Equilibrium fluid-crystal interfacial free energy of bcc-crystallizing aqueous suspensions of polydisperse charged spheres

The interfacial free energy is a central quantity in crystallization from the meta-stable melt. In suspensions of charged colloidal spheres, nucleation and growth kinetics can be accurately measured from optical experiments. In previous work, from this data effective non-equilibrium values for the interfacial free energy between the emerging bcc-nuclei and the adjacent melt in dependence on the chemical potential difference between melt phase and crystal phase were derived using classical nucleation theory. A strictly linear increase of the interfacial free energy was observed as a function of increased meta-stability. Here, we further analyze this data for five aqueous suspensions of charg…

Crystallization in charged two-component suspensions

We report on the crystallization of colloidal crystals comprising of charged particles with different size ratio dispersed in thoroughly deionized water. Single components were characterized carefully and their nucleation behavior was investigated before the preparation of mixtures. Mixtures investigated at constant particle number densities showed body centred cubic structure, conductivity, and shear moduli comply with the assumption of a randomly substituted crystal. Most importantly, for the first time we obtain the dependence of the nucleation rate densities in dependence on the composition and (for one fixed composition) the particle number density. The process of nucleation in random …

Nucleation kinetics in deionized charged colloidal model systems: A quantitative study by means of classical nucleation theory

We have studied the nucleation kinetics of charged colloidal model systems under salt free conditions crystallizing in bcc structure covering a wide range of particle number densities $18\phantom{\rule{0.3em}{0ex}}\mathrm{\ensuremath{\mu}}{\mathrm{m}}^{\ensuremath{-}3}\ensuremath{\le}n\ensuremath{\le}66.3\phantom{\rule{0.3em}{0ex}}\mathrm{\ensuremath{\mu}}{\mathrm{m}}^{\ensuremath{-}3}$. We employed direct video-microscopic observation of individual nucleation events to obtain time resolved nucleation rate densities. Polarization microscopy and static light scattering on the resulting solids in combination with Avrami theory is used to determine the steady state nucleation rate at high unde…

Enhanced crystal stability in a binary mixture of charged colloidal spheres.

We report on the phase behavior of a binary charged sphere mixture of size ratio $\ensuremath{\Gamma}=0.68$ and charge ratio $\ensuremath{\Lambda}\ensuremath{\approx}1$ as a function of composition $p$ and number density $n$. For $p=0.1--0.3$ we observe freezing at densities well below the freezing densities of the pure components. At all compositions our data indicate the formation of substitutional alloy crystals of body centered cubic structure. No indications for compound formation were observed. Rather, our findings point at the first observation of an upper azeotrope. Measurements of the crystallization kinetics reveal a combined density and composition dependence of growth velocities…

Seed- and wall-induced heterogeneous nucleation in charged colloidal model systems under microgravity

Understanding the process that drives an undercooled fluid to the crystal state is still a challenging issue for condensed matter physics and plays a key role in designing new materials. The crystallization kinetics and the resulting polycrystalline morphology are given by a complex interplay of crystal nucleation, growth, and ripening. A great deal of progress has been made in recent years using colloidal suspensions as model systems in the study of crystallization. Close analogies to atomic systems are observed which can be exploited to address questions not accessible in atomic solidification. Here we present systematic measurements of the crystallization kinetics of a charged colloidal …

Solidification Experiments in Single-Component and Binary Colloidal Melts

Phase behaviour of deionized binary mixtures of charged colloidal spheres.

We review recent work on the phase behaviour of binary charged sphere mixtures as a function of particle concentration and composition. Both size ratios and charge ratios are varied over a wide range. By contrast to hard spheres the long ranged Coulomb interaction stabilizes the crystal phase at low particle concentrations and shifts the occurrence of amorphous solids to particle concentrations considerably larger than the freezing concentration. Depending on size- and charge ratios we observe upper azeotrope, spindle, lower azeotrope and eutectic types of phase diagrams, all known well from metal systems. Most solids are of body centred cubic structure. Occasionally stoichiometric compound…

Consistence of the Mean Field Description of Charged Colloidal Crystal Properties

The Debye-Huckel-Potential in combination with an effective or renormalized charge is a widely and often successfully used concept to describe the interaction in charged colloidal model systems and the resulting suspension properties. In particular the phase behaviour can be described in dependence of the parameters particle number density, salt concentration and effective charge. We performed simultaneous measurements of the phase behaviour, the shear modulus and the low frequency conductivity of deionised aqueous suspensions of highly charged colloidal spheres. From the shear modulus the interaction potential at the nearest neighbour distance in terms of a Debye-Huckel potential can be de…

Microscopic investigations of homogeneous nucleation in charged sphere suspensions.

