Dynamics and Structure ofJanus Particles
B4 Okura Tatsuya
Department of Chemical Engineering
Transport Phenomena Lab.
Introduction
Applications
Objective
What is a Janus particle?
2
• two symmetric hemispheres characterized by different surface properties• form a variety of clusters such as micelles, vesicles or layers
analyze the process of cluster forming under shear flow
• design of future nano-materials
[1] Soft Matter, 2015.11, 3767-3771
[1]
• drug delivery• emulsion stabilizers
[2] https://www.google.co.jp/search?q=cell+targeting
[2]
Janus Potential Model
3
jiijjanusijrepulsionjiij UrUU q,q,rq,q,r ˆˆ)(ˆˆ
ijijijrΦj,i,ijU janus rqqqqr ˆˆˆˆ
nijr1
2
nijr1
2
0
2
4 ε
n
ijrσ
n
ijrσ
εrU ijrepulsion
2
exp
ijr
σijrλCσ
ijrΦ
C: interaction strength
: range of the anisotropic interaction
iq̂ijr
jq̂tail
head jiij rrr
: diameter
Potential Energy
Repulsion Potential Janus PotentialTruncated LJ potential
LJU
repulsionU
Multi-particle Simulation
Previous Research
[1] Soft Matter, 2015.11, 3767-37714
<M>
E /N
: Average cluster size
: Shear rate
: Energy per particle
High
Low breakup and reform unstable clusters
destroy clusters:
:
iq̂
jq̂Binary Simulation
Simulation Method
ii VR
otheri
HiiiM FFV
Hiii NΩI
0 fu
pfftf fp )( σIuu
Smoothed Profile Method
a
: Particle radius: Interface width: Interface function
Fundamental EquationsParticles
Host fluid
5R. Yamamoto et al., Phys. Rev. E, 71, 036707 (2005)
Newton – Euler equations
Navier – Stokes equation
6
Results 1• Phase diagram of pair stability
connected
separated
::
::
D4
2
5
10-2
10-2
3)2/,2/( Lu
connectedseparated
10-4 10-3 10-2 10-1
3Tk
D B
DuLPe
7
Results 2= 0.01 = 0.01
high temperature low temperature
8
N = 13icosahedron
Structure
• Narrow peak of N=13
• Various cluster size between N=6 and N=12
[1] Soft Matter, 2015.11, 3767-3771
when
conditions
Numerical analysis of the Structure
9
• Radial distribution function
Rosenthal , Gubbins , and K lapp JCP,136 174901 2012, ( )
rg
iq̂ jq̂
iq̂ jq̂
peak
peak
peak
peak
tail-to-tail
head-to-head
rg parallel
rg elantiparall
10
0rga
0rga
peak
peak
0rg p
0rg p
peak
peak
/r/r
Numerical analysis of the Structure
/r
N = 13icosahedrong a(r
)
g p(r)
g(r)
11
Results 4= 0.2
= 5 C
γ = 0.01
12
Results 50 02.0
gyro layers
= 0.3
02.00
13
iq̂ jq̂
Numerical analysis of Structure
i ijijiija rr
Nr
Vrg rq ˆˆ
4 22
/r
i ijjiijp rr
Nr
Vrg qq ˆˆ
4 22
/r
tetra-layers
g a(r)
g p(r)
0rg p
0rg p
peak
peak
0rga
0rga
peak
peak
14
Rheology
gyro tetra-layers
≃ 0.3 0
: viscosity
02.001.0
15
gyro tetra-layers
≃ 0.3 0 02.001.0
≃ 0.01
micelles(icosahedrons)
elongated micelles
≃ 0.2
Conclusions
Thank you for your attention
16
Appendix
17
18
LJU
repulsionU
Potential Model jiijjanusijrepulsionjiij UrUU q,q,rq,q,r )(
ijijijrΦj,i,ijU janus rqqqqr ˆˆˆˆ
2
exp
ijr
σijrλCσ
ijrΦ
19
0rga
0rga
peak
peak
0rg p
0rg p
peak
peak
/r/r
Numerical analysis of the Structure
/r
g a(r)
g p(r)
g(r)
gyro
≃ 0.30
20
iq̂ jq̂
Numerical analysis of Structure
i ijijiija rr
Nr
Vrg rq ˆˆ
4 22
/r
i ijjiijp rr
Nr
Vrg qq ˆˆ
4 22
/rtetra-layers
g a(r)
g p(r)
0rg p
0rg p
peak
peak
0rga
0rga
peak
peak
g(r)
≃ 0.302.0
21
Appendix
• Compare zigzag with Lees Edwards
• Add terms of potential energy to the Janus potential model x
y
zigzag Lees Edwards
x
yartificial
• Cluster size analysis with algorithm
Rosenthal , Gubbins , and K lapp JCP, 136, 174901 (2012)
22N = 13icosahedron
Pe=50 ,Φ=0.01 , C=5
(a)
i ijijrr
Nr
Vrg
220004
Steady state
/r
rg000
Numerical analysis of the Structure
time
E/N
23
Simulation Conditions 1 box size : 64×64×64
x
y
zigzag
time step : 100×300
2Re
uD
),1,1( uinitial orientation : tail to tail
Binary simulation
: 10-4 ~ 10-2
: 6
: 1
TkB
: 0.036 ~ 0.36
3
ijijijr
σijrλCσ
jiijjanusU rqqq,q,r
ˆˆ2
expˆˆ
where
C: interaction strength
: range of the anisotropic interaction: diameter
24
Simulation Conditions 2 box size : 128×128×128
: 0.01
: 6
: 0.1 ~1
3
TkB
ijijijr
σijrλCσ
jiijjanusU rqqq,q,r
ˆˆ2
expˆˆ
where
time step : 300×500
2Re
uD ),1,1( u
: 0.036 ~ 0.36
Multi-particle simulation
Initial distribution: uniform random
Lees Edwards
x
y
C: interaction strength
: range of the anisotropic interaction: diameter
25
2Re
uD
),1,1( u
ijrjqiqjq,iq,ijr
ˆˆ
2
expˆˆ
ijr
σijrλCσ
janusU
00
0)skrew(
xy
xz
yz
ΩΩΩΩΩΩ
Ω
Appendix
26
27
/r /r
rg000
/r