Dielectric constant worked example

The common example of real potential is the electronic work ftmction of the condensed phase, which is a negative value of af. This term, which is usually used for electrons in metals and semiconductors, is defined as the work of electron transfer from the condensed phase x to a point in a vacuum in close proximity to the surface of the phase, hut heyond the action range of purely surface forces, including image interactions. This point just outside of the phase is about 1 pm in a vacuum. In other dielectric media, it is nearer to the phase by e times, where e is the dielectric constant. 

Variations in dielectric constant should alter the relative strength of acids of different charge types, since the amount of electrical work involved in a proton-transfer reaction must vary with the dielectric constant of the medium. Since a lowering in dielectric constant increases the work required to separate the ions (for example, to ionize an uncharged acid one must create an anion and a cation), any addition of organic solvent should lead to an increase of pXa values. 

Several examples of the use of microelectrodes in highly resistive media exist. The first reported measurements were an examination of the reduction of aromatic hydrocarbons such as perylene in benzene containing tetrahexylammonium perchlorate [57]. Although this electrolyte is presumably in a quite associated state in benzene (or toluene [58]), it does impart sufficient conductivity for electrochemistry to be observed. In subsequent work, this result was confirmed and extended to other low-dielectric-constant solvents [59]. Even voltammetry in hexane has been shown to be possible with a microelectrode [60]. In this sol-... 

Mayer [22], the above correlations indeed work well and are quite useful for predicting values such as the free energy of salt solutions and complex formation in various solvents. Another typical example of the importance of the use of DN and AN as solvent parameters, instead of properties such as the dielectric constant, would be ion pair association constants in isodielectric solvents. For instance, as shown by Mayer [15], association constants of various perchlorates isocyanates, and halides (alkali metal, ammonium, and tetraalkyl ammonium cations) are very different in isodielectric solvents such as nitromethane (DN = 2.7), acetonitrile (DN = 14.1), and DMF (DN = 26.6), whose dielectric constant is around 26 at room temperature. 

In photonic materials, the band gap is determined by geometric arrangement of a dielectric material. The underlying principle of how photonic materials work is best explained using Maxwell s equations (Joannopoulos et al., 1995). Once again, the central importance of Maxwell s equations is confronted when optical properties of materials are discussed. In photonic materials, a periodic stmcture is produced in one, two, or three dimensions. The periodic property is a dielectric constant. A trivial macroscopic onedimensional example would be a collection of individual microscope shdes separated by layers of Saran Wrap . This would produce a one-dimensional modulation in the... 

Problem 7.4 (Worked Example) Consider a suspension of silica particles in water for which the Hamaker constant is 10" J and the dielectric constant is = 50. If the surface charge is 0.1 charges/nm, calculate how high the molarity of NaCl must be to induce flocculation. Remember, each surface charge is that of an electron, e = 1.6 x 10" C, the permittivity of space is q = 8.8 x 10 J m , and the Bjerrum length is ib — 58/s nm. Assume a weak... 

Water is an example of a liquid that works well for supercritical fluid extraction/upgrading. Liquid water at standard conditions can be an excellent solvent for many compounds and electrolytes because of its high dielectric constant, but it is negligibly miscible with hydrocarbons and gases. However, in the supercritical region, water becomes completely miscible wifli hydrocarbons and gases. In this region, there are no phase boundaries and many reactions may proceed without many mass transfer limitations (25). 

Even considering different temperatures, there is a clear relationship between the extracted compounds (and therefore, ECso) the ethanol fiaction used as extracting ag t. For example, better EC50 values were obtained i en working with a mixture water ethanol (80 20) (25°C) that implies a dielectric constant equal to 69 than when working with 100% water at 60°C (dielectric constant equal 60). 

The MD simulation by Marchi [8] of the librational band (Fig. 18) is rather poor in this example. A better simulation is for the translational band (solid line in Fig. 19). The dashed curve represents here the energy loss function determined by the dielectric constant s and calculated in the cited work by Marchi. The shift between the solid and dashed curves represents a specific parameter of the fluid... 

Several other treatments of solvent effects on solvolysis rates have been developed. The equations typically include several terms related to (a) macroscopic nonspecific solvent properties, such as the dipole moment and dielectric constant (b) empirical polarity criteria, such as Ej.(30) (c) solvent electrophilicity and nucle-ophilicity parameters and (d) terms related to solvent cohesivily. The last term accounts for the difference in work required to disrupt structure within the solvent, when, for example, there is expansion in volume between reactants and the TS. 

The increasing use of physical data in laboratory work has also led to developments in the technique of determining the dielectric constant. This constant is an especially useful quantity when the mixture contains water (diel. const. 80) or other components having widely different values. Examples are the mixtures acetic acid (diel. const 6.13)-acetic anhydride (22.2) and methanol-toluene. In the latter system the azeotroj)e has a dielectric constant of 26.8, whilst methanol and toluene have values of 33.8 and 2.37, respectively [65]. The dielectric constant has also proved convenient for determining toluene in benzene, in spite of the fact that the difference in the figures for these two com x>nents is only 0.08 units. 

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