Average molecular weight of polymer -Number average molecular weight -Weight average molecular weight Properties of Polymer Uses/Application of Polymer

1. A verage Mo lec u lar
Weight of
Polymers
Introduction
Polymer molecular weight is important because it determines many physical properties. Some
examples include the temperatures for transitions from liquids to waxes to rubbers to solids and
mechanical properties such as stiffness, strength, viscoelasticity, toughness, and viscosity. If molec-
ular weight is too low, the transition temperatures and the mechanical properties will generally be
too low for the polymer material to have any useful commercial applications. For a polymer to be
useful it must have transition temperatures to waxes or liquids that are above room temperatures
and it must have mechanical properties suffcient to bear design loads.
For example, consider the property of tensile strength. Figure 1 shows a typical plot of
strength as a function of molecular weight. At low molecular weight, the strength is too low for
the polymer material to be useful. At high molecular weight, the strength increases eventually
saturating to the infinite molecular weight result of S∞ . The strength-molecular weight relation
can be approximated by the inverse relation
S = S∞ −
𝑨
𝑴
where A is a constant and M is the molecular weight.
(1)
Many properties have similar molecular
weight dependencies. They start at a low value and eventually saturate at a high value that is
characteristic for infinite or very large molecular weight.
Unlike small molecules, however, the molecular weight of a polymer is not one unique value.
Rather, a given polymer will have a distribution of molecular weights. The distribution will depend
on the way the polymer is produced. For polymers we should not speak of a molecular weight,
but rather of the distribution of molecular weight, P (M ), or of the average molecular weight, (M ).
Polymer physical properties will be functions of the molecular weight distribution function as in
S = S∞ −
𝑨
𝑭[𝑷( 𝑴)]
(2)

2. where F[P (M )] is some function of the complete molecular weight distribution function. For some
properties, F[P (M )] my reduce to simply an average molecular weight. The property will thus bea
function of the average molecular weight, [M], and insensitive to other the details of the molecular
weight distribution function:
S = S∞ −
𝑨
𝑴
(3)
There aremany ways, however, to calculate an averagemolecular weight. The question therefore
is how do you define the average molecular weight for a given distribution of molecular weights.
The answer is that the type of property being studied will determine the desired type of average
molecular weight. For example, strength properties may be influenced more by high molecular
weight molecules than by low molecular weight molecules and thus the average molecular weight
for strength properties should be weighted to emphasize the presence of high molecular weight
polymer. In this chapter we consider several ways of calculating molecular weights. We also
consider the meanings of those averages. Finally, we consider typical distributions of molecular
weights.
Figure 1: A typical plot of tensile strength as a function of molecular
weight.

3. Number Average Molecular Weight
Consider a property which is only sensitive to the number of molecules present — a property that
is not influenced by the size of any particle in the mixture. The best example of such properties
are the colligative properties of solutions such as boiling point elevation, freezing point depression,
and osmotic pressure. For such properties, the most relevant average molecular weight is the total
Weight of polymer divided by the number of polymer molecules. This average molecular
weight follows the conventional definition for the mean value of any statistical quantity. In polymer
science, it is called the number average molecular weight — MN.
To get a formula for MN, we must first realize that the molecular weight distribution is not a
continuous function of M . Rather, only discrete values of M are allowed. The possible values ofM
are the various multiples of the monomer molecular weight — M0. By monomer molecular weight
we mean the weight per monomer that appears in the polymer chain. For condensation reactions,
for example, where molecules of water are typically lost from the monomers during reaction, we will
take M0 as the monomer molecular weight less any weight loss due to the polymerization reaction.
The possible values of M make up a set of numbers with discrete values labeled Mi. Let Ni be the
number of polymers with molecular weight Mi. Then the total weight of all polymers is
Total Weight = ∑∞
𝐢=𝟏 𝑵𝒊 𝑴𝒊 (4)
and the total number of polymer molecules is
Total Number = ∑∞
𝐢=𝟏 𝑵𝒊 (5)
As discussed above, the number average molecular weight is
MN = =
𝐓𝐨𝐭𝐚𝐥 𝐖𝐞𝐢𝐠𝐡𝐭
𝐍𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐏𝐨𝐥𝐲𝐦𝐞𝐫𝐬
=
𝑾𝒆𝒊𝒈𝒉𝒕
𝑷𝒐𝒍𝒚𝒎𝒆𝒓
( 6 )
The term Ni / ∑ 𝑁i is physically the number fraction of polymers with molecular weight Mi. If we
denote number fraction as Xi (i.e., mole fraction) the number average molecular weight is
MN = ∑∞
𝐢=𝟏 𝑿𝒊 𝑴𝒊 (7)
In lab experiments it is more common to measure out certain weights of a polymer rather than
certain numbers of moles of a polymer.It is thus useful to derive an alternate form for MN in
terms or weight fraction of polymers with molecular weight Mi denoted as wi.

