Surface value, dielectric constant

Eluents used in reversed-phase chromatography with bonded nonpolar stationary phases are genei ly polar solvents or mixtures) of polar solvents, such as acetonitrile, with water. The properties of numerous neat solvents of interest, their sources, and their virtues in teversed-phase chromatography have been reviewed (128). Properties of pure solvents which may be of value as eluents are summiuized in Table. VII. The most significant properties are surface tension, dielectric constant, viscosity, and eluotropic value. Horvath e/ al. 107) adapted a theory of solvent effects to consider the role of the mobile phase in determinmg the absolute retention and the selectivity found in reversed-phase chromatography. 

The form of the potential curve depends on the values of the surface potential dielectric constant e, valency z and concentration of ions c, temperature T, Van Der Waals constant A and dimensions of the particles (for instance their radius a). When the discussion is restricted to aqueotis solutions at room temperature which fixes c and Tf and when the particles are assumed to be comparatively large and fiat faced, so that they... 

Revised material in Section 5 includes an extensive tabulation of binary and ternary azeotropes comprising approximately 850 entries. Over 975 compounds have values listed for viscosity, dielectric constant, dipole moment, and surface tension. Whenever possible, data for viscosity and dielectric constant are provided at two temperatures to permit interpolation for intermediate temperatures and also to permit limited extrapolation of the data. The dipole moments are often listed for different physical states. Values for surface tension can be calculated over a range of temperatures from two constants that can be fitted into a linear equation. Also extensively revised and expanded are the properties of combustible mixtures in air. A table of triple points has been added. 

The 2eta potential (Fig. 8) is essentially the potential that can be measured at the surface of shear that forms if the sohd was to be moved relative to the surrounding ionic medium. Techniques for the measurement of the 2eta potentials of particles of various si2es are collectively known as electrokinetic potential measurement methods and include microelectrophoresis, streaming potential, sedimentation potential, and electro osmosis (19). A numerical value for 2eta potential from microelectrophoresis can be obtained to a first approximation from equation 2, where Tf = viscosity of the liquid, e = dielectric constant of the medium within the electrical double layer, = electrophoretic velocity, and E = electric field. 

The value of e ff for A-100 (3 with x = 100) is significantly lower than the dielectric constant of bulk water (e = 78), and it decreases further with decreasing charge density. This behavior is apparently ascribable to the hydrophobicity of the polymer backbone and also to the surface charge (dielectric saturation). 

Manning s theory does not take the local effective dielectric constant into consideration, but simply uses the a value of bulk water for the calculation of E,. However, since counterion condensation is supposed to take place on the surface of polyions. Manning s 2, should be modified to E, by replacing a with aeff. The modified parameters E, is compared with E, in Table 1, which leads to the conclusion that the linear charge density parameter calculated with the bulk dielectric constant considerably underestimates the correct one corresponding to the interfacial dielectric constant. 

Currently, there is a trend of low dielectric constant (low-k) interlevel dielectrics materials to replace Si02 for better mechanical character, thermal stability, and thermal conductivity [37,63,64]. The lower the k value is, the softer the material is, and therefore, there will be a big difference between the elastic modulus of metal and that of the low-k material. The dehiscence between the surfaces of copper and low-k material, the deformation and the rupture of copper wire will take place during CMP as shown in Fig. 28 [65]. 

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. 

Following the concepts of H. Helmholtz (1853), the EDL has a rigid structnre, and all excess charges on the solntion side are packed against the interface. Thus, the EDL is likened to a capacitor with plates separated by a distance 5, which is that of the closest approach of an ion s center to the surface. The EDL capacitance depends on 5 and on the value of the dielectric constant s for the medium between the plates. Adopting a value of 5 of 10 to 20 nm and a value of s = 4.5 (the water molecules in the layer between the plates are oriented, and the value of e is much lower than that in the bulk solution), we obtain C = 20 to 40 jjE/cm, which corresponds to the values observed. However, this model has a defect, in that the values of capacitance calculated depend neither on concentration nor on potential, which is at variance with experience (the model disregards thermal motion of the ions). 

It is conceivable that the lowest descending pKa and the lowest ascending pKa may cross as Rw approaches 100% [162]. It is interesting that the dielectric constant for pure methanol is about 32, the same value associated with the surface of phospholipid bilayers (in the region of the phosphate groups). This point is further explored later. 

Ionizable molecules embedded in the surfaces of lipids, such as octanol (see Fig. 2.8), liposomes (see Fig. 5.2), or micelles, will have their apparent pKa values shifted. With neutral lipids, the pKa of an acid increases and the pKa of a base decreases. This is due to the effect of the decreased dielectric constant in the interfacial zone, as we have already discussed in various sections. 

The uncharged ion is transferred into a solvent with permittivity e = De0y where D is the relative permittivity (dielectric constant) of the medium. No work is gained or lost in this process. In the solvent, the ion is again recharged to the value of the electric potential at its surface,... 

With the addition of a pseudopotential interaction between electrons and metal ions, the density-functional approach has been used82 to calculate the effect of the solvent of the electrolyte phase on the potential difference across the surface of a liquid metal. The solvent is modeled as a repulsive barrier or as a region of dielectric constant greater than unity or both. Assuming no specific adsorption, the metal is supposed to be in contact with a monolayer of water, modeled as a region of 3-A thickness (diameter of a water molecule) in which the dielectric constant is 6 (high-frequency value, appropriate for nonorientable dipoles). Beyond this monolayer, the dielectric constant is assumed to take on the bulk liquid value of 78, although the calculations showed that the dielectric constant outside of the monolayer had only a small effect on the electronic profile. 

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