Fuoss relation

The existence of a discontinuity in the concentration dependence of the reduced viscosity has already been reported for many polyelectrolytes of different natures which indicates that the Fuoss relation is no longer valid at high dilution. Maxima have been reported for both weak and strong polyelectrolytes and many explanations have been proposed e.g. absorption of carbon dioxyde [7], hydrolysis of ionized groups [8], purity of the solvent [9], effect of rate of shear [10]. If the presence of carbon dioxyde can lead to a decrease of viscosity in the case of a weak polyacid, it can be reasonably excluded for the precise case of PVP (pH 4). Owing to the relatively low molecular weight of PVP (M 8 x 10 ), the effect of rate of shear can also... 

Theoretical treatment of the viscosity-concentration relationship for polyelectrolyte solutions would involve both the cumbersome statistics of highly elongated chains beyond the range of usefulness of the Gaussian approximation and the even more difficult problem of their electrostatic interactions when highly charged. There appears to be little hope for a satisfactory solution of this problem from theory. Fuoss has shown, however, that experimental data may be handled satisfactorily through the use of the empirical relation ... 

In order to achieve an adequately large KD, the adjustment of three variables is at our disposal, which are summarised in the Bjerrum-Fuoss equation (2) relating KD to D, the temperature T, and a quantity a which is determined by the distance of closest approach of the ions when paired ... 

An alternative procedure uses the Fuoss conductance-concentration function to relate the measured conductance to the ionic concentrations at equilibrium (8). 

Fig. 2.14 Comparison of the log /

In fact, given the distance dependencies of A0 and V, electron transfer is expected to be dominated by reactants in close contact. In that limit the experimentally observed rate constant is related to ktt and the association constant between reactants, KA, as in equation (32). KA can be estimated for spherical reactants, using the Eigen-Fuoss result in equation (33). The electrostatic term, wR, was defined in equations (19) and (20). 

The Fuoss estimate of is based on a more reasonable model than that of Bjerrum and therefore is preferred. However, there are also problems with the Fuoss treatment in so far as it considers the solvent to be a dielectric continuum. Dielectric saturation effects are expected to be important, especially near the ions involved in ion pair formation. The second problem relates to the choice of the effective size for the ions. In the calculation made here the value of a for MgS04 was chosen to be much bigger than the crystallographic radius of Mg. This presumably is because the cation is strongly hydrated in aqueous solution. One is then faced with the question whether the ion pair involves contact of the two ions or whether it is better considered to be a species in which the two ions are separated by at least one water molecule. These questions can only be properly resolved using other experimental methods. 

Since ionic association is an electrostatic effect for equilibrium properties of electrolyte solutions, it may be included in the Debye-Hiickel type of treatment by explicitly retaining further terms in the expansion of the Poisson-Boltzmann relation eqn. 5.2.8. - A similar calculation was attempted for conductance by Fuoss and Onsager. The mathematical approach and the model employed are similar to those used in their previous calculation, but they keep explicitly the exp (—0 y) term in the new calculation. The equation derived for A is... 

Kirkwood and Fuoss [1941] first showed that G(t) could be recovered by integration from a set of e" values. A general treatment has been given by Macdonald and Brachman [1956], who provided a usefnl set of relations between the varions functions used to describe networks and systems as well as between responses to various types of input. 

Causing particular curiosity and scientific wonderment for researchers was the different observed viscosities of the hyaluronan solutions in presence of the different inorganic salts. The largest viscosity was observed for the solution in distilled water. It was proposed that the viscosity could be related to pH values and solution ionic strength. This phenomenon has become common knowledge but was initially described by R. Fuoss only for solutions of the synthetic polyelectrolytes [10],... 

In 1987 Witten and Pincus [71] presented a theory for the viscosity of polyelectrolyte solutions which was derived for concentrations near the overlap concentration. Again, at the limit Cp > c, the Fuoss law ti, oc c was obtained. Later Rabin [72] derived a similar relation (for the viscosity of poly-electrolyte solutions) on the basis of the theory by Hess and Klein. With some bold simplifications Rabin arrived at... 

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