summary: last week different conformations and configurations of polymers molcular weight of...
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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)
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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
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Solid state of polymers
AmorphousCrystalline
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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
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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 glassy-state 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
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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
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Polymer structures
A: Linear, amorphous
B: Linear, semi-crystalline
C: Branched, amorphous
D: Slightly cross-linked
E: Cross-linked
F: Linear ladder structure
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Crystallinity
Melting temperature of crystalline structures, Tm
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Suitable for natural polymers such as cellulose and proteins that consist of fibrils
Synthetic polymers are found to crystallize such that the macromolecules fold
Folded lamella structure: Fringed-micelle structure:
Crystallinity models
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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
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Crystallinity
Adjacent re-entry Non-adjacent re-entry
Re-entry of each chain in the folded structure can be adjacent or non-adjacent
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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)
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Partly crystalline polymers - thermal transitions
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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
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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
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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)
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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)
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Packing rules
• Notation system in crystallography for planes and directions in crystal lattices
• Miller index in cubic
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Polymer chain
a,b,c – dimensions of crystal lattice
Thickness of lamellae
W = width l = thickness
Lamellae (crystal)
Spherulite
PE sheet
Polymer structurehierarchy
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Packing i.e. different crystal structures
• Crystallization from concentrated solution:– Single crystals– Twins– Dendrites– Shish-kebab
• Melt crystallization:– Micelles– Spherulites– Cylindrites
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Schematic models of polymer crystallites
Flow-induced oriented morphologies i.e. Shish kebab
Spherulite
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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
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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).
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Growth of the spherulites
• At t0 the melt begins to cool
• At t4 the sample is full of spherulites
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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
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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
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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)
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Crystallization kinetics
• Fractional crystallinity (X) - Johnson, Mehl, Avrami:
X t ktm( ) exp 1
X(t) = fractional crystallinityk = temperature dependent growth rate parameterm = nucleation index, temperature independent
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Crystallization rate: Effect of temperature
• Nucleation• Growth of crystals
Rate of crystallization
Rat
e of
cry
stal
lizat
ion
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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.
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Thermal transitions
Melting
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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
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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
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Effect of molecular weight on melting temperature
• Dependence of Tm of PLLA and molecular weight at high molecular weights is expressed with Flory equation:
12 0/ T TR
Hm mm n
M
M
DHm = melting entalphy (J/mol)
Tm
= melting temperature at high molecular weights (K)
Tm = melting temperature (K)
M0 = molecular weight of the monomer (g/mol)
R = gas constant (8.314 J/(molK))
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Main chain flexibility
Ethyleneglycol-based polyesters
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Melting temperatures of crystallites and heat treatment
Degree of crystallinity in PE at different temperatures
crys
talli
nity
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Melting temperature of polymer crystallites and effect of heat treatment
• Gibbs-Thompson formula connects the melting temperature and the lamellar thickness (L)
T T H Lm m 1 2 /
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)DHm = Enthalpy change per volume (288 x 106 J / m3)
L = lamellae thickness
( ) = typical values for PE
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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
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Effect of crystallinity on properties
PE crystallinity as a function of molecular weight
Fragile wax ductile wax
Hard plastic
Soft plastic
Crystallinity %
Soft wax
Oily
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Amorphous state
Glass transition temprerature, Tg
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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
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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
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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
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Theory
• Williams-Landels-Ferry (WLF) equation:
s
sT TTC
TTCa
2
1log
As T
T
T
TTa
= viscosity = characteristic relaxation time of the segments at T and Ts (Ts reference)Ci = empirical constants
17.44log
51.6
g
s g
T T
T T
Universal approximation for values of C:
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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
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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
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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)
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Effect of the backbone on glass transition
• Polyethylene
• Poly(ethylene oxide)
• Poly(dimethylsiloxane)
• Poly(ethylene terephtalate)
• Polycarbonate
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Substituents: Tg of substituted vinyl polymers
Fried, 2nd ed., p. 179
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Side chain: Tg of di-substituted vinyl polymers
Fried, 2nd ed., p. 179
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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:
=the limiting value of Tg at high molecular weight
K = constant for a given polymer
= number average molecular weight
• K is not constant for molecular weights below 10 000 g/mol
Mn
ng
KTT
Mg
gT
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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
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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
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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
211
ggPg T
w
T
w
T
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 (%)
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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
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Simple rule of mixture for binary mixture (polymer blends)
• 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=W1Tg,1+W2Tg,2
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Tg for copolymers of e-caprolactone and D,L-lactide
• Tg for pure, semi-crystalline polycaprolactone is about -60ᵒC and melting temperature (Tm) about 60ᵒC
• Tg for amorphous P(D,L-LA) is 50-57ᵒC
Wada, R. et al., In vitro evaluation of sustained drug release from biodegradable elastomer, Pharmaceutical research , 8 (1991) 1292-1296
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Glass transition in P(CL-DL-LA) co-polymers depending on the monomer ratio
The amount of caprolactone in the monomer feed (%)
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Glass transition in styrene-ethyleneacrylate co-polymers depending on the monomer ratio
The amount of styrene (%)
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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
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Parameters affecting glass transition temperature: summary
Polymer 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
Processing based:
• Plasticizers and solvents• Blends • Fillers• Orientation• Rate of cooling
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Next week:
• Methods to measure thermal transitions: – TGA– DSC– DMA
• Structure characterization: – FTIR– NMR