Phase Transitions in Polymer Systems

1. Phase Transitions in Polymer Systems • Most products utilize polymers in their bulk (solid, condensed) state. For these applications, physical properties are strongly dependent on phase morphology and, as a result, on temperature. • To clarify key concepts, we will handle a few different polymers: • poly(methylmethacrylate) • high density poly(ethylene) • low density polyethylene; poly(ethylene-co-hexene) • poly(tetrafluoroethylene) • poly(isoprene), cis and trans. • Objectives: • gain insight into thermodynamics of phase transtions, • identify amorphous and crystalline states, • relate these to mechanical properties and • predict how each material will behave with respect to temperature changes. J.S. Parent

2. Crystalline State • Under appropriate conditions, some polymers can be cooled from a melt condition can generate an imperfect crystal structure. • The basic units of crystalline polymer morphology are crystalline lamellae, consisting of folded chains. • Nonadjacent Regular adjacent Irregular adjacent • reentry reentry reentry • Crystallization/melting of polymer crystallites is a classical phase transition, identical to that of small molecules. • Below the melting point of the material, a highly organized chain conformation is the most stable state for the polymer. • The lowest-energy conformation of polymer chains depends on composition - hydrogen bonding, van der Waals interactions. J.S. Parent

3. First-Order Phase Transitions • A transition in which the first derivatives of the molar Gibbs energy are discontinuous is defined as a first-order phase transition. • The chemical potential of the material changes abruptly at the transition point, Tt. • Heat Capacity Molar Volume J.S. Parent

4. Specific Volume Changes at Tm • Linear polyethylene: • Open circles: cooled rapidly from the melt to 25°C before fusion. • Solid circles: crystallized at 130°C for 40 days, then cooled to room temperature prior to fusion. J.S. Parent

5. PVT Behaviour at Tm - Polyethylene • HDPE • Specific volume at ambient conditions: • 1.0537 cm3/g • Mw = 126000 • Mw/Mn = 4.5,GPC-PS • Dried in vacuum oven overnight at 50°C • Sample form: pellets J.S. Parent

6. PVT Behaviour at Tm - Nylon 6,6 • Plot of standard PVT run on Nylon 66 • Note the densification (dip) just to the left of line X-Y on crystallization from a partially molten material. J.S. Parent

7. Differential Scanning Calorimetry (DSC) • A DSC instrument controls the energy input to sample and reference so they remain at • the same T throughout a programmed temperature rise. • A DSC trace is a plot of energy • (DH=Hsample-Href) as a function of T. • DSC trace of poly(ethylene • terephthalate-co-p-oxbenzoate), • quenched, reheated, cooled • at 0.5K/min through the • glass transition, and reheated • for measurement at 10K/min. J.S. Parent

8. Factors Influencing Crystallinity • Chain architecture and composition distribution determines whether a polymer exists in a semi-crystalline or completely amorphous state. • 1. Chain symmetry: symmetrical structures that permit close packing of chains favour crystallinity. • atactic poly(propylene) versus isotactic (polypropylene) • poly(tetrafluoroethylene)? • 2. Intermolecular forces: hydrogen bonding and attractive van der Waals forces promote crystallization • atactic-poly(vinyl alcohol) • 3. Branching and molecular mass: packing efficiency deteriorates with increasing branching and the relative number of free chain ends. • isotactic(polypropylene) J.S. Parent

9. Factors Influencing Tm • The fundamental equation of thermodynamics for a closed system states: DGm = DHm - T DSm • where DHm and DSm represent the enthalpy and entropy of fusion per repeat unit, respectively. • At the equilibrium temperature, Tm, DGm= 0, therefore: • Polymers in which DHm is relatively large (strong intermolecular attraction) and DSm relatively small (minimal ordering from melt to crystalline state), the temperature of melting is high. J.S. Parent

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

11. Molecular Weight Influence on Tm J.S. Parent

12. Amorphous Bulk State • An amorphous state is one of relative disorder, where chain orientation is not present on a large scale. Physical properties derived from an amorphous phase are strongly dependent on temperature. Consider, • Plexiglass - poly(methyl methacrylate) • Natural rubber - cis-poly(isoprene) • Both exist in an amorphous phase under conditions of common use, but exhibit very different mechanical properties. • If Plexiglass is heated above 105°C, it becomes rubbery. Cool natural rubber below -73 °C and it becomes a brittle, rigid material. • The transition from a glassy to a rubbery state in amorphous materials is called the glass transition temperature, Tg. • Below Tg, there is insufficient thermal energy to overcome barriers to chain mobility or even chain segmental motion. Only cooperative motion of a few atoms of the main chain or side-groups is present, as well as atomic vibrations. J.S. Parent

13. Second-Order Phase Transitions • A transition in which the first derivatives of the molar Gibbs energy are continuous, but the second derivatives are discontinuous is, by definition, a second-order phase transition. • Molar Volume Heat Capacity J.S. Parent

