<i>In silico</i> cooling rate dependent crystallization and glass transition in <i>n</i>-alkanes

<i>n</i>-Alkanes (C_<i>n</i>H_2<i>n</i>+2) are linear chain compounds spanning length-scales from small molecules to polymers. Intermediate length alkanes (say, <i>n</i> = 10-20) have attracted much interest as organic phase change materials (PCM) for storing energy as latent heat. The cooling rate (<i>γ</i>) determines both the latent heat and temperature of crystallization. While slow cooling of the liquid leads to the crystalline state, rapid cooling leads to a glassy state (glass transition temperature <i>T</i>_g). Albeit scant theoretical investigations concerning the vitrification processes, the role of molecular conformations therein remains completely unexplored. Our work presents an all-atom molecular dynamics study of (a) cooling intermediate length alkanes (<i>n</i> = 12 and 16) at seven different rates, and (b) rapidly cooling 14 <i>n</i>-alkanes (4 ≤ <i>n</i> ≤ 50) for determining <i>T</i>_g(<i>n</i>). We find that for linear molecules the end-to-end distance (<i>R</i>_ee) is of special relevance: the crystal is composed solely of fully stretched molecules (maximal <i>R</i>_ee). Hence one may define the "degree of crystallization" as the area under the maximal <i>R</i>_ee peak in the <i>R</i>_ee distribution. Other peaks in the distribution represent conformations that existed in the supercooled liquid just before vitrification. A peak for the shortest, hairpin rotamer appears only for <i>n</i> ≥ <i>n</i>₀ = 18, and is also manifested in the minimum of <i>R</i>_g/<i>R</i>_ee(<i>n</i>) for liquid <i>n</i>-alkanes. The dependence of <i>T</i>_g on <i>n</i> is represented as two intersecting Ueberreiter and Kanig equations, intersecting near <i>n</i>₀ = 18. Extrapolation gives the asymptotic <i>n</i> → ∞ limit of <i>T</i>_g, <i>T</i>∞g = 250 K, which is probably its most accurate estimate obtained theoretically todate.