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Precipitation Reactions
Precipitation Reactions Manfred Kahlweit Max-Planck-Institut f¨ur Biophysikalische Chemie
I. Qualitative Considerations II. Quantitative Treatment
GLOSSARY Association colloids Thermodynamically stable colloidal particles formed by the association of monomers. Coagulation Coarsening due to collisions between particles. Coarsening (aging) Decrease of particle number density in the later stages of a precipitation reaction. Diffusion-controlled growth Growth rate determined by the transport of monomers from the parent phase to the surface of the particle. Growth rate Net uptake of monomers by a growing particle in unit time. Nucleation rate Number of nuclei formed in unit time per unit volume of the parent phase. Nucleus Submicroscopic particle of the new phase in the supersaturated parent phase. Ostwald ripening Coarsening due to the transport of monomers through the parent phase from smaller to larger particles. Parent phase Original phase, which supplies the material for the nucleation and growth of the new phase. Supersaturation Thermodynamic driving force in the parent phase for the formation of a new phase. Surface-controlled growth Growth rate determined by the incorporation of monomers at the surface of the particle.
A PRECIPITATION REACTION is a first-order phase transformation and involves the formation, growth, and coarsening of a new phase in the supersaturated parent phase. As an example consider the precipitation of liquid droplets from a supercooled vapor. The problem is to analyze the precipitation reaction and to predict the dependence of the number density and the mean size of the particles of the new phase on the experimental conditions of the reaction and the properties of the substance.
I. QUALITATIVE CONSIDERATIONS A. Introduction The kinetics of a first-order phase transformation involve the formation, growth, and coarsening of a precipitate in a supersaturated parent phase. These processes can be discussed either semiquantitatively (as in Section I) or quantitatively (as in Section II). Experience tells us that there are two kinds of phase transitions: discontinuous transitions, in which energy and volume change discontinuously during the transition from one phase to another, and continuous transitions, in which energy and volume change continuously, their temperature derivatives, however, showing singularities. Here, we shall restrict ourselves to phase transitions of the first kind. Figure 1a shows schematically the projection of the density ρ, temperature T , and pressure p equilibrium
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I. Qualitative Considerations II. Quantitative Treatment
GLOSSARY Association colloids Thermodynamically stable colloidal particles formed by the association of monomers. Coagulation Coarsening due to collisions between particles. Coarsening (aging) Decrease of particle number density in the later stages of a precipitation reaction. Diffusion-controlled growth Growth rate determined by the transport of monomers from the parent phase to the surface of the particle. Growth rate Net uptake of monomers by a growing particle in unit time. Nucleation rate Number of nuclei formed in unit time per unit volume of the parent phase. Nucleus Submicroscopic particle of the new phase in the supersaturated parent phase. Ostwald ripening Coarsening due to the transport of monomers through the parent phase from smaller to larger particles. Parent phase Original phase, which supplies the material for the nucleation and growth of the new phase. Supersaturation Thermodynamic driving force in the parent phase for the formation of a new phase. Surface-controlled growth Growth rate determined by the incorporation of monomers at the surface of the particle.
A PRECIPITATION REACTION is a first-order phase transformation and involves the formation, growth, and coarsening of a new phase in the supersaturated parent phase. As an example consider the precipitation of liquid droplets from a supercooled vapor. The problem is to analyze the precipitation reaction and to predict the dependence of the number density and the mean size of the particles of the new phase on the experimental conditions of the reaction and the properties of the substance.
I. QUALITATIVE CONSIDERATIONS A. Introduction The kinetics of a first-order phase transformation involve the formation, growth, and coarsening of a precipitate in a supersaturated parent phase. These processes can be discussed either semiquantitatively (as in Section I) or quantitatively (as in Section II). Experience tells us that there are two kinds of phase transitions: discontinuous transitions, in which energy and volume change discontinuously during the transition from one phase to another, and continuous transitions, in which energy and volume change continuously, their temperature derivatives, however, showing singularities. Here, we shall restrict ourselves to phase transitions of the first kind. Figure 1a shows schematically the projection of the density ρ, temperature T , and pressure p equilibrium
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