Liquid/Solid Surface-01
Some Slip Model
PE/Au
Atomistic representations of the PE/Au system at equilibrium (left) and under constant Couette flow (right).
Sgouros AP, Theodorou DN. Atomistic simulations of long-chain polyethylene melts flowing past gold surfaces: structure and wall-slip. Molecular Physics 2020:1–20. https://doi.org/10.1080/00268976.2019.1706775 .
PE/mica
Schematics for confined polymer melts.
Jeong S, Cho S, Kim JM, Baig C. Molecular mechanisms of interfacial slip for polymer melts under shear flow. J. Rheol. 2017;61(2):253–64. https://doi.org/10.1122/1.4974907 .
Oscillatory Couette flows
(Color online) Positions of fluid monomers (open blue circles) and wall atoms (filled gray circles). The upper wall oscillates with the angular frequency x in the ^x direction (indicated by the double-sided arrow), while the lower wall is always stationary
Priezjev NV. Molecular dynamics simulations of oscillatory Couette flows with slip boundary conditions. Microfluid Nanofluid 2013;14(1-2):225–33. https://doi.org/10.1007/s10404-012-1040-5 .
Some United-Atom PE Force Field
Details of the n-alkanes model
Siepmann JI, Karaborni S, Smit B. Simulating the critical behaviour of complex fluids. Nature 1993;365(6444):330–2. https://doi.org/10.1038/365330a0 .
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The well-known (Siepmann-Karaborni-Smit) SKS united-atom potential model
INTERACTION
form
Parameter
Strectch
U
s
t
r
e
t
c
h
i
n
g
=
k
s
t
r
2
(
l
−
l
e
q
)
2
U_{stretching}=\dfrac{k_{str}}{2}(l-l_{eq})^2
U s t r e t c h i n g = 2 k s t r ( l − l e q ) 2
k
s
t
r
/
k
B
=
452900
K
/
A
˚
2
k_{str}/k_B=452900 \ K/\mathring{A}^2
k s t r / k B = 4 5 2 9 0 0 K / A ˚ 2
l
e
q
=
1.54
A
˚
l_{eq}=1.54 \ \mathring{A}
l e q = 1 . 5 4 A ˚
Bending
U
b
e
n
d
i
n
g
=
k
b
e
n
2
(
θ
−
θ
e
q
)
2
U_{bending}=\dfrac{k_{ben}}{2}(\theta-\theta_{eq})^2
U b e n d i n g = 2 k b e n ( θ − θ e q ) 2
k
b
e
n
/
k
B
=
62500
K
/
r
a
d
2
k_{ben}/k_B=62500 \ K/rad^2
k b e n / k B = 6 2 5 0 0 K / r a d 2
θ
e
q
=
11
4
∘
\theta_{eq}=114^\circ
θ e q = 1 1 4 ∘
Torsion
U
t
o
r
s
i
o
n
a
l
=
∑
m
=
0
3
a
m
c
o
s
m
ϕ
U_{torsional}=\sum\limits_{m=0}^{3}a_mcos^m\phi
U t o r s i o n a l = m = 0 ∑ 3 a m c o s m ϕ
a
0
/
k
B
=
1010
K
a_0/k_B=1010 \ K
a 0 / k B = 1 0 1 0 K ,
a
1
/
k
B
=
2019
K
a_1/k_B=2019 \ K
a 1 / k B = 2 0 1 9 K
a
2
/
k
B
=
136.4
K
a_2/k_B=136.4 \ K
a 2 / k B = 1 3 6 . 4 K ,
a
3
/
k
B
=
−
3165
K
a_3/k_B=-3165 \ K
a 3 / k B = − 3 1 6 5 K
Non-bonded
U
l
j
(
r
)
=
4
ϵ
i
j
[
(
σ
i
j
r
)
12
−
(
σ
i
j
r
)
6
]
U_{lj}(r)=4\epsilon_{ij}[(\dfrac{\sigma_{ij}}{r})^{12}-(\dfrac{\sigma_{ij}}{r})^{6}]
U l j ( r ) = 4 ϵ i j [ ( r σ i j ) 1 2 − ( r σ i j ) 6 ]
C
H
2
:
ϵ
/
k
B
=
47
K
,
σ
=
3.93
A
˚
CH_2: \epsilon/k_B=47 \ K, \sigma=3.93 \ \mathring{A}
C H 2 : ϵ / k B = 4 7 K , σ = 3 . 9 3 A ˚
C
H
3
:
ϵ
/
k
B
=
114
K
,
σ
=
3.93
A
˚
CH_3: \epsilon/k_B=114 \ K, \sigma=3.93 \ \mathring{A}
C H 3 : ϵ / k B = 1 1 4 K , σ = 3 . 9 3 A ˚
Baig C, Mavrantzas VG, Kröger M. Flow Effects on Melt Structure and Entanglement Network of Linear Polymers: Results from a Nonequilibrium Molecular Dynamics Simulation Study of a Polyethylene Melt in Steady Shear. Macromolecules 2010;43(16):6886–902. https://doi.org/10.1021/ma100826u .
这篇论文描述的参数并不能直接输入至LAMMPS 里,需要进行一下单位换算,推荐一个 单位转换工具 ,换算后的结果如下:
k
s
t
r
=
900
k
c
a
l
/
m
o
l
/
A
˚
2
k_{str}=900 \ kcal/mol/ \mathring{A}^2
k s t r = 9 0 0 k c a l / m o l / A ˚ 2
k
b
e
n
d
=
124.2
k
c
a
l
/
m
o
l
/
A
˚
2
k_{bend}=124.2 \ kcal/mol/ \mathring{A}^2
k b e n d = 1 2 4 . 2 k c a l / m o l / A ˚ 2
a
0
=
2
k
c
a
l
/
m
o
l
,
a
1
=
4.01
k
c
a
l
/
m
o
l
,
a
2
=
0.271
k
c
a
l
/
m
o
l
,
a
3
=
−
6.29
k
c
a
l
/
m
o
l
a_0=2 \ kcal/mol, a_1=4.01 \ kcal/mol, a_2=0.271 \ kcal/mol, a_3=-6.29 \ kcal/mol
a 0 = 2 k c a l / m o l , a 1 = 4 . 0 1 k c a l / m o l , a 2 = 0 . 2 7 1 k c a l / m o l , a 3 = − 6 . 2 9 k c a l / m o l
C
H
2
:
ϵ
=
0.0933
k
c
a
l
/
m
o
l
,
C
H
3
:
ϵ
=
0.2265
k
c
a
l
/
m
o
l
CH_2: \epsilon=0.0933 \ kcal/mol, CH_3: \epsilon=0.2265 \ kcal/mol
C H 2 : ϵ = 0 . 0 9 3 3 k c a l / m o l , C H 3 : ϵ = 0 . 2 2 6 5 k c a l / m o l
Capaldi et al.
Capaldi FM, Boyce MC, Rutledge GC. Molecular response of a glassy polymer to active deformation. Polymer 2004;45(4):1391–9. https://doi.org/10.1016/j.polymer.2003.07.011 .
Bolten et al.
Ko MJ, Waheed N, Lavine MS, Rutledge GC. Characterization of polyethylene crystallization from an oriented melt by molecular dynamics simulation. J Chem Phys 2004;121(6):2823–32. https://doi.org/10.1063/1.1768515 .