Lecture23 - EMA 6165 - Polymer Physics Glass Transition...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: EMA 6165 - Polymer Physics Glass Transition Lecture 23 Dr. Anthony Brennan University of Florida Department of Materials Science & 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 Vol Spec (cc/g) Free Volume Approach V0,G α liquid α glass Vf’ fast Flory Fox WLF slow V’ Tf Tf Temperature (K) EMA 6165 Polymer Physics – AB Brennan EMA 3 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 4 EMA 6165 Polymer Physics – AB Brennan EMA 5 Glass Transition Characteristics f = f o + α f ( T − To ) f o = Fractional free volume @ T g To T = generalized transition temperature i.e. Tg = any temperature above Tg i.e. To EMA 6165 Polymer Physics – AB Brennan EMA 6 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 7 Glass Transition Characteristics q Look at t t ∆ ln t = ln t − ln t o = ln to q By definition: t ln aT = ln AT = ln to Shift Factor EMA 6165 Polymer Physics – AB Brennan EMA 8 Glass Transition Characteristics t ln to ln AT Shift Factor ( B f )( T − T ) = ( f α ) +( T −T ) o o f EMA 6165 Polymer Physics – AB Brennan EMA o o 9 Glass Transition Characteristics WLF log10 B AT = − 2.303 f o = C1 ≈ 17.44 fo ≈ 51.6 C2 = αf EMA 6165 Polymer Physics – AB Brennan EMA 10 Glass Transition Characteristics log10 aT = B − ( T − To ) 2.303 f o (f o ) α f + ( T − To ) EMA 6165 Polymer Physics – AB Brennan EMA 11 Glass Transition Glass Shift Factor Shift log10 aT = where − C1 ( T − To ) C2 + ( T − To ) B C1 = + 2.303 f f o - glass o fo α f - CTE glass C2 = αf EMA 6165 Polymer Physics – AB Brennan EMA 12 Glass Transition Glass Shift Factor Shift Normally whereas B ≈ 1 and C1 ≈ 17.44 C2 ≈ 51.6 Thus..... f o = f g = 0.025 α f ≈ ∆α = α e − α g EMA 6165 Polymer Physics – AB Brennan EMA 13 V, H, S liq uid su pe rco ole d Thermodynamic Treatment Melting Gglass = Gliquid lass g S glass ≠ Sliquid xtal Vglass ≠ Vliquid Tg Tm T EMA 6165 Polymer Physics – AB Brennan EMA 14 Glass Transition Glass Ehrenfest Ehrenfest Ehrenfest 1st Order Transition Ehrenfest 1st Glass ∂G = − S ∂ T + V dP ∂G S= ∂T P ∂G V= ∂ PT Cry st Supercooled liquid al G Tg EMA 6165 Polymer Physics – AB Brennan EMA Tm T 15 Glass Transition 2nd Order Transition 2nd 2nd Order ∂G = 2 ∂T P 2 ∂S = ∂T P G T ∂V ∂G 2 = = − βV ∂ P T ∂T T 2 Compressibility EMA 6165 Polymer Physics – AB Brennan EMA 16 Glass Transition Characteristics ∂ ∂ G2 ∂V = = ∂T ∂ P ∂T P T P αV Coefficient of Volumetric Pressure EMA 6165 Polymer Physics – AB Brennan EMA 17 Glass Transition Characteristics Consider ∆P f 2 = f 1 + α f ( T2 − T1 ) − β f ( P2 − P1 ) Assume isothermal compressibility = k over the range of interest then... EMA 6165 Polymer Physics – AB Brennan EMA 18 Glass Transition Characteristics f 2 = f1 and α f ( T2 − T1 ) = β f ( P2 − P1 ) ∆β dT ∆T β f = ≈ = ∆ P α f dP ∆α ff EMA 6165 Polymer Physics – AB Brennan EMA 19 Glass Transition Characteristics Gibbs and Di Marzio Di q Clayperon equation gives Pressure Dependence dT ∆V = dP ∆S q It can be