Semidilute Unentangled Solutions Research Articles

Shear thinning in dilute and semidilute solutions of polystyrene and DNA

The viscosity of dilute and semidilute unentangled DNA solutions, in steady simple shear flow, has been measured across a range of temperatures and concentrations. For polystyrene solutions, measurements of viscosity have been carried out in the semidilute unentangled regime, while results of prior experimental measurements in the dilute regime have been used for the purpose of data analysis, and for comparison with the behaviour of DNA solutions. Interpretation of the shear rate dependence of viscosity in terms of suitably defined non-dimensional variables, is shown to lead to master plots, independent of temperature and concentration, in each of the two concentration regimes. In the case of semidilute unentangled solutions, defining the Weissenberg number in terms of a concentration dependent large scale relaxation time is found not to lead to data collapse across different concentrations. On the other hand, the use of an alternative relaxation time, with the concentration dependence of a single correlation blob, suggests the existence of universal shear thinning behaviour at large shear rates.

Self-Organization in Electrospun Polymer Solutions: From Dissipative Structures to Ordered Fiber Structures through Fluctuations

Self-organization in nonequilibrium systems is a research topic in the statistical physics universally important for formation of patterns or orders in various systems, including nature. In this work, we investigated the self-organization processes of ordered structures via cascade evolutions of various dissipative structures through fluctuations in electrospun poly(vinyl alcohol) aqueous solutions in both mesoscopic and macroscopic length scales. The flowing jets were investigated both in situ, macroscopically with a high speed video imaging and ex situ, mesoscopically under optical and electron microscopies as a function of the polymer concentration. In the semidilute unentangled solutions, the main jet evolved a self-similar, cascade network composed of a set of the bulge and the branched subjets issued from the bulge as a building block of the network. In the semidilute entangled solutions, the main jet evolved a series of bulges elongated along the jet axis without formation of the branched subjets. ...

Viscoelasticity and rheology in the regimes from dilute to concentrated in cellulose 1-ethyl-3-methylimidazolium acetate solutions

Dynamic rheological behaviors of α-cellulose 1-ethyl-3-methylimidazolium acetate ([Emim]Ac) solutions were investigated in a large range of concentrations (0.1–10 wt %) at 25 °C. On the basis of data from the dynamic viscoelastic test, the exponents of the specific viscosity η sp versus concentration c were determined as 1.0, 2.0 and 4.7 for dilute, semidilute unentangled and entangled regimes respectively, which were in accordance with the scaling prediction for neutral polymer in θ solvent. The intrinsic viscosity [η] of the solution was determined to be 253 mL/g at 25 °C. The linear viscoelastic response of the dilute and semidilute unentangled solutions could be described successfully by the Zimm and Rouse model (ν = 0.5 for θ solution) respectively, suggesting that the motion of cellulose chain in [Emim]Ac changed from Zimm to Rouse model with increasing concentration. At low concentrations, failure of the Cox–Merz rule with steady shear viscosity larger than complex viscosity was observed. While as the concentration increased, the deviation from the Cox–Merz rule disappeared due to the formation of homogeneous entanglement structure in cellulose solution.

Linear viscoelasticity of poly(acrylonitrile-co-itaconic acid)/1-butyl-3-methylimidazolium chloride extended from dilute to concentrated solutions

The solution rheology of poly(acrylonitrile-co-itaconic acid) (poly(AN-co-IA)) in 1-butyl-3-methylimidazolium chloride ([BMIM]Cl) spanning dilute, semidilute unentangled and entangled regimes were investigated. The exponents in the specific viscosity ηsp∼overlap parameter c[η] power law were 1, 2 and 4.7 for dilute, semidilute unentangled and entangled regimes, respectively, which were found to be consistent with the scaling prediction for neutral linear polymers in θ-solvent. For dilute solutions (lower than 0.9wt.%), the linear viscoelastic responses were observed to be in good agreement with the Zimm model (Flory exponent ν=0.5). While for semidilute unentangled solutions (between 0.9 and 8wt.%), results obtained had been found to be consistent with Rouse model. Considering Flory exponent ν=0.5 and the concentration dependences of the specific viscosity and relaxation time, it had been evaluated that poly(AN-co-IA) in [BMIM]Cl behaves as a neutral polymer in θ-solvent. It had also been suggested that according to the unusual deviation of Cox-Merz rule, poly(AN-co-IA)/[BMIM]Cl solutions are typical neutral polymeric liquids for the concentrated solutions but have shown a more complicated behavior at high deformation rates.

Solution rheology of cellulose in 1-butyl-3-methyl imidazolium chloride

Solution rheology of cellulose in 1-butyl-3-methyl imidazolium chloride ([BMIm]Cl) is reported using oscillatory and steady shear for cellulose concentrations from 0.1 to 10 wt %, spanning the dilute, semidilute unentangled, and entangled regimes. Although pure [BMIm]Cl is a crystalline solid at room temperature with a melting temperature of 65 °C, all solutions prepared at 75 °C are transparent and visually homogenous at 25 °C, and these supercooled solutions, with of order 0.1 wt % water, show no sign of crystallizing for months in either calorimetry or rheology measurements, allowing the potential for room temperature solution processing of native cellulose, such as fiber spinning. The overlap concentration of our cellulose in [BMIm]Cl is 0.5 wt % and the entanglement concentration is a factor of 4 larger (2 wt %). For semidilute unentangled solutions (between 0.5 and 2 wt %), the specific viscosity, relaxation time, and terminal modulus exhibit concentration dependences ηsp∼c2, τ∼c, and G∼c, respectiv...

