^{1}

### Abstract

The results obtained from molecular dynamics simulations of the friction at an interface between polymer melts and weakly attractive crystalline surfaces are reported. We consider a coarse-grained bead-spring model of linear chains with adjustable intrinsic stiffness. The structure and relaxation dynamics of polymer chains near interfaces are quantified by the radius of gyration and decay of the time autocorrelation function of the first normal mode. We found that the friction coefficient at small slip velocities exhibits a distinct maximum which appears due to shear-induced alignment of semiflexible chain segments in contact with solid walls. At large slip velocities, the friction coefficient is independent of the chain stiffness. The data for the friction coefficient and shear viscosity are used to elucidate main trends in the nonlinear shear rate dependence of the slip length. The influence of chain stiffness on the relationship between the friction coefficient and the structure factor in the first fluid layer is discussed.

Financial support from the National Science Foundation (CBET-1033662) is gratefully acknowledged. Computational work in support of this research was performed at Michigan State University's High Performance Computing Facility.

I. INTRODUCTION

II. MOLECULAR DYNAMICS SIMULATION MODEL

III. RESULTS

A. Chain conformation and relaxation dynamics

B. Fluid density, velocity, and temperature profiles

C. Shear viscosity and slip length

D. The dynamicfriction coefficient

E. Fluid structure near solid walls

IV. CONCLUSIONS

### Key Topics

- Polymers
- 62.0
- Friction
- 44.0
- Shear rate dependent viscosity
- 40.0
- Interface structure
- 18.0
- Shear flows
- 13.0

## Figures

A schematic view of the Couette flow configuration with slip at the lower and upper walls. Steady shear flow is generated by the upper wall moving with a constant velocity *U* in the direction while the lower wall is at rest. The slip length and the slip velocity are related via , where is the shear rate computed from the slope of the velocity profile.

A schematic view of the Couette flow configuration with slip at the lower and upper walls. Steady shear flow is generated by the upper wall moving with a constant velocity *U* in the direction while the lower wall is at rest. The slip length and the slip velocity are related via , where is the shear rate computed from the slope of the velocity profile.

Instantaneous positions of fluid monomers (open blue circles) and fcc wall atoms (filled gray circles) at equilibrium (i.e., both walls are at rest). Each monomer belongs to a polymer chain (*N* = 20) with the bending stiffness coefficient *k* _{θ} = 2.5ɛ. Seven chains are indicated by thick solid lines and filled black circles. The fluid monomer density is ρ = 0.91σ^{−3} and the wall atom density is ρ_{ w } = 1.40 σ^{−3}.

Instantaneous positions of fluid monomers (open blue circles) and fcc wall atoms (filled gray circles) at equilibrium (i.e., both walls are at rest). Each monomer belongs to a polymer chain (*N* = 20) with the bending stiffness coefficient *k* _{θ} = 2.5ɛ. Seven chains are indicated by thick solid lines and filled black circles. The fluid monomer density is ρ = 0.91σ^{−3} and the wall atom density is ρ_{ w } = 1.40 σ^{−3}.

The ensemble averaged , , and components of the radius of gyration *R* _{ gx } (▷), *R* _{ gy } (▽), *R* _{ gz } (◁), and the total radius of gyration *R* _{ g } (○) as a function of *k* _{θ} for polymer chains (a) in contact with the solid walls and (b) in the bulk region. The simulations were performed at the constant fluid density ρ = 0.91σ^{−3} while both walls were at rest.

The ensemble averaged , , and components of the radius of gyration *R* _{ gx } (▷), *R* _{ gy } (▽), *R* _{ gz } (◁), and the total radius of gyration *R* _{ g } (○) as a function of *k* _{θ} for polymer chains (a) in contact with the solid walls and (b) in the bulk region. The simulations were performed at the constant fluid density ρ = 0.91σ^{−3} while both walls were at rest.

The time autocorrelation function of the first normal mode Eq. (11) for polymer chains (a) in the bulk region and (b) near the walls for several values of the bending stiffness coefficient. The inset shows the relaxation time of polymer chains in the bulk.

The time autocorrelation function of the first normal mode Eq. (11) for polymer chains (a) in the bulk region and (b) near the walls for several values of the bending stiffness coefficient. The inset shows the relaxation time of polymer chains in the bulk.

Averaged monomer density profiles near the lower stationary wall for the indicated values of the upper wall velocity *U* and ρ = 0.91σ^{−3}. The bending stiffness coefficients are (a) *k* _{θ} = 0.0ɛ and (b) *k* _{θ} = 3.0ɛ. The left vertical axis at *z* = −12.29σ coincides with the fcc lattice plane in contact with the polymer melt. The vertical dashed line at *z* = −11.79σ denotes the location of the liquid-solid interface.

Averaged monomer density profiles near the lower stationary wall for the indicated values of the upper wall velocity *U* and ρ = 0.91σ^{−3}. The bending stiffness coefficients are (a) *k* _{θ} = 0.0ɛ and (b) *k* _{θ} = 3.0ɛ. The left vertical axis at *z* = −12.29σ coincides with the fcc lattice plane in contact with the polymer melt. The vertical dashed line at *z* = −11.79σ denotes the location of the liquid-solid interface.

Averaged normalized velocity profiles for the upper wall speeds (a) *U* = 0.005σ/τ and (b) *U* = 0.5σ/τ and bending stiffness coefficients *k* _{θ} = 0.0ɛ (black lines), *k* _{θ} = 2.0ɛ (red lines), and *k* _{θ} = 3.0ɛ (blue lines). The vertical axes coincide with the location of the fcc lattice planes (at *z*/σ = −12.29 and 9.73). The vertical dashed lines (at *z*/σ = −11.79 and 9.23) indicate reference planes for computing the slip length.

