Additives, Compounding and Formulations: Ingredients, Carbon Black, Mixing and Vulcanisation

This chapter answers Section XE5.5, Additives, Compounding and Formulations, of XE5 Polymer Science and Engineering, one of the nine optional sections of the Engineering Sciences (XE) paper, any two of which a candidate chooses in the exam. The syllabus reads: “Polymer compounding-need and significance; Different compounding ingredients for rubber and plastics (crosslinkers, antioxidants, heat stabilizers, UV stabilizers, lubricants, processing aids, impact modifiers, flame retardant, antistatic agents. PVC stabilizers and plasticizers) and their function; Use of carbon black; Polymer mixing equipment; Vulcanization and kinetics.” The chapter teaches why a raw polymer is never used alone, what each ingredient does and how it works, carbon black structure and grades, the mixing machines, sulphur vulcanisation systems, the cure curve and the first-order cure kinetics. The numericals are cure time at another temperature (Q10 rule and Arrhenius), cure rate index and the rate constant of cure.

1. Why polymers are compounded

A polymer as made is rarely a useful material. Natural rubber is a sticky gum that flows under load, PVC degrades at the very temperature at which it melts, and polyolefins oxidise in the extruder and crack in sunlight. Compounding is the blending of the base polymer with additives and fillers, by a suitable mixing process, into a formulation that can be processed, that meets the property targets of the product and that lasts through its service life. The reasons are four: to make processing possible (lubricants, processing aids, plasticisers, peptisers), to develop the property (crosslinkers, fillers, impact modifiers, plasticisers), to protect the polymer (antioxidants, heat and UV stabilisers, antiozonants) and to give a special function (flame retardancy, antistatic action, colour, blowing agents), with cost reduction from cheap fillers and extender oils as a fifth.

Rubber formulations are written in phr (parts per hundred parts of rubber by weight), so the rubber is always 100 and every other ingredient is read against it; plastic recipes are often given in phr too, or in weight per cent. An illustrative tyre-tread style recipe is: rubber 100, carbon black 50, process oil 8, zinc oxide 5, stearic acid 2, antidegradant 2, accelerator 1, sulphur 2.5 phr. To convert phr to weight per cent divide by the total: here the total is 170.5, so carbon black is 50/170.5 = 29.3 %.

⚠️ phr is not per cent
Ingredients in phr always sum to more than 100. A compound with 100 phr rubber and 100 phr filler is 50 % filler by weight, not 100 %. Volume fraction, which controls stiffness and viscosity, needs the densities as well.

2. Stabilisers: PVC heat stabilisers, antioxidants and UV stabilisers

PVC heat stabilisers. Above about 100 °C PVC loses HCl from labile sites (allylic and tertiary chlorine), leaving conjugated polyene sequences that absorb visible light, so the polymer yellows, browns and finally blackens. The released HCl catalyses further loss (autocatalysis), and the loss is faster in the presence of zinc or iron chloride. A stabiliser works by (i) absorbing HCl, (ii) replacing the labile chlorine by a stable group, (iii) reacting with the polyenes or with oxygen, or (iv) chelating the harmful metal chlorides. Main families: lead salts (tribasic lead sulphate: cheap, excellent long-term heat and electrical stability, opaque, toxic, being phased out), calcium-zinc soaps (non-toxic; the zinc soap replaces labile Cl but forms ZnCl₂, which itself accelerates breakdown, so calcium soap is added to convert ZnCl₂ back to zinc soap), organotin mercaptides (clear rigid PVC) and epoxidised soybean oil, a co-stabiliser that scavenges HCl through its epoxide rings.

Antioxidants. Oxidation is a radical chain: initiation gives R•, then R• + O₂ → ROO• and ROO• + RH → ROOH + R•, and ROOH splits into more radicals when heated. Primary antioxidants (hindered phenols, aromatic amines) donate a hydrogen atom to ROO•, and the radical they become is too stable to continue the chain: they are chain breakers. Secondary antioxidants (phosphites, thioesters) do not touch radicals; they decompose ROOH into harmless alcohols, so they are hydroperoxide decomposers. The two used together are synergistic. In rubbers the antidegradants are mainly aromatic amines (for example the p-phenylenediamine types), which also protect against ozone cracking by migrating to the surface (the bloom), and wax is added to give a protective surface film.

