MOLECULAR WEIGHT
"Drop the idea of large molecules.
Organic molecules with a molecular
weight higher than 5000 do not exist."
—Advice given to Hermann Staudinger*
MOLECULAR WEIGHT
WHY IS IT IMPORTANT ?
MELT
VISCOSITY
TENSILE
STRENGTH
MOL.WT.
MOL.WT.
Molecular Weight - Some Initial Observations
How does the molecular weight of a high polymer differ
from that of a low-molecular-weight substance ?
But for most polymers there is a
Distribution of Chain Lengths
CH4
16
30
CH3 CH3
Gases
CH3 CH2 CH3
58
CH3 CH2 CH2 CH3
Liquid
CH3 (CH2)6 CH3
CH3 (CH2)30 CH3
"Semi-solid"
CH3 (CH2)30000 CH3
44
Solid
114
450
We must therefore define an
Average Degree of Polymerization ( DP )
420030
Increasing
Molecular Weight
Molecular weight M simply:
(# C atoms x 12) + (# H atoms x 1)
The average number of structural units in the polymer chain
And an
Average Molecular Weight (M )
The average degree of polymerization times the molecular
weight of the structural unit, M0
MOLECULAR WEIGHT
12
Mn ≅ 108, 500
Mw ≅ 118, 200
10
Moles
8
6
4
2
0
0
100000
200000
300000
Molecular Weight
Number Average
Mn =
∑ N x Mx
∑ Nx
Weight Average
∑ Nx Mx
=
∑ N x Mx
2
Mw
METHODS FOR THE DETERMINATION
OF MOLECULAR WEIGHT
A
B
S
O
L
U
T
E
R
E
L
A
T
I
V
E
END GROUP ANALYSIS
OSMOTIC PRESSURE
OTHER COLLIGATIVE
PROPERTY MEASUREMENTS
LIGHT SCATTERING
ULTRA - CENTRIFUGATION
_
Mn
_
Mn
_
Mn
_
Mw
_
_
Mw , Mz
SOLUTION VISCOSITY
_
_
~
Mv
Mw
GPC
Complete
distribution
OSMOTIC PRESSURE
Concentrated
solution
Dilute
solution
A SECTION OF ROOT
A SCHEMATIC OF A LABORATORY
SCALE OSMOMETER
Pure
Solvent
Piston
Polymer
Solution
Pressure
=π
h
Membrane Cap
[A]
[B]
[C]
THE IDEA OF VIRIAL EQUATIONS
THE IDEAL GAS LAW
PV = nRT
1.01
Ideal gas
1.00
N2
0.99
PV
NRT
0.98
CH4
0.97
0.96
C2H4
0.95
0
2
4
6
P (atm)
PV
nRT
VIRIAL EQUATION
2
3
= 1 + B'P + C'P + D'P + - - -
8
10
RELATIONSHIP TO MOLECULAR WEIGHT
PV = nRT
P V
_ = RT
n
moles
n_ = #________
w __
1
= __
V
volume
M V
HENCE
Π
=
c
=
__
c
M
RT
M
NOW CONSIDER AN IDEAL SOLUTION
Osmotic
OsmoticPressure
Pressure
π = RT
c
M
π = RT + Bc + Cc 2 + Dc3 + -----c
Mn
Ideal Solution
Not So Ideal
Solution
2.0
1.5
1.6
π x 10
c
-5
0.4
-2
cm2 sec
1.0
1.2
0.224
-3
π
c x 10 0.8
cm
0.75
0.5
0.3
0.2
0
1
2
3
0.0
0
2
4
6
3
8
10
0.4
-3
c x 10 g cm
Graph of π/c versus c for polystyrene in toluene.
0.21
0.0
0
2
4
6
2
8
10
12
-3
c x 10 g cm
Graph of π/c versus c for polyisobutylene in chlorobenzene.
DERIVATION OF A VIRIAL EQUATION
FROM THE FLORY - HUGGINS EQUATION
Osmotic pressure can
Be related to the
Chemical potential
Expanding the ln term
We obtain
(
)
µ s - µ 0s
2
= ln Φs + 1 - 1 Φ p + Φp χ
RT
Mn
(
)
2
π = - RT ln Φ s + Φp 1 - 1 + Φp χ
Vs
Mn
3
2
ln Φ s = ln ( 1 - Φp )
π = RT
Vs
Φp
Mn
Φp Φ p
- ------= - Φp 2
3
+ Φp
2
(
)
3
1 - χ + Φp + -----2
3
LIGHT SCATTERING
Looks fiendishly difficult because
Of all the equations
Crucial point:
We will end up with a virial equation,
Just as in our treatment of osmotic
Pressure
K (1 + cos 2θ) c
1
1 + 2Γ2c + --=
Rθ
Mw
(
Experimentally
measured parameters
Virial expansion
)
(
1+ S sin
2
( θ2 ) )
(10.61)
Dependence on
angle of observation
THE EXPERIMENT
Incident
beam
Sample
cell
θ
Transmitted
beam
Detector
THE ORIGIN OF LIGHT SCATTERING
Z
λ
E0
φ
time
LIGHT AS AN OSCILLATING ELECTRIC FIELD
z
P
θz
θ
x
Incident beam polarized
in the zx plane
y
Classical description The electric field of
The incident light induces
Oscillations of the
Electrons in the molecule,
So that the molecule now
Emits light in all directions
SCATTERING FROM A GAS
FOR SCATTERING FROM A BUNCH
OF RANDOMLY LOCATED OSCILLATORS
.
.
.
i'θ =
( )
N
V
# scatterers
per unit volume
.
.
.
( )
I0 8π
λ
4
4
( α2 )
(
1 + cos2θ
r2
)
Polarizability
Characteristics of
the incident beam
Geometry of
observation
(10.46)