14. Specific Volume Changes at Tg • Specific volume v plotted against temperature for poly(vinyl acetate) measured after rapid cooling from above the Tg; • 1: 0.02 hours after cooling; • 2: 100 hours after cooling; • Tg and Tg' are the glass transition temperatures measured for the different 2 equilibration times. J.S. Parent

15. Heat Capacity Changes at Tg • Specific heat capacity Cp, plotted against temperature for atactic poly(propylene) showing the glass transition in the region of 260 K. J.S. Parent

16. Differential Scanning Calorimetry (DSC) • DSC trace of poly(ethylene terephthalate-co-p-oxbenzoate), quenched, reheated, cooled at 0.5K/min through the glass transition, and reheated for measurement at 10K/min. • Tg is taken at the • temperature at which • half the increase in • heat capacity has • occurred. • The width of the • transition is indicated • by DT. J.S. Parent

17. PVT Behaviour at Tg • Plot of standard PVT run on poly(ethylene naphthenoate) indicating the crystallization above the glass transition, followed by melting. • Line F-E: hypothetical zero-pressure isobar for a sample remain- ing amorphous. J.S. Parent

18. Factors Influencing Tg • Polymers whose structures are flexible, do not provide for strong intermolecular attraction, and do not “pack” well are those with relatively low Tg’s. • Four factors are generally believed to affect Tg: • 1. Internal chain mobility - rotational freedom along the chain as • influenced by side chains. • 2. Free volume - volume of the material that is not occupied by • polymer molecules • 3. Attractive forces - hydrogen bonding, dipole association • 4. Chain length - shorter chains have greater relative free volume. J.S. Parent

19. Molecular Weight Influence on Tg • Illustrated to the left is the effect • of molecular weight on the Tg of • amorphous polymers. Dependence of Tg on the molecular weight of the styrene block in: sty-dimethylsiloxane diblock,  sty-butadiene diblock,  sty-butadiene-sty triblock,  Also shown are Tgs for PS of various molecular weight, . J.S. Parent

20. Glassy Leathery Rubbery Viscous Static Modulus of Amorphous PS Polystyrene Stress applied at x and removed at y J.S. Parent

21. Models of Semi-crystalline Polymer Structure • Many materials crystallize from the melt into organized structures called spherulites, shown below for poly(ethylene oxide): • Crystals grow out radially to • create aggregates that can • reach a few millimetres in • diameter. • Note that semi-crystalline • polymers are comprised • of crystalline lamellae • and amorphous regions • that “bind” crystallites • together. J.S. Parent

22. Degree of Crystallinity • Even the most easily crystallized polymers contain amorphous defect regions. The extent of crystallization depends on the rate of crystallization for the material and the time during which a melt temperatures are maintained. • Crystallization occurs below Tm, • but segmental mobility of chains • is required. • Below Tg, the crystallization rate • is zero (metastable condition) • Shown is the linear growth rate of • poly(ethylene terephthalate) • (Tg=69°C, Tm=265°C) as a • function of temperature. J.S. Parent

23. Isothermal Crystallization Poly(ether-ether-ketone) Tm = 334oC; Tg = 143oC 315°C 312°C 308°C 164°C 160°C J.S. Parent

24. PEEK Crystallization Kinetics: Avrami Equation • This crystallization kinetic data can be plotted according to: • The result, shown to the right, • is a relatively linear plot from which rate constants can be easily determined. • Note that the linear trend is lost • at high degrees of crystallinity, as growth slows. • This is due to reduced radial growth of spherulites, while crystal thickening and perfecting continues J.S. Parent

25. Simple Crystallization Kinetics: Avrami Equation • Crystallization kinetics have been modeled using a framework analogous to raindrops falling in a puddle. These produce expanding circles of waves which intersect and cover the whole surface. The drops may fall sporadically or all at once, but they must strike the puddle surface at random points. The expanding circles of waves, of course, are the growth fronts of the spherulites, and the points of impact are the crystallite nuclei. • Avrami and other have used this conceptual model to develop an empirical equation for crystallization kinetics: • where k is a rate constant (sec-1) and n is a dimensionless parameter that relates to the type of phase nucleation. • Given that crystallinity is seldom complete, the Avrami equation is commonly modified by the ultimate degree of crystallinity, X: J.S. Parent

26. Thermal Transition Points of Select Polymers J.S. Parent

27. Tg/Tm Demo: Glucosepentaacetate • Glucosepentaacetate is not a polymer, but it does exhibit glass transition and crystallization phenomena in a manner that is consistent with polymeric systems. • Melting point = 110C • Tg = not well defined but approx 5C. • At room temperature, the compound is a crystalline solid. • Heating to 110C melts the solid to generate an amorphous phase of liquid-like viscosity. • Rapid chilling in ice water creates a glassy, brittle solid. • Warming results in a glass to leather transformation • Continued working of the sample • promotes further crystallization • until a solid powder is observed. • Why does it crumble where semi- • crystalline polymers do not? J.S. Parent