The temperature dependence of the Hildebrand solubility parameters of selected hydrocarbon polymers and hydrocarbon solvents: a molecular dynamics investigation

Abstract

ContextTo determine the miscibility of liquids at high temperatures using the concept of Hildebrand solubility parameter δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta$$\\end{document}, the current practice is to examine the difference in δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta$$\\end{document} between two liquids at room temperature, assuming that δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta$$\\end{document} is not sensitive to temperature. However, such an assumption may not be valid for certain polymer blends and solutions. Therefore, a knowledge of the δ values of the liquids of interest at high temperatures is desirable. The determination of δ at high temperatures, especially for high-molecular-weight polymers, is impossible, as polymers have vapor pressures of zero. To this end, molecular dynamics (MD) simulations provide a practical means for determining δ over a wide range of temperatures. In this work, we study the temperature dependence of δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta$$\\end{document} of five hydrocarbon polymers: polyethylene (PE), isotactic and atactic polypropylene (i-PP and a-PP), polyisobutylene (PIB), and polyisoprene (PI) in five hydrocarbon solvents: n-pentane, n-hexane, n-dodecane, isobutene, and cyclohexane. The polymers are modeled as monodisperse chains with 100 repeat units. The average δ values of PE, i-PP, a-PP, PIB, and PI at 300 K are determined as 18.6, 14.9, 14.6, 14.3, and 16.4 MPa1/2, respectively, in a good agreement with experimental data. The δ values of these polymers at various temperatures are also determined. The temperature dependence of δ is fitted to two linear equations, one above and the other below the polymer’s glass transition temperature Tg. The δ values are more sensitive to temperature at T ≥ Tg. The Tg values of the polymers, determined based upon their specific volumes and δ values agree with the experiment qualitatively. The determination of the temperature dependence of δ has a great potential for industrial applications, such as determining miscibility, developing polymeric organogelators as flocculants and oil spill treating agents, and identifying potential solvents and ideal processing temperatures.MethodsThe MD simulations are performed using the GROMACS 2022.3 package with optimized potential for liquid simulations-all atom (OPLS-AA) force field parameters. All polymers are built as extended chains using CHARMM-GUI Polymer Builder.Graphical