Chapter 4. Glass Transition Temperature. in Polymers

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1 Glass Transition Temperature 1. Introduction in Polymers 2. Transition or State of Matters 3. Theory (WLF equation) 4. Time-Temperature Superposition Principle 5. Transition T (T ) and End-use T (T use ) 6. Effect of Chemical Structures on T (Homopolymers, Copolymers & Blends) 7. Effect of Physical Characteristics of Molecules 8. Effect of Plasticizer

2 1. Introduction 1. Introduction PVC (thermoplastic): - tyon tube (masterplex pump) - leather (auto cover sheet) - Pipe Plasticizer Rubber (thermoset) - poly(isoprene) - PDMS, poly(dimethyl siloxane) - ebonite (hard rubber) ; 딱딱함

3 Materflex Pump

4 1. Introduction 1. Introduction T effect PMMA (Lucite, Plexilass ): hard, riid and lassy at RT PS PDMS, poly(isoprene): soft, flexible and rubbery at at RT poly(ethyl acrylate) Variety of chanes in state Variety of mechanical and physical properties

5 2. Transition or State of Matters 1) Thermodynamics V 1) Thermodynamic Point of View small molecules 1st order transition: L V S T T m T v V H S 2nd order transition:

6 2. Transition or State of Matters 1) Thermodynamics α C P = = 1 V V T H T P P

7 2. Transition or State of Matters 1) Thermodynamics low MW crystalline solids (lycerin) V lassy supercooled liquid depends on structure coolin rate crystallization rate crystalline T T m

8 2. Transition or State of Matters 1) Thermodynamics Polymers lassy (brittle) rubbery (soft) melt (viscoelastic) - Tm over certain T rane crystalline in lassy state T in rubbery state T m (2~10 ) - subject to hysteresis effect (rate dependency) - viscoelastic - no ases

9 2. Transition or State of Matters 1) Thermodynamics Summary on T stiff and lassy soften at T and become rubbery (leathery) (T : )

10 2. Transition or State of Matters 1) Thermodynamics Glossary - Transition: Chane of state by chanin T & P - Relaxation ( 이완, 완화 ): time required to respond to a chane in T or P, also implies some measure of molecular motion e.. - Dispersion: emission or absorption of enery at a transition (i.e. a loss peak)

11 2. Transition or State of Matters 2) Molecular Motion a. vibration of atoms about equilibrium position 2) Molecular Motion b. motion of a few (5~ 6 atoms) alon the chain or of the side roups (semental motion or semental diffusional motion) c. co-operative wrilin abd jumpin of approx. 40 ~ 50 carbons d. transitional motion of entire molecules

12 2. Transition or State of Matters 2) Molecular Motion 2) Molecular Motion but not all molecules posses the same eneries at iven T (kt) and they follow Boltzman distribution -rotational/translational motion of sements - short rane diffusional motion -increased slip -some elasticity remains frozen (vibration only) T RP RF -very rapid but -restricted by entanlement

13 2. Transition or State of Matters 2) Molecular Motion 2) Molecular Motion Boltzman distribution

14 Glass Transition Temperature, T onset of lon-rane, coordinated molecular motion at T < T, 1~ 4 chain atoms in motion at T ~ T, 10 ~ 50 atoms in motion 2) Molecular Motion modulus drops a factor of 1,000 in a 20 ~ 30 o C rane

15 3. Theory of Glass Transition Temperature 1) Free Volume Theory 1) Free Volume Theory V(T) = V o (T) + V f (T) V o : occupied volume, V f : free volume V o : occupied by molecule T dependency due to chanes in amplitude of molecular vibrations with T V f : empty space btw molecules rearded as an elbow room that molecules require to un dero rotational and translational motion at T T : frozen (V f critical) as T increases, V f and motion increase

16 3. Theory of Glass Transition Temperature 1) Free Volume Theory V( T) free volume, V f (T) V ( T = 0) + V ( T 0) 0 f = ( T 0) V 0 = V f V 0 ( T) T

