Theory of the Melting Point Depression

Theory of the Melting Point Depression. —At equilibrium between liquid and crystalline polymer, the chemical potentials of the polymer repeating unit in the two phases must be equal, i.e., = 

The temperature at which this condition is satisfied may be referred to as the melting point Tm, which will depend, of course, on the composition of the liquid phase. If a diluent is present in the liquid phase, Tm may be regarded alternatively as the temperature at which the specified composition is that of a saturated solution. If the liquid polymer is pure, /Xn —mS where mS represents the chemical potential in the standard state, which, in accordance with custom in the treatment of solutions, we take to be the pure liquid at the same temperature and pressure. At the melting point T of the pure polymer, therefore, /x2 = /xt- To the extent that the polymer contains impurities (e.g., solvents, or copolymerized units), ixu will be less than juJ. Hence fXu after the addition of a diluent to the polymer at the temperature T will be less than and in order to re-establish the condition of equilibrium = a lower temperature Tm is required. 

The derivation of the quantitative relationship between this equilibrium temperature and the composition of the liquid phase may be carried out according to the well-known thermodynamic procedures for treating the depression of the melting point and for deriving solubility-temperature relations. The condition of equilibrium between crystalline polymer and the polymer unit in the solution may be restated as follows  

In words, the difference between the chemical potential of the crystalline repeating unit and the unit in the standard state, i.e., the pure 

(29) is closely related to the classical melting point depression and solubility expression for solutions of simple molecules. In the case of the ideal solution, for example, m2 m2= In N2, N2 being the 

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The theory of the melting-point depression of crystalline polymers with defects was developed by Flory (/05) and has been applied to copolymers 106,107). According to the theory, the relationship between the equUibrium melting point of a copolymer and that of the corresponding homopolymer is ... 

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