ISCST 2020, Sept. 22, 2020

Mesoscale Modeling of Colloidal Films Dried with Controlling

the Morphology of Aggregated Particles○ Rei Tatsumi(UTokyo)
Osamu Koike(PIA)
Yukio Yamaguchi (PIA)
Yoshiko Tsuji(UTokyo)

2Dispersing

CoatingDrying

Functions

Structures• Strength • Permeability• Porosity• Electrical/Thermal conductivity• Contact network• Optical property

3Particle dispersion/aggregation DLVO potential- - - + + - ++ + - +++ - -- ++- -Electric double layer repulsionℎVan der Waals attraction

Drying: capillary force induced by free surface

Vertical push into liquid

Lateral attraction

Structure formation

4

Modeling of adhesion to describe the various
morphologies of aggregated particles



Effects of adhesion on structure formation during drying

Diffusion*

Diffusion-limited

Adhesion: Fixation of contact points(Reaction)

Reaction-limited5𝛀

𝑀𝑽 = −𝜉𝑽 + 𝑭R + 𝑭cnt + 𝑭DLVO +𝑭cpl

𝑽𝐼 𝛀 = −𝜁𝛀 + 𝑵R + 𝑵cnt
Hydrodynamic force/torque
Drag + Fluctuations → Brownian motion
DLVO force

DLVO potential- + + - ++ ++- + + -- ++- -ℎElectric double layer repulsionℎVan der Waals attraction

Capillary force
Vertical push into liquid

Lateral attraction

6𝑀𝑽 = −𝜉𝑽 + 𝑭R + 𝑭cnt + 𝑭DLVO +𝑭cpl

𝛀𝑽𝐼 𝛀 = −𝜁𝛀 + 𝑵R + 𝑵cnt
Contact force/torque

*

*

Slip

StickAdhesion

NormalShear

Bending

Twist

Constraint on the relative motions

How does adhesion affect the structure of particles?

7Particle diameter: 𝑑 = 10 nm
Zeta potential: 0 mV

Slip

Contact number

12

Stick

Characteristic time ofparticle diffusion: 𝜏D = 𝑑 2 /𝐷0Particle diameter: 𝑑Diffusion coefficient: 𝐷8Constant rate

Drying rate

Evaporation-controlled

Falling rate
Transport-controlled(I) Particle layer growth(II) Drying of particle layer

Drying time
Drying rate vs. Structure

9Drying rate:

𝑈𝑅0=
𝑈0 𝑅0 + 𝑅p

Resistance of evaporation: 𝑅0
Resistance of particle layer: 𝑅p

𝑈

Aggregated particles moving with free surface

𝑅p =𝑟 𝑧 d𝑧
𝑃𝑟 𝑧 =80
𝐷H 𝑧

𝑆tot
2𝑆 𝑧
f

4𝑆f
Hydraulic diameter: 𝐷H =𝐿f𝑧
𝑦𝑥

Cross-sectional area of the flow: 𝑆f
Wetted perimeter: 𝐿f
Cross-section

10Slip

StickFilm height

Drying rate

Particle diameter: 𝑑 = 20 nm
Zeta potential: −50 mV

Drying time

11Slip𝑧

Time unit:
𝑈0 𝑡/𝑑Volume fraction

Stick

12

Drying of colloidal droplets

Compression

Porosity vs. Strength

13

Slip
Apparent diameter: 𝐿Contact number

12

Stick

0Particle diameter: 𝑑 = 20 nm, Zeta potential: −50 mV

Constant drying rate: 𝑈14Strength:−3𝑑 ∗𝐹w 𝑥d𝑥𝑑𝑥w0

Slip

Stick𝐹w2𝐹w1

0𝑥×𝑥𝑥w

0𝑥

15

Slip
Diameter Porosity

StickStrength

Slip

10.20.070.35

Stick11.50.340.64

Strong granule with high porosity

16

CoatingDrying
Aqueous suspensionsof nanoparticles

Example of network structure:
Wakabayashi et al., Langmuir (2007).

Transparent conductive films

How do network structures form?

174Block

Stick

DLVO potential

Contact number

Slipℎℎ0Anisotropic aggregation
×

Chain

Particle diameter: 𝑑 = 10 nm

Fixation of contact
×point

18

Slip

Block

Stick

Chain

19



Modeling of adhesion between particles→ Morphologies of aggregate• Constraint on relative motions between contacting particles→ Fixation of contact points• Possible factor of adhesion in real systems: Binder additionAdhesion → Structures with high porosity formed during drying• High permeability (drying rate)• High strength• Network structures → Transparent conductive films