Biomass Fundamentals
Module 6: Fundamental Principles of Polymer Chemistry
A capstone course for
BioSUCCEED:
Bioproducts Sustainability: a University Cooperative
Center of Excellence in EDucation
The USDA Higher Education Challenge Grants program
gratefully acknowledged for support
This course would not be possible without
support from:
USDA
Higher Education Challenge (HEC) Grants Program
www.csrees.usda.gov/funding/rfas/hep_challenge.html
Polymer Chemistry
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Macromolecules
Polymer Structure/Classification
Molecular Weight Definitions
Molecular Weight Distribution
Viscocity
Polymer Morphology
The Macromolecular Hypothesis
In the late 1800’s it was hypotheses that large
molecules - “Macromolecules” existed as a result
of covalently linked smaller units, and possessed
unique physical and chemical properties.
The Macromolecular Hypothesis
However the scientific community at that time
was unwilling to accept such a notion, explaining
high MW-molecules as being the result of inferior
methodology and/or molecular association of
smaller molecules.
Polymer Structure
Polymers can exist with various skeletal
structures - such as linear, branched or crosslinked or network polymers.
Linear
Branched
Network
Polymer Structure
Variations in skeletal structure give rise to
major differences in polymer properties.
– linear polyethylene has a melting point 20oC higher
than that of a branched polyethylene.
– unlike most linear polymers and branched
polymers, network polymers do not melt upon
heating, and will not dissolve
Polymer Classification
Polymers are commonly classified based on their
underlying molecular structure.
Polymers
Thermoplastics
Crystalline
Amorphous
Elastomers
Thermosets
Thermoplastics
Often referred to as just “Plastics” are linear or
branched polymers which soften upon heating.
They can be moulded (and remoulded) into
virtually any shape
– injection moulding, extrusion
and constitute the largest portions of the polymers
used in industry
Thermoplastics never achieve 100% crystallinity,
but instead are semicrystalline with both
crystalline and amorphous domains.
Thermoplastics
The crystalline phases of such polymers are
characterized by their melting temperature (Tm).
Many thermoplastics are completely amorphous
and incapable of crystallization, these amorphous
polymers (and amorphous phases of semicrystalline
polymers) are characterized by their glass transition
temperature (Tg).
– the temperature at which they transform abruptly from
the glassy state (hard) to the rubbery state (soft).
Thermoplastics
Glass transition temperature (Tg)
This transition corresponds to the onset of chain
motion
•below the Tg the polymer chains are unable to move
and are “frozen” in position.
Both Tg and Tm increase with increasing chain
stiffness and increasing forces of intermolecular
attraction
Elastomers
Elastomers - crosslinked rubbery polymers rubber networks - that can be easily stretched to
high extensions (3x to 10x original dimensions)
– the rubbery polymer chains become extended upon
deformation but are prevented from permanent flow
by crosslinking, and driven by entropy, spring back to
their original positions on removal of the stress.
Thermosets
Thermosets - normally rigid materials - network
polymers in which chain motion is greatly restricted
by a high degree of crosslinking
As with elastomers, they are intractable once formed
and degrade rather than melt upon the application of
heat.
Polysaccharides
The size of polysaccharide molecules can vary,
occurring as polydispersed molecules that have a
range of 100 to 100,000 monosaccharide units
– MW 16,000 - 16,000,000 daltons
There are a number of methods used to determine
the molecular weight of polysaccharides
– viscosity*, light scattering, ultracentrifugation,
osmometry and titration are most common
(*viscosity is routinely used, but is not an absolute method and
can be used only in conjunction with one of the other methods)
Molecular Weight Distribution
The simplest, most common molecular weight is
the number-average molecular weight (n)
– end-group analysis or colligative properties (b.p.
elevation, osmotic pressure, etc)
others commonly used are weight-average
molecular weight (w), z-average molecular
weight (z) and viscosity-average molecular
weight (u)
– light scattering (w), sedimentation equilibrium
(z) and solution viscosity (u)
Number-average molecular weight (n)
– based on methods of counting the number of
molecules in a given weight of polymer
• the total weight of a polymer sample, w, is the sum of the
weights of each molecular species present


i 1
i 1
w   wi  N i M i
N = number of molecules
M = molecular weight

Mn 
w


N
i 1
i
M N
i 1

i
N
i 1
i
i
Weight-average molecular weight (w)
determination of molecular weight based on size
rather than the number of molecules
– the greater the mass, the greater the contribution to
the measurement

