Shear rheology of polymer melts

Transcription

1 Shear rheology of polymer melts Dino Ferri Politecnico Alessandria di Milano, 14/06/ nd October 2014

2 Outline - Review of some basic rheological concepts (simple shear, elastic solid and viscous liquid, viscoelasticity). - Some fundamentals about the structure of polymers. - The Maxwell model and some phenomena related to the elasticity of polymer melts. - The flow curve of polymer melts: the shear thinning. - Some correlations between the features of the flow curve and some structural variables like molecular weight and polydispersity. - Conclusions

3 simple shear y h V=V max F moving surface of area S x y F is a shear force x V=0 surface at rest of area S the flow generates a velocity gradient along the y axis V=V(y) shear strain: shear rate: x y tg d dt V h shear stress: σ F S

4 stress strain elastic body viscous liquid strain stress G G Robert Hooke (1678) constitutive equations d dt Isaac Newton (1687) t 0 t 1 time creep and creep recovery t 0 t 1 time t 0 t 1 time stores elastic energy! t 0 t 1 time dissipates energy!

5 stress strain viscoelastic body James Clerk Maxwell (1868) t 0 t 1 time t 0 t 1 time Stores and wastes at the same time elastic energy of deformation! Deborah number: De mat exp Markus Reiner ( ) even the mountains flowed before the Lord (Prophetess Deborah, Judges, 5:5)

6 G(t) (Pa) Maxwell model stress relaxation a constant strain 0 is imposed and the evolution of the stress is followed G 1 stress relaxation modulus: G(t) σ(t) γ 0 1E-3 G(t) G 0 e (t / ) time constant: 1E high De time (s) low De G

7 The pitch drop experiment (University of Queensland) the sixth drop in drops since 1927! low De (viscous flow) A hammer instead of gravity! high De (ductile fracture)

8 What is a polymer? molecular weight of a single chain: M mp m m m m m m p=6 H H H H H C C C C C... PolyEthylene (PE) H H H H H m=28 H H H H H C C C C C C... PolyStyrene (PS) H H H H m=104

9 The molecular architecture of polymers H H H H H C C C C C... PolyEthylene (PE) H H H H H HDPE m=28 LDPE LLDPE 0.94 g/cm g/cm g/cm 3 some branched structures random star H-shaped T-shaped comb-like crosslinked

10 The peculiar structure of macromolecules 1 6 C 3 C Redrawn from: L. R. G. Treloar, Introduction to polymer science, Wykeham publ., London (1970) 1000 C-C C 1 C 2 4 C 5 (Random Coil) l C-C =4 mm =109.5 R ee =20cm L=4 m

11 Critical molecular weight and entanglements M e for polystyrene the mean molecular weight between entanglements is: M e = the polymer chains are highly entangled: critical molecular weight: M c =2M e = V R(cm) M if M w = R cm V 4 3 R cm 3 m 10 N 6 A g V ρ mol m V 0.019g/cm 3 3 ρ melt 1.05g/cm

12 The most important average values of the molecular weight distribution (MWD) number average molecular weight: M n NiM N i i N1M N 1 1 N N 2 2 M weight average molecular weight: M w Ni Mi N M i i 2 N 1 M1 M N N M 2 2 M N N 1 =5 M 1 = N 2 =5 M 2 =1.000 M M n w 4 5x x x x Mw M n 1.67 We always have: M w M n polydispersity: Mw M n

13 Relative weight fraction Molecular weight distribution of a commercial polystyrene M n = M w = M z = Polystyrene M w /M n = M w 100 monomers monomers

14 Methods to measure rheological properties Steady state measurements Oscillatory regime measurements Characterization of polymer melts by means of: capillary rheometers rotational rheometers equipped with cone-plate geometry Characterization of polymer melts or solids by means of: rotational rheometers equipped with parallel plate geometry rotational rheometers equipped with torsion rectangular geometry

15 some phenomena due to melt elasticity Polymers show elastic components of the stress D 0 D rod climbing die swell B D D 0

