Dielectric constant frequency-dependent

Neumann M, Steinhauser O and Pawley G S 1984 Consistent calculation of the static and frequency-dependent dielectric constant in computer simulations Mol. Phys. 52 97-113... 

Neumann, M., Steinhauser, O. On the calculation of the frequency-dependent dielectric constant in computer simulations. Chem. Phys. Lett. 102 (1983) 508-513. 

Because of very high dielectric constants k > 20, 000), lead-based relaxor ferroelectrics, Pb(B, B2)02, where B is typically a low valence cation and B2 is a high valence cation, have been iavestigated for multilayer capacitor appHcations. Relaxor ferroelectrics are dielectric materials that display frequency dependent dielectric constant versus temperature behavior near the Curie transition. Dielectric properties result from the compositional disorder ia the B and B2 cation distribution and the associated dipolar and ferroelectric polarization mechanisms. Close control of the processiag conditions is requited for property optimization. Capacitor compositions are often based on lead magnesium niobate (PMN), Pb(Mg2 3Nb2 3)02, and lead ziac niobate (PZN), Pb(Zn 3Nb2 3)03. 

Treating the free electrons in a metal as a collection of zero-frequency oscillators gives rise51 to a complex frequency-dependent dielectric constant of 1 - a>2/(co2 - ia>/r), with (op = (47me2/m)l/2 the plasma frequency and r a collision time. For metals like Ag and Au, and with frequencies (o corresponding to visible or ultraviolet light, this simplifies to give a real part... 

To use this equation in evaluating I, one needs a model for e(t ) that is consistent with available experiments on the frequency-dependent dielectric constant. 

Clausius-Mossotti equation). In this expression, V designates the mole volume and Ae, Be, Cf,... are the first, second, third,... virial dielectric coefficients. A similar expansion exists for the refractive index, n, which is related to the (frequency dependent) dielectric constant as n2 = e (Lorentz-Lorenz equation, [87]). The second virial dielectric coefficient Be may be considered the sum of an orientational and a polarization term, Be = B0r + Bpo, arising from binary interactions, while the second virial refractive coefficient is given by just the polarization term, B = Bpo at high enough frequencies, the orientational component falls off to small values and the difference Be — B may be considered a measurement of the interaction-induced dipole moments [73],... 

The coupling of plasmons with LO phonons leads to coupled plasmon-pho-non states. For a cubic crystal with 2 atoms in the elementary cell and one infrared-active eigen frequency cop, the frequency-dependent dielectric constant is according to Eq. (11.17)... 

Both s (to) (called the frequency dependent dielectric constant) and s (co) (called the loss factor) play a role in our applications of the theory. 

The dispersion interaction between an atom and a metal surface was first calculated by Lennard-Jones in 1932, who considered the metal as a perfect conductor for static and time-dependent fields, using a point dipole for the molecule [44], Although these results overestimate the dispersion energy, the correct l/d3 dependence was recovered (d is the metal-molecule distance). Later studies [45 17] extended the work of Lennard-Jones to dielectrics with a frequency-dependent dielectric constant [48] (real metals may be approximated in this way) and took into account electromagnetic retardation effects. Limiting ourselves to small molecule-metal distances, the dispersion interaction of a molecule characterized by a frequency-dependent isotropic polarizability a embedded in a dielectric medium with permittivity esol (note that no cavity is built around the molecule) reads ... 

The molecule is often represented as a polarizable point dipole. A few attempts have been performed with finite size models, such as dielectric spheres [64], To the best of our knowledge, the first model that joined a quantum mechanical description of the molecule with a continuum description of the metal was that by Hilton and Oxtoby [72], They considered an hydrogen atom in front of a perfect conductor plate, and they calculated the static polarizability aeff to demonstrate that the effect of the image potential on aeff could not justify SERS enhancement. In recent years, PCM has been extended to systems composed of a molecule, a metal specimen and possibly a solvent or a matrix embedding the metal-molecule system in a molecularly shaped cavity [62,73-78], In particular, the molecule was treated at the Hartree-Fock, DFT or ZINDO level, while for the metal different models have been explored for SERS and luminescence calculations, metal aggregates composed of several spherical particles, characterized by the experimental frequency-dependent dielectric constant. For luminescence, the effects of the surface roughness and the nonlocal response of the metal (at the Lindhard level) for planar metal surfaces have been also explored. The calculation of static and dynamic electrostatic interactions between the molecule, the complex shaped metal body and the solvent or matrix was done by using a BEM coupled, in some versions of the model, with an IEF approach. 

Conducting particles held in a nonconducting medium form a system which has a frequency-dependent dielectric constant. The dielectric loss in such a system depends upon the build-up of charges at the interfaces, and has been modeled for a simple system by Wagner [8], As the concentration of the conducting phase is increased, a point is reached where individual conducting areas contribute and this has been developed by Maxwell and Wagner in a two-layer capacitor model. Some success is claimed for the relation... 

