MRM 2019, Dec. 12, 2019

Yokohama, Japan

Numerical Simulation of Nanoparticle Network Formation

in Transparent Conductive Coating

○ Rei Tatsumi (UTokyo)

Osamu Koike (PIA)

Yukio Yamaguchi (PIA)

Yoshiko Tsuji (UTokyo)

2

Aqueous suspensions

of nanoparticles

How do network structures form?

← Consideration by numerical simulations

Example of network structure:

Wakabayashi et al., Langmuir (2007).

Coating

Drying

Transparent conductive films

3

Drying: capillary force induced by free surface

Particle dispersion/aggregation + ++++ +

+

+++

- --

---

-

-

- --

--

--

-

DLVO potential

Electric double

layer repulsion

Van der Waals

attraction

ℎ

Vertical push into liquid Lateral attraction

Structure of colloidal films

4

Aggregation Drying

Chains Network

Lateral capillary force

Anisotropic

aggregation

×

×

Fixation of

contact point

5

Anisotropic aggregation

×

ℎ

ℎ

Fixation of contact point

×

* *

Stick Slip

DLVO potential

• Random force: 𝐹𝛼R 𝑡 ~𝑁 0, 2𝜉𝑘B𝑇Δ𝑡 (Gaussian dist.)

𝑀 ሶ𝑽 = −𝜉𝑽 + 𝑭R + 𝑭cpl + 𝑭cnt + 𝑭DLVO

• Capillary force: 𝑭cpl

• Drag force: −𝜉𝑽 (Stokes’ law: 𝜉 = 3𝜋𝜂𝑑 )

6

→ Brownian motion

Liquid InterparticleFree surface𝑽

Vertical Lateral

𝑀 ሶ𝑽 = −𝜉𝑽 + 𝑭R + 𝑭cpl + 𝑭cnt + 𝑭DLVO

7

Liquid InterparticleFree surface𝑽

• Contact force/torque: 𝑭cnt, 𝑻cnt • DLVO force: 𝑭DLVO

+ ++

+ +++

++

+

- --

--

-

-

-

- --

--

--

-DLVO potentialℎ

Electric double layer repulsion

Van der Waals attraction

ℎ

Contact point

→ Dispersion / Aggregation→ Aggregation shapes: Chain / Block

* *

Stick Slip

8

𝑥𝑦𝑧

Periodic boundaries 𝑥, 𝑦

Particles

• Diameter 𝑑 = 10 nm

• Zeta potential −50 mV

• Coverage on substrate 𝟑𝟎, 𝟒𝟎, 𝟓𝟎%(Initial volume fraction 2.3, 3.0, 3.8 vol%)

• Particle contact point stick, slip

Liquid (water)

• Ion concentration 10−3 M

• Drying rate 2.2 × 10−3 m/s

25𝑑

25𝑑

8𝑑

DLVO potential

ℎ

Receding

free surface

(1) Aggregation in liquid

(2) Drying on substrate

6𝑘B𝑇

9

Contact number0 4

Stick Slip

Chain Block

Coverage 40%

10

Stick

Slip

Coverage

30% 40% 50%

11

Stick Slip

Chain Block

Coverage 40%

12

Stick

Slip

Coverage

30% 40% 50%

Percolation

13

◆ A possible mechanism of network formation

• Chain formation in liquid:

Anisotropic aggregation by DLVO potential

+ Fixation of contact point between particles

• Connection of chains by capillary force during drying

◆ Consideration of the mechanism of particle network

formation during drying by numerical simulations

◆ Effects of stick/slip particle contact on network formation

Stick → lower percolation coverage (~40%)