Limiting viscosity number temperature dependence

CD molecules are partially free draining chains and the negative temperature dependence of the limiting viscosity number fn] can be attributed to the temperature dependence of the unperturbed chain dimension A. 

Another similarity between amylose and cellulose is to be found in the variation of the limiting viscosity number with temperature. Cellulose derivatives are unique in having a large, negative, temperature dependence of viscosity. For amylose in dimethyl sulfoxide, it has been shown that the temperature coefficient of viscosity is again negative, although... 

The viscosity of a dilute polymer solution depends on the nature of polymer and solvent, the concentration of the polymer, its average molecular mass and molecular mass distribution, the temperature, and the shear rate. The most important characteristic quantity in a very dilute solution, at vanishing shear rate, is the limiting viscosity number, which is defined as [1]... 

The limiting viscosity number depends on the polymer, solvent, and temperature, but imder a given set of conditions it is related to the molecular weight by the Mark-Houwink relation, [ >] = where K and a are constants and M is the molecular weight of the polymer. Tables of K and a are available for a large number of polymers and solvents (31,32). Excellent summaries of equations, techniques, and references relating to the viscosity of dilute polymer solutions are also available (33,34), as is information on dilute polymer solutions that are shear thinning (35). 

To complete the calculation of C, we must know the temperature dependence of i5y, Vg, and most important, p. This can only be done by solving the self-consistency condition p = h(p), (6.13), in more detail. To reduce the number of free parameters, we use the viscosity data fitted by the parameters in Table II for the temperature dependence of Vy. For this reason, we limit our discussion to systems in which tj has been measured over a wide temperature range. The remaining parameters are then Oq, v, and K to describe/(c) andp, a,A,A, D, and in C. If we scale all volumes by vg taken equal to v , that leaves only v /vq and k = kvo as unknowns in f(v). The latter is constrained, since we know... 

Electrolyte conductivity depends on three factors the ion charges, mobilities, and concentrations of ionic species present. First, the number of electrons each ion carries is important, because A, for example, carries twice as much charge as A . Second, the speed with which each ion can travel is termed its mobility. The mobility of an ion is the limiting velocity of the ion in an electric field of unit strength. Factors that affect the mobility of the ion include (1) the solvent (e.g., water or organic), (2) the applied voltage, (3) the size of the ion (the larger it is, the less mobile it will be), and (4) the nature of the ion (if it becomes hydrated, its effective size is increased). The mobility is also affected by the viscosity and temperature of the solvent. Under standard conditions the mobility is a reproducible physical property of the ion. Because in electrolytes the ion concentration is an important variable, it is usual to relate the electrolytic conductivity to equivalent conductivity. This is defined by... 

The limiting molar ionic conductivities, AJ , are obtained by application of the experimentally measured (and extrapolated to infinite dilution) transference numbers, C and r=l-C Thus A" = t"-A"/v and A = r-A"/v, so that A = v+A -ev A", the being the stoichiometric coefficients of the electrolyte. The limiting (standard) molar ionic conductivities AJ for many ions in water at 25 C are shown in Table 2.11 with uncertainties not larger than 0.01 S cm mol. Between 0 and 100°CA increase about fivefold, mainly because the viscosity of the solvent diminishes in this direction by a similar factor. The transference numbers and t are temperature dependent too, but only mildly. 

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