Dispersion model Drude

To select suitable dispersion model, such Sellimeier model, Cauchy model, Lorentz model, Drude model, effective medium approximation (EMA) model etc., for each layer. Which dispersion model should be selected for a certain layer depends on the specific type of the film and we will discuss later in detail. In the model, some parameters are known and the others are unknown. The unknown parameters will be determined through mathematical inversion method. 

Fig. 4, 33 The Drude model for dispersive interactions. (Figure adapted from Rigby M, E B Smith, W A Wakeham and G C Maitland 1986. The Forces Between Molecules. Oxford, Clarendon Press.)...

Irude model thus predicts that the dispersion interaction varies as 1//. wo-dimensional Drude model can be extended to three dimensions, the result being ... 

The Lennard-Jones potential is characterised by an attractive part that varies as r ° and a repulsive part that varies as These two components are drawn in Figure 4.35. The r ° variation is of course the same power-law relationship foimd for the leading term in theoretical treatments of the dispersion energy such as the Drude model. There are no... 

We now want to study the consequences of such a model with respect to the optical properties of a composite medium. For such a purpose, we will consider the phenomenological Lorentz-Drude model, based on the classical dispersion theory, in order to describe qualitatively the various components [20]. Therefore, a Drude term defined by the plasma frequency and scattering rate, will describe the optical response of the bulk metal or will define the intrinsic metallic properties (i.e., Zm((a) in Eq.(6)) of the small particles, while a harmonic Lorentz oscillator, defined by the resonance frequency, the damping and the mode strength parameters, will describe the insulating host (i.e., /((0) in Eq.(6)). 

Bade WL (1957) Drude-model calculation of dispersion forces. I. General theory. J Chem Phys 27(6) 1280-1284... 

A common alternative is to synthesize approximate state functions by linear combination of algebraic forms that resemble hydrogenic wave functions. Another strategy is to solve one-particle problems on assuming model potentials parametrically related to molecular size. This approach, known as free-electron simulation, is widely used in solid-state and semiconductor physics. It is the quantum-mechanical extension of the classic (1900) Drude model that pictures a metal as a regular array of cations, immersed in a sea of electrons. Another way to deal with problems of chemical interaction is to describe them as quantum effects, presumably too subtle for the ininitiated to ponder. Two prime examples are, the so-called dispersion interaction that explains van der Waals attraction, and Born repulsion, assumed to occur in ionic crystals. Most chemists are in fact sufficiently intimidated by such claims to consider the problem solved, although not understood. 

Although it is impractical, a simple semi-infinite MIM with air as the insulating middle layer can serve as an illustrative example. Fig. 13.15 displays the calculated dispersion relation of different SPP modes for the Ag / air / Ag structure [38]. For simplicity, the lossless Drude model e(o)) = where e , is the... 

All of the coefficients C are negative, implying an attractive interaction. Despite its simplicity, the Drude model gives quite reasonable results if just the Cg term is included then for argon the resulting dispersion energy is only about 25% too small. 

The model was originally proposed by Paul Drude in 1902 as a simple way to describe dispersive properties of materials [108]. A quantum version of the model (including the zero-point vibrations of the oscillator) has been used in early applications to describe the dipole-dipole dispersion interactions [109-112]. A semiclassical version of the model was used more recently to describe molecular interactions [113], and electron binding [114]. The classical version has been subsequently used for ionic crystals [115-120], simple liquids [121-127], water [128-135], and ions [136-139], and in recent decades has seen widespread use in MD and MC simulations. In recent years, the Drude model was extended to interface with QM approaches in QM/MM methods [140], facilitated by the simplicity of the model in that it only includes additional charge centers. 

Bade, W. L, and J. G. Kirkwood, Drude-model calculation of dispersion forces. 11. The linear lattice./. Chem. Phys., 1957. 27(6), 1284-1288. 

The early studied PAN-CSA [133] and PPy doped with perchlorate [165] both had ojc 100 S/cm, indicating that the carriers were reasonably localized. Therefore, the agreement of the optical properties with the localization-modified Drude model (with t 10 s) is expected. However, this model is unable to account for the free electron behavior observed in higher samples because Drude dispersion requires that fcpA 1. 

Metals are denoted as fi ee-electron metals if most of the electronic and optical properties are due to the conduction electrons alone. Examples are Al, Mg, and alkali metals. The dispersion of the optical constants of the fi ee-electron metals is described by the Drude model [72], which can be regarded as a special case of the Lorentz model (1.3.3°) when the restoring (bounding) force is equal to zero, and hence the resonance frequency of free carriers, a>o = -JWfm (here, m is electron mass), is also equal to zero, damping force y results... 

The Maxwell-Helmholtz-Drude dispersion formula (1.46) provides a good model of the dielectric function in the case of moderate to weak TO... 

Another potential function that describes the dispersive forces due to instantaneous polarities arising from fluctuations in the electron clouds is the Drude model series expansion [19] ... 

Sommerfeld A (1916) The Drude dispersion theory from the standpoint of Bohr s model, and the constitution of hydrogen, oxygen, and nitrogen. Ann Phys 51 1... 

A critical point in method A is the not exactly known refractive index n or, in terms of the Drude-Lorentz model, 800 of PEG in the infrared region, because it enters the spectrum calculation but cannot be determined with sufficient accuracy from the spectral fit. Changes of 800 have, other things being equal, opposite effects on ATR reflectivities calculated for bulk material and thin films on metal, respectively. In the present calculation, 8qo = 2.10 (n = 1.45) was used, somewhat smaller than the value np = 1.46 reported in the literature [18] in order to take into account the optical dispersion [19] in an approximate manner. 

The relative dielectric permittivity of plasmonic materials is negative below plasma frequency, and its dispersion is by Drude electron resonance model [298]... 

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