Coil-stretch Transition Research Articles

Coil-stretch transition in deformation flows

We present a novel Monte-Carlo lattice model for the study of the coil-stretch transition for polymer chains in deformation flows. Our results indicate that elongational flows are much more effective than shear flows in stretching polymer chains, in full agreement with experimental observation. Our model data also show that the e˙c∼M−1.5 powerlaw observed experimentally for the dependence of critical flow rate on polymer molecular weight can be fully explained through a nonuniform stretching of the chain by the flow. A higher powerlaw exponent is predicted in more affine deformation cases. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2422–2428, 2000

Direct experimental evidence for flow induced fibrous polymer crystallisation occurring at a solid/melt interface

We report experimental observations on the way that flowing polyethylene melts can crystallise within a processing channel geometry. Using a recently developed Multipass Rheometer (MPR), we present rheological, rheo-optic and coupled X-ray data that follow the evolution of crystallisation, as molten polyethylene flows into a slit geometry. Optical observations show that fibrous crystallisation occurs initially at the walls of the slit and not, as expected, in the entrance region to the slit. The coupled X-ray, rheology and rheo-optic data lead us to speculate that a coil-stretch transition of the polymer chains occurs at the wall of the slit and this acts as the primary cause of fibrous X-ray nucleation. At high wall shear rates we identify evidence to suggest that slip occurs between the flowing polymer and the solid wall and this in turn causes the onset of fibrous crystallisation to be surpressed. The experimental observations are generally consistent with certain theoretical predictions made by Brochard and de Gennes.

Dynamic Properties of an Extended Polymer in Solution

Extended polymers are relevant in a variety of situations ranging from the classic coil-stretch problem to recent single molecule polymer experiments with DNA. We present theoretical calculations and computer simulations of the dynamic properties of extended single polymers. We discuss the effects of tension and hydrodynamics on $\ensuremath{\tau}$, the fundamental relaxation time of the polymer, and find that tension dominates the behavior of $\ensuremath{\tau}$. Furthermore, the symmetry breaking caused by extending the polymer ``splits'' $\ensuremath{\tau}$, leading to distinct longitudinal and transverse relaxation times. Our results are in agreement with recent experiments, and we discuss implications for the coil-stretch transition.

Single-polymer dynamics in steady shear flow.

The conformational dynamics of individual, flexible polymers in steady shear flow were directly observed by the use of video fluorescence microscopy. The probability distribution for the molecular extension was determined as a function of shear rate, gamma;, for two different polymer relaxation times, tau. In contrast to the behavior in pure elongational flow, the average polymer extension in shear flow does not display a sharp coil-stretch transition. Large, aperiodic temporal fluctuations were observed, consistent with end-over-end tumbling of the molecule. The rate of these fluctuations (relative to the relaxation rate) increased as the Weissenberg number, gamma;tau, was increased.

Steady-state behavior of dilute polymers in elongational flow. Dependence of the critical elongational rate on chain length, hydrodynamic interaction, and excluded volume

The steady-state properties of flexible polymer chains in solutions undergoing elongational flow have been studied using Brownian dynamics simulation. The coil–stretch transition is observed when the elongational rate, ε̇ exceeds a certain critical value ε̇c. In this work, we describe in detail the simulation procedure and how to extract polymer dimensions, solution viscosity, and birefringence from the trajectories. Preliminary simulations involving no hydrodynamic interaction (HI) are used to check the simulation procedures by comparing their results with theoretical predictions for such an (unphysical) case. Afterwards, simulations with fluctuating nonaveraged HI are carried out to provide results comparable with experiments. After simulations with and without intramolecular potential, we arrive at a most important conclusion: the chain length dependence of ε̇c is the same in theta conditions as in good solvent conditions. Combining ε̇c with other solution properties such as the longest relaxation time, the intrinsic viscosity, and the radius of gyration, dimensionless compound quantities can be formulated. From our simulation results, we obtain numerical values for such quantities, which include the HI effect, and which are therefore useful for analyzing experimental data.

