RheoFuture 2004 location:Karlsruhe, Germany date:1-2 September 2004
Monitoring the coil-stretch transition of polymers in transient extensional flow fields provides a unique possibility to observe the stress distribution between polymer and solvent even for very dilute solutions (with sub-ppm concentrations). It is generally accepted that for concentrations below the critical concentration (c/c* < O(1)) the steric and frictional interactions of neighboring polymer coils are negligible and the rheological response of the fluid is solely governed by the solvent and the weak hydrodynamical interactions of the isolated polymer coil and the solvent. However, this definition of diluteness is only applicable close to the equilibrium state of polymer coils. Especially in extensionally-dominated flow fields, the coil-stretch transition of a polymer coil leads to an increased interaction volume of the polymer and therefore to polymer-polymer interactions even for concentrations of c/c* < O(1). The term “ultradilute” solution has been introduced recently to describe systems that remain truly dilute even when the polymer chains are in a highly stretched and deformed non-equilibrium state. The Capillary Break-up Extensional Rheometer provides a convenient means for probing chain-chain interactions as a function of polymer concentration through measurements of the characteristic time-scale of the fluid in a strong extensional flow
However, in order to analyze the dynamics of the capillary break-up process it is necessary to answer the question of how much stress is carried by the polymer and how much by the solvent? In other words, under what physical conditions does a coil-stretch transition on the molecular scale occur and affect the resulting macroscopic fluid dynamics so that it is possible to detect a really “ultradilute” solution?
In this paper we will present recent investigations on the capillary break-up behavior of a series of polystyrene solutions with narrowly-distributed molecular weight that are progressively diluted in solvents with different viscosities (Fig. 1).
Figure 1. Radius vs. time in a capillary break-up extensional rheometer experiment for solutions of polystyrene (Mw=1.9 106 g/mol, Mw/Mn=1.03) in styrene oligomers at different concentrations. (end plate diameter 6 mm, initial separation distance 3 mm final distance 10 mm separation time 50 ms).
We show that there exists a critical dilution concentration below which the dominant stress resisting breakup is carried solely by the solvent. This observation is supported by numerical simulation of the stress evolution using a multimode FENE-P mode algorithm based on the one-dimensional analysis of Entov and Hinch for transient extensional flows (Fig.2).
Figure 2. Force balance for a collapsing liquid bridge of a dilute polystyrene solution (Mw=1.9106 g/mol, c=250ppm, stresses in Pa).
The influence of the molar mass as well as a molar mass distribution on the stress evolution and the critical dilution concentration is also discussed. Finally, we consider the influence of the chemical structure of more complex macromolecules as for example cellulose derivatives on the transient extensional flow that arises in capillary break-up rheometers.