


Molar Mass And Molar Mass Distribution
•
•
•
•
Molecular Weight Determination
Laser Light Scattering
Chromatography Size Exclusion (GPC)
Mass Spectroscopy
•
•
•
•
•
Infrared Spectroscopy
Nuclear Magnetic Resonance
X-ray Microscopy
Scanning Electron Microscopy
Atomic Force Microscopy
Structure And Morphology
Dynamic Properties
• Thermal Analysis
Product
Synthesis
Concept
Design
Properties
Fundamentals
11
Structure
Synthesis
Properties
Characterization
12
Limiting Value
Mechanical
Property
General Relationship
Strength,
Modulus,
etc
sB = A - (B\Mn)
DP Critical
Degree of Polymerization
15
General Relationship
[h] = K Ma K and a are constants
Viscosity
Mark-Houwink-Sakurada Relation
Degree of Polymerization
16
Mechanical
Property*
Useful Range
Viscosity
Degree of Polymerization
17
Low molecular weight molecules
Single Value
Molecular Weight
Synthetic Polymers
# of Molecules
Broad Range of Values
Molecular Weight
Biological Polymers
Single Value
# of Molecules
Molecular Weight
18

Number Average Molecular Weight
• End-group analysis
 determine the number of end-groups in a sample
of known mass
• Colligative Properties
 most commonly osmotic pressure, but includes
boiling point elevation and freezing point
depression

Weight Average Molecular Weight
• Light scattering
 translate the distribution of scattered light
intensity created by a dissolved polymer sample
into an absolute measure of weight-average MW

Viscosity Average Molecular Weight
• Viscometry
 The viscosity of an infinitely dilute
polymer solution relative to the solvent
relates to molecular dimension and
weight.

Molecular Weight Distribution
• Gel permeation chromatography
 fractionation on the basis of chain
aggregate dimension in solution.
Measurement of Number Average Molecular Weight
2.3.1 End-group Analysis
A. Molecular weight limitation up to 50,000
B. End-group must have detectable species
a. vinyl polymer : -CH=CH2
b. ester polymer : -COOH, -OH
c. amide and urethane polymer : -NH2, -NCO
d. radioactive isotopes or UV, IR, NMR detectable functional group
Measurement of Number Average Molecular Weight
C.
Mn =
2 x 1000 x sample wt
meq COOH + meq OH
D. Requirement for end group analysis
1. The method cannot be applied to branched polymers.
2. In a linear polymer there are twice as many end of the chain
and groups as polymer molecules.
3. If having different end group, the number of detected end group
is average molecular weight.
4. End group analysis could be applied for
polymerization mechanism identified
E. High solution viscosity and low solubility : Mn = 5,000 ～ 10,000
Colligative properties
Properties determined by the number
of particles in solution rather than the
type of particles.
Vapour pressure lowering
Freezing point depression
Boiling point elevation
Osmotic pressure
How Vapor Pressure Lowering
Occurs
•
•
•
Solute particles take up space in a
solution.
Solute particles on surface
decrease number of solvent
particles on the surface.
Less solvent particles can
evaporate which lowers the vapor
pressure of a liquid.
Vapor Pressures of Pure Water and a Water Solution
The vapor pressure of water over pure water is greater than the
vapor pressure of water over an aqueous solution containing a
nonvolatile solute.
Solute particles take up
surface area and lower
the vapor pressure
Let component A be the solvent and B the solute.
solute B is nonvolatile
*
P

X
P
Applying Raoult’s Law: A
A A
where:
XA
PA= vapor pressure of the solvent in solution
= vapor pressure of the solution
PA*= vapor pressure of the pure
solvent
XA= mole fraction of the solvent
The lowering in vapor pressure,  P
P  P  PA
*
A
 P P XA
*
A
*
A
 (1  X A ) P
*
A
P  X B P
*
A
where:
XB
= mole fraction of solute
When a non volatile solute is added to
solvent:
• Vapor pressure of solvent is lowered
• solution formed must be heated to higher
temperature than boiling point of pure
solvent to reach a vapor pressure of 1 atm.
• This means that non volatile solute elevates
the boiling point of the solvent which we call
boiling point elevation
 RT *2 
X B
T  
  vap H 


XB
mB

 mB M A
1 / M A  mB
where
(for dilute solutions)
MA
is the molar mass of the solvent and
mB
the molality of the solute in
mol/kg
 RTb*2 M A 
 mB
T  
  H 
 vap

Tb  Kb m
where
for dilute solutions
 RTb *2 M A 

Kb  
  H 
 vap

Kb= boiling point constant or
ebullioscopic constant of the solvent
Boiling-point elevation (Ebulliometry)
Tb
(
)C=0 =
C
RT2
+ A2C
HvMn
Tb : boiling point elevation
H v : the latent heats of vaporization
We use thermistor to major temperature. (1×10-4℃)
limitation of Mn : below 20,000
Tf  K f m
(for dilute solutions)
 RTf *2 M A 

where K f  
  fus H 


Kf= molal freezing point depression
constant or cryoscopic constant
Freezing-point depression (Cryoscopy)
RT2
Tf
+ A2C
(
)C=0 =
Hf Mn
C
Tf : freezing-point depression,
C : the concentration in grams per cubic
centimeter
R : gas constant
T : freezing point
Hf: the latent heats of fusion
A2 : second virial coefficient