Zadeh


Clearly another division of the surface region is in order. As illustrated in Figs. V.3b and c, the surface of the solid has a potential o. which may be controlled by potential-determining ions indistinguishable from those already in the solid (as in the case of Agl). Next there may be a layer of chemically bound, desolvated ions such as H or OH on an oxide surface or Cr on Au. If such a layer is present, will be associated with it as indicated in the figure, along with the surface charge density oq. Next will be the Stem layer of compactly bound but more or less normally solvated ions at potential f/ff and net surface charge density a. We thus have an inner, potential-determining compact layer of dielectric constant i an outer compact (Stem) layer of dielectric constant 2 and, finally, the diffuse layer. The Stem layer is rather immobile in the sense of resisting shear, thus there is no reason for the shear plane to coincide exactly with the Stem layer boundary and, as suggested in Fig. V-3c, it may be located somewhat farther out. The potential at this shear layer, known as the zeta potential, is involved in electrokinetic phenomena discussed in Section V-4.  [c.178]

One can write acid-base equilibrium constants for the species in the inner compact layer and ion pair association constants for the outer compact layer. In these constants, the concentration or activity of an ion is related to that in the bulk by a term e p(-erp/kT), where yp is the potential appropriate to the layer [25]. The charge density in both layers is given by the algebraic sum of the ions present per unit area, which is related to the number of ions removed from solution by, for example, a pH titration. If the capacity of the layers can be estimated, one has a relationship between the charge density and potential and thence to the experimentally measurable zeta potential [26].  [c.178]

There are a number of complications in the experimental measurement of the electrophoretic mobility of colloidal particles and its interpretation see Section V-6F. TTie experiment itself may involve a moving boundary type of apparatus, direct microscopic observation of the velocity of a particle in an applied field (the zeta-meter), or measurement of the conductivity of a colloidal suspension.  [c.184]

Calculate the zeta potential for the system represented by the first open square point (for pH 3) in Fig. V-8.  [c.216]

R. J. Hunter, Zeta Potential in Colloid Seience Principles and Applications, Academic, Orlando, FL, 1981.  [c.217]

Double zeta with polarisation  [c.124]

Morokuma studied a number of hydrogen-bonded complexes using this scheme in order to assess the contribution from each component. The systems studied were typically of inter-molecular complexes involving small molecules such as H2O, HF and NH3. In addition, Morokuma and his colleagues also examined a series of electron donor-acceptor complexes such as H3N-BF3, OC-BH3, HF-CIF and benzene-OC(OSf)2. He also studied the basis-set dependence of the results and observed that the energy components were more sensitive than the energy differences. For example, a minimal STO-3G basis set overestimates the charge transfer contribution, whereas double zeta basis sets tend to exaggerate the electrostatic interaction.  [c.143]

Convergence of this iteration is influenced by initial estimates for the true mole fractions, zThe following rules have been found to lead to rapid convergence in all cases.  [c.135]

What is the magnitude of the attainable sedimentation potential given by Eq. V-47 for an aqueous suspension of 300 nm polystyrene latex spheres (density = 1.059 g/cm ) having a zeta potential of 100 mV Assume you are using a typical benchtop centrifuge with a 20-cm rotor radius and 6 cm centrifuge tubes inclin 30° from the vertical. Plot the measurable potential versus the angular velocity of the centrifuge.  [c.217]

Quantitative measurements of flocculation rates have provided estimates of Hamaker constants in qualitative agreement with theory. One assumes diffusion-limited flocculation where the probability to aggregate decreases with the exponential of the potential energy barrier height of the type illustrated in Fig. Vl-5. The barrier height is estimated from the measured flocculation rate other measurements (see Section V-6) give the surface (or zeta) potential leaving the Hamaker constant to be determined from Equations like VI-36 [47 9]. Complications arise from the assumption of constant surface potential during aggregation, double-layer relaxation during aggregation [50-52], and nonuniform charge distribution on the particles [53-55], In studies of the stability of ZnS sols in NaCl and CaC Duran and co-workers [56] found they had to add the Lewis acid-base interactions developed by van Oss [57] to the DLVO potential to model their measurements. Alternatively, the initial flocculation rate may be measured at an ionic strength such that no barrier exists. By this means Apwp was found to be about 0.7 x 10 erg for aqueous suspensions of polystyrene latex [58]. The hydrodynamic resistance between particles in a viscous fluid must generally be recognized to obtain the correct flocculation rates [3].  [c.242]

