Slide-Set-6-Glass-transition

Slide-Set-6-Glass-transition - Glass Transition Behavior:...

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Unformatted text preview: Glass Transition Behavior: Glass Lecture Slide Set #6 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 #6 – Glass Transition Behavior Behavior • Learning Objectives: – Glass transition • Thermodynamic model • Kinetic model • Correlation to mechanical properties – Physical Aging – thermodynamic reversible EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 2 Glass Transition Characteristics Glass • Modulus (1 Hz) – EG ~ 109 Pa > ER~ 105-7 Pa • Viscosity – ηG ~1013 P > η R~ 103-4 P Amorphous by x-ray techniques Amorphous Coefficient of thermal expansion Coefficient αG ∼ 10 to 100 ppm < αR = ~500 ppm dE/dl < 0; dv ≠ 0 EMA 6165 Polymer Physics – AB Brennan 3 Glass Transition Characteristics Glass • Heating: Heating: – Modulus decay of 3 - 4 orders of Modulus magnitude over a 20 to 40°C range magnitude – Volumetric expansion increases in a Volumetric continous manner continous – Viscosity decays Viscosity – Creep increases – CTE increases – Density decreases – RI decreases EMA 6165 Polymer Physics – AB Brennan 4 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 6580 Science of Biomaterials University of Florida Copyright Protected 5 Glass Transition Characteristics • Fox and Flory Vo = V '+β g T • Typical value for free volume fraction i.e. f= Vf V = 0.025 EMA 6165 Polymer Physics – AB Brennan 6 Glass Transition Characteristics • Williams-Landel-Ferry (WLF) Doolittle Equation OR Vo ln η = B V f η = Ae + ln A Vo B V f EMA 6165 Polymer Physics – AB Brennan 7 Glass Transition Characteristics f - Fractional free volume is not a constant value, thus f = f o + α f ( T − To ) Where 1 dV α= V dT P EMA 6165 Polymer Physics – AB Brennan EMA 8 Glass Transition Characteristics ( B f )( T − T ) ∆ ln t = ( f α ) +(T −T ) o o o f o What are the factors to consider now: What f o ,α f T ,t variables constants EMA 6165 Polymer Physics – AB Brennan 9 Glass Transition Characteristics Glass Kinetic Theory Ej φ (V) Ej = Molar energy Eh = Activation energy for disappearance of a hole disappearance Eh ← Volume EMA 6165 Polymer Physics – AB Brennan Reaction Coordinate 10 Glass Transition Characteristics Glass Consider: N * h o υ =N o υ h Vh = Molar volume of hole Molar Eh = Molar excess energy associated with hole associated Ej = Molar energy for disappearance of a hole disappearance e E −h RT Nh* = Equilbrium # of holes holes ν o = molar volume of segments segments No = moles of repeat units units EMA 6165 Polymer Physics – AB Brennan 11 Glass Transition Characteristics Glass Relaxation time for the disappearance Relaxation of a hole: of h −E j h Q τh = * ffdd e RT kT Q where Q h ffdd Q Activated state ∆ N h H * ∝ ∆ CP Partition functions, EMA 6165 Polymer Physics – AB Brennan 12 Free Volume Theory Free • Advantages – Time and Temp of Time Viscoelastic events related to Tg Tg – Coefficients of Coefficients expansion above and below Tg related related 3/1/97 Glass Transition Characteristics • Disadvantages – Actual molecular Actual motion poorly understood understood 13 Kinetic Theory Advantages q Shifts in Tg with Time frame quantitatively determined q Heat capacity determined 3/1/97 Glass Transition Characteristics Disadvantages q No Tg predicted at infinite Time scale Glass Transition Characteristics – Thermodynamic Theory Thermodynamic • Disadvantages – Infinite Time scale Infinite required to verify required – True second order True temperature transition poorly understood understood 3/1/97 • Advantages – Variation of Tg with Variation MW diluent, and crosslink density predicted predicted – Predicts true second Predicts order transition temperature temperature fo predictions by theory predictions Theory Fractional Free Vol (est) WLF 0.025 Hirai & Eyring (Kinetic hole theory) 0.08 Miller 0.12 Simha & Boyer 0.113 EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 16 Glass Transition Characteristics Characteristics • Attempts to unify kinetic rate and Attempts equilibrium behavior equilibrium T = 1.30 ± 8.4% Tg • Adams and Gibbs – WLF predicts that: WLF η→ ∞ T − Tg = −51.6 C 3/1/97 17 Polymer Structure -Property Behavior Polymer Chain Topography • Bulkier side groups Bulkier raise Tg raise • Longer flexible units Longer lower Tg lower EMA 4161C - University of Florida Copyright Protected 18 PEI Physical Aging – Mechanical Response/Properties (Feller 1993) Response/Properties • Physical aging occurs below Tg • Kinetics follow WLF (Tg-50 < te < Tg) Arrhenius Arrhenius (0K < te < Tg-50) • Reversible H3C CH3 O O N N R O O EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 O O O n R 19 PEI Physical Aging – Mechanical Response/Properties (Feller 1993) Response/Properties • Chain diffusion follows an exponential Chain function (Compliance) function 1 − e − t τ D( t ) = Du ( t ) ( Du − Dr ) EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 20 PEI Physical Aging – Thermal Properties (Feller 1993) Properties • Excess Excess enthalpy is a measure of the densification of the glassy polymer phase. phase. EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 21 Summary Summary • Glass transition is a 2nd order thermodynamic transition. thermodynamic • Two approaches, i.e., thermodynamic and Two kinetic, are used to describe Tg kinetic, • Fractional free volume defines the Fractional thermodynamic state thermodynamic • Physical aging is a thermoreversible Physical process that affects glassy phase only process EMA 4161C Phys Prop Poly - University of Florida Copyright 2009 22 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 23 ...
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This note was uploaded on 07/17/2011 for the course EMA 4161c taught by Professor Staf during the Fall '10 term at University of Florida.

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