Colloidal phase transitions

Due to their softness, colloidal crystals are easily shear molten, simply by shaking the sample. They, however readily re-crystallize on the convenient time scale of seconds to hours. Time resolved static light scattering and various forms of microscopy are applied to study phase behaviour including meta-stable transients, crystallization coupled to phase separation, kinetic coefficients for homogeneous and heterogeneous nucleation and possibilities to control crystal formation by applied external shear fields.

Glass transition

Glass

Colloidal glasses are well accepted models of atomic glass formers. In particular hard sphere glasses have been realized and extensively investigated in experiment, theory and simulation. In these systems, the issue of dynamical heterogeneity is of particular interest (Nature Physics 12, 712-717 (2016)).

Recently, we discovered a new class of colloidal glasses existing at low sphere volume fraction and stabilized by electrostatic repulsion (J. Stat. Phys., 074007 (2016)). The current focus is on a comprehensive study of its properties under systematic variation of particle density and interaction strength with special attention to the involved glass transition mechanism and its competition to crystallization.

Melting from within

Freezing and melting are generally regarded as symmetrical phase transitions. The presence of a crystal surface, however breaks this symmetry and melting generally starts there or at inner surfaces like grain boundaries. In colloidal solids melting may also be induced by shear. Only if melting were a symmetrically inverse process to crystallization, it would occur by activated homogenous nucleation at small meta-stability in a mechanically unloaded bulk crystal. Colloidal model crystals may offer the unique opportunity to study such melting from within, as there the heat transport by the suspending solvent is decoupled from particle motion. Given a suitable model system with well controlled interactions, a variation of temperature or interaction strength can be attempted without the need for a mechanical disturbance. Recently, the group of J. Yamanaka succeeded in designing a thermosensitive system of charged colloidal spheres with absorbing ionic surfactant.

Phase_giagram_122 Surfactant_melting

At low temperatures the surfactant tends to adsorb on surfaces, thus the ion concentration in the liquid medium is decreased while the colloidal charge is increased. At high temperature the situation is inverted. Due to the larger ion concentration and lower surface charge, the initially formed colloidal crystals melt. (Langmuir 31,13303-13311 (2015))

An alternative approach is the use of a eutectic mixture, prepared as substitutional bcc alloy undergoing simultaneous phase separation, melting and recrystallization of the majority component. The image shows this process as observable with Dynamic Differential Microscopy.

DDM
Microscopy image of slowly melting crystals. Left Bottom: same sample observed by DDM; highly mobile melt regions appear white; left middle: superposition of structural and dynamical information. Right: Sequence of DDM images of eutectic substitutional alloy crystals melting from both grain boundaries and from within. The spotless dark areas at the grain boundaries are recrystallized bcc single crystals of the smaller majority component.

One may also govern melting by applying a gradient. The melt mechanism then depends on the rate of contamination and the gradient steepness. For vanishing gradients and very low contamination rates, fluid “nucleates” faults and defects in the crystal interior and a swiss cheese pattern emerges (Phil. Mag. 89, 1695 (2009); see also H. Yoshida et al., Langmuir 15, 2684-2702 (1999)).

Melt structure and dynamics

Glass

Does a meta-stable melt behave like an equilibrium liquid? It seems no!
Static structure factors of concentrated charged sphere suspensions show a split in the second peak (see below). The collective dynamics in hard sphere fluids show a singularity coincident with the freezing transition. The stretching exponent of the current-current correlator measured in dynamic light scattering vanishes, so does its characteristic time while the amplitude diverges. Above melting, the formation of density fluctuations before the onset of crystal formation is seen in both static light scattering and multi-speckle correlation techniques.

Crystal nucleation and growth

Structure factor

We have been measuring quantitative nucleation and growth kinetics for quite some time (J. Phys.: Condens. Matter 11, R323 - R360 (1999)) employing direct video microscopic observation (J. Chem. Phys. 123, 174902 (2005)), post solidification grain size analysis (Crystal Growth and Design 10, 2258 – 2266 (2010)) or time resolved static light scattering (Soft Matter 7, 11274-11276 (2011)) and USAXS (J. Phys.: Condens. Matter 22, 153101 (2009)).

Growth measurements interpreted in terms of Wilson-Fenkel reaction limited growth allow to determine the melt meta-stability (Phys. Rev. E 52; 6415-6423 (1995)). This Δµ (or for hard spheres Δµ taken from theory) is subsequently used to interpret crystallization data in the framework of classical nucleation theory (Phys. Rev. E 75, 051405 (1-12) (2007)). In hard sphere systems we could demonstrate a two step nucleation scenario which later was confirmed in computer simulations (Phys. Rev. Lett. 105, 025701, (2010))

Heterogeneous nucleation and homogeneous nucleation scenarios and their competition were compared for both hard spheres and charged spheres. Charged spheres were observed to show a wetting transition with increased meta-stability of the melt (Soft Matter 7, 5685-5690 (2011)), while hard spheres always wet the container walls (Soft Matter 7, 11274-11276 (2011)).

Turnbull coefficient

Recently we performed a first determination of the Turnbull coefficient for an experimental system crystallizing into a body centred cubic structure. The melt crystal equilibrium interfacial fee energy, σ0, is proportional to the enthalpy of fusion ΔHf with a proportionality constant (Turnbull coefficient) of about 0.3 in good agreement with suggestions from computer simulation for bcc metals. The bcc value is significantly smaller than the values found for fcc crystallizing material.

Moreover, we tried to correlate the extrapolated equillibrium interfacial free energy, σ0, to the experimental parameters, like interaction strength, or range, or effective charge, or particle size. No correlation was observed. Hovewer, a clear anti-correlation between the particle polydispersity and σ0 was found (Phys. Rev E 93, 022601 (2016)).

Crystal microstructure

Crystallization at seed

Crystal microstructure determines largely the dynamic and elastic properties of a polycrystalline solid. We are interested in ways to manipulate the microstructure by external fields or prescribe it via heterogeneous nucleation at deliberately positioned seeds. Single crystal of micron sized charged spheres can be grown in the presence of an attractive seed. Conditions can be altered such that the particles are either repelled from touching the seed surface and hence arrange on equilibrium positions (left) rather than molding the seed and generating a polycrystalline domain with many faults (right).

Crystallization in different environments

Eutectic mixtures show characteristic microstructures due to simultaneous demixing and crystallization, which may couple in a feed-back cycle and produce intriguing intercalated patterns. The example shows a mixture of 96% small with 4% large charged spheres with a single crystal grown very slowly from the weakly super-saturated melt. The Bragg microscopic image only shows the majority component. Upon formation of a crystal of small spheres, the large ones are expelled, but also crystallize when their freezing concentration is exceeded. Interestingly, the small particle crystals are below the roughening transition, while the large particle crystals are above.

Microstructure of eutectic mixture

Do crystals melt from their surface or from their interior? In colloidal systems this is governed by the rate of contamination and the gradient steepness. For vanishing gradients and very low contamination rates, fluid “nucleates” faults and defects in the crystal interior and a swiss cheese pattern emerges (Phil. Mag. 89, 1695 (2009); see also H. Yoshida et al., Langmuir 15, 2684-2702 (1999)).

Swiss cheese pattern A Swiss cheese pattern B