Fibre Formation: Polymer Structure, Polymerisation, Spinning Methods and Post-Spinning

This chapter answers the middle part of Section XE9.1 “Textile Fibres” of the Engineering Sciences (XE) paper: “Molecular architecture, amorphous and crystalline phases, glass transition, plasticization, crystallization, melting, factors affecting Tg and Tm; Polymerization of nylon-6, nylon-66, poly (ethylene terephthalate), polyacrylonitrile and polypropylene; Melt spinning processes for PET, polyamide and polypropylene; Preparation of spinning dope; Principles of wet spinning, dry spinning, dry-jet-wet spinning and gel spinning; Spinning of acrylic, viscose and other regenerated cellulosic fibres such as polynosic and lyocell; Post spinning operations such as drawing, heat setting, tow-to-top conversion; Spin finish composition and applications; Different texturing methods.” It teaches the structure of a fibre polymer and its transitions, the five polymerisations, melt and solution spinning, and what is done to the fibre afterwards. The numericals are the Fox equation for Tg, Carothers degree of polymerisation, melt-spinning throughput and draw-down, draw ratio, and false-twist twist.

1. Molecular architecture, phases, Tg, Tm and plasticisation

Molecular architecture means chain length (degree of polymerisation, DP), branching, copolymer composition, configuration (isotactic, syndiotactic, atactic) and the stiffness and polarity of the repeat unit. In a fibre, chains lie mainly along the axis. A semicrystalline fibre is described by a two-phase model: crystalline regions, where chains pack in a regular lattice, and amorphous regions, where they are disordered and accessible to dye, moisture and chemicals. Tie molecules link crystallites through the amorphous phase; these tie molecules carry much of the load, so orientation of the amorphous phase matters as much as crystallinity.

The glass transition temperature Tg is where segmental motion of the amorphous phase freezes or is released: below it the amorphous regions are hard and glassy, above it rubbery. Melting Tm is the disappearance of crystals; thermodynamically Tm = ΔHm/ΔSm, so a polymer melts higher if its crystals have a large enthalpy of fusion (strong hydrogen bonds or dipoles) or a small entropy of fusion (a stiff chain that gains little freedom on melting). Rough guides: Tm is typically 1.4 to 2 times Tg in kelvin for symmetrical polymers.

Typical transition temperatures (approximate)
PolymerTg, °CTm, °C
Polyester (PET)about 70 to 80about 255 to 265
Nylon 66about 50 (dry)about 265
Nylon 6about 50 (dry)about 220
Polypropylene (isotactic)about −10about 165
  • Raise Tg: stiff backbone (p-phenylene rings), bulky or polar side groups, strong inter-chain forces, cross-links, higher molecular weight (up to a limit; Flory–Fox: Tg = Tg∞ − K/Mn, with K a constant for the polymer, so Tg rises as Mn grows and levels off).
  • Lower Tg (plasticisation): a small-molecule plasticiser separates chains and adds free volume. Water is the plasticiser of nylon, wool and cellulose; wet nylon has a Tg near or below room temperature, which is why wet nylon is softer and more extensible. For a compatible mixture the Fox equation gives 1/Tg = w₁/Tg₁ + w₂/Tg₂ (mass fractions, Tg in kelvin).
  • Raise Tm: hydrogen bonding and dipoles (amide, ester), chain symmetry, stiffness. Tm is lowered by copolymerisation, branching and low molecular weight (impurities disrupt crystals).

Crystallisation needs mobility and nucleation, so it occurs between Tg and Tm. At a temperature just above Tg chains barely move; just below Tm the nuclei are unstable. The rate therefore peaks between the two, and cold crystallisation (crystallising on heating from the glassy amorphous state) appears as an exotherm above Tg. Orientation by stretching speeds crystallisation (strain-induced), which is why fibres crystallise within a fraction of a second in the spin line or draw zone.

⚠️ Tg belongs to the amorphous phase only
A highly crystalline polymer shows a weak Tg step, but the crystals do not have a Tg. Do not say that “the whole fibre becomes rubbery above Tg”: the crystals still hold it together until Tm. Also, Tg is a kinetic transition and depends on heating rate, whereas Tm of a given crystal is a thermodynamic one.

