A brief introduction to polymer science
1
1.1. Fundamental definitions
Polymers consist of large molecules, i.e. macromolecules. According to the basic IUPAC
definition [Metanomski, 1991]:
‘A polymer is a substance composed of molecules characterised by the multiple repetition of
one or more species of atoms or groups of atoms (constitutional repeating units) linked to each
other in amounts sufficient to provide a set of properties that do not vary markedly with the
addition of one or a few of the constitutional repeating units’.
The word polymer originates from the Greek words ‘poly’ meaning many and ‘mer’
meaning part. It was the Swedish chemist Jöns Jacob Berzelius (1832) who suggested the term
polymer for any compound with a molar mass that was a multiple of the molar mass of another
compound with the same elemental composition. Figure 1.1 shows the structure of
polypropylene, an industrially important polymer. The constitutional repeating units, which are
also called simply "repeating units", are linked by covalent bonds, and the atoms of the
repeating unit are also linked by covalent bonds. A molecule with only a few constitutional
repeating units is called an oligomer. The physical properties of an oligomer vary with the
addition or removal of one or a few constitutional repeating units to or from its molecules. A
monomer is the substance that the polymer is made from, which in the case of polypropylene is
propylene (propene) (Fig. 1.1). The process that converts a monomer to a polymer is called
polymerisation.
s econdary
bo nd
covalen t
bo nd
Ec=300 GPa
Et=3 GPa
Figure 1.1. The structure of monomer and
polymer (polypropylene). The constitutional
repeating unit is shown between the brackets.
Figure 1.2. Anisotropic nature of polymer crystals.
Approximate moduli for polyethylene parallel (Ec)
and transverse (Et) to the chain axis are shown.
The polymers dealt with in this book are exclusively carbon-based organic polymers. Other
common elements in the organic polymers are hydrogen, oxygen, nitrogen, sulphur and silicon.
The covalent bonds that link the atoms of the polymer chains are very strong with dissociation
energies between 300 and 500 kJ mol-1. The intermolecular bonds, sometimes denoted
secondary bonds, are much weaker with dissociation energies of a few to 50 kJ mol -1. To assess
the stability of primary and secondary bonds, these energies may be compared with the thermal
energy, i.e. RT, where R is the gas constant and T is the absolute temperature given in kelvin.
-1
The thermal energy is approximately 2.5 kJ mol-1 at 300 K and approximately 4 kJ mol at 500
K.
1
The large difference in dissociation energy and bond force constant (‘stiffness’) between the
covalent bonds and the weak secondary intermolecular bonds is of great importance for the
properties. The identity of the molecules, i.e. the entities linked by covalent bonds, is largely
preserved during melting, while the secondary bonds are broken. There are many examples of
polymers that degrade early at low temperatures but where the degradation involves only a few
of the existing primary bonds. Melting involves mainly the rupture and partial re-establishment
of a great many secondary bonds.
Polymer crystals show very direction-dependent (anisotropic) properties. The Young’s
modulus of a polyethylene single crystal at room temperature is approximately 300 GPa in the
chain axis direction and only 3 GPa in the transverse directions (Fig. 1.2). This considerable
difference in modulus is due to the presence of two types of bonds connecting the different
atoms in the crystals: strong and stiff bonds along the chain axis and weak and soft secondary
bonds acting in the transverse directions (Fig. 1.2). A whole range of other properties, e.g. the
refractive index, also shows strong directional dependence. The orientation of the polymer
molecules in a material is enormously important. The Young's modulus of a given polymer can
be changed by a factor of one hundred by changing the degree of chain orientation. This is an
important topic discussed in Chapter 9.
1.2. The covalent bonds
Organic polymers are based on carbon (always), hydrogen (almost always) and occasionally
oxygen, nitrogen, sulphur, halogens, and a few other elements. These atoms are in the case of
polymers connected by covalent bonds. A covalent bond is a chemical bond formed when two
atoms share a pair of electrons. Primary bond is an often-used synonymous expression to
covalent bond. The electronic structure of the elements determines the characteristics of their
covalent bonds to other atoms. Figure 1.3 shows schematically the electronic structures of the
aforementioned elements. Electrons located in different electron shells surround the positively
charged nucleus. The number of electrons is equal to the number of protons in the nucleus of an
uncharged atom. Both theory and experiment indicate that the electronic structures of the rare
gases (e.g. helium, neon and argon) are especially stable; these atoms are said to contain ‘filled
shells’. The way in which the other elements forms covalent bonds can be understood by their
wish to attain filled-shell conditions. The first shell holds only 2 electrons, whereas the second
shell holds 8 electrons. The third can hold 18 electrons, but a very stable configuration is
reached when a shell of 8 electrons is filled (argon structure). Hydrogen needs only 2 electrons
to fill its outermost shell. This can be achieved by forming a covalent bond between two
hydrogen atoms (Fig. 1.4). The two hydrogen atoms share an electron pair and simulate in this
respect the helium configuration with a filled outer shell. Carbon has 4 electrons in the
outermost shell (valence electrons) and it wishes to attain filled shell conditions, 8 valence
electrons. Forming covalent bonds with four hydrogen atoms, as is shown in Fig. 1.4, simulates
the electronic structure of neon. The covalent bonds are very strong and the atoms are not
readily separated. Let us take a look at a few other important elements. Nitrogen has 5 valence
electrons and therefore binds three other atoms as in ammonia (NH3) to attain filled shell
conditions. Oxygen has 6 valence electrons and forms two covalent bonds with the two
hydrogen atoms in water (H2O) to attain the neon structure.
First
electron
s hell
Seco nd
electron
s hell
+1
+2
H
He
+6
+7
+8
+9
C
N
O
F
+10
Ne
Figure 1.3. Electronic structures of common elements in organic polymers.
2
+1
+
+1
H
+1
+1
H
H2
+1
+6
+ 4
+1
+1
+6
+1
H
C
+1
CH 4
Figure 1.4. Formation of covalent bonds: H2 and CH4.
s
p
Energy
The energies of the electrons can take only certain, specific values (quantum theory). The
result of the quantum theory is a series of solutions referred to as wave functions and also called
atomic orbitals, which describe the probability of finding an electron at a certain location
(x,y,z) with respect to the nucleus under the precondition of a certain specific energy. According
to the Pauli exclusion principle, one or two electrons may occupy each atomic orbital. The
orbital with the lowest energy is the s orbital. The electron cloud of the s orbital is spherical
(Fig. 1.5). The next higher energy level is the p orbital, which consists of two symmetrical lobes
(Fig. 1.5). The d orbital consists of four lobes, all in a plane at angles of 90° to each other (Fig.
1.5). The first shell contains only the s orbital with maximum two electrons. The second shell
has one s and three p orbitals, each orbital having 2 electrons. The maximum number of
electrons in the second shell is thus 8. A covalent bond is formed when two atoms (e.g. H
atoms) approach each other. The atomic orbitals overlap and are fused into a molecular
orbital. The nuclei attract the electron cloud of the other atom, but very strong repulsive forces
act on the atoms when the two nuclei come very close. The energy is at a minimum at a certain
interatomic distance, i.e. the bond length (Fig. 1.6). Maximum overlap of the atomic orbitals
affords the strongest bond. The s orbitals with their spherical shape overlap less than the p
orbitals with their stronger directionality.
d
Interatomic distance
Figure 1.5. Schematic drawing of s, p and
d orbitals.
Figure 1.6. Bond energy as a function of
interatomic distance for H2.
The atomic orbitals of carbon are modified into hybrid atomic orbitals as they form
covalent bonds. The new set of orbitals (sp3 orbitals) is obtained by a combination of the s and
p orbitals into four orbitals pointing from the centre of a tetrahedron to its corners (Fig. 1.7). In
methane (CH4) the four sp3 hybrid orbitals of the carbon are combined with 1 s orbitals of
hydrogen to four molecular orbitals that are symmetric about the interatomic axes. Such bonds
are referred to as  bonds. The symmetry allows torsion about such bonds. The sp3 atomic
orbitals are only useful for bonding carbon to four separate atoms.
3
If bonding is required for only three atoms, one s and two p orbitals are used to form three
sp2 orbitals. The sp2 orbitals are symmetrically placed in a plane with an angle of 120° between
each orbital symmetry axis (Fig. 1.7). If two such atoms meet they form a  bond and the two
residual p orbital electrons form a so-called  bond. The  bond is not symmetrical with respect
to the interatomic axis and hence no torsion about a double bond can occur without breakage of
the covalent  bond. The two carbon atoms share four electrons in a double bond. Note that all
the atoms in ethene (ethylene) (C2H4) are located in a single plane. If a carbon atom is bonded
to only two other atoms, only the s and one p orbital electrons are used to generate two sp
hybrid orbitals (Fig. 1.7). The angle between their symmetry axes is 180°. The sp hybrid
orbitals form  bonds with another carbon and hydrogen in ethyne (C2H2). The two remaining p
orbital electrons of the carbon atom can combine with another carbon atom with the same set of
p orbital electrons to form two  bonds. Ethyne is a linear molecule with no torsional mobility
of the carbon-carbon triple bond.
109.28°
sp3
120°
sp2
180°
sp
Figure 1.7. Hybrid atomic orbitals in carbon:
sp3, sp2 and sp.
Figure 1.8. Energetics of main chain covalent
bond in organic polymers. Drawn after Kausch
(1987).
There are a few important concepts with regard to the potential energy of covalent bonds
that need to be explained (Fig. 1.8). The intrinsic binding energy (E) is the energy difference
between the ground state of the molecule and the valency states at infinite interatomic distance.
The dissociation energy (D) is smaller than E; the difference is due to the energy of vibrations
and the sum of the energies of promotion, hybridisation and polar and steric rearrangements to
attain the valency state. The activation energy for bond dissociation is denoted U0. The
dissociation energies of covalent bonds are typically between 300 and 500 kJ mol -1 (120-200RT
at 300 K). A very weak covalent bond is that between the oxygen atoms in organic peroxides (O-O-; D≈ 150 kJ mol-1) which is due to the electrostatic repulsion between the unshared
electron pairs of the oxygen atoms. The bonds become weaker as one proceeds down columns
in the periodic table (e.g. C-F> C-Cl> C-Br). Double bonds are stronger than single bonds. The
bond lengths are between 0.1 and 0.15 nm depending on the atoms involved: 0.11 nm (C-H),
0.135 nm (C=C) and ~0.15 nm (C-C; C-N; C-O).
1.3. Secondary bonds
The interaction between atoms of different molecules (often denoted secondary bonds) is
very important for the properties and the physical behaviour of polymers. The secondary bonds
can be divided into several categories and they are much weaker than the covalent bonds, a few
kJ mol-1 for London dispersion forces to ~50 kJ mol-1 for hydrogen bonds.
We need first to define a few concepts that are important for the further discussion. The first
concept is dipole moment. Two atoms linked with a covalent bond (it can be a single, double
or triple bond) share a number of electrons. The atom with the greater electronegativity attracts
4
the electrons more and it will become negatively charged (-q; note that q is smaller than the
charge of one electron). The other atom, which is more electropositive, will become positively
charged (+q). Note that the charges are equal but that they have different signs. The
electronegativity of an element can be judged from its position in the periodic table: it increases
when going from left to right in the periodic table and it decreases when going downwards in
the periodic table. The dipole moment (u) is simply the product of the charge and the distance
(l) between the charges, i.e. u=ql. The dipole moment is thus a vector. Table 1.1 presents a
number of bond moments relevant for polymers.
Table 1.1. Dipole moments of bonds in Debye units (1 D= 3.336 x 10-30 C m)a,b
C--H+
N--H+
O--H+
F--H+
a
0.4
1.31
1.51
1.94
C+-NC+-OC+-ClC+=O-
0.22
0.74
1.6
2.5
N+-ON+=O-
0.3
2.0
Data collected by Israelachvili (1992).
Symmetrical molecules like methane have dipole moments that point from the carbon atom
to the four hydrogen atoms (Fig. 1.9). The vector sum of the four vectors is zero and hence
methane is a non-polar molecule. Water has two strong dipoles, the vector sum is not zero (Fig.
1.9) and it is therefore a polar molecule. Polyethylene is an example of a non-polar polymer.
Each methylene unit has a weak dipole moment perpendicular to the chain axis (Fig. 1.9). The
net dipole moment is, however, zero for two adjacent methylene groups. Poly(vinyl chloride) is
a polar polymer because of its strong C-Cl dipole moment and the lack of symmetry.
Methan e
Water
Polyethylene
Figure 1.9. Drawings of molecules (methane, water and a repeating unit of polyethylene)
showing their net dipole moments (arrows)
Table 1.2. Electronic polarisabilities of bonds given in (40) Å3 a