Mw 
 wi M i
i 1

w
i 1
i


 Ni M i
2
i 1

N M
i 1
i
i
w = weight fraction
M = molecular weight
N = number of molecules
Z-average molecular weight (z)
some molecular weight determination methods
(e.g. sedimentation equilibrium) yield higher
molecular weight averages - z

Mz 
3
N
M
 i i
i 1

2
N
M
 i i
i 1


 wi M i
2
i 1

w M
i 1
i
i
w = weight fraction
M = molecular weight
N = number of molecules
Number-average molecular weight (n)
Example - a polymer sample consists of 9 molecules of
mw 30,000 and 5 molecules of mw 50,000

Mn 
M N
i 1

i
N
i 1
i
i
(9  30,000)  (5  50,000)

 37,000
(9  5)
Weight-average molecular weight (w)
Consider the previous example - 9 molecules of molecular
weight 30,000 and 5 molecules of molecular weight 50,000
9(30,000) 2  5(50,000) 2
Mw 
 40,000
9(30,000)  5(50,000)
Z-average molecular weight (z)
Consider the previous example - 9 molecules of molecular
weight 30,000 and 5 molecules of molecular weight 50,000
9(30,000)3  5(50,000)3
Mz 
 42,136
2
2
9(30,000)  5(50,000)
104 wi
4.0
A Typical Molecular Weight
Distribution Curve
n = 100 000 g mol-1
w = 199 900 g mol-1
3.0
z = 299 850 g mol-1
2.0
1.0
200 000
400 000
600 000
800 000
1 000 000
Mi (g mol-1)
Molecular Weight Determination
In measurements of colligative properties, each
molecule contributes regardless of weight,
whereas in light scattering, the larger molecules
contribute more because they scatter light more
effectively.
For this reason, w are greater than n , except
when all molecules are of the same weight and
w = n
Molecular Weight Distribution
The narrower the molecular weight range, the
closer are the values of w and n , and the
ratio w / n may thus be used as an
indication of the breadth of the molecular
weight range in a polymer sample.
The ratio is called the polydispersity index,
and any system having a range of molecular
weights is said to be polydispersed
104 wi
4.0
A Typical Molecular Weight
Distribution Curve
n = 100 000 g mol-1
w = 199 900 g mol-1
3.0
z = 299 850 g mol-1
2.0
1.0
200 000
400 000
600 000
800 000
1 000 000
Mi (g mol-1)
Polymer Solution Viscosity
When a polymer is dissolved in a solvent and
then subjected to flow through a narrow
capillary it exerts a resistance to that flow. This
resistance is very informative.
•It provides information on the size of the
polymer
•Its Flexibility and shape in solution
•Its interactions with the solvent it is disolved in.
Polymer Solution Viscosity
For dilute solutions the ratio between flow time of
a polymer solution (t) to that of the pure solvent
(to) is effectively equal to the ratio of their
viscosity (h / ho)
hrel
t
h
 
t o ho
As this has a limiting value of unity, a more useful
quantity is specific viscosity (hsp)

t  to )
hsp  hrel  1 
to
Intrinsic Viscosity [η]
To eliminate concentration effects, the specific viscosity
(hsp ) is divided by concentration and extrapolated to zero
concentration to give intrinsic viscosity [h]
hsp
h  ho
2

 h ] K H h ] c
c
hoc
Thus plotting hsp/c vs c, the intercept is the intrinsic
viscosity [h] and from the slope, KH (Huggins constant,
typically between 0.3 - 0.9) can be determined
Intrinsic Viscosity Determination
h  ho
ho c
3.5

