Ionic constant

S-Poly(L-malic acid) ionizes readily in water giving rise to a highly soluble polyanion. Thus, a 2% solution of the free acid of the polymer from Aureobasidium sp. A-91 showed a pH 2.0 [5]. The ionic constants have been determined to be pKa = 3.6 for the polymer from Aureo-basidumsp. A-9 [5] and pKa (25°C) = 3.45 for/3-poly(L-malic acid) of Mw 24 kDa from F. polycephalum (Valussi and Cesaro, unpublished results) Thus, the polymer is highly charged under physiological conditions (pH 7.0). 

Prepared from ethyne and ammonia or by dehydration of ethanamide. Widely used for dissolving inorganic and organic compounds, especially when a non-aqueous polar solvent of high dielectric constant is required, e.g. for ionic reactions. 

Madeluag constant For an ionic crystal composed of cations and anions of respective change z + and z, the la ttice energy Vq may be derived as the balance between the coulombic attractive and repulsive forces. This approach yields the Born-Lande equation,... 

Added to these interactions are the electrostatic forces related to the dielectric constants and which are important when it is necessary to separate ionic components. 

Dynamic models for ionic lattices recognize explicitly the force constants between ions and their polarization. In shell models, the ions are represented as a shell and a core, coupled by a spring (see Refs. 57-59), and parameters are evaluated by matching bulk elastic and dielectric properties. Application of these models to the surface region has allowed calculation of surface vibrational modes [60] and LEED patterns [61-63] (see Section VIII-2). 

Fig. XrV-6. (a) The total interaction energy determined from DLVO theory for n-hexadecane drops for a constant ionic strength - 5.0 nm) at various emulsion pH (b) enlargement of the secondary minimum region of (a). (From Ref. 39.)...

From equation A2.4.38 we can, finally, deduce Walden s rule, which states that the product of the ionic mobility at infinite dilution and the viscosity of the pure solvent is a constant. In fact... 

The are essentially adjustable parameters and, clearly, unless some of the parameters in A2.4.70 are fixed by physical argument, then calculations using this model will show an improved fit for purely algebraic reasons. In principle, the radii can be fixed by using tables of ionic radii calculations of this type, in which just the A are adjustable, have been carried out by Friedman and co-workers using the HNC approach [12]. Further rermements were also discussed by Friedman [F3], who pointed out that an additional temi is required to account for the fact that each ion is actually m a cavity of low dielectric constant, e, compared to that of the bulk solvent, e. A real difficulty discussed by Friedman is that of making the potential continuous, since the discontinuous potentials above may lead to artefacts. Friedman [F3] addressed this issue and derived... 

L is Avagadro s constant and k is defined above. It can be seen that there are indeed two corrections to the conductivity at infinite dilution tire first corresponds to the relaxation effect, and is correct in (A2.4.72) only under the assumption of a zero ionic radius. For a finite ionic radius, a, the first tenn needs to be modified Falkenliagen [8] originally showed that simply dividing by a temr (1 -t kiTq) gives a first-order correction, and more complex corrections have been reviewed by Pitts etal [14], who show that, to a second order, the relaxation temr in (A2.4.72) should be divided by (1 + KOfiH I + KUn, . The electrophoretic effect should also... 

This fomuila does not include the charge-dipole interaction between reactants A and B. The correlation between measured rate constants in different solvents and their dielectric parameters in general is of a similar quality as illustrated for neutral reactants. This is not, however, due to the approximate nature of the Bom model itself which, in spite of its simplicity, leads to remarkably accurate values of ion solvation energies, if the ionic radii can be reliably estimated [15],... 

The first term represents the forces due to the electrostatic field, the second describes forces that occur at the boundary between solute and solvent regime due to the change of dielectric constant, and the third term describes ionic forces due to the tendency of the ions in solution to move into regions of lower dielectric. Applications of the so-called PBSD method on small model systems and for the interaction of a stretch of DNA with a protein model have been discussed recently ([Elcock et al. 1997]). This simulation technique guarantees equilibrated solvent at each state of the simulation and may therefore avoid some of the problems mentioned in the previous section. Due to the smaller number of particles, the method may also speed up simulations potentially. Still, to be able to simulate long time scale protein motion, the method might ideally be combined with non-equilibrium techniques to enforce conformational transitions. 

The solvent dielectric constant, ionic strength and temperature are chosen to fit the conditions of the experimental studies. The protein dielectric constant is assigned some small value, e.g. 4. The PB calculations are currently carried out with the atomic charges and radii of the PARSE parameter set, developed by Honig and coworkers [17] or that for CHARMM [12]. The PARSE parameter set... 

A cubic lattice is superimposed onto the solute(s) and the surrounding solvent. Values of the electrostatic potential, charge density, dielectric constant and ionic strength are assigned to each grid point. The atomic charges do not usually coincide with a grid point and so the... 

The rate constants for the catalysed Diels-Alder reaction of 2.4g with 2.5 (Table 2.3) demonstrate that the presence of the ionic group in the dienophile does not diminish the accelerating effect of water on the catalysed reaction. Comparison of these rate constants with those for the nonionic dienophiles even seems to indicate a modest extra aqueous rate enhancement of the reaction of 2.4g. It is important to note here that no detailed information has been obtained about the exact structure of the catalytically active species in the oiganic solvents. For example, ion pairing is likely to occur in the organic solvents. 

Table 2.5. Apparent second-order rate constants for the catalysed Diels-Alder reaction between Ic and 2, equilibrinm constants for complexation of 2.4c to different Lewis-acids (Kj) and second-order rate constants for the reaction of these complexes with 2.5 (k at) in water at 2M ionic strength at 25°C.

In determining the values of Ka use is made of the pronounced shift of the UV-vis absorption spectrum of 2.4 upon coordination to the catalytically active ions as is illustrated in Figure 2.4 ". The occurrence of an isosbestic point can be regarded as an indication that there are only two species in solution that contribute to the absorption spectrum free and coordinated dienophile. The exact method of determination of the equilibrium constants is described extensively in reference 75 and is summarised in the experimental section. Since equilibrium constants and rate constants depend on the ionic strength, from this point onward, all measurements have been performed at constant ionic strength of 2.00 M usir potassium nitrate as background electrolyte . 

Table 2.7. Hammett p-values for complexation of 2.4a-e to different Lewis-adds and for rate constants (kcat) of the Diels-Alder reaction of 2.4a-e with 2.5 catalysed by different Lewis-acids in water at 2.00 M ionic strength at 25°C.

All measurements were performed at constant ionic strength (2.00 M using KNO3 as background electrolyte) and at pH 7-8. Ligand-catalyst ratio. 

---