Polymers and Man-made Fibre Spinning

Melt spinning draw ratio

In melt spinning, the draw ratio describes how much the filament is stretched between the spinneret exit and the take-up device. Because the polymer mass flow is conserved along the filament, the draw ratio equals the take-up (winding) velocity divided by the extrusion velocity at the spinneret exit, \mathrm{DR} = v_L / v_0. It can equivalently be written as the ratio of the as-spun linear density to the final yarn linear density, since linear density is inversely proportional to velocity at constant mass flow. Linear density is expressed in denier, defined as the mass in grams of 9000 m of yarn, so the as-spun denier is the mass flow rate divided by the take-up speed, scaled to 9000 m. The effective draw ratio is calculated from the as-spun and final yarn deniers, and it can be lower than the spinneret-to-winder ratio when the filament shrinks after spinning. The spin draw ratio is the ratio of godet (take-up roller) surface speed to extrusion speed, and it does not depend on the spinneret diameter. For a monofilament, the godet speed is v_g = \mathrm{DR} \times v_0, and the godet angular velocity follows from v_g = \pi D N, where D is the godet diameter and N its rotational speed. Continuity of flow links the spinneret orifice area A_0 to the extrusion velocity through Q = A_0 v_0, so the orifice diameter can be found once the flow rate and extrusion velocity are known. When a fibre is drawn in several stages, each stage multiplies the length by (1 + \text{extension}), and a subsequent heat-setting shrinkage multiplies it by (1 - \text{shrinkage}), so the overall draw ratio is the product of these factors.

Fibre polymer chemical linkages

Each fibre-forming polymer is characterised by the linkage that joins its repeat units, and exam questions often test which linkage is absent from a given fibre. The amide linkage is the -\mathrm{CO\text{-}NH}- group that joins units in polyamides such as nylon 6 and nylon 66, in aramids, and in the peptide backbone of wool keratin. The ester linkage -\mathrm{CO\text{-}O}- joins units in polyesters such as poly(ethylene terephthalate). Regenerated cellulose such as lyocell is built from glucose units joined by glycosidic C-O-C linkages, so it contains no amide group. Aromatic groups in the main chain add rigidity and raise both the glass transition and the melting temperature. Poly(ethylene terephthalate) contains a para-phenylene ring in every repeat unit, which places an aromatic group in the main chain, whereas polyolefins and polyacrylonitrile have aliphatic backbones with pendant groups. Melting temperature depends on chain stiffness and interchain attraction. Nylon 6 contains N-H groups that form strong hydrogen bonds with the carbonyl oxygen of neighbouring chains, whereas PET has no N-H groups and its interchain attraction is weaker, so the hydrogen bonding in PET is weaker than in nylon 6. The higher melting point of PET arises from its stiff aromatic rings and regular packing rather than from stronger hydrogen bonding.

Chain-growth vs step-growth polymerisation

Polymers are classified by their mechanism of formation. Chain-growth (addition) polymerisation proceeds by the successive addition of monomers to a growing active centre, such as a free radical, cation or anion. It typically involves vinyl monomers with a carbon-carbon double bond, the polymer molecular weight rises quickly, and no small molecule is released. Acrylonitrile, \mathrm{CH_2{=}CH{-}CN}, forms polyacrylonitrile by free radical addition, so polyacrylonitrile is a chain-growth polymer. Step-growth (condensation) polymerisation proceeds by reactions between functional groups on monomers of any size, and it releases a small molecule such as water or methanol at each linkage. Polyamides and polyesters are made this way. Nylon 66 is formed from hexamethylenediamine, \mathrm{NH_2(CH_2)_6NH_2}, which has six carbons, and adipic acid, \mathrm{HOOC(CH_2)_4COOH}, which has six carbons in total including the carboxyl carbons, so both monomers must have the stated carbon count to yield nylon 66. For PET, high molecular weight is achieved when terephthalic acid and ethylene glycol are present in an exact 1:1 molar ratio, so the mass of glycol needed for a given mass of acid follows from the molar masses of the two monomers. Poly(p-phenylene terephthalamide) is also made by step-growth polycondensation.

Viscose rayon manufacturing

Viscose rayon is a regenerated cellulose fibre. Wood pulp is converted to cellulose xanthate, which is dissolved in dilute caustic soda to form the viscose spinning solution. This solution is extruded through a spinneret into an acid coagulation bath, where the cellulose is regenerated as filament. Because the fibre is formed by precipitation and coagulation in a liquid bath, the spinning method is classified as wet spinning, not melt spinning or dry spinning. Viscose filaments commonly develop a skin-core structure. The skin coagulates and regenerates faster than the core, so it forms a denser outer layer, and the molecular orientation and crystallinity differ between skin and core. The skin-core structure is a recognised feature of viscose, but the explanation of its origin lies in the shear at the spinneret wall, which orients the polymer molecules near the surface more strongly than those at the centre of the filament, not less.

