Chapter I - Introduction and thesis objectives
II.2 Instrumental methods
The Coulter counter is a technique to determine the size distribution of particles by measuring the variation of impedance with electrodes situated before and after an orifice in which particles are going through as shown in Fig. 9.
Fig. 9: Schematic overview of a Coulter Counter.
This variation of impedance is proportional to the volume displaced by the particle passing through the aperture (Eq. 21) and the time dependent intensity of the pulse measured by the instrument is then related to the equivalent spherical size of the particle.
3 1 21 where ΔR represent the change of resistance (similar to impedance but for direct current), d the diameter of a sphere, D the diameter of the aperture, and ρ0 and ρ the resistivity of the fluid in the absence of particle within the orifice and the resistivity in the presence of a particle within the orifice, respectively.
This high resolution and accuracy counting technique has the benefit to be unaffected by the particle intrinsic properties (shape, refractive index, etc) and able to provide size distribution for particles in the range 0.4 to 1'200 μm (by using tubes with different aperture diameters).
This technique was used in this work to investigate the influence of TiO2 ENP concentration on the agglomeration kinetic rate of latex particle (1 μm) by measuring the decrease number of latex particle monomers as a function of time (Chapter III).
II.2.2 Dynamic light scattering and laser Doppler velocimetry
Dynamic light scattering (DLS) is an instrumental technique to determine the size distribution of particles ranging from 1 nm to 10 μm. The time dependent fluctuation of the intensity of the light scattered by the particles undergoing Brownian motion is measured. The particle translational diffusion coefficient (D), which is determined by the help of a correlation function, is then related to the particle hydrodynamic diameter (dh) via the Stokes-Einstein equation (Eq. 22) with assumption of spherical particle and no interaction.
3 22 where kB represent the Boltzmann constant, T the absolute temperature and η0 the solvant dynamic viscosity. The schematic overview of a DLS instrument is shown in Fig. 10.
Fig. 10: Schematic view of a DLS instrument.
To access to a number size distribution, as DLS determines an intensity size distribution, knowledge on the material properties, such as the refractive index and adsorption, and application of Mie's approximation is needed (Mie 1908).
DLS has many advantages such as high precision, large dynamic and concentration range, low sample volume needed and short analysis time. Nevertheless its main drawback is the low resolution in comparison to some other instrumental techniques (nanoparticle tracking analysis, differential centrifugal sedimentation, etc) to determine particle size distribution as the intensity of the light scattered by the particle is proportional to the particle diameter at the power six (I ∝ d6). This biases results towards larger particles (or agglomerates) size, and is thus not very adequate for heterogeneous and polydispersed samples.
Another very useful information delivered by some light scattering instruments, such as the one used in this thesis work, is the possibility to measure the electrophoretic mobility, by laser Doppler velocimetry, to determine the ζ potential which is the potential at the shear plane as shown in Fig. 11. Such information is of high importance when investigating the stability of a dispersion as electrostatic interactions are playing a key role on the resulting particle stability.
Fig. 11: Double layer scheme adapted from Malvern Instruments.
The ζ potential is obtained, by measuring the electrophoretic mobility when analyzing the scattered light intensity fluctuation (variation of phase) of charged particles moving under the application of an electric field and then using the Henry equation:
where UE represents the electrophoretic mobility, ε the dielectric constant, ζ the zeta potential, η the dynamic viscosity and f(κa) the Henry's function. The Henry's function can be approximated depending on the particle size and the properties of the medium of dispersion as shown in Fig. 12. The Schmolukovski approximation is applied when the double layer thickness is small in comparison to the particle size, whereas the Hückel approximation is used when the double layer thickness is large in comparison to the particle size.
Fig. 12: Hückel and Schmolukovski approximations used for the determination of the Henry's function.
These techniques were used throughout this work when investigating the influence, on the stability of TiO2 ENPs, of the aquatic system properties (pH (Chapter III, IV, V, VI and VII), ionic strength (Chapter V), electrolyte concentration and valency (Chapter V), NOM concentration and properties (Chapter IV, V, VI and VII)).
II.2.3 Electron microscopy
In order to access particles (or agglomerates of particles) size and morphology, transmission electron microscopy (TEM) and scanning electron microscopy (SEM) are powerful tools as having high resolution of 0.1 nm and 1 nm, respectively. The schematic overview of TEM and SEM are shown in Fig. 13.
Fig. 13: Schematic overview of TEM (a) and SEM (b).
In TEM an electron beam produced by the thermoionic emission of a heated tungsten cathode is concentrated on a sample with the help of condenser lenses. The electrons are then adsorbed, diffused or transmitted by the sample deposited on a grid. The transmitted electrons are collected by electromagnetic lens-objective and projected onto a CCD detector. The quantity of transmitted electrons is dependent on the electronic density of the analyzed material. For low electronic density substances, such as NOM, a pretreatment with a staining agent is needed to enhance the material contrast. During SEM analysis the focused electron beam is scanning the surface of the sample, coated with conductive material, and a detector collect the secondary electrons reflected by the sample surface whose intensity are dependent on the electron density of the illuminated material. For both electron microscopy techniques, information on the material properties (elementary composition) can be obtain when working with instruments equipped with dispersive x-ray spectroscopy devices. Such microscopy techniques are very useful to characterize the material morphology but the sample preparation is critical to optimize the material concentration, and avoid artifacts such as the agglomeration of material due to capillary effects during the drying process.
SEM analysis were used to determine the distribution of TiO2 ENPs onto the surface of micron-sized latex particles (Chapter III) whereas TEM analysis was used to confirm dispersed and agglomerated state of TiO2 ENPs which is pH dependent, as well as the influence of NOM on TiO2 agglomerate fragmentation (Chapter IV).
II.2.4 Isothermal tiration calorimetry
Isothermal titration calorimetry (ITC) is an instrumental technique to access all interaction thermodynamic parameters and information on mechanisms of interaction in a single experiment. Indeed important thermodynamic parameters such as the binding enthalpy (ΔH), the change of Gibbs free energy (ΔG), the change of entropy (ΔS), but also information on the affinity binding constant (Kb) and reaction stoichiometry (n) can be either determined or calculated. The instrument measures the heat flow needed to maintain a small difference of temperature constant between two cells, a reference cell containing the same solvant used as for the reaction and the reaction cell in which a macromolecule is titrated by a ligand, located in an adiabatic jacket (Fig. 14), to provide a thermogramm which represents the heat flow recorded by ITC as a function of time as the titration (successive injections of ligand) is going on.
The heat exchange (obtained by integration of heat flow per mol of injectant) as a function of ligand over macromolecule molar charge concentration is then fitted with a mathematic model to determine ΔH, Kb and n. The determination of these parameters is then used to calculate ΔG and ΔS with the following equations:
Δ Δ Δ Δ
23 where R and T represent the gas constant and the absolute temperature respectively.
Fig. 14: Schematic overview of ITC.
The advantage of ITC is not only to determine thermodynamic and reaction but also to have a better understanding on interaction processes (agglomeration mechanisms such as micelle formation, coacervation, polymer bridging, etc) due to the high sensitivity and reproducibility of the results obtained with such a technique. One disadvantage of ITC is the high compound concentration needed (especially for the ligand concentration) in order to obtain an optimal response signal. It can be a problem when working with costly products or products difficult to synthesize. Moreover the heat exchange determined by ITC corresponds to the sum of the heat associated to all interaction processes (dilution, precipitation, hydrolysis, redox, etc) and it is also not possible to differentiate the forces that are involved during the association process (hydrophobic interactions, H-bonding, electrostatic interactions, van der Waals interactions, etc).