A symmetrical method to obtain shear moduli from microrheology† †Electronic supplementary information (ESI) available. See DOI: 10.1039/c7sm02499a

Passive microrheology deduces shear elastic moduli from thermally fluctuating motion of probe particles. We introduce and test an analysis method for direct determination of these moduli from the mean-squared displacement of a probe.

[1]  Zach DeVito,et al.  Opt , 2017 .

[2]  F. MacKintosh,et al.  High-frequency microrheology of wormlike micelles. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Mason,et al.  Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids. , 1995, Physical review letters.

[4]  Jay X. Tang,et al.  Correlated fluctuations of microparticles in viscoelastic solutions: quantitative measurement of material properties by microrheology in the presence of optical traps. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  David A. Weitz,et al.  Diffusing-wave-spectroscopy measurements of viscoelasticity of complex fluids , 1997 .

[6]  T. Lubensky,et al.  Principles of condensed matter physics , 1995 .

[7]  B. M. Fulk.  MATH , 1992 .

[8]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[9]  Maggs,et al.  Subdiffusion and Anomalous Local Viscoelasticity in Actin Networks. , 1996, Physical review letters.

[10]  F. C. MacKintosh,et al.  Microscopic Viscoelasticity: Shear Moduli of Soft Materials Determined from Thermal Fluctuations , 1997 .

[11]  Janina Muller.  Microscale Diagnostic Techniques , 2016 .

[12]  C. Schmidt,et al.  Interference model for back-focal-plane displacement detection in optical tweezers. , 1998, Optics letters.

[13]  D. Chandler,et al.  Introduction To Modern Statistical Mechanics , 1987 .

[14]  E. M. Lifshitz,et al.  Statistical physics. Pt.1, Pt.2 , 1980 .

[15]  B. Fornberg.  Generation of finite difference formulas on arbitrarily spaced grids , 1988 .

[16]  R. Kubo.  The fluctuation-dissipation theorem , 1966 .

[17]  A. Leonov.  Constitutive equations for polymer melts and solutions, by R. G. Larson, Butterworths, Boston, 1988, 364 pp., $39.95 , 1989 .

[18]  F. Cacialli.  Journal of Physics Condensed Matter: Preface , 2002 .

[19]  David C. Morse,et al.  Viscoelasticity of concentrated isotropic solutions of semiflexible polymers. 2. Linear response , 1998 .

[20]  William W. Graessley.  The Entanglement Concept in Polymer Rheology , 1974 .

[21]  D A Weitz,et al.  Microrheology probes length scale dependent rheology. , 2006, Physical review letters.

[22]  Denis Wirtz,et al.  Particle Tracking Microrheology of Complex Fluids , 1997 .

[23]  F. MacKintosh,et al.  Microrheology : Rheology and rheological techniques , 1999 .

[24]  Jonathan M. Cooper,et al.  Microrheology with optical tweezers: data analysis , 2012 .

[25]  Nancy R. Forde,et al.  Microrheological Characterization of Collagen Systems: From Molecular Solutions to Fibrillar Gels , 2013, PloS one.

[26]  H. Callen,et al.  Irreversibility and Generalized Noise , 1951 .

[27]  F. C. MacKintosh,et al.  Determining Microscopic Viscoelasticity in Flexible and Semiflexible Polymer Networks from Thermal Fluctuations , 1997 .

[28]  D. Frenkel,et al.  Real-time monitoring of complex moduli from micro-rheology , 2010, Journal of physics. Condensed matter : an Institute of Physics journal.

[29]  Levine,et al.  One- and two-particle microrheology , 2000, Physical review letters.

[30]  M. Tassieri,et al.  Direct conversion of rheological compliance measurements into storage and loss moduli. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  M. Huggins.  Viscoelastic Properties of Polymers. , 1961 .

[32]  F. MacKintosh,et al.  Dynamic shear modulus of a semiflexible polymer network , 1998 .