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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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Colloidal particles are commonly found distributed as a separate phase; the disperse phase, into another substance or substances; the dispersant or continuous phase. In this sense, colloidal systems are heterogeneous material systems. Either of the two phases can be in any of the states of matter: solid, liquid, or gas. The colloidal particles are designed by considering various criteria related to the targeted applications such as particle size distribution, surface polarity, surface reactive groups, and hydrophilic-hydrophobic balance of the surfaces.

2.5 Interparticle Forces

There are three types of intermolecular forces acting between molecules in the colloidal system. Those forces are van der Waals attraction forces, electrostatic repulsion forces, and steric interaction. Together these three forces are used to control the agglomeration and disintegration in our particulate systems as following.

2.5.1 Van der Waals Attraction Forces

The existence of a general attractive interaction between neutral atoms was first postulated by Van der Waals in 1873, to account for certain anomalous phenomena occurring in non-ideal gases and liquids. When nanoparticles are dispersed in a solvent, van der Waals attraction force and Brownian motion play an important role. The influence of gravity becomes negligible in this case. In this Thesis, special emphasis is laid on nanoparticles, although particles in micrometer sizes have similar characteristics. In addition, we will focus on spherical nanoparticles. Van der Waals forces are weak forces and become significant only at a very short distance. Brownian motion ensures that the nanoparticles collide with each other all the time. The combination of van der Waals attraction force and Brownian motion would result in the agglomeration and disintegration of the nanoparticles.

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Figure 2-1 Van der Waals interactions between two particles Van der Waals interaction between two nanoparticles is the sum of the molecular interaction for all pairs of molecules composed of one molecule in each particle, as well as to all pairs of molecules with one molecule in a particle and one in the surrounding medium such as solvent.

van der Waals interactions between two spherical particles of radius r, separated by a distance d, as given in Eq.2.1 and illustrated in Figure 2-1 gives the attraction potential (P.C.

Hiemenz 1977).

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Where; Va is the attraction potential energy and d is surface distance between two equal sized spherical particles.

2.5.2 Electrostatic Repulsion Forces One of the interactions between particles is directly associated with the surface charge and the electric potential adjacent to the interface. The electrostatic repulsion between two particles arises from the electric surface charges, which are attenuated to a varied extent by the double layers. When two particles are far apart, there will be no overlap of two double layers and electrostatic repulsion between two particles is zero. However, when two particles approach one another, double layer overlaps and a repulsive force develops. An electrostatic repulsion between two equally sized spherical particles is given by Eq.2.3

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Where   0r r is the dielectric constant of the solvent,  is the permittivity of vacuum, r is the particle radius, π is the solvent permeability,  is a Debye-Hückel parameter and  is the zeta potential.

2.5.3 DLVO theory In 1945, Derjaguin, Landau, Verwey and Overbeek developed a theory to explain the aggregation of aqueous dispersions quantitatively. This theory is called DLVO theory (B.D.Derjaguin 1939; L.D.Landau 1941). The theory describes the forces between charged surfaces interacting through a liquid medium. It combines the effects of the van der Waals attraction force and the repulsive electrostatic double-layer force. These forces are sometimes referred to as DLVO forces. The stability of the colloidal suspension is treated in terms of energy changes by taking whenever particles approach one another. For instance stabilization can be considered in the case of relation of adding electrolyte into the suspension. The attractive and repulsive forces are assumed to be additive. And they are also combined to give the total energy of interaction between particles as a function of separation distance. DLVO theory suggests that the stability of a particle in solution is dependent upon its total potential energy function VT. Theoretically, the total potential energy is expressed as sum as seen below 2.4 V =V +V +V T A R S Where VS is the potential energy due to the solvent, usually it makes only a marginal contribution to the total potential energy over the last few nanometers of separation. Much more important is the balance between attractive potential VA and the repulsive potential VR.

They potentially are much larger and also operate over a much larger distance. The potential energy due to the solvent is negligible and therefore neglected.

More generally, DLVO theory proposes that the stability of a colloidal system is determined by the sum of these Van der Waals attractive (VA) and electrical double layer repulsive (VR) potential that exist between particles as they approach each other due to the Brownian motion they are undergoing.

V =V +V 2.5 T A R van der Waals attractive potential (VA) promote coagulation while double layer potential (VR) stabilizes dispersions. Taking into account both equations as 2.2 and 2.3, we can approximate total energy between the particles. Due to the total energy, when two particles come close to one another, the explanation of the energy potential can be expressed by using the distance between the particles. The relationship between the interaction energy potential and the separation distance of the particles can be explained with the help of stabilization of the system shown in Figure 2-2. This Figure 2-2 shows the van der Waals attraction potential, electric repulsion potential, and the combination of the two opposite potentials as a function of distance from the surface of a spherical particle (Parfitt 1981). VA increases rapidly as the particles approach each other, while VR decreases somewhat more slowly. At a distance far from the solid surface, both Van der Waals attraction potential and electrostatic repulsion potential reduce to zero. In general, the total potential energy curve passes through a maximum, Vmax, which constitutes an energy barrier against the adherence of the particles. As the particles approach one another, they may overcome Vmax, the repulsive barrier, after which the particles are attracted strongly and the potential energy falls rapidly into the primary minimum. The lower the height of Vmax, the more are the particles, which can potentially come close enough to adhere.

