The document discusses molecular weight (MW) and its importance in determining polymer properties. It provides the following key points: - Polymer properties depend on chain length, which is expressed by MW. Higher MW leads to better mechanical strength but poorer processability. - Synthetic polymers are polydisperse, with a distribution of chain lengths and MWs. Various average MW values are used like number average MW (Mn) and weight average MW (Mw). - MW distribution describes the relationship between number of moles of each polymer species and its molar mass. Broader distributions yield better impact resistance while narrower distributions give more uniform properties. - Degree of polymerization (DP) represents the

1. MOLECULAR WEIGHT

2. Student are able to Identify and calculate
the concepts of molecular weight (MW) and size
(MW average, MWD, solubility and intrinsic
viscosity).

3. Introduction
You have learned in past lecture the
structure and properties of thermoset and
thermoplastic. But do you know the
properties of a polymer depend on its
length??

4. • Polymer consist of repeat units(monomers) which
chemically bonded(covalently) into long chains.
• Physical properties (such mechanical strength ,
solubility and brittleness) require knowledge of the
length of the polymer chain.
• Chain length is often expressed in terms of
molecular weight (MW) of the polymer chain,
related to the relative molecular mass of the
monomer and the number of monomer connected in
the chain.
Introduction

5. Introduction
• However, all synthetic polymer are
polydisperse in the contain polymer chain of
unequal length, so the MW is not a single value
where polymer exist as a distribution of chain
length and MW.
• MW describe as some average MW calculated
from the MW of all the chain in the sample.

6. Introduction
Here are:
10 chains of 100 molecular weight
20 chains of 500 molecular weight
40 chains of 1000 molecular weight
50 chains of 10000 molecular weight
Polydispersity in Polymer chain

7. Introduction
• Some natural polymer (monodisperse) :
– All polymer molecules have same molecular weights.
• Synthetic polymers (polydisperse) :
– The molecular weights of polymers are distributed
• Mechanical properties are influenced by molecular
weight
– much lower molecular weight ; poor mechanical property
– much higher molecular weight ; too tough to process
– optimum molecular weight ; 105 -106 for vinyl polymer
– 15,000 - 20,000 for polar functional group containing
polymer (polyamide)

8. Determination of molecular weight(MW)
There are three (3) method in determining of MW:-
a.Absolute method :
mass spectrometry
colligative property
end group analysis
light scattering
ultracentrifugation.
b. Relative method : solution viscosity
c. Fractionation method : Gel Permeation Chromatography

9. 9
Molecular Weight
• Molecular weight, M: Mass of a mole of chains.
Low M
high M
• Polymers can have various lengths depending on the number of repeat
units.
• During the polymerization process not all chains in a polymer grow to the
same length, so there is a distribution of molecular weights. There are
several ways of defining an average molecular weight.
• The molecular weight distribution in a polymer describes the relationship
between the number of moles of each polymer species and the molar
mass of that species.

10. Definition of Molecular Weight (MW)
• Defined as the sum of the atomic weights of each of
the atoms in the molecule.
• Molecular weight is molecular mass.
• Molecular weight is easily calculated when exact
formula is known:
a) H2O (H=1, O=16)
1+1+16=18 g/mole
b) CH4 (C=12, H=1)
12+1+1+1+1=16g/mole
c) ~~(C2H4)1000~~ (C=12, H=1)
[(12x2) + (1x4)] x 1000= 28,000g/mole

13. Molecular weight
Are the two different? Yes, one is essentially based on
mole fractions, and the other on weight fractions
They will be the same if all the chains are exactly of the
same MW! If not Mw > Mn
Get Mn
from this
Get Mw from
this

14. Number average molecular weight

15. Weight average molecular weight

16. Molecular weight distribution

17. 17
MOLECULAR WEIGHT DISTRIBUTION
Adapted from Fig. 4.4, Callister & Rethwisch 3e.

18. Molecular Weight Distribution (MWD)
• A count of the number of molecules of each Mw, it measure
variation in chain length @ MW of the molecules in a sample.
• Another method to characterizing polymer:
a) Narrow MWD
– Most of the polymers were nearly the same length, it will crystallize
faster, more uniform rate.
– Form a narrower softening/melting temperature range, a lower
stress cracking sensitivity and better chemical resistance.
b) Broad MWD
– The polymers has some short & some long polymer chains, good
impact resistance and good processability.
***(MWD are controlled by the conditions of the polymerization)

19. • How broad the distribution is depends on the type of
polymerization
•The MWD can be affected during the polymerization
reaction by various experimental variables such as:
Changing the monomer concentration in the
reaction mixture
Changing the initiator concentration
Temperature
Pressure
Concentration of added modifiers

20. The effect of molecular weight on physical
properties
With increasing MW, i.e. increasing chain length, the macromolecules
or polymers become increasingly entangled. This hinders their ability to
move freely in the melt and especially their ability to slide past each
other.