UV stabilisers. Sunlight breaks bonds and starts the same oxidation chain. UV absorbers (benzophenones, benzotriazoles) absorb the radiation and release it as harmless heat; they need thickness to work, so they protect thick parts better than thin films. HALS (hindered amine light stabilisers) do not absorb UV: they trap radicals and are regenerated in a cycle, so they protect thin films and fibres for long times. Screeners such as carbon black and titanium dioxide reflect or absorb the light at the surface.

⚠️ Heat stabiliser versus antioxidant
A PVC heat stabiliser fights dehydrochlorination, an acid-driven loss of HCl that needs no oxygen; a phenolic antioxidant fights oxygen radicals. A polyolefin has no labile chlorine, so it needs antioxidants, not a PVC stabiliser. HALS do not absorb UV: calling them UV absorbers is wrong.

3. Plasticisers, lubricants, processing aids, impact modifiers, flame retardants and antistats

A plasticiser is a low-volatility, compatible liquid (the usual one for PVC is DOP, also called DEHP, di-2-ethylhexyl phthalate) that sits between chains, increases free volume and screens the dipolar attraction between chlorine and hydrogen sites. It lowers Tg and the modulus and raises elongation: rigid PVC (Tg about 80 °C) becomes flexible at 30 to 60 phr because Tg falls below room temperature. Plasticisers can migrate, evaporate or be extracted; a secondary plasticiser or extender (epoxidised oil, chlorinated paraffin) is cheaper but less compatible. In rubbers, process oils play the same part as plasticisers and extenders, paraffinic oils for non-staining and aromatic for compatibility with SBR and BR.

Function of the main additive classes
AdditiveHow it worksTypical example
Internal lubricantCompatible, lowers melt viscosity and internal frictionFatty alcohols, esters
External lubricantPoorly compatible, migrates to the metal surface, delays fusion, aids releaseParaffin and PE wax
Processing aidPromotes fusion and melt strength of PVCHigh-molar-mass acrylic copolymer
Impact modifierRubbery particles start crazing and shear yielding that absorb energyMBS, acrylic, CPE; EPDM in PP
Flame retardantGas-phase radical trapping, endothermic water release, or char formationBrominated compound with Sb₂O₃; Al(OH)₃; phosphorus
Antistatic agentMigrates and attracts moisture to conduct charge, or conductive fillerEthoxylated amines, glycerol esters; carbon black

Two numbers are worth remembering. Aluminium hydroxide decomposes endothermically near 200 °C, 2Al(OH)₃ → Al₂O₃ + 3H₂O, releasing 54/156 = 34.6 % of its mass as water, which cools and dilutes the flame, but about 50 to 65 % loading is needed and so it cannot be used in polymers processed much above 200 °C; magnesium hydroxide starts near 330 °C. A halogen flame retardant works with antimony trioxide as a synergist: the pair forms antimony halide species that trap flame radicals in the gas phase.

4. Rubber compounding ingredients

A rubber compound carries ingredients of seven kinds. Base elastomer(s); crosslinkers (sulphur for unsaturated rubbers; organic peroxides such as dicumyl peroxide, which form C–C crosslinks and work in saturated rubbers such as EPDM and silicone and in polyethylene; metal oxides ZnO with MgO for polychloroprene); activators (zinc oxide with stearic acid, which makes soluble zinc soap and so lets the accelerator work); accelerators; fillers (reinforcing carbon black or silica, semi-reinforcing and inert fillers such as clay or calcium carbonate); protective agents and processing aids (oils, peptisers that cut chain length during mastication, tackifiers); and retarders (a pre-vulcanisation inhibitor lengthens the safe scorch time).

The order of addition follows the sensitivity of each ingredient. The rubber is first masticated to soften it, fillers, oil and the zinc oxide and stearic acid are added next, and the curatives (sulphur and accelerator) go last, at the lowest temperature, usually below about 100 °C, so that no crosslinking (scorch) starts in the mixer.

5. Carbon black: structure, reinforcement and grades

Furnace carbon black is made by partial combustion and cracking of aromatic oil in a hot furnace. The growing carbon spheres, the primary particles of roughly 10 to 100 nm, fuse into branched, grape-like aggregates, the smallest unit that survives mixing. Three properties matter. Particle size (equivalently surface area, measured by nitrogen adsorption or iodine number): finer black gives more rubber-filler contact, so higher tensile strength, tear and abrasion resistance, but more heat build-up and higher viscosity. Structure, the degree of branching of the aggregate, measured by oil absorption (DBP) number: high structure traps rubber in its voids (occluded rubber), raising the effective filler volume, so modulus and hardness and viscosity rise and die swell falls. Surface activity controls how much rubber is held as bound rubber, which resists solvent extraction.

