Summary Last week Different conformations and configurations of

Summary: Last week • Different conformations and configurations of polymers • Molecular weight of polymers: – Number average molecular weight (Mn) – Weight average molecular weight (Mw) – Viscosity 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

Key learning outcomes • Glass transition, melting and crystalisation temperatures – How polymer structure can influence these properties – How the transition temperatures determine applicability/how and where the polymers can be used • Crystallinity and crystal growth • Nucelation • Operating and processing temperatures

Relationship between transition temperatures and polymer properties • 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

Polymer morphology • 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 (amorphous regions)

Influence of morphology on properties • Polymers with higher crystallinity are denser, stiffer, harder, tougher and more resistant to solvents • Amorphous domains add flexibility and promote ease of processing below the melting temperature

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 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)

Semi-crystalline polymers - thermal transitions

What encourages 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)

Tacticity and conformation • Atactic and syndiotactic tend to form extended chain or planar zig-zag conformations • Isotactic tends to form helix conformations, due to steric hindrance of pendant groups

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 (size of side groups) – 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

Different crystal structures/geometries • 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, 4 th ed. , p. 27).

Growth of the spherulites • At t 0 the melt begins to cool • At t 4 the sample is full of spherulites

Illustrations of spherulite growth • Film of formation of spherulites: http: //www. youtube. com/watch? v=130 s. Unj. Uxm. Q • More general information regarding formation of spherulites: https: //www. e-education. psu. edu/files/matse 081/animations/lesson 08/u 08_morph. F. 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) = fractional crystallinity t = time k = temperature dependent growth rate parameter m = nucleation index, temperature independent

• Nucleation • Growth of crystals Rate of crystallization Crystallization rate: Effect of temperature Rate of crystallization

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: Flory equation • Dependence of Tm and molecular weight at high molecular weights is expressed with the Flory equation: = melting temperature at high molecular weights (K) Tm = melting temperature (K) R = gas constant (8. 314 J/(mol. K)) = molecular weight of the monomer (g/mol) DHm = melting entalphy (J/mol) 0

Main chain flexibility and melting temperature Ethyleneglycol-based polyesters

Melting temperatures of crystallites and heat treatment Degree of crystallinity in PE at different temperatures crystallinity

Melting temperature of polymer crystallites and effect of heat treatment • Gibbs-Thompson formula connects the melting temperature and the lamellar thickness (L) Tm = melting temperature of a lamellar with thickness L T = melting temperature of a infinitely thick and complete crystallite (414. 2 K) = free surface energy per unit area (79 x 10 -3 J / m 2) DHm = Enthalpy change per volume (288 x 106 J / m 3) 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 1. Free-volume theory 2. Kinetic (rate) theory 3. Thermodynamic (equilibrium) theory

1. Free volume theory http: //faculty. ims. uconn. edu/~avd/class/2006/cheg 351/lec 6. pdf

1. Free volume theory Liquid-glass transition is a manifestation of changes occurring in the microscopic distribution of molecular free volume • Free volume: ’empty’ or ’unoccupied’ space around a molecule in which it can move and undergo segmental motion Approaching transition from the liquid state: as temperature decreases, specific volume decreases and vf decreases as well • Specific volume: the volume or space occupied by a molecule At some point, vf is reduced to a critical value where there is insufficient room for diffusion (net movement of molecules) Tg = temperature at which vf reaches critical value

WLF equation • Williams-Landels-Ferry (WLF) equation: Universal approximation for values of C: = viscosity = characteristic relaxation time of the segments at T and Ts (Ts reference) Ci = empirical constants

2. Kinetic theory • Tg is not a thermodynamic variable • Tg is the temperature at which the relaxation time for the segmental motion in the main chain is of the same order of magnitude as the time scale of experiment – Heating/cooling rate dependency • Theory is concerned with describing the rate at which system approaches the equilibrium

2. Kinetic theory – effect of cooling rate • Upon cooling, the amorphous polymer chains undergo structural relaxation: – The chains confiugre and attempt to reach a state of equilibrium – Faster cooling → less time to configure (less dense arrangement of chains) - More volume (both free and specific) - Lower Tg • The larger the volume, the more room for moelcules to move, less energy required to activate segmental motion, lower Tg

Effect of cooling rate on volume change

3. Thermodynamic theory • Considers a ’thermodynamic glass transition’ which is reached when the conformational entropy (Sc) is zero • Sc: the number of different ways polymer chains can be spatially arranged

Summary of theories

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

Glass transition temperatures of amorphous polymers

Glass transition temperatures of amorphous polymers, aromatic rings

Substituents: Tg of substituted vinyl polymers Fried, 2 nd ed. , p. 179

Side chain: Tg of di-substituted vinyl polymers Fried, 2 nd 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

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 – 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): Tg = glass transtion temperature of the composition Tgp = glass transition temperature of the polymer Tg 1 = glass transition temperature of the plasticizer w 1 = weight fraction of the polymer (%) w 2 = 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=W 1 Tg, 1+W 2 Tg, 2 • W 1 is the weight fraction and Tg 1 (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 co-polymers 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

Tg and polymer operating temperatures • POLYMER Amorphous polymers (high Tg) OPERATING TEMPERATURE Top < Tg – Polycarbonate • Semicrystalline polymer (Tg < 0 °C) Tg < Top < Tm (e. g. PE, PP) – Polyethylene, polypropylene • Thermosets and rigid polymers Top < Tg – Polyurethane, polyimide • Elastomers (rubbers) Top > Tg – Polyisoprene, silicone rubber PROCESSING TEMPERATURE Tpr > Tg Tpr > Tm

Next week: • Methods to measure thermal transitions: – TGA – DSC – DMA • Structure characterization: – FTIR – NMR