Materials Science · Polymers, elastomers and soft materials

Crystallinity, crosslinks and network formation

Useful background: Atoms, bonding, structure and defects; Energy, stability and environmental context. Each worked case explains the quantities it uses.

Back to the chapter

After reading, you can

Distinguish ordered chain regions from a chemically connected network.
Explain how ordered stems, amorphous chain portions, entanglements and chemical junctions constrain motion differently.
Track cluster joining and recognise that a bond count alone is not a network or modulus measurement.
Interpret a bounded calorimetric mass balance, including crystals formed during heating, without treating it as a crosslink measurement.
Combine structural, thermal and time-dependent observations to say which conclusions are supported.

Order and connectivity are different

Crystalline polymer regions contain ordered chain arrangements. Amorphous regions lack that long-range order. A crosslink joins chains and can form a network spanning the material. Crystallinity and crosslink density describe different structural features.

Two specimens show the same melting signal. Above the melting range, one can flow on the observation timescale while the other retains an independently established permanent network. There is no contradiction: melting addresses an ordered arrangement, while the network addresses which chain portions remain chemically connected. We need evidence for each feature.

A polymer backbone is a connected sequence of atoms. Neighbouring chain portions can also interact without being joined by new covalent bonds. Crystallization arranges compatible chain segments into regular packing; it does not, by itself, convert every neighbouring chain into one covalently bonded molecule. Bonding and interactions between atoms supplies that distinction. Crystalline, amorphous and molecular arrangements explains local order versus an extended repeat.

A chain need not belong entirely to one region

In a semicrystalline polymer, ordered regions coexist with less ordered chain portions. A stem is a chain segment passing through a crystalline region. Some chains fold back; others connect different ordered regions through intervening amorphous material. Such a connecting portion is often called a tie chain or tie segment. A drawing of separate coloured blocks must not imply that all molecules stop at the block boundaries.

Regular packing depends on chemistry, sequence, branching, conformation and history. Cooling provides time for both the formation of ordered regions and the molecular rearrangements needed for growth. Cooling faster can leave a different structure, but no cooling-rate rule gives the same result for every polymer. Some chain arrangements cannot crystallize readily in the available conditions.

The amorphous portion is not empty space. It contains chains, interactions and entanglements. Crystallinity can be expressed as a mass fraction or a volume fraction; those are not generally the same number. State which is being used. A fraction alone also omits crystallite orientation, dimensions and connecting-chain organisation, which can change response.

The first figure shows selected fragments of an illustrative covalently connected specimen before and after its ordered regions melt. Straight parallel portions indicate local packing; wavy portions indicate disordered paths. The bridges identify actual stipulated chemical connections. Their drawn lengths and the amount of coloured area are not measurements of crystallinity or deformation.

Original structural cartoon of selected portions of a stipulated conventional covalent network. Four blue chain fragments pass through a shaded ordered region in the upper panel; straight parallel stems there represent crystalline packing, with disordered paths outside. Three orange bridges and their marked endpoints indicate chemical connections between different fragments. In the lower panel the ordered region has melted and the paths are disordered, while the same three chemical connections remain. Chain fragments continue outside the view; this is not a complete bulk network proof. Positions, lengths and shaded area have no molecular, strain or crystallinity scale. Melting order is distinct from cutting or exchanging chemical bonds.

Joining clusters differs from making more bonds inside one cluster

A permanent chemical crosslink connects chain portions through bonds that remain intact over the stated test. Repeated connections can merge molecules into a network extending through the sample. An individual link is not enough to establish a sample-wide network, and a reaction can leave soluble molecules, dangling portions and loops alongside a connected structure.

Use a small connectivity exercise: initially A, B, C and D are four separate chains. An AB link joins two components, leaving three components. A BC link joins C to AB, leaving two. A CA link now closes a cycle within ABC; it adds a bond but does not join D. A CD link finally gives one connected component in this four-chain model. The number of bonds and the number of components answer different questions.

