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

A B Figure 6-9 SEM of silver particles synthesized by addition of different molar ratio of capping agent as A : 1:3:1 ratio and B : 1:2:1 ratio at shear rate 623 s-1 Picture A shows us the presence of small spherical primary particles with size less than 100 nm, where as in picture B particles are stuck together. Here agglomeration in the SEM images is due to dry sample preparation.

Figure 6-10 shows that the tendency of silver particles to agglomerate is more at decreasing shear rate 120 s-1 as compared to Figure 6-9. The difference is considered appropriate due to the presence of hydrophilic capping around the particles which makes the dissolution (dispersion) viable.

A B Figure 6-10 SEM of silver particles synthesized by addition of different molar ratio of capping agent as A : 1:3:1 ratio and B : 1:2:1 ratio at shear rate 120 s-1 The scanning electron microscopy is an analytical technique, which is appropriate for observing particles with sizes above 100 nm. The next section shall deal with transmission electron microscopy for particle size measurements.

**6.1.4.2 Transmission Electron Microscopy (TEM)**

The work described in this section, is about TEM which is used to confirm the capping of citrate to silver particles. Samples for TEM analysis were prepared by placing a drop of colloidal solution of Na-citrate capped silver nanoparticles on a carbon-coated TEM copper grid. After dust protected evaporation of the colloidal fluid, the drop was allowed to dry into the high vacuum of the TEM. These measurements were performed on a CM200 of the Philips/FEI instrument operated at an accelerating voltage of 200 kV.

Figure 6-11 shows transmission electron micrographs for different citrate concentrations. In Figure 6-11A, the particle size is less than 30 nm. The morphology of the particles is spherical with homogeneous distribution yet some clustering was observed due to the presence of capping agent. Figure 6-11B shows polydispersed particle size distribution with mean diameter of 100 nm.

A B Figure 6-11 TEM of silver particles synthesized by addition of different molar ratios of capping agent as A : 1:3:1 ratio and B : 1:2:1 ratio at shear rate 623 s-1 The TEM micrographs in Figure 6-12A shows colloidal silver nanoparticles due to the effect of reducing agent. It shows complete reduction of absorbed silver ions on the surface of the particles. Bigger nanoparticles showed some tendency to form aggregates. The mean particle diameter is 200 nm. Figure 6-12B shows that the electron diffraction analysis revealed all rings indicative of Bragg's reflections conforming to the amorphous nature of nano-Ag.

Close-packed Ag (111) monolayers, which form a face-centered cubic structure, are arranged parallel to the surface.

0.5 0.5 0.01 0.01

-1

-1

The typical TEM histograms of the particle diameter are shown in Figure 6-13. Figure 6-13A analyses particle diameter as d = 29.4 nm, d50,0 =17.6 nm, dmin = 5.8 nm, dmax = 93.6 nm.

Figure 6-13B predicts particle size distribution as d = 54.6 nm, d50,0 = 14.9 nm, dmin =12.5 nm dmax= 96.0 nm. Thus from the TEM images we found shown that morphology of the silver nanoparticles is strongly influenced by citrate ions and reducing agent.

6.2 Experiment and Modeling of Titanium dioxide nanoparticles This works investigates the simultaneous agglomeration and disintegration process of titanium dioxide nanoparticles synthesized by sol-gel process. Further the population balance model for disintegration process of surface stabilized titanium dioxide nanoparticles is also developed. The population balance model for agglomeration and 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 agglomeration and disintegration kernels.

**6.2.1 Simultaneous process of agglomeration-disintegration of titanium dioxide**

This work aims at finding the particle size distribution and morphology with the help of changing process parameters like variation of the stirrer speeds. The experiments were made with only acidic suspension. This is because nitric acid is considered the best solvent in synthesizing titanium dioxide nanoparticles via the sol-gel process. Hence, in all the experiments on this section; HNO3 was used as a medium at 500 C. There is a growing need for a reliable, accurate and rapid means of particle size measurement and materials characterization in the nanometer size range. In our experiments, particle size measurements were performed on the prepared samples using Malvern Master Sizer and Zeta Nanosizer instruments.