Simulation of polymers in dilute solution under elongational flow

The behavior of polymer chains, modeled as chains of finitely extensible non-linear elastic springs, in solutions undergoing elongational flow, has been studied by Brownian dynamics simulation. The coil–stretch transition is observed when the elongational rate, ϵ ̇ , exceeds some critical ϵ ̇ c that is determined, in steady-state condition, as a function of chain length. We have simulated the time dependence of polymer dimensions when ϵ ̇ is increased from below to above ϵ ̇ c , and then decreased to the initial value. In the coil-to-stretch transition there is an induction time, required to observe the onset of the transition, which varies among the chains in a sample. However, the stretch-to-coil transition follows the same path for all the molecules. The observable properties (sample averages) show a hysteresis cycle that is intensified by the effect of hydrodynamic interaction (HI).

The effect of extensional flow on the Raman spectra of dilute polymer solutions

Raman spectroscopy has been used to investigate the dynamics of the coil-stretch transition of dilute polymer solutions. A stagnation-point extensional-flow field was created by an opposed jets apparatus. High molecular weight, closely monodispersed cis-polyisoprene was studied in 1,1.1-trichloroethane, a good solvent for this polymer. Raman spectra were obtained with a spatial resolution of 10 (μm in the extensional flow region. The vibrational frequency of the ν(C = C) stretch at 1664 cm −1 was shown to be sensitive to the strain rate of the extensional flow field. No changes were observed in the Raman spectra until the strain rate was larger than the critical value for the coil-stretch transition. The Raman band was then observed to shift linearly to lower frequency with increasing strain rate before saturating. The observed changes were much smaller, however, than those predicted using a model of a fully extended chain in the flow field.

Brownian dynamics simulation of a polymer molecule in solution under elongational flow

We use Brownian dynamics simulation to study coil–stretch transition of macromolecules in solution. Into a simple elongational flow field, we introduce freely jointed bead-rod chain model molecules in their coiled and stretched states, and follow the conformational changes. We find good agreement of our simulation results with the available theoretical predictions for low and high strain rates (ε̇). At the intermediate elongation rates (near the onset of coil–stretch transition) of the flow field, we find that the residence time required for stretching of an initially coiled chain can be extremely large as compared to predicted (1+ln(√N))ε̇−1, especially for the non-free-draining case. Hence, the chain conformation is dependent on the initial state of the chain molecule for residence time as long as 100ε̇−1. Thus, hysteresis is predicted when chain residence time in such an elongational flow field is limited, as in practical situations. Further, at such intermediate ε̇, the chain molecule is seen to undergo Brownian fluctuation induced jumps between a randomly coiled state and another partially stretched state. This suggests the existence of more than one equilibrium conformation that is unstable to Brownian fluctuations.

Macromolecular dynamics in extensional flows: 2. The evolution of molecular strain

The opposed jets apparatus has been used to investigate the dynamics of the coil-stretch transition of polymer solutions in an idealized stagnation point extensional flow field. Flow simulations generated fluid strain profiles for different geometries. Assuming a molecular uncoiling model, true birefringence profiles have been converted to molecular strains for closely monodisperse, high molecular weight aPS under θ-conditions. This has enabled macromolecular deformation to be followed as a function of position and residence time. Non-linear hydrodynamic friction FENE dumb-bell simulations give qualitative agreement. Initially, molecular uncoiling is non-affine, consistent with changing hydrodynamic screening on extension. Deformation in a good solvent is more affine. Results are compared with PEO/water to investigate the effect of molecular parameters. The effective extensional viscosity has been ascertained by correction for the area of high molecular extension. The increase in extensional viscosity due to molecular stretching is substantial, of the order of the number of equivalent flexible units in the chain. © 1997 Elsevier Science Ltd.

Macromolecular dynamics in extensional flows: 1. Birefringence and viscometry

The opposed jets apparatus is used to investigate the dynamics of the coil-stretch transition of polymer solutions in an idealized stagnation point extensional flow-field. A linear CCD detector allows optical retardation profiles to be recorded as the strain rate is varied. A numerical transformation enables true birefringence profiles to be produced, which enable the assessment of localized molecular orientation and stretching around the stagnation point. High molecular weight, closely monodisperse aPS and PEO are studied in θ and good solvents. Flow modification effects are apparent to extremely low concentration (≈ c ∗/100). Under θ conditions, the width of the transition is consistent with the residual polydispersity. Simultaneous measurements of flow resistance enable the determination of the effective extensional viscosity. The increase in extensional viscosity due to molecular stretching is found to be of the order of the number of equivalent flexible units in the chain, after correction is made for the area of high molecular extension.

