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一、流变学基础知识简介 二、旋转流变仪简介 三、基于旋转流变仪平台的测量技术 2 3 Viscoelastic relaxation modulus of flexible linear polymers. Polym J. 2009, 41(11), 929. Linear Viscoelasticity.

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Presentation on theme: "一、流变学基础知识简介 二、旋转流变仪简介 三、基于旋转流变仪平台的测量技术 2 3 Viscoelastic relaxation modulus of flexible linear polymers. Polym J. 2009, 41(11), 929. Linear Viscoelasticity."— Presentation transcript:

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2 一、流变学基础知识简介 二、旋转流变仪简介 三、基于旋转流变仪平台的测量技术 2

3 3 Viscoelastic relaxation modulus of flexible linear polymers. Polym J. 2009, 41(11), 929. Linear Viscoelasticity

4 unit height strain  unit area  = G(t)  Stress Relaxation (Transient Test) 4

5 t t t1t1 t1t1 t2t2 t2t2 11 22 11 22  1+2   Just for  1  1 (t) = G(t  t 1 )  1 Just for  2  2 (t) = G(t  t 2 )  2 For  1 +  2  1+2 (t) =  1 (t) +  2 (t) = G(t  t 1 )  1 + G(t  t 2 )  2 Superposability of Stress 5

6 t dt' didi t titi  didi  for strain  (t) of arbitrary history t Boltzmann Principle For infinitesimal strain d  i at time   6

7 The principle of linear superposition of stresses and/or deformations : The response to any event is linear ; All consequent events lead to independent responses. The material reacts to the next action as if no former action took place! Rheology: Concepts, methods and applications. Page 61. Boltzmann Superposition Principle 7

8 8 Input Output η * : complex viscosity Linear Viscoelasticity (Oscillatory Shear)

9 Test Input: strain (  ), frequency (  ), and gap (H). Measure: torque (M) and phase angle (  ). Frequency Defined 9

10 The amplitude of the perturbation can be freely chosen for each frequency, and dynamic modulus measurement is so far the most common method of linear viscoelastic characterization currently. Frequency Sweep 10

11 G(t) vs. t G'(ω) vs. ω A is monodisperse with M >M c and C is polydisperse LVE response is very sensitive to the molecular structure of the polymers Stress Relaxation vs. Frequency Spectrum 11

12 Dynamic Compliance J * (ω) Creep Compliance J(t) Retardation Time Distribution L(τ) Relaxation Time Distribution H(τ) Algebraic Equations Integral Equations Integral Transforms Fourier Transforms Dynamic Modulus G * (ω) Relaxation Modulus G(t) Fourier Transforms Laplace Transforms Laplace Transforms 12 Polymeric liquids and networks – Dynamic and rheology. Page 122.

13 13 WLF (Williams-Landel-Ferry) equation Time-Temperature Superposition (TTS)

14 14 Master curve of the linear viscoelastic moduli J Rheol. 2011, 55(5), 987. Thermorheologically simple Time-Temperature Superposition (TTS)

15 Principle of a creep-recovery experiment Recoverable Non-Recoverable J Rheol. 2014, 58(3), Creep – Creep Recovery

16 Retardation Time Distribution L(τ) Relaxation Modulus G(t) Relaxation Time Distribution H(τ) Integral Equations Integral Transforms Dynamic Compliance J * (ω) Dynamic Modulus G * (ω) Creep Compliance J(t) Algebraic Equations Fourier Transforms Fourier Transforms Laplace Transforms Laplace Transforms 16 Polymeric liquids and networks – Dynamic and rheology. Page 122.

17 17 Prog Polym Sci. 2001, 26(6), 895.

18 一、流变学基础知识简介 二、旋转流变仪简介 三、基于旋转流变仪平台的测量技术 18

19 应变控制型 ( SMT ) ARES ARES-G2 AR-Series Hybrid-Series Aton Paar Malvern 应力控制型 ( CMT ) 19 Separate Motor and Transducer

20 FRT Motor Motor/ Transducer Motor Inertia & friction Involved in Torque Measurement Primary Moving Elements Torque Measurement is Unaffected by Motor Inertia & Friction 应变控制型 ( SMT ) 应力控制型 ( CMT ) 20

21 Strain Controlled Good for oscillatory measurements Good for fixed shear rate/strain measurements (Stress relaxation) Motors are really good - good for weak materials Very sensitive torque transducers Stress Controlled OK for oscillatory measurements Good for fixed stress measurements Good for creep measurements Drag cup motors often cannot do low stresses well EC motors often have more inertial effects Often assumes certain type of material response 两种流变仪差别越来越小! 21 Strain vs. Stress controlled

22 22 Torque range (扭矩范围) Angular Resolution (角位移分辨率) Angular Velocity Range (角位移速率范围) Frequency Range (可测频率范围) Normal Force (法向力范围) Motor type (驱动马达类型)

