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 zhangbq@iccas.ac.cn 2014-9-3.

Presentation on theme: "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 zhangbq@iccas.ac.cn 2014-9-3."— Presentation transcript:

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

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

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

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

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.

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

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

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.

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

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.

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

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

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

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.

（SMT） 应力控制型 （CMT） 19 Separate Motor and Transducer

Torque Measurement is Unaffected by Motor Inertia & Friction

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！

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）

Discrete Fourier transformation (DFT)

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

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

Extensional Viscosity Fixture (EVF)

Extensional Viscosity Fixture (EVF)

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)

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

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

Relaxation Modulus G(t) Dynamic Modulus G*(ω)

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),

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

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

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

Oscillation Temperature Ramp

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),

Physics Today. 2009, 62(10), 27.

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

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

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

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

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

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

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

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.