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We present a data analysis procedure that provides the solution to a long-standing issue in microrheology studies, i.e. the evaluation of the fluids' linear viscoelastic properties from the analysis of a finite set of experimental data, describing (for instance) the time-dependent mean-square displacement of suspended probe particles experiencing Brownian fluctuations. We report, for the first time in the literature, the linear viscoelastic response of an optically trapped bead suspended in a Newtonian fluid, over the entire range of experimentally accessible frequencies. The general validity of the proposed method makes it transferable to the majority of microrheology and rheology techniques.

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Microrheology is a branch of rheology having the same principles as conventional bulk rheology, but working on micron length scales and µl volumes.Optical tweezers have been successfully used with Newtonian fluids for rheological purposes such as determining fluid viscosity. Conversely, when optical tweezers are used to measure the viscoelastic properties of complex fluids the results are either limited to the material's high-frequency response, discarding important information related to the low-frequency behaviour, or they are supplemented by low-frequency measurements performed with different techniques, often without presenting an overlapping region of clear agreement between the sets of results. We present a simple experimental procedure to perform microrheological measurements over the widest frequency range possible with optical tweezers. A generalised Langevin equation is used to relate the frequency-dependent moduli of the complex fluid to the time-dependent trajectory of a probe particle as it flips between two optical traps that alternately switch on and off.

We present an experimental procedure to perform broadband microrheological measurements with optical tweezers. A generalised Langevin equation is adopted to relate the time-dependent trajectory of a particle in an imposed flow to the frequency-dependent moduli of the complex fluid. This procedure allows us to measure the material linear viscoelastic properties across the widest frequency range achievable with optical tweezers.PACS numbers: 83.60. Bc, 83.85.Ei In 1986 Ashkin and colleagues reported the first observation of what is now commonly referred to as optical tweezers: a tightly focused beam of light capable of holding microscopic particles stable in three dimensions [1]. Since then, several studies have adopted this technique as a tool for purposes as varied as trapping solid aerosols [2], measuring the viscosity of biomaterials [3,4], the forces exerted by single motor proteins [5] and the compliance of bacterial tails [6], or stretching single DNA molecules [7]. However, there remain a number of issues when optical tweezers are used for microrheological measurements.Microrheology is a branch of rheology having the same principles as conventional bulk rheology (i.e. to study the linear viscoelastic behaviour of materials), but working on micron length scales. The linear viscoelastic properties of a material can be represented by the frequencydependent dynamic complex modulus G * (ω), which provides information on both the viscous and the elastic nature of the material. The conventional method of measuring G * (ω) is based on the imposition of an oscillatory stress σ(ω, t) and the measurement of the resulting oscillatory strain γ(ω, t), or vice versa. The amplitudes of its in-phase and out-of-phase components are both proportional to the stress amplitude, with constants of proportionality defining, respectively, the storage (elastic) G ′ (ω) and the loss (viscous)Optical tweezers have been successfully used with Newtonian fluids for rheological purposes such as determining the fluid viscosity with high accuracy, measuring the hydrodynamic interactions between particles or estimating the wall effect on the Stokes drag coefficient (i.e. Faxn's correction), as reviewed in Ref. [9]. Conversely, when optical tweezers are adopted for measuring the viscoelastic properties of complex fluids the results are limited to the material high frequency response, discarding the essential information related to long times scales (i.e. low frequency) material behaviour. † Electronic address: M.Tassieri@elec.gla.ac.ukThe aim of this letter is to present a self-consistent procedure for measuring the linear viscoelastic properties of materials, from non-oscillatory measurements, across the widest frequency range achievable with optical tweezers. In particular, the procedure consists of two steps: (I) measuring the thermal fluctuations of a trapped bead for a sufficiently long time; (II) measuring the transient bead displacement, from the optical trap centre, in response to a uniform fluid flow field entraining the bead. The...