17 3. Theory of Glass Transition Temperature 1) Free Volume Theory fractional free volume, f at T T : Vf f = V V V f = f = = at T > T : constant f

18 3. Theory of Glass Transition Temperature 1) Free Volume Theory free volume, V f : As T increases, molecular motion and V f increase but

19 3. Theory of Glass Transition Temperature 1) Free Volume Theory By Fox and Flory (1950) T Iso-free volume state f = or 2.5% for most polymers valid for T < T < T + 100

20 3. Theory of Glass Transition Temperature 2) WLF Equation 2) William-Landel-Ferry Equation (WLF) By Doolittle (empirical): internal mobility (expressed by viscosity)is related to fractional free volume (V f, f) viscosity, η occupied volume 과 free volume 과의비에의해결정 cf. Arrhenius equation

21 3. Theory of Glass Transition Temperature 2) WLF Equation at T = T ref,

22 3. Theory of Glass Transition Temperature if T then f ln a ref T lo a T = = = T, f ( f ( α = f f + B f ref α ) + = f )(T T ) B 2.303f f, (T T ) (T T ) f ( α WLF Equation where a T : C 1 and C 2 : T = T - T f (T T ) = ) + (T T ) C1 ΔT C + ΔT 2 2) WLF Equation

23 3. Theory of Glass Transition Temperature 2) WLF Equation

24 3. Theory of Glass Transition Temperature 2) WLF Equation

25 3. Theory of Glass Transition Temperature 2) WLF Equation experimentally for many linear amorphous polymers lo a T = B f f α f (T T (T T f = = = ) ) a α f T = = 4.8 ref 10 4 de T 1 (B =1.0 is assumed) η η η η t t T t: experimental time τ: relaxation time = τ τ T

26 3. Theory of Glass Transition Temperature 2) WLF Equation meanin lo a T = lo η η T lo t t T = (T T ) (T T ) lo at vs. (T-T)

27 4. Time-Temperature Superposition Principle 1) Stress Relaxation Experiment 1) Stress Relaxation Expt ε = constant ε F F (strain) = F(t) / A = stress = σ ε F = = ε(t) constant (Relaxation) Modulus Ε (t,t) = ( ) ( ) 0) σ t,t) ε modulus (riidity): 힘을줬을때변형이일어나기어려운정도

28 4. Time-Temperature Superposition Principle 1) Stress Relaxation Expt a T E r ( 10) lassy rubbery plateau 6.5 reion rubbery flow Mw 10(sec) Time(t) T T - Modulus drops a factor of 100 in a 20~30 C rane - T : The onset of lon-rane, coordinated, molecular motion - T < T : 1-4 chain atoms in motion - T ~ T : 10~50 (semental motion)

29 4. Time-Temperature Superposition Principle 1) Stress Relaxation Expt T RP RF Flow Viscous Frozen (vibration only) 2 Rotation, Transition (chain end, chain loop) 3 Very rapid but restricted motion by entanlement 4 Slip some elasticity remains

30 4. Time-Temperature Superposition Principle 2) t-t Superposition Principle 2) Time-Temperature principle (correspondence=superposition=equivalency) loe t 1 t 2 PS = 125 C T = -68 C t 3 t 4 Poly(isobutylene) T = -68 C -14 2hr 온도에따라 Time scale 이변할수있음

31 4. Time-Temperature Superposition Principle 2) t-t Superposition Principle t 4 t 3 t 3 - Exptally at difference T over modest T rane t 3 t 3 - T: Measure of molecular motion t 4 lo E T 1 T 2 T ref lot lot - WLF: Loarithmic relationship between t & T t & T are equivalent to the extent that data at T 1 can be superimposed on data at T 2 by shiftin data set 1 (or curve)

32 4. Time-Temperature Superposition Principle ( t,t ) E( t, ) E = T2 at a point of overlap 2) t-t Superposition Principle drop subscript on t in mater curve E t a t = E a 1 1,T1, T2 T1, T2, reduced variable if T = T ref, a r = 1, loa r = 0 T > T ref, a r < 1 T < T ref, a r > 1

