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«By Yusuf Nur A thesis submitted to The University of Birmingham for the Degree of DOCTOR OF PHILOSOPHY School of Geography, Earth and Environmental ...»

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Whenever a suspension or pure liquid in a container is rotated around a central point, a centrifugal force, which can be 1000 times greater than the gravitational force is generated (Wallace, 1998). The effect of this force is to drive denser particles in the suspension away from the centre of the rotation toward the outside wall of the container and subsequently accelerate them to the bottom of the container as precipitate in the form of a pellet (Wilson and Walker, 2010). The top layer which is mainly the liquid and the suspended substances which are less dense than the liquid is called supernatant. The rate of sedimentation of the particles depends not only the magnitude of the centrifugal force and the diameter of the rotor driven by an electrical motor around a fixed axis but also the shape, size and density of the particles and viscosity of the liquid (Wallace, 2007). This means particles suspended in a same type of liquid can be separated according to their density by applying fractional centrifugation process. During this process, the size of the centrifugal force is altered through changing of the rotational speed of the rotor and in this way density separation of the components in the suspension is achieved. To compare different rotors, the amount of acceleration which they can provide is used instead of the rotational speed since rotors of the same speed will provide different acceleration and thus different centrifugal forces if their diameters differ from each other.

3.1.2 Transmission Electron Microscopy (TEM) Transmission electron microscopy was first invented and constructed by Max Knoll and Ernst Ruska in Germany in 1932 (Knoll and Ruska, 1932). It took only about four years

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lower limit of the resolution of light microscope which uses light waves to image objects was already achieved and scientific community seriously needed a much higher resolution for their researches (Knoll and Ruska, 1932). The resolving power of an optical instrument is its ability to separate two objects which are very close to each other. The resolution of the traditional light microscope depends on the wave length of the type of light rays used through the classical Rayleigh criterion (Inoue and Spring, 1997, Kapitza, 1994).

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Where δ is the distance between two objects, λ = is the wavelength of the light beam, µ is the refractive index of the medium (usually air, water or oil) and β is the half of the angular aperture of the lens. Given that the refractive index of certain medium and aperture of a lens of a certain microscope do not change during an experiment, the maximum resolution that can be achieved with light microscope is mainly determined by the wave length in the sense that the shorter the wave length of the light the higher the resolution which can be achieved.

Therefore, according to the aforementioned relationship, the highest theoretically possible resolution which can be achieved by conventional light (optical) microscope is around 0.2 mm (O'Keefe, 1956, Born and Wolf, 1999) as correctly predicted by Ernst Abbe in 1870.

In the case of the transmission electron microscope, electron beam is used for imaging of the objects under study and is accelerated through vacuum medium with refractive index equal to 1; the angular aperture is so small that the value of sin(β) can be approximated by the size of

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The wavelength of a beam of electrons is inversely proportional to its speed caused by the applied potential difference. In 1925 Broglie derived an equation showing this relationship (Equation 3-7) which can be used to calculate the wavelength of the electron beam accelerated in a certain predetermined electrical field.

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Where λ is the wavelength of the light and E is field strength. By substituting the value of λ from Equation 3-7 into Equation 3-6, we can calculate the theoretical resolution of the TEM.

TEM has normally much higher resolution than traditional light microscope due to the short wave length of the highly energetic electron beams used in the TEM to get images of the object under study. Modern high resolution TEM is capable of imaging the position of individual atoms in a crystal (Voyles et al., 2002, Singhal et al., 1997) with resolutions below angstrom scale (Nellist et al., 2004) while the resolution of light microscope is at the scale of micrometer. The source of the electron beams in the TEM is tungsten filaments cathode. The electrons are accelerated in a vacuum by potential difference varying from 40 to 100 KV depending on the type of TEM and are focused on the target sample by

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1996) and only transmitted fraction of electrons reach on the viewing screen which is coated with electron beam sensible fluorescent substances. It is on the viewing screen where bright dark images are produced depending on the intensity of the beam reaching on the areas of the image (Figure 3-1).

Figure 3-1: Schematic diagram of the basics of TEM(AtomicWorld, 2012) 3.1.3 Atomic Force Microscopy (AFM) Atomic force microscopy is one of the most popular and useful tools available for research community to image the surface of materials at the nanoscale. The precursor of the AFM, the so called scanning tunneling microscopy (STM) was only limited to study samples which

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1985 the AFM was proposed and invented by Binnig, Quate, and Gerber (Binnig et al., 1986). The main difference between STM and AFM is the fact that the first measures the tunnelling current between the tip and surface of the sample while the second instrument measures the force interaction between the tip and the sample (Meyer, 1992, Pool, 1990).

With the AFM, atomic resolution can be achieved (Mizes et al., 1987) and its possible that single atoms in both insulating and conducting materials can be imaged (Albrecht et al., 1988). Apart from the controller unit, the main parts of the AFM machine are cantilever with a very sharp tip made mainly from Si or Si3N4, the laser beam generator and photodiode detector (Jalili and Laxminarayana, 2004). During the imaging process with AFM, the interaction between the tip of the cantilever and the surface introduces the deflection of the movement of the tip. This deflection causes that the laser beam which was directed on the back of the tip is reflected into different position on a photodiode detector (Hutter and Bechhoefer, 1993) (see Figure 3-2 below).

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This upside down movement of the tip can be used to trace the surface of the sample and generate its topographic map (Basso et al., 1998). How the deflection of the cantilever is related to the Van der Waals attraction/ repulsion forces between the tip and the sample surface can be represented by Hook’s law (Dürig et al., 1986) (Equation 3-8 below) and illustrated in Figure 3-3 below.

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Where F is the force, Z is the deflection distance and K stands for the stiffness of the lever.

