9/26/2016 �������������������������������� Sarah Cotts TA Instruments Rubber Testing Seminar CUICAR, Greenville SC TAINSTRUMENTS.COM TAINSTRUMENTS.COM ������������������������� Rheology: The study of Rheology: The study of stress-deformation relationships stress-deformation relationships ������ ������ ������ = Modulus ���������� = Viscosity TAINSTRUMENTS.COM TAINSTRUMENTS.COM 1
9/26/2016 ����������������������������� " =� $�% !� M # Stress ( σ σ ) σ σ � =� � !� θ θ θ θ Strain ( γ γ γ ) γ �� =� � !� Ω Strain rate ( �� ) Ω Ω Ω r = plate radius h = distance between plates M = torque ( µ N.m) θ = Angular motor deflection (radians) Ω = Motor angular velocity (rad/s) TAINSTRUMENTS.COM TAINSTRUMENTS.COM ���������������������������������� ARES G2 Measured Transducer Torque (Stress) Sample Applied Direct Drive Strain or Motor Rotation Controlled Strain TAINSTRUMENTS.COM TAINSTRUMENTS.COM 2
9/26/2016 ������������� ������������� RPA Elite Measured Transducer Torque (Stress) Applied Direct Drive Strain or Motor Rotation Controlled Strain TAINSTRUMENTS.COM TAINSTRUMENTS.COM !�������������� •Viscoelasticity: Having both Viscous and Elastic properties. •Elastic Behavior: Stress is dependent on Strain � Hooke’s Law of Elasticity: Modulus = Stress/Strain •Viscous Behavior: Stress is dependent on Strain Rate � Newton’s Law of Viscosity: Viscosity = Stress/ Strain Rate •Viscoelastic materials cannot be fully understood using only one of these relationships. Oscillation measurements are able to measure stress as a function of both strain and strain rate. TAINSTRUMENTS.COM TAINSTRUMENTS.COM 3
9/26/2016 "��#�$��%������&��������� •For an Elastic Solid, Stress and Strain have a constant proportionality � = E* � •If the material follows Hooke’s Law, the deformation will be reversible when the stress is removed � The modulus of a Hookean solid will not show any time dependence- the stress depends on the strain, but not the strain rate TAINSTRUMENTS.COM TAINSTRUMENTS.COM '�����$��%������!�������� •For a Viscous Liquid, Stress is proportional to Strain Rate d � / dt by a coefficient of Viscosity � � = � * d � /dt •The deformation of a liquid is non-reversible � Stress Strain Rate TAINSTRUMENTS.COM TAINSTRUMENTS.COM 4
9/26/2016 !���������������� ��� σ = E*ε + η* d ε/ dt Kelvin-Voigt Model (Creep) Maxwell Model (Stress Relaxation) L 1 L 2 Viscoelastic Materials: Force depends on both Deformation and Rate of Deformation and vice versa. TAINSTRUMENTS.COM TAINSTRUMENTS.COM (���)����������!���������������� ��� T is short [< 1s] T is long [24 hours] Deborah Number [De] = τ /T TAINSTRUMENTS.COM TAINSTRUMENTS.COM 5
9/26/2016 �����������&*�������� � Long deformation time: pitch behaves like a highly viscous liquid 9 th drop fell July 2013 � � Short deformation time: pitch behaves like a solid Started in 1927 by Thomas Parnell in Queensland, Australia http://www.theatlantic.com/technology/archive/2013/07/the-3-most-exciting-words-in-science-right-now-the-pitch-dropped/277919/ TAINSTRUMENTS.COM TAINSTRUMENTS.COM (���)����������!���������������� ��� � Silly Putties have different characteristic relaxation times � Dynamic (oscillatory) testing can measure time-dependent viscoelastic properties more accurately and efficiently by varying frequency (deformation time) TAINSTRUMENTS.COM TAINSTRUMENTS.COM 6
9/26/2016 ���+�����������) (��������������!���������������������� Frequency of modulus crossover correlates with Relaxation Time TAINSTRUMENTS.COM TAINSTRUMENTS.COM ������������%���������!������������,������� RUBBER BALL LOSS X (G”) TENNIS BALL X STORAGE (G’) TAINSTRUMENTS.COM TAINSTRUMENTS.COM 7
