Stability Inversion with Lamellar Thickness

The lamellar habit adopted by crystalline polymers adds surface terms to the specific Gibbs function (chemical potential), most importantly the fold surface free energy, ae, which contributes 2ae/Xg for a lamella of thickness k and crystalline density q. In consequence melting points are lowered from T, for infinite thickness, to Tm according to the Hoffman-Weeks equation 

As a straightforward consequence, one may shift the lines in Fig. 4 upwards by 2ae/kg for each crystalline phase to obtain a modified diagram pertinent 

If thin hexagonal lamellae are to be stable within the orthorhombic-stable region of the phase diagram, it is necessary, for the same considerations advanced above, that an orthorhombic lamella melts at a lower temperature than a hexagonal one of the same thickness, i.e. from Eq. 2 

The value of Xs tends to infinity as the denominator (7 0 - 7 h) - 0 as T - Tt. Conversely, as (T 0 - T h) increases, i.e. the hexagonal phase becomes more metastable, A,s decreases as more surface contributions to the free energy, offset by the enthalpy of crystallization, are required, which according to the hypothesis must favour the hexagonal phase. 

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