C-C (aliphatic)
0.48
C-O
C=C (aromatic)
1.07
C=O
C=C
1.65
N-H
C-H
0.65
C-Cl
O-H
0.73
C-Br
a Data collected by Israelachvili (1992).
0.60
1.36
0.74
2.60
3.75
Polarisation is another important phenomenon. All atoms and molecules polarise when they
are subjected to an electric field. Non-polar molecules polarise by the displacement of the
electronic clouds relative to the positively charged nuclei under the influence of the electric
field. This leads to an induced dipole moment (uind), which is given by:
uind  E
(1.1)
where  is the polarisability and E is the electric field strength. Molecules that are charged or
have dipoles will induce dipoles in otherwise non-polar molecules. Table 1.2 shows a list of
bond polarisabilities. Evidently, double bonds ( and  bond) are more polarisable than  bonds
alone. The calculation of molecular polarisability is very easy in some instances; e.g. the
5
polarisability of methane is simply four times the polarisability of C-H. The additivity principle
fail for molecules that have bonds that are interdependent, e.g. molecules with delocalised
electrons as in benzene.
It was established since more than fifty years ago that all intermolecular forces are basically
electrostatic in origin. The Hellman-Feynman theorem states that, once the spatial
distribution of the electron clouds has been determined by solving the Schrödinger equation, the
intermolecular forces may be calculated by classical electrostatics. There is a very serious “but”
here, namely that the exact solution of the Schrödinger equation is not attainable, even for a
simple molecule like H2. This is the main reason why the secondary bonds are divided into
different categories despite the fact that they all have the same origin. The interaction between
two ions with charges Q1 and Q2, although not particularly relevant for organic polymers, is
described by the Coulomb law:
Ur  
Q1 Q2
4 0r
(1.2)
where U is the energy, r is the distance between the charges, 0 is the dielectric permittivity in
vacuum and  is the dielectric constant of the surrounding medium. The coulomb forces
(f=∂U/∂r) extend over long distances; these forces decay with respect to r-2.
The interaction between two permanent dipoles can be calculated on the basis of the
Coulomb law. It is important to note that both attractive and repulsive forces result from the
interaction and that the energy-distance relationship differs from the Coulomb law. The energy
also depends on the angles between the r vector and the two dipole moment vectors (1, 2) and
between the two dipole moments ():
U(r,1, 2 , )  
u1u2
2 cos 1 cos  2  sin 1 sin 2 cos  
4 0 r 3
(1.3)
When the dipoles are separated, particularly when they are shielded in a medium with high
dielectric constant, the interaction energy becomes smaller than the thermal energy (RT) and the
dipoles can rotate freely. In this case, often referred to as the Keesom interaction, the energy
(UDD) shows a more rapid increase with r:
UDD r   
u12 u22
(1.4)
34 0  kTr6
2
The interaction between permanent dipoles and induced dipoles (of molecules that are
originally non-polar), often referred to as the Debye interaction, is described by the following
equation:
UDIDr   
u12 0
(1.5)
4 0 2 r 6
where 0 is the polarisability of the interacting group (induced dipole).
Finally, there is another type of force which acts between all atoms and molecules, even the
neutral atoms like the rare gases and hydrocarbons. These forces have been given many
different names: dispersion forces, London forces, charge-fluctuation forces and induceddipole-induced-dipole forces. Dispersion forces make a very important contribution to the total
van der Waals force, which is thus the sum of the dispersion forces and the forces originating
from interactions between two permanent dipoles, and between permanent and induced dipoles.
Dispersion forces are quantum mechanical in origin, but they can be explained more intuitively
by simple electrostatics. The electrons in an atom (e.g. helium) are moving around their
nucleus. At any given time, there will be a small dipole moment (this will average out to zero
over a longer time period), which will generate a small electric field that will in turn induce a
6
dipole moment in a nearby atom. The interaction between these two temporary dipoles gives
rise to an attractive force between the two atoms. London (1937) derived an expression for the
energy (UDISP) of a bond between two identical atoms:
3 2
 0h
UDISP r    4
4 0 2 r 6
(1.6)
where h is the Planck constant and  is the orbiting frequency of the electron. London also
derived an expression for two dissimilar atoms and it has the same distance dependence as in
eq. (1.6), i.e. UDISP is proportional to r-6. The strength of the dispersion forces is of the order of
one to a few RT (<5 kJ mol-1) at room temperature.
It is striking that eqs. (1.4-1.6) express the same distance dependence,U  r-6. The total van
der Waals energy (UVDW) is the sum of the three contributions:
UVD W  UDD UDID  UDISP  CVD W / r 6
(1.7)
A few important facts can be stated about the van der Waals forces. The dispersion forces
are generally dominant. However, all three terms in eq. (1.7) make contributions to UVDW in
polar systems, whereas for unpolar systems only the third term contributes. Hence, the van der
Waals energies are greater for polar molecules than for non-polar molecules. The van der Waals
energy of A-B can be calculated as the geometric mean value of A-A and B-B. This simple
method is not however valid for interactions involving highly polar molecules e.g. water.
Equations (1.4-1.7) suggest that the energy would be at a minimum for r= 0, but this is
obviously not correct. At very small interatomic distances the electron clouds of atoms overlap
and very strong repulsive forces arise. These forces are sometimes referred to as exchange
repulsion, hard core repulsion or steric repulsion. Atoms behave in a sense like table tennis
balls with a certain radius, which is obvious from X-ray diffraction data. This is expressed in
the so-called van der Waals radius. The repulsive potential (UR) is conveniently described by
the power-law expression:
UR r   A r n
(1.8)
where A is a constant and n is an integer between 9 and 16. The well-known Lennard-Jones
potential brings together the repulsive (with n= 12) and the attractive potential functions:
Ur   A r12  B r 6
(1.9)
where A and B are constants. Figure 1.10 shows schematically the full pair potential function as
a function of the interatomic distance. The slope is very steep indeed for r-values less than the
bond length.
These potential functions are used as input data for molecular dynamics (MD) simulation.
A detailed description of MD simulation is presented in Chapter 2. In this case, the electrostatic
interaction is described by the Coulomb law:
UQ 
Q1Q2
4r
(1.10)
where the dielectric constant () is dependent on r; for very short interatomic distances it
approach unity and it gradually increases with increasing r to finally reach the dielectric
constant of the material.
Alternatively, the electrostatic interaction may be described by the mutual induction method.
The van der Waals interaction is described by the Lennard-Jones potential [eq. (1.9)]. Dipoledipole interaction is thus considered by applying the Coulomb law directly.
7
H
U
H
O
H
O
H
r
Figure 1.10. Energy as a function of
interatomic distance according to the
Lennard-Jones potential.
Figure 1.11. Hydrogen bond established
between two water molecules.
Hydrogen bonds are exceptionally strong intermolecular bonds. They are developed
between hydrogen covalently bound to a strongly electronegative atom (e.g. O, N, F and Cl) and
an electronegative atom of similar type. It is now accepted that the hydrogen bond is
predominantly a strong electrostatic interaction. The strength of the hydrogen bond is between
10 and 50 kJ mol-1, which is greater by an order of magnitude than the van der Waals bonds but
smaller than the strength of the covalent bonds. Hydrogen bonds are very important for
biological systems. The DNA helices are stabilised by hydrogen bonds. The structure and the
very high heat of vaporisation of water are direct consequences of the strong hydrogen bonds
(Fig. 1.11). The intramolecular O-H distance is 0.10 nm. The intermolecular O-H distance is
only 0.176 nm which is much shorter than the sum of the two van der Waals radii, 0.26 nm. The
energy of a hydrogen bond is often described by the 10-12 potential:


