旋转流变仪及其 测量技术简介
DESCRIPTION
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 [email protected] 2014-9-3. 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. Linear Viscoelasticity. V iscoelastic relaxation modulus of flexible linear polymers. Polym J . 2009, 41( 11 ), 929. strain g. unit area. - PowerPoint PPT PresentationTRANSCRIPT
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
2
3
Viscoelastic relaxation modulus of flexible linear polymers.
Polym J. 2009, 41(11), 929.
Linear Viscoelasticity
unit height
strain g unit area
= G(t) g G t
Stress Relaxation (Transient Test)
4
t
tt1
t1 t2
t2
1
2
1 21+2
g
s
Just for g1
1(t) = G(t-t1) g1
Just for g2
2(t) = G(t-t2) g2
Forg1 + g2
1+2(t) = 1(t) + 2(t)
= G(t-t1) g1 + G(t-t2) g2
Superposability of Stress
5
tdt'
dgi
tti
di
for strain g(t) of arbitrary history
t
Boltzmann Principle
i
iittGt )(
( ')( ')
'
d tt
dt
For infinitesimal strain dgi at time
tdttttGt ')'()'()(
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
*0 0/G
* cosG G * sinG G tan G G
0( ) sin( )t t 0( ) sin( )t t Input Output
*( ) ( ) ( )G G iG
*( ) ( ) ( )i
2 2* G G
η*: complex viscosity
( ) ( ) /G ( ) ( ) /G
Linear Viscoelasticity (Oscillatory Shear)
Test Input: strain (g), frequency (w), and gap (H).Measure: torque (M) and phase angle (d).
0( ) sin( )t t
Frequency Defined
9
1 0 0 .01 .0 0 0 E-5 1 .0 0 0 E-4 1 .0 0 0 E-3 0 .0 1 0 0 0 0 .1 0 0 0 1 .0 0 0 1 0 .0 0fre q u e n c y (Hz )
1 .0 0 0 E6
0 .0 1 0 0 0
0 .1 0 0 0
1 .0 0 0
1 0 .0 0
1 0 0 .0
1 0 0 0
1 0 0 0 0
1 .0 0 0 E5
G'
(Pa
)
1 .0 0 0 E6
0 .0 1 0 0 0
0 .1 0 0 0
1 .0 0 0
1 0 .0 0
1 0 0 .0
1 0 0 0
1 0 0 0 0
1 .0 0 0 E5
G'' (P
a)
1 .0 0 0 E5
1 0 0 .0
1 0 0 0
1 0 0 0 0|n
*| (
Pa
.s)
PDMS
PDMS Extended f requency sweep-0001o, Frequency sweep st ep
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<Mc; B is monodisperse with M>>Mc and C is polydisperse
LVE response is very sensitive to the molecular structure of the polymers
Stress Relaxation vs. Frequency Spectrum
11
线性粘弹性函数之间的关系Dynamic
ComplianceJ*(ω)
Creep Compliance
J(t)
Retardation Time
DistributionL(τ)
RelaxationTime
DistributionH(τ)
Algebraic Equations
Integral Equations
Integral Transforms
Fourier Transforms
Dynamic Modulus
G*(ω)
Relaxation Modulus
G(t)
Fourier Transforms
Laplace Transforms
Laplace Transforms
12Polymeric liquids and networks – Dynamic and rheology. Page 122.
13
1
2
( )log
( )g
Tg
C T Ta
C T T
WLF (Williams-Landel-Ferry) equation
Time-Temperature Superposition (TTS)
14
Master curve of the linear viscoelastic moduli
J Rheol. 2011, 55(5), 987.
Thermorheologically simple
Time-Temperature Superposition (TTS)
0
1 1( ) exp ( )a
T
Ea T
R T T
0 0Tb T T
Principle of a creep-recovery experiment
Recoverable
Non-Recoverable
J Rheol. 2014, 58(3), 565.15
0( ) ( )J t t
Creep – Creep Recovery
线性粘弹性函数之间的关系
Retardation Time
DistributionL(τ)
Relaxation Modulus
G(t)
RelaxationTime
DistributionH(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
16Polymeric liquids and networks – Dynamic and rheology. Page 122.
