Summary: Last week
• Different conformations and configurations of polymers
• Molcular weight of polymers:
– Number avarage molecular weight (Mn)
– Weight average molecular weight (Mw)
– Viscocity average molecular weight (Mv)
– Polydispersity (PDI)
Summary: Methods to analyze different
molecular weights
• Primary (absolute values) methods
– Osmometry (Mn)
– Scattering (Mw)
– Sedimentation (Mz) Z-average molecular weight is obtained from
centrifugation data
• Secondary (relevant to reference or calibration) methods
– Gel permeation chromatography (GPC) / size exclusion
chromatography (SEC) to obtain molecular weight distribution
– Intrinsic viscosity for determining viscosity average molecular
weight
Solid state of polymers
Amorphous
Crystalline
Elastomers, fibers, plastics
• Mechanical properties of polymers can be tailored by appropriate
combinations of crystallinity, crosslinking and thermal transitions, Tg
and Tm
• Depending on the particular combination, a specific polymer will be
used as a fibre, flexible plastic, rigid plastic or elastomer (rubber)
• The operating temperature of polymers is defined by transition
temperatures
Glass transition temeprature (Tg) and melting
temperature (Tm)
• The glass transition temperature, Tg, is the temperature at which
the amorphous domains of a polymer take on characteristic glassystate properties; brittleness, stiffness and rigidity (upon cooling)
• Tg is also defined as the temperature at which there is sufficient
energy for rotation about bonds (upon heating)
• The melting temperature, Tm, is the melting temperature of the
crystalline domains of a polymer sample
• The operating temperature of polymers is defined by transition
temperatures
Crystallinity in polymers
• Crystallinity depends on the molecular structure of polymers
• No bulk polymer is completely crystalline
• In semi-crystalline polymers, regular crystalline units are linked by
un-orientated, random conformation chains that constitute
amorphous regions
• Presence of crystalline structures has a significant influence on
physical, thermal and mechanical properties
– Highly crystalline: polyolefins
– Totally amorphous: atactic PS and PMMA
Polymer structures
A: Linear, amorphous
B: Linear, semi-crystalline
C: Branched, amorphous
D: Slightly cross-linked
E: Cross-linked
F: Linear ladder structure
Crystallinity
Melting temperature of crystalline structures, Tm
Crystallinity models
Folded lamella structure:
Fringed-micelle structure:
Synthetic polymers are found
to crystallize such that the
macromolecules fold
Suitable for natural polymers
such as cellulose and proteins
that consist of fibrils
Crystalline state: Ordering of polymer chains
• Some polymers can organize into regular crystalline structures
during cooling from the melt or hot solution
• The basic unit of crystalline polymer morphology is crystalline
lamellae consisting of arrays of folded chains. Thickness of typical
crystallite may be only 100 to 200 Å (10 to 20 nm)
– Even the most crystalline polymers (like HDPE) have lattice
defect regions that contain unordered, amorphous material
• Crystalline polymers exhibit both:
– A Tg corresponding to amorphous regions
– A crystalline melting temperature (Tm) at which crystallites are
destroyed and an amorphous, disordered melt is formed
Crystallinity
Adjacent re-entry
Non-adjacent re-entry
Re-entry of each chain in the folded structure can be adjacent or non-adjacent
Crystallinity
• Ordinary tie-molecules bond two crystalline parts together across
the amorphous part. Two chains can also be entangled together by
a physical bond (entanglement)
Partly crystalline polymers - thermal transitions
Crystallinity
• A polymer’s chemical structure determines whether it will be
crystalline or amorphous in the solid state
• Symmetrical chain structures favor crystallinity by allowing close
packing of polymer molecules in crystalline lamellae
– Tacticity and geometric isomerism (i.e. trans configuration)
favor crystallinity
– Branching and atacticity prevent crystallization
Crystallinity and the effect of hydrogen bonding
• Specific interactions (hydrogen bonding between chains) enhance