Mechanism of Shear Thickening in Reversibly Cross-Linked Supramolecular Polymer Networks

We report here the nonlinear rheological properties of metallo-supramolecular networks formed by the reversible cross-linking of semi-dilute unentangled solutions of poly(4-vinylpyridine) (PVP) in dimethyl sulfoxide (DMSO). The reversible cross-linkers are bis-Pd(II) or bis-Pt(II) complexes that coordinate to the pyridine functional groups on the PVP. Under steady shear, shear thickening is observed above a critical shear rate, and that critical shear rate is experimentally correlated with the lifetime of the metal-ligand bond. The onset and magnitude of the shear thickening depend on the amount of cross-linkers added. In contrast to the behavior observed in most transient networks, the time scale of network relaxation is found to increase during shear thickening. The primary mechanism of shear thickening is ascribed to the shear-induced transformation of intrachain cross-linking to interchain cross-linking, rather than nonlinear high tension along polymer chains that are stretched beyond the Gaussian range.

Structure and linear viscoelasticity of flexible polymer solutions: comparison of polyelectrolyte and neutral polymer solutions

The current state of understanding for solution conformations of flexible polymers and their linear viscoelastic response is reviewed. Correlation length, tube diameter, and chain size of neutral polymers in good solvent, neutral polymers in θ-solvent, and polyelectrolyte solutions with no added salt are compared as these are the three universality classes for flexible polymers in solution. The 1956 Zimm model is used to describe the linear viscoelasticity of dilute solutions and of semidilute solutions inside their correlation volumes. The 1953 Rouse model is used for linear viscoelasticity of semidilute unentangled solutions and for entangled solutions on the scale of the entanglement strand. The 1971 de Gennes reptation model is used to describe linear viscoelastic response of entangled solutions. In each type of solution, the terminal dynamics, reflected in the terminal modulus, chain relaxation time, specific viscosity, and diffusion coefficient are reviewed with experiment and theory compared. Overall, the agreement between theory and experiment is remarkable, with a few unsettled issues remaining.

Solution Rheology of a Strongly Charged Polyelectrolyte in Good Solvent

Solution rheology of poly(2-vinylpyridine) and a random copolymer of 60% N-methyl-2-vinylpyridinium iodide and 40% 2-vinylpyridine in N-methylformamide (NMF) was studied over wide ranges of concentration. The fraction of monomers bearing an effective charge f = 0.31 of these copolymers was measured using dielectric spectroscopy. This low fraction of effectively charged monomers suggests that the polyion disrupts the hydrogen-bonding alignment of NMF that makes the dielectric constant of the pure solvent anomalously large. NMF is a good solvent for neutral poly(2-vinylpyridine) but has a significant quantity of ionic impurities even when freshly distilled. The specific viscosity and relaxation time of dilute and semidilute unentangled solutions exhibit the scaling with concentration expected by theory if cs ≈ 1 mM residual salt is present, identified from the change in slope of viscosity−concentration power laws from 5/4 to 1/2 at concentration c = 2cs/f = 9.5 × 10−3 M (moles of monomer per liter). The spe...

Shear thinning of unentangled flexible polymer liquids

Experimentally, it is well-known that the Rouse model gives a superb description of the concentration dependence of terminal relaxation time, terminal modulus, zero shear-rate viscosity, and diffusion coefficient of semidilute unentangled polyelectrolyte solutions. However, such solutions exhibit shear thinning of the apparent viscosity when the shear rate exceeds the reciprocal of the terminal relaxation time, which is not immediately anticipated by the Rouse model. We present a simple calculation based on the Rouse model for the dependence of the apparent viscosity η on shear rate $\dot{\gamma}$ in steady shear. The derived power law $\eta \sim \dot{\gamma}^{-1/2}$ applies to nearly mono- disperse unentangled polymer melts and polymer solutions that have a high enough concentration so that chains overlap, but have low enough concentration that they are not entangled. We find that the predicted power law agrees nicely with data on unentangled polymer melts and semidilute unentangled solutions of polyelectrolytes. The exponent 1/2 means the empirical Cox-Merz rule applies to Rouse chains. This potentially has far-reaching consequences for entangled polymer melts, for which motion of a Rouse chain confined to a tube describes dynamics.

Charge density effects in salt‐free polyelectrolyte solution rheology

AbstractSolution rheology of 2‐vinyl pyridine andN‐methyl‐2‐vinyl pyridinium chloride random copolymers in ethylene glycol was studied over wide ranges of concentration and effective charge. The fraction of quaternized monomers α and the fraction of monomers bearing an effective chargefof these copolymers were measured using counterion titration and dielectric spectroscopy, respectively. Ethylene glycol is a good solvent for neutral poly(2‐vinyl pyridine), with very few ionic impurities. The viscosity η and relaxation time τ of dilute and semidilute unentangled solutions exhibit the scaling with concentration and effective charge expected by the Dobrynin model. Reduced viscosity data are independent of concentration in dilute solution, giving an intrinsic viscosity that depends on effective charge, and the experimental data obey the Fuoss law in the semidilute unentangled regime. Scaling concentration with the overlap concentration (c/c*) reduces these data to common curves, andc*∼f−12/7as predicted by the Dobrynin model, wherefis the fraction of monomers bearing an effective charge. While the overlap concentration depends strongly on effective charge until counterion condensation occurs, the entanglement concentrationceis surprisingly insensitive to effective charge, indicating that entanglement effects are not understood using the Dobrynin model. The terminal modulusG= η/τ depends only on the number density of chainsG=ckT/Nforc* <c<ce, andG∼c3/2forc>ceindependent of the effective charge. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2001–2013, 2006