Chapter 10
Spinodal Decomposition in Binary
Polymer Blends
M a t E 4 5 4 | A p r i l 2 2 nd, 2 0 1 4
MOHAMMED ALZAYER
EDWARD BRUNS
XIAOLIN BI
Outline
• Introduction
• Theory:
Ideal Solution Model
Regular Solution Model
Flory-Huggins Theory
The Cahn-Hilliard Model
Fox Equation
• Binary Systems Exhibiting SD:
PMMA/ PαMSAN
PMMA/SAN
PEH/PEB
PMMA/PLLA
Incommensurate Films
Composition-dependent heat conductivity systems
• Conclusion
Introduction [1]
• Lower Boundary: thermally
induced mixing
• Upper Boundary: thermally
induced demixing
• Maximum: Highest T for
mixing (UCST)
• Minimum: Lowest T for
demixing (LCST)
[1] Simmons, D. S. (2009). Phase and conformational behavior of lcst-driven stimuli
responsive polymers. (Doctoral dissertation, University of Texas)
Introduction [1]
• Other Behaviors: LCST is the most common
There are others: (a), UCST
but..
only (b), LCST and UCST
curves with multiple
extrema (c and d). merged
LCST and UCST (e), closed
immiscibility loops (f), and
combinations of LCST, UCST,
and closed immiscibility loop
behavior (g and h). Curves
may represent either
spinodal or binodal curves.
[1] Simmons, D. S. (2009). Phase and conformational behavior of lcst-driven stimuli
responsive polymers. (Doctoral dissertation, University of Texas)
Introduction
To be immiscible, i.e. spinodal decomposed:
• Criteria #1:
2 or more chemically different polymers in in a
shared volume
• Criteria #2:
Phase separation between the polymers, macrosized regions of similar-chemical polymer, or single
polymer rich regions dispersed throughout
homogenous mixture
The Ideal Solution Model [2]
• Obeys Raoult’s:
1 (solvent) while 2 (solute). a is the activity of the component, X is
the mole fraction, Pi is the vapor pressure of the solvent before
mixing, and Pf is the vapor pressure of the solvent after mixing
• Enthalpy and entropy of mixing:
[2] Murat, S. (2010). Physical chemistry of polymers: Thermodynamics of solutions
of high polymers. (Doctoral dissertation, Hacettepe University, Ankara, Turkey)
The Ideal Solution Model [2]
• Why does it fail to describe polymer blends?
A solution with a very small solute weight
fraction as well as a small mole fraction
(𝑋2 ) can hardly deviate from the ideality.
Polymer solutions consist of polymeric
solutes with high molecular weights and
mole fractions (99%!)
[2] Murat, S. (2010). Physical chemistry of polymers: Thermodynamics of solutions
of high polymers. (Doctoral dissertation, Hacettepe University, Ankara, Turkey)
The Regular Solution Model [3][4]
• How does it describe SD?
Formation of uni-polymer rich
regions or phase separation
of polymers from a seemingly
uniform matrix/mixture.
• Why does it happen?
SD occurs as a result of
compositions lowering
blend’s Gibbs free energy
[3] Martin, B. (2011). Phase transformations: Nucleation and spinodal
decomposition. MIT. [4] Zang, L. Spinodal Decomposition: Part 1: General
Description and Practical Implications. The University of Utah.
The Regular Solution Model [3][4]
• Notes on the model:
Points where 𝝏𝟐 𝑮/𝝏𝒙𝟐 = 0
called spinodes (inflection
points).
Spontaneous phase separation
faces no thermodynamic
barrier.
i.e. controlled solely by
diffusion.
[3] Martin, B. (2011). Phase transformations: Nucleation and spinodal
decomposition. MIT. [4] Zang, L. Spinodal Decomposition: Part 1: General
Description and Practical Implications. The University of Utah.
Flory-Huggins Theory [5][6]
• considers a low MW solvent and a high MW
polymer in a lattice:
Where xi is molar fraction of the component, Z is coordination number
(nearest # of neighbors in lattice), N is total number of lattice sites, ∆𝑤 is ~
energy of formation, and 𝜑 is fraction of lattice sites occupied.
• And the Flory Parameter is:
[5] Frank, C. (2001). Flory-huggins model for polymer solutions. Stanford
University. [6] Andersson, C. (2008). Flory-huggins theory applied in
atmospheric aerosol modelling. (Master's thesis, Stockholm University)
Flory-Huggins Theory [5][6]
• Why is χ commonly used?
It is independent of concentration
It gives a better approximation of a:
Where 𝑎𝑤 is activity of water, ∅ is volume fraction of
polymer, and r is chain segment number (polymer
volume to water volume ratio).
