Charge density parameter

According to Manning s theory [43-45], a polyion is characterized by a dimensionless charge density parameter B, which is defined by... 

Average axial spacing in A between charged groups on the polyion b Charge density parameter calculated from Eq. 5 using the dielectric constant of bulk water (e = 78)... 

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. 

Fig. 4. Relationship between the electrostatic potential calculated from the PB equation and the charge density parameter at distances 5,10, and 15 A from the axis of a cylinder with 3 A radius. Points indicate experimental data listed in Table 1 [42]...

The DE were determined by titrimetry, and the galacturonic acid (GalA) content was measured by the m-hydroxybiphenyl method [25]. The structural charge density parameter introduced by Lifson and Katchalsky [26], is given by = e2/bDkT(l-DE/100) were e is the electron charge, kT the Boltzman term, b... 

For a univalent counterion the charge density parameter X was found to be A = 1.551a where a value of 7 = 1.06 was employed because of the degree of esterification of the methyl ester of PGA ( 5.34 per cent). A comparison of calculated and experimental values of i,pK -pKl) at different degrees of dissociation is shown in Fig. 2. For pK the values from Table 2 were used. 

The nature of the charge density parameters to be added to those of the structure refinement follows from the charge density formalisms discussed in chapter 3. For the atom-centered multipole formalism as defined in Eq. (3.35), they are the valence shell populations, PLval, and the populations PUmp of the multipolar density functions on each of the atoms, and the k expansion-contraction parameters for... 

When observed structure factors are used, the thermally averaged deformation density, often labeled the dynamic deformation density, is obtained. An attractive alternative is to replace the observed structure factors in Eq. (5.8) by those calculated with the multipole model. The resulting dynamic model deformation map is model dependent, but any noise not fitted by the muitipole functions will be eliminated. It is also possible to plot the model density directly using the model functions and the experimental charge density parameters. In that case, thermal motion can be eliminated (subject to the approximations of the thermal motion formalism ), and an image of the static model deformation density is obtained, as discussed further in section 5.2.4. 

Transferability of Charge Density Parameters Among Related Atoms... 

Transferability of atomic densities was tested by Brock et al. (1991), who applied atomic charge density parameters from an accurate low-temperature study of perylene (I) to data collected at five and six different temperatures on naphthalene (II) and anthracene (III), respectively. The molecules are all aromatic hydrocarbons. To reduce the number of variables, all H atoms were assigned... 

Derive the charge-density parameters required for molecular symmetries equal to 1, to m, and to 4 mm by... 

A linear charge density parameter (Manning parameter) has been defined as ... 

Now, consider B-DNA molecules in an aqueous solution. Manning showed that the electrostatic stability of the DNA is controlled by the dimensionless linear charge density parameter , [17, 31]. The ratio of the Bjerrum length ZB to the charge spacing b of the phosphates defines the linear charge density [17, 31]... 

As before, the total free energy is minimized with respect to 0. Minimization leads to the following results [41]. (a) The minimum value of 0 is identical with Eq. (7) from the line model. This implies that the number of condensed ions is unaffected by the helix and is governed only by the linear charge-density parameter E,. (b) The partition function <2heiix is influenced by the helical structure of the phosphate charges... 

In Manning model, the slope off versus the Coulomb strength or the linear charge density parameter lB lB/l is discontinuous at 1 [31,48], This is a consequence of the fact, that for all less than or equal to unity, / is linear function of 1/s and saturates at unity [31, 35, 48]. The present model indicates a sigmoidal variation off with 1/e and saturates as /H > 0 [48],... 

This work is to be followed by an analysis of an experimental set of intensity data obtained with both the X-ray and polarized neutron techniques. This will allow application of the formalisms described above, and a direct comparison of experimental charge density parameters with theoretical results. 

However, they pointed out that the sensitivity of J(Si-Q to the valence bond equivalent of PssiSc the compounds containing only Si, C, and H is substantially lower. (158) The authors suggest the possibility that this discrepancy arises from the assumption of a constant AE. Correlations with charge density parameters reflecting electron deficiency of the Si-C bond and polarization in the sense Si C are also found. (160)... 

Sonnefeld, L, Determination of surface charge density parameters of silicon nitride, Colloids Surf. A, 108, 27, 1996. 

P. Coppens, R. Boehme, P. F. Price and E. D. Stevens, Electron population analysis of accurate diffraction data. 10. Joint X-ray and neutron data refinement of structural and charge density parameters, Acta Cryst. A37, 857-863 (1981). 

CM-HEC = carboxymethyl-hydroxyethyl cellulose DP = degree of polymerization DS = degree of substitution f = charge density parameter Ap/10 4 m2ft 1 monomoU1, at C = 2 monomol irT3. 

FIG. 1 Variation of the local concentration, C, of the monovalent counterion of radius 0.3 nm with the radial distance, r, from the axis of the cylindrical polyion of radius a = 0.8 nm. The average counterion concentration is marked by Cav, d is the exclusion distance from the polyion axis to the center of the counterion, and/is the fraction of free counterions. The value of the charge density parameter A = 2.83 is typical for aqueous solutions of poly(styrenesulfonates) at 25°C, and the value of the radius of the cell R = 65.2 nm corresponds to the polyelectrolyte concentration CP = 5 X 10 4 monomol dm3. 

The point of interest in NaPA (a weak polyelectrolyte with degree of ionization 1) and NaPSS (a strong polyelectrolyte) is that they have the same linear charge density parameter, A, so that eventual differences in binding parameters would be attributed to their dissimilar hydrophobic character. As stated in the introduction, the charge density of poly(acrylate) anion, PA , can be varied continuously by changing its degree of ionization, a [from a = 0 for poly(acrylic acid), UPA, to a = 1 for the fully ionized salt, NaPA], The relation between A and a is... 

Jelsch, C., Pichon-Pesme, V., Lecomte, C., Aubry, A. Transferability of multipole charge-density parameters application to very high resolution oligopeptide and protein structures, Acta Crystallogr. 54D (1998) 1306-1318. 

The influence of charge density on the catalytic effect can be illustrated by comparing the catalytic activity of 2,4-, 2,6- and 2,10-ionenes with 1 10. These data are compared with results obtained for the VAm-VAl copolymers. The dimensionless linear charge density parameter A of the polycations was calculated according to the rigid rod cell model for polyelectrolytes proposed hy Katchalsky [154]. Activation parameters of thiols in the presence of ionenes and VAm-VAl copolymers at pH 7.8 and T = 298 K are presented in Tkble 6. 

The central parameter of modern polyelectrolyte theories is 5, the linear charge density parameter in the model of l anning (3.) ... 

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