crystallinity
• Within nylons, hydrogen bonding between;
– Amide carbonyl group on one chain
– Hydrogen atom of an amide group of another chain
Conformation and configuration of polymer
chains in the lamellae
• For many polymers, the lowest energy conformation is the
extended chain or planar zig-zag conformation (for example PE,
polymers capable of hydrogen bonding)
• For polymers with larger substituent groups, the lowest energy
conformation is a helix (for example in PP, three monomer units
form a single turn in the helix)
Packing
• The extent to which a polymer crystallizes depends on:
– Whether its structure is prone to packing into the crystalline state
– The magnitude of the secondary attractive forces of the polymer
chains
• Packing is facilitated for polymer chains that have:
– Structural regularity
– Compactness
– Streamlining
– Some degree of flexibility
• This means strongly anisotropic materials (directionally dependent)
Packing rules
• Notation system in crystallography
for planes and directions in crystal
lattices
• Miller index in cubic
Polymer chain
Polymer structure
hierarchy
a,b,c – dimensions of crystal lattice
Thickness of lamellae
W = width
l = thickness
Lamellae (crystal)
Spherulite
PE sheet
Packing i.e. different crystal structures
• Crystallization from concentrated solution:
– Single crystals
– Twins
– Dendrites
– Shish-kebab
• Melt crystallization:
– Micelles
– Spherulites
– Cylindrites
Schematic models of polymer crystallites
Spherulite
Flow-induced oriented
morphologies i.e. Shish kebab
Spherulites
• Following crystallization from the melt or concentrated solution,
crystallites can organize into spherical structures called spherulites
• Each spherulite contains arrays of lamellar crystallites that are
typically oriented with the chain axis perpendicular to the radial
(growth) direction of the spherulite
• Anisotropic morphology results in the appearance of a characteristic
extinction cross (Maltese cross) when viewed under polarized light
Spherulite nucleation and growth
•
•
•
•
Formation of nuclei
Accelerated crystallization: spherulites grow in radius
Crystallization slows: spherulites begin to touch each other
Crystallinity may still increase very slowly
Structural organization within
a spherulite in melt-crystallized
polymer (Odian, 4th ed., p. 27).
Growth of the spherulites
• At t0 the melt begins to cool
• At t4 the sample is full of spherulites
Illustrations of spherulite growth
• Film of formation of spherulites:
http://www.youtube.com/watch?v=130sUnjUxmQ
• More general information regarding formation of spherulites:
https://www.e-education.psu.edu/files/matse081/animations/lesson08/u08_morphF.html
Nucleation
• Crystallization starts via nucleation and continues via crystallite
growth
• Homogeneous or heterogeneous:
– Homogeneous nuclei are formed from molecules or molecular
segments of the crystallizing material itself; called spontaneous
or thermal nucleation
– Heterogeneous nucleation is caused by the surface of foreign
bodies in the crystallizing material such as dust particles or
purposely added nucleating agents
• Crystallization generally occurs only between the Tg and Tm and the
crystallization rate passes through a maximum
Crystallization kinetics
• The extent of crystallization during melt processing depends on the
rate of crystallization and the time during which melt temperatures
are maintained
• Some polymers that have low rates of crystallization (i.e. PCL) can
be quenched rapidly to achieve an amorphous state
• On the other hand, some polymers crystallize so rapidly that a
totally amorphous state cannot be obtained by quenching (PE)
Crystallization kinetics
• Fractional crystallinity (X) - Johnson, Mehl, Avrami:
X (t )  1  exp
 kt m
X(t) = fractional crystallinity
k = temperature dependent growth rate parameter
m = nucleation index, temperature independent
• Nucleation
• Growth of crystals
Rate of crystallization
Crystallization rate: Effect of temperature
Linear growth of spherulites in PET as a function
of temperature (pressure 1 bar)
• Tg = 69°C and Tm = 265°C for
PET
• The maximum growth rate is
observed near 178°C.
