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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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Metal alkoxides are often dissolved in organic solvents before hydrolysis is performed.

Alkoxides are compounds with chemical formula M (OR)Z formed as a result of reactions between metal M and alcohol, ROH. The relative performances of the alkoxides are studied by (Danijela Vorkapic and Themis Matsoukas 2000). The temperature is maintained constant throughout the process. Most commonly used solvents are parent alcohols, which have the same number of carbon atoms as the metal alkoxide. However, it should be noted that solvents are often not chemically inert toward metal alkoxides and that their reactivity can be easily modified by changing the solvent (Harris and Byers 1988; Nabavi, Doeuff et al. 1990).

The alkoxides does not have a significant influence but Titanium isopropoxide is preferred over others because of its high reactivity, and low electronegative value of titanium. Surfactant based Titania nanoparticles For the synthesis of surface stabilized TiO2 nanoparticles, titanium tetra isopropoxide (TTIP) was used as precursor, nitric acid as stabilizer and different surfactants like PEG, EG and NaCl are used in following section as shown in Table 4-8.

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Synthesis of surface stabilized TiO2 nanoparticles Titanium dioxide nanoparticles have been prepared in the laboratory by sol-gel processing in solution prepared by using titanium tetra isopropoxide (TTIP) (Ti(OC3 H7)4) is used as a precursor, Nitric acid (HNO3) as stabilizer as shown in Figure 4-11 and different surfactants such as Polyethleneglycol(PEG) (H(OCH2CH2)nOH), Ethylene Glycol (EG) (HOCH2CH2OH) and Sodium Chloride (NaCl). For generating titanium dioxide nanoparticles, the procedure is as follows.

A specified amount of 0.1 M HNO3 (90 ml) is placed into the batch reactor. Then in separate experiments, 50 ml of surfactant (PEG, EG and NaCl with concentration of 0.1 M) was measured and added to the HNO3 in the reactor. The organic precursor titanium tetra isopropoxide TTIP (9.7 ml) was also measured with the syringe and needle. Then organic precursor was added to the heated solution under stirrer operated at 500 revolutions per minute (500 rpm). An electronic stirrer equipped with water bath and a temperature measuring device was used for homogenizing the solution. Operation temperature of 50 oC was adopted for this investigation. The reactor was inserted into the set up and started. The precursor was introduced after the system attained 50oC operating temperature.

Precipitation is observed to be occurring immediately due to the presence of dilute nitric acid in the reaction mixture. Temperature is maintained at 500C for the rest of the redispersion reaction, accordingly optimal reaction conditions for the titanium dioxide nanoparticles synthesis. Precipitation reaction started instantaneously and the solution was conditioned by stirring continuously for a period of 24 hours at 500C (Opoku-Agyeman 2008).

Table 4-9 below shows the average particle size (d50,0) of titania particles synthesized with different surfactant and stabilizer concentrations, 9.7ml titanium tetra isopropoxide at 500 C at various measurement periods (conditioning times).

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In this section, three different surfactants were used for the synthesis of monodispersed spherical titania particles of variable sizes. The particle size distributions were measured by the dynamic light scattering technique. While this chapter deals with the synthesis of silver and titanium dioxide nanoparticles by various chemical methods, the subsequent chapter talks about population balance modeling.

Chapter 5 Population Balance Modeling

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5 Population Balance Modeling This chapter provides a general overview of different population balance models for particulate processes generating nanoparticles. The problems with existing numerical techniques for solving population balances are discussed here. These models are called Population Balance Models (PBM), describing the dynamics changes in the properties distributions when the conversion terms are known. In this chapter, we particularly consider agglomeration and disintegration processes for titanium dioxide nanoparticles.

