Copolymer melting-point depression ($1/T_m-1/T_m^0=-(R/\Delta h_f)\ln x$)

An ideal dilution estimate for a random copolymer whose comonomer units are excluded from the crystal. Let $x$ be the crystallizable-unit fraction in the melt and $\Delta h_f$ the molar enthalpy of fusion per such unit. Mixing contributes $RT\ln x$ to its liquid chemical potential. Approximate the unmixed liquid-minus-solid chemical-potential difference by $\Delta h_f(1-T/T_m^0)$. Equating the sum to zero gives the displayed relation. For $x<1$, the predicted melting temperature decreases. Nonideal mixing, finite crystallizable sequences, lamellar surface energy and comonomer inclusion can change the result.