2. Polymerisation of nylon-6, nylon-66, PET, PAN and polypropylene

Routes to the five fibre polymers
PolymerMonomers and mechanismKey conditions and points
Nylon-6ε-Caprolactam; hydrolytic ring-opening then addition, a chain polymerisation by ring opening that behaves as a step-growth equilibriumWater starts it, about 250 to 270 °C; an equilibrium leaves roughly 8 to 10% monomer and oligomer, removed by hot-water extraction or vacuum; acetic acid caps chains to fix Mn
Nylon-66Hexamethylenediamine + adipic acid, via 1:1 nylon salt; step-growth polycondensationSalt in water heated in an autoclave under pressure, steam vented, finishing near 270 to 280 °C; the salt fixes exact stoichiometry
PETTerephthalic acid (TPA) or dimethyl terephthalate (DMT) + ethylene glycol (EG); step-growthEsterification (water) or ester interchange (methanol) to bis(hydroxyethyl) terephthalate, then polycondensation near 280 °C under high vacuum removing EG; textile grade intrinsic viscosity about 0.6 to 0.7 dl/g
PAN (acrylic)Acrylonitrile (at least 85% by mass) with comonomers; free-radical chain polymerisationRedox initiator in water (suspension) or in solvent; neutral comonomer (methyl acrylate, vinyl acetate) aids dissolution and dyeing, ionic comonomer (sulphonate, itaconic acid) gives dye sites
PolypropylenePropylene; coordination polymerisationZiegler–Natta (or metallocene) catalyst gives isotactic chains; hydrogen or peroxide controls molecular weight and melt flow

In step-growth polymerisation (nylon-66, PET) high molecular weight appears only at very high conversion p. The Carothers equation gives the number-average degree of polymerisation (average number of monomer residues per chain) Xn = 1/(1 − p) for exact stoichiometry. If the stoichiometric ratio is r (less than 1), Xn = (1 + r)/(1 + r − 2rp). Worked example: for p = 0.99 and r = 0.99, Xn = 1.99/(1.99 − 2 × 0.99 × 0.99) = 1.99/0.0298 = 66.8. Perfect balance would give 100 at the same p, and a small imbalance costs a third of the chain length. That is why nylon salt is made first and why PET plants remove EG so completely. In chain polymerisation (PAN, PP) high molecular weight forms at once, and conversion mostly changes yield.

⚠️ Nylon-6 is not a true step-growth polymer, but behaves like an equilibrium
Nylon-6 forms by ring opening of a single monomer with no by-product, whereas nylon-66 and PET release water, methanol or EG. For nylon-6 the equilibrium monomer content, not by-product removal, sets the conversion limit, so the extraction of residual caprolactam is essential before spinning; for PET and nylon-66 the by-product must be removed to drive the reaction.

3. Melt spinning of PET, polyamide and polypropylene

Melt spinning extrudes molten polymer through fine holes, cools the jets in air, and winds the solidified filaments. The line is: chips (dried: PET and nylon are hygroscopic and would hydrolyse in the melt, so PET is dried to a very low moisture before it is melted) → extruder (screw melts and pumps) → metering gear pump (fixes the flow) → spin pack (filter sand or screens, then the spinneret, a plate with many capillaries) → quench chamber (cross-flow air solidifies the filaments) → spin finish applicator → godets or winder. Spinning temperature is above Tm but well below decomposition: nylon is spun under nitrogen to avoid oxidation, PET at a short residence time to limit hydrolysis and thermal degradation, and polypropylene at lower temperature with stabilisers because it oxidises readily.

