Fiber Science

2008-05-23

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1

Textile Materials

University of Textiles and ClothingJiangnan University

Objectives

� To grasp basic theory related to textile fibers

� To understand the properties of textile fibers

� To enlarge vocabulary of textile fibers

� To keep up with the advance in textile fibers

� To improve four skills of scientific English

and of presentation in English

Course Syllabus

�Textbook

Zhang haiquan, Textile Materials, 2007

�Reference book

Yao, M. et. al. Textile Materials (inChinese), 2nd ed., Textile IndustryPublishing House, 1990

Grading

�Grades for this course are determined by

� Homework (10%),

� Final exam (90%).

� The final grade will be from A to F corresponding to the total score according to the student handbook.

Topical Outline

�Chapter 1 Introduction to Textile Fibers

� 1.1 Fiber Classification

� 1.2 Fiber Polymer

� 1.3 Fiber Theory and Fiber Properties

�Chapter 2 Natural Cellulosic Fibers

� 2.1 Introduction

� 2.2 Cotton

� 2.3 Bast Fibers

Topical Outline

�Chapter 3 Natural Protein Fibers

� 3.1 Introduction of Natural Protein Fibers

� 3.2 Wool

� 3.3 Specialty Hairs

� 3.4 Silk

�Chapter 4 Regenerated Fibers

� 4.1 Viscose

� 4.2 Acetate and Triacetate

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Topical Outline

�Chapter 5 Synthetic Fibers

� 5.1 Nylon

� 5.2 Polyester

� 5.3 Acrylic

� 5.4 Elastomeric

Topical Outline

�Chapter 6 Absorption of Water on Textile Fibers

� 6.1 Introduction of Absorption

� 6.2 Equilibrium

� 6.3 Regain and Relative Humidity

� 6.4 Theories of Moisture Sorption

Topical Outline

�Chapter 7 Thermal, Optical, and Electric

Properties of Textile Fibers

� 7.1 Thermal properties

� 7.2 Optical Properties

� 7.3 Electric Properties

1 Introduction to Textile Fibers

�What is a fiber?

� Large length to width ratio

� Small enough to be flexible

�Textile fibers

� Minimum length: 12.5 mm, desirable: >20

mm.

� Strong enough to be processed

1.1 Fiber Classification

Natural cellulosic fibers

Protein fibers

Mineral fibers

Natural fiber

Man-made fiber

Regenerated fibers

Synthetic fibers

Mineral fibers

1.1.1 Natural cellulosic fibers

�Seed fibers: cotton, kapok

�Bast fibers: jute, hemp, ramie, flax

�Leaf fibers: agave (sisal) , pineapple, abaca

�Nut fibers:coir (coconut)

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1.1.2 Protein fibers

�Animal secretion: wool, specialty hair, fur fibers

�Animal-hair fibers: silk, spider silk

1.1.3 Mineral fiber

� Asbestos

1.1.4 Regenerated fibers

�Regenerated cellulosic fibers

� Tencel

� Modal

� PLA

�Regenerated protein fibers

� Soybean fiber

� Milk fiber

1.1.5 Synthetic fibers

Name Year Company

Nylon 1938 Du pont

Acrylic fiber 1950 E.I. Du Pont

Polyolefin/polypropylene

1959Hercules Incorporated

Spandex 1961 E. I. Du Pont

1.1.6 Fineness of fiber

�Gravimetric (Direct system)

Tex: Mass in grams of 1000 m of fiber

Denier: Mass in grams of 9000 m of fiber

�Metric count Ne : The number of meters per gram. (Indirect system)

1.2 Fiber polymer

�Polymerization

Degree of polymerization

Average molecular weight of polymer =

Molecular weight of thr repeating unit in the polymer

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1.2.1 Types of polymer

�Homopolymer: Polymerized from the same or only one kind of monomer.

�Copolymer: Polymerized from two or more different monomers.

�Alternating copolymer: Two monomers polymerize in an alternating sequence

�Random copolymer: Monomers are polymerized in no particular order.

1.2.2 Inter-polymer forces of attraction

�Van der Waals’ forces

�Hydrogen bonds

�Alt linkages

�Cross-links

1.3 Fiber Theory and Fiber Properties

�Fibers, which are primary materials fromwhich most textile products are made, canbe defined as units of matter of hair-likedimension, with a length at least onehundred times greater than the width.Many substances found in nature can beclassified as fibers according to thisdefinition; however, only a limitednumber of these materials are useful in theproduction of yarns or fabrics.

