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