Static dielectric response

Although quite obvious, it is important to remark that a perfect conductor-like model completely neglects the chemical nature of the metal (i.e., all the metals behave in the same way). This is different to what happens for solvents, where even the simplest models include at least one solvent-specific parameter, the static dielectric constant. However, the chemical nature of the metal is relevant for another aspect of the static dielectric response that is neglected by the conductor model the nonlocal effects. They will be discussed in the following Section, The Response Properties of a Molecule Close to a Metal Specimen Surface Enhanced Phenomena and Related Continuum Models. 

Zope, R. R., Baruah, T., Pederson, M. R., 8c Dunlap, B. I. (2008). Static dielectric response of icosahedral fullerenes from Geo to C2160 characterized by an all-electron density functional theory. Physical Review B, 77,115452. 

The latter, in its turn, changes the measured intensity I oc sin (A /2) of laser light transmitted through the cell and the pair of crossed polarizers. Figure 10-4 shows the transmitted intensity (top trace) versus the applied voltage (bottom traces) at two frequencies (100 kHz and 1 kHz) when the amplitude of the voltage varies slowly with the rate 2.4 V/s. For such a slow rate, the dielectric behavior of DFN can be regarded as a quasi-static dielectric response, where the standard description with an instantaneous relation between the displacement and the field is valid. 

Now let us examine what would happen to the response of the dielectric if we put an alternating voltage on the capacitor of frequency co. If CO is low (a few Hz) we would expect the material to respond in a similar manner to the fixed-voltage case, that is d (static) = e(co) = e(0). (It should be noted that eo, the permittivity of free space, is not frequency-dependent and that E(0)/eo = H, the static dielectric constant of the medium.) However, if we were to increase co to above microwave frequencies, the rotational dipole response of the medium would disappear and hence e(co) must fall. Similarly, as we increase co to above IR frequencies, the vibrational response to the field will be lost and e(co) will again fall. Once we are above far-UV frequencies, all dielectrics behave much like a plasma and eventually, at very high values, e(co)lto = 1. 

Metals are characterized by an infinite static dielectric constant, so that any potential disturbance will be screened out by the electron response. This can be demonstrated most simply by considering a point ion of charge, Ze, immersed at the origin in a free-electron gas of charge density —ep0. The presence of the ion will induce a new electron density, p(r), which can be... 

Inside a rectangular well a dipole rotates freely until it suffers instantaneous collision with a wall of the well and then is reflected, while in the field models a continuously acting static force tends to decrease the deflection of a dipole from the symmetry axis of the potential. Therefore, if a dipole has a sufficiently low energy, it would start backward motion at such a point inside the well, where its kinetic energy vanishes. Irrespective of the nature of forces governing the motion of a dipole in a liquid, we may formally regard the parabolic, cosine, or cosine squared potential wells as the simplest potential profiles useful for our studies. The linear dielectric response was found for this model, for example, in VIG (p. 359) and GT (p. 249). 

Fig. 2. Wave functions and energy levels for the solvated electron in (a) methylamine (MeA) and (b) hexamethylphosphoramide (HMPA). The potential V(r) and wavefunction are based upon the model of Jortner (101) and computed using values of the optical and static dielectric constants of the two solvents. The optical absorption responsible for the characteristic blue color is marked by h v and represents transitions between the Is and 2p states. The radius of the cavity is 3 A in MeA, and —4.5 A in HMPA. 

The origin of the effect here represented by x0) can be derived from modelistic considerations. Solvent molecules are mobile entities and their contribution to the dielectric response is a combination of different effects in particular the orientation of the molecule under the influence of the field, changes in its internal geometry and its vibrational response, and electronic polarization. With static fields of moderate intensity all the cited effects contribute to give a linear response, summarized by the constant value e of the permittivity. This molecular description of the dielectric response of a liquid is... 

In the language of reciprocal space, nonlocal metal response refers to the dependence of the metal dielectric constant on the wavevector k of the various plane waves into which any probing electric fields can be decomposed. Such an effect is often mentioned in reports on SERS, but it is usually neglected. One of the oldest papers addressing the importance of nonlocal effects on the polarizability of an adsorbed molecule is the article by Antoniewicz, who studied the static polarizability of a polarizable point dipole close to a linearized Thomas-Fermi metal [63], The static dielectric constant eTF(k) of such a model metal can be written as ... 

Continuum solvation models consider the solvent as a homogeneous, isotropic, linear dielectric medium [104], The solute is considered to occupy a cavity in this medium. The ability of a bulk dielectric medium to be polarized and hence to exert an electric field back on the solute (this field is called the reaction field) is determined by the dielectric constant. The dielectric constant depends on the frequency of the applied field, and for equilibrium solvation we use the static dielectric constant that corresponds to a slowly changing field. In order to obtain accurate results, the solute charge distribution should be optimized in the presence of the field (the reaction field) exerted back on the solute by the dielectric medium. This is usually done by a quantum mechanical molecular orbital calculation called a self-consistent reaction field (SCRF) calculation, which is iterative since the reaction field depends on the distortion of the solute wave function and vice versa. While the assumption of linear homogeneous response is adequate for the solvent molecules at distant positions, it is a poor representation for the solute-solvent interaction in the first solvation shell. In this case, the solute sees the atomic-scale charge distribution of the solvent molecules and polarizes nonlinearly and system specifically on an atomic scale (see Figure 3.9). More generally, one could say that the breakdown of the linear response approximation is connected with the fact that the liquid medium is structured [105],... 

