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«Dissertation zur Erlangung des akademischen Grades Doktoringenieurin (Dr.-Ing.) von: Yashodhan Pramod Gokhale geboren am: 05. October 1981 in Pune, ...»

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Here, Figure 6-34, Figure 6-35, Figure 6-36 and Figure 6-37 were measured using data from Mastersizer 2000 for different shear rates  =370, 623, 960, 1342 s-1 (see Table 4-2). Particle  sizes are characterized using d10,3, d50,3, d90,3 observed every 10 minutes for 300 minutes of redispersion time. After a certain time, redispersion process becomes more significant as the agglomerates become larger, and slows down the agglomerates growth (identified in cascading curve), creating smaller particles. This type of agglomerates mentioned before are more susceptible to redispersion by fluid shear of eddies turbulent when it is larger.

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Figure 6-37 Typical Decreasing Curve of Particle Sizes for 300 minutes of Redispersion time (using  =1342 s-1)  Figure 6-38 Particle size frequency distribution at 10 minutes of redispersion time by using different kernels (  =1342 s-1)  Figure 6-38 shows comparison of different agglomeration kernels from (Table 5-1). Besides this, the particle size frequency is measured at a redispersion time of 10 minutes. It is observed that shear kernel shows good comparison with initial experimental size distribution.

Figure 6-39 The zeroth moment of size distribution calculated by using different kernels (  =1342 s-1)  In Figure 6-39, the zeroth moment is plotted using different agglomeration kernels along with Diemer disintegration kernel (Gokhale, Kumar et al. 2008). It is observed that shear kernel gives more number of particles as time increases. This shows that shear kernel has less effective aggregation effect as compared to the other two kernels. It should be noted that the total mass of the system remains conserved irrespective of the aggregation and disintegration kernels.

Once the agglomerates are being redispersed, it can agglomerate again since the fluid velocity will still bring particles close to each other. The same phenomena will repeat continuously until it reaches the steady state size of agglomerates due to the balances between agglomeration and redispersion rate. It is considered to have attained steady state when the sizes of particles no longer changed with time.

A certain amount of energy (minimum value) must be present inside hydrodynamic fluid in order to break agglomerates. This energy is strong enough to break the bonds between primary particles in agglomerates. Observation of experimental and modeling data indicates that the higher the shear rate (until a definite value of  ), the narrower the distributions, and  the more they are shifted to smaller agglomerates sizes as a result of higher disintegration rates. The optimum shear rate for generating titanium dioxide nanoparticles would be by using  =1342 s-1. The next section is about disintegration process of surfactant based TiO2  nanoparticles.

6.2.2 Disintegration of Surfactant based Titanium dioxide This work explores the effect on surface stabilization with different surfactants. The steric stabilization of polymer and various functional groups of dispersants is also considered. The influence of various precursor concentrations and different surfactants on the particle size distribution is investigated. The population balance model for disintegration leads to a system of integro-partial differential equations which is numerically solved by the cell average technique. The experimental results are also compared with the simulation using two different disintegration kernels. Effects of Different Surfactants

The physical and optical properties of nano-sized particles are related strongly to their size.

For this reason, there is a growing need for a reliable, accurate and rapid means of particle size measurement and materials characterization in the nanometer size range. Titania nanoparticles are generated by the reduction of ionic precursors in liquid phase in the presence of stabilizers production metal sols. Titania particles of narrow size distributions have been synthesized in the laboratory using titanium tetra isopropoxide as precursor, different surfactant agents notably polymers, viz. Polyethylene Glycol, Ethylene Glycol, and Sodium Chloride.

Figure 6-40 Experimental sol-gel TiO2 nanoparticles in the presence of 0.372 g/ml Ethylene Glycol and simulated evolution of PSD by the Austin kernel The parameters used for this simulation, with the Austin kernel, are  = 0.18,  = 0.08,  = 10, for the selection rate S 0 = 0.50 s-1 and constant  = 0.33 is used.

