Textile physics 1

Textile physics-1
MD LUTFUR RAHMAN

Textile Physics
Reference Books:
1. Physical properties of textile fibres by W.E. Morton and J.W.S. Hearle.
2. Textile Science by E.P.G. Gohl and L.D. Vilensky.
3. Structural Mechanics of Fibers Yarns and Fabrics by Hearle

The Physical Structure of Fiber

Orientation: The alignment of the structural elements of a material. In polymer,
orientation at different structural levels may be observed. Ex: polymer chains, segment
of chains, crystallites etc.
Amorphous polymer orientation : Polymers are oriented or aligned at random fashion
in amorphous region, i.e. shows no particular order of arrangement.
Crystalline polymer orientation : In crystalline regions the polymers are oriented or
aligned longitudinally into more or less parallel order.

Properties of more amorphous fibers :
-Formation of less effective inter-polymer
forces of attraction. (weak)
-Permits easier entry of water and dye
molecules as well as molecules, ions
and/or radicals of degrading agents. So
more absorbent and more easily dyed .
-Allows the polymers to be more readily
displaced when the fiber is subjected to
stresses and strains during wearing.
-less durable
-more easily degraded by chemicals
-more pliable, softer handling
Properties of more crystalline fibers :
-Formation of more effective inter-polymer forces of
attraction.
-Restricts the entry of water and dye molecules as
well as molecules, ions and/or radicals of degrading
agents. So less absorbent and less easily dyed
-Does not allow the polymers to be displaced when
the fiber is subject to stresses and strains during
wearing .
-more durable
-less easily degraded by chemicals
-less pliable, stiffer handling

Requirements of fiber formation or fiber forming polymer
1)Hydrophilic: A fiber is comfortable to wear if its polymer system is made up of hydrophilic
polymers, and the system allows the entry of water molecules. Hydrophobic polymer fibers
whose polymers are non-polar are yet used as fibers for textile applications. In order to make the
textile materials of these fibers more water attracting, absorbent and comfortable, hydrophobic-
polymer fibers need to be blended with the hydrophilic polymer fibers to get desired properties.
2)Chemical resistant: Close packing of the polymers prevents ready entry of chemicals. More the
polymer system is crystalline in nature more will be the resistance of the fibers against
degradation by chemicals. Thus, many synthetic fibers are used in industry to make filter fabrics
and protective clothing. Fiber polymers should be chemically resistant for a reasonable length of
time against the common degrading agents such as sunlight and weather, common types of
soiling, body exudations, laundry liquors and dry cleaning solvents. The most required property
of chemically resistant polymers should be such that it should not be toxic or hazardous to wear
against human skin. Polymer of fibers should be chemically resistant, but they should not be
inert. Chemical inertness of fiber polymers results in detrimental effect on other fiber-forming
requirements. The polymers of chloro-fibers, fluorocarbon, polyethylene and polypropylene may
be regarded as chemically inert from a practical point of view.

3)Linear:
Fiber polymer should be linear i.e. the polymers should not be branched.
Highly linear polymers will form more crystalline regions, which results in a large number of
inter-polymer forces of attraction within the polymer system.
4)Capable of being oriented:
Fiber polymers should be capable of being oriented. The polymers are aligned into more or less
parallel order in the direction of the longitudinal axis of the fiber or filament. The orientation of
polymers in the polymer system of any fiber consists of two forms. The two forms of polymer
orientation are:
• amorphous regions (random)
• crystalline regions (highly ordered, highly oriented)

5)Long:
Fiber polymers should be long. The length of polymers is directly related to the strength of fiber by holding
the crystalline regions together. To produce a fiber with adequate strength, a polymer length of 100
nanometers is required. Polymers of such length can be oriented easily. The orientation of polymers give
rise to sufficiently effective inter-polymer forces of attraction to form a cohesive polymer system and,
hence, a useful fiber. The longer the polymers the more cohesive will be the polymer system and the
stronger will be the fiber. For this to occur the polymers have to be aligned or well oriented so that the
maximum formation of inter-polymer forces can take place.

6)Able to form high melting point polymer systems:
The fibers must have high melting point to withstand the most extreme
heat conditions. Melting point of fiber needs to be above 225° C if it is to
be useful for textile manufacture and apparel use. The longer the polymers
and the better their orientation, the more inter-polymer forces of
attraction will be formed, giving a more cohesive polymer system with a
higher melting point. More heat or kinetic energy will be required to break
the inter-polymer forces of attraction and free the polymers from each
other.

