A Universal Interpretation of Transient Viscoelastic Extensional Dynamics: Application to Single Polymer Experiments

Advances in fluorescence imaging and particle manipulation have enabled the direct observation of single polymer dynamics in model flows such as shear flow and planar extensional flow. The majority of single polymer studies in the literature have focused on chain dynamics using simple step forcing functions. In order to study single polymer dynamics in non-idealized ‘model’ flows, there is a clear need to implement more complicated flow types and transient flow forcing functions. For example, large amplitude oscillatory shear flow (LAOS) has been widely used in recent years to elicit nonlinear viscoelastic responses of materials in bulk rheology, but complementing molecular techniques have not yet been applied.

In this work, we directly probe linear and nonlinear single polymer responses using large amplitude oscillatory extensional flow (LAOE) in precisely controlled microfluidic devices. We are able to generate both small and large amplitude extensional flows in a cross-slot microfluidic device while imaging the conformational dynamics of a single λ-DNA polymers trapped at the stagnation point. Using this technique, the projected extension of the polymer is measured. Our experimental results are in good agreement with Brownian dynamics (BD) simulations. We characterize the projected polymer extension as a function of both the dimensionless input strain rate Wi₀sin(ωt) and its temporal derivative Wi₀ωcos(ωt), and have constructed a series of single polymer Lissajous plots. Responses have been mapped over a range of Weissenberg number amplitudes (Wi, flow strength) and Deborah numbers (De, probing frequency). By applying the sequence of physical processes (SPP) framework, we quantify the instantaneous polymer responses under LAOE through a set of newly-defined rheological parameters that are readily extendable from the single polymer scale up to bulk extensional measurements. The transition dynamics of a single polymer from its linear extensional response to a nonlinear response can also be rigorously quantified through this framework. Additionally, the contribution to overall projected extension from both of the input flow parameters is rigorously determined. These techniques provide a stringent test of extensional theories of polymers on a single-chain basis.