Equilibrium melting point interaction parameters

T ° and T ° are the equilibrium melting point of the blend and the neat crystallizable component, respectively V is the molar volume of the repeating unit of the components (1 = amorphous component and 2 = crystallizable component) A/i is the heat of fusion per mole of repeating unit m is the number of units in the molecule, i.e., the degree of polymerization (f) is the volume fraction and X12 he polymer-polymer interaction parameter. 

According to the Flory-Huggins theory, the equilibrium melting point depression can be related to the polymer-polymer interaction parameter, Xi2> by (46,47) ... 

Here, Tm is the melting point of the polymer in the solvent, is the equilibrium melting point of the polymer, AHl is the equilibrium heat of fusion (J/mol) of the repeating unit, V2 is the molar volume of the polymer, Vi is the molar volume of the solvent Vi is the volume fraction of the solvent, %i is the polymer-solvent interaction parameter, and R is the universal gas constant. This equation can be simphfied to the following form ... 

A depression of die equilibrium melting point of the PLLA component was observed. The interaction parameter between PLLA and PBS showed a negative value of —0.15. 

Equilibrium melting point depression method was applied and a negative interaction parameter and energy density were formd. The negative value of the interaction parameter confirms a thermodynamically miscible blend. 

The equilibrium melting point is indeed very difficult to determine. When crystallized at elevated pressures (500 K and 435 MPa), polyethylene forms so-called extended-chain crystals. These extraordinarily thick crystals melt at temperatures very near the equilibrium melting point. Cormier and Wunderlich (1966) determined the dissolution temperatures for such samples in a variety of solvents and, by fitting eq. (8.23) to the experimental data, the interaction parameter values listed in Table 8.2 were obtained. 

Blends of poly(ethylene oxide) and poly(vinyl chloride) containing up to 50 percent of the latter polymer have a negative interaction parameter, which indicates that the blends have melt compatibility (223). As the poly (vinyl chloride) content increases, the equilibrium melting point decreases in the mixtures. Analysis of the change in melting point indicated that entropic effects made little contribution to the interaction parameter. 

For polymer blends in which one component is crystalline the melting behaviour depends on circumstances. For immiscible blends, where the components are phase separated (prior to crystallisation) and act independently, the crystal melting temperature will be that of the homopolymer. In miscible blends, where the amorphous phase contains both components, the melting temperature will be lower than the equilibrium melting temperature for the crystallisable homopolymer, i.e. the crystalline polymer exhibits a melting point depression as discussed above. The Nishi and Wang approach (Sect 3.2) has been used to estimate the magnitude of the interaction parameters in a niunber of blends (Sect. 7). Poly(e-caprolactone) blends are often semi-crystalline and the above considerations, therefore, apply to many PCL blends. 

In the Matkar-Kyu model, the crystal-amorphous interaction parameter was assumed to be inversely proportional to the absolute temperature, that is, Xca = coAHu/RT, where AH is heat of fusion of the crystal in the pure state and T is absolute temperature. However, the analytical solution for the melting point depression was not sought in their original approach [66, 67]. This deficiency has been remedied recently by Rathi et ol. [75] for a crystalline/amorphous blend by solving the combined FH/PF free energies and obtaining an analytical expression from the equilibrium conditions, viz., df/d i = 0 and/(i )) = 0 as described below ... 

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