UH r,   C r 12  D r10 cos 4 
(1.11)
where C and D are constants and  is the angle between the hydrogen bond and the covalent
bond between the hydrogen and the attached atom. The hydrogen bond has three features that
make it different from the van der Waals bonds: (a) high strength; (b) strong directional
dependence, which is evident from the cosine factor in eq. (1.11); (c) short action range, which
is evident from the high exponent (n= 10) of the attractive term in eq. (1.11).
1.4. Configuration and conformation
The term configuration refers to the ‘permanent’ stereostructure of a polymer. The
configuration is defined by the polymerisation method. A change in configuration requires the
rupture of covalent bonds. Different configurations exist in polymers with stereocentres
(tacticity) and double bonds (cis and trans forms). A polymer with the constitutional repeating
unit –CH2-CHX- exhibits two different stereoforms (configurational base units) for each
constitutional repeating unit (Fig. 1.12). The following convention is adopted to distinguish
between the two stereoforms: One of the chain ends is first selected as the near one. The
asymmetric carbon atom (the one with the attached X atom (group of atoms)) is then placed so
that its H- and X-linkages are pointing upwards. The term dextro (d) form is then given to the
arrangement with the X group pointing to the right (from the observer at the near end). The levo
(l) form is the mirror-image of the d form, i.e. the X-group in this case points to the left. This
convention is not however absolute. If the near and far chain ends are reversed, i.e. if the chain
is viewed from the opposite direction, the d and l notation is reversed for a given chain. When
writing a single chain down on paper, the convention is that the atoms on the left-hand side of
the paper are assumed to be nearer to the observer than the atoms on the right-hand side.
Tacticity is an indication of the orderliness of the succession of configurational base units in
the main chain of a polymer molecule. An isotactic polymer is a regular polymer consisting of
only one species of configurational base unit, i.e. only the d or the l form (Fig. 1.13). These can
be converted into each other by simple rotation of the whole molecule. Thus, in practice there is
no difference between an all-d chain and an all-l chain. A small mismatch in the chain ends
8
does not alter this fact. A syndiotactic polymer consists of an alternating sequence of the
different configurational base units, i.e. ...dldldldldldl... (Fig. 1.13). An atactic polymer has
equal numbers of randomly distributed configurational base units.
near
end
H
H
C
far
end
C
H
X
d (right-hand) form
X
H
far
end
C
C
H
near
end
H
l (left-hand) form
Figure 1.12. Configurational base units of a polymer with the constitutional repeating unit CH2-CHX-. The "X" is an atom or a group of atoms different from hydrogen.
Is otactic chain
Syndiotactic chain
Figure 1.13. Regular tactic chains of [-CH2-CHX-]n, where X is indicated by a filled circle
Carbon-13 nuclear magnetic resonance (NMR) spectroscopy is the most useful method to
assess tacticity. C-13 NMR makes it is possible to assess different sequential distributions of
adjacent configurational units that are called dyads, triads, tetrads and pentads. The two
possible dyads are shown in Fig. 1.14. A chain with 100% meso dyads is perfectly isotactic
whereas a chain with 100% racemic dyads is perfectly syndiotactic. A chain with a 50/50
distribution of meso and racemic dyads is atactic. Triads consist of three adjacent constitutional
repeating units. The following triads are possible: mm, mr and rr (where meso=m; racemic=r).
Tetrads contain four repeating units and the following six sequences are possible: mmm, mmr,
mrm, mrr, rmr and rrr. Sequences with a length of up to five constitutional repeating units, socalled pentads, can be distinguished by C-13 NMR. The following ten different pentads are
possible: mmmm, mmmr, mmrm, mmrr, mrrm, rmmr, rmrm, mrrr, rmrr and rrrr.
Polymers with double bonds in the main chain, e.g. polydienes, show different
stereostructures. Figure 1.15 shows the two stereoforms of 1,4-polybutadiene: cis and trans.
The double bond is rigid and allows no torsion and the cis and trans forms are not readily
transferable into each other. Polyisoprene is a well-known example: natural rubber consists
almost exclusively of the cis-form whereas gutta-percha is composed of the trans form. Both
polymers are naturally abundant, and this shows that stereoregularity was achieved in nature
much earlier than the discovery of coordination polymerisation by Ziegler and Natta. The
polymerisation of diene monomers may involve different addition reactions (Fig. 1.16). The 1,2
9
addition yields a polymer with the double bond in the pendant group whereas 1,4 addition gives
a polymer with the unsaturation in the main chain.
mes o
Cis
racemic
Trans
Figure 1.14. Dyads of a vinyl polymer with the Figure 1.15. Stereoforms of 1,4-polybutadiene
constitutional repeating unit -CH2-CHX, where showing only the constitutional repeating unit
with the rigid central double bond
the X-group is indicated by a filled circle.
Vinyl polymers (-CH2-CHX-) may show different configurations with respect to the head
(CHX) and tail (CH2), viz. head-to-head i.e. -CHX bonded to CH2-, and head-to-head--tail-totail, i.e. -CHX bonded to -CHX followed by –CH2 bonded to -CH2 (Fig. 1.17).
1,4 addition:
1,2 addition:
R
1
2 3
4
CH 2=CH-CH=CH 2
R-CH 2-CH=CH-CH 2
R
1
2
3
4
CH 2=CH-CH=CH 2
R-CH 2-CH-CH=CH 2
Figure 1.16. Different additions of radicals to butadiene
Figure 1.17. Head-to-tail configuration (upper chain) and a chain with a head-to-head junction
followed by a tail-to-tail sequence (lower chain)
The configurational state determines the low-temperature physical structure of the polymer.
A polymer with an irregular configuration, e.g. an atactic polymer, will with very few
exceptions, never crystallise and it freezes to a glassy structure at low temperatures, whereas a
polymer with a regular configuration, e.g. an isotactic polymer, may crystallise at some
10
temperature to form a semi-crystalline material. There is a spectrum of intermediate cases in
which crystallisation occurs but to a significantly reduced level. This topic is further discussed
in Chapters 5 and 7.
A conformational state refers to the stereostructure of a molecule defined by its sequence of
bonds and torsion angles. The change in shape of a given molecule due to torsion about single
() bonds is referred to as a change in conformation (Fig. 1.18). Double and triple bonds,
which in addition to the rotationally symmetric sigma bond also consist of one or two
rotationally asymmetric  bonds, permit no torsion. There are only small energy barriers, from a
few to 20 kJ mol-1, involved in these torsions. The conformation of polymers is the subject of
Chapter 2. The multitude of conformations in polymers is very important for the properties of
polymers.
+120°
Figure 1.18. Examples of conformational states of C7H16. The right-hand form is generated from
the left-hand form by 120° torsion about the  bond indicated by the arrow.
The rapid change in conformation is responsible for the sudden extension of a rubber
polymer on loading and for the extraordinarily high ultimate extensibility of the network. This
is the topic of Chapter 3. The high segmental flexibility of the molecules at high temperatures
and the low flexibility at low temperatures are a very useful signatures of polymers.
1.5. Homopolymers and copolymers
A homopolymer consists of only one type of constitutional repeating unit (A). A
copolymer, on the other hand, consists of two or more constitutional repeating units (A,B, etc).
Several classes of copolymers are possible: block copolymers, alternating copolymers, graft
copolymers and statistical copolymers (Fig. 1.19).
Homopolymer
Block-copolymer
Graft-copolymer
Alternating copolymer
Statis tical copolymer
Figure 1.19. Homopolymer and different classes of copolymers. Unit A: ; unit B: 
11
The different copolymers with constitutional repeating units A and B are named according
to the source-based nomenclature rules as follows: unspecified type: poly(A-co-B); statistical
copolymer: poly(A-stat-B); alternating copolymer: poly(A-alt-B); graft copolymer: poly(Agraft-B). The major constituent (A) is given first. Note that the constitutional repeating unit of
the backbone chain of the graft copolymer is specified first.
A random copolymer is a special type of statistical copolymer. The probability of finding a
given constitutional repeating unit at any given site in a random copolymer is independent of
the nature of the adjacent units at that position. A statistical copolymer may however obey
known statistical laws, e.g. Markovian statistics. The term random copolymer is occasionally
used for polymers with the additional restriction that the constitutional repeating units are
present in equal amounts. The notation for a random copolymer is poly(A-ran-B).
Copolymerisation provides a route for making polymers with special, desired property profiles.
A statistical copolymer consisting of units A and B, for instance, has in most cases properties
intermediate between those of the homopolymers (polyA and polyB). An important deviation
from this simple rule arises if either polyA or polyB is semi-crystalline. The statistical
copolymer (poly(A-stat-B)) is for most compositions fully amorphous. Block and graft
copolymers form in most cases a two-phase morphology and the different phases exhibit
properties similar to those of the respective homopolymers. Di-block (A-B) and tri-block (AB-A) copolymers are often made by so-called living polymerisation (section 1.9). These
polymers have found applications as thermoplastic elastomers and as compatibilisers to
increase the adhesion between the phases in polymer blends. Terpolymers consist of three
different repeating units: A, B and C.
1.6. Molecular architecture
Molecular architecture deals with the shape of a polymer molecule. Examples of polymers
with different molecular architectures are shown in Fig. 1.20.
Figure 1.20. Schematic representation of structures of polymers with different molecular
architectures.
A short-chain branch has an oligomeric nature whereas a long-chain branch is of
polymeric length. A network polymer consists of many inter-connected chain segments and
many differents molecular paths exist between any two atoms. A dendrimer (exact structure)
and a hyperbranched (dendritic polymer with structural irregularities) polymer consist of a
constitutional repeating unit including a branching group. The number of branches increases
according to a power law expression with the number of the "generation" of the polymer. The
molecular architecture is important for many properties. Short-chain branching tends to reduce
crystallinity. Long-chain branches have profound effects on the rheological properties. Ladder
polymers are typically thermally stable and mechanically strong. Dendrimers consist of
molecules with an approximately spherical shape, and it has been shown that their melt
viscosity is significantly lower than that of their linear analogue with the same molar mass.
Crosslinked polymers are thermosets, i.e. they do not melt. They also show little creep under
constant mechanical loading.
12
1.7. Common polymers
A list of common polymers with their constitutional repeating units is presented in Table
1.3. Most polymers are named polyx. If ‘x’ is a single word, the name of the polymer is written
out directly, as in the case of polystyrene. However, if ‘x’ consists of two or more words,
parentheses should be used, as in the case of poly(methyl methacrylate). There are two different
systems for naming polymers. The structure-based names are rigorous but seldom used in
practice. They are simply given as poly(constitutional repeating unit) and the rules of
nomenclature for the constitutional repeating unit are no different from those of any other
organic substance. The source-based names attach ‘poly’ to the name of the monomer.
Polystyrene is a source-based name. Its structure-based equivalent is poly(1-phenylethylene).
Polyethylene (source-based name) is denoted polymethylene according to the structure-based
system. The names of polymers treated in this book are almost exclusively related to the sourcebased system. Most polymers have abbreviated names, which are also presented in Table 1.3. It
is clearly acceptable to use abbreviations in scientific papers and technical reports, but the full
name of the polymer should be given the first time it appears in the text. There are numerous
other names of polymers which are frequently used. ‘Nylon’, ‘Kevlar’ and ‘Vectra’ are a few
well-known examples. The source-based or structure-based names are preferred over these truly
trivial names.
Table 1.3. Constitutional repeating units of common polymers
Polymer name, abbreviation
Polyethylene, PE
Constitutional repeating unit
Polypropylene, PP
Poly(vinyl chloride), PVC
Polystyrene, PS
Poly(vinyl alcohol), PVAL
Poly(vinyl acetate), PVAC
13
Poly(4-methyl-1-pentene)
Poly(1,4-butadiene), PBD
Polyisoprene
Poly(dimethyl siloxane), PDMS
Polyacrylonitrile, PAN
H
H
C
C
H CN
Poly(methyl methacrylate), PMMA
Poly(alkyl methacrylate)s
Poly(alkyl acrylate)s
Poly(ethylene terephthalate), PETP
O
Poly(butylene terephthalate), PBTP
14
H
H
O
O
C
C O
C
C
H
H
Polytetrafluoroethylene, PTFE
Polyamide 6, PA 6
F
F
C
C
F
O
F
H
C (CH2) 5 N
Polyamides n, PA n
Polyamide 6,10, PA 6,10
Polyoxymethylene, POM
Poly(ethyleneoxide), PEO
Poly(vinylidene dichloride), PVDC
Poly(vinylidene difluoride), PVDF
1.6. Molar mass
The enormous size of polymer molecules gives them unique properties. Figure 1.21 shows
the influence of molar mass on the melting point of polyethylene.
Low molar mass substances (oligomers) show a strong increase in melting point with
increasing molar mass, whereas a constant melting point is approached in the polymer molar
mass range. Other polymers show a similar behaviour. Properties such as fracture toughness
and Young's modulus show a similar molar mass dependence with almost constant values being
approached in the high molar mass region. The polymer properties are often obtained in the
molar mass range from 10 000 to 30 000 g mol-1. Rheological properties like melt viscosity
show a progressive strong increase with increasing molar mass even at high molar masses (see
Chapter 6). High molar mass polymers are therefore difficult to process but they yield final
products with very good mechanical properties.
There is currently no polymerisation method available that yields a polymer with molecules
of a single size. Variation in molar mass among the different molecules is characteristic of all
synthetic polymers. The molar mass distribution ranges over three to four orders of magnitude
for many polymers. Monodisperse polymers can however be found in the nature. A full
representation of the molar mass distribution is currently achieved only with size exclusion
chromatography, naturally with a number of experimental limitations. Other methods yield
different averages.
15
Melting point (°C)
150
100
50
0
-50
100
1000
10000
100000
Molar mass (g mol -1)
Figure 1.21. Molar mass dependence of the equilibrium melting point of oligo- and
polyethylene. Drawn after data collected by Boyd and Phillips (1993).
The most commonly used averages are defined as follows. The number-average is given by:
Mn 
 N iM i
i
 Ni
(1.12)
  n iM i
i
i
where Ni is the number of molecules of molar mass Mi, and ni is the number fraction of those
molecules. The mass-average is given by:
Mw 
 Ni M i2
i
 Ni Mi

