Contact charging theory

It is clear that the presence of electrostatic charges, whether due to contact charging, fractoemissions, or some other mechanism, will affect particle adhesion. However, to date there has been no satisfactory attempt made at properly integrating electrostatic forces into partiele adhesion theory. 

Perhaps the most significant complication in the interpretation of nanoscale adhesion and mechanical properties measurements is the fact that the contact sizes are below the optical limit ( 1 t,im). Macroscopic adhesion studies and mechanical property measurements often rely on optical observations of the contact, and many of the contact mechanics models are formulated around direct measurement of the contact area or radius as a function of experimentally controlled parameters, such as load or displacement. In studies of colloids, scanning electron microscopy (SEM) has been used to view particle/surface contact sizes from the side to measure contact radius [3]. However, such a configuration is not easily employed in AFM and nanoindentation studies, and undesirable surface interactions from charging or contamination may arise. For adhesion studies (e.g. Johnson-Kendall-Roberts (JKR) [4] and probe-tack tests [5,6]), the probe/sample contact area is monitored as a function of load or displacement. This allows evaluation of load/area or even stress/strain response [7] as well as comparison to and development of contact mechanics theories. Area measurements are also important in traditional indentation experiments, where hardness is determined by measuring the residual contact area of the deformation optically [8J. For micro- and nanoscale studies, the dimensions of both the contact and residual deformation (if any) are below the optical limit. 

Thus surface-state theory provides a satisfactory basis for discussing contact charging of polymers by electron transfer. The model is, however, probably oversimplified, and it would be unwise to exclude the possibility of penetration of charge into the bulk polymer altogether in view of conduction effects that can usually be observed at high fields in polymers. We must also remember that the results we have been talking about refer to very clean polymer surfaces and that the contact charging in most practical cases can be very different due to the presence of dirt and moisture on the surface. 

Although there is a body of theory to account for contact electrification and a large literature on the subject, it is sufficient here to emphasize that contact charging is a common phenomenon, probably impossible to avoid, and that it is intimately related to composition, electrical conductivity, and the mechanics of contact of surfaces. Because even monomolecular contamination can markedly affect both the amount and the sign of the charge, experimental investigations are notoriously erratic in their observations and conclusions. 

In the usual space-charge limited theory, electrons are injected into the insulator conduction band, and some of these electrons are immobilized in localized defect states. We have considered an alternate mechanism more appropriate to the polymer structure. Contact charge transfer studies in Polyethylene Terephthalate (PET) and other polymers (15-16) suggest that the electronic states accessible from metal contacts are localized molecular-ion states located deep in the forbidden energy gap. Charge transport is by hopping between localized states. 

Since new questions have been raised about the mechanisms of contact charging,(126) are unable to infer one way or the other whether the controversies of the electronic adhesion theory have been put to rest. Once we know exactly how charges are being transferred at the interface, we should be able to draw a better picture about the electrical double layer and its effect on adhesion. 

Assume is -25 mV for a certain silica surface in contact with O.OOlAf aqueous NaCl at 25°C. Calculate, assuming simple Gouy-Chapman theory (a) at 200 A from the surface, (b) the concentrations of Na and of Cr ions 10 A from the surface, and (c) the surface charge density in electronic charges per unit area. 

The analytic theory outlined above provides valuable insight into the factors that determine the efficiency of OI.EDs. However, there is no completely analytical solution that includes diffusive transport of carriers, field-dependent mobilities, and specific injection mechanisms. Therefore, numerical simulations have been undertaken in order to provide quantitative solutions to the general case of the bipolar current problem for typical parameters of OLED materials [144—1481. Emphasis was given to the influence of charge injection and transport on OLED performance. 1. Campbell et at. [I47 found that, for Richardson-Dushman thermionic emission from a barrier height lower than 0.4 eV, the contact is able to supply... 

T. Ioannides, and X.E. Verykios, Charge transfer in metal catalysts supported on Doped Ti02 A Theoretical approach based on metal-semiconductor contact theory, J. Catal. 161,560-569 (1996). 

At present it is impossible to formulate an exact theory of the structure of the electrical double layer, even in the simple case where no specific adsorption occurs. This is partly because of the lack of experimental data (e.g. on the permittivity in electric fields of up to 109 V m"1) and partly because even the largest computers are incapable of carrying out such a task. The analysis of a system where an electrically charged metal in which the positions of the ions in the lattice are known (the situation is more complicated with liquid metals) is in contact with an electrolyte solution should include the effect of the electrical field on the permittivity of the solvent, its structure and electrolyte ion concentrations in the vicinity of the interface, and, at the same time, the effect of varying ion concentrations on the structure and the permittivity of the solvent. Because of the unsolved difficulties in the solution of this problem, simplifying models must be employed the electrical double layer is divided into three regions that interact only electrostatically, i.e. the electrode itself, the compact layer and the diffuse layer. 

This theory will be demonstrated on a membrane with fixed univalent negative charges, with a concentration in the membrane, cx. The pores of the membrane are filled with the same solvent as the solutions with which the membrane is in contact that contain the same uni-univalent electrolyte with concentrations cx and c2. Conditions at the membrane-solution interface are analogous to those described by the Donnan equilibrium theory, where the fixed ion X acts as a non-diffusible ion. The Donnan potentials A0D 4 = 0p — 0(1) and A0D 2 = 0(2) — 0q are established at both surfaces of the membranes (x = p and jc = q). A liquid junction potential, A0l = 0q — 0P, due to ion diffusion is formed within the membrane. Thus... 

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