R. Morrow

Numerical modelling of atmospheric pressure gas discharges leading to plasma production

In this paper, we give a detailed review of recent work carried out on the numerical characterization of non-thermal gas discharge plasmas in air at atmospheric pressure. First, we briefly describe the theory of discharge development for dielectric barrier discharges, which is central to the production of non-equilibrium plasma, and we present a hydrodynamic model to approximate the evolution of charge densities. The model consists of the continuity equations for electrons, positive and negative ions coupled to Poissons equation for the electric field. We then describe features of the finite element flux corrected transport algorithm, which has been developed to specifically aim for accuracy (no spurious diffusion or oscillations), efficiency (through the use of unstructured grids) and ease of extension to complex 3D geometries in the framework of the hydrodynamic model in gas discharges. We summarize the numerical work done by other authors who have applied different methods to various models and then we present highlights of our own work, which includes code validation, comparisons with existing results and modelling of radio frequency systems, dc discharges, secondary effects such as photoionization and plasma production in the presence of dielectrics. The extension of the code to 3D for more realistic simulations is demonstrated together with the adaptive meshing technique, which serves to achieve higher efficiency. Finally, we illustrate the versatility of our scheme by using it to simulate the transition from non-thermal to thermal discharges.We conclude that numerical modelling and, in particular, the extension to 3D can be used to shed new light on the processes involved with the production and control of atmospheric plasma, which plays an important role in a host of emerging technologies.

A unified theory of free burning arcs, cathode sheaths and cathodes

A theoretical method of predicting properties of free burning arcs and their cathodes is presented in a unified treatment. The method combines a one-dimensional model of the non-equilibrium plasma sheath adjacent to the cathode and a two-dimensional model for the arc column and the solid cathode. Two internal boundaries divide the arc-cathode domain into an arc region, a sheath region and a cathode region. The internal boundary conditions are adjusted during the iteration procedure to satisfy the energy conservation and current continuity equations. The effective resistance of the cathode sheath region is obtained from the sheath calculation assuming charge transport using an ambipolar diffusion approximation. No assumptions are made as to the distributions of, current density and temperature at the cathode surface. The model accounts for cathode surface effects and assumes that the cathode is a thermionic emitter. Material functions such as the thermal and electrical conductivities of the arc plasma and cathode are required as input parameters. Predictions are made, for any given arc current and cathode configuration, of the temperature and current density distributions in the arc and the cathode. Information is also provided about sheath properties. The results from a calculation for 200 A arc burning in argon with a thoriated tungsten cathode are in good agreement with the experimental measurements of the arc column and cathode surface temperatures and the arc voltage.

Prediction of anode temperatures of free burning arcs

Predictions of the temperatures of the anode of free burning arcs are made using a theory that treats an arc and its electrodes as a unified system. The theory predicts the temperature distributions of the arc column, the cathode and the anode as a function of the arc operating conditions. Temperature profiles on the surface of copper anodes for arcs in argon are calculated for various arc operating conditions. Theoretical predictions of the threshold current for melting a water-cooled copper anode range from 1260 to 480 A for anode thicknesses ranging from 2 to 10 mm and are in good agreement with experimental results.

Covalent attachment of functional protein to polymer surfaces: a novel one-step dry process

The attachment of bioactive protein to surfaces underpins the development of biosensors and diagnostic microarrays. We present a surface treatment using plasma immersion ion implantation (PIII) to create stable covalent binding sites for the attachment of functional soya-bean peroxidase (SBP). Fourier transform infrared spectra of the surfaces show that protein is retained on the surface after boiling in sodium dodecyl sulphate and sodium hydroxide, which is indicative of covalent attachment. The activity of SBP on the treated surfaces remains high in comparison with SBP attached to control surfaces over the course of 11 days. Surface plasmon resonance was used to show that the surface coverage of the attached protein is close to a monolayer. We describe the potential of the PIII treatment method to be used as a one-step dry process to create surfaces for large-scale protein micro- or nanopatterning.