 Wi Mi
i
i
 Wi
(1.13)
  wi Mi
i
i
where Wi is the mass of the molecules of molar mass Mi, and wi is the mass fraction of those
molecules. The z-average is given by:
Mz 
 N i Mi 3
(1.14)
i
 N i Mi2
i
The viscosity-average is given by:
(1.15)
1
 N M 1a a
i i


Mv   i

  N i Mi 
 i

where a is the exponent in the Mark-Houwink equation (see eq. (1.18). It takes values between
0.5 and 0.8 depending on the combination of polymer and solvent. The viscosity average is
obtained by viscometry. The intrinsic viscosity [] is given by:


(1.16)
  o
 lim




c 0
 co 
16
where c is the concentration of polymer in the solution, o is the viscosity of the pure solvent
and  is the viscosity of the solution. The viscosities are obtained from the flow-through times
(t and to) in the viscometer:
 t

o to
(1.17)
and the intrinsic viscosity is converted to molar mass M according to the Mark-Houwink
viscosity equation (Mark, 1938; Houwink, 1940):
 KM a
(1.18)
where K and a are the Mark-Houwink parameters. These constants are unique for each
combination of polymer and solvent and are tabulated in Brandrup et al. (1999). It is well
established that for linear, flexible-chain polymers under special conditions of temperature
(usually known as the theta conditions; see Chapters 2 and 4 for details) the exponent a is equal
to 0.5. The Mark-Houwink parameters given are in most cases based on measurements on
samples with a narrow molar mass distribution. If eq. (1.18) is used for a polymer sample with a
broad molar mass distribution, the molar mass value obtained is indeed the viscosity average.
The Mark-Houwink equation is sometimes referred to as the Mark-Houwink-Sakurada
equation. Occasionally this equation is also denoted the Staudinger-Mark-Houwink equation.
Staudinger and Nodzu (1930) postulated that the intrinsic viscosity of a polymer solution was
proportional to its molar mass. The Staudinger equation was capable of fitting viscosity data of
solutions of rather low molar mass polymers. Mark (1938) and Houwink (1940) proposed based
on a wide range of experimental data the validity of eq. (1.18), often with an exponent a
between 0.5 and 0.8 for linear flexible-chain polymers. Theoretical work by Kuhn (1934)
indicated that the intrinsic viscosity is proportional to the square root of the molar mass under
theta conditions (a=0.5) and that the exponent a is greater than 0.5 under good solvent
conditions.
All these averages are equal only for a perfectly monodisperse polymer. In all other cases,
the averages are different: Mn  M v  Mw  Mz . The viscosity average is often relatively close
to the weight average.
Let us now show that the mass average is always greater than the number average:
 N i Mi  Mn   0
2
(1.19)
i
 N i Mi   N iM n  2  N i Mi M n  0
2
i
2
i
i
If this last equation is divided by ∑Ni, the following expression is obtained:
 Ni Mi2
i
 Ni
 Mn 2 
i
 Ni Mi2
i
 Ni
2  N i Mi Mn
i
 Ni
0
i
 Mn 2  2Mn 2  0
i
 Ni Mi2
i
 Ni
(1.20)
 M n2
i
The following simplification leads to the desired result:
17
 Ni Mi2
i
 Ni
i
1