5.1 Introduction

P opulation balances is the most frequently used modeling tool to describe and control a wide range of particulate processes like comminution, crystallization, granulation, flocculation, protein precipitation, aerosol dynamics and polymerization. An extensive review of the application of population balances to particulate systems in engineering is given by (D.Ramkrishna 2000). In process modeling, mass and energy balances are essential tools to describe the changes that occur during the physico-chemical reactions. With particulate processes, an additional balance is required to describe the changes in the particle population during the process (McCoy 2002). The terms of the population balance can be included with birth and death of the members, which equally happen in the system for material and energy balances. Furthermore, there is a deviation in population of the member caused by the aging process. It can happen by means of one age group to the other, which is internal to the system.

All in all based on principle, the population balance concepts is on the wide range categories and the system utilizations. The dynamic behavior of the particle size distribution undergoing simultaneous agglomeration and disintegration is given by (D.Ramkrishna 2000) cn (t, x) 1 x     (t, x  y, y ) cn (t, x  y ) cn (t, y )dy  cn (t, x)   (t, x, y ) cn (t, y )dy t 20 0    b(t, x, y ) S (t, y ) cn (t, y )dy  S (t, x) cn (t, x). 5.1 x The term cn (t, x) represents the number concentration of particles with volume x at time t.

The first term on the right hand side of the Eq. 5.1, represents the birth of the particles of volume x as a result of the binary agglomeration of smaller particles of volumes ( x  y) and y. The term 1/2 prevents the double counting of collisions of both particles. The second term describes the disappearance (-) of particles of volume x by binary agglomeration with any other particle y to larger particles ( x  y). The second term is called the death term due to aggregation. Factor  ( x, y) is known to be agglomeration kernel and it is symmetric, i.e.

 ( x, y)   ( y, x). The last two terms appear due to disintegration which is called the birth and the death terms, of the particles of volume x, respectively. The disintegration function b(t, x, y) is the probability density function for the formation of particles of volume x from larger particle of volume y. The selection function S (t, y ) describes the stressing rate at which particles of volume y are selected to disintegrate. Our system of interest consists of titanium (IV)-oxide nanoparticles, which are continually being created and destroyed by processes such as agglomeration and particle disintegration. The phenomelogical treatment of such disintegration and aggregation processes is of prime interest in the population balance modelling of our system (White and Ilievsky 1996). The four mechanisms governing the basic processes are depicted in Figure 5-1

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5.2 Recent survey In 1916, the eminent Polish physicist Marian von Smoluchowski proposed a theory of aggregation that uses the rate equations to describe the microscopic processes of diffusion, collision and irreversible coalescence of multiparticle aggregates. The main parameters of the equations are the rate constants, which determine how various kinetic processes take place.

Once these are supplied, the theory predicts the time-dependent cluster-size distribution (Smoluchowski 1916).

However, the assumptions that the collision efficiency factor is unity and the collisions involve only two particles, are invalid in reality. Further (Camp and Stein 1943) attempted to develop the Smoluchowski‟s approach taking into account the three-dimensional fluid motion. Moreover, (Kramer and Clark 1997) identified two errors in the Camp and Stein model while moving from 2-D to 3-D flow but in practice had little effect since the real-life aggregation processes are not due to laminar flow.

DLVO theory accounts for the combined effect of the electrostatic repulsion and the Van der Waals attraction between two particles, which Smoluchowski did not account for. A comprehensive outlook of the recent developments in this field is given by (H.Kihira and E.Matijevic 1992).

(L.W.Casson and Lawler 1990) proposed a cascade model which states that the collisions between particles are promoted by eddies of a size similar to that of the colliding particles and this fits the experimental data. They stated that the energy used in mixing for the preparation of large eddies is ineffectual. A similar conclusion is reached by (Gregory 1981; Han and Lawler 1992) who modelled the aggregation of a destabilised, monodispersed colloid in laminar tube flow. The assumptions are valid only in the initial stages of aggregation before larger aggregates are involved in the collisions. (Stratton 1994) defined the particle size class as a geometric series i.e.1, 2, 4, 8, which is able to reduce the number of differential equations required to characterise the aggregation kinetics over a given range of particle sizes.

