Modelling Of Precipitation In Reverse Micelles
Two groups have obtained widely divergent number and size of CaCO3 nanoparticles, formed by g-1 precipitation in reverse micelles. These particles are used as a fine suspension in lube-oil additives, where they serve to neutralize acid produced during combustion in engines. Kandori et al. (J. Colloid Interface Sci, 122,1988, 78) obtained particles of about 100 nm size, by passing CO2 through a reverse micellar solution, containing dissolved Ca(OH)2 in the micellar core. Roman et al. (J. Colloid Interface Sci., 144,1991, 324), instead of using lime solution; added micron-sized solid lime particles in the oil and generated the reverse micelles by in situ reaction. This is a commercial process known as overbasing. It led to a higher amount of lime in the micelles as well as unreacted lime particles in oil, at the beginning of the experiment Upon passing CO2, they got particles of only 6 nm in size, compared to 100 nm reported by Kandori et al.. Furthermore, while Kandori et al. found that one particle formed from 108 micelles, Roman et al. got one particle out of only ten micelles.
We have modelled the two processes in a common framework to explain the reported disparity in particle characteristics. A time scale analysis of CO2 mass transfer, reaction, collision-fusion of micelles, nucleation, and growth of particles was carried out It showed that, in the experiments of Kandori et al., the rate limiting steps are nucleation and fusion. The analysis also indicates that the contents of a particular micelle are well mixed and reaction of lime and incoming CO2 can be treated as instantaneous. In the process of Kandori et al., the amount of lime taken initially being very small, the average number of product molecules in a micelle is well below one. Rapid Brownian coalescence and exchange of micellar contents leads to Poisson distribution of CaCO3(l) molecules formed by reaction. The low occupancy therefore suggests that most of the micelles are empty. Nucleation in a particular micelle is much slow and occurs when it has a critical number of molecules. Thus only very few micelles can nucleate. Comparison of nucleation and growth time scales - both intrinsic growth in a micelle and growth during fusion of nucleated and non-nucleated micelles - show that growth is much faster than both nucleation and collision. Hence a micelle can have only one nucleus, with subsequent growth during collisions. A population balance equation (PBE) is written involving the above steps. Solution of the moments of the distribution yields the number of CaCO3 particles, its size, coefficient of variance (COV) etc. The model not only predicts the ratio of number of micelles to particles, obtained experimentally as 108, but also captures the maxima in this quantity with increasing micellar size. The increase in average particle size with micellar size is also predicted well.
The process of of Roman et ai, in addition, involves the time scale of solubilization of solid lime into micelles. Its comparison with other time scales demarcates their experiments into two distinct phases. Phase I consists of reaction of lime initially present in micelles. Time scale analysis also suggests that, as the lime content in the micelles is large, a high degree of supersaturation is rapidly generated. This results in a burst of nuclei. The other conclusions, like, well-mixed micelle, Poisson distribution of CaCO3(l) molecules, instantaneous growth and mono-nucleated micelles are found to hold good. Once the pre-existing lime is finished, relative time scales indicate that, further precipitation is controlled entirely by fresh solubilization of lime. This marks the beginning of phase II. However, solubilization being the slowest step, CaCO3(l) in micelles never builds up for any further nucleation. Phase II thus consists of pure growth of the particles formed in phase I. On developing more general PBEs and with solution of resulting moment equations - written separately for the two phases - the experimental data on number of particles and temporal evolution to the final particle size of 6 nm could be predicted very well. The model also captures the qualitative trend in COV of particle radius with time.
Thus within the same framework we could successfully predict both the results, differing by seven orders of magnitude. The above analysis indicates that relative rates of nucleation, fusion-growth and mass transfer of gas controls the carbonation process. We further simplify the process and obtain an analytical solution in the limit of instantaneous mass transfer. The solution gives close first estimates for both the experiments and also indicates the smallest panicle size that could be obtained for a given experimental condition.
In contrast to g-1 mode, precipitation in 1-1 mode - using two reverse micellar solutions having two reactants- occurs only on coalescence of two micelles. To obviate the solution of multivariate PBEs, we have developed a general Monte Carlo (MC) simulation scheme for nanoparticle formation, using the interval of quiescence technique (IQ). Starting with a fixed number of micelles, we conduct each coalescence-redispersion and nucleation events in this population, in the ratio of their relative frequencies. Our simulation code is much more general and realistic than the scheme of Li and Park (Langmuir, 15,1999, 952). Poisson distribution with realistic micellar occupancies of reactants, binomial redispersion of solutes after fission, a nucleation rate with critical number of molecules and Brownian collision-fusion rates were used. These considerations are based on our earlier findings in g-1 precipitation and those known in the literature too. The simulation of Li and Park then becomes a special case of our code. Our simulation code was then used to predict experimental data on two systems. The results of Lianos and Thomas (Chem. Phys. Lett. 125, 1986, 299 and /. Colloid Interface 5c/., 117, 1987, 505), on number of molecules per CdS particle, as a function of micelle size and reactant concentrations have been predicted very well. For the Fe(OH)3 nanoparticles, our simulation provides a better prediction of the experimental particle size range, than that of Li and Park.
Finally, 1-1 precipitation on mixing two emulsions, having respectively the two reactants, has been simulated. Here, large reactant amount leads to multiple nucleation in a single drop and renders growth rate to be finite. This requires solving a PBE for particle population in each drop. Moreover, emulsions have a drop size distribution due to independent coalescence and breakage. The IQ technique was used for handling these events. Thus a composite model of PBE and MC for a drop population was developed. Simulation of particle size distribution in MgCO3 precipitation shows that nearly monodisperse nanoparticles can be produced in emulsions. Furthermore, average particle size can be controlled by changing reactant concentration in a drop.
The findings of the thesis have provided new issues to be addressed in modelling nanoparticle formation. It points out the importance of finding models for coalescence efficiency and critical nuclear size in micelles. Extension of our model and simulation to precipitation in other organized surfactant assemblies can be done by starting from appropriate time scale analysis.
Advisor:Kumar, R; Gandhi, K S
School:Indian Institute of Science
Source Type:Master's Thesis
Keywords:colliods and surface chemistry suspension nanoparticles reversed micelles nucleated reverse micellar systems nanoparticle formation
Date of Publication:12/01/1999