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:
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
unit height strain unit area = G(t) Stress Relaxation (Transient Test) 4
t t t1t1 t1t1 t2t2 t2t2 11 22 11 22 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
t dt' didi t titi didi for strain (t) of arbitrary history t Boltzmann Principle For infinitesimal strain d i at time 6
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 Input Output η * : complex viscosity Linear Viscoelasticity (Oscillatory Shear)
Test Input: strain ( ), frequency ( ), and gap (H). Measure: torque (M) and phase angle ( ). Frequency Defined 9
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
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
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.
14 Master curve of the linear viscoelastic moduli J Rheol. 2011, 55(5), 987. Thermorheologically simple Time-Temperature Superposition (TTS)
Principle of a creep-recovery experiment Recoverable Non-Recoverable J Rheol. 2014, 58(3), Creep – Creep Recovery
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 Prog Polym Sci. 2001, 26(6), 895.
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
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
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
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 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）
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
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
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
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
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
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
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
Polymer. 2013, 54 (6), Effect of thermally reduced graphite oxide (TrGO) on the polymerization kinetics of poly(butylene terephthalate) 36
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
Evolution of the loss tangent during a curing reaction. The gel point is the point, when tan δ becomes independent of frequency. 38
Cross-linking kinetics of XLPE 39
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),
Physics Today. 2009, 62(10),
Results of flow reversal studies of a 4.80 wt % PP/clay hybrid nanocomposite. Macromolecules. 2001, 34 (6),
Ind Eng Chem Res. 2014, 53(3), Polylactide with long-chain branched structure Strain-hardening coefficient: 43
44 (a) Chewing and (b) bubble gum behavior during start-up of uniaxial extension J Rheol. 2014, 58(4), 821.
45 Prog Polym Sci. 2001, 26(6), 895.
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 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 Rheology: Principles, Measurements, and Applications Ch. W. Macosko 1994 Viscoelastic Properties of Polymers (3rd Revised) John D. Ferry 1980
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
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.