Equation (27d) states that the kernel Jf(r,r ) is asymptotically equal to the Hartree-Kohn-Sham static dielectric function. Thus the expression in Eq. (20) for the Fukui function is just a short-range linear mapping of the frontier density, and the expression in Eq. (21) for the local softness is the same mapping of the local DOS. It is the frontier-orbital density which drives the chemical response measured by the Fukui function, and the local DOS which drives that measured by the local softness. 

In this way, the relative dielectric response to static electric fields of a gas of polarizable molecules that also bear a permanent dipole moment is... 

There are also a number of theories taking into account dipolar solvation dynamics. These theories use the solvent s dielectric response function as the dynamical input and also include effects due to the molecular nature of the solvent. The most sophisticated of these theories, by Raineri et al. [136] and by Friedman [137], uses fully atomistic representations for both solute and solvent and recent comparisons have shown it to be capable of quantitatively reproducing both the static and dynamic aspects of solvation of C153 [110]. In these cases the theoretical nature of solvation dynamics is fully understood. However, it must be remembered that much of the success of these theories rests on using the dynamical content of the complicated function, dielectric response function, determined from experiment. Although there... 

This chapter concentrates on the results of DS study of the structure, dynamics, and macroscopic behavior of complex materials. First, we present an introduction to the basic concepts of dielectric polarization in static and time-dependent fields, before the dielectric spectroscopy technique itself is reviewed for both frequency and time domains. This part has three sections, namely, broadband dielectric spectroscopy, time-domain dielectric spectroscopy, and a section where different aspects of data treatment and fitting routines are discussed in detail. Then, some examples of dielectric responses observed in various disordered materials are presented. Finally, we will consider the experimental evidence of non-Debye dielectric responses in several complex disordered systems such as microemulsions, porous glasses, porous silicon, H-bonding liquids, aqueous solutions of polymers, and composite materials. 

The expression given in Eq. (10) for the work assumes that p = 0, where p is the ionic strength of the medium. AG is the free-energy of the equilibrated excited-state (AG AE00), rD and rA are the molecular radii of the donor and acceptor molecules, e5 is the static dielectric constant or permittivity of the solvent, and z is the charge on each ion. ss is related to the response of the permanent dipoles of the surrounding solvent molecules to an external electrical field. Equation (9), the Bom equation, measures the difference in solvation energy between radical ions in vacuo and solution. 

It is now well understood that the static dielectric constant of liquid water is highly correlated with the mean dipole moment in the liquid, and that a dipole moment near 2.6 D is necessary to reproduce water s dielectric constant of s = 78 T5,i85,i96 holds for both polarizable and nonpolarizable models. Polarizable models, however, do a better job of modeling the frequency-dependent dielectric constant than do nonpolarizable models. Certain features of the dielectric spectrum are inaccessible to nonpolarizable models, including a peak that depends on translation-induced polarization response, and an optical dielectric constant that differs from unity. The dipole moment of 2.6 D should be considered as an optimal value for typical (i.e.. 

AODCST, 2-[4-bis(2-methoxyethyl)amino]benzylidene malononitrile PTPDac-BA2, copolymer, 65% wt N-(4-acryloyloxymethylphenyl)-N -phenyl-N,N -bis(4-methylphenyl)-[ 1,1 -biphenyl]-4,4 -diamine, 35% wt A-butylacetate DOP, dioctyl phthalate DRl-DCTA, 4,4 -di(carbazol-cl-yl)-4"-(2- N-ethyl-N-[4-(4-nitrophenyldzo)phenyl]amine ethoxy)-triphenylamine other abbreviations are defined in the text and Figures, quantum effieieney of mobile charge photogeneration has been estimated where necessary, °a relative static dielectric constant of 3 and a linear electro-optic response have been assumed. 

Waals envelope of the solvent. This projection can be expressed in terms of a response function, whose kernel contains a damping factor (the dielectric constant ) very near to the optical dielectric constant of water, eopt, when the water molecules are held fixed, or rapidly increasing towards the static dielectric constant, when water molecular motions are allowed and their number in the cluster increases. This is the origin of our PCM model (more details can be found in Tomasi, 1982). Surely, similar considerations spurred Rivail and coworkers to elaborate their SCRF method (Rivail and Rinaldi, 1976). An additional contribution to the formulation of today continuum models came from the nice analysis given by Kolos (Kolos, 1979 dementi et al., 1980) of the importance of dispersion contributions. 

The dielectric response in this model is thus characterized by three parameters the electronic Sg and static Sg response constants, and the Debye relaxation time ro. 

Following Marcus, we simplify this picture by assuming that the solvent is characterized by only two timescales, fast and slow, associated, respectively with its electronic and the nuclear response. Correspondingly, the solvent dielectric response function is represented by the total, or static, dielectric coefficient Sg and by its fast electronic component Sg (sometimes called optical response and related to the refraction index n by Sg = n ). includes, in addition to the fast electronic component, also contributions from solvent motions on slower nuclear timescales Translational, rotational, and vibrational motions. The working assumption of the... 

Polarizability (i.e., static dielectric polarizability), a, is a measnre of the linear response of the electronic clond of a chemical species to a weak external electric field of strength E. For isotropic molecnles, the dipole moment, fi, is... 

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