Flory-Krigbaum equation

Equations (18) and (16) define a temperature where Gaussian behavior is observed (the phase separation temperature) where % — 1/2 and thermal energy is just sufficient to break apart PP and SS interactions to form PS interactions. Equation (12) using (17) for Vc is called the Flory-Krigbaum equation. This expression indicates that only three states are possible for a polymer coil at thermal equilibrium ... 

A further development of Equation (3.41) was to use a Flory-Krigbaum model [122] to evaluate the second virial coefficient giving [47]... 

This involves the Flory-Huggins parameter x and hence assumes the same limitation as the rest of the Flory-Huggins approach, i.e. a moderately concentrated solution. Flory and Krigbaum rewrote this equation in terms of some other parameters, i.e. 

The derivation of equation 3.72 assumes no interaction between polymers. Although the use of a three dimensional lattice to represent a polymer solution is admittedly artificial (particularly regarding the assumption that polymer segments and solvent molecules have the same dimensions), equation 3.72 has proven useful in correlating many experimental results. A major drawback, as mentioned previously, is the assumption that the polymer molecules are randomly distributed on the lattice. This assumption becomes untenable in dilute solutions in which polymer molecules exist as isolated islands surrounded by a sea of solvent. Flory [11], Flory and Krigbaum [12] and Ishihara and Guth [13] have derived expressions for the dilute solution case. 

Figure 4.9 The dependences of the melting temperature on the drawing ratio X for PCP. 1 - calculation according to Equation 4.31 at the condition of increasing with growth in A 2 - calculation according to Equation 4.31 at the condition = const. 3 - calculation according to the Flory equation 4 - calculation according to the Krigbaum-Roe equation 5 - experimental data [48]...

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