Macroscopic metals

There is an important case which is intermediate between small bounded systems and macroscopic fully extended systems, namely the description of the surface region of a macroscopic metal. The correlation functions which describe density fluctuations in the surface region are extremely anisotropic and of long range, very unlike their counterparts in the bulk, and the thermodynamic limit must be taken with sufficient care. Consider the static structure factor for a large system of N particles contained within a volume Q,... 

Hyperthermia and thermoablation have been accomplished using capacitive or inductive coupling of rf fields (10-100 MHz), microwaves (> 300 MHz), ultrasound, lasers or external heat [171-177]. Macroscopic metal implants of Cu and other high-conductivity metals have been used to induce eddy-current heating. The absorbed power per mass is called the specific absorption rate (SAR), which can be expressed as... 

Consider a macroscopic metal electrode Its conduction electrons all tend to travel at the outer surface of the electrode, and they will induce positively charged cations to move close to the electrode surface the "electrons inside electrode cations" system is called the Helmholtz32 double layer [19]. If this layer of cations were at a fixed distance d from a flat electrode and if the medium had a uniform dielectric constant e, then a voltage-independent capacitance of this double layer would be (ee0/d) experimentally, these assumptions are invalid, and too simplistic. In fact, gegenions will also... 

Inhibitors were found to be incorporated in 3D metal deposits preferentially at grain and subgrain boundaries [6.39-6.43]. The influence of internal strain on the macroscopic metal deposit properties such as hardness, brittleness, corrosion, etc., was considered in different systems [6.8, 6.41, 6.42, 6.44-6.53]. 

While the process (17.1) involves two electronic states, one on each reactant, a macroscopic metal electrode is characterized by a continuum of electronic states with average occupation given by the Fermi function in terms of the... 

Figure 1. A representation of the successive fragmentation, or division, of a single grain of metal. The inevitable size-induced metal-insulator transition now effectively links the macroscopic (metal) and the microscopic (insulator) regimes. In all cases we identify the approximate particle diameter and nuclearity, and the accompanying (Kubo) average electronic energy gap separating occupied and unoccupied energy levels. This figure is modified from Edwards. ...

This approach (as sketched in Fig. 2) derived from continuum solid-state physics of macroscopic metals is, however, particularly useful in our attempts to quantify, or at least identify, the various electronic regimes of interest in the problem of divided metals.f - - ... 

As indicated above, as we move closer and closer to the microscopic size regime, we become increasingly concerned at the validity of such an approach derived from the continuum physics of macroscopic metals. Conversely, any theoretical treatment originating from the quantum chemistry standpoint (the Atoms and Molecules , regime in Fig. 1) would inevitably become unreasonable as we move from the microscopic to the mesoscopic regimes. This, of course, is the fascination - and the challenge - of the science of divided metals ... 

Fig. 1 demonstrates the slow-down coefficient fi = k/Re(h) of the bundle surface wave in the terahertz (v = 2.5 THz) and infrared (v = 27 THz) ranges for different numbers of CNTs in the bundle. The calculations have been performed for the densely packed (21,0) zigzag CNTs. The coefficient increases 26 times with the N =900 and tends in thick bundles (with Rb > 25 nm) to 1 which is a characteristic for macroscopic metallic wires. The dependence of the slowdown coefficient on the bundle radius is linear up to Rb = 25 nm (see insert in Fig. 1). 

Linear response theory (TDLDA) applied to the jellium model follows the Mie result, but only in a qualitative way the dipole absorption cross sections of spherical alkali clusters usually exhibit a dominant peak, which exausts some 75-90% of the dipole sum rule and is red-shifted by 10-20% with respect to the Mie formula (see Fig. 7). The centroid of the strength distribution tends towards the Mie resonance in the limit of a macroscopic metal sphere. Its red-shift in finite clusters is a quantum mechanical finite-size effect, which is closely related to the spill-out of the electrons beyond the jellium edge. Some 10-25% of the... 

A contraction of the cluster volume with respect to that of an equivalent piece of bulk metal has also been predicted [96]. The calculated cluster radius is smaller than the radius assumed in the spherical jellium model, where the volume is the same as that of an equivalent piece cut out of a macroscopic metal. This global contraction seems to be a general feature of small metallic clusters, and is well documented experimentally [97]. The volume contraction explains the discrepancies between experimentally determined static polarizabilities of small aluminium clusters and those obtained from jellium calculations [98]. The measured polarizabilities of Aljv clusters with N < 40 are smaller than those predicted by a SJM calculation. The classical static polarizability (per atom) for... 

R.M. Bright, K.R. Brown, R.G. Freeman, A. P. Fox, C. D. Keating, M.D. Mu-sick, and M.J. Natan, Two-Dimensional Arrays of Colloidal Gold Particles a Flexible Approach to Macroscopic Metal Surfaces, Langmuir 12, 2353 (1996)... 

The deciding hint for explaining the basic electron transport mechanism in conductive polymers came from studies with nanoparticles of conventional metals like indium, silver, or copper. Nimtz et al. [4] found in 1989 that metallic particles, if prepared on a nanoscale of below 1 p,m down to 10 nm, show some distinct deviations from macroscopic metals (see Figure 1.2). 

For the first time, Nimtz succeeded to prove experimentally that the conductivity of regular metals, if they are prepared in mesoscopic form (i.e., in a size between macro- and microscopic hence nanometals), differs basically from that of macroscopic metals. Not only is the conductivity dependance on temperature no longer purely metallic, but also decreases with the decreasing temperature. 

We first review, before giving a discussion of the experimental findings, what is to be expected for a macroscopic metal/insulator/ metal sandwich, and what differences are expected when the insulator is made thinner. 

Two basic approaches have been used in the preparation of metallic colloidal dispersions disintegration of the macroscopic metallic elements or synthesis of particles from metal salts using appropriate reducing agents, ultrasonics, pulse and laser radiolysis [ ] ... 

Experimental Data for Selected Molecular Electronic and Macroscopic Metal Devices.5-44... 

A fundamental change in behavior is observed when reducing the size of the colloidal particle as a transition from macroscopic metals to semi -conductor-type colloids and further on to atom assemblies and isolated atoms. This transition to the isolating state is observed for most metals in between 2 and 100 atoms. A unique behavior is often observed if a magic number of atoms forms a defect-free nano-crystal. Gold in a perfect nano-crystal is even more stable against oxidation than a macroscopic gold metal sheet. 

The unique interaction of metal nano clusters with an electromagnetic field and with radiation is among the most exciting properties of colloidal particles (Figure 6). In a macroscopic metal electron move unconfined by any material border. This free... 

Although these are preliminary results that need further experimental work, they are a good indication that a very different behavior should be expected when metal evaporation is carried out on a conjugated oligomer as opposed to alkanethiol SAMs. The formation of a macroscopic metallic lead on the organic surface might lead to the solvation of part of the metal within the layer and/or the introduction of conformational disorder in the layer. 

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