University Graz / Austria Institut für Chemie Volker Ribitsch

Transcription

1 University Graz / Austria Institut für Chemie Volker Ribitsch 1

2 Rheology Oscillatory experiments Dynamic experiments Deformation of materials under non-steady conditions in the linear viscoelastic range No relaxation and no creep experiments 2

3 Experiments under oscillatory stress or deformation to describe polymer solutions or polymer melts Polymer properties function correlation Molecular weight and Mw distribution poly-disperse vs. mono-disperse wide vs. narrow MWD Shape of the molecule linear vs. branched type and sequence of monomers in the case of sugar compounds: Monosaccharide, Α or β conformation linkage 1 2; 1 3; 1 4; 1 6 Flexibility and stability of monomer (sugar) linkages Presence of monomer (sugar) substituents type number distribution Presence of charges type - ph dependency? number distribution 3

4 Structure volume relationship of molecules Different effective volume for similar molecular weight Permission of Henc Schols 4

5 Interaction between polymers in solution/melts Entanglement network and gel formation Entanglements 5

6 Some reminder Basic behaviour of materials under stress: Hook s law solids Newton s law liquids T 12 = G*γ T 12 = η*dγ/dt T 12 = shear stress (tensor) /Pa/ γ = deformation / / dγ/dt = shear rate / s -1 / η = viscosity /Pa.s/ G = shear or elastic modulus /Pa/ 6

7 Deformation -F +F s s a a h τ 11 τ 12 τ 13 τ 21 τ 22 τ 23 τ 31 τ 32 τ 33 7

8 Definitions Deformation : (no dimension) Applied force F : shear stress τ 12 tau causes deformation (strain) Applied deformation: causes force, shear stress F Shear rate : Ỷ = dγ/dt resp. D Change of deformation during deformation time Linear viscoelastic region!! deformation stress proportionality 8

9 Relaxation time: Λ = η/g /s/ 9

10 Generalized models Newton η Hook E Maxwel Continous relaxation time distribution E η Voight 10

11 Stress applied at different frequencies Almost no stress Medium stress at low frequencis High stress at high frequencies Almost no stress 11

12 Examples for elastic behaviour - Creeping up a stirrer shaft (normal forces - Weißenberg- effect) 12

13 Oscillatory deformation 13

14 Ideal elastic substances (Hook) 14

15 Ideal viscous substances (Newton) 15

16 Deformation and deformation rate as a function of position 16

17 Viscoelastic substances 17

18 Results 18

19 Phase shift between the τ (t)- function and the γ(t)-function 19

20 Evaluation of a complex equation 20

21 Calculation of G and G storage modulus and loss modulus 21

22 Expressed as viscosity components 22

23 Expression as vector diagram 23

24 Expression as vector diagram 24

25 Experimental set up 25

26 Amplitude variation at constant frequency 26

27 Frequency variation at constant amplitude 27

28 Frequency sweep 28

29 Frequency sweep 29

30 High molecular weight and wide distribution 30

31 General information 31

32 Frequency dependent deformation of chemically cross linked substances 32

33 Mechanically (temporary entanglements) and chemically (permanent entanglements) cross linked substances 33

34 Comparison Storage modulus 34

35 Loss modulus and loss factor 35

36 Modelling viscoelasticity Modeling using a combined HOOKE and NEWTON elements Simplest constitutive equations describing the behavior are linear differential equations with constant coefficients 36

37 The 2-element solid E KELVIN-VOIGT-body Characteristics? E η η There exists a connection between the end points exclusively over HOOKE elements 37

38 The 2-element-fluid E η MAXWELL-Body Characteristics? E η There exists a separation line exclusively over NEWTON elements 38

39 Simple constituitive equation The storage and loss modulus (G, G ) of many polymer systems generally follow a single-relaxation l Maxwell model. AM Maxwell model comprises an elastic component connected in series with a viscous component. In this model G and G are described by the following equation: G' G ω 2 λ = 2 1+ ω λ 2 2 G ωλ G" = ω λ where G reperesent the plateau value of G at the highest frequencies ω is the angular frequency and λ is the relaxation time 39

40 The 2-element-fluid [Pa] G', G" [ G' 4% G" 4% G' 3% G" 3% G' 2.5% G" 2.5% G' 2% G" 2% G' 1.5% G" 15% 1.5% Frequency [Hz] The storage modulus (close symbol) and loss modulus (open symbol) of HEUR models as function of frequency for different concentration. The curves are the best fit of singlerelaxation Maxwell model. 40

41 Experiments under oscillatory loads stress or deformation 41