 Mn 
Mn
 N i Mi 2
i
 Ni
i

 Ni
i
 N i Mi
 Mn
i
and
Mw  M n
(1.21)
Equality occurs only when a sample is truly monodisperse, i.e. when all molecules are of the
same molar mass. It can be shown that the width of the molar mass distribution, expressed as
the standard deviation (), is related to the ratio Mw Mn (polydispersity index) as follows:

Mn

Mw
1
Mn
(1.22)
The standard deviation takes the value zero when Mw Mn =1. The polydispersity index takes
a high value for a sample with a broad molar mass distribution, i.e. a high  value.
There is a large range of methods that can be used for the assessment of molar mass (Table
1.4). Some of the methods require no calibration and they may be referred to as "absolute",
whereas other methods are relative and require calibration with samples of known molar mass.
The concentration of end groups in a given sample provides direct information about the
number of polymer molecules per gram, i.e. the number average molar mass. Infra-red
spectroscopy, NMR and titration of acid or hydroxyl end groups in polyesters have been used
for end-group analysis. One drawback of these methods is that they can only be used on low
molar mass polymers ( Mn ≤ 25 000 g mol-1). Very special techniques using radioactive labelling
have been used for the assessment of polymers with a number average molar mass greater than
1 000 000 g mol-1
Colligative properties are those properties of a solution which depend only upon the number
of solute species present in a certain volume, and not on the nature of the solute species. It is
thus logical that measurement of the colligative properties makes it possible to determine Mn .
The important colligative effects that are used for molar mass determination are boiling point
elevation (ebulliometry), lowering of vapour pressure (vapour-pressure osmometry), freezing
point depression (cryoscopy) and osmotic pressure (membrane osmometry). Ebulliometry and
cryoscopy were earlier restricted to samples with low molar masses, typically less than
10 000 mol-1, but more recent developments of the instrumentation enable the determination of
polymers with number averages of several hundred thousands. The number average molar mass
is in the cases of ebulliometry or cryoscopy obtained according to the following general
equation:
V1 RTo2  1
Tx 


 


 c c 0 
 Hx  M n
(1.23)
where ∆Tx is the change in transition temperature (freezing point or boiling point), c is the
concentration of polymer in the solution, V1 is the molar volume of the solvent, R is the gas
constant, T0 is the transition temperature for the pure solvent and ∆Hx is the transition enthalpy.
Membrane osmometry is useful for samples of Mn ≤ 1 000 000 g mol-1 and the number average
molar mass is obtained from the following expression:
 
RT
  
c c 0 M n
(1.24)
18
where  is the osmotic pressure. Further details about the theoretical basis for this equation are
presented in Chapter 4.
Table 1.3. Experimental techniques for molar mass determination
Method
End group analysis
Result
Mn
Comments
Absolute method,
restricted to low M
Colligative methods:
ebulliometry, cryoscopy
and osmometry
Mn
Absolute methods
Viscometry
Mv
Relative method,
easy to use
Light scattering
Mw
Absolute method
Ultracentrifugation
Mw ; Mz
Absolute method,
requires long time
Size exclusion
chromatography (SEC)
Molar mass distribution
Relative method,
requires calibration
MALDI-TOF-MS
Molar mass distribution
Absolute method,
Restricted to
M<300 000 g mol-1
Size exclusion chromatography (SEC), sometimes referred to as gel permeation
chromatography (GPC), gives the whole molar mass distribution. A dilute solution of the
polymer is injected into a set of packed columns. The flow-through times of the different molar
mass species depend on their hydrodynamic volumes, i.e. on the size of the molecular coil.
Large molecules have little accessibility to the pores of the gel and they are eluated after only a
short period of time. Smaller molecules can penetrate into a much larger volume of the porous
gel and they remain in the column for a longer period of time. The concentration of polymer
passing through the column is recorded continuously as a function of time by measurement of
refractive index, ultraviolet- or infra-red absorption. SEC is a relative method. Calibration with
narrow molar mass fractions of the polymer studied is necessary. It is also possible to use
standards of another polymer and then by calculation, using the Mark-Houwink parameters of
the polymers, to convert the molar mass scale of the calibrant polymer to that of the polymer
studied. This procedure is known as "universal calibration". The hydrodynamic volume is
proportional to the product  M . If calibration is made with polymer (calibrant index: 2), the
universal calibration procedure is carried out according to eq. (1.25), derived as follows:
1 M1  2 M2
K1 M11 a1  K 2 M21 a 2
1
K
1 a 1
1a
M1   2 M2 2 


K1

(1.25)
where the indices 1 and 2 refer to the polymer studied and the calibrant polymer. Direct
determination of the molar mass in the detector cell is nowadays possible by low angle laserlight scattering (LALLS).
Both ultracentrifugation and light scattering are historically important absolute methods
for determining the molar mass. Both methods are capable of assessing very high molar mass
samples. Details about the light scattering method are given in Chapters 2 and 12.
19
Matrix-assisted laser desorption ionisation time-of-flight mass spectrometry (MALDITOF-MS) is a relatively new absolute method for determining the molar mass of low to medium
molar mass polymers (≤ 300 000 g mol-1). The method provides information about the whole
molar mass distribution. The polymer is dissolved in a solvent and stabilised with a matrix (e.g.
a silver salt). The solvent is evaporated, the polymer is ionised with laser pulses and the
polymer ions are detected in a mass spectrometer.
An alternative way of describing the molecular size distribution is by using the degree of
polymerisation (X), which is related to the molar mass (M) as follows:
X
M
Mrep
(1.26)
where Mrep is the molar mass of the constitutional repeating unit. It is useful to define the same
kind of averages for X as is used for molar mass. Different polymerisation methods yield
polymers with different molar mass distributions. Flory originally derived the following chain
length distribution for step-growth polymerisation (see Section 1.9):
1
ni 
Xn
 1 i 1

1  X 


n 
(1.27)
where ni is the number fraction of molecules of X = i and X n is the number-average of the
degree of polymerisation. This distribution is called the most probable (or Schultz-Flory)
distribution. For chain-growth radical polymerisation (see section 1.9) with termination
exclusively through recombination (see section 1.9), the X distribution is described by the
Schultz distribution.

