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Formulation Chemistry - Polymer: The Glass Transition
In the solid state, semicrystalline polymers exhibit both amorphous and crystalline morphology. The glass transition is a property of only the amorphous portion of a semi-crystalline solid.  The glass transition temperature, Tg, is the temperature at which the amorphous materials change between the glassy and rubbery form.
1.1 Amorphous and Crystalline Polymers
The amorphous polymers consist of molecules that are oriented randomly, unlike the crystalline ones which have polymer chains packed in ordered, repeating patterns in the three-dimensional crystal lattice. However the glass transition is different to melting because only amorphous polymers undergo the glass transition. Melting is a transition that occurs in crystalline polymers when these chains are disoriented from the crystal structures and become liquid. A sample of semicrystalline polymer can be composed of both amorphous and crystalline portions, therefore it can have both a glass transition temperature and a melting temperature.
1.2 Glassy and Rubbery States
Below Tg, the amorphous regions of a polymer are in a glassy state and most joining or contact bonds are intact.  The molecules may be able to vibrate slightly, but are virtually motionless in which portions of the molecule wiggle around. Therefore polymer is generally hard, brittle and rigid. As the polymer is heated until it eventually reaches its glass transition temperature, the molecules start to wiggle around. In inorganic glasses, more bonds are broken with increased thermal fluctuations; while in organic polymers, non-covalent bonds between chains also become weaker. By heating above Tg, there is long-range segmental motion where the polymer chains can move around easily. It is now described in its rubbery state which offers flexibility and softness for plastic deformation without fracture.
Below Tg, the chains are firm and unbendable to relieve the force being applied. This is due to either (a) the chains are strong to resist the stress; or (b) the force applied is excessive for the motionless polymer chains to overcome, so the polymer sample will just break or shatter.
Such mobility with temperature is heavily dependent upon the “heat” content because Tg is a kinetic parameter. The Tg decreases with slower melt cooling rate. It is also affected by other factors listed in section 1.4. Heat is a form of kinetic energy that causes random motion of molecules and the pliability of polymer, in comparison to “cold” polymers which lack kinetic energy to move around and hence are brittle on cooling.
Example of this behavior is the glass transition of chewing gum. It is soft and pliable at body temperature, characteristic of an amorphous solid in its elastic, rubbery condition. The gum then turns hard and rigid when it comes into contact with cold drink or ice cube in the mouth.
1.3 Glass Transition vs. Melting
The differences are outlined in the table below:
Happens in the amorphous region
Happens in the crystalline region
A second order transition
A first order transition
Below Tg, disordered amorphous solid with immobile molecules
Below Tm, ordered crystalline solid
Above Tg, disordered amorphous solid in which portions of molecules can wiggle around
Above Tm, disordered liquid
Both are thermodynamic transitions . In first-order transition, polymer undergoes a sudden volume change because heat is transferred between the system and surroundings. In a second-order transition, there is a change in heat capacity but no heat transfer. The volume increases dramatically to compromise the increased motion of the wiggling chains.
The slope of the line FC (fig 1.1) represents the thermal expansion coefficient of the crystalline phase. When polymer reaches the melting point, Tm, volume increases from C to B, then it follows the higher BA slope, which is the expansion coefficient of the liquid phase.
As the liquid is cooled down, it follows the line AB, then line BD from which it solidifies at D, accompanied by a constant decrease in volume. The point D is called the glass transition and occurs at Tg, which is always lower than Tm. From D, it continues toward E, with almost the same slope as CF. It is now described as in an amorphous glassy state, not in a crystalline condition like CF, therefore occupies a larger volume.
As wholly amorphous polymer is heated above its Tg,it is first transferred into a rubbery state. Further heating (increased enthalpy) encourages the transition into liquid state to become a fluid. Tg is, therefore, called the glass-rubber transition temperature. In semicrystalline polymer, the amorphous region may be above or below Tg (in rubbery or glassy condition). The disordered structure in the glassy state can be demonstrated by X-ray diffraction patterns which show short distance order, while crystals have sharp reflections due to long-distance order. Therefore polymer in glassy state encompasses greater volume than crystalline, and such difference is attributed to the distance, called free volume, between the lines FC and ED in Fig 1.1. The free volume is comparable below Tg, but increases rapidly above Tg.
