Dielectric water

An alternative solution to the dielectric water problem that applies in particular to standard TE102 rectangular resonators, is to use a flat cell a rectangular sample holder that is oversized in the vertical direction, and with one small cut-through dimension, say 1 mm, and the other dimension circa 10 mm, that is, approaching the bore of the cavity access holes (Figure 3.11). When in place in the resonator, this cell is rotated about its vertical axis to a position such that the 10 mm dimension points to a direction of minimal /i-field. 

Polymer Labile block (wt%) Stress (MPa) n(TE) n(TM) Void volume (%) Dielectric %Water constant uptake QCM ... 

For the sphere and DAPI both the NLPB and limiting law models (infinite length polymer at infinite dilution) give a slope with salt concentration close in magnitude to the net ligand charge. However, the enthalpy/entropy breakdown of the salt dependence is quite different. In the PB model, there are considerable contributions from electrostatic enthalpy and dielectric (water reorientation) entropy, compared to the cratic entropy of ion release in the limiting law model. 

The external reflection of infrared radiation can be used to characterize the thickness and orientation of adsorbates on metal surfaces. Buontempo and Rice [153-155] have recently extended this technique to molecules at dielectric surfaces, including Langmuir monolayers at the air-water interface. Analysis of the dichroic ratio, the ratio of reflectivity parallel to the plane of incidence (p-polarization) to that perpendicular to it (.r-polarization) allows evaluation of the molecular orientation in terms of a tilt angle and rotation around the backbone [153]. An example of the p-polarized reflection spectrum for stearyl alcohol is shown in Fig. IV-13. Unfortunately, quantitative analysis of the experimental measurements of the antisymmetric CH2 stretch for heneicosanol [153,155] stearly alcohol [154] and tetracosanoic [156] monolayers is made difflcult by the scatter in the IR peak heights. 

Increasingly, dielectric measurements are being used to characterize the water content of emulsions. One model for the dielectric constant of a suspension, ... 

Fig. XIV-2. Dielectric relaxation spectrum of a water-in-oil emulsion containing water in triglyceride with a salt concentration of 5 wt % at a temperamre of 25°C. The squares are experimental points and the lines are fits to Eq. XIV-4. (From Ref. 9.)...

Dielectric Behavior of Adsorbed Water. Determination of the dielectric absorption of adsorbed water can yield conclusions similar to those from proton NMR studies and there is a considerable, although older literature on the subject. Figure XVI-7 illustrates how the dielectric constant for adsorbed water varies with the frequency used as well as with the degree of surface coverage. A characteristic relaxation time r can be estimated... 

Fig. XVI-7. Dielectric isotherms of water vapor at 15°C adsorbed on a-FeiOa (solid points indicate desorption). A complete monolayer was present at P/P = 0.1, and by P/P = 0.8 several layers of adsorbed water were present. (From Ref. 110.)...

Similar, very detailed studies were made by Ebert [112] on water adsorbed on alumina with similar conclusions. Water adsorbed on zeolites showed a dielectric constant of only 14-21, indicating greatly reduced mobility of the water dipoles [113]. Similar results were found for ammonia adsorbed in Vycor glass [114]. Klier and Zettlemoyer [114a] have reviewed a number of aspects of the molecular structure and dynamics of water at the surface of an inorganic material. 

The state of an adsorbate is often described as mobile or localized, usually in connection with adsorption models and analyses of adsorption entropies (see Section XVII-3C). A more direct criterion is, in analogy to that of the fluidity of a bulk phase, the degree of mobility as reflected by the surface diffusion coefficient. This may be estimated from the dielectric relaxation time Resing [115] gives values of the diffusion coefficient for adsorbed water ranging from near bulk liquids values (lO cm /sec) to as low as 10 cm /sec. 

Barker J A and Watts R O 1973 Monte Carlo studies of the dielectric properties of water-like models Mol. Phys. 26 789-92... 

The Hamaker constant can be evaluated accurately using tire continuum tlieory, developed by Lifshitz and coworkers [40]. A key property in tliis tlieory is tire frequency dependence of tire dielectric pennittivity, (cij). If tills spectmm were tlie same for particles and solvent, then A = 0. Since tlie refractive index n is also related to f (to), tlie van der Waals forces tend to be very weak when tlie particles and solvent have similar refractive indices. A few examples of values for A for interactions across vacuum and across water, obtained using tlie continuum tlieory, are given in table C2.6.3. 

Table 2 shows the results of our preliminary calculations of the pKa of the Cys403 residue, for several different models of the enzyme, based on two structures available from the PDB. In the case of the YPT structure, a crystal water molecule is close to Cys403 and was included in some of the calculations as part of the protein (i.e. it was treated with the same internal dielectric as that of the protein). Simulations denoted as -I-H2O in Table 2, include a crystallographically resolved, buried water molecule, situated 3.2lA from... 

T. Simonson. Accurate calculation of the dielectric constant of water from simulations of a microscopic droplet in vacuum. Chem. Phys. Lett, 250 450-454, 1996. 

N is the number of point charges within the molecule and Sq is the dielectric permittivity of the vacuum. This form is used especially in force fields like AMBER and CHARMM for proteins. As already mentioned, Coulombic 1,4-non-bonded interactions interfere with 1,4-torsional potentials and are therefore scaled (e.g., by 1 1.2 in AMBER). Please be aware that Coulombic interactions, unlike the bonded contributions to the PEF presented above, are not limited to a single molecule. If the system under consideration contains more than one molecule (like a peptide in a box of water), non-bonded interactions have to be calculated between the molecules, too. This principle also holds for the non-bonded van der Waals interactions, which are discussed in Section 7.2.3.6. 

On one hand, there are the dielectric properties, which are especially important for polai solvents like water. Bulk properties can, on the other hand, only be modeled by using a supermolecule approach with explicitly defined solvent molecules. 

By using an effective, distance-dependent dielectric constant, the ability of bulk water to reduce electrostatic interactions can be mimicked without the presence of explicit solvent molecules. One disadvantage of aU vacuum simulations, corrected for shielding effects or not, is the fact that they cannot account for the ability of water molecules to form hydrogen bonds with charged and polar surface residues of a protein. As a result, adjacent polar side chains interact with each other and not with the solvent, thus introducing additional errors. 

In this model of electrostatic in teraction s, two atoms (i and j) have poin t charges tq and qj. The magnitude of the electrostatic energy (V[. , [ ) varies inversely with the distance between the atoms, Rjj. fh e effective dielectric constant is . For in vacuo simulations or simulation s with explicit water rn olecules, the den om in a tor equals uRjj, In some force fields, a distance-dependent dielectric, where the denominator is uRjj Rjj, represen is solvent implicitly. 

Use a constant dielectric of 1.0 with TIP3P water molecules m a periodic box. Because of ihe paramelerizatioii of TIP3P molecules, using a distart ce-dependen t dielectric or a value other th an 1.0 gives un Tialiiral results. 

The first modification is to simply scale the dielectric permittivity of free space (T( ) by a scale factorD to rn ediate or dam pen thelong range electrostatic interactions. Its value was often set to be between 1.0 and 7H.0, the macroscopic value for water. A value of D=2..5, so that u=2..5Ug, wasoften used in early CIIARMM calculation s. 

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