Colloidal systems glasses theory

That the classical theories and methods for observing and analyzing dislocations in atomic crystals can be carried over to a large extent to dislocations in colloidal crystals not only is intellectually satisfying, but also gives us confidence that these systems can be used to study complex processes in the deformation of crystals and glasses on a level that is otherwise hard to achieve. Indentation is such a complex process, and only the colloids allow direct observation of the attempts and eventual success of dislocation nucleation. 

To illustrate these ideas let us summarize the general system of equations that constitute the SCGLE theory. In principle, these are the exact results for A (f), F k, f), and t) in Equations 1.20,1.23, and 1.24, complemented with the simplified Vineyard approximation in Equation 1.37 and the simplified interpolating closure in Equation 1.38. This set of equations define the SCGLE theory of colloid dynamics. Its full solution also yields the value of the long-time self-diffusion coefficient which is the order parameter appropriate to detect the glass transition from the fluid side. This is, however, not the only method to detect dynamic arrest transition, as we now explain. 

The discussion of the large- tail in S(q) in Section 7.4.1.1, which is characteristic for a short-ranged attraction, enables one to formulate a simplified theory of bond formation within MCT with the result that the long-time limit of the dynamic structure factor is controlled by a single interaction parameter, F = fP-(p/b. Bond formation occurs at T, = 3.02... [34]. For small values of F, the dynamic structure factor decays to zero for all wavevectors. Physically, this means that concentration fluctuations decay into equilibrium at long times, just as expected for a colloidal fluid. However, for F > F, the solutions yield a nonzero glass form factor, namely, the system arrests in a metastable state. This simple result requires the approximate expression for S(q) given above and needs to be replaced by a full numerical solution whenever this approximation fails. 

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