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

AmorphousCrystalline

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 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

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

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

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

a,b,c – dimensions of crystal lattice

Thickness of lamellae

W = width l = thickness

Lamellae (crystal)

Spherulite

PE sheet

Polymer structurehierarchy

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

Flow-induced oriented morphologies i.e. Shish kebab

Spherulite

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 ktm( ) exp 1

X(t) = fractional crystallinityk = temperature dependent growth rate parameterm = nucleation index, temperature independent

Crystallization rate: Effect of temperature

• Nucleation• Growth of crystals

Rate of crystallization

Rat

e of

cry

stal

lizat

ion

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:

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))

Main chain flexibility

Ethyleneglycol-based polyesters

Melting temperatures of crystallites and heat treatment

Degree of crystallinity in PE at different temperatures

crys

talli

nity

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

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

Hard plastic

Soft plastic

Crystallinity %

Soft wax

Oily

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:

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:

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:

=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

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

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 (%)

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)

• 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

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

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:

• 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

Next week:

• Methods to measure thermal transitions: – TGA– DSC– DMA

• Structure characterization: – FTIR– NMR