1.3.1 Physical Properties

�Color: White or colorless fibers and

filaments are preferred.

�Luster: Luster may be desirable in some

products and undesirable in others.

�Shape: Shape of a fiber can be examined

both in cross section and in its longitud-

inal form.

1.3.2 Mechanical Properties

�Strength or Tenacity

�Tensile strength

�Flexibility

�Resiliency

�Abrasion Resistance

�Pilling

1.3.3 Chemical Properties

�Absorbency

�Effect of Heat

�Flammability

�Chemical Reactivity and Resistance

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2 Natural Cellulosic fibers

�Natural fibers obtained from plants,animals and minerals. Plant or vegetablefibers may come from the stem(flax, hemp,jute and ramie), from the leaves(sisal orabaca) or from the seed(cotton and kapok).

2.1 Introduction

�Relatively high density

�Good conductors of heat and electricity

�Tend to burn easily

�Good resistance to alkalis

�Most insects do not attack cellulosic fibers. (Except for silverfish)

2.2 Cotton

�Cotton is the most widely used naturalfiber. It is almost pure cellulose. It has anumber of qualities making it ideal formaking textiles and clothing.

�It is generally recognized that mostconsumers prefer cotton personal careitems to those containing synthetic fibers.

�Today, cotton is grown in more than 80countries worldwide.

2.2.1 Cotton Species

� Upland cotton

� Egyptian cotton

� Asian and African cottons

2.2.2 Cotton Fiber morphology

�Cross-section of

cotton fiber: kidney-shaped

�Longitudinal section

of cotton fiber: convolution

2.2.3 Structure of cotton fiber

�Cotton fiber is composed of cuticle, primary wall, secondary cell wall, lumen.

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2.2.4 Polymer system

�Cotton polymer is a linear, cellulose

polymer. (C6H10O5)n

�Degree of polymerization is about 5000

�Cotton is a crystalline fiber, about 65 to 70

percent crystalline

2.2.5 Chemical properties

�Cotton fibers are weakened and destroyed

by acids.

�Cotton fibers are resistant to alkalis and

are relatively unaffected by normal

laundering.

2.2.6 Physical properties

�Elastic-Plastic Nature

Relatively inelastic

�Hygroscopic Nature

Very absorbent

�Thermal Properties

Conduct heat energy

2.2.7 Growth and Production

�Field

�Preparation

�Planting

�Irrigation

�Fertilization

�Crop

�Harvesting

�Ginning

2.3 Bast fibers

�Bast fiber or skin fiber is fiber collectedfrom the Phloem (the "inner bark" or theskin) or bast surrounding the stem of acertain, mainly dicotyledonic plants.

�Bast fiber includes flax, ramie, jute andhemp

2.3.1 Fiber classification and morphology

�Flax fiber is classified as a natural,cellulose, bast, multi-cellular fiber.

It has a fiber density of 1.50 g/cm3.

�Cross-section: polygonal

Longitudinal section: nodes

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�Chemically

The flax polymer is a cellulose one.

�Physically

� The flax polymer differs from the cotton polymer. It has a DP of about 18000.

� The flax system is more crystalline than that of cotton.


�Tenacity: Flax is a very strong fiber.

�Elastic-plastic nature: Very inelastic nature is due to its very crystalline polymer system.

�Hygroscopic nature: The reasons given above to explain the hygroscopic nature of cotton apply also to flax.

�Thermal properties: The best heat resistance and conductively of commonly used fibers.

2.3.4 Chemical Properties

�Owing to the similar chemical constitution of cotton and flax, the explanations offered for the chemical properties of cotton may also be applied to flax.

� However, it needs to remembered that linen textile materials are not mercerized.

2.3.5 Processing of flax

�Pulling and rippling

�Retting

�Breaking and scutching

�Hackling

�Spinning

3 .1 Introduction of Natural Protein Fibers

�Natural protein fibers are obtained from animal sources. Most fibers in this group are the hair from animals; the rest are animal secretions.

�They have excellent moisture absorbency.

�Natural protein fibers have poor resistance to alkalies

�Fibers in this group have good resiliency and elastic recovery.

3.2 Wool

�The word wool was wull in old English, wullo in teutonic, and wlna in pre-teutonicdays.