ASTM carbon black grades (N = normal curing)
GradeNameCharacter and use
N110, N220SAF, ISAFVery fine, high abrasion resistance: tyre treads
N330HAFGeneral-purpose reinforcing grade: treads, mechanical goods
N550FEFMedium size, high structure: good extrusion, carcass
N660, N774GPF, SRFCoarser, low heat build-up: inner liners, sidewalls, mouldings
N990MT (thermal)Largest particles, low structure, very high loading, little reinforcement

In the N-number, N stands for normal cure rate and the first digit encodes the particle-size class: N1 is the finest and N7, N9 are progressively coarser, so a smaller digit means a smaller particle and more reinforcement. The usual loading is 30 to 60 phr in tyre compounds; in plastics 2 to 3 % carbon black is used as a UV screener and as a conductive filler. Silica with a silane coupling agent is the main non-black reinforcing filler, favoured for low rolling resistance.

6. Polymer mixing equipment

Mixing has two aims. Dispersive mixing breaks agglomerates of filler down to aggregates: it needs a high stress, above the cohesive strength of the agglomerate, so it happens in the high-shear zones. Distributive mixing spreads the ingredients uniformly in space: it needs large total strain, folding and repeated cutting, not high stress. Every machine does both, in different ratios.

Mixing machines
MachineWhat it doesTypical use
Two-roll millTwo horizontal counter-rotating rolls at different speeds (friction ratio of about 1.1 to 1.25) shear the stock in the adjustable nip; open, cooled rolls, batch, operator cuttingMastication, adding curatives, sheeting out, laboratory and small batches
Internal mixer (Banbury type)Closed chamber with two rotors, a ram pressing the charge down; high shear at the rotor tip clearance; batch of a few minutes; temperature and fill factor controlledLarge-scale rubber compounding, filler dispersion; the dump goes to a mill or extruder
Single-screw extruderFeed, compression and metering zones convey, melt and pump; poor mixing unless a mixing section is addedShaping, pelletising, profiles
Twin-screw extruderIntermeshing, self-wiping screws, positive conveying, modular elements; continuous, strong dispersive and distributive mixing, vents for devolatilisingCompounding and masterbatch of plastics, reactive extrusion

7. Vulcanisation: sulphur systems, accelerators and activators

Vulcanisation converts the plastic, tacky rubber into an elastic network by joining chains at a few sites. Sulphur alone is slow (hours at 140 °C) and needs a high loading; with an accelerator and the activator pair ZnO and stearic acid, the cure takes minutes and is efficient. The accelerator and the zinc soap form an active sulphurating complex that reacts with the allylic positions of the unsaturated chain and gives crosslinks of three kinds: mono-sulphidic (C–S–C), di-sulphidic and poly-sulphidic (Sₓ, x ≥ 3). Crosslinking raises modulus, hardness and resilience, lowers hysteresis, elongation and permanent set, and makes the rubber insoluble: it only swells.

Sulphur vulcanisation systems (typical ranges, phr)
SystemSulphurAcceleratorCrosslinks and properties
Conventional2.0 to 3.50.4 to 1.2Mostly poly-sulphidic: high strength and fatigue life, poor heat ageing and reversion
Semi-EV1.0 to 1.71.2 to 2.4Mixed: a compromise of fatigue and ageing
EV (efficient)0.4 to 0.83 to 6Mostly mono- and di-sulphidic: good heat ageing, low compression set and reversion, lower strength and fatigue

The shift from conventional to EV is a shift to a high accelerator to sulphur ratio: little sulphur is available per crosslink site, so crosslinks stay short. Short, strong C–S–C bonds resist heat; long, weak Sₓ bonds break and re-form under strain, which gives fatigue life but makes them break down in heat (reversion: a fall in modulus on over-cure). Accelerator classes in rising order of speed are guanidines (such as DPG, a secondary accelerator), thiazoles (MBT, MBTS), sulphenamides (CBS, TBBS: fast with delayed onset, so a long safe scorch time), thiurams (TMTD, which can also donate sulphur) and dithiocarbamates (ultra-fast).

