Download presentation

Presentation is loading. Please wait.

Published byShirley Barefield Modified over 3 years ago

1
DWS and µ-rheology 1 Diffusing Wave Spectroscopy and µ- rheology: when photons probe mechanical properties Luca Cipelletti LCVN UMR 5587, Université Montpellier 2 and CNRS Institut Universitaire de France lucacip@lcvn.univ-montp2.fr

2
DWS and µ-rheology 2 Outline Mechanical rheology and µ-rheology µ-rheology : a few examples Mesuring displacements at a microscopic level: DWS The multispeckle « trick » Conclusions

3
DWS and µ-rheology 3 Rheology and... Mechanical rheology: measure relation between stress and deformation (strain) In-phase response elastic modulus G’( ) Out-of-phase response loss modulus G"( )

4
DWS and µ-rheology 4... µ-rheology Active µ - Rheology : seed the sample with micron-sized beads, impose microscopic displacements with optical tweezers, magnetic fields etc., measure the stress-strain relation. Passive µ - Rheology : let thermal energy do the job, measure deformation (« weak » materials, small quantities, high frequencies…)

5
DWS and µ-rheology 5 Passive µ-rheology Key step : measure displacement on microscopic length scales Bead size: 2 m WaterConcentrated solution of DNA (simple fluid) (viscoelastic fluid) Source: D. Weitz's webpage

6
DWS and µ-rheology 6 Outline Mechanical rheology and µ-rheology µ-rheology : a few examples Mesuring displacements at a microscopic level: DWS The multispeckle « trick » Conclusions

7
DWS and µ-rheology 7 A simple example: a Newtonian fluid Mean Square Displacement Water: G'( ) = 0, G"( ) = D. Weitz's webpage 0.5 m T. Savin's webpage

8
DWS and µ-rheology 8 Generalization to a viscoelastic fluid or taking = 1/ Intuitive approach for a Newtonian fluid: Rigorous, general approach: Fourier transformLaplace transform G*( ) = G'( ) + iG"( )

9
DWS and µ-rheology 9 A Maxwellian fluid (from A. Cardinaux et al., Europhys. Lett. 57, 738 (2002)) Plateau modulus: G 0 Relaxation time : r Viscosity: = G 0 r Rough idea: solid on a time scale << r, with modulus G 0 Liquid on a time scale >> r, with viscosity = G 0 r get G 0 rr r G 0 /2 solvent viscosity solvent viscosity

10
DWS and µ-rheology 10 Passive µ-rheology: the key step Measure mean squared displacement Obtain G’( ), G"( ) Seed the sample with probe particles, then : has to be measured on length scales < 1 nm to 1µm ! 0.1 µm 1 nm

11
DWS and µ-rheology 11 Outline Mechanical rheology and µ-rheology µ-rheology : a few examples Mesuring displacements at a microscopic level: DWS The multispeckle « trick » Conclusions

12
DWS and µ-rheology 12 Light scattering: the concept A light scattering experiment Speckle image

13
DWS and µ-rheology 13 From particle motion to speckle fluctuations r(t)r(t) r(t+)r(t+)

14
DWS and µ-rheology 14 From particle motion to speckle fluctuations r(t)r(t) r(t+)r(t+) Weakly scattering media (single scattering) Speckles fluctuate if r( ) ~ ~0.5 µm (Dynamic Light Scattering)

15
DWS and µ-rheology 15 Diffusing Wave Spectroscopy (DWS): DLS for turbid samples Photon propagation: Random walk Detector

16
DWS and µ-rheology 16 Diffusing Wave Spectroscopy (DWS): DLS for turbid samples Photon propagation: Random walk Detector L l * Speckles fully fluctuate for r 2 > N steps = (L/ l* ) 2 << Typically: L ~ 0.1-1 cm, l* ~ 10-100 µm r 2 > as small as a few Å 2 !

17
DWS and µ-rheology 17 How to quantify intensity fluctuations I t Photomultiplier (PMT)signal Intensity autocorrelation function g 2 -1 cc cc (other functions may be used, see L. Brunel's talk) PMT

18
DWS and µ-rheology 18 From g 2 ( )-1 to Well established formalism exists since ~1988 Depends on the geometry of the experiment A good choice: the backscattering geometry Note: no dependence on l* (corrections are necessary for finite sample thickness, curvature, see L. Brunel's talk)

19
DWS and µ-rheology 19 Outline Mechanical rheology and µ-rheology µ-rheology : a few examples Mesuring displacements at a microscopic level: DWS The multispeckle « trick » Conclusions

20
DWS and µ-rheology 20 The problem: time averages! I(t) PMT signal Average over ~ T exp = 10 3 -10 4 max Could be too long! Time-varying samples? (aging, aggregation...) Sample should explore all possible configurations over time (ergodicity). Gels? Pastes? max = 20 s T exp ~ 1 day!