Crystallinity and Amorphous
The structure of a polymer is defined in terms of crystallinity. It is the degree of order or regularity
in how the molecules are packed together. A well-ordered polymer is considered crystalline.
Amorphous is the opposite to crystallinity.

Methods of fiber structure investigation:
• X-ray diffraction method
• Absorption of Infra-red radiation
• Electron microscopic method
• Optical microscopic method
• Thermal analysis
• Nuclear magnetic resonance methods
• Density
• Physical properties
• The chemistry of fiber material

X-ray diffraction method:
X- ray diffraction is a method of determining the arrangement of atoms within a
crystal. When a beam of x-rays strikes a crystal, it scatters into many different
directions. From the angles and intensities of these scattered beams a
crystallographer can produce a three dimensional picture of the density of electrons
within the crystal. From this electron density, the mean positions of atoms in the
crystal can be determined. Crystals are regular arrays of atoms and x-rays can be
considered as waves of electromagnetic radiation. Atoms scatter x-ray waves,
primarily through the atom’s electrons. When a x-ray beam strikes an electron, it
produces secondary spherical waves. This phenomenon is known as elastic
scattering and the electron is known as scattered. A regular array of scatters
produces a regular array of special waves. Although these waves cancel one another
out in mist direction through destructive interference, they add constructively in a
few specific directions determined by Bragg’s law:
n λ = 2d sin θ.
Where n is an integer, λ the wavelength of the X-rays and d the distance between the
atomic layers. These specific directions appear as spots on the diffraction pattern.

Derivation of Bragg’s law:
When a beam of X-rays strikes on a crystal, it is strongly reflected whenever it strikes layer of
atoms at an angle of ϴ° as like fig. such that n λ = 2d sin θ.

Advantages:
• Gives information about crystallinity of a fiber.
• Gives information orientation of a fiber.
• Gives information shape of scattering particles.
• Gives information differences of spacing of
scattering particles.
• More other internal structure information.
Disadvantages:
• Not possible to identify the chemical formula.
• Not influenced by the molecules of amorphous region.

Absorption of IR radiation method
Infra-red (IR) spectroscopy is one of the most common and widely
used spectroscopic techniques. When electromagnetic waves interact
with matter, they are scattered and absorbed. In Infrared
spectroscopy, radiation with wavelengths between 1 -15 μm
is absorbed at certain characteristic frequencies, which yield
structural information.
By using an infrared spectrometer, the variation in absorption can be
found and plotted against wavelength or the wavenumber.
Wavenumber = 1 / wavelength in centimeters
The wavenumber at which absorption takes place depends on
❶ The nature of the two atoms and
❷ The bond between them.
❸ The other groups in the neighborhood

The peaks occur where the frequency of the electromagnetic waves corresponds with the natural frequency
of vibration between
two atoms in the material.
The peaks are due to:
1540 cm-1 uncertain, involves (—NH) and neighboring bonds
1640 cm-1 stretching of C=O
2860 and 2930 cm-1 stretching of =CH2
3305 cm-1 stretching of N—H

The peaks occur where the frequency of the electromagnetic waves corresponds with
the natural frequency of vibration between two atoms in the material. Thus there will be
absorption frequencies characteristic of such groupings as
C- H, C=O, C-O- ,- O- H, N- H, C- C, C= C. , and so on.
To a smaller extent, the absorption frequency is influenced by the other groups in the
neighborhood: for example, the absorption frequency for a carbon–hydrogen bond in a
terminal group, —CH3, is different from that for the same bond in a chain, —CH2—.
The first use of infrared absorption is therefore as an aid to the identification of the
presence of certain groups in the molecule, leading to the determination of its chemical
formula. The method can also be used in routine analysis to identify and estimate
quantitatively the presence of given substances, even in small quantities in a mixture, by
observation of their characteristic spectrum. For instance, it can be used to determine
the amount of water in fibers.

Advantage of IR radiation over X-ray diffraction method
IR radiation X-ray diffraction
• The degree of orientation of the molecules in a
fiber can be known.
• The degree of orientation of the molecules in a fiber
can’t be known.
• IR may also be used to find the direction in which
a particular group points in a molecule of
unknown form.
• X-ray diffraction method can not be used to
investigate the direction of a group points in a
molecule.
• An advantage of the infrared absorption method is
that it is influenced by all the molecules in the
fiber, in both the crystalline and non-crystalline
regions.
• The X-ray diffraction method gives detailed
information only about the crystalline regions of the
fiber.
• The method can also be used in routine analysis to
identify and estimate quantitatively the presence
of given substances, even in small quantities in a
mixture, by observation of their characteristic
spectrum. For instance, it can be used to
determine the amount of water in fibres.
• This method can’t be used to identify the presence of
a given substances.
• Can identify the chemical formula. • Can’t do so.