i


4i
 1

ni 
Xn 12 1 2 
 Xn 1 
(1.28)
1.9. Polymerisation
The polymerisation process can in simple terms be divided into step-growth and chaingrowth polymerisation. A typical example of step-growth polymerisation is the formation of a
polyester from a hydroxy-carboxylic acid.
O
O
HO R C OH + HO R C OH
O
O
HO R C O R C OH + H2O
O
O
O
HO R C OH + HO R C O R C OH
O
O
O
HO R C O R C O R C OH + H2O
The kinetics of this polymerisation is not appreciably affected by the size of the reacting
species. The number of reactive groups, in this case hydroxyl groups and acid groups, decreases
with increasing length of the molecules. At any given moment, the system will consist of a
mixture of growing chains and water. One problem is that all the reactions are reversible, with
equilibrium being established for each reaction. The consumption of reactive groups and the
formation of a high molar mass polymer require the removal of water from the system. The
degree of polymerisation X n is in the case of equal molar amounts of acid and alcohol groups
equal to 1/(1-p), where p is the degree of conversion of reactive groups. The following Xn
values are obtained for the following conversions: p= 0.10, X n = 1.1; p= 0.90, X n = 10; p= 0.99,
20
X n = 100; p= 0.999, X n = 1000; p= 0.9999, X n = 10 000. Polymers with high molar mass can
thus only be obtained by running the reaction to a very high degree of conversion of the reactive
groups.
Step-growth polymerisation is involved in the formation of e.g. polyesters and polyamides.
Different techniques are available for obtaining a high degree of conversion and high molar
mass. If an acid chloride is used instead of the carboxylic acid, HCl is formed instead of water.
The former is more easily removed from the system and higher yields and higher molar masses
are obtained. The long reaction time needed to reach a high conversion is a considerable
disadvantage with step-growth polymerisation. Polymers with different molecular architectures
can be made using monomers of different functionality (Fig. 1.22). Tri-functional monomers
yield branched and ultimately cross-linked polymers.
n A-R-B
......-A-R-B-A-R-B-A-R-B-.......
+ n B-R-B
......-A-R-A-B-R-B-A-R-A-.......
.................
...
n A-R-A
A
B
3n/2 A-R-A + n B-R-B
R
A
B
......-A-R-A-B-R-B-A-R-A-.......
Figure 1.22. Different molecular architectures arising from different combinations of monomers
of different degrees of functionality.
Chain-growth polymerisation involves several consecutive stages: initiation, propagation
and termination. Each chain is individually initiated and it grows very rapidly to a high molar
mass until its growth is terminated. At a given time, there are essentially only two types of
molecules present: monomer and polymer. The number of growing chains is always very low.
Chain-growth polymerisation is divided into several subgroups depending on the propagating
site: radical, anionic, cationic or coordination polymerisation. A generalised scheme for
radical polymerisation is shown below.
The initiation is often accomplished by thermal- or radiation-initiated degradation of an
organic peroxide or similar unstable compound (initiator; denoted I). Free radicals are
generated which attack the double bond of the unsaturated monomer (typically a vinyl
monomer: CH2=CHX) and the radical centre is moved to the end of the "chain".
.
I 
 2R
.
R + M 
 RM
.
Propagation is a chain reaction involving very rapid addition of monomer to the radical
chain.
.
RM + M 
 RMM
.
.
.
RMM + M 
 RMMM etc.
It is possible that a propagating chain radical abstracts a hydrogen from an adjacent polymer
molecule and that the reactive site is moved from one polymer molecule to another (chain
transfer). This leads in most cases to the formation of a molecule with a long-chain branch.
The chain transfer reaction may also be intra-molecular which is the well-known ‘back-biting’
21
mechanism giving short-chain branches (primarily butyl branches) in high-pressure polymerised
polyethylene. These branches, typically at a concentration of one in hundred main chain carbon
atoms, reduces the crystallinity from 70-80% (linear polyethylene) to 50% in the branched
polyethylene produced at high pressure. Poly(vinyl chloride) is another polymer made by
radical polymerisation that have short-chain branches due to intra-molecular chain transfer.
R1
X
CH2 C
H
X
CH2 C
R2
+
R2
X
CH2 C
H
+nM
R3
R2
R3
R1
X
CH2 C
R4
X
CH2 C H + R2
H
X
CH2 C
R3
R3
The propagation is stopped either by combination or by disproportionation:
R1 M
R1 CH2
+
MR 2
X
C
H
+
R1 MMR 2
H
C CH2 R2
X
(combination)
R1 CH2
X
CH
H
+
H
C CH2 R2
X
(disproportionation)
Both anionic and cationic polymerisation includes both initiation and chain-wise
propagation but with one important difference from radical polymerisation: in neither case is
there any natural termination reaction. In both cases, it is possible to achieve the conditions for
living polymerisation, where all chains are constantly growing until all monomer is consumed
and the molar mass distribution of the resulting polymer is narrow. It is also possible to add a
new monomer and to prepare exact block-copolymers. The presence of small traces of an
impurity, e.g. water, leads to chain transfer reactions and termination of the growing polymer
chains. This is very different from radical polymerisation, which is very sensitive to the
presence of oxygen (O2) but essentially unaffected by traces of water.
Karl Ziegler (1955) and Guilio Natta (1955) discovered coordination polymerisation in the
1950s. This technique makes it possible to produce stereoregular polymers like isotactic
polypropylene and linear polyethylene. A Ziegler-Natta catalyst requires a combination of the
following substances: (i) a transition metal compound from groups IV -VIII, (ii) an
organometallic compound from groups I-III, and (iii) a dry, oxygen-free, inert hydrocarbon
solvent. Commonly used systems have involved aluminium alkyls and titanium halides. The
polymerisation is often rapid and exothermic, requiring external cooling. The polymer normally
precipitates around the catalyst suspension. The initial work of Ziegler and Natta involved
unsupported catalysts whereas many of the commercial polymers made by coordination
polymerisation are today accomplished by supported catalysts. From a mechanistic point of
view they are of the same class as the Ziegler-Natta catalysts. The pioneering work was due to
Hogan and Banks (1958) using activated chromic oxides on silica supports. This development
led to the polymerisation of linear polyethylene and linear low-density polyethylene
(copolymers of ethylene and higher 1-alkenes).
The pioneering work of Kaminsky and Sinn (1980) has led to the development of a new
class of catalysts often referred to as metallocenes. They consist of a bent Ti, Zr or Hf complex
with two cyclopentadienyl ligands and two halide or alkyl ligands). The metallocene is often
combined with a cocatalyst. The metallocenes consist of single kind of active site for
polymerisation, which offer some distinct advantages over the multi-site Ziegler catalysts. The
most important feature of the metallocene catalysts is thus the control of polymer structure and
properties by variation of catalyst structure, allowing the production of new polymers,
unavailable by Ziegler catalysts. The metallocene technology is currently very important for the
industry and new polyolefins with controlled molar mass distribution, stereostructure and
comonomer distribution will enter the market.
22
1.10. Thermal transitions and physical structures
It is useful to divide the polymers into two main classes: the fully amorphous and the
semicrystalline. The fully amorphous polymers show no sharp crystalline Bragg reflections in
the X-ray diffractograms taken at any temperature. The reason why these polymers are unable
to crystallise is commonly their irregular chain structure. Atactic polymers, statistical
copolymers and highly branched polymers belong to this class of polymer. Chapters 3, 5 and 6
present further details.
The semicrystalline polymers show crystalline Bragg reflections superimposed on an
amorphous background. Thus, they always consist of two components differing in degree of
order: a crystalline component composed of thin (10 nm) lamella-shaped crystals and an
amorphous component. The degree of crystallinity can be as high as 90% for low molar mass
linear polyethylene and as low as 5% for poly(vinyl chloride). Chapters 7 and 8 deal with the
semicrystalline polymers.
A third, more recently developed group of polymers, is the liquid-crystalline polymers with
their rigid-rod molecules packed in a parallel fashion (orientational order). They are thus
intermediates between the amorphous and the semicrystalline polymers. A detailed discussion
of liquid crystalline polymers is given in Chapter 6.
The differences in crystallinity lead to differences in physical properties. Figure 1.23 shows,
for example, the temperature dependence of the relaxation modulus for different polystyrenes.
The relaxation modulus is defined as the stress divided by the strain as recorded after 10 s of
constant straining, a so-called stress relaxation experiment.
10
I
Se micrystalline
Log E (Pa)
8
II
6
4
Amorphous
III
Crosslinked
IV
V
Low M
High M
2
50
100
150
200
250
Te mpe rature (°C)
Figure 1.23. The logarithm of the relaxation modulus (10 s) as a function of temperature for
semicrystalline (isotactic) polystyrene and fully amorphous (atactic) polystyrene in three
"versions": crosslinked and uncrosslinked low and high molar mass uncrosslinked. Drawn after
data from Tobolski (1960).
At 100°C, the fully amorphous polystyrenes show a drop in modulus by a factor of 1000.
This "transition" is called the glass transition. All fully amorphous polymers show a similar
modulus-temperature curve around the glass transition temperature (Tg). The material is said to
be "glassy" at temperatures below Tg (region I). Under these conditions, they are hard plastics
with a modulus close to 3 GPa. The glassy polymer is believed to show very little segmental
mobility. Conformational changes are confined to small groups of atoms. The deformation is
predominantly due to stretching of secondary bonds and bond angle deformation ("frozen
23
spaghetti deformation"). The glass transition shows many kinetic peculiarities and it is not a
true thermodynamic phase transition as in the melting of a crystal. This is one of the subjects of
Chapter 5. In region II, the transitional region, the polymer shows damping. Such materials are
referred to as "leather-like".
At temperatures above Tg, the materials are rubber-like with a modulus of a few MPa
(region III). Above the glass transition temperature relatively large groups of atoms, of the order
of 100 main chain atoms, can change their conformation. Crosslinked materials show elastic
properties in this temperature region. The rate at which the conformational changes occur is so
high that the strain response to a step change in stress is instantaneous.
Uncrosslinked polymers show a pronounced drop in modulus at higher temperatures. The
temperature region at which the modulus remains practically constant, the so-called rubber
plateau, is much longer for the high molar mass material than for the low molar mass material
(Fig. 1.24). This indicates that the low modulus characteristic of materials in region V is due to
sliding motions of molecules which occur more readily in low molar mass polymers with few