33 4. Time-Temperature Superposition Principle 3) Principle of Correspondin T 3) Principle of Correspondin T for linear and amorphous polymers - Glass polymers ~ dyne/cm 2 - Rubbery zone ~ Two linear and amorphous polymers of the same MWD are approximately equivalent at correspondin T = r T T

34 5. Transition T and End-use T 5. Transition T and End-use T 1) Elastomer - T use > T : Hih semental motion ex) SBR T = -57 Poly(isoprene) T = -70

35 5. Transition T and End-use T 5. Transition T and End-use T 2) Amorphous structure polymers - T < T : Semental motion 이있으면안되 - Glasslike riidity (no motion) - PS, PMMA T = ~100 정도 - Touh leather like polymer: ~T (auto-seat, ladies handba, travel luae) - Hihly crystalline and oriented polymer: T use = T m Semi crystalline. 반결정성 : T < T < T m - LDPE T = ~120, T m = ~-115

36 6. Effect of Composition on T 6. Effect of Composition on T 1) Steric factors - Chain flexibility : Determined by the ease with which rotation can occur about primary chemical bonds (E a = 1~5 kcal/mole) (sterichindrance increases T ) - Intermolecular packin distance (pendant roup effect) : V f, 분자 chain 간이멀어지면 free volume이많아져

37 6. Effect of Composition on T 6. Effect of Composition on T a) Backbone stiffness on flexibility - Stiffenin aent VS 6-(CH 2 ) C O CH 3 C C Para ( 입체구조보다 T 가높음 ) O Epoxy 복합재료, PC T = 150, T m = 267 CH 3

38 6. Effect of Composition on T - Flexibility aent O O 6. Effect of Composition on T C O

39 6. Effect of Composition on T 6. Effect of Composition on T b) Intermolecular packin distance - If pendent roups are bulk/stiff and close to backbone, steric hindrance will be increased. - If substituents ( 치환기 ) are flexible, the effect of increasin intermolecular distance and free volume effect dominate T

40 6. Effect of Composition on T 6. Effect of Composition on T ex 1) PE H PP -10 -CH3 PS 100 Benzene rin

41 6. Effect of Composition on T 6. Effect of Composition on T ex 2) Poly(acrylate) T : ~5 Poly(methaacrylate) T : ~100 Methyl > Ethyl > Propyl: 길수록 flexible T CH 2 : n = 12 Q) Chain이매우길어지면 T 가낮아져야정상, 그러나 N이 12개이상이면 T 가오히려증가한다. Why? A) 12개이상이되면결정이형성되어뭉치고움직임이둔화됨.

42 6. Effect of Composition on T 6. Effect of Composition on T c) Symmetry (backbone) H PP (T = -10, T m = 165 ) ( CH 2 C) n CH 3 CH 3 PDMS (T = -70, T m = 44 ) ( CH 2 C) n CH 3 cf) PVDC (T = 87 ) vs PVC (T = -19 )

43 6. Effect of Composition on T 6. Effect of Composition on T d) Effect of isomerism - Cis - Trans: 열역학적으로안정한상태, 펼쳐져있는상태, T ex) Polyisoprene PB T T m Cis Trans Cis Trans

44 6. Effect of Composition on T 6. Effect of Composition on T e) Effect of Tacticity - Profound effect on T m - (a-, S-, I-) Tacticity in eneral, no effect on T Exception) PMMA Atactic: 104~108 결정이안됨 Isotactic: 42~45 결정이잘됨 Syndio: 105~120

45 6. Effect of Composition on T 6. Effect of Composition on T 2) Intermolecular bondin forces of attraction ex) PP (CH 3 ): -10 PVC (Cl): 85 PAN (C=N): 105 밑으로갈수록 polarity가있음 ( Almost same size of side roups)

