Amorphous Polymer

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Amorphous Polymers

• When is a Polymer Amorphous ? Examples

• Why is a Polymer Amorphous ?

• Amorphous Polymer Properties

• Structure of Amorphous Polymers

–Long Range vs Short Range Order

–Shape of Polymer Chains (Random Coil Models)

–Experimental Confirmations (Neutron Scattering)

–Other Models (Non Random Coils)

• Dynamics of Polymer Chains: Viscosity



When is a Polymer Amorphous ?

• Glassy Polymer

Amorphous below Tg: PS, PMMA, Epoxy at Room Temperature

• Rubbery Polymer

Amorphous above Tg: Crosslinked High Molar Mass Polyisoprene,

Polychloroprene, Silicones, Polybutadiene at room temperature

• Molten Semicrystalline Polymer

Crystallizable Polymer above Tm: PE (T > 140°C), it-PP (T > 170°C),

PET (T > 270°C), PEEK (T > 360°C)

• Between Crystals in Semicrystalline Polymers (T < Tm)



Degree of Crystallinity of Statistical Ethylene Copolymers as

a Function of Branch Content

• Amorphous state stable above Tm

• Some polymers do not crystallize

Why ?

• Crystallization kinetics too slow(next chapter)

• Structure is not conducive to order

• Tacticity defects

• Regio defects

• Branching (copolymerization)

Why is a Polymer Amorphous ?

Macromolecules, 1999



Properties of Amorphous Polymers

• Below TgMolecular motion is very localized (vibrations and few bond rotations)Hard, Brittle and High Modulus

• In the Tg Region

Onset of large-scale molecular motions (vibration and significant bond rotations)Soft, tough and lower Modulus.Properties depend on time/speed/frequency of perturbation

• Rubbery Plateau Region

• Flow Region



Structure of Amorphous Polymers

• Short-Range Order • No Long-Range Order

a) polybutadiene (stretched 535%);

b) Silicone (stretched 540%;

c) sodium metaphosphate glass fibera) liquid benzene

b) glass slide; c) quartz powder

d) single crystal (organic salt)



Chain Size and Chain Statistics (linear polymers)

• Knowing the number of repeat units of a polymer chain, can we calculate its size ?

• Three basic models for linear polymer chains with various levels of approximationand sophistication.

– Random flight or freely jointed chain model:Assume the polymer chain can be described by a random flight in threedimensions (fixed bond length & random valence angle)

– Freely rotating chain model:Add the constraint of fixed valence angle to the previous model

– Hindered rotation model:Add the constraint that the dihedral angles describing the rotation of backboneatoms around single bonds cannot be random.



Random Flight or Freely Jointed Chain Model:(a.k.a. random walk, drunken sailor, etc..)

• Question: What is the distance separating the beginning and the end points of a

random walk of N steps, each of length L ?

• Vectorial Approach:

r

r2=

r

Lii=1

i= N

∑ ⋅r

L j j=1

j= N

∑ =r

Li j=1

j= N

∑i=1

i= N

∑ ⋅r

L j

r

r2=

r

Lii=1

i= N

∑ ⋅r

Li + 2

r

Li ⋅r

L j1≤i< j≤ N

∑

= NL2 + 2 L2 cos ij( ) j=1

j= N

∑i=1

i= N

∑ = NL2

r

r2 = NL2

r

r =r

Lii=1

i= N

∑

zero

mean squared end to end distance



Freely Rotating Chain Model

• Valence angles are identical and fixed and bonds can rotate freelyaround each other preserving the valence angle θ

r

r2

fr = NL2

1− cos1

+ cos

r

r2

fr = 2 NL2

• Since θ > 90° (usually), <r 2>fr > <r 2>fj

In the case of an all-carbon backbone θ = ca. 109° , cos(θ) = -1/3



Hindered Rotation Chain Model

• Rotations around single bonds along the chain are not free.

• Hindered Rotations are due to Steric Repulsions between chemical

groups in neighboring repeat units.

C ∞ =r 2

0

NL2Characteristic

ratio

Steric factor, σ2

r

r2

0= NL2

1− cos

1+ cos

1− cos

1+ cos

mean squared unperturbed

end-to-end distance



Rotational Potential



Molecular Weight Dependence of Chain Size

in the Pure Melt (Theta State)

The results discussed in the previous slide apply to the case of polymer chains

in the melt or in solution at the theta temperature where they have their

“unperturbed” dimensions.



Experimental Evidence

for the Random Coil Model

• SANS: Small Angle Neutron Scattering

• Zimm Plot Radius of Gyration and Weight Average Molar Mass



Structure – Property Correlations:Chain Characteristic Ratio, Packing Length,

Entanglement Molar Mass, Rubbery Plateau Modulus

• Packing Length: p

p can be viewed as the molecular diameter of the repeat unit in a polymer chain.

p is defined as the ratio of the volume occupied by a chain divided by it mean

square end to end distance.

p = M < r 2 >0 N a

< r 2>0= C ∞nl0

2

e

N

M

RT G

8.00=

• Me

: Entanglement Molar Mass

• G N0: Rubbery Plateau Modulus

J. Polym. Sci. Polym. Phys. Ed. 1999, 37, 1023



Other Models of the Amorphous Phase

Amorphous Polymer

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