4. First we note that the concentration of polymer species i is (in weight per unit volume):
ci =
𝑴 𝒊 𝑵 𝒊
𝑽
(8)
Inserting ci for NiMi and expressing Ni in terms of ci results in
MN =
∑∞
𝐢=𝟏 𝒄 𝒊
∑∞
𝐢=𝟏
𝒄 𝒊
𝑴 𝒊
(9)
Dividing numerator and denominator by ∑ 𝑐𝑖 results in
MN =
𝟏
∑∞
𝐢=𝟏
𝒘 𝒊
𝑴 𝒊
( 1 0 )
where wi is the weight fraction of polymer i or the weight of polymer i divided by the total polymer
weight:
𝒘𝒊 =
𝑵 𝒊 𝑴 𝒊
∑∞
𝐢=𝟏 𝑵 𝒊 𝑴 𝒊
=
𝒄 𝒊
∑∞
𝐢=𝟏 𝒄 𝒊
( 1 1)
Weight Average Molecular Weight
Consider of polymer property which depends not just on the number of polymer molecules but
on the size or weight of each polymer molecule. A classic example is light scattering. For such
a property we need a weight average molecular weight. To derive the weight average molecular
weight, replace the appearance of the number of polymers of molecular weight i or Ni in the
number average molecular weight formula with the weight of polymer having molecular weight i or
NiMi. The result is
MW =
∑∞
𝐢=𝟏 𝑵 𝒊 𝑴 𝒊
𝟐
∑∞
𝐢=𝟏 𝑵 𝒊 𝑴 𝒊
( 1 2 )
By noting that NiMi/ NiMi is the weight fraction of polymer with molecular weight i, wi, an
alternative form for weight average molecular weight in terms of weight fractions
𝑴 𝒘 = ∑∞
𝐢=𝟏 𝒘 𝒊 𝑴𝒊 (13)
Comparing this expression to the expression for number average molecular weight in terms of
number fraction (see Eq. (7)) we see that MN is the average Mi weighted according to number
fractions and that MW is the average Mi weighted according to weight fractions. The meanings of
their names are thus apparent.

5. Degree of polymerization =
Number average molecular weight
Molecular weight of the repeat unit
Properties
Of
Polymers
Weight average
molecular weight
Number average
molecular weight
Molecular weight
Amount/frequency
Figure :Average Molecular weight

6. Thermal Properties
In the amorphous region of th e polymer, at lower temperature, the molecules of the polymer
are in, say, frozen state, where the molecules can vibrate slightly but are not able to move
significantly. This state is referred as the glassy state. In this state, the polymer is brittle, hard and
rigid analogous to glass. Hence the name glassy state. The glassy state is similar to a supercooled
liquid where the molecular motion is in the frozen state. The glassy state shows hard, rigid, and
brittle nature analogous to a crystalline solid with molecular disorder as a liquid. Now, when the
polymer is heated, the polymer chains are able to wiggle around each other, and the polymer
becomes soft and flexible similar to rubber. This state is called the rubbery state. The temperature at
which the glassy state makes a transition to rubbery state is called the glass transition temperature
Tg. Note that the glass transition occurs only in the amorphous region, and the crystalline region
remains unaffected during the glass transition in the semi-crystalline polymer.
Melting Point and Glass Transition Temperature
The glass transition temperature is the property of the amorphous region of the polymer, whereas the crystalline
region is characterized by the melting point. In thermodynamics, the transitions are described as first and
second order transitions. Glass transition temperature is the second order transition, whereas the melting point
is the first order transition.
The value of glass transition temperature is not unique because the glassy state is not in equilibrium. The value
of glass transition temperature depends on several factors such as molecular weight, measurement method, and
the rate of heating or cooling. Approximate values of glass transition temperatures of some polymers are listed
in Table 1.
The semi-crystalline polymer shows both the transitions corresponding to their crystalline and amorphous
regions. Thus, the semi-crystalline polymers have true melting temperatures (Tm) at which the ordered phase
turns to disordered phase, whereas the amorphous regions soften over a temperature range known as the glass
transition (Tg). It should be noted that amorphous polymers do not possess the melting point, but all polymers
possess the glass transition temperature.
The polymer melting point Tm is increased if the double bonds, aromatic groups, bulky or large side groups are
present in the polymer chain, because they restrict the flexibility of the chain. The branching of chains causes
the reduction of melting point, as defects are produced because of the branching.
Factors Affecting the Glass Transition Temperature:
Theglass transition temperature depends on the mobility and flexibility (ease of the chain segment to rotate
along the chain backbone) of the polymeric chains. If the polymeric
Second
order
transition