聚合物流变学的“链接”作用
17Prog 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
主要内容
18
旋转流变仪的种类
应变控制型( SMT )
ARESARES-G2
AR-SeriesHybrid-Series
Aton PaarMalvern
应力控制型( CMT )
19Separate Motor and Transducer
20
FRT
Motor
Motor/Transducer
Motor Inertia & friction
Involved in Torque
MeasurementPrimary Moving Elements
Torque Measurement is Unaffected
by Motor Inertia & Friction
旋转流变仪的种类
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
决定流变仪性能的重要参数(时间分辨率)
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)
流变仪如何得到流变数据
From the time into the frequency domain
Discrete Fourier transformation (DFT)
0 1 1( ) , , , , ,n Nt 0 1 1( ) , , , , ,n Nt
一个周期内得到时间间隔为 Δt 的 N 个点
0
1 2sin( )
N
nn
n
N N
0
1 2cos( )
N
nn
n
N N
0
1 2cos( )
N
nn
n
N N
0
1 2sin( )
N
nn
n
N N
* 2 2 arctan( )
* 2 2 arctan( )
*
*G
23
信噪比 (S/N) 与取样速率 (n points/cycle) 关系
12/S N n
24
25
Parallel Plates
○ 用量少 (~0.5 - 3 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 CylinderSingle/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
Cone-plate Plate-plate Concentric Cylinders
L
r rh
stress: = M = M = 1/ M
rate: = = = .
Testing GeometriesM ( 扭矩 ) — τ ( 应力 ) , ω( 角速度 ) — ( 剪切速率)
26
0 0 0 0 0 .L w h L A const 00( ) tA t A e 0
1
20( )
th t h e
0
0
( ) ( )( )
( )t
E
F t F tt e
A t A
0
( )( ) E
E
tt
Extensional Viscosity Fixture (EVF)
0
1 ( )dL t
L dt
27
Extensional Viscosity Fixture (EVF)
对于 ARES-G2
拉伸速率 ≤ 10 s-1, 拉伸应变 28
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
29
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 t ~ M3.4±0.2
10-2 10-1 100 101 102 103 104 105 106 107 108 109
104
105
106
107
T0 = 40 oC
G' (
Pa)
(rad/s)
410K 207K 100K 44K
10-2 10-1 100 101 102 103 104 105 106 107 108
104
105
106
G"
(Pa
)
(rad/s)
Ze262 Ze132 Ze63 Ze28
Delay of orientation/stress relaxation due toentanglement of uncrossable chains
Polybutadiene, 40C
Slow Relaxation Behavior of Linear Chains
31
PBD:Linear Mw=160K6-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
Slow Relaxation of Star-branched Chains
32
J Rheol. 2014, 58(3), 565. 33
Example for the extension of the frequency range using the retardationspectrum obtained from creep-recovery tests (recover time up to 104 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
Oscillation Time Sweep
Macromolecules. 2012, 45 (16), 6648 .
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), 1603.
Effect of thermally reduced graphite oxide (TrGO) on the polymerization kinetics of poly(butylene terephthalate)
36
Oscillation Time Sweep
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
37
Evolution of the loss tangent during a curing reaction. The gel point is the point, when tan δ becomes independent of frequency.
38
Multiwave Oscillation
Oscillation Temperature Ramp
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 Tg
PB/PI with big discrepancyin viscoelasticity
Miscible Metastable Phase-separated
J Phys Chem B. 2004, 108 (35), 13220.40
Oscillation Temperature Ramp
Steady Shear Stress/Rate Sweep
Physics Today. 2009, 62(10), 27. 41
Shear Reversal
Results of flow reversal studies of a 4.80 wt % PP/clay hybrid nanocomposite.
Macromolecules. 2001, 34 (6), 1864. 42
Elongational Test-1
Ind Eng Chem Res. 2014, 53(3), 1150.
Polylactide with long-chain branched structure
Strain-hardening coefficient:
0
( , )( )
3 ( )E
E
tt
t
01
( ) (1 )i
Nt
i ii
t G e
43
Elongational Test-2
44
(a) Chewing and (b) bubble gum behavior during start-up of uniaxial extension
J Rheol. 2014, 58(4), 821.
聚合物流变学的“链接”作用
45Prog Polym Sci. 2001, 26(6), 895.
Further Readings
46
Structure and Rheology of Molten Polymers: From Structure To Flow Behavior and Back AgainJohn M. Dealy , Ronald G. Larson.2006
The Rheology Handbook-For Users of Oscillatory Rheometers ( 3rd ed.)Thomas G. Mezger2013
Further Readings
47
Melt Rheology and Its Applications in the Plastics Industry John M. Dealy , Jian Wang2013
Colloidal Suspension Rheology Norman J. Wagner, Jan Mewis. 2012
Further Readings
48
Rheology: Principles, Measurements, and Applications Ch. W. Macosko 1994
Viscoelastic Properties of Polymers (3rd Revised)John D. Ferry1980
Rheology Related Journals
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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Rheology needs a lot of expe ri ence. Modern rheome ters will give
you num bers, no prob lem, but the ques tion is always whether they
are cor rect. That and the opti miza tion of the para me ters to min i
mize the noise and do what you want to the mate r ial (destroy or
not destroy a struc ture) is what sets a good rhe ol o gist apart from
an inexperienced one.