Solid State Properties Chapter 4 Solid State Properties

Polymer Phases Viscous Liquid Elastomeric Semi-Crystalline Amorphous Polydimethylsiloxane Tg = -123°C; Tm = -40 °C Elastomeric Polyisoprene Tg = -73 °C Polybutadiene, Tg = -85 °C Polychloroprene, Tg = -50 °C Polyisobutylene, Tg = -70 °C Semi-Crystalline Nylon 6,6, Tg = 50 °C; Tm = 265 °C Poly ethylene terephthalate, Tg = 65 °C; Tm =270 °C Amorphous Glassy Polystyrene Tg = 100 °C Polymethyl methacrylate, Tg = 105 °C

Glass phase (hard plastic) Glass-rubber-liquid Amorphous plastics have a complex thermal profile with 3 typical states: Glass phase (hard plastic) Polystyrene Temperature 3 9 6 7 8 4 5 Leathery phase Tygon (plasticized PVC) Log(stiffness) Pa Rubber phase (elastomer) polyisobutylene Tg Liquid PDMS

Mechanical Properties

Heat Distortion Temperature The maximum temperature at which a polymer can be used in rigid material applications is called the softening or heat distortion temperature (HDT). A typical test (plastic sheeting) involves application of a static load, and heating at a rate of 2oC per min. The HDT is defined as the temperature at which the elongation becomes 2%. A: Rigid poly(vinyl chloride) 50 psi load. B: Low-density poly(ethylene) C: Poly(styrene-co-acrylonitrile) 25 psi load. D: Cellulose acetate (Plasticized) 25 psi load.

Transient Testing: Resilience of Cured Elastomers Resilience tests reflect the ability of an elastomeric compound to store and return energy at a given frequency and temperature. Change of rebound resilience (h/ho) with temperature T for: 1. cis-poly(isoprene); 2. poly(isobutylene); 3. poly(chloroprene); 4. poly(methyl methacrylate).

Types of Polymers Polymer Family Tree Polyethylene 33% Vinyls 16% Polypropylene 15% PMMA ABS Nylon Polycarbonate Saturated Polyester PEEK Polyurethane Some are thermosets as well. PVC Not Cross-Linked 90% of market Thermoplastics Will reform when melted Epoxy Melamine Formaldehyde Phenolic Polyester (unsaturated) Polyimide Some are thermoplastic as well. Silicone Urea Formaldehyde Cross-linked 10% of market Thermosets/Elastomers Will not reform Polymer Family Tree

Ballpark Comparisons Tensile strengths Polymers: ~ 10 - 100 MPa Metals: 100’s - 1000’s MPa Elongation Polymers: up to 1000 % in some cases Metals: < 100% Moduli (Elastic or Young’s) Polymers: ~ 10 MPa - 4 GPa Metals: ~ 50 - 400 GPa

Amorphous v Crystalline Polymers Thermo-mechanical properties

Thermal Expansion If a part is to be produced within a close dimensional tolerance, careful consideration of thermal expansion/contraction must be made. Parts are produced in the melt state, and solidify to amorphous or semi-crystalline states. Changes in density must be taken into account when designing the mold.

Thermal Expansion

Stress Strain Studies

Anatomy of a Stress Strain Graph Elongation = 100% x   Initial slope is the Young’s Modulus (E’ or sometimes G) TS = tensile strength y = yield strength Toughness = Energy required to break (area under curve)

Compression and Shear vs. Tensile Tests Stress-strain curves are very dependent on the test method. A modulus determined under compression is generally higher than one derived from a tensile experiment, as shown below for polystyrene. Tensile testing is most sensitive to material flaws and microscopic cracks. Compression tests tend to be characteristic of the polymer, while tension tests are more characteristic of sample flaws. Note also that flexural and shear test modes are commonly employed.