9/26/2016 ������������(������ Deformation • The motor applies an oscillating deformation to the sample at a set Amplitude and Frequency. � Amplitude: Degree of Arc, or % Strain � Frequency: Hz (cycles per second) or CPM (cycles per minute) Torque, S* • The torque transducer measures the response of the sample. � Amplitude: Torque (S*), or Stress Phase Angle � • The phase lag between the deformation and the torque is used to determine the Elastic and Viscous response. TAINSTRUMENTS.COM TAINSTRUMENTS.COM ������������(������ In a purely Viscous material, Stress In a purely Elastic material, Stress is in phase with the Strain is out of phase with the Strain Phase angle= 90° Phase angle= 0° Viscoelastic material 0˚ < Phase angle< 90° TAINSTRUMENTS.COM TAINSTRUMENTS.COM 8
9/26/2016 ������������(������) %����-���)�������������� Elastic Material Viscoelastic material Viscous Material Stress Stress Stress Strain Strain Strain Raw oscillation data can also be plotted as stress vs. strain. An elliptical shape represents a viscoelastic response. TAINSTRUMENTS.COM TAINSTRUMENTS.COM ������������(������ The Phase Angle can be used to separate the stress signal into the elastic and viscous components � G’: Storage Modulus � Measure of elasticity, or the ability to store energy � G’ = (Stress/Strain)*cos( � ) � G”: Loss Modulus � Measure of viscosity, or the ability to lose energy � G” = (Stress/Strain)*sin( � ) � Tan Delta � Measure of dampening properties Loss Modulus � Tan ( � ) = G”/G’ � G*: Complex Modulus � Measure of resistance to deformation � G*= Stress/Strain � � � *: Complex Viscosity � Measure of resistance to flow Storage Modulus � � * = Stress/Strain Rate TAINSTRUMENTS.COM TAINSTRUMENTS.COM 9
9/26/2016 ��,�����+������������������������ ����� TAINSTRUMENTS.COM TAINSTRUMENTS.COM ���+���������������������� Happy & Unhappy Balls 10 8 10 0 Modulus is the same tan δ is very different 10 7 t a n _ d ) e ] Unhappy ball ² [ l t ] a m 10 -1 c ( / n ( y ' d E [ ) 10 6 Happy ball 10 5 10 -2 10 0 10 1 10 -1 10 2 Freq [rad/s] TAINSTRUMENTS.COM TAINSTRUMENTS.COM 10
9/26/2016 �������������������������������� TAINSTRUMENTS.COM TAINSTRUMENTS.COM ����������������������� Apart from chemical nature, tacticity and microstructure, polymers have 3 major characteristics which affect processability 1. Average molecular weight 2. Molecular weight distribution 3. Branching (Type and architecture) TAINSTRUMENTS.COM TAINSTRUMENTS.COM 11
9/26/2016 %�������������������������� ������������.����� • Long Chain Branching (LCB) provides Shear Thinning, Strain Hardening and Melt Strength • Very effective only one per 10000C needed. • Difficult to fully characterize length of branches, number per chain and distribution. TAINSTRUMENTS.COM TAINSTRUMENTS.COM �����������������/������(�����+��� NMR Chromatography (SEC) FTIR TAINSTRUMENTS.COM TAINSTRUMENTS.COM 12
9/26/2016 �������������,���������0���������1$�����12 The G’ and G” curves are shifted to lower frequency (longer time) with increasing molecular weight. 6 10 5 10 Modulus G', G'' [Pa] 4 10 SBR M w [g/mol] G' 130 000 3 10 G'' 130 000 G' 430 000 G'' 430 000 2 10 G' 230 000 G'' 230 000 1 10 -4 -3 -2 -1 0 1 2 3 4 5 10 10 10 10 10 10 10 10 10 10 Freq ω [rad/s] TAINSTRUMENTS.COM TAINSTRUMENTS.COM �������������,0����!�������� The zero shear viscosity increases with increasing molecular weight. TTS is applied to obtain the extended frequency range. 7 10 SBR M w [g/mol] 130 000 The high frequency 6 230 000 10 behavior 320 000 Viscosity η * [Pa s] (slope -1) is 430 000 5 10 independent of the molecular weight η o [Pa s] 4 10 Zero Shear Viscosity Zero Shear Viscosity 10 6 3 10 Slope 3.08 +/- 0.39 5 10 2 100000 10 Molecilar weight M w [Daltons] -4 -3 -2 -1 0 1 2 3 4 5 10 10 10 10 10 10 10 10 10 10 Frequency ω a T [rad/s] TAINSTRUMENTS.COM TAINSTRUMENTS.COM 13
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