Gel and Glass Transitions in Short-Range Attractive Colloidal Systems - Food Colloids: Self-Assembly and Material Science - page 339

results for the gel transition. 21 Here we review some results discussed in detail
elsewhere. 24
In general, the MCT overestimates the location of the glass lines and a non-
negligible mapping must be applied to theoretical curves before comparing
theory with experiment or simulation data. 28,41 Such a mapping has been
evaluated for the same square-well potential discussed so far with an attractive
range of e ¼ 0.03. The mapped attractive glass line has been found 35 to end on
the right side of the spinodal, hence proving that for this range the attractive
glass does not overtake the phase separation.
We have studied the system for different ranges of attraction, ranging from a
few percent of the particle diameter down to e ¼ 5 10 6 , which is very close to
the Baxter limit. As we discussed before, all the thermodynamic results for
short-range systems can be described by the density and the second virial
coefficient, i.e., systems with same virial coefficient and at the same density are
taken as being in the same thermodynamic state. This can be seen in the lower
panel of Figure 8 where the Miller and Frenkel coexisting curve 30 is plotted. As
discussed before, all the data from the simulations for the different ranges can
be plotted using the same variables, and they agree with the numerical Baxter
coexistence curve. In order to quantify the change of the dynamics, we have
studied the tagged MSD h r 2 (t) i that is directly related to the diffusion coe cient
by the Einstein relation:

r 2 ð t Þ

lim
t !1

¼ 6D : ð 11 Þ

t

We consider two state points, also shown in the lower panel of Figure 8, at two
packing fractions, f ¼ 0.2 and 0.4, to the right and the left of the critical point
f c B 0.25, respectively, and with a virial coefficient value B 2 ¼ 0.405 close to

the critical one.
In the upper panel of Figure 8, the MSD is presented for all values of the
range investigated in the case of Newtonian dynamics. As we are interested in
the structural variations of the diffusion constant, we have to take into account
the fact that, in going to the lower limit of the range, we reduce the temperature
and consequently the thermal velocity of the monomer. This is achieved by
multiplying the time by the bare diffusivity of the single monomer. All the MSD
data lie on the same curve, a clear indication that there is no slowing down of
the dynamics for either of the two state points considered. Consequently, we
have to conclude that it is not possible to obtain a dynamic arrest by reducing
the interaction potential range. Similar to what was discussed for the arrested
phase separation, this conclusion does not depend upon the microscopic
dynamics. In the middle panel of Figure 8, we show the same results for BD.
Even if we cannot reach values of the range as short as before, owing to
numerical limitations of BD, we can confirm the prediction from ND. We can
finally add the equi-diffusivity lines to the phase diagram of Figure 8. In doing
so, we have obtained a phase diagram that is universal, not only in its
thermodynamics, but also in its dynamics.