� Wool is the fiber from the fleece ofdomesticated sheep. It is a natural,protein, multi-cellular, staple fiber. Thefiber density of wool is 1.31 g/cm3, whichtends to make wool a medium weight

fiber.

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3.2.1 Fiber morphology

�Longitudinal appearance of wool is over-lapping surface cell structure.

�Cross-section of wool is usually oval in shape.

3.2.2 Felting of wool

�Felting of wool is the irreversible shrink-age of the material.

ScalesDirectional

friction

Wet and heat

Felting

3.2.3 The polymer system

�The wool polymer is linear,keratin polymer, with somevery short side groups and itn o r m a l l y h a s a h e l i c a lconfiguration. The repeatingunit of the wool polymer isthe amino acid which has the

general formula.

3.2.4 Structure of wool

�Wool fiber is composed of surface scale, cortex and medulla layer.


�Effect of acids: Wool is more resistant to acids than to alkalis.

�Effect of alkalis: Wool dissolves readily in alkaline solutions.

�Effect of sunlight and weather: Exposure to sun light and weather tends to yellow white wool textile materials.

�Color-fastness: Wool is easy to dye.


�Tenacity: Wool is a weak fibre.

�Elastic-plastic nature: Wool has very good elastic recovery and excellent resilience.

�Hygroscopic nature: very absorbent

� Thermal properties: Poor heat conduc-tivity of wool and its low heat resistance.

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3.3 Specialty hairs

�Mohair

�Cashmere

�Camel Hair

�Alpaca

�Llama

�Vicuna

3.3.1 Mohair

�Mohair refers to the hair of Angora goat.

�Mohair fiber is approximately25-45µ in diameter. It is bothdurable and resilient. It isnotable for its high luster.Italso takes dye exceptionallywell.

3.3.2 Cashmere

�Cashmere is a type of fiber obtained from the Cashmere goat, or Pashmina.

�cashmere fiber is highly adaptable.

�Cashmere is similar to wool in most properties.

3.3.3 Camel Hair

�Camel-hair are both light inweight and warm; they have adistinctive golden brown colourwith a pleasing lustre. Thefabrics are soft, comfortable, andgood wearing, and they drape

attractively.

3.3.4 Alpaca

�Alpaca offers excellent warmth and insulation. The fibres are strong and glossy and make fabrics similar in appearance to mohair.

3.3.6 Llama

�Llama fibre is soft, strong,and relatively uniform inlength and diameter butsomewhat weaker thanalpaca or camel hair.

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3.3.7 Vicuna

Vicuna is one of thesoftest fibres in the world.It is fine and lustrous, hasa lovely cinnamon brownor light tan colour, and isstrong enough to makevery desirable fabrics. It isalso very light in weightand very warm.

3.4 Silk

�Silk is a natural, protein filament. Its fila-ment density is 1.34 g/cm3, which makes ita medium weight fiber. However, verylight weight silk textile materials may bemanufactured from silk fi laments.

3.4.1 Fiber morphology

�The rounded triangular cross-section of the silk filament can be used to identify silk. This is due to the slit-like opening of the silk secreting glands, one each being located on either side within the mouth of the silk moth larvae.


�Silk polymer is a linear, fibroin one. It differs from the wool polymers as follows:

� Silk is composed of sixteen different ami-no acids compared with the twenty amino acids of the wool polymer .

� Silk polymers are not composed of any amino acids containing sulphur.

� Silk polymer occurs only in the beta-configuration.


�Effect of acids: Silk is regarded more readily by acids than is wool.

�Effect of alkalis: Alkaline solutions cause the silk filament to swell.

�Effect of bleaches: What has been stated for wool also applies to silk.

�Effect of sunlight and weather: The resist-ance of silk to the environment is not as good as that of wool.


�Tenacity: The silk filament is strong.

�Elastic-plastic nature: Silk is considered to be more plastic than elastic.

�Thermal properties: Silk is more sensitive to heat than wool.

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3.4.5 Silk Production

�Laying of the eggs by the silk moth.

�Hatching of the eggs into caterpillars.

�Spinning of a cocoon by the caterpillar.

�Emerging of the silk moth from the cocoon.

4 Regenerated fibers

�Fiber produced by dissolving a naturalmaterial (such as cellulose), thenregenerating it by extrusion andprecipitation, such as viscose, acetate andtriacetate, etc.