⚠️ More sulphur is not more efficient
Conventional systems use the most sulphur but make the fewest useful short crosslinks; EV systems use the least sulphur and the most accelerator. Sulphur vulcanisation needs double bonds, so it works for NR, SBR, BR and NBR; saturated rubbers need peroxides or other crosslinkers.

8. The cure curve and cure kinetics

A curemeter records torque against time at a fixed temperature, and the torque is proportional to the shear modulus, hence to crosslink density. The curve gives: ML, minimum torque (compound viscosity); ts2, the scorch time, the time for the torque to rise 2 units above ML; MH, maximum torque; t90, the optimum cure time, the time to reach ML + 0.9 (MH − ML); and the cure rate index CRI = 100/(t90 − ts2) in min⁻¹. After MH natural rubber may show reversion, a falling torque, while some synthetic rubbers show a rising, marching torque. The torque rise ΔM = MH − ML is a relative measure of crosslink density.

Kinetics. The state of cure is α = (M − ML)/(MH − ML), from 0 to 1. After the induction period, to a good approximation the cure is first order: dα/dt = k (1 − α), so ln (1 − α) = − k (t − ts) and a plot of ln (1 − α) against t is a straight line of slope − k. At t90, α = 0.9, so k = ln 10/(t90 − ts) = 2.303/(t90 − ts). The temperature dependence is Arrhenius, k = A exp(−Ea/RT), so between two temperatures (in kelvin) t₂ = t₁ exp[(Ea/R)(1/T₂ − 1/T₁)], with R = 8.314 J mol⁻¹ K⁻¹. The shop-floor form is the Q10 rule: the cure time halves for every 10 °C rise, t₂ = t₁/2^[(T₂ − T₁)/10], which corresponds to an activation energy near 100 kJ/mol at about 150 °C.

Worked example. A compound has t90 = 24 min at 140 °C. By the Q10 rule at 160 °C, which is two steps of 10 °C, t90 = 24/2² = 6 min. With Arrhenius and Ea = 90 kJ/mol, the time of 18 min at 150 °C (423.15 K) becomes, at 170 °C (443.15 K), t = 18 exp[−(90000/8.314)(1/423.15 − 1/443.15)] = 18 exp(−1.1546) = 5.67 min, because (1/423.15 − 1/443.15) = 1.0666 × 10⁻⁴ K⁻¹, times 10825 K gives 1.1546, and e^−1.1546 = 0.3152, so 18 × 0.3152 = 5.67 min. For thick articles, the interior lags the surface: the cure is judged by the equivalent cure ∫ 2^[(T − Tref)/10] dt, and the state at the coldest centre sets the press time, while the surface may over-cure.

Key takeaways

  • Compounding makes a polymer processable, gives it the property target, protects it in service and adds special functions; rubber recipes are in phr (parts per hundred rubber), so the ingredients sum to more than 100 and weight per cent is phr divided by the total.
  • PVC degrades by autocatalytic loss of HCl, so its stabilisers (lead, Ca/Zn, organotin, epoxidised oil) absorb HCl or replace labile chlorine; primary antioxidants break the radical chain, secondary ones decompose hydroperoxides, UV absorbers need thickness while HALS trap radicals and do not.
  • Plasticisers lower Tg and modulus; internal lubricants are compatible and cut melt viscosity, external ones migrate to metal and delay fusion; impact modifiers are rubbery particles; Al(OH)₃ releases 34.6 % water near 200 °C and Mg(OH)₂ near 330 °C; antistats migrate and bind moisture or are conductive fillers.
  • Carbon black: finer particles raise abrasion resistance, tensile strength and hysteresis; higher structure (DBP number) raises modulus and viscosity and cuts die swell; N-number first digit small means fine; mixing is dispersive (high stress) and distributive (large strain), done in mills, internal mixers and twin-screw extruders.
  • Sulphur vulcanisation needs double bonds and ZnO with stearic acid as activator; conventional systems (high S, low accelerator) are poly-sulphidic and fatigue-resistant but reversion-prone, EV systems (low S, high accelerator) are mono- and di-sulphidic and heat-stable; curatives are added last and cold to avoid scorch.
  • Cure curve: ML, ts2, MH, t90 = time to ML + 0.9(MH − ML), CRI = 100/(t90 − ts2). First-order cure gives ln(1 − α) = −k(t − ts), k = 2.303/(t90 − ts); the Arrhenius shift is t₂ = t₁ exp[(Ea/R)(1/T₂ − 1/T₁)], and the Q10 rule halves the time per 10 °C.