Mass balance. Mass flow per hole equals take-up speed times linear density of one filament: w (g/min) = v (m/min) × denier/9000 (or × dtex/10,000). Total throughput is w × number of holes. The extrusion velocity in the capillary is v₀ = Q/A with Q = w/ρ (melt density) and A the capillary area, and the draw-down ratio is v/v₀. Worked example: 72 holes of diameter 0.25 mm, melt density 1.20 g/cm³, take-up 3000 m/min, 3.0 denier filaments. w = 3000 × 3.0/9000 = 1.0 g/min per hole; throughput = 72 g/min = 4.32 kg/h. Q = 1.0/1.20 = 0.833 cm³/min = 8.33 × 10⁻⁷ m³/min; A = π(0.25 × 10⁻³)²/4 = 4.91 × 10⁻⁸ m²; v₀ = 17.0 m/min; draw-down = 3000/17.0 = 177. The filament speeds up by the draw-down ratio, so its cross-section shrinks by that factor, and most of the attenuation, and the first orientation, happens in the spin line.

Take-up speed and the yarn produced (PET, indicative)
Take-up speedNameStateNext step
Up to about 1500 m/minLow-oriented yarnAlmost amorphous, low birefringenceSeparate drawing, 3 to 5 times
About 2500 to 3500 m/minPartially oriented yarn (POY)Part-oriented, stableDraw-texturing in one step
4000 m/min and aboveHighly oriented yarnOriented and partly crystallineUsed with little or no drawing

4. Spinning dope and wet, dry, dry-jet-wet and gel spinning

A spinning dope is the polymer solution that is filtered, de-aerated (bubbles break filaments) and metered to the spinneret. Its concentration is a trade-off: high enough for strength and for a coherent filament, low enough to be pumped. The four solution methods differ in how the filament solidifies.

  • Wet spinning: the spinneret is submerged in a coagulation bath; solvent diffuses out and non-solvent diffuses in (or a reaction regenerates the polymer). Slow (tens to a few hundred m/min), the cross-section is often irregular. Used for viscose and for some acrylic.
  • Dry spinning: the dope in a volatile solvent is extruded into a heated gas column and the solvent evaporates (acetone for cellulose acetate, dimethylformamide for acrylic). Faster than wet spinning, with solvent recovery; dog-bone cross-sections are typical because the skin forms first and then collapses.
  • Dry-jet-wet spinning: the dope leaves the spinneret into a short air gap and then enters the coagulation bath. In the gap the filament can be stretched under tension, orienting the chains (or the liquid-crystalline domains) before they are fixed; the method suits viscous, high-concentration dopes, such as para-aramid in sulphuric acid and lyocell.
  • Gel spinning: a dilute solution of a very high molecular weight polymer (UHMWPE in a solvent such as decalin or paraffin oil, at a few per cent) is extruded and cooled to a gel, so chains are lightly entangled, then solvent is extracted and the gel filament is hot-drawn many times, giving nearly fully extended chains.

Viscose dope. Pulp is steeped in about 18% sodium hydroxide to give alkali cellulose, pressed, shredded and aged (oxygen shortens the chains to the target DP), then treated with carbon disulphide to form orange cellulose xanthate, which dissolves in dilute alkali to give the viscose dope; it is ripened, filtered and de-aerated. The spin bath contains sulphuric acid (regenerates cellulose), sodium sulphate (dehydrating, speeds coagulation) and zinc sulphate (retards regeneration so the filament can be stretched before it is fully set). Rapid skin formation followed by core regeneration gives the skin-core structure and serrated cross-section. Polynosic (high wet modulus) fibre uses higher-DP pulp, little ageing, a dilute, cool, zinc-rich bath and heavy stretch, so there is no skin: a round, fibrillar, more oriented fibre with a high wet modulus and dimensional stability. Lyocell dissolves cellulose directly in hot N-methylmorpholine N-oxide (NMMO) hydrate, with no derivative and no carbon disulphide, spins by dry-jet-wet into water, and recovers the solvent in a closed loop; it has a round, homogeneous section, high wet strength, and a tendency to fibrillate when wet and abraded.

5. Post-spinning operations and spin finish

Drawing stretches the as-spun fibre several times its length, above Tg, to orient chains and raise strength and modulus. Because volume is conserved, the draw ratio DR = L/L₀ = v₂/v₁ (delivery to feed speed) and the linear density after drawing is the original divided by DR: a 4.5 denier as-spun filament drawn 3.75 times is 1.2 denier. Many fibres draw by necking at the natural draw ratio, where the neck propagates along the filament and the draw ratio is fixed by the polymer; drawing is done hot (over hot plates, in a hot bath or steam) for PET, cold or warm for nylon. The more it is drawn, the higher the orientation and tenacity and the lower the extension, until breaks occur.

