Glass Temperature

The Glass Transition

• On cooling, some polymer melts don't crystallize
rather they form a glass;

Vitrify

Force

Temperature

Soft -- above Tg

Hard -- below Tg

Specific Vol.

Temperature

≈

Total

Volume

Occupied

Volume

• Coefficient of expansion of the polymer liquid (melt)

is approximately twice that of the glass.

• Tg is rate dependent; higher heating/cooling rates

or higher frequencies test rates give higher values
for Tg.

• Both cooling and heating rates should be specified

when measuring and reporting Tg.

• After fast cooling a polymer below Tg, the sample

will try and find the most thermodynamically stable
state through reorganization.

• Possible 'Aging' and embrittlement of polymer held

at up to 50° below Tg.

Practical determination of Tg

• DSC or DTA; use large samples and as high a
heating rate as possible to amplify poor signals.

∆

T or

∆

Temperature

• Several thermal 'definitions' of Tg including;

Onset + (Extrapolated);

Mid line intersection;

Return + (Extrapolated);

Inflection point;

Derivative.

• Tg as measured by thermal methods often show
'peaks' near the transition.

Fast

Slow

∆

T or

∆

Temperature

Specific Vol.

Temperature

• Exotherm near Tg explained as the 'melting out' of

holes or of frozen in 'free volume".

• Experimentally observed Tg is a function of several

variables including :-

Molecular weight

Plasticizer content

Test Rate/Frequency

Sample size

Copolymers/Blends

Cross-linking

Crystallinity

Tacticity

Influence of Crystallinity and Orientation

• Ratio of energy dissipated by viscous component

vs. energy stored by the elastic component;
Tan

(Loss Tangent) is maximum near Tg.

Drawn (x3.5)

Drawn (x5.4)

Crystalline

Amorphous

Tan

Loss Tangent

Temperature (°C)

• Crystallinity

Tg ;

restrain amorphous chains.

• Cold drawing , Tg ;
tension in amorphous
chains.

• Fox-Flory equation:-

Tg = Tg

∞

-K/Mn (K

≈

25x103)

Mn -1

∞

≈

25x10 3

• Situation regarding molecular weight dependence is

experimentally more complicated, some systems
show 2 or 3 straight line regions.

• Transition from entangled coils to isolated coils to

rod like systems. Rods pack more efficiently than
coils so free volume associated with chain end is
lower for rods.

Isolated
coils

Rod-like

molecules

Mn-1

Tangled

coils

• Different K's for different molecular weights;

K from one region can't predict Tg in another.

Note

•

Some RING compounds follow Fox-Flory!!!

•

Hydroxyl terminated PPO has no mol.wt.

dependence of Tg; K=0.!! CH3 terminated K>0.

•

Tg(upper) - restrained amorphous; folds.

Tg(lower) - free amorphous; cilia, loose loops.

Influence of Branching and Cross-links

• Intuitively, adding cross-links increases Tg; restrain

chains more than in uncrosslinked state.

• However, consider joining two chains together

whose molecular weights are M1 and M2.

Type of Join

# of

Ends

End to end

"T" junction

Middles as

"X" joint

• If chains are crosslinked anticipate increase in Tg.

Decrease free volume. Inhibit chain motion.
Increase average size of moving units.

Tg = Tg

∞

-K/M + Kx.(# crosslinks/gm)

Predicted

Observed

% Cross-Links

• Network is a copolymer. If cross-link agent is ‘like’

the polymer the equation above works. If the
chemistry of the cross-link is different could see a
maximum in Tg vs. # of cross-links.

• At very high cross-link densities Tg rises faster than

predicted.

Influence of Copolymerization, Blending and

Plasticization

• Equations developed for these systems depend on

the assumption that free volume is additive.

• General form of the equation for diluents

(plasticizers) is given by :-

p.Vp.Tgp +

d.(1 - Vp).Tgd

Tgs = –––––––––––––––––––––––

p.Vp +

d.(1 - Vp)

Where

= Volume fraction of polymer.

= Coefficient of expansion of

free polymer volume.

Tgp

= Tg of the polymer.

• How do we find

d and Tgp for a low molecular

weight liquid.

Remember;

≈

g; so,

(free volume)

≈

assume

p or

d to be

≈

10-3 for many liquids.

• Make up one or two mixtures and measure Tgs;

then derive Tgd using the above equation.

• For copolymers and blends simplify the previous

equation with some assumptions:-

Tg(copolymer or miscible blend) =

p1.Vp1.Tgp1 +

p2.(1 - Vp1).Tgp2

–––––––––––––––––––––––––––

p1.Vp1 +

p2.(1 - Vp1)

Now,

≈

and Vp1 + Vp2 =1

and many polymer have

≈

the same density so

Vp1

≈

Xp1 - Mole fraction or weight fraction.

so,

Tg(cop/blend)

≈

X1.Tg1 + X2.Tg2

alternatively, 1/Tg(cop)

≈

(W1/Tg1) + (W2/Tg2)

• The above equations hold for immiscible blends and

random copolymers.

• Block copolymers and Immiscible blends phase

separate and show individual Tg's for each phase.

Tg1

Tg2

Composition

Blocks and

Immiscible blends

Random

copolymers

• For crystallizable copolymers Tg depends on the

composition of the amorphous phase. This could
be different from overall copolymer composition;
polymer chains rich in the most crystallizable
component will preferentially crystallize.

-CH -CH -

-CH -CH

-CH

C-

-CH

C-

-CH -CH

+ CH

Influence of Structural Parameters

• Explanations based on the concept of free volume.

-CH

C-

-CH

C-

(

)

• Flexible side groups introduce more free volume.

• More 'linear' Trans chain can pack better reduces

free volume and raises Tg.

-CH

CH -

C=C

CH -

-CH

C=C

Trans

Cis

≈

-120 Tg

≈

-48

x x

• Tg (iso) PS

≈

Tg (atactic) PS;

but, for most polymers Tg (iso) < Tg (atactic)

Rotation is 'easier' in Isotactic materials, favors
changes in conformation chain mobility.
Energy minima are deeper in less crowded
syndiotactic form.