Experimental Observation of Structural Crossover in Binary Mixtures of Colloidal Hard Spheres

Abstract

Using confocal microscopy, we investigate the structure of binary mixtures of colloidal hard spheres with size ratio q 0:61. As a function of the packing fraction of the two particle species, we observe a marked change of the dominant wavelength in the pair-correlation function. This behavior is in excellent agreement with a recently predicted structural crossover in such mixtures. In addition, the repercussions of structural crossover on the real-space structure of a binary fluid are analyzed. We suggest a relation between crossover and the lateral extension of networks containing only equally-sized particles that are connected by nearest-neighbor bonds. This is supported by Monte Carlo simulations which are performed at different packing fractions and size ratios. DOI: 10.1103/PhysRevLett.98.198303 PACS numbers: 82.70.Dd, 61.20.ÿp Most systems in nature and technology are mixtures of differently sized particles. Each distinct particle size introduces another length scale, and its competition gives rise to an exceedingly rich phenomenology in comparison with single-component systems. Already, the simplest conceivable multicomponent system, i.e., a binary mixture of hard spheres, exhibits interesting and complex behavior. Just a few examples include entropy driven formation of binary crystals [1][2][3], frustrated crystal growth [4], the Brazil nut effect [5], glass-formation [6,7], and entropic selectivity in external fields [8]. Although interaction potentials in atomic systems are more complex than those of hard spheres, the principle of volume exclusion is ubiquitous and thus always dominates the short-range order in liquids [9]. Accordingly, hard spheres form one of the most important and successful model systems in describing fundamental properties of fluids and solids. It has been demonstrated that many of their features can be directly transferred to atomic systems where fundamental mechanisms are often obstructed by additional material specific effects [10]. Binary hard-sphere systems are fully characterized by their size ratio q S = B with i the diameters of the small (S) and big (B) spheres and the small and big sphere packing fractions S , B , respectively.The pair-correlation functions, g ij r , are the central measure of structure in fluids; they describe the probability of finding a particle of size i at distance r from another particle of size j. It is well known that all pair-correlation functions in any (isotropic) fluid mixture with short-ranged interactions (not just hard spheres) exhibit the same type of asymptotic decay, which can be either purely (monotonic) exponential or exponentially damped oscillatory [11] (and references therein). This prediction, which is valid in all dimensions [12] as well as for anisotropic pair interactions [13], suggests that all pair-correlation functions decay with a common wavelength and decay length in the asymptotic regime r ! 1. For binary hard-sphere mixtures where B S or S B , this is rather obvious since the system is dominated by either big or smal...

Direct observation in 3d of structural crossover in binary hard sphere mixtures

“…Moreover the pole analysis mentioned above was not employed so the authors were not able to ascertain the nature of crossover. 26 A later x-ray diffraction and microscopy study on monolayers of bimodal nanoparticles reported packing structures resembling what might be expected for structural crossover. 27 In contrast, our present study employs 3d confocal microscopy combined with 3d MC simulations and liquid state theory for hard spheres to investigate the nature of the crossover.…”

“…24 We also note that the true correlation length is important in current research on the glass transition. 25 A previous study, carried out by Baumgartl et al, 26 on a binary mixture of small and big colloidal particles with size ratio q = 0.61 provided some evidence for structural crossover and attempted to relate crossover to the sizes of networks containing connected big or connected small particles. However, Ref.…”

Direct Measurement of Thermodynamic Properties of Colloidal Hard Spheres

“…Because real liquids are only a perturbation away from a hard-sphere fluid, it now becomes feasible to explore the relation between local geometrical quantities and thermodynamics beyond hard spheres as well [34][35][36][37][38]. For example, the presented method can be applied to a suspension of bidisperse colloids [39,40]. Another possible extension lies in the use of nonspherical hard colloids, for example, fluorescent rods [41,42], or polyhedral colloids [43] where exactly the same concepts can be applied.…”

Communication: Radial distribution functions in a two-dimensional binary colloidal hard sphere system

“…Note that for a binary mixture with two distinct diameters, a discontinuous change of the wavelength of oscillations in the asymptotic regime of the radial distribution functions g ij (r), the so-called structural crossover, was predicted 46,47 based on the theory of asymptotic decays of correlation functions, and found experimentally. 48 For the size ratio used here, however, the diameters are too similar to expect structural crossover.…”