Chapter 12.Chapter 12.Polymer blends, Copolymers, and 

Liquid‐crystal polymers

12.1 Polymer blends

-Miscibility

y

MiscibilityΔGm <0

-Flory-Huggins interaction parameterΔΗm = kTχ12x1x2

ΔG = kT [(x1ln x1)/N1+ (x2ln x2)/N2 + χv1v2]ΔGm  kT [(x1ln x1)/N1+ (x2ln x2)/N2 + χv1v2]

- Miscibility and compatibilization

Statistical thermodynamics for regular sol’n

• ΔSm by lattice modelFilli & l l i + ll– Filling n1 & n2 molecules in n1+n2 = n cells

• volume of 1 ≈ volume of 2 (small molecules)

Boltzmann relation S = k ln P– Boltzmann relation, S = k ln P • P ~ number of (distinguishable) ways 

x ~ mol fractionn ~ numberx1 = n1/(n1+n2)

n = n1 + n2

x1 n1/(n1+n2)

– applying molar quantities,N ~ number of molesN = N1+ N2R = k NA

• heat of mixing– for small molecules in the absence of specific interaction b dbetw 1 and 2

ΔE ~ heat of vapΔE heat of vap

• free energy of mixing

• among polymersΔG = kT [(x1ln x1)/N1+ (x2ln x2)/N2 + χx1x2]ΔGm = kT [(x1ln x1)/N1+ (x2ln x2)/N2 + χx1x2]

– betw B and S ~ metastable

• B ~ binodal point

– at B, dG/dx1 = μ1 = μ2 = dG/dx2• local minor composition fluctuation 

– raise energy

– back to homogeneous solution

• major fluctuation like nucleation• major fluctuation like nucleation

– phase separate to B comp

– ‘nucleation and growth’g

– outside B’s ~ stable

• single phase is stable

LCST vs. UCST

When?

Experimental detection of miscibility

Thermal analysis-Thermal analysis

-Microscopic analysisMicroscopic analysisSEM, TEM, AFM …

-Spectroscopy

what else?-what else?

Experimental detection of miscibility-Thermal analysis-Thermal analysis

miscible

miscibleImmiscible

miscible

miscible

Experimental detection of miscibility-SpectroscopySpectroscopy

Compatibilizationp

- Using compatibilizerex. block or graft copolymerg p y

- Reactive compatibilizationReactive compatibilization

Compatibilization – block or graft copolymer

Compatibilization – Reactive blendingp g

Principal polymer typesp p y yp

Morphologyp gy

How about their properties and applications?How about their properties and applications?

12.3 Copolymersp y

See p 361See p. 361

What will be the difference betweenWhat will be the difference between copolymers and blends?

Self‐assembly of Block Copolymers

PMMA PS B Sph.

A Sph.

Lamella

Sph.p

BA• Phase morphology depends on 

relative polymer‐block chain lengths Gyroid

BCyl.

ACyl.

lengths• Length scale : 10 – 100 nm• PS‐b‐PMMA: PMMA can be easily 

GyroidA B

ODTDisorderedy

removed (etched).fA (A component Volume Fraction)

spheres cylinders lamellae inversecylinders

inversespheres

gyroid inversegyroid

Cocontinuous gyroid phase

Copolymers combining elastomeric and rigid components

Segmented polyurethaneg p y

Tg of copolymers combining elastomeric and rigid componentselastomeric and rigid components

Block Copolymer Thin Film TemplateBlock Copolymer Thin Film Template

Ordering of diblock copolymer on a substratePerpendicular order of cylindrical domains of block copolymer can be obtained by tuning the interactions.

Using Random Copolymer Brushto Produce Neutral Surface

Passivation of SiOx Surfaceto Form Si-H Surfaceto Produce Neutral Surface to Form Si H Surface

t ~ L0

PSPSPMMAP(S-r-MMA)Silicon wafer

12.4 Liquid crystal polymersq y p y

Q What is LC state? Is it liquid or crystal?Q. What is LC state? Is it liquid or crystal?

LC polymer and mesogenic groupLC polymer and mesogenic group

Main chain LC polymer

Side chain LC polymers