Averaged normalized velocity profiles for the upper wall speeds (a) *U* = 0.005σ/τ and (b) *U* = 0.5σ/τ and bending stiffness coefficients *k* _{θ} = 0.0ɛ (black lines), *k* _{θ} = 2.0ɛ (red lines), and *k* _{θ} = 3.0ɛ (blue lines). The vertical axes coincide with the location of the fcc lattice planes (at *z*/σ = −12.29 and 9.73). The vertical dashed lines (at *z*/σ = −11.79 and 9.23) indicate reference planes for computing the slip length.

Temperature profiles across the channel for the indicated values of the upper wall velocity and bending stiffness coefficients (a) *k* _{θ} = 0.0ɛ and (b) *k* _{θ} = 3.0ɛ. The vertical axes denote the location of the fcc lattice planes (at *z*/σ = −12.29 and 9.73) in contact with fluid molecules. The dashed lines (at *z*/σ = −11.79 and 9.23) mark the position of the liquid-solid interface.

Temperature profiles across the channel for the indicated values of the upper wall velocity and bending stiffness coefficients (a) *k* _{θ} = 0.0ɛ and (b) *k* _{θ} = 3.0ɛ. The vertical axes denote the location of the fcc lattice planes (at *z*/σ = −12.29 and 9.73) in contact with fluid molecules. The dashed lines (at *z*/σ = −11.79 and 9.23) mark the position of the liquid-solid interface.

Shear rate dependence of the polymer viscosity μ (in units of ɛτσ^{−3}) for selected values of the bending stiffness coefficient. The dashed line indicates a slope of −0.37. Solid curves are a guide for the eye.

Shear rate dependence of the polymer viscosity μ (in units of ɛτσ^{−3}) for selected values of the bending stiffness coefficient. The dashed line indicates a slope of −0.37. Solid curves are a guide for the eye.

Variation of the slip length *L* _{ s }/σ as a function of shear rate for the indicated values of the bending stiffness coefficient. The solid curves are drawn to guide the eye.

Variation of the slip length *L* _{ s }/σ as a function of shear rate for the indicated values of the bending stiffness coefficient. The solid curves are drawn to guide the eye.

Log-log plot of the friction coefficient *k* = σ_{ xz }/*V* _{1} (in units of ɛτσ^{−4}) as a function of the slip velocity of the first fluid layer *V* _{1} (in units of σ/τ) for the tabulated values of the bending stiffness coefficient. The dashed curve is the best fit to Eq. (12) with *k* ^{*} = 1.88ɛτσ^{−4} and . The solid curves are guides for the eye.

Log-log plot of the friction coefficient *k* = σ_{ xz }/*V* _{1} (in units of ɛτσ^{−4}) as a function of the slip velocity of the first fluid layer *V* _{1} (in units of σ/τ) for the tabulated values of the bending stiffness coefficient. The dashed curve is the best fit to Eq. (12) with *k* ^{*} = 1.88ɛτσ^{−4} and . The solid curves are guides for the eye.

The normalized structure factor at the main reciprocal lattice vector **G** _{1} = (7.23 σ^{−1}, 0) (a), contact density (b), and temperature (c) of the first fluid layer as a function of the slip velocity *V* _{1} (in units of σ/τ). The values of the bending stiffness coefficient are *k* _{θ} = 0.0ɛ (○), *k* _{θ} = 2.0ɛ (◁), and *k* _{θ} = 3.0ɛ (▷).

The normalized structure factor at the main reciprocal lattice vector **G** _{1} = (7.23 σ^{−1}, 0) (a), contact density (b), and temperature (c) of the first fluid layer as a function of the slip velocity *V* _{1} (in units of σ/τ). The values of the bending stiffness coefficient are *k* _{θ} = 0.0ɛ (○), *k* _{θ} = 2.0ɛ (◁), and *k* _{θ} = 3.0ɛ (▷).

The structure factor (a), number of consecutive monomers per chain (b), and bond orientation (c) in the first fluid layer as a function of the slip velocity. The values of the bending stiffness coefficient are *k* _{θ} = 0.0ɛ (○), *k* _{θ} = 2.0ɛ (◁), and *k* _{θ} = 3.0ɛ (▷). The data for *S*(**G** _{1})/*S*(0) are the same as in Fig. 11 (a).

The structure factor (a), number of consecutive monomers per chain (b), and bond orientation (c) in the first fluid layer as a function of the slip velocity. The values of the bending stiffness coefficient are *k* _{θ} = 0.0ɛ (○), *k* _{θ} = 2.0ɛ (◁), and *k* _{θ} = 3.0ɛ (▷). The data for *S*(**G** _{1})/*S*(0) are the same as in Fig. 11 (a).

Log-log plot of the inverse friction coefficient *k* ^{−1} = *V* _{1}/σ_{ xz } (in units of σ^{4}/ɛτ) as a function of *S*(0)/ [*S*(**G** _{1}) ρ_{ c } σ^{3}] computed in the first fluid layer. The values of the bending stiffness coefficient are tabulated in the inset. The dashed line *y* = 0.041 *x* ^{1.13} is taken from Ref. 42 and it is shown for reference.

Log-log plot of the inverse friction coefficient *k* ^{−1} = *V* _{1}/σ_{ xz } (in units of σ^{4}/ɛτ) as a function of *S*(0)/ [*S*(**G** _{1}) ρ_{ c } σ^{3}] computed in the first fluid layer. The values of the bending stiffness coefficient are tabulated in the inset. The dashed line *y* = 0.041 *x* ^{1.13} is taken from Ref. 42 and it is shown for reference.

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