46 6. Effect of Composition on T 6. Effect of Composition on T ex) Poly(Methyl acrylate): 3 Poly(Acrylic acid): 106 Poly(Zinc acrylate): Ionic bondin > 400 T 가점점증가하는방향 : Van der Waals H-bonds Ionic bonds Chemical crosslinkin

47 7. Effect of Physical Characteristics of Molecules 7. Effect of Physical Characteristics of Molecules 1) MW effect T K K = T T = T + Mw Mw T T - 분자량이적으면 chain end 수증가 free volume T 1 T m - T 에는분자자체의 volume보다 free volume의크기가더중요

48 7. Effect of Physical Characteristics of Molecules 2) Branch effect 7. Effect of Physical Characteristics of Molecules - For small no. of branchin, T = T : Linear chain with infinite Mw T α f : Thermal coefficient θ y ρ N α M f A w θ : Contribution of chain ends to U f - For hih density of branchin T increases (due to restriction of chain mobility)

49 7. Effect of Physical Characteristics of Molecules 7. Effect of Physical Characteristics of Molecules T f>10 Cyclic polymer f=2 (end roup) f=3 Linear Mn -1

50 7. Effect of Physical Characteristics of Molecules 7. Effect of Physical Characteristics of Molecules 3) Crosslinkin effect T T 0 = M C 4 : Not T crosslinked 0 : Molecular weiht between crosslinks M C Specific volume - Specific volume 을가지고측정 - As mole of DVB is added, T increases but becomes obscure. T

51 8. Effect of Plasticizer 8. Effect of Plasticizer 1) Plasticizer - A substance which is added to material to improve it s processibility (melt viscosity), flexibility (T ) and strechability. (deformability or elastic modulus) - W/O alterin chemical nature of the polymer

52 8. Effect of Plasticizer 8. Effect of Plasticizer 2) Plasticization - Refers to a process of makin a material more susceptible to flow ex 1) H 2 O for paper (cellulose T = 225 ) Steam ironin for cotton fabric ( 물이가소화역할 ) H 2 O for nylon poly acrylate methacrylate ex 2) CO 2 for lassy polymers PC ΔT = 9 K at 6.8 atm (as를이용해서가소화 )

53 8. Effect of Plasticizer 8. Effect of Plasticizer ex 3) Weakly polar ester for PVC (phthalate: 86%) DIOP/DOP: 40% 정도차지 DIOP (di iso octyl phthalate) O C H 2 5 C OCH CHC 2 4H9 DOP (n-dioctyl phthalate) C O ( CH2 ) C CH3 O CH3 5

54 8. Effect of Plasticizer 8. Effect of Plasticizer a) External plasticizer - By dissolves ases on liquids in polymers - Add to weaken intermolecular forces by salvation - No stoichiometric upper limit to plasticizer uptake - Oranic, non-polymeric (exude to the surface polymeric) plasticizer: 분자량수천, hih bp, weakly polar compounds Plasticizer T 가낮다 (T : -50~150 C 정도 )

55 8. Effect of Plasticizer 8. Effect of Plasticizer G (Shear modulus) T T 가 broad 하게변함 T m T p T T Wt% plasticizer T p T : Plasticizer 의 T : Polymer 의 T T 가가소제영향을많이받음 Due to limited compatibility

56 T T 1 T = TAΦ WA = + TA ΦAαP = Φ α 8. Effect of Plasticizer A A P + W T B B T + T B Φ B ( 1 Φ ) p ( 1 Φ ) p 8. Effect of Plasticizer Rule of thumb ΔT = 2 K Φ n = 1 vol%

57 8. Effect of Plasticizer b) Internal plasticizer 8. Effect of Plasticizer - Selective copolymer of monomers leadin to hih T and monomers leadin to low T - Random copolymers - Very limited

Chapter 13 - Polymers Introduction

Chapter 13 - Polymers Introduction I. Nomenclature A. Polymer/Macromolecule polymer - nonmetallic material consisting of large molecules composed of many repeating units - from Greek: poly (many) and meros