Stress Strain Graphs   Chains in neck align along elongation direction: strengthening  Elongation by extension of neck 

Beyond “B”, the yield strength, deformations are plastic

Ductility & Elongation (EL) EL < 5% Brittle EL > 5% Ductile Thermosets = strong & brittle Not Ductile Thermolastics = depends on T

Cold Drawing above the Tg

TENSILE RESPONSE: • Compare to responses of other polymers: Stress-strain curves adapted from Fig. 15.1, Callister 6e. Inset figures along elastomer curve (green) adapted from Fig. 15.14, Callister 6e. (Fig. 15.14 is from Z.D. Jastrzebski, The Nature and Properties of Engineering Materials, 3rd ed., John Wiley and Sons, 1987.) • Compare to responses of other polymers: --brittle response (aligned, cross linked & networked case) --plastic response (semi-crystalline case) 25

Elastomer Molecules High entropy Low entropy Low energy High energy Model of long elastomer molecules, with low degree of cross‑linking: (a) unstretched, and (b) under tensile stress. Low entropy Low energy High energy

YOUNG’S MODULI: COMPARISON Graphite Ceramics Semicond Metals Alloys Composites /fibers Polymers E(GPa) Based on data in Table B2, Callister 6e. Composite data based on reinforced epoxy with 60 vol% of aligned carbon (CFRE), aramid (AFRE), or glass (GFRE) fibers. 13

Linear Elasticity: Possion Effect • Hooke's Law:  = E  • Poisson's ratio, : metals:  ~ 0.33 ceramics: ~0.25 polymers: ~0.40 Units: E: [GPa] or [psi] n: dimensionless Why does  have minus sign?

Poisson Ratio • Poisson Ratio has a range –1    1/2 Look at extremes No change in aspect ratio: Volume (V = AL) remains constant: V =0. Hence, V = (L A+A L) = 0. So, In terms of width, A = w2, then A/A = 2 w w/w2 = 2w/w = –L/L. Hence, Incompressible solid. Water (almost).

Poisson Ratio: materials specific Metals: Ir W Ni Cu Al Ag Au 0.26 0.29 0.31 0.34 0.34 0.38 0.42 generic value ~ 1/3 Solid Argon: 0.25 Covalent Solids: Si Ge Al2O3 TiC 0.27 0.28 0.23 0.19 generic value ~ 1/4 Ionic Solids: MgO 0.19 Silica Glass: 0.20 Polymers: Network (Bakelite) 0.49 Chain (PE) 0.40 Elastomer: Hard Rubber (Ebonite) 0.39 (Natural) 0.49

Example: Poisson Effect Tensile stress is applied along cylindrical brass rod (10 mm diameter). Poisson ratio is  = 0.34 and E = 97 GPa. Determine load needed for 2.5x10–3 mm change in diameter if the deformation is entirely elastic? Width strain: (note reduction in diameter) x= d/d = –(2.5x10–3 mm)/(10 mm) = –2.5x10–4 Axial strain: Given Poisson ratio z= –x/ = –(–2.5x10–4)/0.34 = +7.35x10–4 Axial Stress: z = Ez = (97x103 MPa)(7.35x10–4) = 71.3 MPa. Required Load: F = zA0 = (71.3 MPa)(5 mm)2 = 5600 N.

Negtive poisson’s ratio foams

Compression Radial n = -1.24 Axial n = 0 Lakes, R. S., "No contractile obligations", Nature, 1992, 358, 713-714.

Anisotropic Materials 1) Compaction of UHMWPE powder 2) Sintering 3) Extrusion

Mechanical properties are sensitive to temperature FIGURE 10.9 Effect of temperature on the stress-strain curve for cellulose acetate, a thermoplastic. Note the large drop in strength and increase in ductility with a relatively small increase in temperature. Source: After T.S. Carswell and H.K. Nason. Manufacturing Processes for Engineering Materials, 5th ed. Kalpakjian • Schmid Prentice Hall, 2008.