16 stress (Pa) The normal stress can be greater than the shear stress! Polystyrene M w = M w /M n =1.71 The shear stress is given by: 2 M 3M 3 R F 10 3 shear stress normal stress low De shear rate (s -1 ) high De The normal stress is given by: N 1 2F R 2

17 Nature of polymer melts elasticity and viscosity the elasticity of polymer melts is of entropic nature shear stress R g the viscous contribution is mainly due to the friction between entanglements R g shear stress

18 G(t) Stress relaxation modulus of polymers at T>T g Segmental relaxation (T g ) G g Monodisperse with M w <M c Monodisperse with M w >M c Polydispersed with M w >M c G N 0 G 0 N RT M e reptation time

19 M c is a signature of the chain flexibility polymer polyethylene polybutadiene polyisobutylene polyvinylacetate polymethylmetacrilate polydimethylsiloxane polystyrene M c

20 viscosity (Pa s) The flow curve of molten polymers: the shear thinning newtonian region capillary data cone-plate data best fit with Cross equation Polystyrene M w =170 kda T=200 C power law region 0 =7.000 =0.14 m= shear rate (s -1 ) Cross equation: η(γ) (1 η0 λγ) m low De high De

21 viscosity (Pa s) Flow curve of a polyethylene and processing rotomolding compression molding pipe extrusion blow molding thermoforming film extrusion injection molding fiber spinning coating shear rate (s -1 )

22 Rheology and processing

23 Viscosity (Pa s) Non-newtonian behavior and processing PS M w = T=200 C Shear rate (s -1 )

24 Viscosity (Pa s) Unrealistic newtonianbehavior and processing PS M w = T=200 C Shear rate (s -1 )

25 viscosity (Pa s) Viscosity and molecular weight M w =275 KDa 10 4 M w =180K Da M w =124 KDa shear rate (s -1 ) An important feature of high molecular weight polymer melts: M w

26 The critical molecular weight divides two regimes Log 0 + cost if M w < M c : 0 M w PDMS PIB PE PB PS PMMA PEG PVAC PS Log (M w /cost) Adapted from: G. C. Berry e T.G. Fox, Adv. Polym. Sci, 5, (1968) if M w > M c : M w

27 Can we explain the huge M w dependence of the viscosity for high molecular weight polymers? in solution in the melt R g The random coil shape is recovered only after a certain «relaxation» time due to memory effects The relaxation time increases with increasing molecular weight and decreases with incresing temperature For melts the motion is essentially one-dimensional: reptation! The chain takes a «disengagement» time to relax out of the tube: d 2 L D but D M 1 L M thus d M 3

28 viscosity (Pa s) Viscosity and polydispersity 10 4 Polystyrene M w = M w /M n = Polystyrene M w = M w /M n =2.56 T=200 C shear rate (s -1 ) The greater the polydispersity, the broader the flow curve

29 viscosity (Pa s) Viscosity and temperature 10 5 PS M w =280 kda, M w /M n = C 200 C 220 C 240 C shear rate (s -1 ) The greater the molecular weight, the greater the viscosity

30 B die swell T=180 C T=195 C T=210 C D D Polystyrene M w = shear rate (s -1 ) B D D 0 low De high De

31 apparent shear stress (Pa) Polymer melts and melt fracture 10 6 sharkskin stick-slip transition 10 5 gross melt fracture LLDPE 10 4 smooth apparent shear rate (s -1 )

32 Conclusions - Polymer melts are complex fluids exhibiting a significant degree of elasticity. - The viscosity of polymer melts strongly depends on the strain history and generally exhibits shear thinning behavior. - The structure of polymers is unique and allows us to describe their rheological behavior by rather simple scaling laws.

33 Associazione Italiana di Reologia Scuola di Reologia Corso di formazione ed aggiornamento per ricercatori e tecnici industriali dino.ferri@versalis.eni.com dino.ferri@sir-reologia.it Il Viale delle Rose Parco Giardino Sigurtà Valeggio sul Mincio september 2015