KH[η2]
3.0

2.5

2.0

[h]
0.2
0.4
0.6
0.8
1.0
C (g dl-1)
Viscosity-Molecular Weight Relations
Intrinsic viscosity [h] can be related to molecular weight
by the Mark-Houwink-Sakurada Equation
Applicable for a given polymer-solvent system at a given temperature
h ]  KM
a
υ
Log [h] vs log M (w or n) for a series of fractionated
polymers produces log K (intercept) and a (slope)
A wide range of values have been published
– a ~ 0.5 (randomly coiled polymers)
~ 0.8 (rod-like, extended chain polymers)
– K between 10-3 and 0.5
Typical Mark-Houwink-Sakurada Equation Constants for
Several Polysaccharides
Solvent
Temp K (x10-3)
o
C
ml g-1
a
MW
Method
-3
(x10 )
Cellulose
Cadoxen
Cuprammonium
25
25
33.8
8.5
0.77
0.81
20-100
10-100
SD
OS
DMSO
Water
25
20
1.25
13.2
0.87
0.68
20-300
30-220
LS
LS
25
34
97.8
10.3
0.50
0.25
2-10
80
LS
LS
Amylose
Dextran
Linear
Water
Branched Water
Typical Intrinsic Viscosities, a and K values for Several
Naturally Occurring Polymeric Materials
Solvent
Kraft Lignin
Temp [h]
o
C dl g-1
a
K (x10-3)
ml g-1
MW
Dioxane
25
0.06 0.12
1638
50,000
Celluose
CED
25
1.81 0.75
54.0
50,000
xylan
CED
25
2.16 1.15
0.85
50,000
The degree of expansion or shape of the molecular coils
of a polymer can be ascertained from its a values (Table 2)
•lignin (Newtonian sphere), cellulose (nonfreedraining coil) and xylan (freedraining coil)
Viscosity-average molecular weight (u)
– viscosity, like light scattering, is greater for the largersized polymer molecules than the smaller ones, and is
much closer to Mw than Mn
1a

a
M u   wi M i 
 i 1


1a

a 1 
  Ni M i 
  i 1



N
M

 i 1 i i 

w = weight fraction
N = number of moles
M = molecular weight
a = A constant
– When a = 1, u= w , usually a ~ 0.5-0.9
– a is a measure of the the hydrodynamic volume of the
polymer
– varies with polymer, solvent and temperature
Polymer Morphology
The ultimate properties of any polymer (plastic,
fiber, or rubber) result from a combination of
molecular weight and chemical structure.
Polymers require a
Mechanical Property
particular MW, which
depends largely on the
chemical structure, to
have desirable
mechanical properties.
Molecular Weight
Polymer Morphology
The mechanical properties result from attractive
forces between molecules
– dipole-dipole interactions, H-bonding, induction forces,
London forces or ionic bonding, ion-dipole interactions
+
C
dipole-dipole
-
O
+
-
O
+ C
O
C
R
O
-
R
R
H
N
O
H
N
-
R
H-bonding
+
C
O
A lower MW polyamide will produce good fiber
properties as compared to the polyester  H-bonding
Polymer Morphology
• Hydrogen Bonding
– A dipole-dipole interaction for hydrogens bonded to
electronegative elements
• Electrostatic Interaction
H
R
R
O
O
H
O
R
H
H
O
very important
in cellulose
R
Weak bond ~ 5 kcal mol-1 (c-c ~ 81 kcal mol-1 )
Require short bond distance ~ 2.5Å (c-c ~ 1.46Å)
Polymer Morphology
Intermolecular forces drop off very rapidly with
distance  important polymer molecules be able to pack
together closely to achieve maximum cohesive strength.
ex. Natural Rubber
unstretched state - molecules are randomly distributed
 low modulus
stretched state - molecules become aligned, at 600%
elongation  high modulus
(2000 times higher than unstretched)
unstretched - amorphous / stretched - crystalline