This finite map is not a numerical model of the bulk gel point. It contains no chain lengths, spatial statistics, load transfer or elastic modulus. Network strands, loops and loose ends do not all contribute equally to a mechanical response. A claim about crosslink density must define what is counted and cannot be inferred from a crystallinity percentage.

Entanglements constrain how long chains move past one another without being new covalent bonds. Their constraints can persist for the duration of one experiment and relax over a longer time. Physical junctions, including crystallites or associating domains, can also produce a connected structure while those junctions persist. A gel can contain a physical rather than a covalent network; the word gel alone does not identify its bonds.

Original finite connectivity exercise. The four named chains are vertices, and the listed added links are edges; spatial layout and bulk gelation are not modelled.
Stage	New link	Connected groups	Number of components
Start	None	A \| B \| C \| D	4
1	AB	AB \| C \| D	3
2	BC	ABC \| D	2
3	CA	ABC \| D	2
4	CD	ABCD	1

Both can restrict motion

Crystals, entanglements and crosslinks can restrict chain rearrangement through different mechanisms. Heating can melt crystalline regions, whereas a conventional permanent covalent network does not become a freely flowing melt merely by passing that transition. Degradation can intervene instead.

Melting removes crystalline packing in the relevant regions. It does not normally cut the polymer backbone or a conventional permanent chemical network. The network can therefore remain connected while its disordered strands become more mobile. “Permanent” here means no bond scission or exchange on the specified test timescale; degradation or a deliberately exchangeable network requires a different account.

The glass transition concerns the timescale of segmental motion in an amorphous portion. It is distinct from melting crystalline order. A crosslinked material can undergo a glass transition and become more compliant without losing its network. A semicrystalline polymer can contain an amorphous portion with its own mobility change as well as a melting range.

After physical crystallite junctions melt, long uncrosslinked chains may still be entangled. They need not flow instantly; the observation time matters. Conversely, a material that shows little movement in a brief test is not thereby proven to have permanent covalent links. Viscoelasticity, temperature and time develops controlled creep and relaxation tests. Thermoplastics, thermosets and elastomers separates response and processing categories.

A heat signal can estimate ordered mass under a stated model

Differential scanning calorimetry compares the heating power of a sample with a reference as temperature changes. A baseline removes the chosen background sensible-heating contribution. Here q(T) is the remaining power per gram of the complete specimen, in W/g, positive when a transition absorbs heat. The sign convention is stated because instruments can display it the other way round.

Use an original idealised teaching record: a constant heating rate β = 1.00 K/s; fully separated triangular transition signals; no mass loss, cure, degradation or other overlapping transition; one crystalline polymer phase; and a stipulated constant fusion enthalpy H* = 200 J per gram of fully crystalline polymer. This is a fictional reference value, not the value of every polymer or a borrowed supplier specification. Heat capacity and thermal conductivity prepares energy versus heating power.

During a temperature interval dT, the elapsed time is dt = dT/β. Transition enthalpy per gram is therefore the area under q(T) divided by β. A triangle of temperature width 40 K and power height 3.00 W/g has area 60 W·K/g; division by 1.00 K/s gives 60 J/g. For a 0.0100 g specimen that is 0.600 J. Temperature-axis area is not an energy until the time conversion is included.

If some crystals form during heating, their later melting contributes to the melt signal too. Call the positive melt-absorption magnitude H_m and the positive magnitude of the earlier crystallization release H_cc. Under this simplified constant-H* account, the initial crystalline polymer mass fraction is X_c,initial = (H_m − H_cc)/(w_pH*), where w_p is the polymer mass divided by the complete specimen mass. Both H values are normalised per gram of the complete specimen. For a neat polymer w_p = 1.

The subtraction estimates what was crystalline before the scan, rather than counting newly formed crystals as already present. It assumes all those new crystals subsequently melt in the integrated range and share the same stipulated enthalpy per crystalline gram. Real reference enthalpies, baselines, temperature dependence, reorganisation, polymorphs, incomplete melting and overlapping reactions can invalidate this simple estimate. Thermal evidence should be compared with structural evidence, not promoted to a universal absolute fraction.

