Determining elasticity from single polymer dynamics

Abstract

The ability to determine polymer elasticity and force-extension relations from polymer dynamics in flow has been challenging, mainly due to difficulties in relating equilibrium properties such as free energy to far-from-equilibrium processes. In this work, we determine polymer elasticity from the dynamic properties of polymer chains in fluid flow using recent advances in statistical mechanics. In this way, we obtain the force-extension relation for DNA from single molecule measurements of polymer dynamics in flow without the need for optical tweezers or bead tethers. We further employ simulations to demonstrate the practicality and applicability of this approach to the dynamics of complex fluids. We investigate the effects of flow type on this analysis method, and we develop scaling laws to relate the work relation to bulk polymer viscometric functions. Taken together, our results show that nonequilibrium work relations can play a key role in the analysis of soft material dynamics.

Nonequilibrium thermodynamics of dilute polymer solutions in flow

“…Recently, a work relation was used to study polymer stretching in hydrodynamic flow, wherein the terminal states are defined as a polymer maintained at a fixed molecular extension, which corresponds to an equilibrium state. 25,26 In the present work, however, the terminal states are defined by a polymer chain maintained at a constant flow rate, which corresponds to a nonequilibrium state and fundamentally distinct compared to transitions between ESSs. 20,21,25,26 We begin by differentiating between ESSs and NESSs.…”

“…25,26 In the present work, however, the terminal states are defined by a polymer chain maintained at a constant flow rate, which corresponds to a nonequilibrium state and fundamentally distinct compared to transitions between ESSs. 20,21,25,26 We begin by differentiating between ESSs and NESSs. Consider a classical system in contact with a heat bath at temperature T, such that the evolution of the configuration probability distribution p is described by the Fokker-Planck equation.…”

“…3 In addition to the development of FTs, numerical and experimental investigations have demonstrated the validity of FTs. Several reports have focused on equilibrium steady-states (ESSs), [20][21][22][23][24][25][26] though recently, an expression was developed for determining nonequilibrium thermodynamic quantities for systems nearequilibrium. 27 In this work, we report the direct determination of farfrom-equilibrium thermodynamic properties for dilute polymer solutions in flow using a combination of simulations and single molecule experiments.…”

Free energy evaluation in polymer translocation via Jarzynski equality

“…In this article we provide numerical evaluations of the free energy in the polymer translocation problem via the Jarzynski Equality (JE) [25][26][27]. With the help of cloud computing resources [28] we have been able to introduce statistical ensembles and study polymer chains which are considerably larger than the ones usually taken in the literature.…”

Flow of DNA in micro/nanofluidics: From fundamentals to applications

“…In particular, stretching of up to 0.5 (normalized by contour length) length units in both parallel and perpendicular direction to the flow has been reported. 214 Since polymer conformation has been linked to elastic stresses in the fluid, 94,95 which in turn provides the driving force for elastic turbulence, 85 the mechanism could be validated by visualizing polymer conformation in straight channels.…”