This document summarizes research on using large amplitude oscillatory shear (LAOS) to study the nonlinear viscoelastic properties of thixotropic materials like Laponite gel. It discusses using Fourier transform rheology on LAOS data to obtain plateau moduli and higher harmonic parameters. It also proposes a repeated time sweep method to study time-variant viscoelasticity in thixotropic materials under LAOS. Experiments are in progress to apply these methods to Laponite gels and analyze the evolution of moduli and harmonics with gel aging.

1. Large amplitude oscillatory shear (LAOS) on thixotropic materials Speaker: Sun, Weixiang Advisor: Prof. Tong, Zhen Research Institute of Materials Science, South China University of Technology, Guangzhou (510641), P. R. China

2. Locations

3. Group members Prof. Zhen Tong ( 童真） Ruiwen Shu ( 疏瑞文 ) Yanrui Yang ( 杨燕瑞 ) Weixiang Sun ( 孙尉翔 ) May, 2010

4. Contents LAOS methods for thixotropic materials Our work: LAOS study on Laponite? gel LAOS under time-stable condition LAOS time sweep (in progress)

5. Viscoelastic materials as a system Causal G ( t )

6. Viscoelastic materials as a system Causal Linear G ( t )

7. Viscoelastic materials as a system Causal Linear Time-invariant G ( t )

8. Viscoelastic materials as a system G ( t ) Fourier transform G * ( ω ) = G’ + iG’’ Oscillatory shear

9. The structure of Laponite gel charged discs suspension in water House of Cards a synthetic hectorite, [Mg 5.34 Li 0.66 Si 8 O 20 (OH) 4 ]Na 0.66 Layer size: 30 nm in diameter & 1 nm in thickness t w

10. Rheology of Laponite gel Thixotropy Yielding – nonlinear Aging – time-dependent t w G Sample loading Pre-shear Aging

11. Nonlinear viscoelasticity G ( t, γ ) Fourier transform G * ( ω , γ )

12. Dealing with nonlinear viscoelasticity Fourier expansion σ 1 σ 3 σ 5 σ 7

13. Dealing with nonlinear viscoelasticity Fourier expansion σ 1 σ 3 σ 5 σ 7 Medium Amplitude Oscillatory shear (MAOS): avoid varying number of harmonics K, Hyun et al. J. Rheol. 2007 , 51 , 1319-1342

14. Dealing with nonlinear viscoelasticity Lissajous figure R. Ewoldt et al. J. Rheol. 2008 , 52 , 1427-1458

15. Dealing with nonlinear viscoelasticity Lissajous figure R. Ewoldt et al. J. Rheol. 2008 , 52 , 1427-1458 Pedal mucus of snails

16. ARES in our lab ARES RFS Transducers: 20g & 1K FRT Software: TA Orchestrator 7.2.1, “Arbitrary Waveshape Tests”.

17. LAOS of time stable gel Experiment window: t w G Sample loading Pre-shear Aging LAOS

18. LAOS of time stable gel The windows for MAOS is small. Laponite 2.0 wt% NaCl 5.0 mM Fourier transform rheology:

19. LAOS of time stable gel Laponite 2.0 wt% NaCl 5.0 mM Fourier transform rheology: Plateau values

20. LAOS of time stable gel MCT prediction Fourier transform rheology: J. M. Brader et al. Phys. Rev. E , 2010, 82 , 061401. Plateau values

21. LAOS of time stable gel Fourier transform rheology: Laponite 2.0 wt% Varying NaCl concentrations Effect of salt concentration γ 0 = 500%

22. LAOS of time stable gel Fourier transform rheology: Styrene-BA particle suspension Effect of salt concentration S. Kallus et al. Rheol. Acta , 2001, 40 , 552-559.

23. LAOS of time stable gel Fourier transform rheology: Laponite 2.0 wt% NaCl 6.0 mM Maxima in higher harmonics.

24. LAOS of time stable gel Fourier transform rheology: Maxima in higher harmonics. V. Carrier and G. Petekidis, J. Rheol. , 2009, 53 , 245-273. 1 Hz 10 Hz Occurs at increasing ω I 3/1 I 5/1 I 7/1 % PS@PNIPAM suspension

25. LAOS of time stable gel Fourier transform rheology: Maxima in higher harmonics. Occurs at decreasing particle concentrations I 3/1 (%) V. Carrier and G. Petekidis, J. Rheol. , 2009, 53 , 245-273. PS@PNIPAM suspension φ v ↑

26. LAOS of time stable gel γ 0 = 5 % γ 0 = 250 % The gel is turned into viscous fluids under LAOS. Lissajous figures: Laponite 2 wt% NaCl 5 mM

27. LAOS of time stable gel Lissajous figure parameters: The proposed parameters reproduce the trend of the fundamental harmonic. G M G L

28. LAOS of time stable gel Lissajous figure parameters: All but the fundamental harmonics are extracted. W. Sun et al. , Polymer , 2011, 52 , 1402-1409.