Practice questions (16)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

  1. During the heat processing of PVC, which species released by the polymer speeds up its own further degradation?

    1. Hydrogen chloride, which catalyses further dehydrochlorination
    2. Molecular hydrogen, which hydrogenates the chain and softens it
    3. Carbon dioxide, which oxidises the backbone to carbonyl groups
    4. Water vapour, which hydrolyses the carbon-chlorine bond
    Show answer

    Answer: A — Hydrogen chloride, which catalyses further dehydrochlorination

    PVC loses HCl from labile chlorine sites and the HCl catalyses further loss, so a stabiliser must absorb HCl or replace the labile chlorine. Water hydrolysis is not the route: the degradation proceeds without water or oxygen, and the other gases listed are not the autocatalyst.
  2. A hindered phenol is added to polypropylene as a primary antioxidant. How does it protect the polymer?

    1. It absorbs ultraviolet light and converts it into heat
    2. It decomposes hydroperoxides into stable alcohols without reacting with radicals
    3. It neutralises acid residues of the polymerisation catalyst
    4. It donates a hydrogen atom to a peroxy radical and so breaks the oxidation chain
    Show answer

    Answer: D — It donates a hydrogen atom to a peroxy radical and so breaks the oxidation chain

    Primary antioxidants are chain breakers: they give an H atom to ROO• and become a stable radical. Decomposing hydroperoxides without touching radicals is the role of secondary antioxidants such as phosphites, and that is the tempting wrong choice. UV absorption is the job of UV absorbers.
  3. A calcium-zinc stabiliser is used in flexible PVC, with the calcium soap in large excess over the zinc soap. What does the calcium soap do?

    1. It plasticises the polymer and lowers its glass transition temperature to below room temperature
    2. It turns the ZnCl₂ back into zinc soap, as ZnCl₂ speeds degradation
    3. It absorbs ultraviolet light so that the zinc soap is not consumed
    4. It crosslinks the chains so that the polyene sequences cannot form
    Show answer

    Answer: B — It turns the ZnCl₂ back into zinc soap, as ZnCl₂ speeds degradation

    Zinc soap replaces labile chlorine but forms ZnCl₂, a strong catalyst of further dehydrochlorination (zinc burning). Calcium soap exchanges with ZnCl₂ to regenerate zinc soap and form harmless CaCl₂. It is not a plasticiser or UV absorber, and PVC stabilisation does not involve crosslinking.
  4. Two compounds differ only in the carbon black: one uses the very fine N220 grade and the other the coarse N774 grade, both at 50 phr. Which statement is correct?

    1. The N774 compound has the higher abrasion resistance because coarse particles resist wear
    2. The N220 compound has the lower heat build-up because its aggregates are smaller
    3. The N220 compound has higher abrasion resistance and tensile strength but more heat build-up
    4. The two compounds behave alike, because only the loading governs reinforcement
    Show answer

    Answer: C — The N220 compound has higher abrasion resistance and tensile strength but more heat build-up

    Finer black gives a larger rubber-filler interface and so higher abrasion resistance, tensile strength and tear, at the price of more hysteresis (heat build-up) and a higher viscosity. The coarse grade is the other way round, so the first and second claims are reversed, and particle size matters even at equal loading.
  5. At constant loading and particle size, a carbon black of higher structure (a higher DBP oil absorption number) is used in a rubber compound. Which set of changes is expected?

    1. Higher modulus and viscosity and lower die swell, as more rubber is occluded in aggregates
    2. Lower modulus and viscosity, because the aggregates act as lubricating spheres
    3. Higher modulus but lower viscosity, because structure only affects the cured state of the compound
    4. No change in any property, since structure and particle size are the same thing
    Show answer

    Answer: A — Higher modulus and viscosity and lower die swell, as more rubber is occluded in aggregates

    A branched aggregate traps rubber in its voids, raising the effective filler volume, so modulus, hardness and uncured viscosity rise and die swell falls. Structure is a separate property from particle size and acts in the uncured state too, so the claim of no change fails.
  6. An NR engine mount must keep its modulus after long service at 100 °C, with low compression set, and fatigue life is secondary. Which vulcanisation system suits it best?

