The excitement of watchingpaints dry

Mahesh S TirumkuduluDepartment of Chemical Engineering

Coating Flows

AtomizationCrackingin Geological Systems

Film Formation and Cracking in Films

FLUID MECHANICS

SOLID MECHANICS

COLLOIDS & INTERFACES

Craquelure

Film Formation & Cracking•Paints contain pigments, binder, solvents, additives•Traditional paints contained volatile organic compounds•VOCs soften particles during deformation, BUT•VOCs are health hazard, regulation to limit their use.

Drying

thic

knes

s

Evaporation

cracking

coalescenceParticledeformation

pigment binder(polymerparticles)

Latex: Water-borne dispersion

(φ≥φrcp)Drying

uniform evaporation

2 wa

cP

r!

= "

“Coffee ring” problem

transverse flow transverse flow

Capillary rise

!

P = "2#waR

!

P = 0

!

2R!

P = 0

Particle DeformationLiquid menisci

!

F

!

F

!

F"R2

~ G# 2

“non-linear”

!

F

!

F

spring

!

F = kx

“linear”

Equivalent“model” film

Particle pairs replaced by non-linear springs

Network of springsG: particle modulusε : strain

Drying and Cracking

microscope

Polymer particles (350 nm) in water

~500 microns

Why do drying films crack ?

Drying film Bimetallic strip!

"1

!

"2

!

("1 >"2)

If the metal films areseparate when cooled :

For the bimetallic strip : TensileCompressive

Lowpressure

Measurement of Transverse Stress

laserpositiondetector

mirror

substrate

latex dispersion

α

( )

3

6s

xxf s

h GL H H h

!" =

+

hs : substrate thicknessH : film thicknessLf : length of filmG : Young’s modulus of substrate

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

2oR!"

# $% &' (

(b)

(c)

(d)

(e)

(f)

(a)

ˆ /( (1 ))o ot tE h )* +

(b) (c) (d)

(f)

(e)

(a)

Non-film forming dispersionCritical Cracking Stress

•Stress-Strain relation

•Recovered Elastic energy,

•Increase in Surface energy,

•Critical Stress for cracking,

!

" ~ G#2

!

Eelastic ~ h2"#

!

Esurface ~ "h

!

" c ~ G13 # h( )

23

!o!

substrate

h!

Critical Stress for Cracking

menisci

Elastic energy = Surface energy

(Stress=modulus x strain2)

(~stress x strain x vol)

Critical stress vs. film thickness

0.01

0.1

1

10 100 1000

PPG342: Experiment

PPG342: Short time limit

PPG342: Long time limit

GMA610: Experiment

GMA610: Short time limit

GMA610: Long time limit

,

2c i oR!

"

# $% &' (

2o o

o c

hN

R)

)

# $* % &' (

Identical particles

!

" c ~ G13 # h( )

23

(Tirumkudulu & Russel, Langmuir, 2005)

Critical Cracking Thickness

A B

Hei

ght

(Ang

stro

ms)

Scan Length (mm)

(Styrene Butadiene particles, 2Ro=250 nm, Tg=65 oC)

Maximum Crack Free Thickness

!

" ~ G13 # h( )

23 ~ $Pmax % h ~ #G

12

$Pmax( )32

menisci

!

P = "2#waR

!

P = 0

!

P = 0

Maximum Crack Free thickness

Stress-Limited Regime

10-13 10-12 10-11 10-10 10-9 10-8 10-7 10-610-7

10-6

10-5

10-4

10-3

103 104 105 106

101

102

hmax

/ R

GM!rcp

R / 2 "

hmax

= 0.41 (GM!rcp

R3/2")1/2

hma

x ,

(m)

GM!rcpR3/2" , (m2)

acrylic styrene-butadiene silica alumina polystyrene zirconia

Acrylic: 82-353 nm; 0.8 GPaS-B: 250 nm; 1.0 GPaSilica: 22, 330 nm; 31 GPaAlumina: 230-489 nm; 156 GPaPolystyrene: 300 nm; 1.6 GPaZirconia: 200 nm; 81 GPa

1 33 2 2rcp

maxmax

20.64

2o

o

GM Rh

P R

! ""

# $ # $% &= % &% & '( )( )

(Singh & Tirumkudulu, Phys Rev Lett, 2007)

Identical particles

Gives a guideline for formulation of paints & coatings

Multiple Cracks

2W = 3.4076 h

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E-06 1.E-05 1.E-04 1.E-03 1.E-02

h (m)

2W (m

)

Alumina, 13nm (Shorlin)

PMMA, 95nm (MT&WBR)

Styrene-Butadiene, 250nm (IITB)

Acrylic, 82nm (IITB)

Acrylic, 133nm (IITB)

Thickness:

Crack spacing vs Thickness

Latex Blends• Closer to “real” paints and coatings• Mixture of hard and soft particles: pigments

and binder• How to predict the mechanical properties of

such a film ? What is the effective modulus ?• Will the same theoretical framework apply to

blends ?

Singh et al, Langmuir 2009(a,b)

Conclusions• Capillary pressure is responsible for cracking.

• Scaling for the critical stress for an isolated crackagrees well with experiment for stable dispersion.

• Critical cracking thickness, measurements agree withpredictions

• Blends-mixed results, more theoretical work required

Acknowledgement

StudentsKarnail Singh (PhD)Laxman Bhosale (MTech)Girish Deoghare(DD)V Ranganath (MTech)Arijit Sarkar (PhD student)T Venugopal (MTech student)

CollaboratorsMartin Murray (AkzoNobel)

FundingDST, IndiaAkzoNobel, UK