A wide variety of systems, including granular media, colloidal suspensions and molecular systems, exhibit non-equilibrium transitions from a fluid-like to a solid-like state, characterized solely by the sudden arrest of their dynamics. Crowding or jamming of the constituent particles traps them kinetically, precluding further exploration of the phase space. The disordered fluid-like structure remains essentially unchanged at the transition. The jammed solid can be refluidized by thermalization, through temperature or vibration, or by an applied stress. The generality of the jamming transition led to the proposal of a unifying description, based on a jamming phase diagram. It was further postulated that attractive interactions might have the same effect in jamming the system as a confining pressure, and thus could be incorporated into the generalized description. Here we study experimentally the fluid-to-solid transition of weakly attractive colloidal particles, which undergo markedly similar gelation behaviour with increasing concentration and decreasing thermalization or stress. Our results support the concept of a jamming phase diagram for attractive colloidal particles, providing a unifying link between the glass transition, gelation and aggregation.

We demonstrate the use of an ordinary white-light microscope for the study of the q-dependent dynamics of colloidal dispersions. Time series of digital video images are acquired in bright field with a fast camera and image differences are Fourier-analyzed as a function of the time delay between them. This allows for the characterization of the particle dynamics independent on whether they can be resolved individually or not. The characteristic times are measured in a wide range of wavevectors and the results are found to be in good agreement with the theoretically expected values for Brownian motion in a viscous medium. 1Microscopy and light scattering are widely used in physics, chemistry, biology and medical laboratories to access information on the structure and dynamics of mesoscopic systems.While microscopy gives direct access to real space images, scattering techniques work in reciprocal space, where information on the structure and dynamics of the system is obtained respectively from the angular and time dependence of the scattered light intensity [1]. These two complementary techniques have in general very different experimental requirements.White light sources are usual choices in microscopy, while a certain degree of coherence of the illuminating beam is required in scattering experiments; this is usually achieved by using a laser. In the past many attempts have been made to build a scattering apparatus based on a microscope; all of these attempts involved the use of a laser as an illumination source (see for example Refs. [2-6] and references therein). In some cases special care was taken to ensure the capability to perform microscopy and scattering experiments simultaneously, thereby allowing for a powerful combination of the complementary information obtained by both techniques [2,3]. More recently, microscope-based laser Dynamic Light Scattering (DLS) experiments have been developed to study the dynamic properties of samples of biological interest, such as living macrophage and red blood cells [5,6]. In practice, due to the intrinsic difficulties in building such instruments, the use of such techniques has been restricted to those laboratories, where a sufficient expertise in the realization of optical instrumentation was at hand.In this letter, we present a conceptual scheme to interpret and analyze microscopy images that are obtained from samples containing moving entities. This technique, which we term Differential Dynamic Microscopy (DDM), does not entail any special experimental requirements, being based on the use of a standard light microscope with a normal illumination source and a digital video camera. By using the tools of Fourier Optics [7] we provide the means to access information about the sample dynamics that are equivalent to the one obtained in multi-angle dynamic light scattering (DLS) experiments [8]. We test DDM by analyzing time sequences of microscopy images obtained with an aqueous dispersion of colloidal particles with diameter 73 nm, well below the resolution limit ...

The rheological data of weakly attractive colloidal particles are shown to exhibit a surprising scaling behavior as the particle volume fraction, straight phi, or the strength of the attractive interparticle interaction, U, are varied. There is a critical onset of a solid network as either straight phi or U increase above critical values. For all solidlike samples, both the frequency-dependent linear viscoelastic moduli, and the strain-rate dependent stress can be scaled onto universal master curves. A model of a solid network interspersed in a background fluid qualitatively accounts for this behavior.

We describe the use of a bright-field microscope for dynamic light scattering experiments on weakly scattering samples. The method is based on collecting a time sequence of microscope images and analyzing them in the Fourier space to extract the characteristic time constants as a function of the scattering wave vector. We derive a theoretical model for microscope imaging that accounts for ͑a͒ the three-dimensional nature of the sample, ͑b͒ the arbitrary coherence properties of the light source, and ͑c͒ the effect of the finite numerical aperture of the microscope objective. The model is tested successfully against experiments performed on a colloidal dispersion of small spheres in water, by means of the recently introduced differential dynamic microscopy technique ͓R. Cerbino and V. Trappe, Phys. Rev. Lett. 100, 188102 ͑2008͔͒. Finally, we extend our model to the class of microscopy techniques that can be described by a linear space-invariant imaging of the density of the scattering centers, which includes, for example, dynamic fluorescence microscopy.