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{{cite journal
{{cite journal
|author=Mason Weitz
|author=Mason Weitz
|year=1995
|date=1995
|title=
|title=
|journal=[[Physical Review Letters]]
|journal=[[Physical Review Letters]]
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|bibcode = 1995PhRvL..74.1250M }}</ref> is a technique to measure the [[rheology|rheological properties]] of a medium, such as [[microviscosity]], via the measurement of the trajectory of a [[flow tracer]] (a micrometre-size particle). It is a new way of doing [[rheology]], traditionally done using a [[rheometer]]. The size of the tracer is around a micrometre. There are two types of microrheology: ''passive microrheology'' and ''active microrheology''. Passive microrheology uses inherent [[thermal energy]] to move the tracers, whereas active microrheology uses externally applied forces, such as from a [[magnetic field]] or an [[optical tweezer]], to do so. Microrheology can be further differentiated into 1- and 2-particle methods<ref name="Crocker2000">
|bibcode = 1995PhRvL..74.1250M }}</ref> is a technique to measure the [[rheology|rheological properties]] of a medium, such as [[microviscosity]], via the measurement of the trajectory of a [[flow tracer]] (a micrometre-size particle). It is a new way of doing [[rheology]], traditionally done using a [[rheometer]]. The size of the tracer is around a micrometre. There are two types of microrheology: ''passive microrheology'' and ''active microrheology''. Passive microrheology uses inherent [[thermal energy]] to move the tracers, whereas active microrheology uses externally applied forces, such as from a [[magnetic field]] or an [[optical tweezer]], to do so. Microrheology can be further differentiated into 1- and 2-particle methods<ref name="Crocker2000">
{{cite journal
{{cite journal
|author=Crocker, John C. and Valentine, M. T. and Weeks, Eric R. and Gisler, T. and Kaplan, P. D. and Yodh, A. G. and Weitz, D. A.
|author=Crocker, John C. |display-authors=4 |author2=Valentine, M. T. |author3=Weeks, Eric R. |author4=Gisler, T. |author5=Kaplan, P. D. |author6=Yodh, A. G. |author7=Weitz, D. A.
|year=2000
|last-author-amp=yes |date=2000
|title=Two-Point Microrheology of Inhomogeneous Soft Materials
|title=Two-Point Microrheology of Inhomogeneous Soft Materials
|journal=[[Physical Review Letters]]
|journal=[[Physical Review Letters]]
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.<ref name="Levine2000">
.<ref name="Levine2000">
{{cite journal
{{cite journal
|author=Levine, Alex J. and Lubensky, T. C.
|author=Levine, Alex J. |author2=Lubensky, T. C.
|year=2000
|last-author-amp=yes |date=2000
|title=One- and Two-Particle Microrheology
|title=One- and Two-Particle Microrheology
|journal=[[Physical Review Letters]]
|journal=[[Physical Review Letters]]
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{{cite journal
{{cite journal
|author=
|author=
|year=2002
|date=2002
|title=
|title=
|journal=[[European Physical Journal E]]
|journal=[[European Physical Journal E]]
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A related method of passive microrheology involves the tracking positions of a particle at a high frequency, often with a quadrant photodiode.<ref name="Schnurr1997">
A related method of passive microrheology involves the tracking positions of a particle at a high frequency, often with a quadrant photodiode.<ref name="Schnurr1997">
{{cite journal
{{cite journal
|author=Schnurr, B. and Gittes, F. and MacKintosh, F. C. and Schmidt, C. F.
|author=Schnurr, B. |author2=Gittes, F. |author3=MacKintosh, F. C. |author4=Schmidt, C. F.
|year=1997
|last-author-amp=yes |date=1997
|title=Determining Microscopic Viscoelasticity in Flexible and Semiflexible Polymer Networks from Thermal Fluctuations
|title=Determining Microscopic Viscoelasticity in Flexible and Semiflexible Polymer Networks from Thermal Fluctuations
|journal=Macromolecules
|journal=Macromolecules
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|issue=25 |arxiv = cond-mat/9709231 |bibcode = 1997MaMol..30.7781S }}</ref> From the position, <math>x(t)</math>, the power spectrum, <math><x_{\omega}^2></math> can be found, and then related to the real and imaginary parts of the response function, <math>\alpha(\omega)</math>.<ref name="Gittes1997">
|issue=25 |arxiv = cond-mat/9709231 |bibcode = 1997MaMol..30.7781S }}</ref> From the position, <math>x(t)</math>, the power spectrum, <math><x_{\omega}^2></math> can be found, and then related to the real and imaginary parts of the response function, <math>\alpha(\omega)</math>.<ref name="Gittes1997">
{{cite journal
{{cite journal
|author=Gittes, F. and Schnurr, B. and Olmsted, P. D. and MacKintosh, F. C. and Schmidt, C. F.
|author=Gittes, F. |display-authors=4 |author2=Schnurr, B. |author3=Olmsted, P. D. |author4=MacKintosh, F. C. |author5=Schmidt, C. F.
|year=1997