Thermal transitions
Melting
Thermal transitions
• Generally affected in the same manner by:
– Molecular symmetry
– Structural rigidity
– Secondary attractive forces of polymer chains
• High secondary forces (due to high polarity or hydrogen bonding)
lead to strong crystalline forces requiring high temperatures for
melting
• High secondary forces also decrease the mobility of amorphous
polymer chains, leading to high Tg
Melting temperature of polymers
• Loss of crystalline structure causes many changes in properties
when a material changes into viscous fluid
• Polymer melting takes place over a wide temperature range due to
the presence of different sized crystalline regions and the
complicated process for melting large molecules
• Changes in various properties can be used to measure Tm:
•
•
•
•
•
Density
Refractive index
Heat capacity
Enthalpy
Light transmission
Effect of molecular weight on melting
temperature
• Dependence of Tm of PLLA and molecular weight at high molecular
weights is expressed with Flory equation:
2 RM 0
1 / Tm  Tm 
H m M n

Tm  = melting temperature at high molecular weights (K)
Tm = melting temperature (K)
R = gas constant (8.314 J/(molK))
M0 = molecular weight of the monomer (g/mol)
Hm = melting entalphy (J/mol)
Main chain flexibility
Ethyleneglycol-based
polyesters
Melting temperatures of crystallites and heat
treatment
Degree of crystallinity in PE at
different temperatures
Melting temperature of polymer crystallites
and effect of heat treatment
• Gibbs-Thompson formula connects the melting temperature and the
lamellar thickness (L)


Tm  T 1  2 / Hm L
Tm = melting temperature of a lamellar with thickness L
T = melting temperature of a infinitely thick and complete crystallite (414.2K)
 = free surface energy per unit area (79 x 10-3 J / m2)
Hm = Enthalpy change per volume (288 x 106 J / m3)
L = lamellae thickness
( ) = typical values for PE
Effect of crystallinity on properties
• In most common semi-crystalline thermoplastic polymers, the
crystalline structure contributes to the strength properties of the
plastics
– Crystalline structures are tough and hard and require high
stresses to break them
• Mechanical properties of semi-crystalline polymers are mostly
dependent on the average molecular weight and degree of
crystallinity
• Crystallinity affects the optical properties
– The size and structure of crystallites
Effect of crystallinity on properties
PE crystallinity as a function of molecular weight
Fragile wax
ductile wax
Crystallinity %
Hard
plastic
Soft wax
Oily
Soft
plastic
Amorphous state
Glass transition temprerature, Tg
Amorphous state
• Completely amorphous polymers exist as long, randomly coiled,
interpenetrating chains
• Chains are capable of forming stable, flow-restricting
entanglements at high molecular weight:
– In the melt, long segments of each polymer chain moves in
random micro-Brownian motions
– As the melt is cooled, a temperature is reached at which all long
range segmental motions cease (glass transition temperature,
Tg)
• In the glassy state, at temperatures below Tg, the only molecular
motions that can occur are short range motions i.e. secondary
relaxations
Critical molecular weight
• The minimum polymer chain-length or critical molecular weight
Mc for the formation of stable entanglements depends on the
flexibility of polymers chain
• Relatively flexible polymer chains (such as PS) have a high Mc
while more rigid chain polymers (with an aromatic backbone)
have a relatively low Mc
• Typically, the molecular weight of most commercial polymers is
significantly greater than Mc in order to have maximum thermal
and mechanical properties
• Molecular weight of a commercial polymer is typically 100 000 to
400 000 g/mol while the Mc is only about 30 000 g/mol
Theories on glass transitions
• Glass transition is at least a partially kinetic phenomenon
• The experimentally determined value varies significantly with the
timescale of the measurement
• Free volume theory:
– Glass transition temperature is the temperature with a certain
free volume. Many polymers follow the William-Landel-Ferry
(WLF) equation
• Kinetic theories:
– Free volume disappears following kinetic that can be correlated
with temperature with Arrhenius. At glass transition the
relaxation times are about the same magnitude as measuring
times
Theory
• Williams-Landels-Ferry (WLF) equation:
log aT 
aT 
C1  T  Ts 
C2  T  Ts 
T  T

T  T
s
Universal approximation for values of C:
 17.44  T  Tg 
log 
s
51.6  T  Tg 
A
 = viscosity
 = characteristic relaxation time of the segments at T and Ts (Ts reference)
Ci = empirical constants
Effects of the structure on Tg
• Glass transition temperature is affected by:
–
–
–
–
–
Polar, intermolecular forces increase Tg
Bulky side groups increase Tg
Syndiotacticity increases Tg
