Slide-Set-7-Diffusion-and-Crystallinity

Slide-Set-7-Diffusion-and-Crystallinity - Crystallization:...

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Unformatted text preview: Crystallization: Crystallization: Lecture Slide Set #7 Dr. Anthony Brennan University of Florida Tel: 352.392.6281 Email: abrennan@mse.ufl.edu EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 1 Slide Set #7 – Crystallization Slide • Learning Objectives: – Chain Diffusion • Reptation • Fickian and non-Fickian Diffusion – Crystallization • First order thermodynamic transition EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 2 Section 1 CHAIN DIFFUSION CHAIN EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 3 Chain Diffusion Models – Rouse Chain • Rouse Model – Bead and Spring (Hookean) – • 3k T ∆ x f= Where k – Boltzman’s constant, T is temperature (K), ∆ x is displacement, r is end to Where end distance end r2 Consider the recovery force, f as the viscous force on the chain, then: where τ is the relaxation time, η is the melt viscosity, p is the running index, c where is the polymer concentration is 6η 0 M i2 τ p ,i = 2 π c R T M w p2 EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 4 Chain Diffusion Models – de Gennes • Reptation Theory – chain in a tube d rn = bJ n dt – Where r represents the position vector, t is the time to Where move, J is the “defect current” move, C A B C B A D∝M −2 Tr ∝ M 3 At T>Tg - Diffusion constants vary from 10-10 to 10-17 cm2/s EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 5 3 Diffusion – PS-SO H Diffusion EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 6 Section 2 CRYSTALLIZATION CRYSTALLIZATION EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 7 Phase Diagram Semi-crystalline Glass/Crystal “Solid” Liquid/Crystal “Rubbery” Liquid “Viscous Liquid” l o V c e p S ) g / c ( αmix (T< Tg) αMix (Tg<T<Tm) αMix (T>Tm) V0,G Tg Tm Temperature (K) EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 8 Crystalline Morphology Of Polymers Polymers • Fringed Micelle Staudinger - PET, Nylon 10 nm EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 9 Single Crystal of PE Single Adjacent Re-entry model If ∆ hf is known one can calculate σ e If Huseby, Bair, Salovey measured P.E. that was gamma irradiated to prevent thickening σ e = 93 ± 8 ergs/cm2 Tm = 146 oC EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 EMA 10 Adjacent Reentry Morphology Adjacent HEAT HEAT EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 11 Spherulite - Lamellae Spherulite • • • • Spherulite Lamellae Tie Molecules Growth Growth Direction Direction • Branching PEO Crystallization Video EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 12 Spherulite Morphology Spherulite http://spm.phy.bris.ac.uk/research/polymers/spherulites/ EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 13 Rate of growth Edge view Top view EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 14 Rate of growth Rate EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 15 AFM Image of Spherulite Growth http://spm.phy.bris.ac.uk/research/polymers/spherulites/ EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 16 Rate of growth Rate • Rate of Growth Rate Avrami Keith and Padden Hoffman Measure by: Optical Microscopy Synchroton Radiation Dilatometry Calorimetry EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 17 Crystal Morphology - Process Crystal EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 18 Polymer Structure -Property Behavior Behavior Crystallites • Spherulite – – – – – lamellae folded chain tie chain/molecule quiescent conditions flexible chain • Row nucleated – lamellae – shear field, i.e., shear extruded melt extruded • Mozaic – – – – – – liquid crystalline smectic nematic cholesteric high shear, solution rigid rod chain or rigid side chain side EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 19 Crystal Morphology of PTT Crystal O O O O n • Fig 8. PLM micrographs of Fig PTT spherulites crystalliezed at (a) 443K; (b) 448 K; © 453 K; (d) 458 K; (e) 463 K; (f) 469 K; (g) 473K; (h) 478 K; (i) 483 K; (j) 488 K; (k) 490K and (l) 493K. Adapted from Hong et al, Polymer 43 (2002), 3335Polymer 3343 EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 20 EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 EMA 21 Avrami Kinetics Avrami χ ( t ) = 1 − exp( − kt n ) ∀ χ (t) – growth parameter determined experimentally, i.e., normally a linear term such as mm/second but generally refers to volume fraction of crystal phase refers • k – (Z in Sperling's Text) – volume term – – Vt = 3/2 π g3 l where g is growth rate (radius/time) and l is a rate term based upon assumptions of # of nuclei growing term EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 22 Crystalization Mechanism Avrami Constants Z Spheres Avrami Constants Restrictions n 4.0 3 D 4/3π g3LL 3.0 3 D Sporadic [π/3 ]g3ld 3.0 2 D Estimated Rods 2/3π g3l Estimated Discs Sporadic π g3Ld 3.0 2 D Sporadic [π/4 ]g3ld2 3.0 1 D Estimated 1 /2 π g3Ld2 3.0 1 D Adapted from Sperling 3rd Edition, Table 6.4, 2001 EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 EMA 23 Avrami Kinetics of PTT Avrami Fig 8 Adapted from Hong et al, Polymer 433 (2002), 3335-3343 EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 24 Keith-Padden Theory Keith-Padden • • • • Thermodynamics of Thermodynamics Crystallization – Crystallization D δ= G where δ is the lateral dimensions of where the lamellae, D is the diffusion coefficient of the impurity in the melt and G is the radial growth rate and Thus, δ is a measure of spherulite Thus, texture: texture: 1 dδ 1 dD 1 dG = − δ dT D dT G dT Thus, the radial growth rate is: ∆Gcrystal = G0 e • Chain Axis Orientation ∆E RT e − ∆F * Growth Direction RT where ∆ F* is the free energy of where F* formation of a surface nucleus of cirtcal size cirtcal EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 25 Hoffman Theory Hoffman • Thermodynamics of Thermodynamics Crystallization – Crystallization ∆Gcrystal = 4 xl σ + 2 x 2σ e − x 2l ( ∆f ) • • where x is the width of lamellae where (crystal), l is the stem length, σ is the lateral surface interfacial free energy, and ∆ f is the bulk free energy of is fusion fusion Free energy of fusion is Free defined by: defined ∆f = ∆h f − T∆S f = ∆h f − • T∆h f T fo = ∆h f ( ∆T ) x x T fo So at the melting So temperature: temperature: 2σ e o T f = T f 1 − ∆h f l EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 26 Rate of growth • Regime I Nucleation (one site) GI =bo il = bo ao ns i Stem thickness Alternatively ( Stem length * Stem width ) nuclei depostion rate # of stems of width a0 ( # stems * GI = G0 * exp QD RT * exp − K g I T ∆T QD* = activation energy of reptation (steady state) Kg = nucleation constant 27 ) Artificially boundaries for illustrative purposes only GI σ l Chain fold Surface bo g* g Sk L=na 28 Rate of growth G0 = l * ( kT h) ns J1 * exp ( 2abσ e Ψ kT ) J = exp ( − ∆ f RT ) This allows for possible energy This barriers not explicitly identified barriers 29 07/17/11 07/17/11 Rate of growth • Regime II GII =b0 ( 2ig ) 0 .5 GII =b ( ST g aN ) Sk = mean separation of sites 0.5 Nk = number of nucleation sites sites 0.5 1 2g Sk = = Nk i 07/17/11 07/17/11 30 Regime II Regime GII σ l g* bo Sn g Sk 07/17/11 31 Regime III – Rapid Cooling Regime GIII = b0iL = b0i ' n a0 ' s 07/17/11 32 Thermal Transitions Thermal EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 33 WAXD and DSC of PTT WAXD Fig 1 Adapted from Hong et al, Polymer 433 (2002), 3335-3343 EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 34 Summary Summary • Melting point is a first order thermodynamic Melting transition. transition. • Crystal morphology is a function of both time Crystal and temperature and • Crystallization growth rates are limited by Crystallization either diffusion or nucleation either • Methods of detecting crystal structure Methods include density, x-ray, thermal, NMR, FTIR, scattering. scattering. • No polymer is 100% vol crystal EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 35 References References • Introduction to Physical Polymer Science, 4th Edition, Lesley H. Sperling, Wiley Interscience (2006) ISBN 13 978-0-471-70606-9 ISBN • Principles of Polymer Chemistry, P.J. Flory (1953) Principles Cornell University Press, Inc., New York. Cornell • The Physics of Polymers, Gert Strobl (1996) The Springer-Verlag, New York. Springer-Verlag, • “The physical aging of poly(etherimide)” Frederick The Feller, III, Master of Science Thesis, University of Florida, 1993. Florida, EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 36 ...
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