Flory viscosity constant

Here

1/2 in cm), regardless of polymer species, solvent species, and temperature. 

Fig. 35. Dependence of the Flory viscosity constant

The proportionality constant is a universal constant, called the Flory viscosity constant. Thus, Flory and Fox provided, partially, the meanings of K and a in the Mark-Houwink equation. At the 0 temperature, K is defined by Eq. (8.23) and... 

For each sample, the Flory Huggins constants (k, Eq. 5.25) were also determined (by viscosity measurements) as function of sonication time and are given in Tab. 5.17. 

Flory-Huggins interaction parameter a packing coefficient, medium viscosity initial viscosity, constant... 

Flory-Fox viscosity constant, at zero excluded volume in a good solvent, under theta conditions, of HW chain in the limit XL oo... 

Huggins constant, k 3k /4NA and [7] is the intrinsic viscosity. Here, the second equation is obtained by using the Flory-Fox equation, [ j ] = < > where 0 is the Flory viscosity factor. 

One of the main assumptions which have been made in the study of polyesterifications is the concept of equal reactivity of functional groups. It was first postulated by Flory1 who, studying various polyesterifications and model esterifications, found the same orders of reaction and almost the same rate constants for the two systems. He concluded that the reaction rate is not reduced by an increase in the molecular weight of the reactants or an increase in the viscosity of the medium. The concept of equal reactivity of functional groups has been fully and carefully analyzed by Solomon3,135 so that we only discuss here its main characteristics. Flory clearly established the conditions under which the concept of equal reactivity can be applied these are the following ... 

The global rate of the process is r = rj + r2. Of all the authors who studied the whole reaction only Fang et al.15 took into account the changes in dielectric constant and in viscosity and the contribution of hydrolysis. Flory s results fit very well with the relation obtained by integration of the rate equation. However, this relation contains parameters of which apparently only 3 are determined experimentally independent of the kinetic study. The other parameters are adjusted in order to obtain a straight line. Such a method obviously makes the linearization easier. 

The constant 0, called the Flory-Fox viscosity parameter, has an experimental value of x2.5 x 1023 mol-1 [44]. The corresponding value for x2 is then ... 

A kinetic study for the polymerization of styrene, initiated with n BuLi, was designed to explore the Trommsdorff effect on rate constants of initiation and propagation and polystyryl anion association. Initiator association, initiation rate and propagation rates are essentially independent of solution viscosity, Polystyryl anion association is dependent on media viscosity. Temperature dependency correlates as an Arrhenius relationship. Observations were restricted to viscosities less than 200 centipoise. Population density distribution analysis indicates that rate constants are also independent of degree of polymerization, which is consistent with Flory s principle of equal reactivity. 

Here % is the Flory-Huggins interaction parameter and ( ), is the penetrant volume fraction. In order to use Eqs. (26)—(28) for the prediction of D, one needs a great deal of data. However, much of it is readily available. For example, Vf and Vf can be estimated by equating them to equilibrium liquid volume at 0 K, and Ku/y and K22 - Tg2 can be computed from WLF constants which are available for a large number of polymers [31]. Kn/y and A n - Tg can be evaluated by using solvent viscosity-temperature data [28], The interaction parameters, %, can be determined experimentally and, for many polymer-penetrant systems, are available in the literature. 

Similarly, the values for a =(3/d )-l follow from the Fox-Flory relationship (Eq. 26), again under the condition that (bj, does not change with the number of branching points per cluster. The assumption of constant and constant are not strictly fulfilled. Nonetheless the scafing relationship of Eq. (40), and the corresponding one for the intrinsic viscosity, lead to very reasonable results, which were indeed observed. Here the full power of the fractal concept becomes evident. 

M and v are the molecular weight and the partial specific volume of the polymer, jjo p are the viscosity and the density of the solvent, respectively, and P and O are functions of relative chain length L/A and of the parameter of hydrodynamic interaction, d/A, respectively. These functions have been represented in an analytical form and tabulated over a wide range of changes in the L/A and d/A parameters At extremely high molecular weights (at IVA -> ), functions P and ap oach an asymptotic limit P— Po = 5.11 — 4>, = 2.862 x 10 (the Flory constant). This corresponds to the conformation of a hydrodynamically undrained Gaussian coil. 

In the case of low-molecular-weight polar resins such as VE resins, relatively thin and dense adsorption layers can be assiuned. This should result in low viscosities due to low effective phase volumes of the dispersed phase and weak interparticulate interactions forces according to steric stabilization. However, addition of a solvent like styrene will influence the Hamaker constant of the liquid medium and of the adlayer and the structure of the adlayer in terms of swelling and/or multilayer formation. In particular, any multilayer formation could result in surface layer entanglement depending on the solvency of the liquid medium expressed in terms of the Flory-Huggins parameter % [11]. These effects should dramatically influence the viscosity and rest structure of the dispersion, as seen in the experiments. 

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