Commercial granular and fibrous activated carbons have been studied for the removal of heavy metals from aqueous solutions. A wood based activated carbon (AUG WHK) and an activated carbon cloth (KoTHmex TC-66 C) based on polyacrylonitrile fibre as a precursor, were oxidised for different periods of time using nitric acid, ozone and electrochemical methods to introduce various acidic groups at the surface, thereby, enhancing metal binding capacity. Modified samples were subsequently studied for the specific removal of cadmium and mercury ions in solution and compared with the performance of a commercially available weak acid fibrous exchange material (Ecofil-Deco Ltd. K-4). Carbonaceous adsorbents were physically characterised by scanning electron microscopy, surface area and porosimetry (using N2 adsorption at 77K). There was a decrease in BET surface area betweenu ntreateda nd oxidised samples. Acid and electrochemically oxidised samples were completely stable although there was clear evidence of physical damage to ozone-oxidised carbons. Samples were also chemically characterised by pH titration, direct titration, X-ray photoelectron spectroscopy and elemental analysis. A significant increase in oxygen content was obtained after oxidation, which increased the total ion exchange capacity by a factor of approximately 3.3 compared to commercial as-received carbonaceous adsorbents. As the degree of oxidation increased, the point of zero charge was shifted to lower pH values, i. e. from 4.5 to 3.6. (Continues...).

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Ma thèse se situe à l'intersection de \textit {la théorie des groupes géométrique} et \textit{la théorie des groupes mesurée}. Une question majeure dans la théorie des groupes géométrique est d'étudier la classe de quasi-isométrie (QI) et la classe d'équivalence mesurée (ME) d'un groupe, respectivement. $L^p$-équivalence mesurée est une relation d'équivalence qui est définie en ajoutant des contraintes géométriques avec d'équivalence mesurée. En plus, QI est une condition géométrique. Il est une question naturelle, si deux groupes sont QI et ME, si elles sont $L^p$-ME pour certains $p>0$. Dans mon premier article, en collaboration avec R. Tessera, nous répondons négativement à cette question pour $p\geq 1$, montrant que l'extension centrale canonique d'un groupe surface de genre plus élevé ne sont pas $L^1$-ME pour le produit direct de ce groupe de surface avec $\mathbb{Z}$ (alors qu'ils sont à la fois quasi-isométrique et équivalente mesurée).Dans mon deuxième papier, j'ai observé un lien général entre la géométrie des expandeurs, defini comme une séquence des quotients finis ( l'espace de boîte) d'un groupe finiment engendré, et les propriétés mesurée theorique du groupe. Plus précisément, je l'ai prouvé que si deux <<espaces de boîte>> sont quasi-isométrique, les groupes correspondants doivent être <<mesurée équivalente uniformément >>, une notion qui combine à la fois QI et ME. Je prouve aussi une version de ce résultat pour le plongement grossière, ce qui permet de distinguer plusieurs classe des expandeurs. Par exemple, je montre que les expandeurs associé à $SL(m, \mathbb{Z})$ ne grossièrement plongent à les expandeurs associés à $SL_n(\mathbb{Z})$ si $m>n$. / My thesis lies at the intersection of \textit{geometric group theory} and \textit{measured group theory}. A major question in geometric group theory is to study the quasi-isometry (QI) class and the measure equivalence (ME) class of a group, respectively. $L^p$-measure equivalence is an equivalence relation which is defined by adding some geometric constraints with measure equivalence. Besides, quasi-isometry is a geometric condition. It is a natural question if two groups are QI and ME, whether they are $L^p$-ME for some $p>0$. In my first paper, together with R. Tessera, we answer this question negatively for $p\geq 1$, showing that the canonical central extension of a surface group of higher genus is not $L^1$-ME to the direct product of this surface group with $\mathbb{Z}$ (while they are both quasi-isometric and measure equivalent). In my second paper, I observed a general link between the geometry of expanders arising as a sequence of finite quotients (box space) of a finitely generated group, and the measured theoretic properties of the group. More precisely, I proved that if two box spaces' are quasi-isometric, then the corresponding groups must be `uniformly measure equivalent', a notion that combines both quasi-isometry and measure equivalence. I also prove a version of this result for coarse embedding, allowing to distinguish many classes of expanders. For instance, I show that the expanders associated to $SL(m,\mathbb{Z})$ do not coarsely embed inside the expanders associated to $SL_n(\mathbb{Z}$ if $m>n$.