Lecture19 - EMA 6165 - Polymer Physics Glass Transition...

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Unformatted text preview: EMA 6165 - Polymer Physics Glass Transition Lecture 19 Dr. Anthony Brennan University of Florida Department of Materials Science & Department Engineering Engineering EMA 6165 Polymer Physics – AB Brennan EMA 1 Agenda • Glass Transition values – Organic Organic – Inorganic Inorganic • Thermodynamic Treatment of Tg • Kinetics of Tg • Physical Aging Behavior EMA 6165 Polymer Physics – AB Brennan EMA 2 Glass Transition Characteristics Characteristics of a glass • Modulus (1 Hz) q EG ~ 109 Pa > ER~ 105-7 Pa q Viscosity q η G ~1013 P > η R~ 103-4 P q Amorphous by X-Ray techniques EMA 6165 Polymer Physics – AB Brennan EMA 3 Glass Transition Characteristics Characteristics of a glass q Coefficient of Thermal Expansion q α G ∼ 10 to 100 ppm < α R = ~500 ppm q DG < DR ∂E ≠0 ∂l and ∆v ≠0 EMA 6165 Polymer Physics – AB Brennan EMA 4 Glass Transition Characteristics Upon heating: • Modulus decay of 3 - 4 orders of Modulus magnitude over a 20 to 40°C range magnitude q Volumetric expansion increases in a discontinuous manner q Viscosity drops nearly 10 orders q Creep rises q C.T.E. increases EMA 6165 Polymer Physics – AB Brennan EMA 5 Glass Transition Characteristics Upon heating (con’t): • Optical properties q Damping increases q ∆ CP increases q Thermal Conductivity q Permeability EMA 6165 Polymer Physics – AB Brennan EMA 6 Vol Spec (cc/g) Glass Transition Characteristics α glass α liquid V f’ fast V0,G Flory Fox WLF slow V’ Free Volume Approach T Temperature (K) EMA 6165 Polymer Physics – AB Brennan EMA 7 Vol Spec (cc/g) Glass Transition Characteristics α glass α liquid Vf’ fast V0,G slow Flory Fox WLF Free Volume Approach V’ Simha-Boyer Tf Temperature (K) EMA 6165 Polymer Physics – AB Brennan EMA 8 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 EMA 9 Glass Transition Characteristics • Williams-Landel-Ferry (WLF) Doolittle Equation Vo ln η = B + ln A V f V OR η = Ae B o V f EMA 6165 Polymer Physics – AB Brennan EMA 10 Glass Transition Characteristics η = Ae • • • Vo B V f Based in viscosity measurements of Based n-alkanes. Consider the chain segments as spheres A minimum free volume is required for free rotation and thus cooperative motion. EMA 6165 Polymer Physics – AB Brennan EMA 11 Structure EMA 6165 Polymer Physics – AB Brennan EMA 12 EMA 6165 Polymer Physics – AB Brennan EMA 13 Glass Transition Characteristics • Energy P =e ( − ∆E ACT kT ) • Time ln t P = C = − ∆E ACT kT + ln t EMA 6165 Polymer Physics – AB Brennan EMA 14 Glass Transition Characteristics ln t = C + ∆E ACT kT ∆ ln t =− ∆E ACT kT ∆T 2 EMA 6165 Polymer Physics – AB Brennan EMA 15 Glass Transition Characteristics ∆ ln t = − ∆E ACT kT ∆T Consider as t T ↑↓ 2 In terms of molecular motion, f is a necessary factor EMA 6165 Polymer Physics – AB Brennan EMA 16 Glass Transition Characteristics ∆E ACT B' = kT f − ∆E ACT Similar to ln P = kT thus, B ln t P = C = − + ln t f EMA 6165 Polymer Physics – AB Brennan EMA 17 Glass Transition Characteristics B ln t P = C = − + ln t f ↓ 1 ∆ ln t = B∆ f EMA 6165 Polymer Physics – AB Brennan EMA 18 Glass Transition Characteristics Fractional free f - Fcractionalvalue,volume is not a onstant thus f = f o + α f ( T − To ) Where 1 dV α= V dT P EMA 6165 Polymer Physics – AB Brennan EMA 19 Glass Transition Characteristics Differentiate 1 ∆ ln t = B∆ f 1 1 ∆ ln t = B − fo f EMA 6165 Polymer Physics – AB Brennan EMA 20 Glass Transition Characteristics Substitution leads to 1 1 ∆ ln t = B − f +α (T −T ) f o o f o Rearrangement and division by α f leads to.... EMA 6165 Polymer Physics – AB Brennan EMA 21 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: T ,t variables f o ,α f constants EMA 6165 Polymer Physics – AB Brennan EMA 22 Summary • Glass Transition is a second order Glass thermodynamic transition. thermodynamic • Glass Transition is a fictive temperature Glass dependent upon time, temperature, rate, pressure and thermal history. pressure • WLF equation describes behavior from WLF above Tg to Tg-50°C. above • Kinetics of Tg process appear Arrhenius. EMA 6165 Polymer Physics – AB Brennan EMA 23 References • Introduction to Physical Polymer Science, 3rd Edition, Lesley Introduction H. Sperling, Wiley Interscience (2001) ISBN 0-471-32921-5 • Principles of Polymer Chemistry, P.J. Flory (1953) Cornell Principles University Press, Inc., New York. University • The Physics of Polymers, Gert Strobl (1996) Springer-Verlag, The New York. New • Some figures were reproduced from Some • Principles of Polymer Chemistry, P.J. Flory (1953) Cornell Principles University Press, Inc., New York. University EMA 6165 Polymer Physics – AB Brennan EMA 24 ...
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