Microrheology and the fluctuation theorem in dense colloids

We present experiments and computer simulations of a “tracer” (or “probe”) particle trapped with optical tweezers and dragged at constant speed through a bath of effectively hard colloids with approximately the same size as the probe. The results are analyzed taking the single-particle case and assuming effective parameters for the bath. The effective microscopic friction coefficient and effective temperature of the tracer are obtained. At high probe velocities, the experimental microviscosity compares well with the viscosity from bulk rheology, whereas a correction due to hydrodynamic interactions (absent in the simulations) is necessary to collapse the simulation data. Surprisingly, agreement is found without any need of hydrodynamic corrections at small probe velocities. The dynamics of the tracer inside the trap shows, both in the simulations and experiments, a fast relaxation due to solvent friction and a slow one caused by the collisions with other particles. The latter is less effective in dissipating the energy introduced by the moving trap and causes increasing fluctuations in the tracer motion, reflected as higher effective temperature. Copyright c © EPLA, 2011 Using tools such as optical tweezers, it is now possible to manipulate and measure the response of soft matter on the sub-micron scale. In active microrheology [1], a known external force is applied to a bead in a complex environment, and the response of the bead (and, less frequently, of the environment) is recorded. Experimentally, one of the attractions is that such microrheological techniques require much smaller samples than bulk rheology. Theoretically, by studying fluctuating quantities at mesoscopic length scales, microrheology raises issues of fundamental statistical mechanics related to fluctuations and irreversibility [2]. In microrheology, effective friction coefficients, γ, are defined through the stationary relation 〈F〉= γ〈U〉, where 〈U〉 and 〈F〉 are the mean velocity of and force on the tracer, respectively. In this letter, we are concerned with the microrheology of colloidal suspensions. Here, theories have been developed for low particle concentrations [3] and up to vitrification [4], relating 〈U〉 and 〈F〉 in the (a)Present address: The Rowland Institute at Harvard 100 Edwin H. Land Boulevard, Cambridge, MA 02142, USA. (b)E-mail: [email protected] absence of hydrodynamic interactions (HI). Two limiting situations are possible: dragging a probe particle by a constant F, or translating it at constant U. When the probe is held in a trapping potential, e.g. using laser tweezers, and translated through the sample, a mixed mode appears which reduces to constant U in a stiff trap. Simulations have shown that these two limits are indeed different [5]. Experimentally, Habdas et al. [6] have dragged magnetic beads through a hard sphere (HS) colloidal suspension with a constant F, and their results have been compared with theory [4]. Earlier, Meyer et al. [7] studied the forces acting on a probe particle held by optical tweezers in suspensions of teflon particles being translated at constant U, where the probes were significantly larger (∼×10) than the bath colloids. Their results do not agree with bulk rheology, but more recent experiments by the same group [8] compare well with the theoretical work of Squires and Brady [3]. Other microrheological experiments have confirmed the fluctuation theorem (FT), which states that the ratio of the probabilities of producing an entropy σ and −σ is equal to exp(στ), where τ is the length of the interval over which σ is measured, for large τ [9–11]. The single-particle