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.

1. Nikolai V. Priezjev
Department of Mechanical and Materials Engineering
Wright State University
Movies, preprints @
http://www.wright.edu/~nikolai.priezjev
Effect of chain stiffness on interfacial slip in nanoscale polymer films:
A molecular dynamics simulation study
N. V. Priezjev, “Interfacial friction between semiflexible polymers and crystalline surfaces”,
J. Chem. Phys. 136, 224702 (2012).
N. V. Priezjev, “Fluid structure and boundary slippage in nanoscale liquid films”, chap. 16 in
“Detection of Pathogens in Water Using Micro and Nano-Technology”, IWA Publishing (2012).
Acknowledgement:
NSF (CBET-1033662)x


2. Motivation for investigation of slip phenomena at liquid/solid interfaces
• Navier model: slip velocity is proportional to shear rate via
the slip length. Very important in micro- and nanofluidics
and tribology. Slip length Ls as a function of shear rate:
Thompson and Troian, Nature (1997).
Priezjev, Phys. Rev. E (2007) Linear & nonlinear dependence.
• Degree of slip depends on the structure of the first fluid layer
in contact with the periodic surface potential.
Thompson and Robbins, Phys. Rev. A 41, 6830 (1990).
Barrat and Bocquet, Faraday Disc. 112, 109 (1999).
Priezjev, Phys. Rev. E 82, 051603 (2010).
• Polymer chain architecture: slip velocity is reduced for
liquids which consist of molecules that can easily conform
their atoms into low-energy sites of the substrate potential.
Vadakkepatt, Dong, Lichter, Martini, Phys. Rev. E (2011).
Ls
h liquid
solid wall
Top wall velocity U
slip γV sL 
Navier slip
condition
5.0
)/1()( 
 c
o
ss LL  
Thermal atoms of FCC wall
Molecular Dynamics simulations
x
hexadecane PEB8<Vs Vs

3. -10
-5
0
5
10
/zσ
Fluid monomer density:  = 0.91  3
Weak wall-fluid interactions: wf = 0.8 
FENE bead-
spring model:
2
2
FENE o 2
o
1 r
V (r) kr ln 1
2 r
 
  
 
k = 30 2 and ro = 1.5
Molecular dynamics simulations: polymer melt with chains N=20 beads
Lennard-Jones
potential:
FCC walls with density w = 1.40  3
12 6
LJ
r r
V (r) 4
 
 
    
     
     
ij
i i i
i j i
V
my m y f
y

    

 
1
friction coefficient
Gaussian random forceif
 
 

BLangevin thermostat: T=1.1 k
Ls
h
solid wall
Top wall velocity U
slip γV sL 
z
y x
z
u



)cos1()(V    kbend
Bending
potential:
 5.2kchain stiffness:

4. -12 -10 -8 -6 -4
z/σ
0
1
2
3
ρσ3
0
1
2
3
ρσ3
kθ = 0.0ε
U = 0.01 σ/τ
kθ = 3.0ε
U = 4.0 σ/τ
U = 0.01 σ/τ
U = 4.0 σ/τ
(a)
(b)
0
0.2
0.4
0.6
0.8
1
Vx/U
-12 -8 -4 0 4 8
z/σ
0
0.2
0.4
0.6
0.8
Vx/U
U = 0.5 σ/τ
U = 0.005 σ/τ
(a)
(b)
Density and velocity profiles for different chain stiffness coefficients k
Department of Mechanical and Materials Engineering Wright State University
c = contact density decreases with U
Shear rate  = slope of the velocity profiles
UpperwallspeedU
slip velocity =
= slip velocity
Lower stationary wall
Lower stationary wall
0k
 0.3k
Flexible chains
Stiffer chains
• Layering near the walls is more
pronounced for stiffer chains. • Surprisingly, slip velocity for stiff
chains is larger (smaller) for lower
(higher) upper wall speed U.
γ
• Stiffer chains: residual order in
shear flow due chain orientation.

