We demonstrate a novel method for measuring the microrheology of soft viscoelastic media, based on cross correlating the thermal motion of pairs of embedded tracer particles. The method does not depend on the exact nature of the coupling between the tracers and the medium, and yields accurate rheological data for highly inhomogeneous materials. We demonstrate the accuracy of this method with a guar solution, for which other microscopic methods fail due to the polymer's mesoscopic inhomogeneity. Measurements in an F-actin solution suggest conventional microrheology measurements may not reflect the true bulk behavior. PACS numbers: 87.19.Tt, 83.70.Hq, 83.80.Lz Many interesting and important materials such as polymers, gels, and biomaterials are viscoelastic; when responding to an external stress, they both store and dissipate energy. This behavior is quantified by the complex shear modulus, G ‫ء‬ ͑v͒, which provides insight into the material's microscopic dynamics. Typically, G ‫ء‬ ͑v͒ is measured by applying oscillatory strain to a sample and measuring the resulting stress. Recently a new method, called microrheology, has been developed which determines G ‫ء‬ ͑v͒ from the thermal motion of microscopic tracer particles embedded in the material [1,2]. Microrheology offers significant potential advantages: it provides a local probe of G ‫ء‬ ͑v͒ in miniscule sample volumes and can do so at very high frequencies. While microrheology provides an accurate measure of G ‫ء‬ ͑v͒ for simple systems, its validity in common complex systems is far from certain. If the tracers locally modify the structure of the medium, or sample only pores in an inhomogeneous matrix, then bulk rheological properties will not be determined. Such subtle effects currently limit many interesting applications of microrheology.In this Letter, we introduce a new formalism, which we term "two-point microrheology," based on measuring the cross-correlated thermal motion of pairs of tracer particles to determine G ‫ء‬ ͑v͒. This new technique overcomes the limitations of single-particle microrheology. It does not depend on the size or shape of the tracer particle; moreover it is independent of the coupling between the tracer and the medium. We demonstrate the validity of this approach with measurements on a highly inhomogeneous material, a solution of the polysaccharide guar. Two-point microrheology correctly reproduces results obtained with a mechanical rheometer, whereas single-particle microrheology gives erroneous results. We also compare ordinary and two-point microrheology of F-actin [2-4], a semiflexible biopolymer constituent of the cytoskeleton. Different results are obtained with the two techniques, suggesting that earlier interpretations of F-actin microrheology should be reexamined. Conventional microrheology [1,2] uses the equation:wherer 2 ͑s͒ is the Laplace transform of the tracers' mean squared displacement, ͗Dr 2 ͑t͒͘, as a function of Laplace frequency s, and a is their radius. Equation (1) (1) is subject to the same conditions as the...

We develop a multiple particle tracking technique for making precise, localized measurements of the mechanical microenvironments of inhomogeneous materials. Using video microscopy, we simultaneously measure the Brownian dynamics of roughly one hundred fluorescent tracer particles embedded in a complex medium and interpret their motions in terms of local viscoelastic response. To help overcome the inherent statistical limitations due to the finite imaging volume and limited imaging times, we develop statistical techniques and analyze the distribution of particle displacements in order to make meaningful comparisons of individual particles and thus characterize the diversity and properties of the microenvironments. The ability to perform many local measurements simultaneously allows more precise measurements even in systems that evolve in time. We show several examples of inhomogeneous materials to demonstrate the flexibility of the technique and learn new details of the mechanics of the microenvironments that small particles explore. This technique extends other microrheological methods to allow simultaneous measurements of large numbers of probe particles, enabling heterogeneous samples to be studied more effectively.PACS number͑s͒: 83.85. Ei, 83.10.Pp, 82.35.Pq, 62.25.ϩg

Abstract. We use near-infrared dynamic multiple scattering of light ͓diffusing-wave spectroscopy ͑DWS͔͒ to detect the activation of the somato-motor cortex in 11 right-handed volunteers performing a finger opposition task separately with their right and left hands. Temporal autocorrelation functions g ͑1͒ ͑r , ͒ of the scattered light field are measured during 100-s periods of motor task alternating with 100-s resting baseline periods. From an analysis of the experimental data with an analytical theory for g ͑1͒ ͑r , ͒ from a three-layer geometry with optical and dynamical heterogeneity representing scalp, skull, and cortex, we obtain quantitative estimates of the diffusion coefficient in cortical regions. Consistent with earlier results, the measured cortical diffusion coefficient is found to be increased during the motor task, with a strong contralateral and a weaker ipsilateral increase consistent with the known brain hemispheric asymmetry for right-handed subjects. Our results support the interpretation of the increase of the cortical diffusion coefficient during finger opposition being due to the functional increase in cortical blood flow rate related to vasodilation.

In this paper we report on the charging behavior of latex particles in aqueous suspensions. We use static light scattering and acid-base titrations as complementary techniques to observe both effective and bare particle charges. Acid-base titrations'at various ionic strengths provide the pH dependent charging curves. The surface chemical parameters (dissociation constant of the acidic carboxylic groups, total density of ionizable sites and Stem capacitance) are determined from tits of a Stem layer model to the titration data. We find strong evidence that the dissociation of protons is the only specific adsorption process. Effective particle charges are determined by tits of integral equation calculations of the polydisperse static structure factor to the static light scattering data. A generalization of the Poisson-Boltzmann cell model including the dissociation of the acidic surface groups and the autodissociation of water is used to predict effective particle charges from the surface chemical parameters determined by the titration experiments. We find that the light scattering data are best described by a model where a small fraction of the ionizable surface sites are sulfate groups which are completely dissociated at moderate pH. These effective charges are comparable to the predictions by a basic cell model where charge regulation is absent. 0 I994 American Institute of Physics.

We report on experiments on the rheology of gels formed by diffusion-limited aggregation of neutrally buoyant colloidal particles. These gels form very weak solids, with the elastic modulus, G 0 ͑v͒, larger than the loss modulus, G 00 ͑v͒, and with both G 0 ͑v͒ and G 00 ͑v͒ exhibiting only a very weak frequency dependence. Upon small but finite strains g , 0.45 the elastic modulus increases roughly exponentially with g 2 . We explain the observed strain hardening with the highly nonlinear elastic response of the rigid backbone of the gel to elongational deformation. [S0031-9007 (98) Colloidal particles aggregating by attractive interactions form highly disordered clusters; these structures are, on average, self-similar, and the mass of a cluster, M, scales with its radius, R, aswhere a is the size of the colloidal monomer and M 0 is its mass [1]. The fractal mass exponent d f characterizes the ramification of the cluster and varies between d f 2.1 for reactionlimited cluster aggregation and d f 1.8 for diffusionlimited cluster aggregation (DLCA) [2]. In the latter case the distribution of cluster sizes is fairly narrow and the characteristic cluster size grows linearly with time. Aggregation of clusters eventually leads to a spacefilling structure which is no longer fractal on all length scales but which can instead show long-range correlations as revealed by a scattering peak corresponding to a characteristic cluster size R c aw 1͑͞d f 23͒ , where w is the initial volume fraction of monomer particles [3,4]. The clusters themselves are close packed, forming a ramified, tenuous gel structure. This structure should be an elastic material with unique properties, which are determined not only by d f , but also by the connectivity or chemical dimension, d b , which characterizes the scaling of the contour length within the cluster.