The same initial fraction can give different scans and different connectivity

Invented neat specimens A and B each have no crystallization peak during heating and a melt triangle from 120 to 160°C with height 3.00 W/g. They both give H_m = 60 J/g and initial X_c = 0.300 = 30.0% under the model. A is stipulated to have no permanent network; B has a separately established conventional covalent network. Nothing in this enthalpy calculation distinguishes them.

Specimen C has a negative crystallization triangle from 70 to 110°C with depth 2.00 W/g, followed by a positive melt triangle from 120 to 160°C with height 5.00 W/g. Their magnitudes are H_cc = 40 J/g and H_m = 100 J/g. The difference remains 60 J/g, so C also starts at 30.0% in the stipulated model. It forms an additional crystalline mass fraction 0.200 during heating and reaches 0.500 immediately before melting. A larger melt peak does not by itself prove a larger initial crystalline fraction.

No crystallization peak in A or B does not mean 100% crystallinity. It only says that no additional crystallization event was supplied within this ideal scan. It gives no measurement of chemical junction count either. The second figure draws these exact fictional signals. Both A and B share one blue curve because their thermal records coincide; that overlap is not evidence of identical molecular connectivity.

For a separate filled specimen with w_p = 0.800, a complete-specimen enthalpy difference of 60 J/g gives initial crystalline polymer fraction 60/(0.800 × 200) = 0.375. Its crystalline polymer mass is only 0.800 × 0.375 = 0.300 of the whole specimen. The two percentages use different masses. Assume the inert filler contributes no signal in the integrated intervals; do not apply the correction to an unknown reacting filler.

Invented calorimetric records at β = 1.00 K/s and H* = 200 J/g of fully crystalline polymer. H values are per gram of whole specimen; fractions concern its polymer.
Record	Polymer mass fraction w_p	H_m (J/g)	H_cc magnitude (J/g)	Initial crystalline polymer fraction	Permanent chemical network
A	1.000	60	0	0.300	Stipulated absent
B	1.000	60	0	0.300	Established separately
C	1.000	100	40	0.300	Not determined by this scan
Filled transfer	0.800	60	0	0.375	Not determined by this scan

Original fictional baseline-corrected calorimetry at constant heating rate 1.00 kelvin per second. Positive power per specimen gram is endothermic. A and B share a blue dashed triangular melt signal from 120 to 160 degrees Celsius, height 3.00 watts per gram at 140; its enthalpy is 60 joules per gram. C has an orange solid negative triangle from 70 to 110, depth 2.00 watts per gram at 90, followed by a positive triangle from 120 to 160, height 5.00 at 140. Its crystallization and melting enthalpy magnitudes are 40 and 100 joules per gram. At the stipulated constant fusion reference 200 joules per crystalline polymer gram, all three neat specimens start at 30.0 percent crystalline mass, although C forms another 20.0 percentage points before melting. The common scan of A/B does not identify their different stipulated chemical connectivity. These are invented signals, not measured polymer data or heating instructions.

Keep the conclusion as specific as the observation

Diffraction or suitable spectroscopy can examine ordered arrangements; calorimetry follows transition heat; mechanical tests examine a response under specified loading, temperature and time. None of these alone is a complete molecular map. Crystallite junctions in a mechanical model are not necessarily chemical crosslinks: they can represent chain attachments to an ordered region.

Suppose A flows during a stipulated long observation above its complete melting range, while B shows substantial recovery in the same small-load comparison. Those responses are compatible with the separately known architectures. The response alone would not prove a permanent network in B: a long-lived physical structure or a limited observation window could also restrict flow. A meaningful conclusion combines the specified response with independent evidence of the connections.

Likewise, an insoluble swollen remainder can support a network interpretation only under conditions that actually dissolve the comparable unconnected chains and do not create, break or preserve confounding junctions. Fillers, crystallites, poor solvent conditions and incomplete extraction can otherwise leave a remainder. This lesson gives no solvent procedure or conversion from an insoluble fraction to a crosslink density.