29. LAOS of time stable gel Lissajous figure parameters: W. Sun et al. , Polymer , 2011, 52 , 1402-1409. Avoid selecting arbitrary number of harmonics Normalized by the fundamentals

30. LAOS of time stable gel Problems in current method of obtaining G L , G M , etc.: Software: MITlaos It uses the Fourier transformed results to calculate G M , etc. Based on a limited number of harmonics

31. Time-variant viscoelastic materials G ( t ; t w ) Fourier transform G * ( ω ; t w )

32. Time-variant viscoelastic materials G ( t ; t w ) Fourier transform G * ( ω ; t w ) Examples: Thixotropy Physical aging of amorphous polymers Chemical reactions

33. Time-variant viscoelastic materials G ( t ; t w ) Fourier transform G * ( ω ; t w ) Shortest time of data acquisition: one cycle (2 π / ω ).

34. Dealing with time-variant viscoelasticity Traditional frequency sweep: t w G * ( ω ; t w ) … ω t w1 t w2 t w3 Not fast enough

35. Dealing with time-variant viscoelasticity E. E. Holly et al. J. Non-Newtonian Fluid Mech. , 1988, 27 , 17-26. Multiwave method – valid only under linear viscoelastic condition. O ( ω min -1 ) << O ( t w )

36. Dealing with time-variant viscoelasticity J. C. Scanlan et al. Macromolecules , 1991, 24 , 47-54. O ( ω min -1 ) << O ( t w ) t w ω Dynamic frequency sweep direction Continuous frequency sweep: Data interpolation t w1 t w2 t w3 ω G * ( ω ) ω G * ( ω ) ω G * ( ω )

37. Dealing with time-variant viscoelasticity t w Δ t > 2 π / ω (one cycle) O ( ω min -1 ) << O ( t w ) Repeated time sweep:

38. Dealing with time-variant viscoelasticity Repeated time sweep: ω ↑ The phenomena should be exactly repeated at each ω . O ( ω min -1 ) << O ( t w ) A. S. Negi and C. O. Osuji, Phys. Rev. E , 2010, 82 , 031404. Laponite gelation

39. Rheology of Laponite gel Experiment window: t w G Sample loading Pre-shear Aging LAOS time sweep

40. LAOS time sweep of Laponite gel Aging occurs at large strains γ 0 = 1 ~ 20% ω = 5.0 rad/s Laponite 2.0 wt% NaCl 6.0 mM

41. LAOS time sweep of Laponite gel Yielding occurs earlier at larger strains Laponite 2.0 wt% NaCl 6.0 mM γ 0 = 1 ~ 20% ω = 5.0 rad/s

42. LAOS time sweep of Laponite gel Laponite 2.0 wt% Varying NaCl concentrations Times and strains of G’ , G’’ crossover:

43. LAOS time sweep of Laponite gel What about the higher harmonics? The NonLinMon parameter in Orchestrator is I 3/1 . γ 0 = 1 ~ 20% ω = 5.0 rad/s

44. LAOS time sweep of Laponite gel What about the higher harmonics? The Arbitrary Waveshape Test of Orchestrator is not optimized for prolonged tests.

45. LAOS time sweep of Laponite gel NI USB-9215A with BNC 4 channels / 16 bits / 100 kS/s LabView SignalExpress (Full Edition) The raw data manipulation is formidable manually!

46. LAOS time sweep of Laponite gel Just-in-time calculation and saving of I n /1 data. In progress… Identify real fundamental frequency Obtain G M , etc. avoiding Fourier transform Multi-frequency sweep

47. Thank you! Open for questions …

48. 4 月份做的事 编 MATLAB 程序 看 Scheutjens-Fleerg 理论 计算势能 调试 ARES 损耗角

49. 把 Laponite 当成半径 a = 15 nm = 1.5 ×10 -8 m 的球体来考虑。 范德华力： ， x = h /2 a 位阻作用： , ( h < 2 δ ) 双电层重叠：

50. Scheutjens-Fleer 划格子 放链段和溶剂 数构象数、相互作用  G Min{ G } 吸附浓度 平均回转半径

51. Langevin 函数

52. Langmuir 吸附

53. DLVO Total