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 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

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

Melting temperature of crystalline structures, Tm 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

Non-adjacent re-entry 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 structure hierarchy 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, 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) = fractional crystallinity t = time k = temperature dependent growth rate parameter m = nucleation index, temperature independent

Crystallization rate: Effect of temperature Nucleation Growth of crystals Rate of crystallization 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/(molK)) 0 = molecular weight of the monomer (g/mol) DHm = melting entalphy (J/mol)

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 (414.2K)  = 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 Crystallinity % Hard plastic Soft plastic Soft wax Oily

Glass transition temprerature, Tg 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 Kinetic (rate) theory Thermodynamic (equilibrium) theory

1. Free volume theory http://faculty.ims.uconn.edu/~avd/class/2006/cheg351/lec6.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

Universal approximation for values of C: 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, 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

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 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 co-polymers 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

The amount of caprolactone in the monomer feed (%) Glass transition in P(CL-DL-LA) co-polymers depending on the monomer ratio The amount of caprolactone in the monomer feed (%)

The amount of styrene (%) 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 Amorphous polymers (high Tg) 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