| Kinetic barriers cause polymers to crystallize incompletely, into nanoscale lamellae interleaved with amorphous regions. As a result, crystalline polymers are full of crystal-melt interfaces, which dominate their physical properties. The structure of these interfaces has new relevance, because of accumulating evidence that polymer crystals often nucleate via a metastable, partially ordered ``rotator'' phase. To compute nucleation barriers, we require both interfacial tension values, and bulk free energy differences. For phases of comparable bulk free energy, the one with lower interfacial tension has a lower nucleation barrier. We present a new theory of the crystal-melt interface, which represents the amorphous region as a grafted brush of loops in a self-consistent pressure field. We predict the adjacent reentry fraction, interfacial tension, and tilt angle of crystal-melt interfaces. We find a much lower melt interfacial tension for the rotator than for the crystal phase. Then, we combine experimental information for transition entropies of stable rotator phases in normal alkanes (oligomeric PE wax), with measurements of the melting and crystallization temperatures versus lamellar thickness, to infer the bulk free energy driving force for both crystal and rotator nuclei. We find nucleation via rotator phase is indeed preferred; our results provide the first theoretical support for the role of rotator phases in polymer crystallization. |