Heat setting holds the drawn fibre or fabric at fixed length or controlled tension at a temperature above any later processing temperature (and above the drawing temperature) but below Tm, so crystals perfect and grow and residual strain relaxes. It raises crystallinity and density, lowers shrinkage and gives dimensional stability and crease retention; it lowers dye uptake somewhat. Tow-to-top conversion turns a continuous rope of many thousand filaments (tow), usually crimped and drawn, into a top, a sliver of staple fibre fit for worsted or cotton-system spinning, either by cutting to a fixed staple length or by stretch breaking (tow broken between rollers into a distribution of lengths, giving a wool-like top); the output is then blended and gilled.

Spin finish is an aqueous emulsion (a small percentage of the fibre mass) applied after quench or after drawing. It contains lubricants (mineral oil or ester, for fibre–metal and fibre–fibre friction), antistatic agents (ionic or ethoxylated surfactants, for static charge), emulsifiers and cohesion agents (so the filaments hold together as a yarn), with bactericide and anticorrosion additives. A finish for filament yarn emphasises cohesion and lubrication at high speed, whereas a staple finish emphasises friction control and antistatic action for carding and drafting.

6. Texturing methods

Texturing converts smooth continuous-filament yarn into bulky, extensible yarn with the loft and touch of staple yarn, using the thermoplastic nature of the fibre.

  • False-twist texturing (the main method for polyester POY and nylon): yarn is twisted, heat-set in the twisted state above Tg, cooled, then untwisted. After the twister the yarn has almost no net twist, but the filaments keep a helical memory, which gives bulk and stretch. Twist inserted in the heating zone is spindle (or disc) speed divided by yarn speed; for 300,000 rpm and 100 m/min it is 3000 turns/m. Pin spindles, and now friction discs, are used; draw-texturing combines drawing of POY with texturing.
  • Air-jet texturing: overfed yarn is blown with turbulent compressed air, forming random loops and entangled filaments, giving a spun-yarn-like appearance and handle; no heat or twist is needed, and any fibre, including non-thermoplastic ones, can be used.
  • Stuffer-box crimping: yarn or tow is forced into a heated box, folding into a zigzag crimp that is set (used for carpet yarn and staple tow). Other methods are gear crimping, edge crimping (pulling the yarn over a blade), and knit-de-knit (knit, heat-set, unravel, giving a kinked yarn).
⚠️ Where the bulk comes from
False-twist and stuffer-box methods rely on heat setting above Tg, so they need a thermoplastic fibre; air-jet texturing relies on mechanical entanglement, so it does not. In false twisting the yarn leaves the spindle with essentially zero twist, so the twist is a transient, not something you can count in the product.

Key takeaways

  • Semicrystalline fibres have crystalline and amorphous phases; Tg is an amorphous-phase transition raised by stiffness and bulk and lowered by plasticisers (Fox: 1/Tg = w₁/Tg₁ + w₂/Tg₂), while Tm = ΔHm/ΔSm is raised by hydrogen bonds and chain stiffness.
  • Nylon-6 is ring-opened from caprolactam with an equilibrium monomer residue to extract; nylon-66 comes from a 1:1 salt and PET by esterification or ester interchange then vacuum polycondensation; PAN and PP are chain polymers (radical and Ziegler–Natta). Carothers: Xn = 1/(1 − p), and (1 + r)/(1 + r − 2rp) with imbalance.
  • Melt spinning: dried chips, extruder, metering pump, spin pack, quench, finish, take-up. Per-hole flow = speed × denier/9000; draw-down = take-up speed ÷ extrusion speed; higher take-up gives POY and more as-spun orientation.
  • Wet spinning coagulates in a bath, dry spinning evaporates solvent, dry-jet-wet adds an air gap for stretch before coagulation, gel spinning draws a gel of UHMWPE. Viscose uses xanthate and an acid–sulphate–zinc bath; polynosic has no skin; lyocell dissolves cellulose directly in NMMO.
  • Drawing above Tg orients chains (DR = v₂/v₁, denier after = before ÷ DR); heat setting at fixed length below Tm stabilises; tow-to-top is by cutting or stretch breaking; spin finish gives lubrication, antistatic action and cohesion.
  • Texturing: false twist (twist, set, untwist; twist = spindle rpm ÷ yarn speed), air-jet (loops by turbulent air, works on any fibre), stuffer-box (zigzag crimp), plus gear, edge and knit-de-knit.