A reheating scan also examines a changed history: cooling after the first melt may create a new crystalline arrangement. It cannot automatically reconstruct the original manufactured state. Report the state, baseline, reference enthalpy, heating rate and mass basis with the estimate. Preserve uncertainty and unresolved connectivity rather than assigning a processing or lifetime guarantee from one fraction.

Worked examples

Follow which constraint survives melting

A polymer’s crystal regions melt while its crosslinked network remains connected. Must the whole material flow like an uncrosslinked melt?

Melting removes crystalline order.
Permanent network connections can remain.
Flow requiring chains to separate is still constrained.
In the fictional B record, 60 J/g divided by the stipulated 200 J/g reference gives 30.0% initially crystalline polymer. That fraction describes order, not the density or survival of chemical junctions.
After those crystalline regions melt, the conventional covalent connections are stipulated to remain intact. More mobile disordered strands can change shape within that connected structure without becoming independent freely separating chains.
Keep the test time, temperature and absence of bond exchange or degradation explicit. A very brief no-flow observation alone would not establish those chemical facts.

No. Loss of crystals does not necessarily remove network connectivity. The calorimetric signal and the independently known permanent connections answer separate questions.

Subtract crystals formed during the measurement

Use C’s 1.00 K/s triangular signals and the constant H* = 200 J/g model. What fraction was crystalline initially, what was added before melting, and what would dividing only the melt enthalpy by H* get wrong?

The crystallization triangle has magnitude (110 − 70) × 2.00/2 = 40 W·K/g. Divide by β to obtain H_cc = 40 J/g.
The melt triangle has magnitude (160 − 120) × 5.00/2 = 100 W·K/g, giving H_m = 100 J/g.
Initial fraction = (100 − 40)/200 = 0.300. Newly formed fraction = 40/200 = 0.200; immediately before melting the total is 0.500 within this model.
Using 100/200 = 0.500 as the initial fraction would overstate it by 0.200, or 20.0 percentage points. It counts the crystals formed during the heating as if they had existed before the scan.

Initially 30.0%, with another 20.0 percentage points formed during heating. The melt signal alone corresponds to the later 50.0% state, not the initial one.

Correct the mass basis before comparing filled and neat samples

An invented 0.0100 g filled specimen contains 80.0% polymer by mass. Its baseline-corrected net transition energy is 0.600 J, with no filler transition, reaction or mass loss in the interval. Using H* = 200 J/g and the same model, find the crystalline fraction of polymer and of the whole specimen.

Polymer mass is 0.800 × 0.0100 = 0.00800 g. The reference energy for that polymer to be entirely crystalline is 0.00800 × 200 = 1.600 J.
The crystalline polymer fraction is 0.600/1.600 = 0.375 = 37.5%. Equivalently, net energy per specimen gram is 60 J/g and 60/(0.800 × 200) gives the same answer.
Crystalline polymer mass is 0.375 × 0.00800 = 0.00300 g. Divide by the whole specimen mass to get 0.300 = 30.0%.
Neither calculation identifies the filler’s volume fraction, chemical crosslink density or a mechanical modulus. The assumed nonparticipating filler and constant fusion reference remain necessary.

37.5% of the polymer mass, or 30.0% of the complete specimen mass, is initially crystalline in the stated model.

A loop can add a bond without joining another chain

In the finite A/B/C/D exercise, AB, BC and CA have already formed, and D remains separate. Compare adding one more AB link within the existing ABC component with adding CD. Can the link counts determine a bulk modulus?

The existing ABC cycle is one component and D is another: two connected components.
An additional connection between already connected A and B stays within ABC. There are still two components despite the increased bond count.
A CD link instead joins D to ABC and leaves one component containing all four model chains.
The finite connectivity result contains neither 3D spatial statistics nor elastically active strand lengths and constraints. It gives no bulk gel-point conversion, modulus or strength.

Only CD merges the remaining components. Counting added bonds alone does not determine either connectivity or bulk mechanical response.