[5] Frank, C. (2001). Flory-huggins model for polymer solutions. Stanford
University. [6] Andersson, C. (2008). Flory-huggins theory applied in
atmospheric aerosol modelling. (Master's thesis, Stockholm University)
The Cahn-Hilliard Model [7]
• Why another model?
1) Regular & ideal too simple to model real cases
2) It considers chemical kinetics
The difference in concentration is given by
where c is the concentration , 𝑅𝑚 is the amplification factor of the
fastest growing wavelength, t is time, 𝛽 is wavenumber, and 𝛽𝑚 is
the dominate wavenumber during system decomposition.
[7] Bukusoglu, E., Pal, S. K., De Pablo, J. J., & Abbott, N. L. (2014).
Colloid-in-liquid crystal gels formed via spinodal decomposition. Soft
Matter, (10), 1602-1610.
The Cahn-Hilliard Model [7]
• Why another model?
Dynamics of the SD modeled as a function of the
depth of the thermal quench (∆𝑇):
[7] Bukusoglu, E., Pal, S. K., De Pablo, J. J., & Abbott, N. L. (2014).
Colloid-in-liquid crystal gels formed via spinodal decomposition. Soft
Matter, (10), 1602-1610.
Fox Equation [8]
• What is it?
Fox Equations among others utilized to predict Tg
[8] Madbouly, S. A. (2014). Mat E 454: Polymer composites and processing
(Lectures). Iowa State University.
Fox Equation [8]
• What is it?
Fox Equations among others utilized to predict Tg
[8] Madbouly, S. A. (2014). Mat E 454: Polymer composites and processing
(Lectures). Iowa State University.
PMMA/ PαMSAN [9]
• Preparation:
1) Drying at r.t., 3 days, cast solution in Petri.
2) Further dried by vacuum for 3 days at 90 °C.
3) Meltpressing on a hot chamber, at constant T.
4) After annealing, thin film obtained, t=40 mm.
tetrahydrofuran
PMMA
PαMSAN (31 wt% acrylonitrile)
𝑀𝑊 , PDI
14000 g/mol, 2.1
96500 g/mol, 2.26
Techniques: Optical, DSC (10 °C/min), Timeresoloved light scattering (632.8 nm He-Ne)
[9] Madbouly, S. A., & Ougizawa, T. (2004). Spinodal decomposition in binary blend
of PMMA/ PαMSAN: Analysis of early and late stage demixing. Macromolecular
Chemistry and Physics, 205(7), 979–986.
PMMA/ PαMSAN [9]
• Some observations: Near critical composition
75:25. 1-phase (150 °C) to 2 phases (180 °C).
Connectivity not clear until 20 mins. Annealing
time increased, contrast of 2-phase increased.
Late stage of SD (50 mins), co-continuity lost
result of coarsening. “fragmented particles.”
10 min
20 min
50 min
[9] Madbouly, S. A., & Ougizawa, T. (2004). Spinodal decomposition in binary blend
of PMMA/ PαMSAN: Analysis of early and late stage demixing. Macromolecular
Chemistry and Physics, 205(7), 979–986.
PMMA/ PαMSAN [9]
• Notes: LCST, miscible at a limited T range,
miscible at entire w range (1 common 𝑇𝑔 , Fox), χ
increases a lot with T (slope shift from negative
to a small positive) agrees with LCST.
[9] Madbouly, S. A., & Ougizawa, T. (2004). Spinodal decomposition in binary blend
of PMMA/ PαMSAN: Analysis of early and late stage demixing. Macromolecular
Chemistry and Physics, 205(7), 979–986.
PMMA/SAN [10]
• Why add nanoparticles?
Ability to control morphology, improve electrical
properties, change phase separation T and phase
diagram. Behavior becomes more complicated.
One of the polymers absorbs the other, changing
the thermodynamics.
PMMA
SAN
𝑀𝑊 , PDI
15.9 × 104 , 1.64 14.1 × 104 , 2.08
𝑇𝑔
96 °𝐶
105 °𝐶
[10] Gao, J., Huang, C., Wang, N., Yu, W., & Zhou, C. (2012). Phase separation of
PMMA/SAN blends in the presence of silica nanoparticles. Polymer, 53(8), 1772–1782.
PMMA/SAN [10]
• Ajji and Choplin’s Equation to get Ts and Tb:
[10] Gao, J., Huang, C., Wang, N., Yu, W., & Zhou, C. (2012). Phase separation of
PMMA/SAN blends in the presence of silica nanoparticles. Polymer, 53(8), 1772–1782.
PMMA/SAN [10]
• Effect of size: The bigger the particle, the lower
the Tb. Micron sized hardly have an effect (Tb ~ Tb
pure). Tb increases with more particles added.
SiO2 content
3%
3%
3%
-
1%
5%
SiO2 diameter (nm)
12
30
1000
-
30
30
Tb (°C)
172.2 171.8
169
167
171.3
174.5
[10] Gao, J., Huang, C., Wang, N., Yu, W., & Zhou, C. (2012). Phase separation of
PMMA/SAN blends in the presence of silica nanoparticles. Polymer, 53(8), 1772–1782.