4.1 Viscose fibres

�Viscose is a viscous organic liquid used tomake rayon and cellophane. Cellulosefrom wood or cotton fibers is treated withsodium hydroxide, then mixed withcarbon disulfide to form cellulosexanthate. The resulting viscose is extrudedinto an acid bath a spinneret to makerayon. The acid converts the viscose backinto cellulose.

4.1.1 Historical review

�Major breakthrough in production of man-made fibers occurred in 1862 when Ozanam

invented spinnerette.

�Viscose process was discovered in 1891 by English scientists C. F. Cross and E. J. Bevan.

�Process for manufacturing viscose was patented by British scientists, Charles Frederick Cross, Edward John Bevan and Clayton Beadle, in 1891.

4.1.2 Manufacture

Pulp

Alkali cellulose

Xanthate cellulose

Viscose Viscose filaments

4.1.3 Modified viscose fibres

�Modified viscose fibers differ from the regular rayon fibers in both strength and elongation properties.

� High-wet-modulus rayon: They have better dimensional stability, better strength, and better elongation than regular rayon.

� Cuprammonium rayon

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�It is a linear, cellulose polymer, similar to that of cotton. However, the viscose polymer does not have the spiral configuration of the cotton polymer.

�The viscose polymer system is very amorphous, being about 35 - 40 percent crystalline and about 65 – 60 percent amorphous.


�Tenacity: Viscose is weaker than cotton.

�Elastic-plastic nature: Viscose is limp because its amorphous system.

�Hygroscopic nature: The most absorbent fiber in common use.

�Thermal properties: Viscose has somewhat similar thermal properties to cotton.


�Chemical properties of cotton and viscose are similar.

�Shorter polymers and very amorphous nature of viscose are responsible for the much greater sensitivity to acids, alkalis, bleaches, sunlight and weather, when compared with cotton.

�Viscose can color more brightly.

4.2 Acetate and Triacetate

�Fibers in which forming substance is cellulose

acetate where not less than 92% of hydroxyl

groups are acetylated: replacing -OH groups

with -COCH3.

�Acetate: 2 of 3 -OH groups in each 6-member

ring are acetylated.

�Triacetate: Nearly all -OH groups are replaced

2.91~2.96.

�Major use: lining fabrics for suits, coats.

4.2.1 Structures

�Surface: straited

�Cross-section: lobed

�Skin-core structure

�DP: 250-300

�Much less H-bond than in rayon

4.2.2 Properties

�Acetate: hydrophilic, thermoplastic

�Triacetate: hydrophobic, higher melting and softening temperature, high crystallinity

�Wrinkle easily in hot water: dry cleaning only

�Swells in water, mechanical properties change in water

�Resist to weak alkali and acids

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4.2.2 Properties

�Soluble in acetone

�Degrade in UV light

�Burns, melts, forms black beads with vinegar like odder

4.2.3 Production

�Similar to cellulose rayon for the first a few steps

�Cellulose mixed with acetic acid and acetic anhydride, a sulfuric acid catalyst is added

�Degradation of the polymer making DP low

�Triacetate is made first

�When water added, some acetyl groups are removed

5 Synthetic Fibers

�Synthetic fibers are generally made from coal, petroleum or natural gas.

�In general, synthetic (man-made) fibers are created by forcing, usually through extrusion, fiber forming materials through spinnerets into the air,

forming a thread.

5.0 Types of spinning methods

�Melt Spinning: Using heat to melt polymer to a viscosity suitable for extrusion.

�Dry Solvent Spinning: This type of spinning is used for easily dissolved polymers. polymer solution is extruded through a spinnerette into gas or vapor.

�Wet Solvent Spinning: Polymer solution is extruded into a precipitation bath.

5.1 Nylon

�Man-made fibers in which fiber forming

substance is any long-chain synthetic polyamide

in which less than 85% of the amide linkages are

attached to 2 aromatic rings.

�Invented in 1938 in Du Pont

�Market: carpet fiber 80%, tire cord and ropes

14%, apparel 11% .