    1. Conventional: high sulphur (about 2.5 phr) with low accelerator, giving mostly poly-sulphidic crosslinks
    2. Sulphur alone at 5 phr with no accelerator, giving the longest crosslinks
    3. EV: low sulphur (about 0.5 phr) with high accelerator, giving mostly mono- and di-sulphidic crosslinks
    4. No crosslinker, since natural rubber is already elastic
    Show answer

    Answer: C — EV: low sulphur (about 0.5 phr) with high accelerator, giving mostly mono- and di-sulphidic crosslinks

    Short mono- and di-sulphidic crosslinks are thermally stable, resist reversion and give low compression set; this is what the EV system makes. The conventional system makes weaker poly-sulphidic links that break down in heat, which is the tempting choice only if fatigue life were the priority. Unvulcanised rubber flows and sets permanently.
  7. A rubber recipe is: rubber 100, carbon black 45, process oil 5, zinc oxide 5, stearic acid 2, accelerator 1, sulphur 2 (all in phr). What is the carbon black content in weight per cent of the whole compound, to one decimal place?

    1. 45.0 %
    2. 30.4 %
    3. 22.5 %
    4. 28.1 %
    Show answer

    Answer: D — 28.1 %

    Total = 100 + 45 + 5 + 5 + 2 + 1 + 2 = 160 phr, so carbon black = 45/160 = 28.1 %. Reading 45 phr as 45 % ignores the other ingredients, and 30.4 % (45/148) wrongly leaves out the oil, zinc oxide and stearic acid from the total.
  8. A polyethylene film must resist sunlight for years, but the film is only 40 µm thick. Which UV stabiliser is the better choice, and why?

    1. A UV absorber alone, because a thin film absorbs the most light per unit mass of additive
    2. HALS, which trap radicals and regenerate, so they work independent of thickness
    3. Calcium stearate, which absorbs the ultraviolet light as heat
    4. A lubricant, which makes the surface smooth and so reflects the light
    Show answer

    Answer: B — HALS, which trap radicals and regenerate, so they work independent of thickness

    A UV absorber needs path length (thickness) to remove enough radiation, so a 40 µm film is poorly protected by it. HALS act by trapping radicals in a regenerative cycle and do not depend on thickness, which is why they are the standard choice for films and fibres. Calcium stearate and lubricants are not UV stabilisers.
  9. A polyamide is melt-compounded at 250 °C and needs a halogen-free flame-retardant filler at high loading. Aluminium hydroxide begins to decompose, releasing water, at about 200 °C, and magnesium hydroxide at about 330 °C. Which choice is sound?

    1. Aluminium hydroxide, because its higher water yield makes it more effective in the melt
    2. Either, because both decompose only in the flame and never during compounding
    3. Antimony trioxide alone, as it is an endothermic water-releasing filler
    4. Magnesium hydroxide, because aluminium hydroxide would release its water and foam the melt during compounding
    Show answer

    Answer: D — Magnesium hydroxide, because aluminium hydroxide would release its water and foam the melt during compounding

    At 250 °C aluminium hydroxide would already dehydrate in the extruder, wasting its fire-retardant action and creating voids. Magnesium hydroxide is stable up to its onset near 330 °C, so it survives compounding. A higher water yield is irrelevant if the water is lost early, and antimony trioxide is a synergist for halogens, not a water-releasing filler.
  10. Which of the following statements about additives for PVC and other plastics are correct?

    1. A plasticiser such as DOP lowers the glass transition temperature and the modulus of PVC
    2. An internal lubricant is poorly compatible and migrates to the metal surface of the die
    3. An external lubricant migrates to the hot metal surface and delays the fusion of PVC
    4. A plasticiser raises the tensile modulus and lowers the elongation at break
    Show answer

    Answer: A — A plasticiser such as DOP lowers the glass transition temperature and the modulus of PVC; C — An external lubricant migrates to the hot metal surface and delays the fusion of PVC

    A plasticiser lowers Tg and modulus and raises elongation, so the first claim holds and the last is its reverse. External lubricants are poorly compatible and migrate to metal surfaces, delaying fusion and aiding release, so that claim holds. The internal lubricant is the compatible one, which lowers melt viscosity; assigning migration to it mixes up the two classes.
  11. Which statements about carbon black in rubber are correct?