Poly(methyl methacrylate)

Lower elastic modulus, yield and ultimate properties Stress Strain Polymers Metals Ceramics Lower elastic modulus, yield and ultimate properties Greater post-yield deformability Greater failure strain

Polymers: Thermal Properties In the liquid/melt state enough thermal energy for random motion (Brownian motion) of chains Motions decrease as the melt is cooled Motion ceases at “glass transition temperature” Polymer hard and glassy below Tg, rubbery above Tg

Polymers: Thermal Properties Tg Tm semicrystalline log(Modulus) crosslinked linear amorphous Temperature

Polymers: Thermal Properties Stress Strain decreasing temperature or increasing crystallinity

Properties depend on amount of cross-linking Increasing cross-linking Figure 8.13 M. P. Groover, “Fundamentals of Modern Manufacturing 3/e” John Wiley, 2007

Phase diagram for semi-crystalline polymer

Polymer Phases Volume Tg Tm Tb Temperature Polymers don’t exist in gas state; RT for boiling is higher than bond energies Glassy Solids Polystyrene Tg 100 °C PMMA Tg 105 °C Polycarbonate Tg 145 °C Rubber Tg -73 °C Liquid Volume Crystalline Solids Polyethylene Tm 140 °C Polypropylene Tm 160 °C Nylon 6,6 Tm 270 °C Glassy Solid Crystalline Solid Liquids Injection molding & extrusion Polydimethylsiloxane Tm -40 °C Tg Tm Tb Temperature

Differential Scanning Calorimetry (DSC)

Modulus versus temperature

Viscous Response of Newtonian Liquids The top plane moves at a constant velocity, v, in response to a shear stress: v A y F Dx There is a velocity gradient (v/y) normal to the area. The viscosity h relates the shear stress, ss, to the velocity gradient. h has S.I. units of Pa s. The shear strain increases by a constant amount over a time interval, allowing us to define a strain rate: Units of s-1 The viscosity can thus be seen to relate the shear stress to the shear rate:

Measuring viscosities 1 pascal second = 10 poise = 1,000 millipascal second 10-100,000 cP Requires standards

Viscosity of Polymer Melts Shear thinning behaviour For comparison: h for water is 10-3 Pa s at room temperature. Poly(butylene terephthalate) at 285 ºC

h ~ tTGP Scaling of Viscosity: h ~ N3.4 h ~ N3.4 N0 ~ N3.4 Why? 3.4 Data shifted for clarity! 3.4 h ~ tTGP Viscosity is shear-strain rate dependent. Usually measure in the limit of a low shear rate: ho h ~ N3.4 N0 ~ N3.4 Universal behaviour for linear polymer melts Applies for higher N: N>NC Why? G.Strobl, The Physics of Polymers, p. 221

Concept of “Chain” Entanglements If the molecules are sufficient long (N >100 - corresponding to the entanglement mol. wt., Me), they will entangle with each other. Each molecule is confined within a dynamic “tube”. Tube G.Strobl, The Physics of Polymers, p. 283

Network of Entanglements There is a direct analogy between chemical crosslinks in rubbers and “physical” crosslinks that are created by the entanglements. The physical entanglements can support stress (for short periods up to a time tT), creating a “transient” network.

An Analogy! There are obvious similarities between a collection of snakes and the entangled polymer chains in a melt. The source of continual motion on the molecular level is thermal energy, of course.

“Memory” of Previous State Poly(styrene) Tg ~ 100 °C

Development of Reptation Scaling Theory Pierre de Gennes (Paris) developed the concept of polymer reptation and derived scaling relationships. Sir Sam Edwards (Cambridge) devised tube models and predictions of the shear relaxation modulus. In 1991, de Gennes was awarded the Nobel Prize for Physics.