The time-dependent development of electric double-layers in saline solutions

We have studied the time-dependent development of electric double-layers (ionic sheaths) in saline solutions by simultaneously solving the sodium and chlorine ion continuity equations coupled with Poissons equation in one dimension. The study of the effects of time-varying electric fields in solution is relevant to the possible health effect of radio-frequency electric fields on cells in the human body and to assessing the potential of using external electric fields to orient proteins for attachment to surfaces for biosensing applications. Our calculations, for applied voltages of 10?175?mV between the electrode and the solution, predict time scales of ~0.1?110??s for the formation of double-layers in solutions of concentration between 0.001 and 1.0?M. We develop an empirical equation that can predict the double-layer formation time to within 10% over this wide parameter range. The method has been validated by comparing the solutions obtained, once the program has run to a steady state, with the standard non-linear Poisson?Boltzmann equations. Excellent agreement is found with the Gouy?Chapman solution of the non-linear Poisson?Boltzmann equation. Thus the method is not restricted in accuracy and applicability as is the case for the linear Poisson?Boltzmann equation. The method can also provide solutions for cases where there are orders of magnitude changes in the ion densities; this has not been the case for previous studies where small perturbation analysis has been employed. The method developed here can readily be extended to two and three dimensions using time-splitting methods.

The time-dependent development of electric double-layers in pure water at metal electrodes: the effect of an applied voltage on the local pH

Water maintains a pH value of 7 owing to a balance between dissociation into hydronium (H3O+) and hydroxide (OH−) ions and their recombination. An examination is made of the effect of applying voltages from 0.1 to 0.82 V on these ions between metal electrodes which act as blocking electrodes. The movement of hydronium ions away from and hydroxide ions towards the anode is followed. This movement results in the formation of an ion double-layer with a steeply rising electric field and a maximum pH of approximately 12. At the cathode, the opposite occurs and the pH reaches a minimum of approximately 1.7. The time constant for double-layer formation is found to increase exponentially with voltage, and the pH at each electrode varies linearly with voltage; thus, the pH can be controlled systematically at each electrode. The dimensions of the double-layers are such that large biomolecules at the electrodes will be immersed in a pH environment close to the extreme values at the electrode. This means that the charge on the molecules may be controlled as they adsorb onto the electrode; this may prove valuable for the operation of biosensors.

Time-dependent electrical double layer with blocking electrode

This paper deals with the experimental observation of time-dependent electrical double layer (EDL) in electrolyte. A potential-distance diagram is used to fully understand different stages in the formation of EDL. The influence of the thickness of the blocking layer and the ionic strength to the formation of EDL is discussed based on the equivalent circuit. With this simple method, it is found that in addition to Debye screening length, the frequency has to be considered if an alternating electric field is used to control the movement of charged biomolecules inside EDL.

Functional attachment of horse radish peroxidase to plasma-treated surfaces

Controlling the interaction of surfaces with macromolecules, such as proteins and antibodies, is the key to producing biocompatible prosthetic devices, biosensors and diagnostic arrays. The development of technologies to control these interactions will result in the early detection of disease and have the potential to dramatically reduce costs associated with clinical treatment. For example, tethering functional anti-bodies to a surface in a patterned array allows the selection of specific proteins from a microlitre serum sample, immediately identifying diseases, well before the symptoms are manifested. Unfortunately, simple physical absorption of proteins onto most surfaces results in changes in their structure and loss of function. The use of ions from plasmas allows flexibility in surface modification by accessing a variety of ion energies and activated chemical species. In this paper we describe plasma based techniques which are being developed to modify the chemistry and morphology of surfaces in order to optimise their interaction with biomolecules. Early results of plasma processes to activate surfaces for non specific attachment of proteins by hydrophilic /hydrophobic interactions are presented, with particular attention to the time stability of such treatments, which is of special interest.