Fibre Structure and Properties

Linear density and fibre diameter

Linear density is the mass of a fibre per unit length and is the basic measure of fineness. In the direct system, denier is the mass in grams of 9000 m of fibre, and tex is the mass in grams of 1000 m, so one denier equals 9 tex in the same sample. For fibres of one polymer, linear density is proportional to density times cross-sectional area, and for a circular fibre the area is A = \pi d^2/4. Therefore \text{denier} \propto d^2, so the diameter ratio equals the square root of the linear density ratio. A fibre with three times the denier of another has a diameter about \sqrt{3} \approx 1.73 times larger. Converting a measured diameter into fineness is a unit exercise: express the diameter in cm, compute A in cm^2, multiply by density in g/cm^3 to obtain g/cm, and multiply by 9 \times 10^5 cm to obtain the mass in grams for 9000 m, which is the denier. The yarn count (tex) of a yarn with fixed diameter and packing density is proportional to the fibre density, because the yarn's mass per unit length equals its cross-sectional area multiplied by the packing density and the fibre density. Two yarns of the same construction therefore have counts in the ratio of their fibre densities. For a hollow fibre, the linear density counts only the wall: A = \frac{\pi}{4}(D^2 - d^2), where D is the outer and d the inner diameter. Since tenacity is breaking force divided by linear density, a known breaking force and tenacity give the tex, the solid-equivalent area, and then the outer diameter. Bending rigidity is B = EI, and for a circular fibre of radius r the second moment of area is I = \pi r^4/4, so B \propto r^4. A finer fibre therefore bends far more easily than a coarser one of the same material. Specific surface area (surface per unit mass) is 2/(\rho r) for a solid circular fibre, so it increases as the fibre becomes finer.

Moisture regain calculations

Moisture regain and moisture content are two different ways of expressing the water held by a textile. Moisture regain R is the mass of water W taken relative to the bone-dry mass D, so R = \frac{W}{D} \times 100. Moisture content M is the mass of water relative to the total wet mass, so M = \frac{W}{W + D} \times 100. Because the denominator of R is always smaller, regain is always numerically larger than content for any moisture present. The two are equal only when W = 0, so their common value is 0 %. The two definitions convert into each other by M = \frac{100R}{100 + R} and R = \frac{100M}{100 - M}. For example, if regain is double the content, substituting R = 2M gives 100 + 2M = 200, so M = 50 %. When moisture content is given, the dry mass is found by subtracting the absorbed water from the wet mass, since M = m_{w}/m_{\text{wet}}. From the dry mass, the fibre volume follows from density, and dividing by the length gives the cross-sectional area and hence the diameter. For a blend, the regain is approximated as the mass-fraction-weighted average of the regains of its components, R_{\text{blend}} \approx \sum f_i R_i.

Fibre chemical composition

Each fibre family is identified by the chemical linkages in its repeating units, and these linkages determine the atoms present and the behaviour of the fibre. Nitrogen-containing fibres carry amide, imide or nitrile groups. Polyamides such as nylon 6 contain the -\text{NH-CO-} linkage, aromatic polyamides such as Kevlar contain amide linkages between aromatic rings, and acrylic (polyacrylonitrile) contains the -\text{C}\equiv\text{N} group. Polyester, in contrast, contains only carbon, hydrogen and oxygen, so it has no nitrogen. Cellulosic fibres are built from \beta-D-glucose units joined by 1,4-glycosidic bonds. Regenerated fibres such as Polynosic and Lyocell and the natural bast fibre ramie all retain this linkage, whereas silk is a protein whose chain is held together by peptide bonds and has no glycosidic linkage. Lignin is a phenolic polymer that accompanies cellulose in bast and hard fibres, which are called lignocellulosic. Jute is a bast fibre in which cellulose is bound with lignin and hemicellulose. Cotton is almost pure cellulose, and wool and silk are protein fibres, so none of these contains lignin.

Wool keratin structure

Wool keratin is a fibrous protein whose polypeptide chains are largely in the \alpha-helix conformation, stabilised by intra-chain hydrogen bonds and by cross-links such as disulfide bonds. The high extensibility of wool comes from the reversible conversion of the \alpha-helix into the extended \beta-sheet form under tension, with return to the helix on relaxation. This conformational change allows the fibre to elongate far more than most synthetic fibres before breaking. The surface scales, the cross-links and the \beta-sheet form itself do not provide this extension; the cross-links in fact restrict chain movement. The wool fibre has an outer cuticle of overlapping scales around a cortex that holds most of the keratin. The keratin backbone is built from amino acids joined by amide (peptide) linkages. Ester linkages are not a defining feature of wool keratin, since its main cross-links are disulfide bonds, and ester groups are characteristic of polyester.

Fibre characterisation techniques

Each property of a fibre is measured by a technique suited to it. Crystallinity is determined from wide-angle X-ray diffraction (WAXD), in which sharp crystalline peaks are separated from the diffuse amorphous background. Thermal stability is assessed by thermogravimetric analysis (TGA), which records mass loss as temperature rises. Surface morphology is examined by scanning electron microscopy (SEM), and molecular orientation is measured by birefringence. Chemical structure is identified by infrared (IR) spectroscopy, which detects the characteristic absorption bands of functional groups and therefore distinguishes polymer types such as polyester, nylon and acrylic. Differential scanning calorimetry (DSC) and dynamic mechanical analysis (DMA) give thermal transitions and viscoelastic behaviour, and TGA gives thermal stability, so none of these three identifies the chemical structure directly.

Silk fibre composition (sericin)

Raw silk is a composite of two proteins. Fibroin forms the structural filament core that carries the load. Sericin is a water-soluble, gummy protein that coats and cements the fibroin filaments together in the cocoon thread. Sericin is removed in the degumming process, which is carried out before dyeing and finishing to give the soft lustrous silk. Serine is only one of the amino acids that build these proteins, not the gummy substance, and keratin is the protein of wool and hair, not of raw silk.

Cotton fibre length uniformity

Variation in cotton fibre length is expressed by the uniformity index, which is the ratio of the mean fibre length to the mean length of the longer half of the fibres, expressed as a percentage. A higher value means the fibres are more uniform in length. This index is distinct from yarn evenness measures such as U% and the index of irregularity, which describe mass variation in slivers and yarns rather than fibre length.