The equilibrium intrinsic crystal–liquid interface of colloids

Abstract

We use confocal microscopy to study an equilibrated crystal-liquid interface in a colloidal suspension. Capillary waves roughen the surface, but locally the intrinsic interface is sharply defined. We use local measurements of the structure and dynamics to characterize the intrinsic interface, and different measurements find slightly different widths of this interface. In terms of the particle diameter d, this width is either 1.5d (based on structural information) or 2.4d (based on dynamics), both not much larger than the particle size. This work is the first direct experimental visualization of an equilibrated crystal-liquid interface.surface tension ͉ capillary waves ͉ confocal microscopy T he interface between crystal and liquid phases of a material governs phenomena such as wetting, lubrication, and crystal nucleation (1, 2). Interfaces are poorly defined at the atomic level: Capillary waves cause fluctuations in the interface position (3-6), and locally the structure varies in a smooth way from ordered to disordered (2). Existing literature makes a distinction between the intrinsic interface (presumed to be sharp) (3), and the observed surface blurred by capillary waves (4, 7). The standard equilibrium interface profile is well defined and contains fluctuations at all length and time scales, due to these capillary waves. Because of the rapid time scales of capillarywave fluctuations, along with the small length scales at the interface, it is difficult to study these interfaces directly (1). Thus, computer simulations provide useful information about model crystal-liquid interfaces, such as hard-sphere systems (2,8,9) and Lennard-Jones systems (10, 11).Recently, crystal-liquid interfaces were directly studied in colloidal suspensions by using confocal microscopy (6, 12). Colloids are systems of solid particles in a liquid and are a good model system for phase transitions (5,6,13,14). Microscopy allows direct observation of structure and dynamics of the colloidal particles (15). However, the previous experiments focused on nonequilibrium cases where samples were crystallizing and did not provide data on equilibrium interfaces, such as those studied by simulation (2,(8)(9)(10)16). Furthermore, these experiments did not examine the intrinsic interface, perhaps because they were nonequilibrium studies, and thus crystalline particles were present in the ''liquid'' side and vice versa, which confuse the structure near the interface.In this work, we present confocal microscope observations of an equilibrated colloidal crystal-liquid interface. By following the positions of several thousand colloidal particles on both sides of the interface, we directly visualize the interface. An example of our data is shown in Fig. 1A, where blue particles are crystalline and yellow/red particles are liquid-like. This interface has a low surface tension, and we see capillary waves. We are able to remove the influence of these capillary waves from the data and measure the intrinsic surface profile. In particular, we find that capill...

Phase-field crystal modelling of crystal nucleation, heteroepitaxy and patterning

“…While the intrinsic thickness of the interfacial layer might be fairly small [22], due to capillary waves the shape of these particles fluctuates, so that its time average may lead to a broader, diffuse interface as in the case of planar interfaces [22]. In qualitative agreement with the classical nucleation theory, the free energy of formation of these heterophase fluctuations shows a maximum as a function of size [19].…”

Shortcomings of the bond orientational order parameters for the analysis of disordered particulate matter

“…Neighborhood definitions based on cutoff radii are widely used, e.g., with cutoff radii 1.2σ and 1.4σ 11,18,24,37,47 or with the value of the cutoff radius determined by the first minimum of the two-point correlation function g(r). 9,14,15,25,48 Alternatively, the Delaunay graph of the particle centers 49,50 is used to define NN. 5,20,23,41,51 In this parameterfree method, every sphere which is connected to a sphere a by a Delaunay edge is considered a NN of a.…”

“…[10][11][12] They are also used to study melting transitions 10,13,14 and interfaces in colloidal fluids and crystals. 15 For the study of glasses and super-cooled fluids, q 6 and Q 6 have become the most prominent order parameters when searching for glass transitions [16][17][18][19] and crystalline clusters. 4,8,11,[20][21][22] While q l is defined as a local parameter for each particle, other studies have used global averages of bond angles (Q l ) to detect single-crystalline order across the entire sample.…”

“…Several authors have defined bond order functions 39 closely related to the q l for the identification of crystalline clusters. 11,15,21,40 As a different application from the identification of locally crystalline domains, it has been proposed to use averages q l over all spheres to quantify the degree of order of a configuration. Averages q 6 have been analyzed (as functions of some control parameters such as temperature, pressure, strain, or packing fraction) for random sphere packings, 20 granular packing experiments, 41 model fluids, 42 molecular dynamics simulations of water, 43 or polymer melts.…”

Liquids: Condensed, disordered, and sometimes complex

“…This special issue of PNAS features 18 articles (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) to illustrate research in this area (liquid interfaces, structural glass formers and dense packing, polymer networks, chemical dynamics) exhibiting current tools of experiment and theory. The field is too big to capture it all with such a small collection, but the examples give a feeling for its scope and possibilities.…”