For the other disintegration kernel we used, Diemer kernel, parameters p = 2, c = 10 and for the selection rate S 0 = 0.50 s-1 and constant  = 0.70 have been considered. The 4-hour experimental result has been held as the initial condition for the cell average scheme. The comparisons are done for the cumulative size distributions for each PSD at different time intervals. Various experimental results are tabulated, graphically represented and explained further.

It can be seen from Figure 6-40 and Figure 6-41 that during the initial stages, polydispersed particles were obtained with ethylene glycol. In both cases, monodispersed particles were obtained after a reaction period of 10 hours. After the simulation we observed from Figure 6-40 that the Austin kernel shows good comparison with the experimental. However for the Diemer kernel in Figure 6-41, simulation shows good behavior for PSD with experimental data.

Figure 6-41 Experimental sol-gel TiO2 nanoparticles in the presence of 0.372 g/ml Ethylene Glycol and simulated evolution of PSD by the Diemer kernel Figure 6-42 and Figure 6-43 show the comparisons for PEG-TiO2 between the experimental and the simulation results by using the Austin and Diemer kernels, respectively. It is found that the simulation results, using the Austin kernel, are in excellent agreement with the experimental results for each time interval. From Figure 6-43, it is found that Diemer kernel gives good predictions with the experimental results. The fact that the reaction time influences the synthesis process of titania particles is self-explanatory.

Figure 6-42 Experimental sol-gel TiO2 nanoparticles in the presence of 0.374 g/ml Polyethylene Glycol and simulated evolution of PSD by the Austin kernel.

Figure 6-43 Experimental sol-gel TiO2 nanoparticles in the presence of 0.374 g/ml Polyethylene Glycol and simulated evolution of PSD by the Diemer kernel There is a general decreasing trend of particle size as the conditioning (homogenization) progresses from the beginning to the end of the synthesis period of 10 hours. As seen in the figures, the particle size decreases as the homogenization time increases from 4 hours to 10 hours, for 0.374 g/ml of PEG in the reaction solution.

Figure 6-44 Experimental sol-gel TiO2 nanoparticles in the presence of 0.720 g/ml NaCl and simulated evolution of PSD by the Austin kernel.

Figure 6-45 Experimental sol-gel TiO2 nanoparticles in the presence of 0.720 g/ml NaCl and simulated evolution of PSD by the Diemer kernel Smaller particle size distributions were obtained with salt after 8 hours with the NaCl. In general, polydispersed particles were obtained during the initial stages of the precipitation reaction as can be seen from Figure 6-44 and Figure 6-45.

From Figure 6-44 it is observed that the Austin kernel over predicts the results slightly at 6 hrs, but gives accurate results with 8 hrs and 10 hrs. Similarly, the case of Polyethylene Glycol and Ethylene Glycol, the Diemer kernel also indicates the exact predictions with the experimental data for NaCl as well. Particles were synthesized in all the three different cases of surfactants after 10 hrs.

A totally different behavior is witnessed as the surfactant concentrations are increased in the reaction solutions. NaCl showed a great growth in the particle size, Ethylene Glycol also showed a small rise whereas a marginal change was observed with Polyethylene Glycol. A clear assessment can be made from a combined graph showing both results below.

Figure 6-46 Experimental sol-gel TiO2 nanoparticles in the presence of 0.0607 g/ml TTIP and different surfactant concentrations after 10 hours Titanium dioxide nano particles of varying particle sizes and particle size distributions were obtained using different surfactant concentrations as shown in Figure 6-46. The lower salt concentration shows smaller particle sizes than Polyethylene Glycol. The steric hindrance influences the particle size distributions. Therefore to improve the population balance model, the steric hindrance needs to be minimized. In our case, Ethylene Glycol shows narrow size distributions than other surfactants. In general, polydispersed particles were obtained during the initial stages of the precipitation reaction as can be seen from all the figures above.

However, after 10 hours, monodispersed particles were synthesized in all the different cases of varying concentrations of surfactants (Gokhale, Kumar et al. 2009).