5. Friction coefficient: k =  / LsN.V. Priezjev, J. Chem. Phys. 136, 224702 (2012).
0.0001 0.001 0.01 0.1
γ
.
τ
0
6
12
18
24
30
36
Ls/σ
kθ = 0.0ε
kθ = 1.0ε
kθ = 2.0ε
kθ = 3.0ε
kθ = 3.5ε
Department of Mechanical and Materials Engineering Wright State University
• Local minimum in Ls
is related to shear-
thinning and friction.
Priezjev, Phys. Rev. E (2010).
• Unexpectedly, incre-
asing chain stiffness
produces larger slip
lengths at low shear
rates but smaller Ls at
high shear rates.
Flexible chains
Stiffer chains
= shear rate
chain stiffness
Dependence of the slip length Ls on the chain stiffness coefficient k
Ls =  / k

6. 0.001 0.01 0.1 1
V1 τ/σ
0.4
1
8
k[ετσ−4
]
kθ = 0.0ε
kθ = 2.0ε
kθ = 3.0ε
kθ = 3.5ε
kθ = 1.0ε
35.02
11 ])/(1[/ 
 VVkk
N=20
Dashed curve = best fit
Priezjev, Phys. Rev. E (2010)
Department of Mechanical and Materials Engineering Wright State University
When the
friction coefficient
is independent of
the chain stiffness.

 11 VV
N.V. Priezjev, J. Chem. Phys. 136, 224702 (2012).
Local maximum in
friction for stiffer
chains: shear-
induced alignment
of chain segments.
chain stiffness
Friction coefficient at polymer-solid interface k as a function of slip velocity V1
k
Friction
coefficient:
k =  / Ls

7. 0.001 0.01 0.1 1
V1 τ/σ
0.4
0.6
0.8
<cos2
θ>
4
6
Nseg
0.04
0.08
S(G1)/S(0)
(a)
(b)
(c)
0.001 0.01 0.1 1
V1 τ/σ
1
2
T1kB/ε
2.5
3
3.5
ρc
σ3
0.04
0.08
S(G1)/S(0)
(a)
(b)
(c)
 0.3k
 0.2k 0k
Structure factor in the first fluid layer:
2rG
1
1
1
)G( 

 ji
l
e
N
S
Temperature
x

Nseg = average number of consecutive
monomers per chain in the first layer
 = average bond orientation
• Shear-induced alignment of
semiflexible chain segments.
 0.3k
0k
Fluid structure in the first layer near the wall as a function of slip velocity V1

8. Analysis of the fluid structure in the first layer near the solid wall
Structure factor in the first fluid layer:
The amplitude of density oscillations ρc
is reduced at higher slip velocities Vs
(by about 10%).
Fluid density profiles near the solid wall:
c = contact density (max first fluid peak)
1st fluid layer
Liquid-solid interface
21
)( 

 ji
l
e
N
S
rk
k
4
8
12
16 0
3
6
0
1
2
3S(k)
kxσ
(a)
kyσ
4
8
12
16 0
3
6
0
1
2
3S(k) (b)
kxσ
kyσ
Sharp peaks in the structure factor (due
to periodic surface potential) are reduced
at higher slip velocities Vs
)( 1GS
N.V. Priezjev, Phys. Rev. E 82, 051603 (2010).

9. 1 10 50
S(0) [S(G1)ρc
σ3
]
−1
0.1
1
4
k-1
[σ4
/ετ]
kθ = 0.0ε
kθ = 2.0ε
kθ = 2.5ε
kθ = 3.0ε
kθ = 3.5ε
kθ = 0.5ε
kθ = 1.0ε
kθ = 1.5ε
Slope = 1.13
lattice vector contact density N.V. Priezjev, J. Chem. Phys.
136, 224702 (2012).
structure factor
Friction coefficient k
at the polymer-solid
interface correlates
well with the struc-
ture of the first fluid
layer near the solid
wall.
Department of Mechanical and Materials Engineering Wright State University
2rG
1
1
)G( 

 ji
l
e
N
S
In-plane structure factor:
low shear
rates
high shear
rates
chain stiffness
Correlation between k and fluid structure in the first layer near the solid wall
Friction
coefficient:
k =  / Ls

10. Conclusions:
• Nonlinear shear rate dependence of the slip length is determined by the ratio of the
shear-rate-dependent polymer viscosity and the dynamic friction coefficient.
• Stiff chains: large slip length at low shear rates and almost no-slip at higher rates.
• A strong correlation between the friction coefficient and fluid structure in the first layer
near the solid wall.
• 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.
http://www.wright.edu/~nikolai.priezjev Wright State University
N. V. Priezjev, “Interfacial friction between semiflexible polymers and crystalline surfaces”,
J. Chem. Phys. 136, 224702 (2012).
x

Friction coefficient: k =  / Ls
NSF (CBET-1033662)
k = k [S(G1)ρc]
Ls =  / k