|last-author-amp=yes |date=1997
|title=Determining Microscopic Viscoelasticity in Flexible and Semiflexible Polymer Networks from Thermal Fluctuations
|title=Determining Microscopic Viscoelasticity in Flexible and Semiflexible Polymer Networks from Thermal Fluctuations
|journal=[[Physical Review Letters]]
|journal=[[Physical Review Letters]]
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{{cite journal
{{cite journal
|author=A.R. Bausch et al.
|author=A.R. Bausch et al.
|year=1999
|date=1999
|title=Measurement of local viscoelasticity and forces in living cells by magnetic tweezers|journal=[[Biophysical Journal]]
|title=Measurement of local viscoelasticity and forces in living cells by magnetic tweezers|journal=[[Biophysical Journal]]
|volume=76
|volume=76
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}}</ref><ref>
}}</ref><ref>
{{cite journal
{{cite journal
|author=K.S. Zaner and P.A. Valberg
|author=K.S. Zaner |author2=P.A. Valberg
|last-author-amp=yes |date=1989
|year=1989
|title=Viscoelasticity of F-actin measured with magnetic microparticles|journal=[[Journal of Cell Biology]]
|title=Viscoelasticity of F-actin measured with magnetic microparticles|journal=[[Journal of Cell Biology]]
|volume=109
|volume=109
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}}</ref><ref>
}}</ref><ref>
{{cite journal
{{cite journal
|author=F.Ziemann, J. Radler, and E. Sackmann
|author=F.Ziemann |author2=J. Radler |author3=E. Sackmann
|last-author-amp=yes |date=1994
|year=1994
|title=Local measurements of viscoelastic moduli of entangled actin networks using an oscillating magnetic bead micro-rheometer|journal=[[Biophysical Journal]]
|title=Local measurements of viscoelastic moduli of entangled actin networks using an oscillating magnetic bead micro-rheometer|journal=[[Biophysical Journal]]
|volume=66
|volume=66
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}}</ref><ref>
}}</ref><ref>
{{cite journal
{{cite journal
|author=F.G. Schmidt, F. Ziemann, and E. Sackmann
|author=F.G. Schmidt |author2=F. Ziemann |author3=E. Sackmann
|last-author-amp=yes |date=1996
|year=1996
|title=
|title=
|journal=[[European Biophysics Journal]]
|journal=[[European Biophysics Journal]]
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{{cite journal
{{cite journal
|author=F. Amblard et al.
|author=F. Amblard et al.
|year=1996
|date=1996
|title=Subdiffusion and Anomalous Local Viscoelasticity in Actin Networks|journal=[[Physical Review Letters]]
|title=Subdiffusion and Anomalous Local Viscoelasticity in Actin Networks|journal=[[Physical Review Letters]]
|volume=77
|volume=77
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{{cite journal
{{cite journal
|author=E. Helfer et al.
|author=E. Helfer et al.
|year=2000
|date=2000
|title=Microrheology of Biopolymer-Membrane Complexes|journal=[[Physical Review Letters]]
|title=Microrheology of Biopolymer-Membrane Complexes|journal=[[Physical Review Letters]]
|volume=85
|volume=85
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{{cite journal
{{cite journal
|author=Manlio Tassieri et al.
|author=Manlio Tassieri et al.
|year=2012
|date=2012
|title=Microrheology with optical tweezers: data analysis|journal=[[New Journal of Physics]]
|title=Microrheology with optical tweezers: data analysis|journal=[[New Journal of Physics]]
|volume=14
|volume=14
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|bibcode = 2012NJPh...14k5032T }}</ref><ref>
|bibcode = 2012NJPh...14k5032T }}</ref><ref>
{{cite journal
{{cite journal
|author=David Engström, Michael C.M. Varney, Martin Persson, Rahul P. Trivedi, Kris A. Bertness, Mattias Goksör, and Ivan I. Smalyukh
|author=David Engström |display-authors=4 |author2=Michael C.M. Varney |author3=Martin Persson |author4=Rahul P. Trivedi |author5=Kris A. Bertness |author6=Mattias Goksör |author7=Ivan I. Smalyukh
|last-author-amp=yes |date=2012
|year=2012
|title=Unconventional structure-assisted optical manipulation of high-index nanowires in liquid crystals
|title=Unconventional structure-assisted optical manipulation of high-index nanowires in liquid crystals
|journal=[[Optics Express]]
|journal=[[Optics Express]]
|volume=20
|volume=20
|pages=7741-7748
|pages=7741–7748
|doi=10.1364/OE.20.007741
|doi=10.1364/OE.20.007741
|issue=7
|issue=7
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* [http://www.formulaction.com/microrheology_viscoelasticity.html Illustrated description of microrheology and a microrheology analysis, with movies ]
* [http://www.formulaction.com/microrheology_viscoelasticity.html Illustrated description of microrheology and a microrheology analysis, with movies ]
* [http://www.lsinstruments.ch/technology/diffusing_wave_spectroscopy_dws/microrheology/ Microrheology Overview with Animations]
* [http://www.lsinstruments.ch/technology/diffusing_wave_spectroscopy_dws/microrheology/ Microrheology Overview with Animations]