21
DWS and µ-rheology 21 The Multispeckle technique Average g 2 ( )-1 measured in parallel for many speckles I1(t)I1(t+)I1(t)I1(t+) I2(t)I2(t+)I2(t)I2(t+) I3(t)I3(t+)I3(t)I3(t+) I4(t)I4(t+)I4(t)I4(t+) … CCD or CMOS camera

22
DWS and µ-rheology 22 The Multispeckle technique (MS) max = 20 s T exp ~ 20 s! slow relaxations, non-stationary dynamics non-ergodic samples (gels, pastes, foams, concentrated emulsions...) Smart algorithms needed to cope with the large amount of data to be processed, see L. Brunel's talk

23
DWS and µ-rheology 23 Outline Mechanical rheology and µ-rheology µ-rheology : a few examples Mesuring displacements at a microscopic level: DWS The multispeckle « trick » Conclusions

24
DWS and µ-rheology 24 µ-rheology and DWS: a well established field, but in its commercial infancy! µ-rheology First paper: Mason & Weitz, 1995 (306 citations) Since then: > 680 papers DWS First papers: 1988 Since then: > 1470 papers

25
DWS and µ-rheology 25 MSDWS µ-rheology g 2 ( )-1 r 2 ( )G'( ), G"( ) Multispeckle DWS µ-rheology Reduced T exp Time-varying dynamics Non-ergodic samples Sensitive to nanoscale motion Good average over probes Optically simple & robust No stringent requirements on optical properties (turbidity...) Linear response probed No inhomogeneous response Full spectrum at once No need to load/unload rheometer Cheaper

26
DWS and µ-rheology 26 Useful references Useful references: [1] D. Weitz and D. Pine, Diffusing Wave Spectroscopy in Dynamic Light Scattering, Edited by W. Brown, Clarendon Press, Oxford, 1993 [2] M.L. Gardel, M.T. Valentine, D. A. Weitz, Microrheology, Microscale Diagnostic Techniques K. Breuer (Ed.) Springer Verlag (2005) or at http://www.deas.harvard.edu/projects/weitzlab/papers/urheo_chapter.pdfMicroscale Diagnostic Techniques

27
DWS and µ-rheology 27 Additional material

28
DWS and µ-rheology 28 µ-rheology: from to G’, G" General formulas: or Simpler approach (T. Mason, see [2]) assume that locally be a power law: then, with and

29
DWS and µ-rheology 29 DWS: qualitative aproach Weitz & Pine l l*l* l = 1/ scattering mean free path l* transport mean free path l* = l / Number of scattering events along a path across a cell of thickness L: N ~ (L/ l * ) 2 (l * / l ) [L/ l * 10-100, typically] Change in photon phase due to a particle displacement r (over a single random walk step): ~ ~ k 0 2 Total change in photon phase for a path (uncorrelated particle motion): ~ k 0 2 (L/ l * ) 2 Complete decorrelation of DWS signal for ~ 2 r 2 > (L/ l * ) 2 << [ r 2 > as small as a few Å 2 !!]

30
DWS and µ-rheology 30 DWS: quantitative approach Intensity correlation function g 2 (t)-1 = [g 1 (t)] 2 with t/ = k 0 2 / 6, k 0 = 2 /, and P(s) path length distribution (example: for brownian particles, = 6Dt and t/ = t k 0 2 D (incoherent) sum over photon paths Note: P(s) (and hence g 1 ) depend on the experimental geometry! for analytical expression of g 1 in various geometries (transmission, backscattering) see Weitz & Pine [1]

31
DWS and µ-rheology 31 Backscattering geometry g 1 (t) ~ independent of l*: don’t need to know/measure l*! = (k 0 2 D) -1

32
DWS and µ-rheology 32 Transmission geometry g1(t)g1(t) = (k 0 2 D) -1 Note: l* has to be determined. Measure transmission Calibrate against reference sample

Similar presentations

OK

Results and discussion Samples and simulation technique Sébastien Vincent-Bonnieu, Reinhard Höhler, Sylvie Cohen-Addad Recent experiments have shown that.

Results and discussion Samples and simulation technique Sébastien Vincent-Bonnieu, Reinhard Höhler, Sylvie Cohen-Addad Recent experiments have shown that.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on shell structures pdf Ppt on data hiding in video using least bit technique Ppt on earthquake resistant building construction Ppt on edgeworth box Ppt on fire extinguisher types for electronics Best ppt on geothermal energy Download ppt on motivational stories Ppt on producers consumers and decomposers activities Ppt on print media vs electronic media Ppt on standing order act 1946