Molecular dynamics simulation of a polymer chain in solution by collisional dynamics method

This article describes the collisional dynamics (CD) method adapted for molecules with geometrical constraints within a description using Cartesian coordinates for the atoms. In the CD method, stochastic collisions with virtual particles are included in usual molecular dynamics simulations to couple the considered polymer molecule to a solvent. The actual presence of the solvent is not explicitly included in the simulation. The results-of CD simulations of a polymer chain immersed in the time-dependent elongational flow field are presented. The influence of nonbonded interactions on the coil-stretch transition of the chain occurring in the flow is discussed. © 1996 John Wiley & Sons, Inc.

Molecular dynamics simulation of a polymer chain in solution by collisional dynamics method

This article describes the collisional dynamics (CD) method adapted for molecules with geometrical constraints within a description using Cartesian coordinates for the atoms. In the CD method, stochastic collisions with virtual particles are included in usual molecular dynamics simulations to couple the considered polymer molecule to a solvent. The actual presence of the solvent is not explicitly included in the simulation. The results-of CD simulations of a polymer chain immersed in the time-dependent elongational flow field are presented. The influence of nonbonded interactions on the coil-stretch transition of the chain occurring in the flow is discussed. © 1996 John Wiley & Sons, Inc.

How do polymers stretch in stagnation point extensional flow-fields?

In this paper we present an analysis of salient existing evidence on the nature of the coil-stretch transition for dilute polymer solutions in extensional flows around stagnation points. Some experiments support the idea of a transition which is critical in strain-rate to a highly extended final state, other studies report a non-critical extension and only a low degree of final strain. This situation is mirrored by theoretical and computational approaches, where the existence of a critical transition has long been a controversy. We also present new experimental evidence which leads us to maintain our previous arguments for criticality of the transition and close to full stretching.

Non-aqueous retention measurements: ultrafiltration behaviour of polystyrene solutions and colloidal silver particles

The retention behaviour of polyimide ultrafiltration membranes was investigated using dilute solutions of polystyrene in ethyl acetate as test solutions. It is shown that flow-induced deformation of the polystyrene chains highly affects the membrane retention. This coil-stretch transition is not instantaneous, but gradual. The concept of a deformation resistance has been ontroduced to explain this behaviour. This concept can be applied to describe the flux behaviour of the membranes during the tests as well. Solute deformation allows comparison of the pore size distributions of the membranes qualitatively. Retention measurements were also performed with silver sol particles that were prepared in mixtures of ethanol and water; these sols remain stable as long as the ethanol concentration does not exceed 57 vol%. The sols were completely retained by the membranes, which is probably caused by the fact that the effective diameter of the particles is much larger than that observed by transmission electron microscopy.

Comparison of the extensional and shear viscosity characteristics of aqueous hydroxyethyl cellulose solutions

The extensional viscosity characteristics of aqueous solutions of varying concentrations of three samples of hydroxyethylcellulose (HEC) of differing molecular masses have been determined using a commercially available opposed jet extensional rheometer. The results have been compared to the shear flow characteristics of the solutions and the Trouton ratio, T R , of the various systems calculated. For all polymer solutions studied, T R was found to approach the predicted Newtonian value of 3 at low extensional strain rates. This observation was taken as a strong indication that the opposed jet rheometer was producing reliable extensional viscosity data. At higher strain rates, T R generally increased with increasing strain rate and, for any given sample, with increasing polymer concentration thereafter. All HEC solutions studied were found to exhibit strain-thinning behavior in extensional flow and shear-thinning behavior in shear flow, with the most pronounced effects being observed with the highest molecular mass sample (M v ∼4.5×10 5 g/mol). The relative degrees of strain and shear thinning exhibited by the various HEC solutions have been quantified using the power law analysis. For the two samples of lowest molecular mass (M v ∼6.5×10 4 and ∼1.9×10 5 g/mol) the value of a power law index, n, in both extensional and shear flow, was close to unity. For all solutions of the sample of highest molecular mass, the value of n in extensional flow was significantly higher than that observed in shear flow. Regions of apparent strain thickening were observed for a few of the lowest viscosity solutions, but these observations were attributed to the onset of significant inertial effects rather than any coil-stretch transition phenomena

Stretch transition in a polymer brush.

