Structure and Properties of Polymers

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

Glass

Equilibrium line

0

Specific volume

T

1. Cool slowly 2. Heat quickly

Specific volume

Tg depends on time scale of observation

Slow cool Fast heat

Anneal

0

T

0

T

3.2 Polymeric states

Molecular weight

Increase molecular weight to infinity (chemically linked) → All RUBBER in this region

Tg Glass Rubber

Viscous melt

T

1 GPa Glass

log E

Rubber 1 MPa Temperature

~ 10 MPa Viscous creep

Spring: purely elastic, σ = Eε Dashpot: purely viscous, σ = ηε

stiff spring model elasticity of glass (Eg)

dashpot controls short relaxation time processes (frees upon reaching Tg)

Eg-Er

Er

weak spring model elasticity of glass (Er) dashpot for longest relaxation time processes (frees for rubber-melt transition)

η1(T)

η2(T)

η1 and η2 solid → glass: Eg η2 solid, η1 free → rubber: Er

viscosity, η = σ/ε

4.1 Behavior of spring/dashpot models

σ

ε

Maxwell element

Time

tot

=

E

+

− CON. EQN

σ σ0 at time t = τ, σ = σ0/e

0

t

σ ε = σ0/E

t

Voigt element

Add stresses,

σtot = Eε + ηε − CON. EQN ③

Constant ε, ε = 0

σ = Eε

Constant σ, σ = 0

4.2 How realistic?

Assumptions: (i) Viscosity Newtonian η ≠ f (ε) Not very good assumption at high strain rate (ii) Only two relaxation processes

τ1

τ2

LHS controls Tg...