Particles crystal growth kinetics

An important goal of materials science is the controlled and specific synthesis of well-defined nanoparticles. It is essential to obtain particles with uniform diameters and shapes and - for the purpose of particular apphcations - to func-tionahze the surface and embed the particles in a superstructure. To produce inorganic nanoparticles, bulk materials are mechanically crushed or the particles are synthesized from precursor compounds by controlhng the crystal growth kinetics. In order to stabihze the extremely large specific surface, appropriate ligands have to be added. 

From the above statements it follows that it should be possible to derive the growth kinetics and calculate the growth rate of uncontaminated electrolyte crystals when the following parameters are known molecular weight, density, solubility, cation dehydration frequency, ion pair stability coefficient, and the bulk concentration of the solution (or the saturation ratio). If the growth rate is transport controlled, one shall also need the particle size. In table I we have made these calculations for 14 electrolytes of common interest. For the saturation ratio and particle size we have chosen values typical for the range where kinetic experiments have been performed (29,30). The empirical rates are given for comparison. 

The development and refinement of population balance techniques for the description of the behavior of laboratory and industrial crystallizers led to the belief that with accurate values for the crystal growth and nucleation kinetics, a simple MSMPR type crystallizer could be accurately modelled in terms of its CSD. Unfortunately, accurate measurement of the CSD with laser light scattering particle size analyzers (especially of the small particles) has revealed that this is not true. In mar cases the CSD data obtained from steady state operation of a MSMPR crystallizer is not a straight line as expected but curves upward (1. 32. 33V This indicates more small particles than predicted... 

The scope of kinetics includes (i) the rates and mechanisms of homogeneous chemical reactions (reactions that occur in one single phase, such as ionic and molecular reactions in aqueous solutions, radioactive decay, many reactions in silicate melts, and cation distribution reactions in minerals), (ii) diffusion (owing to random motion of particles) and convection (both are parts of mass transport diffusion is often referred to as kinetics and convection and other motions are often referred to as dynamics), and (iii) the kinetics of phase transformations and heterogeneous reactions (including nucleation, crystal growth, crystal dissolution, and bubble growth). 

The present study begins with Zhdanov s results and describes the influences of the alkali, Si02 source, K ions and temperature on the progress of the reaction and particle size spectrum of zeolite A. Comprehensive evaluation of these kinetic investigations permits predictions about nu-cleation and crystal growth which are not restricted to the formation of zeolite A, which had been chosen as a model reaction in the present case. 

In contrast to more or less well defined kinetics of the crystal growth (5,6,12-16), various nucleation mechanisms have been proposed as zeolite particles forming processes. Most authors explained the formation of primary zeolite particles by nucleation in the liquid phase supersaturated with soluble silicate, aluminate and/or aluminosilicate species (1,3,5,7,16-22), with homogeneous nucleation (1,5,7,17,22), heterogeneous nucleation (5,2 1), cell walls nucleation (16) and secondary nucleation (5) as dominant processes of zeolite particles formation, but the concepts dealing with the nucleation in the gel phase are also presented in the literature (2,6,11,12,1 1,23-25). 

Because of the difficulties associated with the characterisation of heteronuclei in solution, few studies have attempted to explain experimental results in a quantitative way. If it is assumed that, once nucleation occurs, the particles grow without recrystallisation, then it is possible to get information about the particle density from a consideration of the geometry of the particles and the growth kinetics. One approach is to add heteronuclei to supersaturated solutions and measure the crystallisation kinetics and, from the data obtained, estimate the surface area of the growing crystals. In this way, it is feasible to obtain information about the nucleation capability of different heteronuclei and the effects of pretreatments on the nucleation capability. An example of such an application will be discussed in Sect. 5.4. 

Numerous kinetic studies have been made of the spontaneous precipitation of calcium phosphates from solutions containing concentrations of lattice ions considerably in excess of the solubility values (33, 34). Although attempts, are usually made to control the mixing of reagent solutions, it is difficult to obtain reproducible results from such experiments since chance nucleation of solid phases may take place on foreign particles in the solution. Many of these difficulties can be avoided by studying the crystal growth of well-characterized seed crystals in metastable supersaturated solutions of calcium phos.phate. 

In the processing of nanoparticles, coarsening is common, and may be accompanied by phase transformation to the macroscopic stable structure. Here we will focus on the kinetics of phase transformations and crystal growth in nanocrystalline particles. We will show later that conventional kinetic models that are widely employed for analysis of macroscopic materials behavior may have to be modified prior to their application to nanomaterials. 

Much of the work to date on particle size effects on phase transformation kinetics has involved materials of technological interest (e.g., CdS and related materials, see Jacobs and Alivisatos, this volume) or other model compounds with characteristics that make them amenable to experimental studies. Jacobs and Alivisatos (this volume) tackle the question of pressure driven phase transformations where crystal size is largely invariant. In some ways, analysis of the kinetics of temperature-motivated phase transformations in nanoscale materials is more complex because crystal growth occurs simultaneously with polymorphic reactions. However, temperature is an important geological reality and is also a relevant parameter in design of materials for higher temperature applications. Thus, we consider the complicated problem of temperature-driven reaction kinetics in nanomaterials. 

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