22. The Degree of Polymerization (DP)
• DP in a polymer molecule is the number, n, of
repeating units in the polymer chain.
• The molecular weight of a particular polymer molecule
is a product of the degree of polymerization and the
molecular weight of the repeating unit. For instance a
particular polyethylene molecule with DP = 1000 will
have a molecular weight of 28,000.

23. Degree of Polymerization, DP
DP = average number of repeat units per chain
i
im
f
m
m



:
follows
as
calculated
is
this
copolymers
for
unit
repeat
of
weight
molecular
average
where
C C C C C C C C
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
C C C C
H
H
H
H
H
H
H
H
H
( ) DP = 6
mol. wt of repeat unit i
Chain fraction
m
M
DP
n


24. Degree of polymerization
– Other ways to define polymer MW
– Degree of polymerization
• Represents the average number of mers in a chain.
The number and weight average degrees of
polymerization are
m
M
n
n
n 
m
M
n
w
w 
m is the mer MW in both cases. In the case of a copolymer
(something with two or more mer units), m is determined by

 j
jm
f
m
fj and mj are the chain fraction and molecular weight of mer j

26. Example 1

27. Answer: Basic MW calculation
a) H2O (H=1, O=16)
1+1+16=18 g/mole
b) CH4 (C=12, H=1)
12+1+1+1+1=16g/mole
c) ~~(C2H4)1000~~ (C=12, H=1)
[(12x2) + (1x4)] x 1000= 28,000g/mole

28. Example of MW calculation

30. Example 2
Calculate number average of molecular weight
(Mn) and weight average molecular weight ( Mw)
for 9 moles, molecular weight (Mw) = 30,000
and 5 moles, molecular weight ( Mw) = 50,000

31. EXAMPLE 2: molecular weight calculation
Calculate Mn and Mw for:-
a. 9 moles, molecular weight (Mw) = 30,000
5 moles, molecular weight ( Mw) = 50,000
Mn=
9 mol + 5 mol
(9 mol x 30,000 g/mol) + (5 mol x 50,000 g/mol)
= 37,000 g/mol
Mw =
9 mol(30,000 g/mol) + 5 mol(50,000 g/mol)
9 mol(30,000 g/mol)2 + 5 mol(50,000 g/mol)2
= 40,000 g/mol
Answer-Example 2

32. Example 3
From Figure 1 below, a distribution of chain length showed 10 chains of
100 molecular weight, 20 chains of 500 molecular weight, 40 chains of
1000 molecular weight and 5 chain of 10,000 molecular weight.
Calculate the number average of molecular weight (Mn), weight
average molecular weight ( Mw) and polydispersity index.
Given;

33. Answer-Example 3

34. Example 4
Calculate degree of polymerization(DP = average number
of repeat units per chain) for Polypropylene (C3H6)n with
number average molecular weight is 1,000,000 g/mol
where m=repeat unit molecular weight. Given;
****Given that average molecular weight is 1,000,000 g/mol

35. Answer-Example 4

36. Example 5

37. – Given the following data determine the
• Number average MW
• Weight average MW
• Number average degree of polymerization How to find Mn?
1. Calculate xiMi
2. Sum these!
mol
g
M n /
150
,
21

Number average MW (Mn)
MW range (g/mol) Mean (Mi)
Min Max xi (g/mol)
5000 10000 0.05 7500
10000 15000 0.16 12500
15000 20000 0.22 17500
20000 25000 0.27 22500
25000 30000 0.20 27500
30000 35000 0.08 32500
35000 40000 0.02 37500
xiMi (g/mol)
375
2000
3850
6075
5500
2600
750
Answer-Example 5

38. 38
Answer-Example
5

39. Number average degree of polymerization
– (MW of H2C=CHCl is 62.50 g/mol)
m
M
n
n
n 
MW range (g/mol) Mean (Mi)
Min Max wi (g/mol)
5000 10000 0.02 7500
10000 15000 0.10 12500
15000 20000 0.18 17500
20000 25000 0.29 22500
25000 30000 0.26 27500
30000 35000 0.13 32500
35000 40000 0.02 37500
How to find Mw?
1. Calculate wiMi
2. Sum these!
mol
g
M w /
200
,
23

wiMi (g/mol)
150
1250
3150
6525
7150
4225
750
10
.
1
/
150
,
21
/
200
,
23


mol
g
mol
g
M
M
n
w
338
/
50
.
62
/
150
,
21


mol
g
mol
g
Weight average molecular weight (Mw)
Answer-Example 5

40. 40
Answer-Example
5