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XRD for polymers

XRD for polymers. X-ray Diffraction. Semi-crystalline polymers: arcs not spot More diffuse (crystallites are usually small, a few hundred A); many imperfection. X-ray diffraction patterns for various morphology. Solution-grown single crystal.

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XRD for polymers

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  1. XRD for polymers

  2. X-ray Diffraction • Semi-crystalline polymers: • arcs not spot • More diffuse (crystallites are usually small, a few hundred A); many imperfection

  3. X-ray diffraction patterns for various morphology

  4. Solution-grown single crystal • Small (optical miscroscope: maybe; electron microscope: YES) • The crystals are normally precipitated either by cooling from a hot solution or by the addition of a non-solvent • crystal thickness: order of 100 A

  5. Continued Lamella (plate-like) 10X10 um Orthorhombic polyethylene [001] Lamella folds up/down Perpendicular (or nealy) to the crystal surface

  6. Folding • Random re-entry: a molecule leaves and re-enters a crystal randomly • Adjacent re-entry: a molecule leaves and re-enters a crystal in adjacent position • This is a leading model for single crystal grown from dilute solution

  7. Solid-state polymerized single crystals Example: polydiacetylene X-ray rotation photography: fig 4.2

  8. Semicrystalline polymers • When concentrated solution or melt is used, crystal morphologies change and more complex crystal forms are obtained • In the melt, chain entanglements are more irregular than those obtained from dilute solution. • Semi-crystalline (crystalline + amorphous)

  9. Spherulites • Melt-crystallized polymer • Thin film by sectioning a bulk sample or casting the film • Not a single crystal, but consists of numerous crystals radiating from a central nucleus

  10. Continued Crystals radiating from the central nucleus and terminating at the spherulite boundaries Crystals are Lamellar Edge shows 100 A thickness

  11. Degree of Crystallinity Density method: Xc = rc/r((r-ra)/(rc-ra)) Wide-angle x-ray scattering (WAXS) Xc = A c / (Aa + A c) Other methods: DSC based on DHm IR and NMR crystalline Non-crystalline

  12. Crystal Thickness and chain extension • Lamellae: thickness which controlled by the crystallization condition • Lamellar thickness increases with increasing crystallization temperature Determination methods (1) shadowing (2) interference microscopy (3) SAXS n l = 2d sinq For thickness ~100 A, l~ 1 A q is very small

  13. For a given solvent, the lamellar thickness from solution-grown is found to increase with increasing crystallization temperature Controlled by the difference between the crystallization temperature, Tc and solution temperature, Ts

  14. Isothermally melt-crystallized polyethylene Similar to that in solution-grown crystals, crystallization temperature Molar mass has a strong effect upon lamellar thickness Melt pressure

  15. Crystallization with orientation If under stress, morphologies will be very different Implications: Many polymers are processed in the form of fiber, injection moulded or extruded, and others involved applying stress on the materials during crystallization Oriented polymer structures are extremely important high uni-directional strength

  16. Crystallization • Nucleation • Tendency for random tangled molecules in the melt to become aligned and form small ordered regions (nuclei) • Homogeneous • Heterogeneous • Growth • r = v t • Spherulite radius • v: growth rate • Growth rate strngly depends on the crystallization temperature • Figure 4.25 (viscosity)

  17. Crystallization Kinetics • Polymer melt of mass W0 • Homogeneous nucleation • The rate of nucleation (# of nuclei formed per unit time and unit volume) is a constant • The total # of nuclei formed in time interval, dt will be NW0dt/rL After time t, these nuclei will grow into spherulites of radius, r The total mass of each spherulite dWs dWs= 4/3pv3t3rsNW0dt/rL Eq 4.19 valid only in the intial stage of crystallization WL/W0 = 1- pNv3t4rs/3rL depends on t4; if nuclei are formed instantaneously, t3 dependence is expected

  18. Crystallization Kinetics • Impingement of spherulites • Reduction of overall volume of the system • Spherulites move closer to each other • Impingement by Avrami equation • Equation 4.25

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