fluid monomer density is $\rho =0.89{\sigma }^{-3}$ and the wall density is ${\rho }_w=1.80{\sigma }^{-3}$. The rest of parameters for the system 5 are given in Table .

Figure 3

(Color online) Averaged normalized velocity (a) and density (b) profiles across the channel for the upper wall speeds $U=0.5\sigma /\tau$ and $U=4.0\sigma /\tau$. The uniform monomer density of the polymer melt $N=20$ away from the walls is $\rho =0.89{\sigma }^{-3}$ (system 5 in Table ). The vertical axes indicate the location of the fcc lattice planes (at $z/\sigma =-11.30$ and 15.14) in contact with the fluid. The dashed lines at $z/\sigma =-10.80$ and 14.64 denote reference planes for computing the slip length.

Figure 4

(Color online) Shear rate dependence of the fluid viscosity $\mu$ (in units $\epsilon \tau {\sigma }^{-3}$) for the indicated systems (listed in Table ). The dashed line with a slope $-0.37$ is shown for reference. Solid curves are a guide for the eye.

Figure 5

(Color online) Slip length $L_s/\sigma$ as a function of shear rate for polymer melts with chains $N=20$ and $N=10$ (see inset). The system parameters are listed in Table . Open circles in the inset represent the (111) face of the fcc lattice atoms in contact with the fluid. The vertical blue arrow indicates the shear flow direction with respect to the $\left[11\overline{2}\right]$ fcc lattice orientation (systems 5 and 7). The horizontal black arrow shows the flow direction with respect to the $\left[1\overline{1}0\right]$ orientation (systems 6 and 8).

Figure 6

(Color online) Log-log plot of the friction coefficient $k=\mu /L_s$ (in units $\epsilon \tau {\sigma }^{-4}$) as a function of the slip velocity $V_s=L_s\dot{\gamma }$ (in units $\sigma /\tau$) for systems listed in Table . The values of the normalization parameters $V_s^{\ast }$ and $k^{\ast }$ are presented in Fig. 7. The dashed curves $y={\left(1+x^2\right)}^{-0.35}$ are the best fit to the data.

Figure 7

(Color online) The normalization parameters $V_s^{\ast }$ (in units $\sigma /\tau$) and $k^{\ast }$ (in units $\epsilon \tau {\sigma }^{-4}$) used to fit the data in Fig. 6 to Eq. (7). The indices in the inset denote systems listed in Table . The dashed line with a slope $-1.30$ is shown for reference.

Figure 8

(Color online) The mean square displacement of monomers in the first fluid layer at equilibrium (i.e., $U=0$) as a function of time $t$ (in units $\tau$) for selected systems listed in Table . The dashed lines are shown for reference.

Figure 9

(Color online) A correlation between the characteristic slip time $t_s^{\ast }$ of the first fluid layer and the diffusion time $t_d$ of fluid monomers between nearest minima of the surface potential. The system parameters are given in Table . The dashed line $y=x$ is shown as a reference.

Figure 10

Two-dimensional structure factor $S\left(k_x,k_y\right)$ computed in the first fluid layer for $N=1$ and $U=0.05\sigma /\tau$ [systems (a) 19 and (b) 17 in Table ]. The wall-fluid interaction energy is (a) ${\epsilon }_{\text{wf}}=0.3\epsilon$ and (b) ${\epsilon }_{\text{wf}}=0.4\epsilon$. The shear flow direction (denoted by the horizontal arrow) is parallel to the $\left[11\overline{2}\right]$ orientation of the (111) face of the fcc wall lattice (open circles).

Figure 11

Structure factor $S\left(k_x,k_y\right)$ averaged in the first fluid layer for $N=20$ polymer systems (a) 5 and (b) 6 (see parameters in Table ). The sharp peaks are located at (a) $\left(7.86{\sigma }^{-1},0\right)$ and $\left(3.93{\sigma }^{-1},6.81{\sigma }^{-1}\right)$, and (b) $\left(6.81{\sigma }^{-1},3.93{\sigma }^{-1}\right)$ and $\left(0,7.86{\sigma }^{-1}\right)$. In each case, horizontal arrows indicate the shear flow direction with respect to the orientation of the (111) plane of the fcc wall lattice (denoted by open circles). The upper wall speed is $U=0.05\sigma /\tau$ in both cases.

Figure 12

Structure factor $S\left(k_x,k_y\right)$ computed in the first fluid layer for $N=20$ polymer system 12 (see Table ). The upper wall speed and slip velocity are (a) $U=0.05\sigma /\tau$ and $V_s=0.012\sigma /\tau$ and (b) $U=2.0\sigma /\tau$ and $V_s=0.51\sigma /\tau$, respectively. The location of the main induced peak in the shear direction is $\left(6.18{\sigma }^{-1},0\right)$. The horizontal arrow denotes the shear flow direction with respect to the orientation of the (001) face of the bcc wall lattice (open circles).

Figure 13

(Color online) Log-log plot of the ratio $L_s/\mu$ (in units ${\sigma }^4/\epsilon \tau$) as a function of the variable $S\left(0\right)/\left[S\left({\mathbf{G}}_1\right){\rho }_c\right]$ computed in the first fluid layer at low shear rates. The system parameters are listed in Table . The dashed line $y=0.041x^{1.13}$ is the best fit to the data.

Figure 14

(Color online) Log-log plot of the ratio $L_s/\mu$ (in units ${\sigma }^4/\epsilon \tau$) as a function of variables (a) $S\left(0\right)/\left[S\left({\mathbf{G}}_1\right){\rho }_c\right]$ and (b) $S\left(0\right)/S\left({\mathbf{G}}_1\right)$ computed in the first fluid layer at all shear rates examined. The system parameters are given in Table . The black line with a slope 1.13 is shown for reference.