Weight Flory-Huggins expression

AG/6V. =0 (spinodal) using the Flory-Huggins expression (14,7) for a 50 50 AB polymer blend. Here M is the number average molecular weight for the two component system, which allows for the possibility that the two monodisperse homopolymers in the blend may not be of identical molecular weight. 

Note that the Flory-Huggins expression for the entropy of mixing of polymer and solvent corresponds to volume fraction statistics. This should be compared with the analogous mole fraction statistics that are exhibited by ideal minimolecules in the Bragg-Williams approximation. Mole fraction statistics are inappropriate to polymer-solvent systems because the disparity in molecular weights means that the mole fraction of solvent is always close to unity, except at extremely high polymer volume fractions. 

To formulate the melting temperature relation we start with the Flory-Huggins expression for the free energy of mixing of a set of chemically identical species with a low molecular weight diluent.(67,68) This expression is given as (7)... 

To analyze the fusion of mixtures of homopolymers and low molecular weight diluents we return to equations (11), (14) and (15). Equation (11) was derived by utilizing lattice techniques. In effect, the Flory-Huggins expression for the free energy of mixing was used. We are, therefore, limited at this point to situations where the polymer segments and diluent are uniformly distributed in space. Dilute solutions are therefore excluded from the present discussion but will be considered separately subsequently. It has also been assumed that the diluent is excluded from the crystal lattice. This condition has been satisfied by almost all the polymer-diluent mixtures that have been studied. 

Use the Flory-Huggins expression for the solvent chemical potential in Equation 3.8 to show that in the semi-dilute regime, Vj 1 and therefore ln(l-V2) -V2-v /2, this model would predict that for high-molecular-weight polymers the osmotic pressure would scale as vf. Compare with the scaling law result. To what can you attribute the difference ... 

The Einstein theory shows that volume fraction is the theoretically favored concentration unit in the expansion for viscosity, even though it is not a practical unit for unknown solutes. As was the case in the Flory-Huggins theory in Chapter 3, Section 3.4b, it is convenient to convert volume fractions into mass/volume concentration units for the colloidal solute. According to Equation (3.78), 0 = c(V2/M2), where c has units mass/volume and V2 and M2 are the partial molar volume and molecular weight, respectively, of the solute. In viscosity work, volumes are often expressed in deciliters —a testimonial to the convenience of the 100-ml volumetric flask In this case, V2 must be expressed in these units also. The reader is advised to be particularly attentive to the units of concentration in an actual problem since the units of intrinsic viscosity are concentration when the reduced viscosity is written as an expansion of powers of concentration c. (The intrinsic viscosity is dimensionless when the reduced viscosity is written as an expansion of powers of volume fraction 0.) With the substitution of Equation (3.78), Equation (42) becomes... 

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. 

In a rough approximation, Flory-Huggins equation also gives the practical expression for the measurement of molecular weight M, as... 

The polymer, which is assumed to be linearly and amorphous, occurs in solution as a random coil. The dimensions of the coil depend on the type of solvent, in good solvents the coil dimensions are large whereas in poor solvents the coil dimensions are much smaller. If the solvent is very poor then the coils aggregate and precipitation may occur. The qualit) of the solvent can be expressed by the Flory-Huggins interaction parameter%. An increase of the molecular weight will also result in an increase in coil dimension. 

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