Figure 3-3: Interatomic force variation versus distance between AFM tip and sample(Jalili and Laxminarayana, 2004).

Reprinted with permission from copyright 2004 Elsevier.

Among the different modes of the AFM, the contact, non-contact and tapping modes are mostly applied in determining the size and the shape of the materials in the nanoscale (Dufrêne, 2002). These modes differ mainly in the distance between the tip of the cantilever and the surface atoms of the samples. In the contact mode the tip in contact with the surface

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touching atom (Blackman et al., 1990) while by non-contact AFM mode the cantilever tips oscillates near the surface of the sample and the change of this vibration caused by the interatomic forces is detected and translated into topographical images of the sample surface.

The distance between the tip and surface atoms in tapping mode is somewhere between the other two modes explained above and changes as the tip comes into contact with the surface of the sample under study. Due to its versatility, AFM has been applied in many branches of sciences including surface science, material science, nanoscience and biology (Butt et al., 2005, Yang et al., 2007).

3.1.4 Dynamic Light Scattering (DLS) Dynamic light scattering (DLS) also known as photon correlation spectroscopy (PCS) is one of the most applied measuring techniques used in determining the size of nanoparticles in liquid media(Berne and Pecora, 2000). This technique uses the scattering of light from particles in a liquid media. Due to the random Brownian motion of the particles caused by the bombardment of the continuous motion of the liquid media surrounding the particles(Tscharnuter, 2006).

The movement of the particles cause Doppler Effect to the wavelength of the incoming light and thus to the scattered light (Angus et al., 1969). The intensity fluctuation of the light scattered, which is related to the size of the particles, gives fluctuating speckle. A photon correlator continuously monitors the speckle fluctuation which can be used to calculate the time-dependent intensity correlation function (Berne and Pecora, 2000). The correlation

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of decay of the correlation function provides information about line width (Ѓ) of the scattering light which is related to the diffusion coefficient (D) through Equation 3-9 below.

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Where θ is the angle of scattering measurement, λ is the wavelength of the laser beam, 0 is the refractive index of the liquid media. The above two equation can be used to find the diffusion coefficient of the particles. By assuming that the particles are spherical in shape, we can use the classical Stokes-Einstein Equation 3-11 (Einstein, 1905) which provides a relation between diffusion coefficient of the particles in motion and their size radius.

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sample, KB is the distribution Boltzmann constant,  is the viscosity of the solvent and A is the radius of the spherical particles.

3.1.5 Zetapotential Apart from hydrodynamic diameter measurements described above, DLS instrument from Malvern is used to measure the electrophoretic mobility of the particles in an electric field which in turn can be used to calculate the Zetapotential of the samples by applying either Smoluchowski or Huckel Henry (Smoluchowski, 1903) equations depending on the nature of the media. Zeta potential is a good indicator of the repulsion forces between particles and is used to estimate the stability of nanoparticles in the media (Eilers and Korff, 1940). By nature, equally charged particles in a media tend to repel each other due to repulsive electrostatic force in contrast, there is also Van der waals attraction force between particles regardless their charge which mainly depends on the distance of the particles (Hamaker, 1937). It is the combined effect of these two opposing forces which determines whether particles aggregate or not as explained by the classical DVLO theory (Derjaguin, Landau, Verwey and Overbeek theory)(Deryagin and Landou, 1941, Verwey and Overbeek, 1948) which can be summarised in Equation 3-12 (Malvern, 2001).

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charges of equal sign on the particles, VA is the van der Waals attractive potential and VS is the solvent’s potential energy which is less important than the other two potential.

Since particles are in continuous movement due to the Brownian motion, they can come too close together if they have enough kinetic energy to overcome the effect of the repulsive forces and then Van der Waals forces pull particles together to form aggregates ( see Figure 3-4 below ) (Honigmann, 1970).

Figure 3-4: Repulsion and attraction potential as function of the distance from the charged particle(Honigmann, 1970) To understand the scientific meaning of zetapotential, consider of a negatively charged spherical particles in a dispersion media, the positively charged ions in the media will be attracted to the surface to counter-balance the charge. This generates potential difference around the particles which can be illustrated in Figure 3-5. Since the particle is in Brownian motion, the strongly attracted positive ions will move with the particles forming the stern or stationary layer while less bonded ions will form a dynamic diffusive layer. The imaginary

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the electrical potential difference between this plane and a point in the bulk media far away from the negatively charged particle is defined as zetapotential. As mentioned earlier in this section, Zeta potential cannot be measured directly from the solution but it is calculated from the electrophoretic mobility (EPM) which is the rate of migration of charged particles in stationary liquid medium due to the effect of an applied external electric field. DLS instrument has ability to measure the EPM by filling the NPs solution in to a cell and applying external electric field. How fast particles move is directly proportional to the strength of the external applied electric field, the viscosity of the liquid medium and the charge and the size of the particles. There are two opposing forces acting on these moving particles which are the electric field force and the drag forces due to the viscosity of the liquid. When these two forces are in equilibrium the particles gain steady speed. Equation 3-13 below shows the relationship between the velocity of the particles and the strength of the electric field.

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field in V/cm and µ is the electrophoretic mobility and its unit is thus cm2/Vsec. Henry equation establishes the link between the zeta potential and elctrophoretic mobility (Henry, 1931).

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Where µE is the elctrophoretic mobility, ε stands for dielectric constant, Z is the zeta potential,  is the viscosity of the media, K is Debye-Huckel constant and fk(a) is the Henry function. In most practical situations, where particle size is bigger than the thickness of the double layer and there is sufficient electrolyte concentration, simplified Marian Smoluchowski’s approximation (Smoluchowski, 1918) with fk(a) = 1.5 can be used instead to calculate zeta potential from elctrophoretic mobility using Equation 3-15.

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