[[Category:Rheology]]
[[Category:Rheology]]
[[Category:Soft matter]]
[[Category:Soft matter]]

Revision as of 17:40, 31 January 2015

Microrheology[1] is a technique to measure the rheological properties of a medium, such as microviscosity, via the measurement of the trajectory of a flow tracer (a micrometre-size particle). It is a new way of doing rheology, traditionally done using a rheometer. The size of the tracer is around a micrometre. There are two types of microrheology: passive microrheology and active microrheology. Passive microrheology uses inherent thermal energy to move the tracers, whereas active microrheology uses externally applied forces, such as from a magnetic field or an optical tweezer, to do so. Microrheology can be further differentiated into 1- and 2-particle methods[2] .[3]

Passive microrheology

Passive microrheology uses the thermal energy (kT) to move the tracers. The trajectories of the tracers are measured optically either by microscopy or by diffusing-wave spectroscopy (DWS). From the mean squared displacement with respect to time (noted MSD or <Δr2> ), one can calculate the visco-elastic moduli G′(ω) and G″(ω) using the generalized Stokes–Einstein relation (GSER). Here is a view of the trajectory of a particle of micrometer size.

Observing the MSD for a wide range of time scales gives information on the microstructure of the medium where are diffusing the tracers. If the tracers are having a free diffusion, one can deduce that the medium is purely viscous. If the tracers are having a sub-diffusive mean trajectory, it indicates that the medium presents some viscoelastic properties. For example, in a polymer network, the tracer may be trapped. The excursion δ of the tracer is related to the elastic modulus G′ with the relation G′ = kBT/(6πaδ2).[4]

Microrheology is another way to do linear rheology. Since the force involved is very weak (order of 10−15 N), microrheology is guaranteed to be in the so-called linear region of the strain/stress relationship. It is also able to measure very small volumes (biological cell).

Given the complex viscoelastic modulus G(ω)=G′(ω)+iG″(ω) with G′(ω) the elastic (conservative) part and G″(ω) the viscous (dissipative) part and ω=2πf the pulsation. The GSER is as follows:

G~(s)=kBTπas⟨Δr~2(s)⟩

with

G~(s): Laplace transform of G
kB: Boltzmann constant
T: temperature in kelvins
s: the Laplace frequency
a: the radius of the tracer
⟨Δr~2(s)⟩: the Laplace transform of the mean squared displacement

A related method of passive microrheology involves the tracking positions of a particle at a high frequency, often with a quadrant photodiode.[5] From the position, x(t), the power spectrum, <xω2> can be found, and then related to the real and imaginary parts of the response function, α(ω).[6] The response function leads directly to a calculation of the complex shear modulus, G(ω) via:

G(ω)=16πaα(ω)

Active microrheology

Active microrheology may use a magnetic field [7][8][9][10][11] or optical tweezers[12][13][14] to apply a force on the tracer and then find the stress/strain relation.

