Structure And Properties Of Polymers Essay

3266 words - 14 pages

C 10 Lecture Notes
Freely jointed chain, a “phantom” chain n links of same length, ak Joints permit completely free rotation

Mean squared end to end length = nkak2 Contour (stretched out) length Lc=nkak

Persistence length aq=ak/2

What is the size of the blob?

For an ideal Kuhn chain RG2 = RL2/6 (approx.) RG: Characteristic radius of blob

3. Non-crystalline Polymer (Physical States of Matter) 3.1 Glass transition temperature
Specific volume
a) Tg occur in all materials where crystallinity doesn’t get in the way Melt/Rubber
b) Because it is not an equilibrium phase, glass transition is not a thermodynamic transition


Equilibrium line

Specific volume

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1 Modulus of glass
Eg ~ E of van der Waals solid (held together by VdW forces), approx. 1 GPa Einorganic glass ~ 65 GPa → combinations of ionic bonding and Si – Si Emetal : steel ~ 210 GPa Al ~ 70 GPa Epolymer chain pulled out ~ 250 GPa

5.2 Viscosity of η1 dashpot
In region of Tg, (a) Time-temperature superposition (Fig 5.1) (b) Superimposed curve, made by shifting data by log aT (Fig 5.2 b) (c) Plot of shift factor aT vs. temperature (Fig 5.2 c)

Williams-Landel-Ferry (WLF) found empirical equation to describe (c)

Ts ~ reference temperature, works well if Ts = Tg With C1 = 17.4 , C2 = 51.6 K

Implication: log aT (i.e. η1) turns to ∞ when T = Tg – C2 → (Tg – 51.6) K ∴Creep of polymer glass turns to zero at temperature (Tg – 51.6) K or lower

Justification of WLF in terms of free volume
Specific volume

Occupied volume



Second Input: Doolittle Equation

5.3 Elasticity of Rubber Spring

5.4 Viscosity of
Rubber ⇄ viscous melt?


Viscous flow ~ relative motion of centers of masses of molecules

A. Reptation Model
Molecules effectively confined in tube by entangling neighbours Constraints physical cross-linked points Reptation - Molecule can only escape lengthwise Parameters:

Need two other equations:

Above critical molecular weight for entanglement,

Below entanglement molecular weight,

For a monomer, critical distance

e.g. High molecular weight PE,

6. Crystallization and crystal structure of polymer 6.1 Why are some polymers not crystalline?

T Tm

TTT Diagram

i) PE crystallizes very fast, non quenchable


ii) PC crystallizes very slow, long anneal between Tg and Tm  crystallization iii) PET, few seconds at maximum rate (faster when stretching the melt)

Tg log t


Atactic - different stereoregular isomers joined together at random e.g. 1) Atactic PS, Tg ~ 100˚C Exceptions: PVOH

But some crystals have very small OH groups and can fit into crystal 2) atactic PVC glass, Tg ~ 80˚C But 12% crystallinity, very important for plasticization


Crystallinity lost



100% A

100% B

- neither will fit easily into a crystal lattice

Branced PE



incorporate in crystal defect


rejection from crystal on growth (think LDPE)

sits in amorphous components

PMMA 80%


Me C Ester C

Ester C Me C


C Ester


Side View

6.2 Crystallization: Process & Morphology
(a) Thermodynamic Consider crystallization from dilute solution, so one molecule produces one crystal.
Fold surface → high energy σf = 0.06 J m-2






Stem For new stem, 50% probability of remaining Long period, measure with small angle X-ray diffraction

At equilibrium, T will be the melting point of crystal of thickness L.

For finite crystallization rate ~ need additional undercooling:

What is

Tm =...

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