Scaling Concepts in Polymer Physics Cornell University Press, 1979 There once was a theorist from France who wondered how molecules dance. “They’re like snakes,” he observed, “As they follow a curve, the large ones Can hardly advance.” D ~ M -2 de Gennes P.G. de Gennes Scaling Concepts in Polymer Physics Cornell University Press, 1979

Entanglement Molecular Weights, Me, for Various Polymers Me (g/mole) Poly(ethylene) 1,250 Poly(butadiene) 1,700 Poly(vinyl acetate) 6,900 Poly(dimethyl siloxane) 8,100 Poly(styrene) 19,000

Amorphous Glasses (< Tg) This is a self siphoning gel. Add a dispersant such as alcohol to separate the resin particles inhibiting the formation of large insoluble lumps. Any water soluble alcohol can be used as long as it is dry. Mix 20-25 ml of the alcohol with 3 to 4 grams of polyethylene oxide in a clean dry 600-ml beaker. Swirl the mixture to completely wet the resin with alcohol. Add 350-400 ml of tap water into the mixture “in one pour” and stir until the resin has gelled completely. Pour the gel into a second 600-ml beaker and then back and forth between the two beakers. The gel can be made to siphon by raising one beaker above the other while gradually pouring the gel. Once the gel starts to pull, separate the two beakers and turn the upper vessel vertically. The gel will move up the sidesw of the beaker as a thin film which forms thick strands as it falls. This process can be continued indefinitely. Add 100 ml of water to the empty beaker and swirl to wet the sides. Pour the gel into the water and then back into the original container. The siphoning process speeds up considerably pulling the gel quickly out of the upper beaker. (Even small strands can start the siphoning process emptying the beaker unexpectedly. The gel can be disposed of in the waste paper basket, it’s 99% water. The glassware can be rinsed with plenty of tap water and dried. Tg: 40 carbons in backbone Starting moving in concert

Glass transition temperature

Rate of cooling affects Tg

Polymer Tg ( °C)

Polymer Tg ( °C)

Factors that affect Tg Polar groups increase packing density; more thermal energy is needed to created volume

Factors that affect Tg Other polar vinyl polymer:

Factors that affect Tg

Factors that affect Tg Main chain stiffness: reduced flexibility

Polyarylenes

Nylons or polyamides

Factors that affect Tg Side Chain Rigidity Long chains plasticize Anchors to movement

Long chains plasticize movements

Factors that affect Tg poly(methyl methacrylate)

Factors that affect Tg Tacticity

Factors that affect Tg Symmetry of substituents asymmetric symmetric Asymmetric have higher Tg’s

Factors that affect Tg: Mw

Factors that affect Tg: Crosslinking

Factors that affect Tg: Plasticizer Phthalates

Immiscible (Two phase) and miscible (blends) polymers

Tg as a function of film thickness

Glass Transition Rigid group in backbone Flexible polymer backbone Steric Hinderance Long plasticizing side groups Symmetrical substituents Polar functionalities Plasticizers

Additional Kinds of Transitions

Amorphous Polymers Thermo-mechanical properties

Crystallinity in Polymers Maltese cross spherulites Sheaf-like arrangement of lamellae in a blend of polyethylenes System: Polyethylene (PE), Composition: LPE:BPE 3:1 An image of an alkane crystal taken by AFM System: Alkane, Composition: C36H74 An image of a single crystal alkane System: Alkane, Composition: C294H590 Single PE spherulite AFM

Thermodynamics of melting and crystallization: First order transitions

Amorphous v Crystalline Polymers Thermo-mechanical properties

Low density polyethylene (LDPE) 915-929 45-65 Medium density polyethylene (MDPE) 930-939 65-75 High density polyethylene (HDPE) 940-965 75-90 Material Density (kg/m3) % Crystallinity Shrinkage, Stiffness, Tensile strength, Hardness, Heat deflection, Chemical resistance Density Increase Property Impact strength, Ductility Weatherability