**Simulation Conditions**

The simulation is used to study the evaluation and prediction of the dynamic behavior of particle size distributions undergoing simultaneous agglomeration and disintegration of the synthesis of titanium (IV)-oxide nanoparticles via the sol-gel process. As mentioned in chapter 5, this work uses the cell average technique to discretized the continuous population balance model (Eq. 5.1) for agglomeration and disintegration of the titania nanoparticles in suspension. Further the simulation is compared with the experimental results. The experimental results are gathered at shear rates 370, 623, 960 and 1342 s-1 for process time 4, 6, 8 and 10 hours. The calculation for these shear rates is summarized in Appendix A. For the simulation, the 4 hours experimental data is considered as an initial condition and then we compare the results at 6, 8 and 10 hours. The comparisons are performed for the cumulative size distributions Q0 i.e. numbered based for each PSD at different time intervals. In all the figures, we plot the particle size distributions Q0 are plotted on the Y-axis against the particle sizes on X-axis. Various experimental results are tabulated, graphically represented and explained further. The simulation calculations were carried out with MATLAB.

In the following two sub-sections, we discuss the effect of different agglomeration kernels like shear kernel and sum kernel as well as the effect of different disintegration kernels like Austin kernel and Diemer kernel on particle size distributions.

6.2.1.1 Austin kernel and Shear kernel

960 and 1342 s-1.

In Figure 6-14, shear rate =370 s-1 did not show much difference in particle size distribution compare to shear rate 623 s-1(Figure 6-15) and 960 s-1 (Figure 6-16) that shifted and resulted in slightly narrower distributions than previous shear rates. This figure shows the influence of the different shear rates on the particle size distributions under process time. Figure 6-14 expounds that predominantly the formation of the bigger agglomerates has happened at a lower shear rate from starting process until 6 hours. Another important observation is that increase in the redispersion time can reduce the particle sizes as expected. Moreover, during the first 6 hrs, there is higher kinetic mechanism of agglomeration than redispersion, making the particle size big. After 8 hrs, the redispersion dominates the process. The agglomerate diameter becomes much smaller when compared to the previous process time.

It is seen from Figure 6-17, that particles size distribution shifted to left at applied shear rate =1342 s-1, indicating that very fine particles of titanium dioxide were dominated. It also gave smaller size distribution among others. The initial stages show that polydispersed particles were obtained due to low shear rates. In both cases monodispersed particles were obtained after the reaction period of 10 hours. After the simulation, we observed that due to the simultaneous agglomeration and disintegration process, shear kernel and Austin kernel compared with the experimental results. This is shown in Figure 6-17.

Figure 6-14 Effect of shear rate 370 s-1 on PSD by Austin kernel Figure 6-15 Effect of shear rate 623 s-1 on PSD by Austin kernel Figure 6-16 Effect of shear rate 960 s-1 on PSD by Austin kernel Figure 6-17 Effect of shear rate 1342 s-1 on PSD by Austin kernel 6.2.1.2 Diemer Kernel and Shear kernel The numerical and experimental results of the particle size distributions Q0 for the combined process of aggregation and disintegration are discussed. For disintegration Diemer kernel is used which is given as, p x c ( y - x)c ( c 1)( p -2) c (c 1)( p -1) !

b ( x, y ) y pc ( p -1) c ! c (c 1)( p - 2) !

along with the selection function S ( x) S0 ( x). The exponent p describes the number of fragments per disintegration event and c 0 determines the shape of the daughter particle distribution. For agglomeration, the same shear kernel has been used as discussed in previous section.

In this case, the simulation parameters are p = 2, c = 11, = 0.70 and S 0 = 0.50 s-1. It can be seen from Figure 6-18, Figure 6-20 and Figure 6-21 that the Diemer kernel gives accurate results with 6hours, 8 hours and 10 hours experimental results. From Figure 6-19 it is observed that the Diemer kernel deviates slightly from the results at 6 hours and 10 hours, but are in good agreement with 8 hours. The formation expound that predominantly the formation of the bigger agglomerates has happened at a lower shear rate from starting process until 6 hours. Another important observation is that increasing the redispersion time can reduce the particle sizes as expected. After 8 hours, the redispersion dominates on the process. The agglomerate diameter becomes much smaller when compared to the previous process time as shown in Figure 6-20 and Figure 6-21.

