This thesis is concerned with the exploitation of carbon paste electrodes and heterogeneous mixtures, such as emulsions or solutions only containing miceller structures, for the accumulation or trapping of analytes of interest and their subsequent electroanalysis. In Chapter 4, the reduction of oxygen is studied in aqueous solutions of pH 6.22 - 8.01, at a carbon paste electrode fabricated from dioctyl phthalate (oil) and graphite. Two two-electron voltammetric waves are usually seen on carbon electrodes, associated with the formation of hydrogen peroxide and water, respectively. However, an additional signal is seen on the carbon paste electrode, which is attributed to the initial formation of the superoxide radical anion, O2.-. Data is presented to show that the predominant source of oxygen for this reaction is that dissolved in the carbon paste material, rather than in the aqueous solution, and that the superoxide is likely formed at the graphite/oil/water triple phase boundary. Kinetic and thermodynamic parameters for the O2/ O2.-redox couple are reported. In Chapter 5, a novel electrochemical procedure is developed that allows the amount of oxygen in cetyltrimethylammonium bromide (CTAB) micelles to be effectively titrated and hence the oxygen solubility in the micelles to be determined. The electroreduction of oxygen is studied in aqueous phosphate buffer solutions, using a microelectrode. The addition of micelle forming surfactants to solutions pre-saturated with oxygen leads to a reduction of the oxygen signal allowing the oxygen uptake by the micelles to be measured. For CTAB micelles, a concentration of oxygen of 6.7 ± 0.72 mM was observed, and shown to remain constant with increasing CTAB concentration in the bulk solution. The method has general applicability. In Chapter 6, the electrochemistry of nitroblue tetrazolium chloride (NBTC) is investigated in aqueous solutions of pH 6.97, on a glassy carbon macroelectrode and at a carbon fibre microelectrode; the adsorption properties of the electrochemically produced diformazan are also studied. A reduction and overall mechanism is proposed based on the analysis of the obtained results. A carbon paste electrode, fabricated using dioctyl phthalate and graphite powder, is then used as a non-enzymatic sensor. The sensitivity of the diformazan oxidation signal to the presence of superoxide is taken advantage of to detect superoxide. The paste electrode is first immersed in aqueous superoxide solutions. It is subsequently equilibrated with NBTC, by immersing it into aqueous NBTC solutions. The reduction of NBTC (by superoxide) thus takes place in the paste so allowing the quantification of the superoxide in the aqueous phase by means of the diformazan oxidation signal. A value for the practical limit of detection of 0.059 nM is obtained. In the final chapter (Chapter 7), a carbon paste recipe is optimised for the detection of phenols via a procedure in which phenols are allowed to accumulate in the paste via transfer from an aqueous solution prior to electro-oxidation. Importantly, the use of such paste electrodes is shown to substantially overcome the "self-passivating" behaviour of the phenol oxidation which usually constrains the electrode process to low concentrations and single-shot experiments. Here, 4-phenoxyphenol could be detected in the range from 2.5 to 40 μM, phenol from 2.5 μM to 60 mM and 4-methoxyphenol from 5.0 to 40 μM. The electrodes were re-usable without surface renewal for phenol concentrations up to 1.0 mM. The use of a bulk phenol solution for pre-concentration via absorptive uptake into a bulk phase followed by electrochemical quantification represents a new form of electroanalysis which is here termed "absorptive stripping voltammetry". This novel approach is complementary to "adsorptive stripping voltammetry", where accumulation ii occurs via adsorption on an electrode surface. The value of absorptive stripping voltammetry is demonstrated through the application of the approach to the sensitive detection of Δ9-tetrahydrocannabinol (THC) in both aqueous solutions of pH 10.0 and in synthetic saliva solutions; an optimised carbon paste electrode, fabricated from graphite powder and mineral oil, is here utilised. Practical limits of detection of 0.50 μM and 0.10 μM are determined for THC in stationary and stirred aqueous borate buffer solutions, respectively, while THC concentrations as low as 0.50 μM are detected in synthetic saliva solutions. "Absorptive Stripping Voltammetry" can thus be reliably applied to the detection of Δ9-tetrahydrocannabinol, after suitable optimisation of the assay.