Polymer molecular weight from degree of polymerisation

The degree of polymerisation, DP, is the number of repeat units in a polymer chain. The molecular weight is obtained by multiplying DP by the molar mass of the repeat unit, M_0, so M = DP \times M_0. The repeat unit is the smallest portion of the chain that is repeated along the backbone, and its molecular formula must be determined before its mass is calculated. For polypropylene, the repeat unit is -\mathrm{CH_2CH(CH_3)}-, with formula \mathrm{C_3H_6}, so its mass is found from the atomic masses of carbon and hydrogen and the molecular weight of the polymer is simply DP times that value. The reverse calculation is also common in examinations. Given the number-average molecular weight of a polymer, the degree of polymerisation is DP = M_n / M_0. For poly(ethylene terephthalate), the repeat unit has formula \mathrm{C_{10}H_8O_4} and a molar mass of about 192 g/mol, so DP is the number-average molecular weight divided by this value and must be rounded to a whole number of repeat units.

Polydispersity index and molecular weight averages

A synthetic polymer contains chains of different lengths, so it has several molecular weight averages. The number-average molecular weight, \bar{M}_n, weights each chain equally, while the weight-average molecular weight, \bar{M}_w, weights each chain by its mass. The polydispersity index is defined as PDI = \bar{M}_w / \bar{M}_n, and it is always 1 or greater. A monodisperse polymer has PDI = 1. Rearranging the definition gives \bar{M}_n = \bar{M}_w / PDI, which allows one average to be found when the other and the PDI are known. For a mixture of monodisperse samples mixed by number of chains, \bar{M}_n = \sum N_i M_i / \sum N_i and \bar{M}_w = \sum N_i M_i^2 / \sum N_i M_i, where N_i is the number of chains of molar mass M_i. Applying these sums to a blend of three samples with different proportions yields the PDI of the mixture, which is then the ratio of the two averages. Because the weight-average is weighted toward the longer chains, a blend containing a few long chains gives a PDI noticeably above 1.

DSC degree of crystallinity

Differential scanning calorimetry measures the heat absorbed or released when a polymer is heated or cooled. For a semicrystalline polymer, the degree of crystallinity is estimated from the melting enthalpy, using X_c = \Delta H_m / \Delta H_m^{0} \times 100\%, where \Delta H_m^{0} is the heat of fusion of a hypothetically 100 % crystalline polymer, a standard reference value for each polymer. If a second sample of the same polymer shows only a melting endotherm, its crystallinity is found by scaling its melting enthalpy against the same reference value, which can be back-calculated from a sample of known crystallinity. In the first heating cycle of an as-spun fibre, however, the amorphous chains may crystallise during the scan. This cold crystallisation is exothermic and appears as a peak before melting, so the enthalpy of cold crystallisation must be subtracted from the melting enthalpy before the crystallinity is calculated, using X_c = (\Delta H_m - \Delta H_{cc}) / \Delta H_m^{0} \times 100\%. The corrected value gives the crystallinity that existed in the fibre before heating.

Wet spinning of acrylic fibre

In wet spinning, a polymer solution is extruded through a spinneret into a coagulation bath, where the solvent is removed and the polymer precipitates to form the filament. Acrylic fibres are usually wet spun from solutions in dimethylformamide or dimethylacetamide. During coagulation, solvent diffuses out of the filament while non-solvent diffuses in, so mass transfer is two-way and proceeds in both directions at the same time. The coagulation bath is not solvent alone. It contains a non-solvent, usually water, which precipitates the polymer, together with a controlled amount of solvent that moderates the rate of coagulation and so controls the structure and density of the fibre. Because the filament diameter is set by the coagulated solid, a dried filament is smaller than the as-spun filament. If the solids content of the solution is known and the specific gravities of polymer and solvent are equal, the mass fraction equals the volume fraction of solids. Keeping the length constant, the cross-sectional area then scales with the volume fraction, so the dried diameter is the original diameter multiplied by the square root of that fraction.

Glass transition temperature of polymers

The glass transition temperature, T_g, is the temperature below which the amorphous regions of a polymer become rigid and above which segmental motion of the chains becomes possible. It depends mainly on the flexibility of the backbone and on the strength of intermolecular forces. A flexible backbone with single bonds allows easy rotation and gives a low T_g. Polyethylene is the most flexible of the common fibre and plastic polymers, since it has an unbranched -\mathrm{CH_2}- backbone with no bulky side groups or polar interactions, so its amorphous T_g is very low, about -120\,^\circ\mathrm{C}. Polypropylene, with a methyl side group, is higher, and polystyrene, with a bulky phenyl group, is higher still. Poly(ethylene terephthalate) has a rigid aromatic ring and polar ester groups, which restrict chain motion and place its T_g well above room temperature. The factors that raise T_g are bulky side groups, aromatic groups in the backbone, and polar groups, because each restricts segmental rotation or increases intermolecular attraction. A linear aliphatic backbone does the opposite and lowers T_g.

Melt rheology die-swell

Die swell, also called extrudate swell, is the increase in diameter of a polymer melt as it leaves a capillary or spinneret. The melt is stretched and its molecular chains are oriented while flowing through the die, and on exit the chains relax toward their random coil configuration. This recovery of entropy is elastic in origin, so die swell is an entropic effect. The swell ratio is defined as the extrudate diameter divided by the die diameter. It decreases as the capillary length-to-diameter ratio increases, because a longer capillary allows more time for stress relaxation before the melt emerges. It increases with shear rate, because higher shear produces larger normal stress differences and stores more elastic strain in the melt. Die swell also depends on processing temperature, since temperature changes the relaxation time of the melt. For a circular orifice, the die diameter follows from the volumetric flow rate and the extrusion velocity through A = Q/v and D = \sqrt{4A/\pi}. The maximum extrudate diameter is then the swell ratio multiplied by this die diameter.