Chapter 7 Conclusions

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7 Conclusions and Outlook

7.1 Conclusions T his work examines the formation of nanoscale silver particles produced by chemical double reduction method. In this, colloidal silver is obtained from silver powder. This powder is prepared initially by the of sodium formaldehyde sulphoxylate (SFS) and tri-sodium citrate external surfactant cum reducing agents. It is important that one can prepare large surface capped particles in the first place and then isolated particles of smaller dimension i.e. typically in the nano-meter regime via a colloidal stage.

TEM analysis of colloidal silver nano-particles obtained from this method showed the particle size to be less than 30 nm. The morphology of the particles is spherical with homogeneous distribution, despite some clustering is observed due to the presence of capping agent. It may be due to the increase in the value of aggregation rate constant than disintegration rate constant. The tendency of silver particles to agglomerate is more at low shear rate. The amount of capping agent had a very desirable effect on the size of the particles. The molar concentration of capping agent increases and the size of the nanoparticles decreases. The amount of reducing agent has an undesirable effect on the size of nanoparticles and it is found that the size increases with the amount of reducing agent for a given shear rate and temperature.

Surface stabilized spherical titania particles have been synthesized in this study via the sol-gel process. Titanium tetra isopropoxide was used as a precursor. Three different surfactants were used for the synthesis of spherical titania particles of variable sizes. The particle size distributions were measured by the dynamic light scattering technique. The results from dynamic light scattering showed that the different stabilizers lead to entirely different particle size distributions. It has been shown that size and dispersity of colloidal particles can be controlled by appropriate choice of surfactants and polymers or salt that is added during the synthesis.

All experiments showed that after some time particle size distribution reaches a steady state.

In the initial phase of experiments, large particles are observed, due to agglomeration process.

Disintegration of agglomerates becomes more significant as the agglomerates become larger;

it slows down the growth of agglomerates and creates smaller particles. Steady state condition is reached as the two opposing mechanisms balance each other. Application of various shear rates i.e., (  =370, 623, 960, 1342s-1) to the reaction condition gives a tendency in which the  higher the shear rates, the lower is the particle size distributions. Among the entire applied shear rates,  =1342 s-1 has been determined as the optimum shear rate for generating the  smallest titanium dioxide nanoparticles.

A continuous population balance model is used for describing the simulation of the simultaneous agglomeration and disintegration process during the sol-gel synthesis of titanium dioxide nanoparticles. The population balance model leads to a system of integro-partial differential equations which is numerically solved by a new numerical scheme, the cell average technique(CAT) used in this work (Kumar 2006). The cell average technique follows a two step strategy, one to calculate average size of the newborn nanoparticles in a discretized cell, and the other to assign them to neighboring nodes such that the zeroth and the first moments are properly preserved. For experimental methods, agglomeration rates are determined by measuring the evolution of particle size distributions with time. A modeling framework is developed by using different agglomeration kernels like Brownian, sum, and shear kernel while for disintegration Austin and Diemer kernels are used.

The hydrodynamic factor like the shear rate has been included in the mathematical form of solution of the kernel. Numerically derived results from a population balance model that accounts for agglomeration and disintegration, are in reasonable agreement with experimental observations. From the population balance model it is possible to distinguish the kernel that best describes the experimental data based on comparison of the particle size distributions and their moments. It is found that shear kernel and Austin kernel stands as the best fit to the experimental data.

The experiment results of the sol-gel synthesis for titania particles are also compared with the numerical simulation using two different disintegration kernels. The modeling and their simulation are used are used to have a comfiration of the experiment of the sol-gel synthesis for titania particles in addition to different surfactants.

We have observed that Austin and Diemer kernels stand in good agreement with the experimental particle size distributions (PSD). It is also found that the Austin kernel stands as the best fit to the experimental data as compared to the Diemer kernel. The computational features for this method are such that, this model can be computed easily on a personal computer.

7.2 Outlook

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