Viscosity molecular origins

In SEC, universal calibration is often utilized to characterize a molecular weight distribution. For a universal calibration curve, one must determine the product of log(intrinsic viscosity molecular weight), or log([7j] M). The universal calibration method originally described by Benoit et al. (9) employs the hydro-dynamic radius or volume, the product of [tj] M as the separation parameter. The calibration curves for a variety of polymers will converge toward a single curve when plotted as log([7j] M) versus elution volume (VJ, rather than plotted the conventional way as log(M) versus V, (5). Universal calibration behavior is highly dependent on the absence of any secondary separation effects. Most failures of universal calibration are normally due to the absence of a pure size exclusion mechanism. 

The original poly(vinyl alcohol) was studied in both aqueous and DMSO solutions. Viscosity-molecular weight relationships have been reported for each of these solutions at 30°C as shown in Equations 19 and 20 (3). 

The Molecular Origins of Mass Diffusivity. In a manner directly analogous to the derivations of Eq. (4.6) for viscosity and Eq. (4.34) for thermal conductivity, the diffusion coefficient, or mass diffusivity, D, in units of m /s, can be derived from the kinetic theory of gases for rigid-sphere molecules. By means of summary, we present all three expressions for transport coefficients here to further illustrate their similarities. 

Theoretical treatments on the viscosity of solutions of polymer chains are too numerous to give even a brief summary. Originally their principal objective was to explain the intrinsic viscosity-molecular weight relationship as described in Eq. (5). Now the major interest goes far beyond that and toward a better understanding of the solution properties of polymers. Our brief discussion will be confined only to general terms. The approach... 

To explain the molecular origin of the change in solution viscosity with... 

Tanaka and co-workers [158] have used the high-temperature turbidimetric titration procedure originally described by Morey and Tamblyn [153] for determining the MWD of cellulose esters. This method has been applied to the measurement of the MWD of PP. They found that the type of MWD of this polymer is a log-normal distribution function in a range of I M) (cumulative wt%) between 5 and 90%. The effect of heterogeneity in the MWD of PP on the viscosity-molecular weight equation was examined experimentally - the results agreed with those calculated from theory. Strict temperature control ( 0.15 °C) is necessary in these determinations [159]. 

The fractional free volume f, which is the ratio of the free volume to the overall volume, occupies a central position in tr5nng to understand the molecular origins of the temperature dependence of viscoelastic response. The main assumption of the free-volume theory is that the fractional free volume assumes some universal value at the glass transition temperature. The Williams-Landel-Ferry (WLF) equation for the thermal dependence of the viscosity tj of polymer melts is an outgrowth of the kinetic theories based on the free volume and Eyring rate theory (35). It describes the temperature dependence of relaxation times in polymers and other glass-forming liquids above Tg (33-35). The ratio of a mechanical or dielectric relaxation time, Tm or ra, at a temperature T to its value at an arbitrary reference temperature To can be represented by a simple empirical, nearly universal function. 

This equation appears to have a number of names, of which the Mark-Houwink equation is the most widely used. In order to use it, the constants K and a must be known. They are independent of the value of M in most cases but they vary with solvent, polymer, and temperature of the system. They are also influenced by the detailed distribution of molecular masses, so that in principle the polydispersity of the unknown polymer should be the same as that of the specimens employed in the calibration step that was used to obtain the Mark-Houwink constants originally. In practice this point is rarely observed polydispersities are rarely evaluated for polymers assigned values of relative molar mass on the basis of viscosity measurements. Representative values of K and a are given in Table 6.4, from which it will be seen that values of K vary widely, while a usually falls in the range 0.6-0.8 in good solvents at the 0 temperature, a = 0.5. 

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