Lajos Nyikos

Diffusion to fractal surfaces-II. Verification of theory

Decay of the diffusion controlled current of particles diffusing from an initially homogeneous medium to a completely absorbing fractal boundary was previously shown to exhibit t−α time-dependence instead of the conventional t−12 one with the exponent α being determined by the fractal dimension, Df, of the interface as α =(Df−1)/2. In electrochemical terms this corresponds to a generalized Cottrell equation (or Warburg impedance) and can be used to describe the frequency dispersion caused by surface roughness effects. We verify the predicted behaviour for fractal surfaces with Df>2 (rough interface), and Df<2 (partially blocked surface or active islands on inactive support). In addition, the fractal decay kinetics is shown to be valid for both contiguous and non-contiguous surfaces. Computer simulation, a mathematical model, and direct experiments on well defined fractal electrodes are the tools for verifying the fractal decay law for the different surfaces. The predicted power law behaviour is observed, and the predicted α(Df) relationship was seen to prevail in each case.

Diffusion to fractal surfaces—III. Linear sweep and cyclic voltammograms

Abstract The expressions describing the shape of voltammograms of reversible redox couples are generalized for a fractal boundary. It is shown that they are analogous to the conventional ones except for the need to use a Riemann-Liouville transformation of order q= −α instead of q= − 1 2 to bring the fractal voltammogram to the same simple and perturbation-invariant form. The order −α, determined by the fractal dimension, Df, of the interface as α=(Df−1)/2, is the same fractional value which appears in the fractal Cottrell expression and the fractal Warburg impedance. The theoretical results are verified by computer simulation and by direct experiment of fractal electrodes.

Electrochemical determination of the fractal dimension of fractured surfaces

An electrochemical method, based on the analysis of the time dependence of the diffusional flux of molecular species to a surface, for accurately (⩽ ± 0.02) determining the fractal dimension of rough surfaces 2 ⩽ Df < 2.4) in the 1–100 μm size range is described. We discuss how this method can be used for the measurement of the fractal dimension of fractured steel surfaces prepared by the Charpy impact test.

Electrochemistry at fractal interfaces: the coupling of ac and dc behaviour at irregular electrodes

Abstract Impedance models pertaining to the ideally polarizable (blocking) fractal interface and those describing diffusion-limited charge transfer across fractal surfaces are reviewed. In the blocking case no general prediction can be made: although the non-trivial frequency dispersion often exhibits constant phase angle behaviour, the frequency exponent, α, is not uniquely related to the fractal dimension of the interface. In contrast, the generalized diffusion impedance (or Contrell response) is universal, owing to the fact that the time-dependent “yardstick”—the diffusion length—measures the fractal dimension proper. After discussing some consequences of these models, a new conjecture is presented: the ac behaviour of the blocking interface and the Tafel slope of the dc polarization curve measured in the presence of an electroactive material are interrelated at fractal electrode surfaces. Three examples are given where the modified Tafell slope of the irregular electrode is in fact the original value—which is characteristic to the electrode reaction and which is observed at smooth, planar interfaces—multiplied by the frequency exponent, α, of the blocking impedance.

Geminate ion decay kinetics in nanosecond pulse irradiated cyclohexane solutions studied by optical and microwave absorption

Abstract The decay kinetics of the ions present, on a nanosecond timescale, in a pulse irradiated solution of biphenyl, φ2, in cyclohexane have been investigated using microwave and optical absorption techniques. The ratio of Gmicro (yield×mobility), determined using microwaves, to Gϵ (yield × extinction coefficient), determined optically at 600 nm, is found to increase with time over a period of several hundred nanoseconds for the same conditions of biphenyl concentration and total dose in the pulse. This effect is thought to be due to electrob transfer from φ2− to cyclohexyl radicals. For times longer than 50 ns, the decrease in Gmicro with time is found to obey quite well a linear dependence on the reciprocal square root of the time for solutions φ2, SF6+NH3 and CO2+C6H6. From the intercepts of Gmicro vs 1 √t plots at infinite time, values of the sum of the mobilities of the ions in these solutions are determined to be 6.3, 8.8 and 9.7×10−4cm2V−1s−1, respectively. The slopes of such plots are in good agreement with values derived from ion scavenging data and transport properties of ions in cyclohexane. The experimental data are also in agreement with theoretical calculations based on solution of the Smoluchowski equation for ion pairs but are limited to a timescale which is not short enough to be able to discriminate between different possible ion pair separation distribution functions.

Mobility of localized and quasifree excess electrons in liquid hydrocarbons

The dependences of excess electron mobility on temperature and conduction state energy in saturated liquid hydrocarbons are measured in order to evaluate the mobilities in the localized and in the quasifree state and the energies of the localized state. These quantities appeared earlier as adjustable parameters of a two‐state electron model. Localized electron mobility is described in terms of the motion of a microscopic bubble. The transport of the quasifree electrons is regarded as that of a plane wave scattered by density fluctuations of the liquid. This model, combined with the mobility equation of Cohen and Lekner, finds reasonable agreement with experimental values which vary between 34 and about 400 cm2 V−1 sec−1.

Diffusion kinetics at fractal electrodes

Abstract Rough, porous or partially active electrodes are often modelled as fractals and the laws of electrode kinetics are derived accordingly. The theories dealing with diffusion-controlled currents towards fractal interfaces are surveyed and their applicability to real rough electrode surfaces is discussed.

Diffusion to fractal surfaces-V. quasi-random interfaces

Abstract The validity of a particular fractal modification of the Cottrell equation is verified by computer simulation for quasi-random boundaries.

High-frequency synaptic input contributes to seizure initiation in the low-[Mg2+] model of epilepsy

High‐frequency field potential activity between 50 and 400 Hz occurs throughout seizure‐like events recorded from the CA3 region of juvenile rat hippocampal slices under low‐[Mg2+] condition. Another (400–800 Hz) component occurred mainly during preictal paroxysmal spiking and the onsets of seizure‐like events (97%) and less frequently during tonic and clonic phases (38% and 70%, respectively). Short epochs of oscillations in this range were associated with fast negative field potential deflections at the start of field potential transients. Voltage‐clamp recordings from putative CA3 pyramidal cells showed the occurrence of synaptic inputs in the same frequency range at the onset of seizure‐like events and the beginning of preictal or clonic paroxysmal spikes, while the frequency of action potentials never reached that range. The amplitude of fast negative field potential deflection, the rise time of membrane potential or voltage‐clamp current changes and the mean phase coherence were consistent with an increase of synchronization towards the onset of a seizure‐like event. Their parallel changes indicate the involvement of both synaptic and nonsynaptic mechanisms in the synchronization of neuronal activity and the development of seizure‐like events in the low‐[Mg2+] model of epilepsy.

Diffusion to fractal surfaces-IV. The case of the rotating disc electrode of fractal surface

The limiting current of a fast electrode reaction on a rotating, inactive disc with an electrochemically active fractal subset was theoretically predicted to be proportional to ωα, with ω being the rotation frequency, and the exponent α was determiend by the fractal dimension, Df, of the active area as α = (Df−1)/2. The experimental verification is presented.