We studied the homogeneous nucleation kinetics of an aqueous suspension of charged colloidal spheres under de-ionized conditions. Samples of equilibrium crystalline structure were shear molten and the metastable melt left to solidify after cessation of shear. At low particle number densities n, corresponding to low metastability of the melt, nucleation was monitored directly via video microscopy. We determined the nucleation rates gamma(t) by counting the number of newly appearing crystals in the observation volume per unit time. Using a suitable discrete adaptation of Avrami's [J. Chem. Phys. 7, 1003 (1939); ibid.8, 212 (1940); ibid.9, 177 (1941)] model for solidification via homogeneous n…

Colloids as model systems for liquid undercooled metals

Physical review / E 79(1), 4 (2009). doi:10.1103/PhysRevE.79.010501

Experimental determination of effective charges in aqueous suspensions of colloidal spheres

Abstract We determined the low frequency conductivity σ , the phase behaviour and the shear modulus G of colloidal fluids, respectively solids prepared from deionised aqueous suspensions of highly charged spherical particles. Conductivity measures the number of freely moving small ions Z * σ and thus relates to the ion condensation process in the electric double layer under conditions of finite macro-ion concentrations. Phase behaviour and elasticity data are consistently described by a Debye–Huckel pair potential assuming pair-wise additive macro-ion interactions. Like Z * σ , also the effective charges Z * G derived from the elasticity data scales with the ratio of macro-ion radius to Bje…

Drude-type conductivity of charged sphere colloidal crystals: Density and temperature dependence

We report on extensive measurements in the low-frequency limit of the ac conductivity of colloidal fluids and crystals formed from charged colloidal spheres suspended in de-ionized water. Temperature was varied in a range of 5 degrees CTheta35 degrees C and the particle number density n between 0.2 and 25 microm(-3) for the larger, respectively, 2.75 and 210 microm(-3) for the smaller of two investigated species. At fixed Theta the conductivity increased linearly with increasing n without any significant change at the fluid-solid phase boundary. At fixed n it increased with increasing Theta and the increase was more pronounced for larger n. Lacking a rigorous electrohydrodynamic treatment f…

Properties of mixed colloidal crystals

We prepared colloidal crystals from aqueous suspensions of spherical, charged polystyrene spheres under deionised conditions. Using a home-built multipurpose light scattering apparatus we measured the static structure factor, the static shear modulus and the intermediate scattering function. In addition we also monitored also the conductivity as a function of the composition and the particle number density. For the mixture investigated the data are well described assuming the formation of randomly substituted body-centered-cubic crystals.

Qualitative characterisation of effective interactions of charged spheres on different levels of organisation using Alexander’s renormalised charge as reference

Abstract Effective interactions are conveniently determined from experimental or numerical data by fitting a Debye–Huckel potential with an effective charge Z ∗ and an effective electrolyte concentration c ∗ as free parameters. In this contribution we numerically solved the Poisson–Boltzmann equation to obtain the so-called renormalised charge Z PBC ∗ . For sufficiently large bare charge Z one finds a saturation of Z ∗ which scales as Z ∗ = A a / λ B , where a is the particle radius, λ B the Bjerrum length and A a proportionality factor of order (8–10). The saturation value increases with increased total micro-ion concentration and shows a shallow minimum as a function of packing fraction. …

Competition between heterogeneous and homogeneous nucleation near a flat wall

We studied the competition between heterogeneous and homogeneous nucleation of an aqueous suspension of charged colloidal spheres close to the container walls. Samples of equilibrium crystalline structure were shear-melted and the metastable melt left to solidify after the cessation of shear. The crystallization kinetics was monitored using time-resolved scattering techniques: at low particle number densities n we applied an improved static light scattering method while at large particle concentrations ultra-small-angle x-ray scattering was applied for the first time. Our results show some unexpected behavior: the heterogeneous nucleation at the container walls is delayed in comparison to t…