Figure 6-18 Effect of shear rate 370 s-1 on PSD by Diemer kernel Figure 6-19 Effect of shear rate 623 s-1 on PSD by Diemer kernel Figure 6-20 Effect of shear rate 960 s-1 on PSD by Diemer kernel Figure 6-21 Effect of shear rate 1342 s-1 on PSD by Diemer kernel 6.2.1.3 Effect of Sum and Austin kernel on PSD In this section, the comparisons are done by using the sum aggregation kernel i.e.

( x, y) x y along with the Austin disintegration kernel. We have used the parameters γ = 10, φ = 0.1, λ = 4 for Austin kernel. For the selection rate S 0 = 0.50 s-1 and = 0.70 is taken. From Figure 6-22, Figure 6-23 and Figure 6-24 it follows that Austin kernel indicates the exact predictions with the experimental data. Figure 6-25 shows that Austin kernel over predicts the results slightly at 10 hrs, but gives accurate results with 6 hrs and 8 hrs.

Figure 6-22 Effect of Sum and austin kernel at 370 s-1 on PSD Figure 6-23 Effect of Sum and Austin kernel at 623 s-1 on PSD Figure 6-24 Effect of Sum and Austin kernel at 960 s-1 on PSD Figure 6-25 Effect of Sum and Austin kernel at 1342 s-1 on PSD 6.2.1.4 Effect of Sum and Diemer kernel on PSD Here, the simulation and experimental results are compared for the sum aggregation kernel and Diemer disintegration kernel. The simulation parameters are p = 2, c = 11 and for the selection rate S 0 = 0.50 s-1 and = 0.70 is used.

Figure 6-26 Effect of Sum and Diemer kernel at 370 s-1 on PSD Figure 6-27 Effect of Sum and Diemer kernel at 960 s-1 on PSD Figure 6-28 Effect of Sum and Diemer kernel at 1342 s-1 on PSD It can be seen from Figure 6-26 and Figure 6-28 that Diemer kernel gives accurate results at each process time interval. However from Figure 6-27 a slight under prediction of particle sizes is observed at 6 hrs. Similarly, the Diemer kernel indicates the exact predictions with the experimental data.

6.2.1.5 Effect of Process parameters on particle size distributions

sizes along with redispersion time. The applied shear rate used for experiments is =370, 623, 960, 1342, s-1 equal to 500, 750, 1000, 1250 min-1 of number of revolutions per minute (see Table 4-2).

According to the standard condition for synthesis of titanium dioxide nanoparticles via the sol-gel process, the large particles perceived at the initial stage of the experiment are due to the primary particle agglomeration. Figure 6-29 shows particle size frequency distribution q3(d) at 0, 10 and 50 minutes of redispersion time. There is a shifting of distribution to the left as time passes, indicating that smaller particles are being produced and induced by shear rate . The distributions continue to shift until the size of particles reaches a steady state.

Examples of graph are only taken for shear rate =1342 s-1, which give clear view.

Figure 6-30 compares cumulative particle size distribution in volume basis Q3(d) from different shear rates [ =370 s-1; 623 s-1; 960 s-1; 1342 s-1] at the initial time of redispersion (10 minutes). The same pattern of shifting distribution is observed through whole time of redispersion, not just at the initial time.

Influence of shear rate on particle size distribution The median is defined as d50,3 or d(0.5) in volume basis. This is the value of particle size which divides the population exactly into two equal halves. There is 50% of the distribution above this value and 50% below. Terms d10,3 denote that there are only less than 10% of particle having this diameter value, while d90,3 denote that majority of population (90%) lay before this diameter value.

Mastersizer 2000 (MS 2000) was used at initial time of experiments of total 10 hours, measuring samples every 10 minutes. Characterization was being made by stating particles diameter in d10,3, d50,3, d90,3.

For all characterized diameter (d10,3, d50,3, d90,3) was observed at the beginning of the experiment due to agglomeration process. The purpose of applying shear rate is to create a condition where the velocity gradients of fluid bring the particle close enough to collide. The colliding session could end in agglomeration of particles or repulsion of particles depending on the value of the repulsive interactions between particles. Agglomeration may continue to form large, porous, and open structures agglomerates.

This Figure 6-31, Figure 6-32 and Figure 6-33 show the dependency of particle sizes upon applied shear rates at specific time chosen (varies on each graph). Particle sizes are characterized using d10,3, d50,3, d90,3 for applied shear rates =370, 623, 960, 1342 s-1.

**Particle Sizes during Redispersion Time, t=300 minutes**