Static dielectric permittivity

The first term, which contains the the static dielectric permittivities of the three media , 2, and 3, represents the Keesom plus the Debye energy. It plays an important role for forces in water since water molecules have a strong dipole moment. Usually, however, the second term dominates in Eq. (6.23). The dielectric permittivity is not a constant but it depends on the frequency of the electric field. The static dielectric permittivities are the values of this dielectric function at zero frequency. 1 iv), 2 iv), and 3(iv) are the dielectric permittivities at imaginary frequencies iv, and v = 2 KksT/h = 3.9 x 1013 Hz at 25°C. This corresponds to a wavelength of 760 nm, which is the optical regime of the spectrum. The energy is in the order of electronic states of the outer electrons. 

Charge attached to a water molecule Complex, static dielectric permittivity (dimensionless quantity)... 

ZD, ZA are the charges of the donor and acceptor ions, and e0 is the static dielectric permittivity of the medium where the tunneling electron transition occurs. 

The dielectric properties of electrolytes are almost identical to those of water with the addition of a a term in Eq. (1) due to the ionic conductance of the dissolved ion species. The static dielectric permittivity of electrolytes of usual physiological strength (0.15 N) is about two units lower than that of pure water (4), a negligible change. 

Three dielectric parameters are characteristic of the electrical and viscous properties of tissue water a) the conductance of ions in water, b) the relaxation frequency fc, and c) the static dielectric permittivity eQ observed at f fc =... 

The percolation behavior is manifested by the rapid increase in the dc electrical conductivity a and the static dielectric permittivity ss as the system approaches the percolation threshold (Fig. 7). 

Figure 7. The percolation behavior in AOT-water-decane microemulsion (17.5 21.3 61.2 vol%) is manifested by the temperature dependences of the static dielectric permittivity es (A left axis) and conductivity r (Q right axis). Toa is the temperature of the percolation onset Tp is the temperature of the percolation threshold. Insets are schematic presentations of the microemulsion structure far below percolation and at the percolation onset. (Reproduced with permission from Ref. 149. Copyright 1998, Elsevier Science B.V.)...

The solvents used in electrochemical experiments should exhibit fairly high static dielectric permittivity, exceeding 10, in order to decrease the formation of ion-pairs, and consequently to guarantee good conductivity. The dielectric permittivity is also important in the calculation of the rate constant of the charge-transfer processes on... 

If vdielectric permittivity in vacuum will then be equal to 80. This is the so-called static permittivity. The permittivity of the vaccum is 0.855x 10 C m. The static dielectric permittivity near the ion or the surface of the charged electrodes, however, will exhibit smaller values. For instance, in the case of water at the electrode surface is assumed to approach 6. When applying the Marcus theory [8] both static and optical permittivities are used in calculations. These parameters therefore are listed in Table 1. In other calculations and correlations of the rate constants of electrode reactions and the dynamic relaxation properties of the solvents, the relaxation time of the solvents is used (Thble 1). 

The charge is assumed to be uniformly distributed on the surface of the sphere. Such an ion is transferred from vacuum, with a relative dielectric permittivity equal to 1, to the solvent, which is considered to be a structureless dielectric continuum characterized by the static dielectric permittivity, This transfer may be divided into two processes the transfer of a noncharged sphere from vacuum to continuum and the charging (to ne) of the transferred sphere. 

The nature of the solvent is represented in the Born equation only by the static dielectric permittivity e, which includes all types of polarization. The Born assumption on the structureless nature of the solvent may be only approximately fulfilled in the case when the ion is cdhsiderably larger than the solvent molecules. The problem of ion size and the applicability of the dielectric model has been discussed by Evans et al. [23]. 

All these correlations may be influenced by the ion-pair formation process, more advanced in solvents of lower static dielectric permittivity. This process, with free energy, AGfpf, given by... 

In Eq. (28) e is the charge of the electron, r the radius of the reactant, Avo-gadro s number, and d the reactant-electrode distance. The solvent was considered here as a continuous medium with a fast electronic polarization characterized by the optical dielectric permittivity and a slower oscillatory plus orientational polarization characterized by the static dielectric permittivity... 

Solvent Static dielectric permittivity, Outer Helmholtz plane potential, zero charge vs. potential of the Foe /Foe electrode (V)... 

In the analysis of experimental kinetic data, more attention should be paid to a careful determination of the longitudinal relaxation times. In the literature there are discrepancies between permittivities used for calculation of that parameter from the Debye relaxation time. Static dielectric permittivities and, to some extent, the Debye relaxation times exhibit a dependence on the electrolyte concentration. Therefore, in any analysis of the kinetic data, carefully measured and selected values fo the above parameters should be used. 

