Dynamics and structure of a colloidal glass former in two dimensions

Abstract

The system investigated in this work consists of two types of super-paramagnetic colloidal spheres with different diameters. They are confined at a water-air interface due to gravity where they are subjected to Brownian motion. The system can be considered as ideally two dimensional, since the motion in the vertical direction is only in the range of a few tens of nanometers. The dipolar pair interaction between particles is controlled over a wide range via an external magnetic field which is expressed in a dimensionless interaction parameter Gamma. This can be interpreted as the inverse system temperature. Video microscopy provides trajectories of typically 3000 particles on all relevant time and length scales. The long-time stability of the experimental setup enables sample stabilization over many months and data acquisition over several days. It was found that this binary mixture of magnetic dipoles is a good model system of a 2D glass former as the dynamics and structure shows characteristic glassy behavior: when the interaction strength is increased, the system viscosity increases over several orders of magnitude while the global structure remains amorphous. The dependency on dimensionality appears not characteristic as the system exhibits the full range of glass phenomenology like 3D glass formers. Experimental data was compared with Mode Coupling Theory: the mean square displacements agree with those of a 2D glass former of hard discs for more than four decades in time, provided that the interaction strength of the dipoles and the packing fraction of the hard discs are properly related to each other. The relation between interaction strength and system viscosity behaves Arrheniuslike which is characteristic for a strong glass former. For all measured interaction strengths the system shows no long-range order as probed with bond order correlation functions. However, on a local scale it reveals non-trivial ordering phenomena: partial clustering and local crystallinity: Partial clustering means that the small particles tend to form loose clusters while the big particles are homogeneously distributed. The origin of this effect is traced back to the negative nonadditivity of the dipolar pair potential. The clustering of small particles introduces an additional length scale that is accompanied by a small wave vector prepeak in the static structure factor of the small particles. Furthermore, the detailed partial clustering scenario is quantified using Minkowski functionals. Changing the interaction strength ¡ reveals that the principle scenario does not qualitatively depend on the interaction strength. However, the strength of the effect is correlated with the relative concentration. The partial clustering leads locally to a heterogeneous relative concentration and for increasing interaction strengths to a variety of stable local crystallites (local crystallinity). This originates from the tendency of the binary mixture to crystallize into a small set of crystal structures: hexagonal order of big particles, chains of small particles, simple quadratic, and rhombic. This was shown on one hand by the appearance of extended stable crystal grains and on the other hand by the peaks of the pair correlation functions which are in unique agreement with these lattice structures. Changing the relative concentration of the mixture does not affect the positions of the peak structure in the pair correlation functions, but it modifies the relative peak heights. This demonstrates that crystal structures do not change by themselves but only their relative contribution to the globally disordered state. The rapid decay of the fourfold bond order correlation function reveals that increasing the interaction parameter does not significantly enhance long-range order but strongly enhances local fourfold order, as found in the local bond order statistics. Three selection criteria (local relative concentration, local bond order, and local bond lengths) were combined to probe the amount of square unit cells for a given interaction strength. A continuous increase with some indication of a change in slope near Gamma=50 is found which might indicate an underlying phase transition. The saturation at high Gamma values depends on the individual history and local composition of the sample. The local dynamics as visualized by displacement-fields and integrated individual squared displacement fields, reveals a strong spatial heterogeneous velocity distribution: dynamical heterogeneities. The qualitative appearance is strongly dependent on the interaction strength.