Fuoss et al

More quantitative information about solvation equilibria resulted when the association of picric acid was studied in mixtures of acetonitrile (AN) with several hydroxylic solvents (water, MeOH, EtOH) and in water-EtOH mixtures. The dependence of In Ka on 1/e is in no case linear and with two binary solvent systems (AN—MeOH, AN—EtOH) In Ka even increases with e. Fuoss et al. introduced a... 

The Poisson-Boltzmann equation for the potential distribution around a cylindrical particle without recourse to the above two assumptions for the limiting case of completely salt-free suspensions containing only particles and their counterions was solved analytically by Fuoss et al. [1] and Afrey et al. [2]. As for a spherical particle, although the exact analytic solution was not derived, Imai and Oosawa [3,4] smdied the analytic properties of the Poisson-Boltzmann equation for dilute particle suspensions. The Poisson-Boltzmann equation for a salt-free suspension has recently been numerically solved [5-8]. 

The Poisson-Boltzmann equation (6.61) subject to boundary conditions (6.63) and (6.64) has been solved independently by Fuoss et al. [1] and Afrey et al. [2]. The results are given below. 

We will recall in this paragraph, in our rationalised notation, a non-exhaustive list of the most important results arising from the principal theoretical models which have been proposed and which may be adapted to the case of DNA. A critical comparison of these various models has already been published by Manning [16]. All the models suppose, as a starting point, that DNA is rigid rod with cylindrical symmetry and proceed, in general, by a resolution of the Poisson-Boltzmann equation for the system polyion plus electrolyte (first treated by Alfrey et al. [17] and Fuoss et al. [18]). 

PyCH=CHPy however, only a slight effect was observed. Further, no difference between the rates of the second quater-nization step of l,3-(bis-4-pyridyl)propane and l,2-(bis-4-pyridyl)-ethane was detected. These results indicate that inductive effects do not contribute significantly to the relative nucleophilicity of the second amino function. Steric effects are also eliminated by the failure of the additional methylene spacer to influence the second quaternization rate. Fuoss et al. concluded that the rate decreases observed between the first and second quaternization steps in the model compounds could be attributed to a volume field effect, i.e.,an electrostatic effect produced at the site of the second nitrogen by the positive charge on the initially quaternized nitrogeh. 

Braun derived an expression for k E) from the 1934 Onsager theory by use of the expression given by Fuoss and Accascina (1959) and Eigen et al. (1964) for the zero-field equilibrium constant for the dissociation of an ion pair. Assuming a field-independent lifetime, Braun determined the field dependence of the charge-transfer state dissociation probability as... 

Figure 15. Empirical —aG° values for metal cation HPOj, complexes (1 = 0) plotted against t.+7.J(ym + ri/po j, with thpo = 3.15 A based on Izatt et al. (60) and Wells (27). — aG° for AlHPOj, is an estimate. The smooth plotted curve has no statistical significance. (F) Fuoss model.

In the absence of added electrolytes the reduced viscosity, Jjsp/C, of a polyelectrolyte rises upon dilution in a striking manner as a result of the expansion of the polymer chains (Fuoss and Strauss, 1948 Hermans and Overbeek, 1948 Kuhn et al., 1948). Empirically, Fuoss and Strauss have found that the viscosity data can be represented by the equations... 

TWO DISTINCT FORMS OF ION pairs IN solution were suggested by Sadek and Fuoss (I) and Winstein et al. (2) in 1954. These forms are now customarily referred to as either (a) loose or solvent-separated ion pairs or (b) tight or contact ion pairs. During the past few decades, these species have been studied in great detail with optical and magnetic resonance techniques and conductivity methods. Numerous experiments carried out by Szwarc (3) showed that ion pairs are well-defined chemical species with their own physical properties. For instance, the rate of anionic polymerization reactions can change by a factor of 103 from free (unassociated) solvated ionic species to completely associated ones (3). 

Gileadi et al. [22], in their study of the conductivity characteristics of certain salts, namely AlBr3-LiBr and AlBr3-KBr, in toluene, have observed a behavior similar to that found by Fuoss and Kraus. The model proposed by them is based on a hopping mechanism of ionic species from one cluster to another. 

This conclusion is not quite original. As early as the 1930s, Kuhn [71] and Fuoss and Kirkwood [72] suggested that conformational transitions in certain local regions of a macromolecule should be accompanied by deformation of valence angles and bonds in other regions. Similar theoretical models of polymer deformation were considered by Schatzki [73], Boyer [74], Pechhold [75, 76] Gotlib et al. [77-79], and Robertson [80]. 

Viscometric measurements were carried out in DMSO solutions at 30°C using a Tuan-Fuoss (Gumule et al., 2003a) viscometer fabricated in our research laboratory at a different concentrations ranging from 1.00 to 0.031%. Intrinsic viscosity (ri) was... 

It is recognized that FHFP equation accounts for the concentration dependence of electrolyte solutions up to moderate concentrations and yields more reliable association constants than the Shedlovsky or Fuoss-Kraus equations. However, it was observed that the FHFP Equation (4.18), or the more simple Shedlovsky Equation (4.16), give similar fitting results, for some supercritical electrolyte solutions at low density (p < 0.3 g cm" ). The contribution of the electrophoretic effect to the concentration dependence of the molar conductivity is expected to be lower in supercritical water than in ambient water because of the much smaller viscosity and dielectric constant. Moreover, the higher-order terms in Equation (4.18) nearly cancel each other at moderate concentration in supercritical water (Ibuki et al., 2000). This could be the reason why differences among several conductivity equations vanish at supercritical conditions. 

In more concentrated solutions, further aggregation to ion triplets, quadruplets, and so on, may occur (see, e.g., Erdey-Grdz, 1974, pp. 434-436 Fuoss and Accascina, 1959, pp. 249-272). This and the pairing of ions that have unequal charges make for mathematical complications, especially in the interpretation of the dependence of the conductance on concentration, and in kinetics. Balakrishnan et al. (2001) found that... 

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