    1. A higher DBP oil absorption number indicates higher structure
    2. Bound rubber is the rubber held on the black surface that resists solvent extraction
    3. Increasing structure lowers the viscosity and raises the die swell of the uncured compound
    4. In the N-number, the larger first digit means the finer particle and more reinforcement
    Show answer

    Answer: A — A higher DBP oil absorption number indicates higher structure; B — Bound rubber is the rubber held on the black surface that resists solvent extraction

    The DBP number measures the voids of the aggregates, hence structure, and bound rubber is by definition the portion that cannot be extracted. Higher structure does the opposite of the third claim: it raises viscosity and cuts die swell. In the N-system the smaller digit means the finer black, so the last claim is reversed.
  12. Which statements about polymer mixing equipment are correct?

    1. Dispersive mixing needs a stress above the cohesive strength of the filler agglomerates
    2. A two-roll mill works by running its two rolls at different speeds, the ratio being called the friction ratio
    3. An internal mixer is a continuous machine that discharges a steady stream of stock
    4. A co-rotating twin-screw extruder cannot be vented, so it cannot devolatilise
    Show answer

    Answer: A — Dispersive mixing needs a stress above the cohesive strength of the filler agglomerates; B — A two-roll mill works by running its two rolls at different speeds, the ratio being called the friction ratio

    Breaking agglomerates needs high local stress, and the mill shears the stock in the nip because the rolls run at different speeds. An internal mixer processes closed batches of a few minutes, not a steady stream. Twin-screw extruders are routinely vented for devolatilisation, so the last claim is false.
  13. A rubber compound has an optimum cure time t90 = 24 min at 140 °C. Use the Q10 rule (the cure time halves for every 10 °C rise in temperature) to find t90 at 160 °C, in minutes.

    Numerical answer — type the value.

    Show answer

    Answer: 6

    The rise is 20 °C, which is two steps of 10 °C, so t90 = 24/2² = 24/4 = 6 min. Halving only once (12 min) is the common slip.
  14. The optimum cure time of a compound is t90 = 18 min at 150 °C. Assume Arrhenius behaviour of the cure rate, with t90 inversely proportional to the rate constant, so t₂ = t₁ exp[(Ea/R)(1/T₂ − 1/T₁)], with Ea = 90 kJ/mol, R = 8.314 J mol⁻¹ K⁻¹ and T = °C + 273.15. Find t90 at 170 °C in minutes, to two decimal places.

    Numerical answer — type the value.

    Show answer

    Answer: 5.67

    T₁ = 423.15 K and T₂ = 443.15 K. Ea/R = 90000/8.314 = 10825 K. 1/T₂ − 1/T₁ = −1.0666 × 10⁻⁴ K⁻¹, so the exponent is −1.1546 and t₂ = 18 × e^−1.1546 = 18 × 0.3152 = 5.67 min. A positive exponent (a longer time at a higher temperature) is the sign slip to avoid.
  15. A cure curve at 160 °C gives a scorch time ts2 = 3.5 min and an optimum cure time t90 = 12.5 min. Using CRI = 100/(t90 − ts2), with the times in minutes, find the cure rate index in min⁻¹, to two decimal places.

    Numerical answer — type the value.

    Show answer

    Answer: 11.11

    t90 − ts2 = 12.5 − 3.5 = 9.0 min, so CRI = 100/9.0 = 11.11 min⁻¹. Using t90 alone (100/12.5 = 8) forgets that the induction time must be subtracted.
  16. For a curemeter run, ML = 1.0 dN·m and MH = 19.0 dN·m. The torque at 6.0 min is 10.5 dN·m. Take the state of cure α = (M − ML)/(MH − ML), assume first-order cure dα/dt = k(1 − α) with negligible induction time (so α = 0 at t = 0), and find k in min⁻¹, to three decimal places.

    Numerical answer — type the value.

    Show answer

    Answer: 0.125

    α = (10.5 − 1.0)/(19.0 − 1.0) = 9.5/18 = 0.5278, so 1 − α = 0.4722. For first order, ln(1 − α) = −kt, so k = −ln(0.4722)/6.0 = 0.7503/6.0 = 0.125 min⁻¹. Taking α as 10.5/19 (forgetting ML) gives a different, wrong value.