Fiber type Degree of
crystallinity
amorphous < 10%
Semi-crystalline 20-40%
crystalline 40-60%
More-crystalline >60%

Tensile properties
The properties that describes fiber behavior under forces and deformation applied along the
fiber axis is called tensile properties.
Modes of Tensile testing
1)CRL(loading)
2) CRE(extension)

Work of rupture:
It is the energy or work required to break the specimen. Or total energy consumed by the
specimen up to complete failure.

Flexural Properties
The behavior shown by the materials during bending is known as flexural properties.

Flexural Properties Influences:
1. Behavior of yarn
2. The drape and handle properties of fabrics
3. The recovery from bending
4. The wear of fabric
5. The arrangement of fiber in the yarns.
Bending Recovery: Recovery from a given curvature is called
Bending recovery.
Bending Modulus: The ratio of bending stress and bending
strain is called Bending Modulus.

Flexural rigidity for small curvature:
The problem is similar to that of the bending
of beams.
•Suppose we have a specimen of
length 𝑙𝑙, bent through an angle θ to a radius
of curvature r.
•Its outer layers will be extended and its inner
layers compressed, but a plane in the center,
known as the neutral plane, will be
unchanged in length.
As a result of the extension and compression,
stresses will be set up that give an internal
couple to balance the applied couple
•Consider an element of area of cross-section
δA, at a perpendicular distance 𝑥. from the
neutral plane:

Friction: It is the resistance that one surface or object encounters
when moving over another.
Frictional properties: During processing friction is developed
between textile materials. Due to that friction, the properties
shown by the textile materials is called frictional properties of
textile materials.
Types of friction:
1. Static Friction: The friction between two or more solid objects
that are not moving relative to each other. The coefficient of
static friction, typically denoted by as µs, is usually higher than
the coefficient of kinetic friction.
2. Kinetic Friction: Kinetic friction occurs when two objects are
moving relative to each other and rub together. The coefficient
of kinetic friction, typically denoted by as µk, is usually less than
the coefficient of static friction.

Merits: -
1) Friction is the force that holds together the fibers in a spun
yarn and the interlacing threads in a fabric. Friction holds the
fibers in a sliver and hence the sliver does not break due to its’
own weight.
2) If the friction is too low, the yarn strength will fall, and the
dimensional stability of cloth will be reduced. Here high
friction is an advantage, enabling a greater proportion of the
strength of the individual fibers to be utilized.
3) Uniform tension can be maintained during winding & warping
because of friction.
4) Friction helps in drafting and drawing.
5) Friction helps to make yarn by twisting during spinning.
6) Friction increases luster and smoothness of the yarn and the
fabric.
7) Friction makes more clean material.
8) There are some aspects influenced by the frictional
characteristics of the fibers: the handle and wear resistance of
fabrics; the behavior of fibers during drafting; and, especially
in wool, the process of felting.

Demerits –
1)High friction in yarn passing increases the breakage and
over straining may cause the permanent damage. High
static friction causes high breakage of yarn during weaving.
2) If the frictional force is high, the handle properties of
fabric will be low.
3) In stitching, high friction of needle with fabric causes it
red hot. Threads can not slide over one another. These lead
to high thread breakage at the seam line.
4) Friction causes nep formation, Friction increases yarn
hairiness.
5)Friction worn out parts of machine.
6) Friction generates temperature and therefore static
electricity is developed which attracts dust, dirt etc. and the
materials become dirty.

Definition: When a fiber absorbs water, they change in
dimension (length, width) and swelling is occurred
transversely (widthwise) and axially (lengthwise). The
swelling may be expressed in terms of the fractional
increase in diameter, area, length or volume.
Types of swelling: The swelling may be expressed in
terms of the increase in diameter, area, length or
volume.

