Glass Transition Temperature (Tg)

Presented byDevansh GuptaM.Sc Polymer

ScienceSemester 2

Contents•Brief Information About Crystallinity •Glass Transition Temperature (Tg)•Free Volume Theory For Tg •Factors Influencing Glass Transition Temperature (Tg)•Sources

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Crystallinity• One of the significant characteristics of polymers is

crystallinity, or the degree of structural order in a polymer.• When the macromolecular chains of a polymer sample are

arranged in an orderly fashion, it is known as a crystalline polymer. • When the chains are not arranged in ordered crystals and are

disordered, even though they are in solid state, the polymer is identified as amorphous.• In most cases, there are no fully crystalline polymers;

therefore, we have semi-crystalline polymers, which are composed of both amorphous and crystalline regions. This is why the same sample of a polymer can have both a glass transition temperature and a melting temperature.

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• Crystalline• Ordered

• Amorphous• Random

• Semi-crystalline• Consists of both

Crystallinity

Crystalline Region

Amorphous Region

Glass Transition Temperature• Glass transition temperature is a temperature at which the

polymer experiences the transition from the glassy state to the rubbery state.• Glassy state is hard & brittle state of material which is consist

of short-range vibrational & rotational motion of atoms in polymer chain, while Rubbery state is soft & flexible state of material which is a long-range rotational motion of polymer chain segments.

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Glassy StateHard & Brittle

Rubbery StateSoft &

FlexibleTg

• Some polymers are used above their glass transition temperature, and some are used below.•Hard plastics like polystyrene and poly methyl methacrylate are used below their glass transition temperature; that is in their glassy state. Their Tg’s are well above room temperature.• Elastomers like polyisoprene and polyisobutylene are used above their Tg’s, that is in the rubbery state, where they are soft & flexible.

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Heating Through Tg Leads To Following

• Break down of Van Der Waals Forces.•Onset of large scale molecular motion.• Polymer goes from glassy/rigid to rubbery behaviour.•Upper service temperature in amorphous polymers.

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Free Volume Theory• One of the most useful approaches to analysing the glass

transition temperature of polymer is to use the concept of Free Volume.• The free volume is the space in a solid or liquid sample that is

not occupied by molecules, that is the ‘empty space’ between molecules.• Free volume is high in liquid state than solid, so molecular

motion is able to take place relatively easy because the unoccupied volume allows the molecules to move.• The theory was originally developed for amorphous polymers

and the glass-transition in those polymers.

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• But semi-crystalline polymers also consist of amorphous regions, so this theory can also be applied to semi-crystalline polymers.• An amorphous polymer can be considered to be made up of occupied volume and free volume. As the temperature is changed, the free volume and the occupied volume both will change.• As the temperature of the melt is lowered, the free volume will be reduced until eventually there will not be enough free volume to allow molecular motion or transition to take place.

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T

V

Tg

Restrictedlocal motion

Greater localmotion

Freevolume

Brittle and glassy Soft and Flexible

Schematic illustration of the total, free, and occupied volume

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• The total sample volume V therefore consists of volume occupied by molecules V0 and free volume Vf such that

V= Vf +Vo• At any given temperature, the fraction of the free volume is

• Around Tg and above Tg, the fraction of free volume can be expressed as,

• Where fg is the fraction of free volume at Tg and αf is an expansion coefficient for the fraction free volume. αf is approximately αm – αg, or the difference between the thermal expansion coefficients of the polymer above and below Tg. • αm stands for melt• αg stands for glass

Where, the approximation is based on Vf << V0. 

Factors Influencing Glass Transition Temperature

• From the previous discussion we know that at the glass transition temperature there is a large scale cooperative movement of chain segments. Therefore it is expected that any structural features or externally imposed conditions that influence chain mobility will also affect the value of Tg.

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• Some of these factors are shown below.

1. Chain Flexibility & Rigidity

2. Steric Effects 

3. Effect of Intermolecular Forces

4. Copolymerization

5. Cross linking & Crystallinity

6. Plasticizer14

1. Chain Flexibility & Rigidity • As Tg depends on the ability of a chain to undergo internal rotations, we

expect chain flexibility to be associated with low glass transitions.• For Example, Poly(dimethyl siloxane) is an extremely flexible polymer

due to the large separation between the methyl substituted silicon atoms. As compared to other polymeric materials, poly(dimethyl siloxane) has the lowest glass transition temperature (Tg = -123.15°C)

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-93.15°C-67.15°C

89.85°C

79.85°Cn

• As shown in previous slide, polymers that contain −CH2−CH2− sequences and ether linkages in the main-chain have relatively easy internal rotations and therefore low Tg values. •While substitution of ethylene groups with p-phenylene units leads to increased chain rigidity and high glass transition temperature.

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2. Steric Effects• The presence of bulky side groups hinders rotation of the

backbone atoms due to steric hindrance, and therefore results in an increase in Tg. The magnitude of this effect depends on the size of the side groups.• This is illustrated in the following Table for vinyl polymers

having the general structure, —[CH2 — CHX ]—

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-93.15°C

-20.15°C

99.85°C

134.85°C

3. Effect of Intermolecular Forces• The presence of polar side groups leads to strong

intermolecular attractive interactions between chains which hinders molecular motion thus causing an increase in Glass transition temperature. • This effect is illustrated in the following table for the polymers

of type −[CH2−CHX ]−

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-20.15°C

80.85°C

84.85°C

4. Copolymerization• It is possible to alter the glass transition of a homo polymer by

copolymerisation with a second monomer. If the two homo polymers prepared from the monomers have different Tgs, then it is reasonable to expect that their random copolymer should have a glass transition which is intermediate between the Tgs of the homo polymers. This is observed experimentally.• The glass transition of a random copolymer is related to the Tgs of the

homo polymers, Tg1 and Tg2, as follows

• Where w1 is the weight fraction of homo polymer 1 and w2 is the weight fraction of homo polymer 2.

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1/Tg = w1/Tg1 + w2/Tg2*

5. Cross-linking & Crystallinity

• Both cross-linking and crystallinity cause an increase of the glass transition temperature.• It is very easy to explain why cross-linking increases Tg since

the presence of covalent bonding between chains reduces molecular freedom and thus the free volume. • Similarly, the presence of crystalline regions in an semi-

crystalline material restricts the mobility of the disordered amorphous regions; thus the glass transition temperature increases which is totally depends on the percentage of crystallinity.

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6. Plasticizer• Sometimes, a polymer has a high Tg than our requirement. To

tackle this proble we just mix something in it called a plasticizer. • Plasticizers are small molecules which will get in between the

polymer chains, and space them out from each other. Thus the free volume will increase. When this happens they can slide past each other more easily. When they slide past each other more easily, they can move around at lower temperatures than they would without the plasticizer. • By this way, the Tg of a polymer can be lowered, to make a

polymer more applicable, and easier to work with.

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Sources• Practical Polymer Analysis By T.R. Crompton (595-629)• Polymer Chemistry - The Basic Concepts By Paul C. Hiemenz (199)• Polymer Physics By ULF W. Gedde (77-95)• Text Book Of Polymer Science By Fred W. Billmeyer (320)• Polymer Science By V.R. Gowariker (113-130)

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