Flory constant

Flory constant, M M/3/2 for linear flexible chains at high molecular weights. 

The second is the hydrodynamic model of Flory and Fox (27) which represents the polymer molecule by an equivalent nondraining hydro-dynamic sphere. Assuming the Flory constant to be the same for linear and branched polymers, the degree of branching is given by the g3/2 rule ... 

Because in some cases the production of methane does not obey the Schulz-Flory distribution, kj is allowed to differ from kj. The Schulz-Flory constant is defined as a = rn/rn i, for n 3,... 

Schulz-Flory constant a stst (or < >) steady state. 

If the Flory constant CF is replaced by the value C = 134/105, as suggested earlier [Stockmayer 20, 238) Fixman (SS)], the numerical constant in the last term of Eq. (31) is changed to 2.865 10 s. This cannot alter the value of L2)0/ obtained by the extrapolation but just doubles the value of flic2. 

Deviations from the Schulz-Flory distribution arc possible if secondary reactions such as cracking on acidic supports or insertion of product olefins into the growing chain occur [42]. It has been reported recently that the Schulz Flory constant a has a tendency to increase from C3 to C, [45]. This may be the reason why the values found are usually higher for methane and lower for Cj and C) j.)., as would be expected for an ideal Schulz-Flory distribution [40]. Investigations by Madon et at. on partly sulfur-poisoned iron/copper catalysts revealed a dual product distribution. This was explained by the assump tion of > 2 types of active sites for hydrocarbon chain formation, each with a slightly different value of the chain growth probability [46]. 

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. 

Fig. 2.5. Flory constant 0 from Zimm theory evaluated by various methods of calculation plotted against hydrodynamic interaction parameter h Circles from eigenvalues of difference equation (2.18) thin lines from Eq. (2.41) thick line result of Tschoegl from Eq. (2.20). Values of h are shown, and cross mark indicates N = 104 for a given value of h = hN 112 (72)...

For real polymer coils in solution the Flory constant is lower, depending on the conversion factor Several attempts for a theoretical calculation of a Flory constant have been published (Flory and Fox calculated a value of =4.17x10 mol"0 according to Yamakawa [76] a practical Flory constant for different polymer-solvent systems at theta conditions is... 

An experimental verification of the Flory constant is possible with known Rq-M-and [f]j-M-relationships for a polymer solvent system. A substitution of Eqs. (6.1), (8.25), and (8.26) in Eq. (8.33) yields the following expression for the Flory constant ... 

The importance of viscosimetry as an independent area in the field of polymer analytics becomes clear through the Nobel prices awarded for two works in this area. The name of the 1953 honored Prof. Hermann Staudinger for his proof of the existence of polymers is still used in viscosimetry in the intrinsic viscosity (German "Staudingerindex ) (see "Intrinsic viscosimetry in Chap. 4). In 1974, Prof. Paul J. Flory was honored with the Nobel price for his groundbreaking works on the conformation of polymers in solution and his name is conserved for posterity in the Flory constant (see "The Fox-Flory theory in Chap. 8). 

Correction factor of the Flory constant for non-theta-conditions Volume fraction Flory constant... 

Flory constant at theta-condition Shear rate... 

The extrapolation point to the vertical axis in the limit of n oo gives the theta temperature, while the slope of the curve gives the Shultz-Flory constant Such an analysis is called a Shultz-Flory plot. 

Different assumed values for the viscosity function F (or Flory constant) used to relate intrinsic viscosities to molecular dimensions in solution... 

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