5.1.1 Types

�Types:

� Mostly: Nylon 6 and Nylon 6,6

� Small amount: nylon 3, nylon 4, nylon 5, nylon 7, nylon 8, nylon 12, nylon 4,6, nylon 6,10

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5.1.2 Structure

�Polymerization: condensation, eliminating a H2O

molecule

�Functional group: amide group

�Molecular configuration: linear zigzag molecules

forming well closely packed pleated sheets

�IMF: H-bond

�Crystallinity: High 65~86%

�Cross-sectional and longitudinal shape: can be

any type

5.1.3 Properties

�Tenacity: high due to high orientation and

crystallinity

�Elongation: high due to zigzag structure

�Recovery: high due to zigzag

�Energy of rupture: high due to high tenacity and

high elongation.

�Abrasion resistance: high

�Water absorption: highest among all synthetic

fibers

5.1.3 Properties

�Smooth round cross-section and uniformity

permit close packing

�Swells when absorbing moisture

�Static: not enough water absorption

�Low specific gravity: 1.14g/cc

�Resilience: high: wrinkle free

�Can be laundered but not easy to clean

�Vulnerable to degradation in acids

�Low resistance to sunlight

5.2 Polyester

�Manufactured fibers in which fiberforming substance is any long-chainpolymer composed of at least 85% byweight of a subst i t uted ar omat i ccarboxylic acid, including but notrestricted to substituted terephthalic units.

�Generic group members:

PET (polyethylene terephthalate) ~95%

5.2.2 Types

�PCDT: poly(1,4-cyclohexylene dimethylene), Eastman Kodak

�PEB: poly(ehtylene oxybenzoate), produced in Japan, 70’s and 80’s

5.2.3 Structure

�Smooth, even diameter

� Diameter generally 12-25 mm

� White or off-white colors

�Intermolecular forces:

� Dipole-dipole between benzene rings

�Linear polymer: DP 115-140

� Crystallinity: 35%

� Orientation: very oriented

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5.2.4 Properties

�High tenacity due to high orientation

�High failure elongation

�Elastic recovery

� High with low stress: 97% at 2% strain.

� Low with high stress because dipole-dipole bonding is not strong enough to hold, leading to intermolecular slippage

�Low compressional resilience: not good for

carpet fiber

5.2.4 Properties

�Very low moisture regain

�Low level of wicking due to hydrophobic surface

�High electrical resistivity: static charge likely at

low humidity

�Medium specific gravity

�Pilling

�High dimensional stability

�High Tm 450~500 degree F

5.2.4 Properties

�Resistant to acids, potentially degrades in concentrated alkalies

�No UV degradation

�Flammable with black smoke

�Melt drip

�Best thermal resistant among all general use synthetics

5.2.4 Properties

PCDT

�Lower tenacity and elongation

�Superior elastic recovery

�Better compressional resilience: good for end uses such as carpets, rugs, knitwear and fiberfill

�Less pilling due to lower tenacity

5.2.5 Production

�Polymerization

�Form chips

�melt spinning

�drawing

�heat setting to increase crystallinity and orientation, reduce elongation and shrinkage

5.2.6 Modification

�High tenacity for tire cord (higher DP and crystallinity)

�Wicking

�Sheath-core: polyester core, low melt polymer sheath

�Du Pont Coolmax: 20% more surface area and maybe hydrophilic treated for wicking

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5.3 Acrylic

�Invented in conceptually in 1893

�Produced initially in 1944 and full scale in 1950

�End uses:

� 75% in apparel

� 18% household

� 7% Industrial and consumer textiles

5.3.1 Polymerization

�Addition or chain growth

�Homopolymer: polyarylonitrile strong but compact and highly oriented

� virtually impossible to dye

�Copolymers: other types of monomers are included for a dyeable fiber and easier to process:

� e.g. acrylic acid and vinylpyrrolidone

� most acrylic fibers are copolymers

5.3.2 Structure

�Microscopic

� Cross-section:

•dog-bone shaped

•kidney-bean shaped

•round

� Longitudinal

•uniform diameter

•rod-like shape

5.3.2 Structure

�Molecular

� DP = 1000

� IMF: dipole-dipole interaction between nitrile groups -C≡N

� Crystallinity is not well-defined

5.3.3 Properties

�Mechanical properties similar to wool but stronger

�Medium tenacity, better than wool

�Failure strain: medium

�High elastic recovery at low strain level 90 - 95% at 1 % strain

�Moderate abrasion resistance

5.3.3Properties

�Bulky: tend to crimp

�Wick but do not absorb water

�Low specific density: 1.12 - 1.19 g/cm3

�Static electricity built up

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5.4 Elastomeric

�Elastomeric is polyurethane-based fibre.

