where [H⁺]₀ signifies the proton concentration at the surface of the dissolving and reacting solid.

The flow cell experiments were carried out on macroscopic samples of solid calcium carbonate. In order to probe the interfacial kinetics we had to flow the solution very fast otherwise the solid dissolved at a rate simply controlled by the rate of mass transport to the calcite surface. Indeed previous measurements - in static solutions - had concluded that the reaction was 'diffusion controlled'. By flowing we had outrun the transport and could probe, for the first time, the interfacial kinetics of the surface reaction! We then considered the implications of our data for the dissolution of calcite particles; considering them for simplicity as reacting spheres and supposed that when added to a lake - as in the liming activity - that these would slowly descend to the bottom of the lake with a steady terminal velocity. The rate of mass-transport to the surface of a solid 'falling sphere' has been addressed by chemical engineers and is characterised by a mass-transport coefficient, [3] k_MT, where

For particles of small radius, r, the transport is essentially purely diffusional and

where D is the diffusion coefficient of species A. For large radii convective transport dominates and k_MT becomes radius-independent. It is interesting to compare the values of k_het and k_MT and consider the mechanism of proton reaction at the CaCO₃ as a two step process,

where again subscript '0' denotes 'at' the calcite surface. It follows that two different rate determining steps can operate:

i) At large r when k_MT < k_het the slow step will be proton transport and the reaction will be controlled by the rate of proton diffusion to the surface as observed in countless experiments using macroscopic CaCO₃.

whereas, if it stops at the two electron stage,

the energy output of the fuel drops to a worthless level. Much effort is presently devoted to seeking efficient oxygen catalysts to reduce the overpotential for the reduction of oxygen.

The search for oxygen reduction catalysts involves making 'nanomaterials' - often some composite of exotic species such as conducting polymers, metal oxides, nanoparticle decorated carbon or nanotubes, etc., usually combined in a combinatorially complex blend! Evaluation of the 'nanocomposite' most commonly involves comparing the reduction of O₂ on some substrate (say C or Au) with that of the electrode modified with a layer of the new 'electrocatalyst'. Invariably a decrease of the overpotential is seen as being manifested by a lowering of the O₂ reduction linear sweep peak potential. This is deemed diagnostic of an increased rate of electron transfer. Indeed this is a possible explanation. However, this interpretation neglects the probable changes in mass- transport resulting from modifying the electrode with a nanocomposite, for a decrease in overpotential can also result from a reduced rate of mass transport as compared to the semi-infinite diffusion prevailing on the planar un-modified electrode [4, 5]. Such changes in the mass transport can easily happen from the changed geometry on the electrode surface. Thus our recent simulations show that if the nanocomposite layer has porosity or even significant roughness as compared to the flat surface deceptive shifts in the overpotential readily arise [5]. It is tempting to believe that many if not the vast majority of oxygen electrocatalysts characterised by qualitatively interpreted linear sweep voltammetry reflect nothing more than the porosity of the modifying layer rather than authentic 'catalysis' by which is meant a change of electrochemical rate constant.

Further, the claims of improved selectivity between different analytical targets - often some subset of dopamine, serotonin, ascorbic acid, uric acid, etc. - is also readily explained by the 'porosity' model. Here the voltammetric peaks overlap under conditions of semi-infinite diffusion at a macroelectrode but shift differentially towards their various formal potentials when studied under 'thin layer' conditions as shown in simulations and confirmed experimentally [6, 10].

At the same time as the use of nanoparticles explodes relatively little is known about the possible toxic effect of these materials. That said silver nanoparticles represent the largest group of manmade nanoparticles reaching the environment. In the UK alone it is estimated that 8.8 tonnes of silver nanoparticles are released into the environment per annum [13]!

Changed behaviour at the nanoscale is commonly attributed to size effects where the reduced particle size leads to 'quantum confinement' phenomena [16]. Further, in electrochemistry the changed surface morphology - with more steps and fewer terraces as a particle shrinks in size - can profoundly alter the adsorption and hence the mechanism of many electrochemical processes. That said and noting that these two effects are predicted for nanoparticles of size tens of nanometres or smaller, is there a possible role of mass-transport?

The opinion of the authors is that mass-transport might play a significant role in nanotoxicity. We have recently been interested in the electrochemical behaviour of silver nanoparticles and studied the reduction of oxygen in neutral media on silver nanoparticle modified electrodes [17]. The process was seen to occur via the following mechanism

Of course whilst Ag⁺ ions are in themselves toxic it is nevertheless evident that the nature of the products formed in the above scheme will be nanoparticle size dependent. For smaller particles H₂O₂ will be formed whilst at macro-silver H₂O can be the product. Size might switch between a toxic and non-toxic product. Again mass-transport conditions can explain a size dependent phenomenon since H₂O₂ and other reactive oxygen species (ROS) are likely toxic in cells when formed at a concentration much higher than is ambient in cellular environment.

It is the opinion of the authors that mass transport conditions might explain the possible toxic effect of some nanoparticles and why these effects might operate for nanoparticles of sizes considerably greater than would correspond to quantum confinement effects or altered adsorption (certainly for particles greater in size than cf. tens of nanometres these latter considerations would be expected to be minimal). Indeed the mechanism applies not only to O₂ reduction at silver, explaining the formation of H₂O₂ vs. H₂O but also for any multi-step heterogeneous electron transfer process. Consider the reaction

where B is a solution phase species and k_het is a surface catalysed process. Clearly, depending on the values of k_het relative to prevailing mass-transport the reaction products can switch from D to B as the nanoparticle shrinks. A whole plethora of changed reactivity is possible at the nanoscale, simply because of the changed mass transport!

References