chain entanglements. Crosslinked polymers show no region V behaviour because the crosslinks
prevent the sliding motion.
Semicrystalline polystyrene shows a weak glass transition at 100°C (Fig. 1.23), due to a
softening of the amorphous component of this two-phase polymer. The author did not report the
fraction of crystalline component but it was probably about 20%. The crystalline component
remains unchanged through the glass transition region. The crystallites act as crosslinks and the
rubber modulus of the amorphous component is higher than that of the wholly amorphous
polystyrene. The glass transition is hardly visible in high-crystalline polymers like
polyethylene. The pronounced drop in modulus occurring at 230°C is due to the melting of the
crystalline component. The morphology and phase transitions of semicrystalline polymers are
important parts of polymer physics and are treated in Chapters 7 and 8.
1.11. Polymer materials
It is common to divide plastic materials into thermoplastics and thermosets. Thermoplastics
are composed of linear or branched polymer molecules and for that reason they melt.
Thermoplastics are first synthesised and then at a later stage moulded. Thermosets are crosslinked polymers that do not melt. An uncrosslinked prepolymer is given the desired final shape
and then crosslinked to produce the detail.
The properties of a polymer material are determined by the structure of the polymers used,
the additives and the processing methods and conditions. It is for example possible to make an
extremely stiff and strong fibrous material from polyethylene. Conventionally processed
polyethylene has a stiffness of only about 1 GPa, whereas fibrous polyethylene may exhibit a
longitudinal modulus of 100 GPa. Some polymer materials are almost pure with only a small
content of additives, whereas others consist of predominantly non-polymeric constituents.
Composites consist of reinforcing fibres in a polymer matrix and the function of the polymer is
merely to provide the shape of the product and to transfer forces from one fibre to another. The
reinforcing fibres give the composites their high strength and stiffness.
This book deals primarily with the polymers but additives nevertheless play an important
role. Polymers would not be used to the extent that they are if it were not for the additives.
Some polymers like polyethylene may contain only a small portion of antioxidant to prevent the
polymer from oxidising. Other polymeric materials, particularly rubbers, contain both large
numbers and large amounts of additives, e.g. antioxidants, carbon black, oil, fillers, reinforcing
fibres, initiators, an accelerator for vulcanisation, and an inhibitor in order to avoid early
crosslinking.
An increasingly important field is to reduce the risk of fire without using halogen-containing
polymers. This is accomplished with the use of flame retardants. Some polymers like poly(vinyl
chloride) are used with plasticisers, i.e. miscible low molar mass liquids. Numerous polymeric
materials contain large fractions of fillers. The purpose of using fillers can be cost-reduction,
reduced mould-shrinkage, promotion of crystal nucleation and improvement of mechanical
properties. The list of additives used in polymers can be made long but for our purposes the list
presented here is sufficient.
24
1.12. Short polymer history
It is intended in this section to give only a very short presentation of the development of
polymer materials and ideas in polymer science in this section. Morawetz (1985) and Rånby
(1993) give a detailed presentation of this field.
The first polymers used were all obtained from natural products. Natural rubber from the
Hevea trees was being used by the American Indians when Columbus arrived in 1492. Cellulose
in different forms, starch and collagen in leather are other examples of native polymers.
Modification of native polymers started in the mid-nineteenth century and the first wholly
synthetic polymer was made in the beginning of the 20th century. The science of polymers
began in the 1920s.
The development of polymer science and technology has occurred primarily during the last
80 years and the commercial introduction of new polymers had proceeded through three timestages giving rise to three generations of polymers:
The first generation was introduced before 1950 and includes polystyrene, poly(vinyl
chloride), low-density polyethylene, polyacrylates, polymethacrylates, glass-fibre-reinforced
polyesters, aliphatic polyamides, styrene-butadiene rubber and the first synthetic paints
(alkyds).
The second generation of polymers was introduced during 1950-1965 and includes a number
of commodity and engineering plastics like high-density polyethylene, isotactic polypropylene,
polycarbonates, polyurethanes, epoxy resins, polysulphones and aromatic polyesters, also used
for films and fibres. New rubber materials, acrylic fibres made of polyacrylonitrile and latex
paint were also introduced.
The third generation, introduced since 1965, consists mainly of speciality polymers with a
more complex chemical structure. The signatures of these polymers can be very high thermal
and chemical stability and high strength/stiffness. Examples of these materials are
poly(phenylene sulphide) (Ryton®), polyaryletherketone (PEEK®), polyimides (Kapton®),
aromatic polyesters (Ekonol® and Vectra®), aromatic polyamides (Nomex® and Kevlar®) and
fluor-containing polymers (Teflon® and Viton®). Parallel to this development of new
polymers, existing polymers such as polyethylene have undergone significant improvement.
Crosslinked polyethylene and new fracture-tough thermoplastic polyethylenes are examples of
the more recently introduced materials.
A "polymer calender" is presented below with the important progress steps indicated. Many
important accomplishments have however been omitted to keep the list reasonably short.
1839: Charles Goodyear (USA) discovered that sulphur-containing natural rubber turned elastic
after heat-treatment. Vulcanisation was discovered and utilised.
1848: Thomas Hancock (USA) made polymer blends based on natural rubber and gutta percha.
1861: Thomas Graham, a British chemist, found that starch and cellulose could not pass
through fine filters. He proposed that these substances represented a different organisation of
matter, colloids (after kolla, the Greek word for glue). He believed that these substances
consisted of relatively small molecules held together by association forces.
1862: Alexander Parks (USA) modified cellulose with nitric acid to form cellulose nitrate and
by mixing this polymer with a plasticiser he made a material named ‘Parkesine’. A few years
later, John and Isaiah Hyatt patented a similar material named ‘celluloid’ (cellulose nitrate
plasticised with camphor).
1880: The French chemist Gustave Bouchardat created a rubber-like substance from isoprene.
Isoprene had been obtained some 20 years earlier by Greville Williams (UK) by distillation
from natural rubber.
1904: Carl Harries (Germany) proposed that the rubber-like substances made from isoprene
formed a ring structure that remained closely packed by strong association forces.
1907: The Belgium-born Leo Baekeland (USA) made "Bakelite", the first wholly synthetic
polymer. Bakelite is a thermoset made from phenol and formaldehyde.
1911: PS was made by Matthews (UK) but it took almost 20 years before it came into
commercial use (IG Farben, Germany).
1912: PVC was first synthesised by the Russian Ostromislensky. It took another 25 years before
it became commercial (B. F. Goodrich, USA).
25
1920: Hermann Staudinger, a German organic chemist, formulated the macromolecular concept.
Staudinger based his idea on results obtained by studies of materials derived from the
compound ketene. Staudinger presented the idea at a lecture already in 1917. Despite the fact
that the general view at this time was that these materials (including rubbers) consisted of
relatively small molecules held together by association forces, the concept of large molecules
was not new. Peter Klason, a Swedish chemist reported already in 1897 that lignin in wood was
formed mainly from coniferyl alcohol units connected to ‘large molecules’, mainly by ether
bonds. A statement of a German chemist after a debate with Staudinger in 1926: ‘We are
shocked like zoologists would be if they were told somewhere in Africa an elephant was found
who was 1600 feet long and 300 feet high’. Staudinger received the Nobel Prize in chemistry in
1953. Staudinger proposed incorrectly, however, that the polymer molecules were rigid rods.
Herman Mark, a German chemist that moved to USA, opposed to this view and suggested
correctly that the polymer molecules had a considerable flexibility.
1925: Theodor Svedberg (Sweden; Nobel Laureate in chemistry in 1926) constructed the
ultracentrifuge and was the first to make an unambiguous determination of a very high molar
mass.
1929: Styrene-butadiene rubber (Buna-S) was made by I. G. Farben, Germany.
1930s: Carl Marvel at the University of Illinois (USA) contributed strongly to the US Synthetic
Rubber Project. This giant project that involved 1000 chemists was largely motivated by World
War II. In 1942 production of synthetic rubber in USA reached 20 000 tons.
1930s: Werner Kuhn, Herman Mark and Eugene Guth found evidence that polymer chains in
solution were flexible and that the viscosity in solution was related to the molar mass of the
polymer.
1934-: The statistical mechanical theory for rubber elasticity was first qualitatively formulated
by Werner Kuhn, Eugene Guth and Herman Mark. The entropy-driven elasticity was explained
on the basis of conformational states. The initial theory dealt only with single molecules, but
later development by these pioneers and by other scientists formulated the theory also for
polymer networks. Eugene Guth and Hubert James formulated the first stress-strain equation
based on statistical mechanics in 1941.
1930s: Wallace Hume Carothers, a brilliant research chemist at DuPont Experimental Station,
USA, studied polycondensation reactions first synthesising aliphatic polyesters, and later and
more importantly polyamide 6,6 (nylon). Later work with radical polymerisation led to the
synthesis of polychloroprene. Carothers' research not only supported the macromolecular
concept but also demonstrated the industrial importance of synthetic polymers.
1930s: Paul Flory, at one time a member of Carothers research group, derived and
experimentally confirmed the Gaussian molar mass distribution for polymers made by stepgrowth polymerisation. Later Flory showed that polymers made by anionic polymerisation
adapted to the narrower Poisson distribution of chain lengths. Flory also postulated the
existence of chain-transfer reactions in chain-growth polymerisation. Flory received the Nobel
Prize in chemistry in 1974 for these and later fundamental achievements in the physical
chemistry of macromolecules.
1933: Low-density polyethylene was made by Eric William Fawcett (ICI, UK). This is how the
story is told in most textbooks. In fact, many more scientists and practitioners were greatly
involved. The story is beautifully told by Harmar-Brown [1954) and Gibson (1980): On 27th
March1933, E. W. Fawcett and R. O. Gibson, two UK chemists at ICI performed the
experiment that yielded the white, waxy solid. They attempted to examine the possibility to
react benzaldehyde and ethylene gas at very high pressure, a suggestion made by Professor
Robert Robinson, UK. Elemental analysis of the substance showed however no presence of