1.4 Factors Affecting Tg
The value of Tg depends not only on the molecular weight distribution of polymer, but also on its thermal history, on measurement conditions and methods, on the presence of additives, and on the rate of heating or cooling .
The inverse relationship between thermal motion and the attractive forces between chains is relatively important, because the chain will be subject to stronger thermal motion when it has more freedom to undergo conformational changes. Therefore chain stiffness is mainly governed by:
- Chain flexibility, which is opposed by bulky main group, high degrees of cross link, and larger side groups.
- Effect of main group
–[CH2–CH2] n– PE, polyethylene, Tg = –120°C
PET, polyethyleneterephtalate, Tg = 69°C
- Effect of cross links
An increase in Tg can be resulted from the presence of cross links that limit the mobility of chains. The detection limit of vulcanized rubber for increased Tg is at 1 to 2% of sulphur, so that Tg level is hardly varied by the vulcanization process. Tg of unsaturated polymer also increases to a greater extent when the number of atoms between cross-linkings becomes lesser.
- Effect of side groups – increasing size of side groups reduces chain flexibility and gives rise to increased Tg.
PMA, poly (methyl acrylate), Tg = 9°C
Poly (methyl methacrylate), Tg = 105°C
- Chain interactions
Decreased interaction is favoured by lower chain stiffness and Tg, and this can be achieved by increasing the distance between chains (E.g. long, branched side chains).
–[CH2–CH]n–PP, polypropylene, Tg = –15 °C
–[CH2–CH]n–PB, polybutylene-1, Tg = –25 °C
Increasing dipole forces between chains also increases Tg, though chain mobility can be unaffected due to similar side group size.
–[CH2–CH]n–PP, polypropylene, Tg = –15 °C
–[CH2–CH]n–PVC, polyvinylchloride, Tg = 81 °C
–[CH2–CH]n–PAN, polyacrylonitrile, Tg = 120 °C
PVC Tg = 81 °C
PVC + 30% dioctylphtalate (DOP) Tg = 0 °C
- Rate of Cooling
Tg value is relatively higher with very rapid cooling than with slow cooling.
d) Chemistry of the polymer
Addition of modifiers such as a) monovalent metals (Na, K), b) divalent metals (Ca, Mg, Ba), and c) multivalent elements (Al, B) in a fused silica glass have valency of less than 4, so they will decrease the Tg by breaking up the three-dimensional lattice of covalent bonds. Adding P, in contrast, will raise the Tg as it has a valency of 5 and helps reestablish the molecular lattice. Higher proportions of trivalent ions also make the glass more chemically resistant than monovalent ions.
Additives such as plasticizers in the polymer matrix can actually reduce Tg because the small plasticizer molecules are embedded between the polymer chains, thus increasing the distance of chains and free volume. This allows the polymers to become more flexible and move past one another easily at lower temperature. Combination of two polymers blended together, or a copolymer system, can also be used to achieve the desired glass transition, depending on the temperature of intended use.
1.6 Measurement of Tg
Properties such as thermal expansion and heat capacity show an abrupt change at Tg, such effects can be used to measure Tg by DSC (differential scanning calorimetry). Heat capacityas a function of temperature, measured by calorimetry (fig 1.2), shows an increase in specific heat. Meanwhile, volumeas a function of temperature can be measured by a dilatometer. A change in slope is detected at Tg, indicating a change in the thermal expansion coefficient. 
Common heating rates of DSC and dilatometry are
3-5 K/min and 10 K/min, respectively. Heating rate during
measurement should be same as the rate of sample being
cooled from temperatures well above Tg. 
Figure 1.2 DSC measurement of Tg, which is the point A.
1.7 Glass Transition Temperature of some Polymers
These are only mean values, as Tg can be dependent upon factors mentioned in 1.4.
Polyvinyl acetate (PVAc)28
Polyvinyl chloride (PVC)81
Polyvinyl alcohol (PVA)85
Poly (methyl methacrylate) (atactic)105
Soda lime glass520-600
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