�Elastomeric consists of polymers which are at least 85 % segmented polyurethanes.

�Polyurethane is synthesised from urea: H2NCONH2.

�Elastomeric has a fibre density of 1 g/cm³, the lightest apparel fibre in common use.

5.4.1 Fibre morphology

�Longitudinal appearance has distinct striations and specks.

�Cross-section of fiber has the dump-bell or dog-bone shape

5.4.2 The polymer system

�Two types of elastomeric polymers are synthesized. Each is extruded into filaments with excellent elastic properties but differing in their resistance to alkalis.

� The polyether type (for example Lycra) resistant to alkalis

� The polymer type (for example, Vyrene)


�Tenacity: Elastomeric are weak.

�Elastic-plastic nature: Excellent recovery

�Hygroscopic nature: Elastomeric are hydrophobic

�Thermal properties: Elastomeric are thermo-plastic.


�Effect of acids: Elastomeric textile material in general are resistant to acids.

�Effect of alkalis: The elastomeric is sensitive to alkalis.

�Colour-fastness: Elastomeric textile material tend to be difficult to dye owing to the hydrophobic and very crystalline nature of their polymer system.

6.1 Introduction of absorption

�Adsorption in a non-swelling medium, forexample, the adsorption of gases oncharcoal, is a comparatively simpleprocess, but the absorption of water byfibers is an example of a process thatcomes midway between these two andpartakes of some features of each.

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6.2 Equilibrium

�When a textile material is placed in a given atmosphere, it takes up or loses water at a gradually decreasing rate until it reaches equilibrium, when no further change takes place. This is a dynamic equilibrium.

6.3 Regain and relative humidity

�Relative humidity(RH)=

p(H2O)－Partial pressure of water vaporp*(H2O)—Saturation vapor pressure

�Regain

G －Mass of undried specimen

G0－Mass of dried specimen

2

*2

(H O)100%

(H O)

p

p×

0

0

100%G G

WG

−= ×

6.4 Theories of moisture sorption

�Sorption refers to the action of eitherabsorption or adsorption. As such it is theeffect of gases or liquids beingincorporated into a material of a differentstate and adhering to the surface ofanother molecule.

6.4.1 The effect of hydrophilic groups

�As absorption, we take account of interac-tion between water molecules and molec-ules of the fiber. All the natural animal and vegetable fibers have groups in their molecules that attract water, such as –NH2, —CONH, —OH, —COOH.

6.4.2 Directly and indirectly attached water

�The first water molecules are absorbeddirectly onto hydrophilic groups, but, forthe others: They may be attracted to otherhydrophilic groups, or they may formfurther layers on top of water molecules.

H2O H2O H2O

H2O H2O H2O

Fiber

Direct

Indirect

H2O H2O

6.4.3 Absorption in crystalline regions

�In crystalline region, the fiber moleculesare closely packed together in a regularpattern. Thus it will not be easy for watermolecules to penetrate into a crystallineregion, and, for absorption to take place,the active groups would have to be freedb y t h e b r e a k i n g o f c r o s s - l i n k s .

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7 Other properties of textile fibers

�Thermal, optical and electric are important properties of textile fibers, which decide the performance of the processing and usage of textile fibers.

7.1 Thermal properties

�Thermal conductivity: Thermal conduc-tivity is a property of materials thatexpress the heat flux(W/m2) that will flowthr ough the mater ia l i f a cer ta intemperature gradient DT(K/m) exists over

the material.

Fiber material Thermal conductivity[mW/(m.k]

Cotton 71

Wool 54

Silk 50

7.2 Optical properties

�When light falls on a fiber, it may be partly transmitted, absorbed or reflected.

�Refractive index niso of an isotropic fiber is given by the mean of the refractive indices of an oriented fiber in 3 directions:

� Polarized parallel to fiber axis

� Polarized perpendicular to fiber axis

1/ 3( 2 )ison n n⊥

= +�

n�

n⊥

7.3 Electric properties

�The electronic properties of fibers are of less obvious technical importance than the mechanical properties, the electronic properties are interrelated.

�Resistance can be defined:

� l—Distance between the ends of specimen, cm

� N —Number of ends of yarn or fiber

� T —Linear density of yarn or fiber, tex

510s

lR R

NT= ×

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