References

  1. ↑ Mason Weitz (1995). Physical Review Letters. 74: 7. Bibcode:1995PhRvL..74.1250M. doi:10.1103/physrevlett.74.1250. {{cite journal}}: Missing or empty |title= (help)
  2. ↑ Crocker, John C.; Valentine, M. T.; Weeks, Eric R.; Gisler, T.; et al. (2000). "Two-Point Microrheology of Inhomogeneous Soft Materials". Physical Review Letters. 85 (4): 888–891. Bibcode:2000PhRvL..85..888C. doi:10.1103/PhysRevLett.85.888. {{cite journal}}: Unknown parameter |last-author-amp= ignored (|name-list-style= suggested) (help)
  3. ↑ Levine, Alex J.; Lubensky, T. C. (2000). "One- and Two-Particle Microrheology". Physical Review Letters. 85 (8): 1774–1777. arXiv:cond-mat/0004103. Bibcode:2000PhRvL..85.1774L. doi:10.1103/PhysRevLett.85.1774. {{cite journal}}: Unknown parameter |last-author-amp= ignored (|name-list-style= suggested) (help)
  4. ↑ European Physical Journal E. 8: 431–436. 2002. Bibcode:2002EPJE....8..431B. doi:10.1140/epje/i2002-10026-0. {{cite journal}}: Missing or empty |title= (help)
  5. ↑ Schnurr, B.; Gittes, F.; MacKintosh, F. C.; Schmidt, C. F. (1997). "Determining Microscopic Viscoelasticity in Flexible and Semiflexible Polymer Networks from Thermal Fluctuations". Macromolecules. 30 (25): 7781–7792. arXiv:cond-mat/9709231. Bibcode:1997MaMol..30.7781S. doi:10.1021/ma970555n. {{cite journal}}: Unknown parameter |last-author-amp= ignored (|name-list-style= suggested) (help)
  6. ↑ Gittes, F.; Schnurr, B.; Olmsted, P. D.; MacKintosh, F. C.; et al. (1997). "Determining Microscopic Viscoelasticity in Flexible and Semiflexible Polymer Networks from Thermal Fluctuations". Physical Review Letters. 79 (17): 3286–3289. arXiv:cond-mat/9709228. Bibcode:1997PhRvL..79.3286G. doi:10.1103/PhysRevLett.79.3286. {{cite journal}}: Unknown parameter |last-author-amp= ignored (|name-list-style= suggested) (help)
  7. ↑ A.R. Bausch; et al. (1999). "Measurement of local viscoelasticity and forces in living cells by magnetic tweezers". Biophysical Journal. 76 (1 Pt 1): 573–9. Bibcode:1999BpJ....76..573B. doi:10.1016/S0006-3495(99)77225-5. PMC 1302547. PMID 9876170. {{cite journal}}: Explicit use of et al. in: |author= (help)
  8. ↑ K.S. Zaner; P.A. Valberg (1989). "Viscoelasticity of F-actin measured with magnetic microparticles". Journal of Cell Biology. 109 (5): 2233–43. doi:10.1083/jcb.109.5.2233. PMC 2115855. PMID 2808527. {{cite journal}}: Unknown parameter |last-author-amp= ignored (|name-list-style= suggested) (help)
  9. ↑ F.Ziemann; J. Radler; E. Sackmann (1994). "Local measurements of viscoelastic moduli of entangled actin networks using an oscillating magnetic bead micro-rheometer". Biophysical Journal. 66 (6): 2210–6. Bibcode:1994BpJ....66.2210Z. doi:10.1016/S0006-3495(94)81017-3. PMC 1275947. PMID 8075354. {{cite journal}}: Unknown parameter |last-author-amp= ignored (|name-list-style= suggested) (help)
  10. ↑ F.G. Schmidt; F. Ziemann; E. Sackmann (1996). European Biophysics Journal. 24: 348. doi:10.1007/bf00180376. {{cite journal}}: Missing or empty |title= (help); Unknown parameter |last-author-amp= ignored (|name-list-style= suggested) (help)
  11. ↑ F. Amblard; et al. (1996). "Subdiffusion and Anomalous Local Viscoelasticity in Actin Networks". Physical Review Letters. 77 (21): 4470–4473. Bibcode:1996PhRvL..77.4470A. doi:10.1103/PhysRevLett.77.4470. PMID 10062546. {{cite journal}}: Explicit use of et al. in: |author= (help)
  12. ↑ E. Helfer; et al. (2000). "Microrheology of Biopolymer-Membrane Complexes". Physical Review Letters. 85 (2): 457–60. Bibcode:2000PhRvL..85..457H. doi:10.1103/PhysRevLett.85.457. PMID 10991307. {{cite journal}}: Explicit use of et al. in: |author= (help)
  13. ↑ Manlio Tassieri; et al. (2012). "Microrheology with optical tweezers: data analysis". New Journal of Physics. 14 (11): 115032. Bibcode:2012NJPh...14k5032T. doi:10.1088/1367-2630/14/11/115032. {{cite journal}}: Explicit use of et al. in: |author= (help)CS1 maint: article number as page number (link)
  14. ↑ David Engström; Michael C.M. Varney; Martin Persson; Rahul P. Trivedi; et al. (2012). "Unconventional structure-assisted optical manipulation of high-index nanowires in liquid crystals". Optics Express. 20 (7): 7741–7748. Bibcode:2012OExpr..20.7741E. doi:10.1364/OE.20.007741. {{cite journal}}: Unknown parameter |last-author-amp= ignored (|name-list-style= suggested) (help)
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