Wax appearance temperature (WAT), defined as the temperature at which the first solid paraffin crystal appears in a crude oil, is one of the key flow assurance indicators in the oil industry. Although there are several commonly-used experimental techniques to determine WAT, none provides unambiguous molecular-level information to characterize the phase transition between the homogeneous fluid and the underlying solid phase. Molecular Dynamics (MD) simulations employing the statistical associating fluid theory (SAFT) force field are used to interrogate the incipient solidification states of models for long-chain alkanes cooled from a melt to an arrested state. We monitor the phase change of pure long chain n-alkanes: tetracosane (C24H50) and triacontane (C30H62), and an 8-component surrogate n-alkane mixture (C12-C33) built upon the compositional information of a waxy crude. Comparison to Diffusion Ordered Spectroscopy Nuclear Magnetic Resonance (DOSY NMR) results allows the assessment of the limitations of the coarse-grained models proposed. We show that upon approach to freezing, the heavier components restrict their motion first while the lighter ones retain their mobility and help fluidize the mixture. We further demonstrate that upon sub-cooling of long n-alkane fluids and mixtures, a discontinuity arises in the slope of the self-diffusion coefficient with decreasing temperature, which can be employed as a marker for the appearance of an arrested state commensurate with conventional WAT measurements.