shown using L’ Hopitals Rule dT2 = dP ∂ ∆V ∂ T = ∂ ∆S ∂ T EMA 6165 Polymer Physics – AB Brennan EMA V∆αTg ∆C P 20 Glass Transition Isothermal Compressibility Isothermal OR dT2 ∂ ∆V ∂ P ∆β = = dP ∂ ∆S ∂ P ∆α EMA 6165 Polymer Physics – AB Brennan EMA 21 Glass Transition Characteristics Originally derived in terms of viscosity Originally assuming: assuming: Vf < < 1 Vf Vo ≅ Vf Vo + V f ≅ EMA 6165 Polymer Physics – AB Brennan EMA f 22 Glass Transition Characteristics Thus..... ln η − ln ηo = B B ln A − ln Ao+ − fo f EMA 6165 Polymer Physics – AB Brennan EMA 23 Glass Transition Characteristics η = ln ηo t ln to ln AT = Time dependent quantity ( γ) EMA 6165 Polymer Physics – AB Brennan EMA 24 Glass Transition Characteristics Typically, ( ( ) ) 17.44 T − Tg η log = − ηo 51.6 + T − Tg EMA 6165 Polymer Physics – AB Brennan EMA 25 Glass Transition Characteristics ∞ log AT η( t ) = ∫ E ( T ,t ) dt 0 0 -20 -10 0 +60 +1 EMA 6165 Polymer Physics – AB Brennan EMA 0 T - Tg (K) 26 Glass Transition Characteristics ( E Tg , t ref ρ( T1 ) T1 )= t E T2 , A T ρ( T2 ) T2 ρ( To ) To t E T , A E To ,t = T ( T) T ρ () EMA 6165 Polymer Physics – AB Brennan EMA 27 Glass Transition Characteristics Kinetic Theory Ej φ (V) Eh Ej = Molar energy Eh = Activation energy for disappearance of a hole hole ← Volume Reaction Coordinate EMA 6165 Polymer Physics – AB Brennan EMA 28 Glass Transition Characteristics Consider: * h N υ o = No e 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 Eh − RT Nh* = Equilbrium # of holes holes ν = molar volume of segments segments No = moles of repeat units units EMA 6165 Polymer Physics – AB Brennan EMA 29 Glass Transition Characteristics Relaxation time for the disappearance Relaxation of a hole: of h −E j h Q RT τh = * ffdd e kT Q where Q h ffdd Q Activated state ∆N h H * ∝ ∆C P Partition functions, EMA 6165 Polymer Physics – AB Brennan EMA 30 Scan table EMA 6165 Polymer Physics – AB Brennan EMA 31 Glass Transition Characteristics Kovacs • Apparent Activation Energy d log AT 2 E A = − RT d T q e.g., Poly(styrene) kcal E A ≈ 210 mol where T = Tg EMA 6165 Polymer Physics – AB Brennan EMA 32 Glass Transition Thermodynamic Approach Thermodynamic Gibbs and DiMarzio 0.2 0.1 SCONFOR 0 Theory 350 400 450 500 Temp (K) EMA 6165 Polymer Physics – AB Brennan EMA 33 Glass Transition Characteristics • Partition function to define Partition conformational states. conformational Q = ∑ w( f1nx ...., f i nx ...no ) e EMA 6165 Polymer Physics – AB Brennan EMA ( ff ) 34 Glass Transition Characteristics E = ( f 1nx . . . . , f i nx . . . no ) n = D. P . ∂ ln Q + k ln Q S = kT ∂ T υ ,n EMA 6165 Polymer Physics – AB Brennan EMA 35 Enthalpy Glass Transition Characteristics qA > qB 0 T (K) EMA 6165 Polymer Physics – AB Brennan EMA 36 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 37 ...
View Full Document

This note was uploaded on 07/20/2011 for the course EMA 6165 taught by Professor Brennan during the Spring '08 term at University of Florida.

Ask a homework question - tutors are online