Figure 2-2 Schematic representation of the interaction potentials in the approach of the Particles (Elimelech, J.Gregory et al. 1995) The DLVO theory considers only dilute systems in which contacts between particles occur occasionally. However, most industrial applications of colloidal dispersions require concentrated suspensions. Another method of controlling the stability of particles is based on the steric and electrostatic stabilizations of the particles. Details of both methods are discussed in previous sections.

2.5.4 Steric Interaction

Adsorption is another kinetic mechanism happening during the aggregation process. One of the important roles of aggregation phenomena is played by adsorbed layers. The steric interaction comes to the colloidal particulate suspension when there is a large amount of polymeric concentration. These polymers make the particle surface become or even overwhelm with the adsorbed layers. As the particles move closer to each other, the layers come into contact involving the interpretation of the hydrophilic chains. If these chains are hydrated, these overlapped layers would get some dehydration. And also it increases in both the free energy and the repulsion between particles.

2.6 Colloidal Stabilization

Stability of colloidal particles means the ability of the particle in suspension stays in the solution as long as possible without any disturbance in both physical and chemical way.

Stability of dispersion is one of the most important physical properties required for industrial suspension products such as paints and inks. The dispersion stability governs the ease of production; storage stability, application properties, and the performance of finished products.

There are two fundamental mechanisms that affect dispersion stability: electrostatic stabilization and steric stabilization. Types of colloidal stabilization are shown in Figure 2-3.

Each mechanism has its benefits for particulate systems (Napper 1983).

Figure 2-3 Types of colloidal stabilization 2.6.1 Steric Stabilization Steric stabilization, well known as polymeric stabilization, is a method widely used in stabilization of colloidal dispersions. It is less well understood as compared with electrostatic stabilization method. It is a simple process requiring just the addition of a suitable polymer.

This involves polymers added to the system adsorbing onto the particle surface and causing repulsion. Whenever the colloidal suspension has a polymer molecule in the solution, the particle in the suspension is adsorbed by the polymer on its surface as a layer. The polymer molecule on the particle surface categorizes into two types- homopolymer and copolymer (graft copolymer and block copolymer). The resulting polymer layer masks the attractive force and also provides a repulsive force. This is what we know as “Polymer-induced stability”. The polymer induced stability is often referred to as steric stability. Steric stabilization of the colloidal dispersion is achieved by the long chain molecules of colloidal particles. When they approach to one another due to the Brownian motion, the limited interpenetration of the polymer chain leads to an effective repulsion stabilizing the suspension against flocculation.

2.6.2 Electrostatic Stabilization

An electrostatic interaction between charged particles, molecules and ions is the central theme of colloidal science. This stabilization occurs when there are charges on the surface of the particle. It is because the surface charge influences the distribution of nearby ions in the polar medium. It also concerns about a major aspect of the electrostatic stabilization of colloids.

The surface charge occurs whenever the different phases between solids and liquids in the colloid suspensions are in contact with each other in the polar medium. The stability depends on the balance of particle interaction, between attraction and repulsion forces. But the problem is that the configuration of particles inside the fluid is not as simple as anybody could imagine. Each particle consists of layers, containing ions with different signs. There are also interactions between ions and particles forming electrical double layers as in Figure 2-4.

Consider a negative particle inside the fluid as an example. The surface potential named as Nernst potential 0. The fluid contains ions with different signs and with particles called counter-ions (here, positive sign) and ion with the same sign called co-ions (here, negative sign). Because of the electroneutrality principle, counter-ions are attracted toward the particle surface. A part of these counter-ions called potential determining ions is adsorbed directly on the particle surface to form Stern layer. The Stern layer is a fairly immobile layer of ions that adhere strongly to the surface of the colloidal particle, which may include water molecules.

This layer has potentiality named Stern potential S. The rest of the counter-ions together with co-ions are in Brownian motion surrounded in the area of Gouy Chapman layer.

Counter-ions have the highest concentration near surface particles, However it is vice versa with co-ions. The area of shear plane exists between Stern layer and Gouy Chapman layer. It is the area where ions stick to particles, and move along with particles when an external electric field is applied, thus creating a phenomenon of electrophoresis. The electric potential at the surface of the shear that is relative to its value in the distant, bulk medium is called the  potential or the electrokinetic potential. The primary role of the electric double layer is to confer kinetic stability to the colloidal particles.

+ +

- + +

–  –  –

Figure 2-4 The electrical double Layer (ROTH 1991) The simplest quantitative treatment to the diffuse part of the double layer of a flat surface is given by Gouy and Chapman on the following assumptions.

 The ions in the diffuse part are point charges distributed according to the Boltzmann distribution.

 The surface is flat and of infinite extent and uniformly charged.

 There is only a single electrolyte, which is symmetrical and has charge number.

 The solvent influences the double layer only through its dielectric constant, which is assumed to have the same value throughout the diffuse part.

For the practical calculations here we used, the thickness of the electrochemical double layer is the Debye length δк the decrease of the potential to 1/e of the surface potential (Elimelech, J.Gregory et al. 1995)

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