23 From the time into the frequency domain Discrete Fourier transformation (DFT) 一个周期内得到时间间隔为 Δt 的 N 个点 23

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25 25 Parallel Plates ○ 用量少 (~ mL) ○ 非均匀应变 ○ 制样简单 ○ 可用于变温测试 ○ Gap 可变,用于界面滑移 的表征 ○ Gap 可变, shear rate 随之 改变 Cone Plate ○ 用量少 ( ~ 1 mL) ○ 均匀应变 (真实粘度 ) ○ 第一法向应力差测试 ○ 不适用于较大粒子的分散体 系 ○ 对间距设置更敏感 ○ 不适用于变温测试 ○ 高粘度流体制样有困难 Concentric Cylinder Single/double-gap ○ 适用于低粘度样品 ○ 均匀应变场 ○ 样品用量大 (~9 mL) ○ 清洁困难 ○ 末端效应校正 Testing Geometries

26 M ( 扭矩 ) — τ ( 应力 ) , ω( 角速度 ) — ( 剪切速率) 26

27 Extensional Viscosity Fixture (EVF) 27

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29 一、流变学基础知识 二、旋转流变仪简介 三、基于旋转流变仪平台的测量技术 29

30 30 Oscillation tests  Frequency sweep  Time sweep  Strain/stress sweep (LVE)  Temperature ramp  Temperature/Frequency sweep (TTS)  Fast Sampling  Multiwave Transient tests  Stress relaxation  Creep & creep recovery others  Elongational test Flow tests  Constant shear rate  Continuous stress/rate ramp and down  Steady state shear rate sweep  Flow temperature ramp  Flow reversal  LAOS  Strain-Rate Frequency Superposition (SRFS) Rheological Measurements

31 relaxation time  ~ M 3.4±0.2 Delay of orientation/stress relaxation due to entanglement of uncrossable chains Polybutadiene,  C Slow Relaxation Behavior of Linear Chains 31

32 PBD: Linear Mw=160K 6-arm star Ma=77K Relaxation time  ~ exp(0.6M arm /M e ) Much stronger delay for star chain cf.  ~ M 3.4±0.2 for linear chain Slow Relaxation of Star-branched Chains 32

33 J Rheol. 2014, 58(3), Example for the extension of the frequency range using the retardation spectrum obtained from creep-recovery tests (recover time up to 10 4 s). 利用蠕变测试扩展 SAOS 测试频率

34 Dynamic Modulus G * (ω) Relaxation Modulus G(t) Fourier Transforms 利用应力松弛测试扩展 SAOS 测试频率 UHMWPE ARES-G2 DFreq SR 34

35 Macromolecules. 2012, 45 (16), Re-entanglement kinetics of freeze-dried polymers (a) Buildup of modulus in polystyrene samples with time. (b) Equilibrium entanglement time of samples freeze-dried from solutions with different original concentrations. 35

36 Polymer. 2013, 54 (6), Effect of thermally reduced graphite oxide (TrGO) on the polymerization kinetics of poly(butylene terephthalate) 36

37  The total strain amplitude should not exceed the linear viscoelastic regime  The test time is the same as the dynamic single point experiment under the fundamental frequency 37

38 Evolution of the loss tangent during a curing reaction. The gel point is the point, when tan δ becomes independent of frequency. 38

39 Cross-linking kinetics of XLPE 39

40 Phase separation temperature of polymer blends Dynamic temperature s ramp for a 50:50 PS 38K/PVME-23K blend PS/PVME with big difference in T g PB/PI with big discrepancy in viscoelasticity MiscibleMetastablePhase-separated J Phys Chem B. 2004, 108 (35),

41 Physics Today. 2009, 62(10),

42 Results of flow reversal studies of a 4.80 wt % PP/clay hybrid nanocomposite. Macromolecules. 2001, 34 (6),

43 Ind Eng Chem Res. 2014, 53(3), Polylactide with long-chain branched structure Strain-hardening coefficient: 43

44 44 (a) Chewing and (b) bubble gum behavior during start-up of uniaxial extension J Rheol. 2014, 58(4), 821.

45 45 Prog Polym Sci. 2001, 26(6), 895.

46 46 Structure and Rheology of Molten Polymers: From Structure To Flow Behavior and Back Again John M. Dealy, Ronald G. Larson The Rheology Handbook-For Users of Oscillatory Rheometers ( 3rd ed.) Thomas G. Mezger 2013

47 47 Melt Rheology and Its Applications in the Plastics Industry John M. Dealy, Jian Wang 2013 Colloidal Suspension Rheology Norman J. Wagner, Jan Mewis. 2012

48 48 Rheology: Principles, Measurements, and Applications Ch. W. Macosko 1994 Viscoelastic Properties of Polymers (3rd Revised) John D. Ferry 1980

49 49  Journal of Rheology  Rheologica Acta  Journal of Non-Newtonian Fluid Mechanics  Applied Rheology  Korea-Australia Rheology Journal  Nihon Reorogi Gakkaishi (Journal of Society of Rheology Japan)  Macromolecules  Langmuir  Soft Matter  Physical Review Letters  Physical Review E  Journal of Chemical Physics

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54 54 Rheology needs a lot of expe­ri­ence. Modern rheome­ters will give you num­bers, no prob­lem, but the ques­tion is always whether they are cor­rect. That and the opti­miza­tion of the para­me­ters to min­i­ mize the noise and do what you want to the mate­r­ial (destroy or not destroy a struc­ture) is what sets a good rhe­ol­o­gist apart from an inexperienced one.


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