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