Drozd-Rzoska, A., Rzoska, S. J., and Czupiyhski, K. (2000) Phase transitions from the isotropic liquid to liquid ciystalhne mesophases studied by linear and nonlinear static dielectric permittivity, Phys. Rev. E 61, 5355-5360 Rzoska, S. J., Paluch, M., Drozd-Rzoska, A., Paluch, M., Janik, P., Ziolo J., and Czupryhski, K. (2001) Glassy and fluidlike behavior of the isotropic phase of mesogens in broad-band dielectric, Europ. Phys. J. E 7, 387... 

A convincing but indirect proof indicating a close connection between the motions of hydrogen atoms and the dielectric properties of aqueous fluids follows from the comparison of the static dielectric permittivity ss of ice Ih and ice II. In the former, where the proton disorder is emphasized, ss 100, while in the latter, where such a disorder is lacking, ss = 3.66 [17]. 

The extended simple point charge (SPC/E) model [59] is used. This model is known to give reasonably accurate values of static dielectric permittivity of liquid water at ambient conditions [60]. The MD simulations were performed for both H2O and D2O with the system size of 1024 particles at 220 K, 240 K, 267 K, 273 K, 300 K, and 355 K. The parallel molecular dynamics code for arbitrary molecular mixtures (DynaMix) is implemented by Lyubartsev and Laaksonen [61]. The simulations have been carried out on a Linux cluster built on the Tyan/Opteron 64 platform, which enables calculations of relatively long trajectories for a system of 1024 water molecules. The simulation run lengths depend on temperature and are in the range between 1 ns and 4 ns for the warmest and coldest simulation, respectively. As the initial condition was a cubic lattice, the equilibration time was chosen to be temperature dependent in the range from 200 ps at 355 Ktol ns at 200K. 

The magnitude of the dipole moment depends on the size and symmetry of the molecule. Molecules with a center of symmetry, for example methane, carbon tetrachloride, and benzene are apolar (zero dipole moment) whereas molecules with no center of symmetry are polar. Table 1.2 gives relative static dielectric permittivity... 

Below the percolation onset, both the conductivity a and static dielectric permittivity e of the microemulsions increase as a function of the volume fraction of droplets

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Unlike the mechanism of increasing conductivity below the percolation onset as a function of temperature, the temperature behavior of static dielectric permittivity has been hitherto puzzling. The static dielectric permittivity of dipolar... 

The dielectric measurements performed for the AOT/water/decane and AOT/water/hexane micro emulsions at the volume fraction of the dispersed phase of (p= 0.13 demonstrate the significant shift of the percolation region to the direction of high temperatures when the oil chain lengfli decreased (Fig. 18) (118, 119). However, the values of s for bofli die microemulsions are die same at low temperatures, i.e., below die percolation onset. Thus, diose results do not support die hypothesis that the clustering can be responsible for the temperature behavior of die static dielectric permittivity at F < and it must be the internal processes within a droplet diat determine the behavior of the dielectric polarization in the system. 

Figure 18 Static dielectric permittivity vs. temperature for the AOT-water-decane microemulsions for various volume fractions 0ofthe dispersed phase 0.39 (1) 0.26 (2) 0.13 (3) 0.043 (4). In the inset a similar plot for the AOT-water-decane (3,0) and AOT-water-hexane (3, o) microemulsions for < > = 0.13. The value W= [water]/[AOT] is kept constant at 26.3 for all the microemulsions. The lines are drawn as a guide for the eye. (From Ref 5. With permission from Elsevier Science B.V.)...

In order to ascertain the origms and mechanisms responsible for the observed temperature behavior of die static dielectric permittivity, let us analyze the total dielectric relaxation behavior of ionic mieroemulsions. Dynamic aspects of the dielectric polarization can be taken into account... 

A percolation phenomenon was found in ionie miero-emul-sion droplets when the water fraction, tiie temperature, the pressure, the strength of the electric field, or the ratio of water to the surfactant was varied (95-98, 101). Basieally, the pereolation behavior is manifested by the rapid inerease in eleetrical conductivity a and static dielectric permittivity e as the system approaehes flie percolation threshold (Fig. 17). 

Relaxation profiles obtained as loss peak in imaginary dielectric curve and as step jump of real permittivity line Partial miscibility might exhibit multiple relaxation peaks overlaying or towards individual components, or display diverse relaxation rate even >T, Non-isothermal crystallization by isochronal temperature sweep DSC (cold crystallization and melting discernible as sudden drop and steep rise of static dielectric permittivity, respectively) Crystallization onset predicted using DRS relaxation time in coupUng model faster than the experimental time... 

The value of e at low frequencies (the static dielectric permittivity) is determined in the simplest case by the Clausius-Mosotti equation... 

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