The behavior of a grafted chain of length K inside an otherwise monodispersed (of length N) polymer brush is investigated. For the case of K\ensuremath{\le}N, the stretching of the chain increases abruptly as K approaches N, analogous to the coil-stretch transition. By generalizing previous results, we derive the scaling forms for the stretching parameter and its mean square fluctuations. We also extend our investigation to the K>N regime and obtain results for the stretching parameter by scaling calculations. We show that the chain is maximally stretched as K\ensuremath{\rightarrow}N from above. Furthermore, we perform a Monte Carlo simulation using the bond-fluctuation model to study the chain end position and its fluctuations. Our data indicate that both the stretching of the chain and its fluctuation are maximal at K=N and the system exhibits a first-order phase transition. The scaling form for the stretching parameter is verified and the scaling function is obtained.

Simulation of non-linear models for polymer chains in flowing solutions

Two non-linear bead and spring models are considered for the Brownian dynamics simulation of the behaviour of polymer chains in a dilute solution under shear or elongational flow. One of them is the HYBRID model whose springs are Hookean at low elongation, and beyond some spring length they follow a Morse potential with a given dissociation energy. This model is suitable for studying polymer fracture in strong flows. In this paper we describe the model and check that it has the proper behaviour in the two regions. The second model is a chain of finitely extensible, non-linear elastic (FENE) springs. Our simulations show several features of the FENE model that agree well with observation. In shear flow, the deformation of the FENE chain at high shear rate deviates from the square law followed at low shear, in agreement with some experiments. The model also predicts the typical shear-thinning, non-Newtonian behaviour of the shear viscosity. In elongational flows, the variation of the chain properties with the elongation rate shows a rather sharp increase at some critical rate that is reminiscent of the so-called coil-stretch transition.

Flow of monodisperse polystyrene solutions through porous media

In this work, we study the origin of the extension thickening commonly observed when solutions of flexible polymers flow through porous media and ideal elongational flows. We have used randomly packed beds of glass beads as porous media. We have performed experiments with closely monodisperse atactic polystyrene of different molecular weights dissolved in organic solvents. The use of a closely monodisperse polymer allowed us to make a more meaningful comparison between the results obtained using opposed jets and porous media flow, as compared to previous works on polydisperse polymers. The results indicate that the coil-stretch transition of isolated polymer molecules in solution cannot be the only mechanism responsible for the extension thickening. It is clear that part of the observed effect is due to the extension of isolated molecules, but the main factor causing a great increase in the elongation viscosity beyond a critical strain rate is the formation of transient entanglement networks.

Simple shear flow of a suspension of fibres in a dilute polymer solution at high Deborah number

The behaviour of fibre suspensions in dilute polymer solutions at high Deborah numbers is analysed. In particular, we calculate the change to the extension of the polymers and the orientation of the fibres caused by hydrodynamic interactions between the polymers and the fibres. At a sufficiently high Deborah number the combined effect of the fibre velocity disturbances and the mean shear flow produce a dramatic increase in the extension of the polymers, similar to the coil-stretch transition observed in extensional flow.The non-Newtonian stresses caused by the polymers produce a perturbation to the angular velocity of the fibres, giving rise to a net drift across Jeffery orbits towards the vorticity axis. Unlike the second-order-fluid analysis of Leal (1975), this effect does not depend on the second-normal-stress difference.

Viscous finger narrowing at the coil-stretch transition in a dilute polymer solution

We present results of an experimental study of Saffman-Taylor fingers in dilute solutions of polystyrene in dioctyl phthalate (DOP). While fingers in pure DOP obey classical scaling laws, we observe transitions to narrow fingers in polysterene solutions of concentrations as low as 1 part per million. The onset of narrowing occurs at a shear rate which roughly equals the inverse of the polymer Zimm relaxation time and depends only weakly on concentration. The onset of instability occurs earlier than in Newtonian fluids and is often initiated by small-amplitude oscillations.