Practice questions (17)

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. Which structural change in the backbone of a polyester would be expected to raise its glass transition temperature most?

    1. Lengthening the flexible aliphatic spacer between the ester groups
    2. Replacing flexible CH₂ units by rigid p-phenylene rings
    3. Adding a small-molecule plasticiser to the polymer
    4. Introducing flexible ether linkages into the chain
    Show answer

    Answer: B — Replacing flexible CH₂ units by rigid p-phenylene rings

    Rigid ring units hinder rotation about backbone bonds, so more thermal energy is needed to free segmental motion and Tg rises. A longer flexible spacer, ether linkages and a plasticiser all increase mobility or free volume and lower Tg; the plasticiser is the tempting wrong choice because it is a classic Tg-modifier, but it acts in the opposite direction.
  2. A glassy, amorphous PET sample is heated slowly in a differential scanning calorimeter. Which sequence of events occurs on heating?

    1. Melting endotherm, then cold-crystallisation exotherm, then a glass transition step
    2. Cold-crystallisation exotherm, then a glass transition, then melting endotherm
    3. Glass transition, then melting endotherm, then cold-crystallisation exotherm
    4. Glass transition, then a cold-crystallisation exotherm, then a melting endotherm
    Show answer

    Answer: D — Glass transition, then a cold-crystallisation exotherm, then a melting endotherm

    Chain mobility is released at Tg first; once chains can move they crystallise (cold crystallisation, exothermic) before the crystals so formed melt (endothermic) at Tm. Crystallisation cannot precede the glass transition because below Tg the chains are frozen, and melting cannot precede crystals that do not yet exist.
  3. Nylon-66 is made by first preparing a 1:1 salt of hexamethylenediamine and adipic acid. The main reason for this step is to

    1. convert the step-growth reaction into a chain reaction
    2. avoid any release of water during the polycondensation stage
    3. ensure exact stoichiometric balance of the two monomers
    4. make the polymer isotactic
    Show answer

    Answer: C — ensure exact stoichiometric balance of the two monomers

    Step-growth reaches high molecular weight only if the two functional groups are exactly equal in number; any imbalance caps Xn at (1 + r)/(1 − r) even at full conversion. The salt is a crystalline compound with the two monomers locked in 1:1 ratio. Water is still released on heating the salt, the mechanism stays step-growth, and tacticity is irrelevant to a polyamide with no stereocentres.
  4. In the final stage of PET production the melt is held at about 280 °C under high vacuum. The vacuum is used to

    1. remove ethylene glycol and drive the reversible reaction forward
    2. prevent crystallisation of the melt before spinning
    3. extract unreacted caprolactam monomer from the polymer
    4. raise the glass transition temperature of the final product
    Show answer

    Answer: A — remove ethylene glycol and drive the reversible reaction forward

    Polycondensation of PET is an equilibrium; ethylene glycol is the by-product and its removal, aided by vacuum and high temperature, shifts the equilibrium to long chains. Caprolactam belongs to nylon-6, and vacuum has no role in preventing crystallisation or altering Tg directly.
  5. Compared with ordinary viscose rayon, polynosic fibre is made using

    1. a hot spin bath rich in sulphuric acid to regenerate the cellulose as quickly as possible, with little stretch
    2. higher-DP pulp, little ageing, a dilute cool bath and heavy stretch, giving a skinless fibrillar structure
    3. lower-DP pulp, extensive ageing and no stretching
    4. direct dissolution of cellulose in N-methylmorpholine N-oxide
    Show answer