7. TABLE 1. Glass Transition Temperatures of Some Polymers
chains can move easily, then the glassy state can be converted to the rubbery state at
lower temperature, that is, the glass transition temperature is lower. If somehow the
mobility of the chains is restricted, then the glassy state is more stable, and it is
difficult to break the restriction causing the immobility of the polymer chains at the
Liquid
Rubbery
state
Glassy
state
Glass
Semi crystalline
Solid transition
Specific volume
Crystalline
solid
First order Melt state
transition
Tg
Tm
Tm
Tg
Temperature
Figure. Melting point and glass transition temperature of polymer.

8. lower temperature, because more energy is required to make the chains free. Thus, i n
this case, the glass transition temperature is raised.
I. Intermolecular Forces. Strong intermolecular forces cause higher Tg. For example, PVC
(Tg = 80°C) has stronger intermolecular forces than polypropylene (Tg = −18°C) because of
the dipole–dipole forces from the C—Cl bond.
II. Chain Stiffness. The presence of the stiffening groups (such as amide, sulfone, carbonyl, p
phenylene etc.) in the polymer chain reduces the flexibility of the chain, leading to higher glass
transition temperature. For example, polyethyleneterephthalete is stiffer than polyethylene
adipate due to the presence of benzene ring. Therefore, Tg value is higher for
polyethyleneterephthalate.
III. Cross-Linking. The cross-links between chains restrict rotational motion and raise the glass
transition temperature. Hence, higher cross-linked molecule will show higher Tg than that with
lower cross-linked molecule.
IV. Pendant groups. The presence of pendent group can change the glass transition
temperature.
(a) Bulky pendant groups: the presence of bulky pendant group, such as a benzene ring, can
restrict rotational freedom, leading to higher glass transition temperature. As in polystyrene,
the presence of benzene ring increases the Tg In polypropylene, there is no benzene ring that
eads to lower Tg value.
(b) Flexible pendant groups: the presence of flexible pendant groups, for example, aliphatic
chains, limits the packing of the chains and hence increases the rotational motion, tending to
less Tg value. In polybutylmethacrylate, the presence of large aliphatic chain reduces the Tg
value when compared with that of polymethylmethacrylate.
V. Plasticizers. Plasticizers are low molecular weight and non-volatile materials added to
polymers to increase their chain flexibility. They reduce the intermolecular cohesive forces
between the polymer chains, which in turn decrease Tg.

9. VI. Molecular Weight. The glass transition temperature is also affected by the molecular
weight of the polymer (Fig. A1.8). Tg is increased with the molecular weight. The molecular
weight is related to the glass transition temperature by the Fox–Flory Equation:
Tg = Tg,∞ −
𝐾
𝑀
(Fox–Flory Equation)
where Tg,∞ is the glass transition temperature at the molecular weight of infinity, and K is the
empirical parameter called Fox–Flory parameter related to the free volume inside the polymer.
It is observed that Tg is increased up to the molecular weight of approximately 20 000, and
after this limit, the Tg is not affected appreciably.
Mechanical Properties
It is of great importance to be familiar with some basic mechanical properties of the material
before its application in any field, such as how much it can be stretched, how much it can be
bent, how hard or soft it is, how it behaves on the application of repeated load and so on.
a. Strength: In simple words, the strength is the stress required to break the sample. There are
several types of the strength, namely tensile (stretching of the polymer), compressional
(compressing the polymer), flexural (bending of the polymer), torsional (twisting of the
polymer), impact (hammering) and so on. The polymers follow the following order of
increasing strength: linear < branched < cross-linked < network.
Factors Affecting the Strength of Polymers
1. Molecular Weight: The tensile strength of the polymer rises with increase in molecular
weight and reaches the saturation level at some value of the molecular weight. The tensile
strength is related to molecular weight by the following equation.
𝜎 = 𝜎∞ −
𝐴
𝑀
𝜎∞ is the tensile strength of the polymer with molecular weight of infinity. A is some constant,
and M is the molecular weight. At lowermmolecular weight, the polymer chains are loosely
bonded by weak van der Waals forces and the chains can move easily, responsible for low
strength, although crystallinity is present. In case of large molecular weight polymer, the chains
become large and hence are entangled, giving strength to the polymer.
2. Cross-linking: The cross-linking restricts the motion of the chains and
increases the strength of the polymer.

