1. 金建青年学术沙龙第十期
旋转流变仪及其 测量技术简介
工程塑料实验室
张宝庆

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
主要内容
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

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

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

5. Superposability of Stress1 2 1 2
1+2 g s
Just for g1
1(t) = G(t-t1) g1
Just for g2
2(t) = G(t-t2) g2
Forg1 + g2
1+2(t) = 1(t) + 2(t)
= G(t-t1) g1 + G(t-t2) g2

6. Boltzmann Principle For infinitesimal strain dgi at time
dt'
dgi ti 
di 
For infinitesimal strain dgi at time
for strain g(t) of arbitrary history t

7. Boltzmann Superposition Principle
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.

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

9. Frequency Defined Test Input: strain (g), frequency (w), and gap (H).
Measure: torque (M) and phase angle (d).

10. Frequency Sweep
Curve of a frequency sweep used to talk about oscillation modes; talk about other ways to run the experiment like time sweeps, temp sweeps; ability to do in both controlled strain and stress mode and advantage of each
the waveform and why that is important(and unique to us)
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.

11. Stress Relaxation vs. Frequency Spectrum
G(t) vs. t
G'(ω) vs. ω
the amplitude of the perturbation can be freely chosen for each frequency,
A is monodisperse with M<Mc; B is monodisperse with M>>Mc and C is polydisperse
LVE response is very sensitive to the molecular structure of the polymers

12. 线性粘弹性函数之间的关系 Dynamic Compliance J*(ω) Dynamic Modulus G*(ω) Relaxation
G(t)
Fourier
Transforms
Algebraic
Equations
Fourier
Transforms
Creep
Compliance
J(t)
Integral
Equations
Laplace
Transforms
Laplace
Transforms
Retardation Time
Distribution
L(τ)
Relaxation
Time
Distribution
H(τ)
Integral
Transforms 12
Polymeric liquids and networks – Dynamic and rheology. Page 122.

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

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

15. Creep – Creep Recovery Recoverable Non-Recoverable
Principle of a creep-recovery experiment
J Rheol. 2014, 58(3), 565.

16. 线性粘弹性函数之间的关系 Dynamic Compliance J*(ω) Modulus G*(ω) Creep J(t)
Algebraic
Equations
Fourier
Transforms
Fourier
Transforms
Relaxation
Modulus
G(t)
Integral
Equations
Laplace
Transforms
Laplace
Transforms
Retardation Time
Distribution
L(τ)
Relaxation
Time
Distribution
H(τ)
Integral
Transforms 16
Polymeric liquids and networks – Dynamic and rheology. Page 122.

17. 聚合物流变学的“链接”作用
Prog Polym Sci. 2001, 26(6), 895. 17

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
主要内容
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

19. 旋转流变仪的种类 AR-Series Hybrid-Series Aton Paar ARES Malvern ARES-G2 应变控制型
（SMT）
应力控制型
（CMT） 19
Separate Motor and Transducer

20. Torque Measurement is Unaffected by Motor Inertia & Friction
旋转流变仪的种类
FRT
Torque Measurement is Unaffected by Motor Inertia & Friction
Motor Inertia & friction Involved in Torque Measurement
Motor/ Transducer
Primary Moving Elements
Motor
The SMT architecture is preferable to the CMT architecture because the most massive moving element (the motor) is physically isolated from the torque measurement. The motor is also where the largest motions occur. This is in contrast to the CMT in which the motor and sample torque are conflated because the heavy, large moving element is used to measure (apply) the torque.
应力控制型
（CMT）
应变控制型
（SMT） 20

21. Strain vs. Stress controlled
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！

22. 决定流变仪性能的重要参数（时间分辨率） 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. 流变仪如何得到流变数据 一个周期内得到时间间隔为Δt的N个点 From the time into the frequency domain
Discrete Fourier transformation (DFT)

24. 信噪比(S/N)与取样速率(n points/cycle)关系

25. Testing Geometries Concentric Cylinder Parallel Plates
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
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

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

27. Extensional Viscosity Fixture (EVF)

28. Extensional Viscosity Fixture (EVF)
对于ARES-G2
拉伸速率 𝜺 𝑯 ≤ 10 s-1, 拉伸应变 𝜺 ≤ 3.𝟒 (𝒇𝒐𝒓 𝟏 𝒎𝒎 𝒕𝒉𝒊𝒄𝒉𝒏𝒆𝒔𝒔)

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
主要内容
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

30. Rheological Measurements
Flow tests
Constant shear rate
Continuous stress/rate ramp and down
Steady state shear rate sweep
Flow temperature ramp
Flow reversal
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
LAOS
Strain-Rate Frequency Superposition (SRFS)

31. Slow Relaxation Behavior of Linear Chains
Polybutadiene, 40C
relaxation time t ~ M3.4±0.2
Delay of orientation/stress relaxation due to
entanglement of uncrossable chains

32. Slow Relaxation of Star-branched Chains
PBD:
Linear Mw=160K
6-arm star Ma=77K
Relaxation time
t ~ exp(0.6Marm/Me)
Much stronger delay
for star chain
cf.  ~ M3.4±0.2
for linear chain

33. 利用蠕变测试扩展SAOS测试频率
Example for the extension of the frequency range using the retardation
spectrum obtained from creep-recovery tests (recover time up to 104 s).
J Rheol. 2014, 58(3), 565.

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

35. Oscillation Time Sweep
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.
Macromolecules. 2012, 45 (16),

36. Oscillation Time Sweep
Effect of thermally reduced graphite oxide (TrGO) on the polymerization kinetics of poly(butylene terephthalate)
Polymer. 2013, 54 (6), 1603.

37. Multiwave Oscillation
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

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

39. Oscillation Temperature Ramp
Cross-linking kinetics of XLPE

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

41. Steady Shear Stress/Rate Sweep
Physics Today. 2009, 62(10), 27.   

42. Shear Reversal
Results of flow reversal studies of a 4.80 wt % PP/clay hybrid nanocomposite.
Macromolecules. 2001, 34 (6), 1864.

43. Elongational Test-1 Polylactide with long-chain branched structure
Strain-hardening coefficient:
Ind Eng Chem Res. 2014, 53(3), 1150.

44. Elongational Test-2
(a) Chewing and (b) bubble gum behavior during start-up of uniaxial extension
J Rheol , 58(4), 821.

45. 聚合物流变学的“链接”作用
Prog Polym Sci. 2001, 26(6), 895. 45

46. Further Readings
The Rheology Handbook-For Users of Oscillatory Rheometers ( 3rd ed.)
Thomas G. Mezger
2013
Structure and Rheology of Molten Polymers:
From Structure To Flow Behavior and Back Again
John M. Dealy , Ronald G. Larson.
2006

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

49. Rheology Related Journals
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. Rheology needs a lot of expe­ri­ence
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 min­i­mize 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.