In these notes we will examine the main forms of arrested states that are encountered in colloidal and soft matter systems. The two main categories of arrested states will be discussed, namely glasses and gels. While glasses can be attributed to the effect of either dominant repulsive (e.g. excluded-volume or electrostatic) or dominant attractive (e.g. depletion) interactions, gels can only arise by means of attraction. However, the type of attraction, being isotropic or directional, or the presence of additional repulsion can significantly alter the properties of the resulting gel state. Another aspect that we will address is the role of softness of the particles in the formation of the arrested state, a crucial way to tailor the rheology of the macroscopic materials. As an example of a glass-forming soft system, which has been recently investigated in a joint experimental and theoretical effort, we will focus on star polymers. Finally we will also examine the case of competing interactions, e.g. short-range attraction and long-range repulsion, which give rise to arrested states mediated by finite-size clusters rather than by particles. Our description is largely based on the role of effective colloidal interactions and mainly focused on recent theoretical and numerical results, with strong reference to related experimental observations.
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