Try the reasoning

Does amorphous imply uncrosslinked?
Show the answer and reasoning
No.
A disordered polymer can form a network. Disorder describes the arrangement; a persistent chemical connection describes which chain portions remain linked. Both can occur in one material.
Does crystallinity have to be all or nothing?
Show the answer and reasoning
No.
Many polymers contain both crystalline and amorphous regions. Also distinguish mass fraction from volume fraction and retain orientation and history; one percentage is not a complete structure map.
A and B have identical 60 J/g melt enthalpy and no crystallization release in the invented neat-polymer model. A report calls both uncrosslinked because their curves coincide. Which conclusion is supported and which is not?
Show the answer and reasoning
They both have initial crystalline polymer fraction 0.300 in this model. Their permanent chemical connectivity is not determined by those signals.
The energy balance counts crystalline mass through a stipulated reference enthalpy. It contains no variable for chemical junction number or network connectivity. The separately established B network is compatible with the same fraction.
Reanalyse C’s net 60 J/g with a different stipulated fusion reference H* = 240 J/g, keeping the same one-phase, no-overlap assumptions and w_p = 1. What initial fraction follows? Is 30.0% independent of the reference choice?
Show the answer and reasoning
60/240 = 0.250 = 25.0%; it depends on the reference.
The 200 J/g value was an explicit teaching input. A real material needs a justified phase- and temperature-appropriate reference with its uncertainty. Arithmetic alone cannot validate a reference or make the estimate absolute.
In a separate ideal signal-to-energy exercise, keep C’s exact q(T) triangles but change the supplied constant β to 2.00 K/s. What enthalpies and initial fraction follow? Does this predict that doubling a real scan rate halves crystallinity?
Show the answer and reasoning
The specified signals give H_m = 50 J/g, H_cc = 20 J/g and X_c,initial = 0.150. No universal rate prediction follows.
The same temperature-axis areas are divided by twice the rate. In a real repeat scan, kinetics and thermal response can change q(T); holding those triangles fixed is the artificial condition of this unit-conversion exercise, not a claim that a fixed initial structure changes merely by changing units or scan settings.
A shows no cold-crystallization signal in this scan. May it be called 100% crystalline, and does a softening response identify crystal melting rather than a glass transition?
Show the answer and reasoning
Neither conclusion follows.
The supplied enthalpy balance gives A only 30.0% initially crystalline. An absent additional peak does not replace that mass account. A glass-transition mobility change and crystal melting are distinct and require appropriate thermal/structural interpretation.
An unknown specimen shows a broad heat-release peak while curing in the same range as a possible crystallization peak. A worksheet subtracts the full release from the melt enthalpy using this lesson’s formula. What assumption is unverified?
Show the answer and reasoning
That the integrated release is solely the formation of crystals subsequently melted under the same reference account.
Curing can release heat through a chemical reaction, while crystallization changes order. Their contributions and baselines must be resolved before using the simple subtraction. A negative or above-one result should prompt a model/data check, not automatic clipping to a physically convenient fraction.
A specimen barely moves during a 1 s test above its observed melting range. Is a conventional permanent network proven? What additional evidence would help?
Show the answer and reasoning
No. State a longer, controlled response and independently investigate the nature and persistence of its connections.
Entanglements or persistent physical domains can restrict motion over a finite window. Test temperature, time, stress and absence of degradation matter. An extraction remainder also needs suitable nonreacting conditions and separation of fillers/physical junctions; no one observation alone supplies a chemical-network certificate.

What to carry forward

Order and network connectivity require separate descriptions.
Identify which constraints survive a thermal transition.
A chain can pass through ordered and amorphous regions; the amorphous portion contains material and constraints.
Joining previously separate components and adding an intracomponent loop are different connectivity changes.
Calorimetric fractions require a mass basis, transition assignment, rate conversion and justified reference; they do not count chemical crosslinks.
Combine thermal, structural and controlled-time evidence; no melting peak or brief no-flow result alone proves a permanent network.

References

Teaching resources and research supporting this lesson’s explanations and examples.