A double-zeta (DZ) basis in which twice as many STOs or CGTOs are used as there are core and valence AOs. The use of more basis functions is motivated by a desire to provide additional variational flexibility so the LCAO-MO process can generate MOs of variable difhiseness as the local electronegativity of the atom varies.  [c.2171]

A triple-zeta (TZ) basis in which tlnee times as many STOs or CGTOs are used as the number of core and valence AOs (and, yes, there now are quadniple-zeta (QZ) and higher-zeta basis sets appearing in the literature).  [c.2171]

The next step in iin proving a basis set could be to go to triple zeta, quadruple zeta, etc. Ifone goes in this direction rather than adding functions of higher angular quantum number, the basis set would not be well balanced. With a large number of s and p functions only, one finds, for example, that the equilibrium geometry of am monia actually becomes planar. The next step beyond double z.ela n sit ally in voices addin g polarization fn n ciion s, i.e.. addin g d-  [c.260]

A deficiency of the basis sets described so far is their inability to deal with species such as anions and molecules containing lone pairs which have a significant amount of electron density away from the nuclear centres. This failure arises because the amplitudes of the Gaussian basis functions are rather low far from the nuclei. To remedy this deficiency highly diffuse functions can be added to the basis set. These basis sets are denoted using a thus the 3-21+G basis set contains an additional single set of diffuse s- cind p-type Gaussian functions. ++ indicates that the diffuse functions are included for hydrogen as well as for heavy atoms. At these levels the terminology starts to become a little unwieldy. For example, the 6-311-f- -G(3df, 3pd) basis set uses a single zeta core and triple zeta valence representation with additional diffuse functions on all atoms. The (3df, 3pd) indicates three sets of d functions and one set of f functions for first-row atoms and three sets of p functions and one set of d functions for hydrogen. This latter convention is probably the most generic one commonly encoxmtered example is the 6-31G(d) basis set, which is synonymous with 6-31G.  [c.91]

Run a single point STO-3G calculation of the total energy of H2O at the MM3 geometry in the GAMESS implementation. Compare your result with the identical calculation in the GAUSSIAN implementation. Repeat the calculation using the double zeta valence (DZV) and triple zeta valence (TZV) basis sets in the GAMESS implementations. Comment on the relative energies calculated by single, double, and triple zeta basis sets.  [c.317]

Double zeta valence or triple zeta valence calculations can be carried out by putting DZV or TZV in place of STO NGAUSS = 3 in the second line of the INPUT file in the GAMESS implementation. The calculated energies become progressively lower (better) for double and triple zeta basis sets  [c.318]

Plot the curve of the bond energy of H2 vs. intemuclear distance for the H2 molecule using the STO-3G, double zeta valence (DZV), and triple zeta valence (TZV) basis sets in the GAMESS implementation.  [c.318]

A double-zeta (DZ) basis in which twice as many STOs or CGTOs are used as there are  [c.468]

A triple-zeta (TZ) basis in which three times as many STOs or CGTOs are used as the number of core and valence atomic orbitals.  [c.468]


See pages that mention the term Zadeh : [c.323]    [c.150]    [c.432]    [c.182]    [c.2426]    [c.2428]    [c.2674]    [c.260]    [c.262]    [c.264]    [c.270]    [c.90]    [c.90]    [c.90]    [c.124]    [c.188]    [c.319]    [c.468]    [c.158]    [c.180]   
Advanced control engineering (2001) -- [ c.3 ]