Molecular dynamics simulation of a pressure-driven liquid transport process in a cylindrical nanopore using two self-adjusting plates.

Abstract

Fluid transport through a nanopore in a membrane was investigated by using a novel molecular dynamics approach proposed in this study. The advantages of this method, relative to dual-control-volume grand-canonical molecular dynamics method, are that it eliminates disruptions to the system dynamics that are normally created by inserting or deleting particles from control volumes, and that it functions well for dense systems due to the number of particles being fixed in the system. Using the proposed method, we examined liquid argon transport through a nanopore by performing nonequilibrium molecular dynamics (NEMD) simulations under different back pressures. Validation of the code was performed by comparing simulation results to published experimental data obtained under equilibrium conditions. NEMD results show that constant pressure difference across the membrane was readily achieved.

Full text

Page 1

Molecular Dynamics Simulation of a Pressure-
Driven Liquid Transport Process in a Cylindrical
Nanopore Using two Self-Adjusting Plates
Cunkui Huang1, Kumar Nandakumar2,
Phillip Choi2, and Larry Kostiuk1
1Department of Mechanical Engineering
2Department of Chemical and Materials Engineering
University of Alberta
1

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Outline
• Introduction and motivation
• Governing equations
• Validation of MD code
• Results and discussion
• Conclusions
2

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Introduction
membrane
bulk water
membrane
bulk water
membrane
Unit
cell
• Zhu et al.
External-Field Driven NEMD
Disadvantage: flow rate
•
Zhang et al.
DCV-GCMD
Disadvantage:
disturbing dynamic field
flow rate
Inserting
Deleting
NEMD: Non-equilibrium Molecular Dynamics
DCV-GCMD: Dual-Control-Volume Grand-Canonical Molecular Dynamics
F. Zhu, E. Tajkhorshid, and K. Schulten, Biophysical Journal 2002, Vol. 83, pp154-160
Q. Zhang et al., Journal of Chemical Physics 2002, Vol. 117, No.2, pp 808-818
3

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Motivation
Propose a novel method that can easily, accurately
and automatically create a constant pressure
difference across nanopore in a membrane, and
simultaneously overcomes the disadvantages
existed in External-Field Driven NEMD and DCV-
GCMD methods.
4

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Governing equations
• Newton’s Second Law
• Lennard-Jones 12-6 Potential
ij
ij
LJ
ij
dr
d
F
φ
−=
v
∑
=
, 1
≠
=
LJ
n
ijj
LJ
ijii
Fam
v
v
⎥
⎦
⎥
⎤
⎢
⎣
⎢
⎡
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
612
4
ij
ij
ij
ij
ijij
rr
σσ
εφ
(note: parameters for liquid argon are ε=1.67×10-21J, σ=0.3405 nm)
5

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Validation of MD code
0.0
0.5
1.0
1.5
2.0
2.5
3.0
24681012
g(r)
Comparison of the radial distribution function of liquid
argon obtained by MD simulation (solid line) with Eisenstein
and Gingrich’s x-ray experimental measurement (filled
symbol) at T=91.8 K and ρ ρ=1.3664 g/cm3.
r(Å)
0.E+00
1.E-14
2.E-14
3.E-14
4.E-14
020406080100120140160180200
Mean square displacement (cm-2)
Integrating time (t-t0) (ps)
Relationship of mean square displacement of
liquid argon with respect to integrating time at
T=90 K and ρ ρ=1.374 g/cm3.
sec 10
×
43. 2
sec
10
×
38 . 2)() (
tr
i
)( 6
1
−
25
25
2
0
0
cm Experiment
cmtr
tt
D
is
−
−
=
=−=
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Simulation set-up
Membrane
Front reservoirBack reservoir
Self-adjusting plate
(applied Pf)
Self-adjusting plate
(applied Pb)
(a)
Y
X
(b)(c)(d)
Snapshot of single nanopore in a membrane. (a) vertical section through axis of
nanopore, (b) cross-section at the middle of the front reservoir, (c) cross-section
at the middle of nanopore, (d) cross-section at the middle of the back reservoir.
Cunkui Huang, K. Nandakumar, Phillip Y.K. Choi and Larry W. Kostiuk, Journal of Chemical Physics 124, 234701, 2006
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Inlet
Outlet
Results and discussion (pressure)
0
10
20
30
40
50
60
70
80
90
100
0200400 600800100012001400 1600 1800 2000
Inlet pressure (Pb=80MPa)
Outlet pressure
(Pb=40, 20, 10MPa)
Inlet and outlet pressures (MPa)
Transport time (ps)
Pressure at the inlet and outlet of the nanopore as a function of
transport time under different back pressures
8

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Inlet
Outlet
Pf=80MPa
Pb=10MPa
Results and discussion (pressure)
-40
-20
0
20
40
60
80
100
46810121416182022 24
Distance z (nm)
Pressure (MPa)
Nanopore
Pressure
Virial component
Kinetic component
∑∑
i
∑
i
>
+
∀
−=
NN
ij
ij ij
N
iii
Fruum
βαβα αβ
σ
1
Pressure distribution averaged on whole cross-section versus distance z
for the case with Pf=80MPa and Pb=10MPa
9

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Results and discussion (pressure)
-100
-50
0
50
100
150
200
0.000.200.40 0.600.801.00
Radial distance (nm)
Pressure (MPa)
Inlet(z=1 1 .5 nm)
z=1 5.5
z=1 2.5
z=1 6.5
z=1 3.5
z=1 7.5
z=1 4.5
Outlet(z=1 8.5)
Total pressure distribution as a function of radial distance at different
location z for the case with Pf=80MPa and Pb=10MPa
10

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Results and discussion (pressure)
Pb=40MPa
Pb=20MPa
Pb=20MPa
Pb=10MPa
0
20
40
60
80
100
46810121416182022
Distance z (nm)
Pressure (MPa)
Pb=40MPa
Pb=10MPa
Nanopore
Pf=80MPa
Pressure distribution as a function of distance z under different back pressures
11

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Results and discussion (density)
0
4
8
12
16
20
24
28
-1.50-1.25-1.00-0.75-0.50-0.250.000.250.50 0.75 1.001.251.50
Distance x (nm)
Number density (1/nm3)
Inlet(z=10 nm)
z=13
z=15
z=17
Outlet(z=20)
Wall
Wall
Number density distribution at entrance part, nanopore and exit part
versus radial distance for case with Pf=80MPa and Pb=10MPa
12

Page 13

Results and discussion (density)
0
5
10
15
20
25
30
-1.50-1.25 -1.00-0.75-0.50-0.250.000.250.500.75 1.00 1.251.50
Distance x (nm)
Number density (1/nm3)
Pb=40MPa
Pb=40MPa
Pb=20
Pb=20MPa
Pb=10
Pb=10MPa
Wall
Wall
Effect of back pressure on number density distribution in the nanopore
13

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Results and discussion (density)
Variation of number density distributions as a function of distance z
under different back pressures.
0
5
10
15
20
25
46810121416 182022
Distance z (nm)
Number density (1/nm3)
Pb=40MPa
Pb=20MPa
Pb=10MPa
Nanopore
14

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Results and discussion (velocity)
0
5
10
15
20
25
30
35
-1.50-1.25-1.00-0.75-0.50-0.250.000.250.500.75 1.001.251.50
Distance x (nm)
Streaming velocity (m/s)
Inlet(z=10 nm)
z=13
z=15
z=17
Outlet(z=20)
Wall
Wall
Streaming velosity distribution at entrance part, nanopore and exit part
versus radial distance for case with Pf=80MPa and Pb=10MPa
15