1. Traverse diameter swelling:
Fractional increase in
diameter of fiber is traverse
diameter swelling. It is
expressed by, 𝑆 𝐷 =
∆𝐷
𝐷
2. Traverse area swelling:
Fractional increase in area of
fiber is traverse area
swelling. It is expressed by,
𝑆𝐴 =
∆𝐴
𝐴
3. Axial swelling: Fractional
increase in length of fiber is
axial swelling. It is expressed
by, 𝑆𝑙 =
∆𝑙
𝑙
4. Volume swelling: Fractional
increase in volume of fiber is
volume swelling. It is
expressed by, 𝑆 𝑉 =
∆𝑉
𝑉

Relation among 𝑺 𝑽, 𝑺𝒍 and 𝑺 𝑨:
For a fiber that is uniform along its length,
We have original volume of fiber,
𝑉 = 𝐴𝑙
Where, 𝑙 is original length and A is the original area of the
fiber.
After swelling the swollen volume of fiber,
𝑉 + ∆𝑉 = 𝐴 + ∆𝐴 . (𝑙 + ∆𝑙)
Or, ∆𝑉 = 𝐴∆𝑙 + 𝑙∆𝐴 + ∆𝐴∆𝑙
Now we get from the definition of volume swelling,
𝑆 𝑉 =
∆𝑉
𝑉
=
𝐴∆𝑙 + 𝑙∆𝐴 + ∆𝐴∆𝑙
𝐴𝑙
=
∆𝑙
𝑙
+
∆𝐴
𝐴
+
∆𝐴
𝐴
∗
∆𝑙
𝑙
= 𝑆𝑙 + 𝑆𝐴 + 𝑆𝑙 𝑆𝐴

Relation between 𝑺 𝑨 and 𝑺 𝑫:
We know that,
Transverse area swelling, SA = ∆A / A
Transverse dia swelling, SD = ∆D / D
For a circular fiber, area A = (π/4)D2
For a swollen fiber, we get, A+∆A = (π/4)(D+∆D)2
= (π/4)(D2 + 2D. ∆D + ∆D2)
Now,
SA = ∆A / A
= (A+∆A-A) / A
= {(π/4) (D2 + 2D. ∆D + ∆D2) - (π/4) D2}/ (π/4) D2
= (π/4) (D2 + 2D. ∆D + ∆D2 - D2) / (π/4) D2
= (2D. ∆D + ∆D2) / D2
= (2D. ∆D / D2) + (∆D2/ D2)
= 2(∆D / D) + (∆D2/ D2)
= 2 SD + SD
2

Measurement of volume swelling:
Consider a specimen of mass 1gm at dry state. We have,
𝑉 =
1
𝜌0
[𝜌0=density at dry state]
After swelling,
𝑉 + ∆𝑉 =
1+𝑚
𝜌 𝑠
[m=mass of absorbed water, 𝜌𝑠=swollen density]
=
1+
𝑟
100
𝜌 𝑠
[r=% regain]
Now, 𝑠 𝑣 =
∆𝑉
𝑉
=
𝑉+∆𝑉−𝑉
𝑉
=
𝑉+∆𝑉
𝑉
- 1
=
1+ ൗ𝑟
100
𝜌 𝑠
1
𝜌0
- 1
=
100+𝑟
100
∗
1
𝜌 𝑠
1
𝜌0
- 1 =
100+𝑟
100.𝜌 𝑠
х𝜌0 - 1
=
𝜌0
𝜌 𝑠
х
100+𝑟
100
-1 =
𝜌0
𝜌 𝑠
[1 +
𝑟
100
] – 1

Measurement of Transverse swelling:
Because fibres have such a small diameter,
measurements of changes in transverse
dimensions are not easy to make. The accuracy of
a microscopical method is limited by the
resolution of the microscope, which is of the order
of magnitude of the wavelength of light used, say,
0.5µm. If a fibre of 20µm diameter is examined, it
will be possible to distinguish detail down to one-
fortieth of the fibre diameter, but, if the diameter
swelling is 10%, it will be possible to measure this
to an accuracy of only 0.5 in 2. This means that
there may be an error of 25%. However,
microscopy methods are used, either for
examining the fibre profile and measuring the
apparent diameter or for examining sections and
measuring the diameter, or the area of cross-
section, with a planimeter. Figure shows the
outlines of a viscose rayon fibre, swollen and
unswollen. This makes clear the fact that diameter
swelling is not a sound way of expressing the
transverse swelling of a fibre with an irregular
cross-section, since it will vary according to the
position in which the ‘diameter’ is drawn. For
irregular fibres, area swelling must be used.

