Vacuum-metal interface model

Model 2a.2 Vacuum-Metal Interface with Dipole Moment Correction... 

Model 2a.3 Vacuum-Metal Interface with Applied Electric Field... 

Modeling the Aqueous—Metal Interface in Ultrahigh Vacuum via Cryogenic Coadsorption... 

In the literatme, the work function of a metal, p (in eV), is often used to estimate the degree of charge transfer at semiconductor/metal junctions. The work function of a metal is defined as the minimum potential experienced by an electron as it is removed from the metal into a vacuum. The work function ip is often nsed in lieu of the electrochemical potential of a metal, because the electrochemical potential of a metal is difficult to determine experimentally, whereas tp is readily accessible from vacuum photoemission data. Additionally, the original model of semiconductor/metal contacts, advanced by Schottky, utilized differences in work functions, as opposed to differences in electrochemical potentials, to describe the electrical properties of semiconductor/metal interfaces. A more positive work function for a metal (or more rigorously, a more positive Fermi level for a metal) would therefore be expected to produce a greater amount of charge transfer for an n-type semiconductor/metal contact. Therefore, use of metals with a range of tp (or fip.m) values should, in principle, allow control over the electrical properties of semiconductor/metal contacts. 

In addition to the solvent contributions, the electrochemical potential can be modeled. Application of an external electric field within a metal/vacuum interface model has been used to investigate the impact of potential alteration on the adsorption process [111, 112]. Although this approach can model the effects of the electrical double layer, it does not consider the adsorbate-solvent, solvent-solvent, and solvent-metal interactions at the electrode-electrolyte interface. In another approach, N0rskov and co-workers model the electrochemical environment by changing the number of electrons and protons in a water bilayer on a Pt(lll) surface [113-115]. Jinnouchi and Anderson used the modified Poisson-Boltzmann theory and DFT to simulate the solute-solvent interaction to integrate a continuum approach to solvation and double layer affects within a DFT system [116-120]. These methods differ in the approximations made to represent the electrochemical interface, as the time and length scales needed for a fiilly quantum mechanical approach are unreachable. 

Figure 5.7. Schematic representation of the definitions of work function O, chemical potential of electrons i, electrochemical potential of electrons or Fermi level p = EF, surface potential %, Galvani (or inner) potential

The Vacuum Reference The first reference in the double-reference method enables the surface potential of the metal slab to be related to the vacuum scale. This relationship is determined by calculating the workfunction of the model metal/water/adsorbate interface, including a few layers of water molecules. The workfunction, — < ermi. is then used to calibrate the system Fermi level to an electrochemical reference electrode. It is convenient to choose the normal hydrogen electrode (NHE), as it has been experimentally and theoretically determined that the NHE potential is —4.8 V with respect to the free electron in a vacuum [Wagner, 1993]. We therefore apply the relationship... 

Fig. 2-10. Profile of electron density and electronic potential energy across a metal/vacuum interface calculated by using the jellium model of metals MS = jellium surface of metals Xf = Fermi wave length p. - average positive charge density P- s negative charge density V = electron exchange and correlation energy V, - kinetic energy of electrons. [From Lange-Kohn, 1970.]...

In the first model, the mnneling electron mainly interacts with the electronic polarization of water ( = 1.88) since tunneling was assumed to be fast in comparison with the orientational response of the dipolar molecules of the liquid. Considering water as a dielectric continuum between a jellium spherical tip and planar substrate yields an effective barrier for tunneling that is about 1 eV lower than that for the vacuum case [95]. This result is consistent with photoemission studies of metal/aqueous interfaces, which reveal electron emission into water at 1 eV below the vacuum level [95-97]. Similar models have been employed to examine the effect of thermal fluctuations on the tunneling current [98-100]. Likewise, a related model assessing the noise associated with the reorientation of adsorbed molecules has been presented [101]. 

Experiments show that the values for the double layer capacity at single crystal metal surfaces depend on the nature of the metal. This indicates that the metal surface cannot be considered as a perfect conductor, as was done in classical theories. It is well known that an overspill of metal electrons can occur at the boundary of a metal with vacuum. A similar overspill expected at a metal-solution interface would alter the double layer capacity by an amount depending on the type of metal. Models have been constructed in which the metal is represented by an electronic plasma in a uniformly, positively charged background, which is known as the jellium model [81,82]. The inclusion of the electron overspill into the integral equation theories of the electric double layer has been performed basically with the HAB model. 

The evolution and decomposition of metal clusters in the polysiloxanes has been quantified (49), and a diffusion-plus-reaction model for cluster growth at the surface and in the near subsurface region of a polymer film has been developed (SO). Collectively, the studies show that organometallic chemistry at the polymer/vacuum interface can have profound effects on both the dynamics of polymer chains at the surface and the evolution of low nuclearity clusters (SO, 51). 

To get around the difficulties involved in preparing for study an interface consisting of a monolayer of polyimide on a metal substrate, vapor-deposited components of polyimide (9-111 and model molecules for parts of the polyimide (11-121 on metals have been studied recently. Due to the limited size of these model molecules, they can be vapor-deposited in monolayers on the surface of clean metallic substrate in an ultra high vacuum system. In this way, useful information concerning the initial interface formation of (parts of) polyimide on a metal surface can be obtained. 

A. Kohlmayer, W. Witschel, E. Spohr, Molecular dynamics simulation of water/metal and water/vacuum interfaces with a polarizable water model, Chem. Phys., 213 (1996) 211-216. 

The use of single crystal surfaces, their chemistry, and their influence on various surface chemistry types is exemplified in the first five chapters which represent a well-chosen selection of the diversity of surface chemistry and catalysis studied on metal-based single crystal model systems, and the depth of molecular information obtained from such studies. Metallic single crystals can also serve as model surfaces of electrochemical surface science, and these in-situ electrochemical interfaces can be similar to the interfaces encountered in ultrahigh vacuum surface science studies but with some significant differences as summarized by Stamenkovic and Markovic. 

One major complication that distinguishes electrocatalytic reactions from catalytic reactions at metal-gas or metal-vacuum interfaces is the influence of the solvent. Modeling the role of the solvent in electrode reactions essentially started with the pioneering work of Marcus [68]. Originally these theories were formulated to describe relatively simple electron-transfer reactions, but more recently also ion-transfer reactions and bond-breaking reactions have been incorporated [69-71]. Moreover, extensive molecular dynamics simulations have been carried out to obtain a more molecular picture of the role of the solvent in charge-transfer processes, either in solution or at metal-solution interfaces. 

CdCN2 decomposed [68] in vacuum within the interval 865 and 989 K to yield metal, cyanogen and nitrogen E = 159 kJ mol ) for which the ur-time exudes were fitted by the contracting volume equation. The reaction in oxygen, which formed metal oxide, nitrogen and carbon dioxide = 82 kJ mol ) followed the same kinetic model and both reactions are believed to proceed by an interface advance mechanism. 

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