Mechanism of growth of supramolecular crystals in concentrated suspensions of monodisperse spherical silica particles (MSSP)
A.F. Danilyuk, V.V. Serdobintseva, D.V. Kalinin
According to Williams, Grandall, Wojtowicz, Okubo, diluted (to several vol. %) deionized suspensions of monodisperse spherical silica particles (MSSP) as well as polystyrene 100 nm in size exhibit the ability to volume crystallization. It was assumed that regular structures result from the gravitational particle packing in concentrated (>50 vol. %) soles of large MSSP stabilized with alkali or ammonia. As found, the concentrated suspensions in a particular range of the stabilizer concentration can crystallize on cooling as metal alloys. Parameters of crystallization and the mechanism of growth of such over molecular crystals from MSSP are of interest from the point of general regularities of the over molecular crystallization and the problems of mesoporous material synthesis.
MSSP suspension 200±10 nm in size were prepared by tetraethoxysilane Si(OC2H5)4 hydrolysis in aqueous-alcohol solutions in the presence of ammonia. Ammonia concentration determines the electrical properties and dimensions of the double diffusion layer around particles. For the given size of MSSP, the ammonia concentration was 0,0001–0,0002 mol/l in fresh suspensions. Using the equation χ=(8πe2z2n/εkT)½, where z and n are charge and concentration of an counter ion in the solution, ε is the dielectric constant of alcohol, we have calculated the Debye parameter, which is about (1,2–1,3)·105 cm-1. The thickness of the charged diffusion zone of counter ions (1/χ) is about 70–80 nm.
Actual distances (H) between particles in the crystal structure formed are always 25–30 nm lower than 2/χ. This may be attributed to rearrangement in the density of diffusion ion atmospheres around particles on crystallization. Because the parameter of crystal lattice has the same order as the length of white light waves, the crystals are clearly seen due to their bright diffraction coloring. The Bragg equation permits one to estimate distance H between the particles by the maximal wave length (λ).
Using a horizontal microscope supplied with test glasses, in which crystallization occurs, we have observed the crystal growth, and measured linear rates R of crystal growth. We used MSSP suspensions with a volume concentration >50 vol. %, which was obtained by centrifuging the initial sole. The concentrated suspensions were heated to 35°C and then cooled slowly. A 50-fold magnification permitted us to observe crystal formation at the range 20–28°C. For the reverse heating, the temperature of the initial crystal melting was set as an equilibrium one (T0). The measuring accuracy was 0,5°C.
Crystallization of suspensions with fixed MSSP concentration and χ results in formation of cell polycrystal structures. The crystal size is determined by a deviation of crystallization temperature ΔT from T0. For ΔT=5°C, the size of crystals was up to 1 mm, whereas at ΔT~1°C, the size was about 5–7 mm.
Even for minimum sizes, the crystals are not cut. Their shape is usually close to the isometric one with twisting or angle outlines on accretion. The polycrystal structure is similar to the structure of metals. This crystallization morphology indicates an isotropic growth of crystals. The rough surface of growing crystals is nicely observed at the optical range. An electron microscope permits one to observe a twisting and difficult-to-detect interface which is masked by structurally ordered blocks 1000 nm in size presented in the suspension. Most probably, these blocks are involved in crystal formation. However, the formation exhibits the properties characteristic of the mechanism of continuous growth by the Jackson model.
For ΔT=5°C, the optical measurements of R provide high values at (0,5–1,5)·10-3 mm/min and indicate a direct dependence between rate of growth R and ΔT. For normal growth, Hilling and Turnbull suggested to calculate R by a simple equation R=DΔSΔT/LT0, where ΔS is the molar melting entropy, D is the diffusion coefficient, and L is the length of a particle path. An approximate value of ΔS can be found from the concentration dependence and is 8–12 J/mol·grad. This low values of ΔS agrees with the presence of the apparent nearest order in the suspension. The value of D with an allowance for size and weight of MSSP can be assumed as 2·10-6 mm2/min. When the particle path range is about 100 nm, ΔT=5°C, and ΔS=10 J/mol·grad, R is about 0,4·10-3 mm/min, which agrees satisfactorily with the measured results.
According to the calculations of the total potential energy of MSSP binary interaction performed by the DLVO theory (Deryagin, Landau, Verwey, Overbeek), crystallization goes under predominant action of the electrostatic repulsion of particles at χ from 1,2·105 cm-1 to 3,5·105 cm-1, and, consequently, it requires strained conditions that may be generated by gravitational concentration. As was established for constant T0, crystallization of suspensions with a low ammonia concentration (χ=1,2·105 cm-1) proceeds at lower volume concentrations of MSSP (~55%). Higher concentrations of MSSP (~65%) correspond to high concentrations of ammonia (χ=3·105 cm-1).
So, the crystallization of concentrated suspensions of MSSP is determined by parameters such as MSSP concentration, effective particle diameter (de=d+1/χ), which depends on the electrolyte concentration, and temperature. There is a slight linear growth in T0 when the MSSP concentration increases. Moreover, as χ increases, the crystallization isotherms shift to the region of lower temperatures. As a result, a simple model of the normal growth may transform into a more complex growth with a degraded interphase and cluster growth. Such transformations were experimentally observed but this fact is the concern of a separate publication.
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