    Answer: B — higher-DP pulp, little ageing, a dilute cool bath and heavy stretch, giving a skinless fibrillar structure

    Polynosic (high wet modulus) fibre needs slow, gentle regeneration so no skin forms, high-DP chains and heavy stretch for orientation; the result is a round, fibrillar fibre with high wet modulus. A hot concentrated acid bath is what produces the fast skin of ordinary viscose, direct NMMO dissolution defines lyocell, and low DP with no stretch would give a weak fibre.
  6. Lyocell differs from viscose in that lyocell

    1. is made from a cellulose derivative that is later hydrolysed
    2. uses carbon disulphide and recovers it from the spin bath
    3. is melt-spun above the melting point of cellulose
    4. dissolves cellulose directly in a solvent, with no derivative
    Show answer

    Answer: D — dissolves cellulose directly in a solvent, with no derivative

    In the lyocell process cellulose dissolves physically in NMMO hydrate with no chemical derivatisation and the dope is dry-jet-wet spun into water with solvent recycling. Viscose is the process that uses a derivative (xanthate) and carbon disulphide; cellulose does not melt, so melt spinning is impossible.
  7. UHMWPE cannot be processed by conventional melt spinning, and is gel spun instead, mainly because

    1. it dissolves in water
    2. it decomposes at a temperature well below its melting point, so it cannot be melted
    3. its melt viscosity is extremely high at such a molecular weight
    4. its Tg is above 300 °C
    Show answer

    Answer: C — its melt viscosity is extremely high at such a molecular weight

    At molar masses of millions the entanglement density makes the melt almost non-flowing, so it cannot be extruded through fine capillaries; a dilute solution with light entanglement can be extruded, gelled and ultra-drawn. UHMWPE is hydrophobic, melts at about 150 °C without decomposing, and has a Tg far below room temperature.
  8. A spin-drawn PET fibre has been drawn and then heat-set at fixed length at a temperature between its Tg and Tm. Compared with the unset drawn fibre it will show

    1. higher density and lower shrinkage, as crystals grow and strain relaxes
    2. lower crystallinity because the crystals melt partially
    3. lower density and higher boiling-water shrinkage
    4. no change at all, because heat setting acts only on the amorphous phase and not on crystals
    Show answer

    Answer: A — higher density and lower shrinkage, as crystals grow and strain relaxes

    Annealing at fixed length above the drawing temperature lets crystals perfect and grow and relaxes frozen-in strain, so density and crystallinity rise and shrinkage falls. Crystals do not melt because the temperature is below Tm, and the process clearly changes the structure of both phases.
  9. Which texturing method can bulk a yarn made of a non-thermoplastic fibre because it relies on mechanical entanglement rather than heat setting?

    1. False-twist texturing with a heater
    2. Air-jet texturing
    3. Knit-de-knit with heat setting
    4. Stuffer-box crimping with a heated box
    Show answer

    Answer: B — Air-jet texturing

    Air-jet texturing forms loops by turbulent air acting on overfed yarn and needs no heat or twist, so the fibre need not be thermoplastic. The other three all depend on setting a deformed shape thermally above Tg.
  10. Which statements about drawing and heat setting of synthetic fibres are correct?

    1. Drawing is carried out above Tg so that amorphous chains can be oriented along the fibre axis
    2. Drawing raises tenacity and lowers breaking extension
    3. Heat setting is carried out below Tg to avoid any change in crystallinity
    4. A filament drawn 4 times in length has a linear density four times that of the undrawn filament
    Show answer

    Answer: A — Drawing is carried out above Tg so that amorphous chains can be oriented along the fibre axis; B — Drawing raises tenacity and lowers breaking extension

    Drawing above Tg orients chains, which increases tenacity and modulus and reduces extension. Heat setting is done above the drawing temperature and below Tm to raise crystallinity and stability, not below Tg. With volume conserved a four-fold length increase makes the linear density one quarter, not four times.
  11. Which of the following fibres are normally melt spun?