In a study of the breakage (disintegration) kinetics (Calabrese, Wang et al. 1992) proposed that the Fibonacci series as they found the lack of detail offered by the geometric series.

(Delichatsios and Probstein 1974) utilized the self-similarity phenomenon to assist in the calculation of the aggregation of the latex particles in the turbulent flow. (Koh, Andrews et al.

1986) and (Spicer and Pratsinis 1996) also reported self-similarity. (Spicer and Pratsinis 1996a) attributed the nature of this self-similarity to the particular breakage mechanism during mixing. (Fair and Gemmell 1964) showed the importance of breakage in the aggregation modelling, and the effect of the different break-up assumptions on the aggregation model.

(Costas, Moreau et al. 1995) simulated particle aggregation and breakage based on a series of simplified kernels. (Peng and Williams 1993) proposed a breakage model setting the rate of breakage in proportion with the floc size. Similarly, (Spicer and Pratsinis 1996a) proposed a breakage model where the rate terms this time were assumed to be proportional to both the floc size and the shear rate.

(Parker, Kaufman et al. 1972) studied the activated flocculation process using the model to describe the changes of the settling characteristics. However, the model did not allow the overall modelling of the settler. It only provided information about primary particles in the supernatant (overflow) and effluent (underflow) suspended solids. In fact the sludge can be viewed as a segregated population of individual flocs even though they are actual lump biophase. The conversion terms are usually given as aggregation and redispersion (Nopens, Biggs et al. 2002). They consider the flocs size as the floc property and the number distribution based on floc size c n becomes

5.2dcn = Agglomeration- Disintegration dt

The main difference between Parker‟s models & PBM is the changes in the complete particle size distribution. It is not considered only the fraction of the primary particles. The PBM has been applied to various processes which are dealing with the particle or droplet populations.

In 2000, Biggs introduced another description to explain the activated sludge flocculation process. He showed the PBM based on the aggregation model firstly led by (Hounslow, Ryall et al. 1988). The main keywords for the aggregation and disintegration process are „birth‟ and „death‟ of the flocs of the certain size. The number distribution of particle volumes vi due to the four mechanisms of the two processes can be given by (Hounslow 1990; Nopens, Biggs et al. 2002; Ding, Hounslow et al. 2006)

5.3 dcn =BAgg. -DAgg. +BDist. -DDist.. dt

The aggregation births BAgg and aggregation deaths DAgg in the above equation are given by (Hounslow, Ryall et al. 1988). In order to get the solutions of such an integro-partial differential equation, several numerical schemes are available based on space discretization.

The discretization divides the particle size range into a certain number of classes, which are represented by floc size and volume.

5.3 Kinetics of the Simultaneous Agglomeration and Disintegration Sub-Processes Process engineers produce particulate materials such as powders and slurries by various particulate processes such as milling, flocculation, precipitation and crystallization etc. In these processes, the dispersed phase contains particles whose properties change in time and space. It interacts with the continuous phase (air or liquid) which may be stationary, or in motion, through mass transfer or chemical reactions.

For example, particles may become smaller via breakage due to mass transfer or chemical reactions with the continuous phase. Similarly, the particles may become larger via aggregation or growth due to mass transfer and chemical reaction with the continuous phase.

In general, the precipitation and crystallization processes consist of simultaneous aggregation-disintegration processes, which means, the formed particles are continuously agglomerated and disintegrated into the primary particles again.

5.3.1 Agglomeration Sub-Process

Aggregation or agglomeration is a process where two or more particles agglomerated form a large particle. The total number of particles reduces in an aggregation process that shifts the particle distribution towards larger sizes while mass remains conserved.

Agglomeration also may reduce the particle surface area for condensation and/or chemical reaction. In general agglomeration phenomenon is very common in nature. For example formation of snow flocs from a cloud of very fine ice cryptals. They are used to form larger flocs falling due to the gravitational action. Coalescence occurs between bubbles or droplets in a variety of dispersed phase systems in industrial processes, like waste water treatment, food processing, and clinical diagnostics.

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