Predicting maximum strain hardening factor in elongational flow of branched pom-pom polymers from polymer architecture

Abstract

We present a model-driven predictive scheme for the uniaxial extensional viscosity and strain hardening of branched polymer melts, specifically for the pom-pom architecture, using the small amplitude oscillatory shear mastercurve and the polymer architecture. A pom-pom shaped polymer is the simplest architecture with at least two branching points, needed to induce strain hardening. It consists of two stars, each with q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q$$\\end{document} arms of the molecular weight Mw,a\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${M}_{w,a}$$\\end{document}, connected by a backbone of Mw,b\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${M}_{w,b}$$\\end{document}. Despite the pom-pom constitutive model, experimental data of systematic investigations lack due to synthetic complexity. With an optimized approach, we synthesized polystyrene pom-pom model systems with systematically varied Mw,a\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${M}_{w,a}$$\\end{document} and Mw,b\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${M}_{w,b}$$\\end{document}. Experimentally, we identify four characteristic strain rate dependent regimes of the extensional viscosity, which can be predicted from the rheological mastercurve. Furthermore, we find that the industrially important maximum strain hardening factor depends only on the arm number by [q2/ln(3q)]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[{q}^{2}/{{{{{\\mathrm{ln}}}}}}({\\sqrt{3}}q)]$$\\end{document}. This framework offers a model-based design of branched polymers with predictable melt flow behavior.