Importance of swelling:
1. Swelling improves the absorption of dyes and chemicals in
fiber, thus fastness of dyed material is improved
2. Due to swelling the pores of closely interlaced woven fabric
will be completely blocked and thus it may act as water proof
fabric.
3. Swelling changes the dimensional stability of fabric.
4. Swelling changes the tensile and electric properties of fiber
i.e. Static electricity is reduced.
5. It has chemical consequences in the dimensional stability of
the fabric, the predominant transverse swelling results in
shrinkage.

The effect of hydrophilic groups
Cellulose Fiber: The cellulose molecule contains three hydroxyl groups for each
glucose residue, and hydrogen bonds can be formed between water molecules and the
hydroxyl groups.
The molecular weight of water is 18, and that of the glucose residue is 162, so that if one
water molecule were attached to each hydroxyl group the regain would be 33.3%.
Although glucose and cellulose are chemically very similar, they behave differently when
placed in water. Glucose dissolves, but cellulose swells to only a limited extent. The limited
swelling is due to the penetration of water into the non-crystalline regions or between fibrils
and its failure to penetrate into crystalline regions. The noncrystalline regions tend to
dissolve as glucose does, the cellulose molecules moving apart and so giving room for the
water to enter, but the cellulose molecules cannot break away completely, since they are
held firmly in the crystalline regions.
In crystalline regions, the fibre molecules are closely packed together in a regular pattern.
The active groups form crosslinks between the molecules, by hydrogen bonding in cellulose.
Thus it will not be easy for water molecules to penetrate into a crystalline region, and, for
absorption to take place, the active groups would have to be freed by the breaking of
crosslinks.

In regenerated cellulose, there is a slightly less compact crystal structure and
there is a change of crystal structure on absorption. This is due to the formation of
a hydrate, which probably contains one water molecule to every three glucose
residues. This would correspond to a regain of about 3.7% in the crystalline region
(about 1% regain in the whole fibre). When the regenerated cellulose is wet, there
is a further modification of the crystal structure owing to the formation of a
hydrate with about three water molecules to every two glucose residues.
In cellulose acetate, all or most of the hydroxyl groups have been replaced by the
comparatively inert acetyl (CH3·COO—) groups. These groups do not attract water
strongly, so the absorption of water by acetate is low. In particular, there is no
rapid rise at low humidities owing to the initial absorption on strongly attractive
groups.
Protein Fibers: The protein fibres contain amide groups (—NH—) in the main
chain, to which water can be hydrogen bonded, and other water-attracting groups
such as —OH, —NH₃⁺ , —COO–, —CO·NH₂, in the side chains. Wool contains many
active groups in the side chains, but silk contains only a few.

Synthetic fibers: All the synthetic fibres so far produced contain few if any
water-attractive groups, and this accounts for their low moisture absorption. The
polyamide fibres, nylon 6.6 and 6 and aramids, contain one amide (—NH—) group
for every six carbon atoms in the chain, which would give a regain of 16% of each
amide group held one water molecule. The polyester fibres, polyethylene
terephthalate, are composed only of benzene rings, —CH2— groups, and —
CO·O— groups, none of which attracts water strongly. Polyethylene is simply a -
CH2-chain, polypropylene has additional –CH3 side groups, and the vinyl fibres are
similar except for the substitution of —Cl, —O·CO·CH3, or other comparatively
inert groups for some of the hydrogen atoms, and consequently these fibres
absorb little water. Acrylic fibres, containing —CN groups and other groups from
the minor components, absorb slightly more than the other vinyl fibres, and
polyvinyl alcohol, containing some —OH groups, absorbs still more.
Inorganic fibres, including carbon, do not attract water absorption.

Specific Heat: The specific heat is the amount of heat per unit
mass required to raise the temperature by one degree Celsius.

HEAT OF WETTING
The absorption of water, which as a liquid has a specific heat of 4.2J/(gK), would be expected to increase the
specific heat of fibers. For changes in temperature at constant regain, a simple mixture law would give the
relation:
mixture specific heat =
Where, 𝑐0= specific heat when dry and r = fractional regain.
Even at constant regain, however, equation will not predict actual specific heats, for two reasons. Firstly, the
absorbed water may not be behaving like liquid water: it may be more like ice with a specific heat of about
2J/(gK). Secondly, the absorption of water, which loosens up the fiber structure, may change the effective
specific heat of the polymer molecules. A correction term, ∆C, will therefore be added to C′ to give the actual
specific heat, C. The term ∆C can be related to changes in the heat of wetting with temperature.
The values of the ∆C term ranged from about 0.1J/(gK) at medium regains and room temperature to
0.4J/(gK)at high regains and 60°C, so that the correction is small but appreciable