10. 3. Crystallinity: The crystallinity of the polymer increases strength, because in the crystalline
phase, the intermolecular bonding is more significant. Hence, the polymer deformation can
result in the higher strength leading to oriented chains.
b. Percent Elongation to Break (Ultimate Elongation): It is the strain in the material on its
breakage, as shown in Fig. A1.10. It measures the percentage change in the length of the
material before fracture. It is a measure of ductility. Ceramics have very low (<1%), metals
have moderate (1–50%) and thermoplastic (>100%), thermosets (<5%) value of elongation to
break.
c. Young’s Modulus (Modulus of Elasticity or Tensile Modulus): Young’s Modulus is the ratio
of stress to the strain in the linearly elastic region. Elastic modulus is a measure of the stiffness
of the material.
E =
𝑇𝑒𝑛𝑠𝑖𝑙𝑒 𝑆𝑡𝑟𝑒𝑠𝑠 (𝜎)
𝑇𝑒𝑛𝑠𝑖𝑙𝑒 𝑆𝑡𝑟𝑎𝑖𝑛 (𝜀)
d. Toughness: The toughness of a material is given by the area under a stress–straincurve.
Toughness = ∫ 𝜎 d𝜀

11. Uses of

12. Polymers
a) Thermo plastics
1. Acrylonitrile-butadiene-styrene (ABS):
 Outstanding strength and toughness,
 resistance to heat distortion;
 good electrical properties;
 flammable and soluble in some organic solvents.
Application: Refrigerator lining, lawn and garden equipment, toys, highway safety devices.
2. Acrylics (poly-methyl-methacrylate)
 Outstanding light transmission and resistance to weathering;
 only fair mechanical properties.
Application: Lenses, transparent aircraft enclosures, drafting equipment, outdoor signs
3. Fluorocarbons (PTFE or TFE)
 Chemically inert in almost all environments,
 excellent electrical properties;
 low coefficient of friction;
 may be used to 260
o
C;
High way Safety Device

13.  relatively weak and poor cold-flow properties.
Application: Anticorrosive seals, chemical pipes and valves, bearings, anti adhesive coatings,
high temperature electronic parts.
4. Polyamides (nylons)
 Good mechanical strength,
 abrasion resistance, and toughness;
 low coefficient of friction;
 absorbs water and some other liquids.
Application: Bearings, gears, cams, bushings, handles, and jacketing for wires and cables
5. Polycarbonates
 Dimensionally stable:
 low water absorption;
 transparent;
 very good impact resistance and ductility.
Application: Safety helmets, lenses light globes, base for photographic film.
6. Polyethylene

14.  Chemically resistant and electricallyinsulating;
 tough and relatively low coefficient of friction;
 low strength and poor resistance to weathering.
Application: Flexible bottles, toys, tumblers, battery parts, ice trays, film wrapping materials.
7. Polypropylene
 Resistant to heat distortion;
 excellent electrical properties and fatigue strength;
 chemically inert; relatively inexpensive; poor resistance to UV light.
Application: Sterilizable bottles, packaging film, TV cabinets, luggage
8. Polystyrene
 Excellent electrical properties and optical clarity;
 good thermal and dimensional stability;
 relatively inexpensive
Application: Wall tile, battery cases, toys, indoor lighting panels, appliance housings.

15. 9. Polyester (PET or PETE)
 One of the toughest of plastic films;
 excellent fatigue and tear strength, and resistance to humidity acids, greases, oils and
solvents
Application: Magnetic recording tapes, clothing, automotive tire cords, beverage containers.
b) Thermo setting polymers
1. Epoxies
 Excellent combination of mechanical properties and corrosionresistance;
 dimensionally stable;
 good adhesion;
 relatively inexpensive;
 good electrical properties.
Application: Electrical moldings, sinks, adhesives, protective coatings, used with fiberglass
laminates
.

16. 2. Phenolics
 Excellent thermal stability to over 150
o
C;
 may be compounded with a large number of resins, fillers, etc.;
 inexpensive.
Application: Motor housing, telephones, auto distributors, electrical fixtures.
Prepared By
Md. Asiqul Alam
B.Sc in Textile Engineering
Port City International University, Chittagong