Infracrystallization in monodisperse system of amorphous of silica as a model of infracrystallization and growth of “photonic crystals”
V.V. Serdobintseva
The charged monodisperse spherical silica particles (MSSP) along with double diffusion cloud of couterions (NH4+, K+, Na+) in disperse medium (water, alkochol, ester, acetone) represent structural units (SU) of infracrystals (IC) – the crystals with the lattice parameters >10 nm. The thickness of ion atmosphere (τ) is defined by electrolyte concentration and calculated by the Debye parameter χ, as τ=1/χ. The MSSP in the solid-like IC are divided by liquid interlayers and situated at the distance of H≈2τ.
Infracrystallization occurs in concentrated stable suspensions in the state of aggregation. The calculation ofvenergy of electrostatic repulsion of SU Ui and the energy of molecular gravitation Um according to the equations of the DLFO theory for real electrolyte concentrations demonstrates that Ui>>Um. Differentiation of these equations according to H allows us to take into account the force of interaction (disjoining pressure) and gravitational forces, which appear as the equivalent of forces of molecular gravitation. The equation of force balance, which physically corresponds to pretransitional state, makes possible calculation of the thickness of concentrated layer (h), which is necessary for crystallization start at different concentration of potential-forming electrolyte. The calculated h correlate well with the experimental data. The force balance at the moment when the activation barrier is overcame predetermine the possibility to use the Alder-Hoover model of phase transition (for noninteracting spherical bodies) in the analysis of crystallization isotherms corrected for a certain compression of ion atmospheres. Correspondingly, the concentration of SU in the concentrated layer of pretransitional state is ≈49–50 vol. %, and the volumetric effect of crystallization at great χ is about 10%.
The rate of linear growth of infracrystals (R) depends on temperature and χ value. The energy of activation at low χ reaches 35 kcal/mol. At the interphase the process has diffusion character and conforms to the linear dependence (the Turnbull-Hilling equation of growth). The mechanism of growth conforms to isotropic normal growth with rough interphase, which is characteristic for low-entropic phases.
The action of gravitational forces and limitation of volume are obligatory to overcome activation barrier. The mechanical action on IC, which exceeds the forces of gravity, returns them to the state of suspension .The output of infracrystals (A) during the second volumetric crystallization of these suspensions is described by the following equation: A=1–exp[–(kt)m], where k4=παR3/3; α – a possibility of formation of one centre of crystallization in a unit of time. The number of crystallization centres (N) in a unit of volume (V), influencing the size of the obtained crystals N is determined as ~0,9V·(α/R)4/3.
Ion atmospheres of SU form the surface of IC nuclei. A smooth transition for the MSSP surface to dispersed medium occurs here. In this case the surface energy is of minor importance, and the work of nucleation is determined by the SU mole volume and the energy of SU interaction. In the experiment the number of N correlates to the degree of suspension deionization (χ value). The experimental values of N and R allow evaluating α and, then, the work of nucleation, which depends on the value of the Ui. Structures with large IC (“photonic crystals”) appear when the value of Ui is maximum. The crystallization in the system of MSSP is convenient to study general rules of infracrystallization in other monodispersed systems.
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