Normal alkanes have a simple molecular structure, but display a surprising variety of ordered phases, including an orthorhombic crystal, followed on heating by two partially ordered rotator phases RI and RII. These phases are interesting both because of the weakly first-order transitions that separate them, and because rotator phases are implicated in the nucleation of crystals in polyethylene. To understand this interesting and technologically important phenomenon, a clear picture of the rotator phase is essential. We conducted all-atom simulations of pure C(23) and mixed C(21)-C(23) normal alkanes. Among potentials we tried, only Flexible Williams gave good agreement with the experimental sequence of phases and transition temperatures. Physical properties of the simulated phases, including lattice dimensions and transition entropy between orthorhombic and rotator RII phase are in good agreement with experiment. We define order parameters for investigating pretransitional fluctuations in RI and RII phases; we observed only very short-range correlations in these phases, but slower temperature scans may be necessary to properly investigate these weakly first-order transitions.