La Mer model

La Mer ° and others have related the bridging efficiency factor to the fractional surface coverage of polymers (9). The original La Mer model and subsequently modified models can be generally described as... 

The major distinction between the model of La Mer and that developed for uniform latex particles lies in the incorporation of colloidal stability of small particles. The La Mer model assumes that each nucleus is colloidally stable and survives at the end of the reaction at the center of a particle. The aggregation models argue that stabilizing primary small particles is difficult, but aggregation does not necessarily result in a broad particle-size distribution. When schemes for control of particle-size distribution are developed, the result of accepting the notion that colloidal stability can play an important role is that attention is focused away from the length of the nucleation period and towards the colloidal properties of the growing particles. 

Fig. 1. Scheme depicting the stages of nucleation and growth for the preparation of monodisperse particles in the framework of the La Mer model (Cone pre denoted the precursor concentration) [46]. 

The two major theories of flocculation, the bridging model (1) and the electrostatic patch model (2, 3 ), provide the conceptual framework for the understanding of polymer-aided flocculation, but they do not directly address the kinetics of the process. Smellie and La Mer (4) incorporated the bridging concept into a kinetic model of flocculation. They proposed that the collision efficiency in the flocculation process should be a function of the fractional surface coverage, 0. Using a modified Smoluchowski equation, they wrote for the initial flocculation rate... 

Figure 2 (a) Schematic illustrating La Mer s model for the stages of nucleation and growth for monodisperse colloidal particles, (b) Representation of the synthetic apparatus employed in the preparation of monodisperse NQDs. (Reprinted, with permission, from the Annual Reviews of Materials Science, Volume 30 2000 by Annual Reviews www.annualreviews.org)... 

Guyot, M. (1991) Les molecules marines modeles et outils. Biojutur Special Issue La Mer, 106, 52-54. 

We emphasize some of the fundamental aspects of monodisperse nanoparticle formation. Two models are proposed for the formation of the particles the first is based on the La Mer diagram, and the second is based on the thermodynamic stabilization of the particles. In the first case, the particle size varies as a function of either the size of the inner water cores or the precursor concentration in the second case, the particle size is independent of these parameters. 

Two models have been proposed to explain the variation of the size of the particles with the precursor concentration and with the size of the aqueous droplets. The first is based on the La Mer diagram [16,17], which has been proposed to explain the precipitation in an aqueous medium and thus is not specific to the microemulsion. This diagram (Fig. 2) illustrates the variation of the concentration with time during a precipitation reaction and is based on the principle that the nucleation is the limiting step in the precipitation reaction. In the first step, the concentration increases continuously with increasing time. As the concentration reaches the critical supersaturation value, nucleation occurs. This leads to a decrease of the concentration. Between the concentrations and CIm the nucleation occurs. Later, the decrease of the concentration is due to the growth of the particles by dif-... 

These two models are limiting models the La Mer diagram does not take into account the stabilization of the particles by the siufactant, and the thermodynamic stabilization model does not take into account that the nucleation of the particles is more difficult than the growth by diffusion. 

Fig. 1. A molecular model of a condensed phase polymer blend. The example shown is used to study a mixture containing atactic polystyrene 40-mer (2 chains) and atactic poly(methyl methacrylate) 40-mer (2 chains). Figure la shows the cell with the molecules configured as they are in space the parts of the molecules lying outside the cell occupy adjacent cells in the periodic structure. To convey the space filling nature of the construction, Figure lb shows the same molecules packed in the cell. The model system was constructed using the Amorphous Cell module in the Materials Studio software package distributed by Accelrys (103). The amorphous cell system was constructed at a density of 1.12 g/cm at 300 K and the subsequent 80 ps of NPT dynamics at the same temperature and zero pressure equilibrated the system to a density of 1.057 g/cm .

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