Flexibility, Extensibility, and Ratio of Kuhn Length to Packing Length Govern the Pinching Dynamics, Coil-Stretch Transition, and Rheology of Polymer Solutions

We elucidate the influence of chemical structure on macromolecular hydrodynamics, rheological response, and pinching dynamics underlying drop formation/liquid transfer using polyethylene oxide (PEO) and 2-hydroxyethyl cellulose (HEC) as two polymers with distinct Kuhn length and matched overlap concentrations. We contrast the filament pinching dynamics and extensional rheology response using dripping-onto-substrate rheometry protocols. Even though dilute aqueous solutions of both polymers at matched concentrations display comparable shear viscosity, the PEO solutions exhibit distinctively higher values of extensional relaxation time, extent of strain hardening, and transient extensional viscosity, as well as an overall delay in pinch-off. We critically analyze the radius evolution for a pinching filament to posit that the solutions of flexible PEO macromolecules exhibit signatures of underlying coil-stretch transition manifested as a discontinuous, nonmonotonic variation in the extensional rate. In contrast, the solutions of semiflexible HEC show a monotonic increase in extensional rate in response to rising interfacial stress in the pinching filament, implying that the macromolecules undergo progressive stretching and orientation without undergoing coil-stretch transition. We show that the chemistry-dependent contrast in macromolecular dynamics and extensional rheology response can be characterized a priori in terms of three ratios: contour length to Kuhn length (flexibility), contour length to unperturbed coil size (extensibility), and packing length to Kuhn length (a parameter we termed as segmental dissymmetry). We identify the influence of the three ratios - flexibility, extensibility, and segmental dissymmetry - on the critical minimum concentration below which elastocapillary response and extensional relaxation time cannot be measured, the critical concentration above which the influence of concentration fluctuations disappears, and also define a stretched overlap concentration below which the extensional relaxation time becomes concentration-independent.