    1. Polyester (PET)
    2. Polyacrylonitrile (acrylic)
    3. Isotactic polypropylene
    4. Nylon 66
    Show answer

    Answer: A — Polyester (PET); C — Isotactic polypropylene; D — Nylon 66

    PET, polypropylene and nylon 66 melt below their decomposition temperatures and are spun from the melt. Polyacrylonitrile has such strong dipolar attraction that it decomposes before it melts, so acrylic is spun from solution (wet or dry).
  12. Which of the following are functions of a spin finish?

    1. Lubrication, to cut fibre–metal and fibre–fibre friction
    2. Dissipation of static charge
    3. Raising the melting point of the polymer
    4. Permanent cross-linking of the polymer chains
    Show answer

    Answer: A — Lubrication, to cut fibre–metal and fibre–fibre friction; B — Dissipation of static charge

    A finish is a thin emulsion that lubricates, controls static and gives cohesion so the fibre runs through machinery. It is a surface treatment and does not change Tm, nor does it cross-link the polymer.
  13. A polymer with Tg = 350 K is plasticised with 10% by mass of a plasticiser with Tg = 200 K. Assuming the Fox equation 1/Tg = w₁/Tg₁ + w₂/Tg₂ with mass fractions w and temperatures in kelvin, the Tg of the mixture in kelvin, to one decimal place, is ____.

    Numerical answer — type the value.

    Show answer

    Answer: 325.6

    1/Tg = 0.90/350 + 0.10/200 = 0.0025714 + 0.0005000 = 0.0030714 K⁻¹, so Tg = 325.6 K. A simple mass-weighted average would give 335 K, the usual wrong answer, and ignores that the reciprocal temperatures average.
  14. A melt-spinning line has 72 holes per spinneret. Each filament is 3.0 denier (1 denier = 1 g per 9000 m) and the take-up speed is 3000 m/min. The polymer throughput of the spinneret in kg/h, to two decimal places, is ____.

    Numerical answer — type the value.

    Show answer

    Answer: 4.32

    Mass per metre per filament = 3.0/9000 g/m. Per hole w = 3000 × 3.0/9000 = 1.0 g/min. For 72 holes this is 72 g/min = 4320 g/h = 4.32 kg/h.
  15. In the line above each capillary has a diameter of 0.25 mm, the melt density is 1.20 g/cm³, and each hole delivers 1.0 g/min. The draw-down ratio (take-up speed 3000 m/min divided by the average extrusion velocity in the capillary), to the nearest integer, is ____.

    Numerical answer — type the value.

    Show answer

    Answer: 177

    Volumetric flow per hole Q = 1.0 g/min ÷ 1.20 g/cm³ = 0.8333 cm³/min = 8.333 × 10⁻⁷ m³/min. Area A = π(0.25 × 10⁻³ m)²/4 = 4.909 × 10⁻⁸ m². Extrusion velocity v₀ = Q/A = 16.98 m/min. Draw-down = 3000/16.98 = 176.7, so 177.
  16. A polyamide is made by step-growth polymerisation with a stoichiometric ratio r = 0.99 (ratio of the deficient to the excess functional group). At conversion p = 0.99 of the deficient group, the number-average degree of polymerisation (monomer residues per chain) from the Carothers equation Xn = (1 + r)/(1 + r − 2rp), to the nearest integer, is ____.

    Numerical answer — type the value.

    Show answer

    Answer: 67

    Xn = (1 + 0.99)/(1 + 0.99 − 2 × 0.99 × 0.99) = 1.99/(1.99 − 1.9602) = 1.99/0.0298 = 66.8, so 67. With perfect balance the same conversion would give 1/(1 − 0.99) = 100.
  17. In a false-twist texturing machine the spindle runs at 300,000 rpm and the yarn is delivered at 100 m/min. The twist inserted in the yarn in the heating zone, in turns per metre, is ____.

    Numerical answer — type the value.

    Show answer

    Answer: 3000

    Twist (turns/m) = spindle speed (turns/min) ÷ yarn speed (m/min) = 300,000/100 = 3000 turns/m. After the spindle the yarn is untwisted again, so its net twist is nearly zero.