MATS3004 · Polymer Science and Engineering 1
Amorphous and Crystalline Polymers
Weeks 7-8 distinguish the amorphous state (the glass transition Tg, free volume) from the semi-crystalline state (chain folding, spherulites, degree of crystallinity, melting temperature Tm). Students relate the thermal transitions measured by DSC to chain regularity and predict how crystallinity changes stiffness and clarity. A recurring exam item is computing the degree of crystallinity from density, alongside reasoning about what raises Tg and Tm.
What this chapter covers
- 01Amorphous polymer: no long-range order (random coil), transparent; atactic or irregular chains
- 02Glass transition Tg: a kinetic, second-order-like transition (step in heat capacity, no latent heat) detected by DSC
- 03Free-volume picture: below Tg segmental motion is frozen, above Tg free volume allows large-scale chain motion
- 04Factors that raise Tg: chain stiffness, bulky/polar side groups, hydrogen bonding, crosslinking, high molar mass
- 05Semi-crystalline structure: chain-folded lamellae (~10 nm) organizing into spherulites; polymers are never 100% crystalline
- 06Degree of crystallinity from density Xc = ρc(ρ − ρa)/[ρ(ρc − ρa)], or from XRD/DSC
- 07Melting temperature Tm (first-order, latent heat) ≈ ΔHm/ΔSm; Tm > Tg (rule of thumb Tg ≈ 0.5-0.8 Tm in K)
- 08Requirement for crystallinity: regular chains (linear, stereoregular iso/syndiotactic, or symmetric like PE/PTFE)
Degree of crystallinity of polyethylene from density
- +1Write the mass-fraction crystallinity from the two-phase model: Xc = ρc(ρ − ρa) / [ρ(ρc − ρa)]. The sample density lies between the amorphous and crystalline limits, so 0 < Xc < 1.
- +1Numerator: ρc(ρ − ρa) = 1.000 × (0.940 − 0.855) = 1.000 × 0.085 = 0.085.
- +1Denominator: ρ(ρc − ρa) = 0.940 × (1.000 − 0.855) = 0.940 × 0.145 = 0.13630.
- +1Xc = 0.085 / 0.13630 = 0.624, i.e. about 62% crystalline by mass. The value sits sensibly between 0 and 1, and it is above the halfway point because ρ (0.940) is closer to ρc than to ρa.
Key terms
- Amorphous polymer
- A polymer with no long-range order — a tangle of random coils, typically from atactic or irregular chains. It is transparent (no crystallites to scatter light) and shows a glass transition but no sharp melting point.
- Glass transition temperature (Tg)
- The temperature range over which an amorphous polymer changes from a hard, brittle glass to a soft, rubbery state. It is a kinetic, second-order-like transition (a step in heat capacity, no latent heat) detected by DSC, and it is raised by chain stiffness, bulky/polar side groups, hydrogen bonding and crosslinking.
- Free volume
- The unoccupied space between chains that permits segmental motion. Below Tg the free volume is frozen and large-scale motion is arrested; above Tg it increases, allowing chains to move and the polymer to become rubbery.
- Semi-crystalline polymer
- A polymer containing crystalline lamellae (chain-folded, ~10 nm thick, organized into spherulites) interspersed with amorphous regions. Polymers are never fully crystalline, and only regular chains (linear, stereoregular or symmetric) can crystallize at all.
- Degree of crystallinity (Xc)
- The fraction of a polymer that is crystalline. It can be found from density via Xc = ρc(ρ − ρa)/[ρ(ρc − ρa)], from the XRD crystalline-to-total peak-area ratio, or from DSC as ΔHm/ΔHm°. Higher crystallinity means greater stiffness and opacity.
- Melting temperature (Tm)
- The first-order transition (with latent heat) at which crystalline regions melt, Tm ≈ ΔHm/ΔSm. It always exceeds Tg (rule of thumb Tg ≈ 0.5-0.8 Tm in kelvin) and is raised by chain stiffness, polarity/hydrogen bonding, symmetry and high molar mass.
Amorphous and Crystalline Polymers FAQ
What is the difference between the glass transition and melting?
They are different kinds of transition affecting different regions. The glass transition Tg is a gradual, kinetic (second-order-like) change in the amorphous regions from glassy to rubbery — it shows up in DSC as a step in the baseline (a change in heat capacity) with no latent heat. Melting Tm is a sharp, first-order transition of the crystalline regions, with a definite latent heat that appears in DSC as an endothermic peak. A wholly amorphous polymer shows only a Tg; a semi-crystalline polymer shows both a Tg (amorphous part) and a Tm (crystalline part), with Tm always above Tg.
Why can't a polymer be 100% crystalline?
Because the chains are long and get kinetically trapped. As a polymer crystallizes, chains fold back and forth into thin lamellae, but the melt is a tangle of entanglements and chain ends that cannot all reel into perfect order before the material solidifies. The result is a two-phase structure: crystalline lamellae embedded in amorphous tie regions, with the crystals gathered into spherulites. Only chains regular enough to pack — linear, stereoregular (isotactic/syndiotactic) or symmetric like polyethylene and PTFE — crystallize appreciably at all; atactic or bulky-irregular chains stay amorphous.
What raises a polymer's Tg and Tm?
Broadly the same structural features that make chains stiffer or stickier. Tg rises with chain stiffness (aromatic or ring backbones), bulky or polar side groups, strong secondary bonding (especially hydrogen bonding), crosslinking and higher molar mass; it falls with flexible backbones, long flexible side chains and added plasticizer. Tm rises with chain stiffness, polarity and hydrogen bonding, chain symmetry and high molar mass. Because both track backbone stiffness and intermolecular attraction, the two temperatures tend to move together, keeping the rough Tg ≈ 0.5-0.8 Tm ratio.
How is this examined in MATS3004?
As a degree-of-crystallinity calculation (most often from density, sometimes from XRD or DSC data), and as reasoning about thermal transitions — identifying Tg and Tm on a DSC trace, and predicting how a structural change shifts them or shifts crystallinity, stiffness and clarity. Watch the density-formula placement and check that Xc lands between 0 and 1. Confirm the examinable models and any provided data on the UNSW course outline / Moodle.
Exam move
Make the density-crystallinity formula reliable — Xc = ρc(ρ − ρa)/[ρ(ρc − ρa)] — and always sanity-check that the answer sits between 0 and 1 and that ρc is the largest density. Be able to read a DSC trace at a glance: a baseline step is Tg (second-order, no latent heat), an endothermic peak is Tm (first-order, latent heat), and an exothermic peak is crystallization. Memorise the two lists of what raises Tg and Tm (stiffness, bulky/polar groups, hydrogen bonding, crosslinking, molar mass) since 'predict the shift' is a common short-answer item, and keep the Tm > Tg rule of thumb. Link crystallinity to properties (more crystalline = stiffer, more opaque, higher Tm). Confirm the assessed scope on the UNSW course outline / Moodle.
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