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.. 

We are faced with special problems if the volume of the sample, e.g. of a polymer, is varied by swelling. Sorption on such materials may be investigated by means of a horizontally arranged rotary pendulum [7,8] in combination with gravimetric density determinations [9]. Sophisticated pendulum experiments may be replaced by impedance measurements for the determination of the (frequency-dependent) dielectric constant [10]. 

Figure 1 Real(top) and imaginary (bottom) parts of the frequency dependent dielectric constant for the TIP4P-FQ model (solid lines), compared to experiment (dotted lines).

Figure 7 Calculated frequency dependence of the real part of the dielectric constant versus frequency for an array of quantum dots connected by one-dimensional wires (from Ref. 57). The inset presents the measured frequency dependent dielectric constant for four different samples of HCSA doped polyaniline of differing conductivities (from Refs 44...

The role of the medium, in which contacting and pull-off are performed, has been mentioned but not considered so far. However, the surroundings obviously influence surface forces, e.g., via effective polarizability effects (essentially multibody interactions e.g., by the presence of a third atom and its influence via instantaneous polarizability effects). These effects can become noticeable in condensed media (liquids) when the pairwise additivity of forces can essentially break down. One solution to this problem is given by the quantum field theory of Lifshitz, which has been simplified by Israelachvili [6]. The interaction is expressed by the (frequency-dependent) dielectric constants and refractive indices of the contacting macroscopic bodies (labeled by 1 and 2) and the medium (labeled by 3). The value of the Hamaker constant Atota 1 is considered as the sum of a term at zero frequency (v =0, dipole-dipole and dipole-induced dipole forces) and London dispersion forces (at positive frequencies, v >0). 

The frequency dependent dielectric constant for a damped anharmonic oscillator of characteristic frequency wg and damping constant 7 is given by... 

Here and Ss are the frequency-dependent dielectric constants of the metal and the solution, respectively. Using known pyridine polarizability and silver dielectric data, large enhancements could be obtained (up to 10 ). In terms of the molecular picture, a several-eV decrease of level spacing was involved. This shift, however, strongly depends on the frequency, through the dielectric constant of the metal. This is a dynamic shift and the resonance is really a joint metal-molecule-photon excitation. This is different from a shift of levels under static fields. This point has often been misunderstood. 

For frequencies below E , the contribution of the two effects leads to a frequency-dependent dielectric constant (w) given by ... 

Furthermore, in a non-magnetic (where the permeability 4= 1) medium, n is related to the complex frequency-dependent dielectric constant (cop), and the dielectric susceptibility Xg, by... 

The frequency-dependent dielectric constant of a conducting medium e(approaches zero. Ionic solutions conduct, hence the static dielectric constant e(0), at least as it is usually defined, becomes infinite. Thus if we refer to the static dielectric constant of an ionic system, it is necessary to define that term precisely. An excellent discussion of this question has been recently given by Hubbard, Colonomos, and Wolynes. For ionic solutions it is possible to define an apparent dielectric constant,... 

There has been much controversy in the past several years concerning the relation of the dispersion of the dielectric constant to the molecular dipole-moment correlation function (see Titulaer and Duetch, 1974). Fatuzzo and Mason (1967) have shown that the autocorrelation function of the net dipole moment of a sphere imbedded in a medium of the same dielectric constant is related to the frequency-dependent dielectric constant by... 

Dipole-dipole interaction between molecules placed in an oscillating electric field results in energy being transferred from the oscillating field to the sample. This phenomenon manifests itself as a frequency dependent dielectric constant and is a property common to all materials. The physical basis of the measurement is expressed by Equation 3. 

Let us first discuss estimates fi om DR measurements that provide several important pieces of information. These experiments measure the frequency-dependent dielectric constant and provide a measure of a liquid s polarization response at different frequencies. In bulk water, we have two dominant regions. The low-frequency dispersion gives us the well-known Debye relaxation time, Tq, which is equal to 8.3 ps. There is a second prominent dispersion in the high-frequency side with relaxation time constant less than Ips which contains combined contributions from low-frequency intermolecular vibrations and libra-tion. Aqueous protein solutions exhibit at least two more dispersions, (i) A new dispersion at intermediate frequencies, called, d dispersion, which appears at a timescale of about 50 ps in the dielectric spectrum, seems to be present in most protein solutions. This additional dispersion is attributed to water in the hydration layer, (ii) Another dispersion is present at very low frequencies and is attributed to the rotation of the protein. 

The dielectric spectra of aqueous protein solutions exhibit anomalous dielectric increments where the value of the static dielectric constant of the solution is significantly larger than that of pure water. A typical experimental result illustrating the dielectric increment is shown in Figure 8.3, where the real part of the frequency-dependent dielectric constant of myoglobin is evident. Both the increment at zero frequency and the overall shape of this curve have drawn a lot of attention. 

---