Thermal Transition Points of Select Polymers

Rule of Thumb for Tg’s and Tm’s For symmetrical polymers: Tg = 0.5 Tm (Kelvin) Polyvinylidene chloride Tg = -18 + 273 = 255 K Tm = Tg/0.50 = 255/0.5 = 510 K or 237°C Experimentally Tm = 200 °C For asymmetrical polymers: Tg = 0.66 Tm (Kelvin) Polyvinyl chloride Tg = 81 + 273 = 377 K Tm = Tg/0.66 = 354/0.66 = 536 K or 263°C Experimentally Tm = 273 °C

Rule of Thumb for Tg’s and Tm’s Caution: Its just a rule of thumb: Atactic polystyrene Tg = 104 + 273 = 377 K Tm = Tg/0.66 = 377/0.66 = 571 K or 298 °C Experimentally Tm = 523 K or 250 °C

Crystalline Polymers (really semicrystalline) Polar functionality

Thermodynamic of Crystallization For melting Sf is positive

Intramolecular interactions (Hf) favor crystallization & higher Tm Van der Waals: 2 kJ/mole Hydrogen bonding 20 kJ/mol

Explain why Nylon 6 has a lower Tm than Kevlar

Entropic Contributions to Tm

Flexible Chains have numerous conformations Nylon 6

Rigid Chains have fewer conformations Kevlar example

Polymer symmetry and Melting Point

Molecular Weight Influence on Tm Melting temperatures of n-alkanes (up to C100) as a function of chain length.

Methods for Inducing Crystallization in Polymers Slow cooling of molten polymer Annealing between Tg and Tm Evaporation of solvent Shear & disintanglement Stretching and alignment of macromolecules

Characterization of Crystalline Polymers: Diffraction

Rare to get single crystals: Powder XRD or films

Polyethylene’s Orthorhombic Unit cell

Vinyl Polymer Crystals: Substituents favor helical conformation

Characterization of Crystallinity in Polymers Polymers generally have crystalline and amorphous contributions

Lamellar Structure of Polymer crystals

Polymer single crystals: Graduate students nightmare Still lamellar structures

Validation of Models

Dislocations in Polymer Crystals

From singhle crystals to Aggregate structures

Polyethylene Spherulites

Spherulite Growth from Lamellar crystals

Crystalline structures in polymers TEM of spherulite structure in natural rubber(x30,000). Chain-folded lamellar crystallites (white lines) ~10nm thick extend radially.

• % Crystallinity: % of material that is crystalline. --TS and E often increase with % crystallinity. --Annealing causes crystalline regions to grow. % crystallinity increases.

Tensile Response: Brittle & Plastic Stress-strain curves adapted from Fig. 15.1, Callister 6e. Inset figures along plastic response curve (purple) adapted from Fig. 15.12, Callister 6e.

Amorphous polymer properties do not depend on cooling rate. Semicrystalline polymer properties depend on final degree of crystallinity, and hence the rate of cooling. Lower % S-Cryst Temperature Tg E Achieved using slower cooling rates. Higher % S-Cryst Cooling rates for semi-crystallines are important!

Micrographs of Polymer Spherultes

Seeing Maltese Crosses: Polarizing Microscopy

Polarizing Optical Microscopy

Formation of Ring Pattern: Lamellar Twisting

Microfibriallar Morphology

Polyethylene Fibers Nucleated on Si-C fibers: Shish-Kebobs

Branching on Crystallinity Which one will be more likely to crystallize?

Linear crystallizes easier (HDPE = linear; LDPE = branched)

Nucleation Rates between Tg and Tm

Primary Crystallization

Quenching Slow Cooling Crystallinity (%) Cooling rate (oC/s) 40 30 20 10 0.01 0.1 1.0 10 100 Cooling rate (oC/s)

Early stages of crystallation of PEEK in the presence of a carbon fibre.

Effects of Crystallinity Strength: Stronger & Stiffer Optical: Opaque (scattering by spherulites) Higher density Less Soluble Less Permeable Smaller interchain distances Stronger intermolecular forces