Kinetic Analyses of the Colloidal Crystallization of Silica Spheres As Studied by Reflection Spectroscopy

Solution properties of star polyelectrolytes having a moderate number of arms

We investigate polyelectrolyte stars having a moderate number of arms by molecular dynamics simulations of a coarse-grained model over a range of polyelectrolyte concentrations, where both the counter-ions and solvent are treated explicitly. This class of polymeric materials is found to exhibit rather distinct static and dynamic properties from linear and highly branched star polyelectrolyte solutions emphasized in past studies. Moderately branched polymers are particle-like in many of their properties, while at the same time they exhibit large fluctuations in size and shape as in the case of linear chain polymers. Correspondingly, these fluctuations suppress crystallization at high polymer concentrations, leading apparently to an amorphous rather than crystalline solid state at high polyelectrolyte concentrations. We quantify the onset of this transition by measuring the polymer size and shape fluctuations of our model star polyelectrolytes and the static and dynamic structure factor of these solutions over a wide range of polyelectrolyte concentration. Our findings for star polyelectrolytes are similar to those of polymer-grafted nanoparticles having a moderate grafting density, which is natural given the soft and highly deformable nature of both of these "particles."

Colloidal crystal growth monitored by Bragg diffraction interference fringes

We monitored the crystal growth kinetics of crystallization of a shear melted crystalline colloidal array (CCA). The fcc CCA heterogeneously nucleates at the flow cell wall surface. We examined the evolution of the (1 1 1) Bragg diffraction peak, and, for the first time, quantitatively monitored growth by measuring the temporal evolution of the Bragg diffraction interference fringes. Modeling of the evolution of the fringe patterns exposes the time dependence of the increasing crystal thickness. The initial diffusion-driven linear growth is followed by ripening-driven growth. Between 80 and 90 microM NaCl concentrations the fcc crystals first linearly grow at rates between 1.9 and 4.2 microm/s until they contact homogeneously nucleated crystals in the bulk. At lower salt concentrations interference fringes are not visible because the strong electrostatic interactions between particles result in high activation barriers, preventing defect annealing and leading to a lower crystal quality. The fcc crystals melt to a liquid phase at >90 microM NaCl concentrations. Increasing NaCl concentrations slow the fcc CCA growth rate consistent with the expectation of the classical Wilson-Frenkel growth theory. The final thickness of wall-nucleated CCA, that is determined by the competition between growth of heterogeneously and homogenously nucleated CCA, increases with higher NaCl concentrations.

Crystallization kinetics of colloidal spheres under stationary shear flow

A systematic experimental study of dispersions of charged colloidal spheres is presented on the effect of steady shear flow on nucleation and crystal growth rates. In addition, the nonequilibrium phase diagram as it relates to the melting line is measured. Shear flow is found to strongly affect induction times, crystal growth rates, and the location of the melting line. The main findings are that (1) the crystal growth rate for a given concentration exhibits a maximum as a function of the shear rate; (2) contrary to the monotonic increase in the growth rate with increasing concentration in the absence of flow, a maximum of the crystal growth rate as a function of concentration is observed for sheared systems; and (3) the induction time for a given concentration exhibits a maximum as a function of the shear rate. These findings are partly explained on a qualitative level.

Kinetic Analyses of Colloidal Crystallization in a Wide Range of Sphere Concentrations as Studied by Reflection Spectroscopy

The nucleation and growth rates in the colloidal crystallization of silica spheres (103 nm in diameter) from 0.006 to 0.04 in volume fraction (straight phi) have been measured by reflection spectroscopy. Kinetics of the crystallization has been discussed in a wide sphere concentration range (from straight phi=0.0005 to straight phi=0.04) using the data of this work and the previous work (110 nm in diameter) in exhaustively deionized aqueous suspensions. The induction period for nucleation decreases sharply as the sphere concentration increases. The nucleation rate increases substantially from 1x10(-3) to 1x10(7) mm(-3) s(-1) when straight phi increases from 0.0005 to 0.04. The crystal growth process consists of the fast growing step toward metastable crystals (rate v(1)) and slow growth accompanied with the reorientation toward stable ones (rate v(2)). The v(1) values increase first from 5 to 20 µm/s and then turn back to 5 µm/s after passing a maximum. v(1) above straight phi=0.01 remains at 5 µm/s and is insensitive to sphere concentration. The slow step is observed in the high-sphere concentrations only, and v(2) decreases sharply from 3 µm/s to 0.7 nm/s when sphere concentration increases from 0.004 to 0.04 in volume fraction. Importance of the electrostatic intersphere repulsion by overlapping of the electrical double layers and the cooperative and synchronized fluctuation of colloidal spheres in the crystallization processes are supported strongly. Copyright 2000 Academic Press.

Kinetic Analyses of Colloidal Crystallization in a Sinusoidal Electric Field as Studied by Reflection Spectroscopy

The effect of a sinusoidal electric field on crystal growth rates in the colloidal crystallization of silica spheres (110 nm in diameter) in exhaustively deionized aqueous suspensions has been studied by reflection spectroscopy. Sphere concentration is 0.0016 in volume fraction. Nucleation time is shorter than 1 s. The crystal growth rates, v, of the body-centered cubic lattices have been determined from the increase in the cube root of the intensity in the sharpened reflection peaks. The v value is 20 µm/s in the absence of an electric field. v decreases from 20 to 8 µm/s as the voltage applied increases from 0 to 10 V at 1 Hz. v decreases from 30 to 15 µm/s when frequency increases from 0.01 to 10 Hz at E = 6 V, and remains constant irrespective of frequencies higher than 10 Hz up to 10 kHz. Interestingly, the crystallization of bcc lattices is enhanced at low frequencies between 0.01 and 0.5 Hz. The main causes for the retardation of crystallization at high frequencies and voltages are (a) the additional translational fluctuation of the spheres and the surrounding electrical double layers by the electric field, and (b) the partial melting of the crystals by the shearing forces in an electric field. The importance of electrostatic intersphere repulsion resulting from overlap of the electrical double layers and cooperative and synchronized fluctuation of colloidal spheres in crystallization processes is strongly supported. Copyright 1999 Academic Press.

Kinetic Analyses of Colloidal Crystallization in Alcoholic Organic Solvents and Their Aqueous Mixtures As Studied by Reflection Spectroscopy

Reflection spectroscopy is used for the kinetic analyses of the nucleation and growth process of colloidal crystals of silica spheres (110 nm in diameter) in exhaustively deionized suspensions of purely alcoholic organic solvents (methyl alcohol, ethyl alcohol, and ethylene glycol) and aqueous mixtures with alcohols (methyl, ethyl, n-propyl, and n-butyl alcohols and ethylene glycol). Sphere concentrations studied range from 0.001 to 0.01 in volume fraction, rather high compared with those in water. Induction periods are from 5 to 2000 s and are prolonged with decreasing sphere concentration. Nucleation rates are 10(-3) to 10(3) mm-3 s-1 and increase sharply as sphere concentration increases. The crystal growth rates, v have been determined from the increase of intensity in the sharpened reflection peaks. Values of v range from 1 to 27 µm/s and decrease linearly as the reciprocal sphere concentration increases. Nucleation and crystallization rates decrease sharply as the fraction of the organic solvents increases in the mixtures with water. The importance of the electrostatic intersphere repulsion through the electrical double layers and the cooperative and synchronized fluctuation of colloidal spheres in the crystallization processes is supported. Copyright 1998 Academic Press.