oxygen and Fawcett and Gibson correctly concluded that the substance was a polymer based on
ethylene. Several explosions occurred in later experiments and the project was stopped. This
grand discovery was however preceded by very important work on high-pressure apparatus,
which originated from Antonius Michels in the Netherlands. A few years later, after Vigars,
Manning and Colbeck development of new safer equipment, Paton, Williams and Bebbington
made 8 g low-density polyethylene in a reactor at 200 MPa. The date was 20 th December 1935.
Michels continuous gas compressor and a pressure vessel designed by Manning was used for
pilot plant work in 1938 and the first ton of polyethylene was made this year. In 1938, Mr. J. N.
Dean of Submarine Cables Ltd., UK learned about polyethylene and recognized its potential
value for insulating submarine cables. ICI delivered 150 tons of polyethylene for the two
26
Scotland-Norway cables during the period 1939-1940. This was the birth of the commercial
success of polyethylene.
1936: Epoxy resins were made by Pierre Castan (Switzerland)
1938: Silicone rubbers were made by Eugene Rochow (USA).
1939: Polytetrafluoroethylene (Teflon®) was made by Roy Plunkett (USA).
1942: Paul Flory and Maurice Huggins (USA) presented, independently, the thermodynamic
theory for polymer solutions.
1940s: Flory was very active in many areas during this decade. He made his contribution to
rubber elasticity together with Rehner, developed a theory for gelation, by which the gel point
can be predicted from the degree of "conversion", and developed a theory for the excluded
volume effect of polymer molecules in solution. Flory introduced the theta solvent concept.
Under theta conditions, the polymer molecules have unperturbed dimensions. Flory also
predicted that the shape of molecules in a pure melt should be the same as under theta
conditions.
1940s: Glass-fibre reinforced polyester was made in Germany.
1954: Karl Ziegler (Germany) and Guilio Natta (Italy) discovered that polymerisation in the
presence of certain metal-organic catalysts yielded stereoregular polymers. Both were awarded
the Nobel Prize in chemistry in 1963. Their work led to the development of linear polyethylene
and isotactic polypropylene. The preparation of linear polyethylene using chromium oxide
catalyst by Paul Hogen and coworkers at Phillips Petroleum Co, USA occurred also during the
1950s.
1949-56: Theories for liquid crystals of rod-like polymers were proposed by Lars Onsager in
1949 and by Paul Flory in 1956.
1955: Malcolm Williams, Robert Landel and John Ferry (USA) presented an empirical but very
general equation (WLF equation) describing the viscoelasticity of amorphous polymers.
1956: Michael Szwarz, USA, discovered living anionic polymerisation. This technique
permitted the preparation of narrow molar mass fractions and ‘exact’ di- and tri-block
copolymers. Thermoplastic elastomers, like Kraton® (Shell Chemical Co, USA) are prepared
by living anionic polymerisation.
1957: Andrew Keller, Bristol, UK, found that polymer molecules were folded at the large
surfaces of lamella shaped single-crystals of polyethylene. The general shape of the single
crystals and the crystal axes orientation but without the explicit expression about the chain
folding was also reported by Erhart Fischer (Germany) and Paul Till (USA) in 1957. The first
suggestion about chain folding goes back however to Keith Storks in 1938 dealing with guttapercha but it passed largely unnoticed by the scientific community.
1960: Polyoxymethylene (Delrin®) was made by DuPont Co, USA.
1961: Aromatic polyamide (Nomex®) was made by DuPont Co, USA.
1962: Blends of poly(phenylene oxide) (PPO) and polystyrene with the commercial name
Noryl® (General Electric Co, USA) were first made.
1968: Stefanie Kwolek and Paul Morgan, research chemists at DuPont reported that solutions of
poly(phenylene terephthalamide) could be spun to super-strong and stiff fibers. They showed
that the solutions possessed liquid crystalline order. The fibres were later commercialised under
the name Kevlar®.
1970-1985: Ultra-oriented polyethylene with mechanical properties approaching those of metals
was made by solid-state processes, in some cases combined with solution processes. A number
of scientists were active in the field: Ian Ward (UK), Roger Porter (USA), Albert Pennings, Piet
Lemstra and Paul Smith (Netherlands), and Dusan Prevorsek (USA). The pioneering work of
elucidating the mechanisms of transformation from the isotropic to the fibrous polymer is due
to Anton Peterlin (USA).
1971: Pierre-Gilles deGennes, a French physicist who was awarded the Nobel Prize in physics
in 1992, presented the reptation model which describes the diffusion of chain molecules in a
matrix of similar chain molecules. Masao Doi and Sam Edwards later further developed the
reptation model.
1972-: The first melt-processable, later categorised as thermotropic, liquid crystalline polymer,
based on p-hydroxybenzoic acid and bisphenol terephthalate, was reported by Steven Cottis in
1972. This polymer is now available on the market under the name Xydar ®. In 1973, Herbert
Kuhfuss and W. Jerome Jackson, Eastman Kodak Co, USA patented the first well-characterised
thermotropic polymer, a copolyester of p-hydroxybenzoic acid and ethylene terephthalate. They
27
reported the discovery of liquid crystalline behaviour in this polymer in 1976. In the beginning
of the 1980's, the Celanese Company developed a family of processable thermotropic liquid
crystalline polymers based on p-hydroxybenzoic acid and p-hydroxynaphthoic acid, later named
Vectra®.
Mid 1970's-: Theories for the crystallisation of polymers were introduced by John Hoffman
(USA) and coworkers and later in the 1980's by David Sadler (UK).
1976: The research group of Frisch (USA) published the first report on interpenetrating
polymer networks (IPN).
1977: The first electrically conductive polymer was prepared by doping of polyacetylene by
Alan MacDiarmid (USA), Alan Heeger (USA) and Hideka Shirikawa (Japan). These scientists
received in 2000 the Nobel Prize in chemistry.
1978: The German scientists Heino Finkelmann, Michael Happ, Michael Portugall and Hellmut
Ringsdorf suggested that a decoupling of the main chain and the mesogen motion was possible
through the insertion of a flexible spacer in side-chain liquid crystalline polymers. After this
breakthrough, an abundance of side-chain polymers have been synthesised and the
combinations of main chains, spacers and mesogens appear to be infinite.
1980s: The molecular interpretation of relaxation processes in polymers developed strongly
using molecular mechanics modelling particularly due to the work of Richard Boyd, USA.
David Bassett and associates at the University of Reading, UK introduced the permanganic
etching technique, which led to a strong development in the understanding of the morphology
of polymers.
1984: Dendrimers were first synthesised by Donald Tomalia and coworkers (USA).
Hyperbranched polymers were made a few years later at the DuPont Experimental Station
(USA).
1990s: Polyolefins with uniform molecular structure and a narrow molar mass distribution were
made by a new polymerisation technique using metallocene catalysts. The technological startup with a demonstration plant was by Exxon in 1991. The scientific foundation was provided
by the pioneering work of Walter Kaminsky (Germany) dating back to the late 1970s.
1.13. Summary
This chapter should be considered as a basic introduction to polymer science outlining those
concepts that are necessary for the understanding of the following chapters. Fundamental
concepts are introduced. The fundamental aspects of the covalent and intermolecular bonds are
presented. The difference between configuration and conformation is explained. Polymer
synthesis is briefly described. Molar mass averages are defined and the methods used for their
measurement are briefly presented. The properties of polymer materials are determined not only
by their polymer constituents but also by the low molar mass additives and by the processing
methods used. The major thermal transitions are briefly described. The use of native polymers
is many thousand years old, but it took until the beginning of the 20 th century for the first
wholly synthetic polymer (Bakelite) to be made. The history of polymer science began in 1917
with Hermann Staudingers introduction of the macromolecular concept. Finally, a list of
important accomplishments in polymer science and technology is presented.
1.14. Exercises
1.1 When was the first synthetic polymer made? What polymer was it?
1.2. Plot the potential energy as a function of the interatomic distance for a pair of atoms
assuming London forces and hydrogen bond.
1.3. Calculate the net dipole moment for dimethyl ketone using the bond dipole moments
provided in Table 1.1.
1.4. Write the constitutional repeating unit structures of the following polymers: PE, PP,
PMMA and PA8
1.5. Explain briefly the difference between the concepts of configuration and conformation.
1.6. Why can atactic polystyrene not crystallize?
28
1.7. Calculate the number average and the weight average molar masses for a blend of three
monodisperse fractions with the following molar masses (in g mol -1): 1000, 10 000 and
100 000. Case a: equal number of molecules of the three fractions; Case b: equal masses of the
three fractions.
1.8. What are the main differences between step-growth and chain-growth polymerisation?
1.9. What kind of branches is obtained in a copolymer of ethylene and 1-octene?
1.10. Is it possible to make isotactic polystyrene by radical polymerisation?
1.11. Give names of techniques that reveal the entire molar mass distribution?
1.12. Is it possible to determine the molar mass distribution of a hyperbranched polymer using
size exclusion chromatography after calibration with monodisperse polystyrene fractions?
1.13. Explain why measurement of colligative properties yields the number average molar mass.
1.15. References
Berzelius, J. (1832) Jahres-Bericht Fortschr. Phys. Wissensch., 11, 44.
Boyd, R. H. and Phillips, P. J. (1993) The Science of Polymer Molecules, Cambridge University
Press, Cambridge.
Brandrup, J., Immergut, E. H. and Grulke, E. A. (eds.) (1999) Polymer Handbook, 4th ed.,
Wiley, New York.
Gibson, R. O. (1980) Chemistry and Industry, 16 August, 635.
Harmar-Brown, F. M. S. (1954) ICI Magazine, September, 258.
Hogan, J. P. and Banks, R. L. (Phillips Petroleum Co.) (1958) U.S. Patent 2,825,721.
Houwink, R. (1940) J. Prakt. Chem., 157, 15.
Israelachvili, J. (1992) Intermolecular and Surface Forces, 2nd ed., Academic Press, London.
Kausch, H. H. (1987) Polymer Fracture, Springer-Verlag, Berlin.
Kuhn, W. (1934) Kolloid Z., 68, 2.
London, F. (1937) Trans. Faraday Soc., 33, 8.
Mark, H. (1938) in Der Feste Körper, Sänger, R. (ed.), Hirzel, Leipzig.
Metanomski, W. V. (ed.) (1991) Compendium of Macromolecular Nomenclature, Blackwell
Scientific, Oxford.
Morawetz, H. (1985) Polymers: The Origins and Growth of a Science, Wiley, New York.
Natta, G., Pino, P., Corradini, P. Danusso, F., Mantica, E. and Moraglio, G. (1955) J. Am.
Chem. Soc., 77, 1708.
Rånby, B. (1993) Background- polymer science before 1977, in Nobel Symposium 81,
Conjugate Polymers and Related Structures, Oxford University Press .
Staudinger, H. and Nodzu, R. (1930) Ber., 63, 721.
Tobolski, A. V. (1960) Properties and Structure of Polymers, Wiley, New York.
Ziegler, K., Holzkamp, E., Breil, H. and Martin, H. (1955) Angew. Chem., 67, 541.
29