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

金建青年学术沙龙第十期

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

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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 ）

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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）

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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

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信噪比 (S/N) 与取样速率 (n points/cycle) 关系

12/S N n

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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）

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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

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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

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Rheology: Principles, Measurements, and Applications Ch. W. Macosko 1994

Viscoelastic Properties of Polymers (3rd Revised)John D. Ferry1980

Rheology Related Journals

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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

仪器公司网站

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仪器公司网站

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仪器公司网站

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仪器公司网站

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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.