Trans-isomers have higher Tg than cis-isomers
Main chain flexibility lowers Tg
Molecular structure
• Rigidity of polymer chains is especially high when there are cyclic
structures in the main polymer chains
– Polymers such as cellulose have high Tg and Tm values
• Polymers with rigid chains are difficult or slow to crystallize, but the
portion that does crystallize will have a high Tm
• The extent of crystallinity can be significantly increased in such
polymers by mechanical stretching to align and crystallize the
polymer chains
Main chain structure
• Ring structures or unsaturated chemical bonds in the polymer
backbone stiffen the chain structure and increase the Tg
• Strong polar interactions increase the glass transition temperature
– Side groups in polyacrylnitrile are not large but due to polarity Tg
is (104 °C)
Effect of the backbone on glass transition
• Polyethylene
• Poly(ethylene oxide)
• Poly(dimethylsiloxane)
• Poly(ethylene terephtalate)
• Polycarbonate
Substituents: Tg of substituted vinyl polymers
Fried, 2nd ed., p. 179
Side chain: Tg of di-substituted vinyl polymers
Fried, 2nd ed., p. 179
Effect of molecular weight on glass transition
temperature
• For many polymers, Tg increases as average molecular weight
increases until a limiting value. After this any further increase in
molecular weight does not increase the Tg
• Fox-Flory equation can be used to estimate the dependence of Tg
on molecular weight:
Tg  Tg 
K
Mn
Tg =the limiting value of T at high molecular weight
g
K = constant for a given polymer
M n = number average molecular weight
•
K is not constant for molecular weights below 10 000 g/mol
Effect of branching on Tg
• Branches lower the glass transition temperature which is mainly
due to the increased number of end groups
• Poly(vinyl acetate)
• Highly branched Tg = 25.4 °C
• Only few branches Tg = 32.7 °C
Effect of crosslinking on glass transition
• Long range segmental motion is restricted by crosslinking, thus
crosslinking elevates the glass transition temperature
– Tg increases with an increase in the degree of crosslinking
• Note! Extensive crosslinking causes high chain rigidity which
completely prevents crystallization
Effect of plasticizer on Tg
• Tg of a good plasticizer needs to be lower than the Tg of the polymer
• Inverse rule of mixtures (Fox equation when applied to Tg):
1
w1 w2


Tg TgP Tg1
Tg = glass transtion temperature of the composition
Tgp = glass transition temperature of the polymer
Tg1 = glass transition temperature of the plasticizer
w1 = weight fraction of the polymer (%)
w2 = weight fraction of the plasticizer (%)
Co-polymers and polymer blends
• Co-polymer is usually softer than its homopolymers and the Tg is
lower
• Blends:
– A mixture of two homopolymers has two glass transition
temperatures near the temperatures of the homopolymers
– The miscibility of the blend affects the transitions
Simple rule of mixture for binary mixture
(polymer blends)
Tg=W1Tg,1+W2Tg,2
• W1 is the weight fraction and Tg1 (in Kelvins) the glass transition
temperature of the component 1
• Good approximation for blends of two or more polymers but
overpredicts the Tg when one component is a low molecular weight
organic compound
Tg for copolymers of e-caprolactone and D,Llactide
• Tg
for pure, semi-crystalline
polycaprolactone is about -60ᵒC and
melting temperature (Tm) about 60ᵒC
• Tg for amorphous P(D,L-LA) is 5057ᵒC
Wada, R. et al., In vitro evaluation of sustained drug release from biodegradable
elastomer, Pharmaceutical research , 8 (1991) 1292-1296
Glass transition in P(CL-DL-LA) co-polymers
depending on the monomer ratio
The amount of caprolactone in the monomer feed (%)
Glass transition in styrene-ethyleneacrylate
co-polymers depending on the monomer ratio
The amount of styrene (%)
Second order transitions
• A first order transition is defined as one for which a discontinuity
occurs in the first derivative of the Gibbs free energy
– In polymers, the first order transition occurs as discontinuity in
volume and thus crystalline-melting temperature is such a
transition (Tm)
• Tg is a second order transition involving a change in the
temperature co-efficient of the specific volume and a discontinuity in
specific heat
• The value of glass transition measured depends on the method
and the rate of the measurement
Parameters affecting glass transition temperature:
summary
Polymer based:
Processing based:
• Chain stiffness:
•
•
•
•
•
•
•
•
•
•
Structure of the backbone
Side groups and branching
Stereoregularity
Crosslinking
Copolymers
• Intra- and intermolecular
secondary interactions
• Average molecular weight
• Degree of crystallinity
Plasticizers and solvents
Blends
Fillers
Orientation
Rate of cooling
Next week:
• Methods to measure thermal transitions:
– TGA
– DSC
– DMA
• Structure characterization:
– FTIR
– NMR