Multivalency parameter

These equations allow either to predict the swelling degree (w = l/(p) as a function of external conditions or to calculate the network parameters from the correlation between the theoretical and experimental dependencies w(q) or w(p) [22, 102], An example of such a correlation is given in Fig. 2 and 5. As can be seen, theoretical predictions are in good agreement with experimental data. However, when the outer solution contains multivalent cations, only a semi-quantitative agreement is attained. 

T. K. Dam, R. Roy, D. Page, and C. F. Brewer, Thermodynamic binding parameters of individual epitopes of multivalent carbohydrates to concanavalin A as determined by reverse isothermal titration microcalorimetry, Biochemistry, 41 (2002) 1359-1363. 

The internal structure of the complexes can directly determine the mechanism of transfection [4, 23, 25]. We have found that for Lac CL-DNA complexes, the membrane charge density (aM) is a predictive parameter for transfection efficiency [21] (see Sect. 2), i.e., the data for monovalent and multivalent cationic lipids are described by a simple bell-curve. In contrast, for inverted hexagonal HnC CL-DNA complexes, TE is independent of aM, suggesting a distinctly different mechanism of transfection. Consistent with the TE data, confocal microscopy revealed distinctly different CL-DNA complex pathways and interactions with cells, which depended on both the structure (HnC vs Lac) and, for Lr/ complexes, on aM [25]. Thus, the mechanism of transfection by CL-DNA complexes is dependent both on their structure and, for a given structure, on chemical and physical parameters of the complexes. 

Although there are still some discrepancies in the hterature regarding zinc levels in dialysis patients, most studies have found decreased levels of the element in serum [64,65] and muscles whereas the levels in bone [63] and other tissues seem to be normal or even increased suggesting translocation of the element in uremia. The dialysis treatment itself seems to have little or no effect on the serum zinc concentrations. Zinc deficiency in uremic patients has been associated with anorexia, disturbances in taste and sexual performance [66] whereas decreased plasma zinc seem to correlate with erythrocyte superoxide dismutase levels [67]. As evaluated by Tiirk et al. [68], zinc supplementation did not have any effect on the restoration of immune parameters or enhancement of the antibody response to multivalent influenza vaccine in hemodialysis patients. On the ofher hand however, has zinc supplementation been reported an effective means of improving serum levels of zinc and cholesterol in the hemodialysis patient [69]. 

Qualitatively, the phase diagram fits very well to the phase diagram known for single-chain polyelectrolytes, the phase boundaries are only slightly shifted. In principle, the parameter space for polyelectrol ffes has far more dimensions, such as the solvent quality parameter, the valency of monomers or counterions, and additional salt concentration in the system. Especially for multivalent counterions, one can expect an even more complex picture, since correlation effects are known to play an important role even for single chains. 

As noted above, multivalent cations in solution tend to be hydrated or coordinated with water molecules and thus may be called aquocomplexes. The extent of hydration of a cation is proportional to its ion size parameter ( ,). (This parameter is used in the Debye-Hiickel equation for ion activity coefficients see Chap. 4). For strongly hydrated Li", a, = 6 A, whereas for unhydrated Cs", a, = 2.5 A. This compares with the unhydrated sixfold coordination radii of 0.76 A for Li+ and 1.76 A for Cs" in minerals (Shannon 1976). 

The presence of organic ions or (hydrolyzed) multivalent metal ions requires an even more sophisticated approach to the EIL, and the modelling is usually more speculative. Common practice usually leaves open the problem of the point charge concept, in contrast to the homogeneous charge. Another problem which is not considered in practical applications is the structure of water in the interfacial region, which is connected to the homogeneity of the available space and the choice of the value of the relevant permittivity. The use of bulk permittivity results in an apparent value of all the space parameters of the EIL. 

Practically any experimental kinetic curve can be reproduced using a model with a few parallel (competitive) or consecutive surface reactions or a more complicated network of chemical reactions (Fig. 4.70) with properly fitted forward and backward rate constants. For example, Hachiya et al. used a model with two parallel reactions when they were unable to reproduce their experimental curves using a model with one reaction. In view of the discussed above results, such models are likely to represent the actual sorption mechanism on time scale of a fraction of one second (with exception of some adsorbates, e.g, Cr that exchange their ligands very slowly). Nevertheless, models based on kinetic equations of chemical reactions were also used to model slow processes. For example, the kinetic model proposed by Araacher et al. [768] for sorption of multivalent cations and anions by soils involves several types of surface sites, which differ in rate constants of forward and backward reaction. These hypothetical reactions are consecutive or concurrent, some reactions are also irreversible. Model parameters were calculated for two and three... 

The preceding discussion shows that salinity is represented in different ways, but it is most important that the input values for the initial formation water and the injected brines are consistent with the laboratory data. Note that C50 and C60 are the UTCHEM input parameters for the concentrations of all the anions and the divalent cations, respectively, in the initial formation brine. C(M,5,1) and C(M,6,1) are the UTCHEM input parameters for the concentrations of all the anions and the divalents in the injection water, respectively. Inside the parentheses, M represents the injection well number, 5 represents all anions (mainly Cl ), 6 represents divalents or multivalents (mainly Ca " ), and 1 represents water phase. These concentrations are explained in Example 3.1 later in this chapter. 

The different properties of anions and cations in the sample will affect the method development. These include whether the ion is organic or inorganic, multivalent or monovalent, and so on. The following discussion illustrates how these parameters can become important. 

Up to now only monovalent ions have been investigated. For multivalent ions the prediction of the PB theory is that for the distribution function P(r) only the product of the Manning parameter and the counterion valence v matters. Therefore a system of monovalent ions at ln = 3a is claimed to have the same distribution function as a system of trivalent ions at B = lo It will now be shown that this statement is an artifact of the PB approximation. Figure 9 shows examples of systems that are complementary in the described sense. Not only is the condensation enhanced as compared to PB theory, but the enhancement is stronger for the case involving multivalent ions. Two different reasons may be suggested to explain this effect ... 

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