Physica A Precursors of long-range order and local disorder in colloids

M. Mayorga et al. / Physica A 388 (2009) 1973–1977 1975Fig. 1. Pair correlation function g(r) for our model potential plotted against reduced distance r ∗ . At the packing fraction η = 0.494 and η = 0.545 wecan observe the appearance of the precursor and the presence of a structural long range order, respectively. The shoulder is practically flat, thus indicatingthat particles have a higher degree of packing. The inset enhances the split which resembles the structural precursor to freezing observed in hard-spheresystems [16].Fig. 2. This image shows the translational long range order for the colloidal particles at η = 0.545, for the values of the parameters that were used toobserve the freezing precursor.energy barrier corresponding to the clustering process, and consequently to a decrease of the surface tension in accordancewith the classical theory of nucleation [13].The precursor of freezing is manifested through the shoulder that appears on the left hand side of the second peak inFig. 1, in the range of reduced distances (1.85, 1.95) which is included in the corresponding interval found in Figure 6 ofRef. [16], obtained in the case of hard spheres. The shoulder, identical to the one reported for the hard sphere system at thesame packing fraction, namely η = 0.494, with α = 0.945 and β = 14.15, is the signature of the formation of crystallineclusters and thus constitutes a crystalline-structure precursor, in addition. For each time-step, we calculate the position ofthe particles from which we obtain the snapshot of the system showing the presence of spatial and orientational order, aswe can see in Figs. 2 and 3. Once the precursor arises, cluster formation becomes favored by fixing the value of β. Increasingthe packing fraction of the system at the value η = 0.545, we obtain a tightly-packed hexagonal-closed array. This featurebecomes manifest in the dashed line in Fig. 1. On the other hand, for the above values of the potential parameters, theeffective width of the attractive well is less than one-third of the particle’s diameter. We observe, in addition, that thefreezing precursor is still observed when the parameter β increases, i.e. decreasing the ratio effective width/diameter. Thislast situation is of interest to colloidal systems with a very short-range attraction for which it is well known that there existonly two stable phases: fluid and crystal [19], or for colloids with an even narrower attractive well, with two solid phasesthat differ only in density [20].Following a protocol similar to the one previously outlined, we observe a transition from an ordered structure forβ = 11.910 to the formation of amorphous clusters for β = 11.905 maintaining the values α = 0.945 and the packing