PEH/PEB [11]
𝑀𝑊
Contains
Thickness and shape
PEH
PEB
110000g/mol
70000g/mol
2 mol% hexane
15 mol% butane
0.5 mm dog bone
• Preperation: Heat treatments (separation at 130
oC), quenched into liquid nitrogen causing
fracture, etched by 1% potassium permanganate
in a mixture of sulfuric acid and orthophosphoric
acid for contrast.
[11] Yang, L., Yanhua, N., Wang, H., & Wang, Z. (2009). Effects of spinodal
decomposition on mechanical properties of a polyolefin blend from high to low
strain rates. Polymer, 50(13), 2990–2998.
PEH/PEB [11]
• High strain rate (0.01s-1): interfacial relaxation
between phase domains cannot be detected.
• Low strain rate (0.001s-1): drop of tensile
properties with separation when Tc is low. The
effect disappears at high Tc.
[11] Yang, L., Yanhua, N., Wang, H., & Wang, Z. (2009). Effects of spinodal
decomposition on mechanical properties of a polyolefin blend from high to low
strain rates. Polymer, 50(13), 2990–2998.
PMMA/PLLA [12]
• In the figure: “Tapping-mode
AFM images of monolayers
mixtures (25/75,50/50, and
75/25 weight fraction) deposited
on mica at surface pressure 1, 5,
10, and 12 mN/m. Fibrils at
surface pressure higher than 10
mN/m are crystallized PLLA
lamella.”
[12] Sato, G., Nishitsuji, S., & Kumaki, J. (2013). Two-dimensional phase separation of a
poly(methyl methacrylate)/poly(l-lactide) mixed langmuir monolayer via a spinodal
decomposition mechanism.The Journal of Physical Chemistry, 117(30), 9067–9072.
PMMA/PLLA [12]
• 2D: Analogous to 3D’s nucleation and growth
• Spinodal ring: FFT shows doughnut like pattern
in inserts. Phase-separated structures possess
concentration fluctuation with a specific λ:
• Early Stage: wavelength of dominant mode is
independent of t, whereas the concentration
fluctuations, Δϕ(t), grow with time
[12] Sato, G., Nishitsuji, S., & Kumaki, J. (2013). Two-dimensional phase separation of a
poly(methyl methacrylate)/poly(l-lactide) mixed langmuir monolayer via a spinodal
decomposition mechanism.The Journal of Physical Chemistry, 117(30), 9067–9072.
PMMA/PLLA [12]
• Intermediate stage: described by both λ and
Δϕ(t) growing with time.
• Final stage: λ increases with time, while Δϕ(t)
already saturates to its equilibrium value.
[12] Sato, G., Nishitsuji, S., & Kumaki, J. (2013). Two-dimensional phase separation of a
poly(methyl methacrylate)/poly(l-lactide) mixed langmuir monolayer via a spinodal
decomposition mechanism.The Journal of Physical Chemistry, 117(30), 9067–9072.
Incommensurate Films [13]
• Top: 2.5 µm of film
surface at 160 min,
majority perpendicular
lamellar morphology
(PS dark, PMMA light).
• Bottom: SCFT calculation of mixed morphology
intermediate state.
[13] Peters, R. D., Pawel, S., Matsen, M. W., & Dalnoki-Veress, K. (2013). Morphology
induced spinodal decomposition at the surface of symmetric diblock copolymer
films. ACS Macro Letters, 2(5), 441–445.
Composition-dependent Heat
Conductivity Systems [14]
• Quench conditions: structure resulting from SD
varies with quench condition.
• Example: in the figure, the left wall is
quenched, while the right wall is insulated
[14] Molin, D., & Mauri, R. (2008). Spinodal decomposition of binary mixtures with
composition-dependent heat conductivities. Chemical Engineering Science, 63(9),
2402–2407.
Composition-dependent Heat
Conductivity Systems [14]
λ stands for heat
conductivity ratio,
while â is a
characteristic length
and D is a mass
diffusivity
parameter. Overall,
the 105 â2/D
translates between
1-10 seconds. NLE,
the lewis number,
stands for the ratio
of thermal to mass
diffusivity.
[14] Molin, D., & Mauri, R. (2008). Spinodal decomposition of binary mixtures with
composition-dependent heat conductivities. Chemical Engineering Science, 63(9),
2402–2407.
Conclusion
• From this presentation: we can
conclude that spinodal
decomposition is important in
polymers science.
• We can take it further: improve the
miscibility of blends by introducing a
third polymer (compatibilizar).
• It’s beyond this chapter: no longer
binary, but rather ternary.
• Why ternary? High concentration of
third polymer is needed.