Thermal conductivity(often denoted k, λ, or κ):
Thermal conductivity is the property of a material to conduct heat.
Thermal conductivity is the rate of heat transfer along a body by conduction.
Heat transfer occurs at a lower rate across materials of low thermal conductivity than across materials of
high thermal conductivity. Correspondingly, materials of high thermal conductivity are widely used in heat
sink applications and materials of low thermal conductivity are used as thermal insulation.
The protein fibers have a lower conductivity than the cellulosic fibers.

Structural changes due to heat setting:
• Synthetic fibers, mainly polyester and nylon, consist of long chain molecules and are held
together by inter-chain bonds.
• Just after spinning the chains are irregularly distributed at random in fiber but after
stretching several times they become parallel to the fiber axis.
• As a result of stretching the fiber molecules come closer to each other and held together
by intermolecular forces, hydrogen bonding or by a combination of Van der Waals' forces
and H-bonds. Thus intermolecular forces and density increases.
• The H-bonds are formed at random and there are strains between the chains. The single
chains are not usually completely stretched out; and are still kinked having a zigzag
configuration.
• After cold drawing process, when they are heated above the point at which molecular
motion sets in, they will progressively shrink until they reach the point of thermodynamic
equilibrium represented by figure A.

• In a straightened condition of fiber, if energy in the form of heat is supplied, the
chain molecules starts vibrating, some of these interchain bonds break and some
parts of the molecular chains have a greater freedom and relax. Under tension and
relax of the molecules they move to crystallize.
• The supply of energy is stopped as soon as the minimum potential energy is reached
and the fibers are cooled as quickly as possible, one succeeds in " freezing" the H-
bonds.
• The newly formed bonds are more difficult to break and the fibers are dimensionally
stable and will not shrink at approximately 10℃ below the temperature of heat
setting.
• At this juncture the process temperature commences to produce a new heat
memory and Tg is changed.

Introduction
• A fabric can reflect, absorb or transmit visible light falling on it.
• The hue of a fabric depends on the extent to which the light is
reflected, absorbed or transmitted.
• Thus, the optical properties of fabrics need to be taken into
consideration when dyeing, printing or color matching fabrics.

Polarization and light
Light is an electro magnetite wave and unpolarized light. When light travels, it is distributed in
two ways such as electric field and magnetic field.
The process of transforming unpolarized light into polarized light is known as polarization.
Polarized light has its E field in one direction.

Refraction: when light photons are transmitted through a material, they
causes polarization of the electrons and in-turn the speed of light is reduced
and the beam of light changes direction.

Factors affect on birefringence: -
This depends on two factors:
1)the degree of orientation of the molecules.
2)the degree of asymmetry of the molecules themselves.
• Highly oriented fibers will have high birefringence value.
• The magnitude of birefringence ranges from 0.005 for Triacetate to 0.188 for
Terylene.
• If all the atoms in a molecule are arranged in a straight chain (fig a) if, as usually
happens, the bond polarizabilities are greatest along the line joining the atoms
then a high birefringence will be expected.

• The actual molecules in fibers do not have this form and their birefringence
will be reduced for two reasons. Firstly, most main chains have a zigzag form
(Fig b) but, provided that the bonds diverge from the main axis by less than
about 55°, this still gives a positive birefringence.
• The coiling of the keratin molecule will have a similar effect in wool.

-There will be side groups attached to the main chain, as in Fig. c, and these
will have the effect of providing atomic bonds at right angles to the main
axis. This will increase the value of n⊥ and reduce the birefringence.
In triacetate and acrylic fibers, the side groups have a greater effect than
the main chain, and the birefringence is negative.

Optical orientation factor:
We have seen that the difference in the refractive indices depends on the
relation between
the direction of polarization of the light and
the direction of alignment of the molecular chain.
It is therefore to be expected that the birefringence will be greatest when the
molecules are all lined up parallel to the fiber axis and that it will be zero when
they are randomly directed.
Hermans has defined an optical orientation factor
‘f’ as the ratio of the birefringence of the fiber to that of an ideal fiber in which
the molecules are perfectly oriented parallel to the fiber axis.
Strictly, the expression should be corrected for differences in density by
dividing each birefringence by the corresponding value of the density.

Textile physics 1

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