At the nanometer scale several physical principles govern the growth of nanoparticles through redox reactions in solution. These include the competition between diffusion and electron transfer for a redox agent at the surface of a very small particle, the dependence of electron transfer kinetics upon the size of the nanoparticle, and a coulomb charging of the nanoparticle which affects the kinetics of the reaction. Using the growth of a metal nanoparticle as an example, mathematical models describing these principles have been formulated, and rates of growth predicted as a function of particle size, electrochemical potential of the redox agent, and the rate constant for electron transfer. The growth rate is seen to be nonlinear with time.
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