Coil-stretch Transition Research Articles

Flow Characteristics of Partially Hydrolyzed Polyacrylamides during Converging into a Capillary

ABSTRACTPartially hydrolyzed polyacrylamides (HPAMs) are the most widely used polymers in enhanced oil recovery (EOR). This study presents capillary flow measurements of three different molecular weight HPAMs in synthetic brine. Polymer solutions having similar viscoelasticity were forced to flow through a 0.23 mm (radius) stainless steel capillary to investigate their flow characteristics including mobility reduction (apparent viscosity) and mechanical stability, represented by the extent of mechanical degradation (DR). The results indicated that the apparent viscosity of the polymer solutions markedly dropped with increasing flow rate until 5 mL/min, corresponding to the shear rate of 8,730s−1; after that a slight viscosity decrease was observed. The high-molecular-weight HPAMs (6.5 and 8.0 × 106 g/mol) began to have slightly greater apparent viscosity than the low-molecular-weight HPAM (1.0×106 g/mol) above the shear rate of 26,180 s−1; this might result from the occurrence of the coil-stretch transition. All the HPAMs experienced very similar percentages of mechanical degradation (10%) at shear rates between 1750 and 8730 s−1; however, above 8730s−1 the high-molecular-weight HPAMs exhibited a steep increase in mechanical degradation (DR). On the other hand, in the case of the low-molecular-weight HPAM, the DR curve almost leveled off at 12%. Therefore, low-molecular-weight HPAMs are generally suggested for EOR applications. These results, we suggested, should be useful to improve the efficiency of polymer EOR by minimizing mechanical degradation.

Ring Polymer Dynamics Are Governed by a Coupling between Architecture and Hydrodynamic Interactions

The behavior of linear polymer chains in dilute solution flows has an established history. Polymers often possess more complex architectures, however, such as branched, dendritic, or ring structures. A major challenge lies in understanding how these nonlinear chain topologies affect the dynamic properties in nonequilibrium conditions, in both dilute and entangled solutions. In this work, we interrogate the single-chain dynamics of ring polymers using a combination of simulation, theory, and experiment. Inspired by recent experimental results by Li et al., we demonstrate that the presence of architectural constraints has surprising and pronounced effects on the dynamic properties of polymers as they are driven out of equilibrium. Ring constraints lead to two behaviors that contrast from linear chains. First, the coil–stretch transition occurs at larger values of the dimensionless flow strength (Weissenberg number) compared to linear chains, which is driven by coupling between intramolecular hydrodynamic in...

Flow-Induced Crystallization of Polymers: Molecular and Thermodynamic Considerations

Flow-induced crystallization (FIC) of polymers is a long-standing, industrial relevant, nonequilibrium thermodynamic challenge. Thanks to the development of in situ time and spatial resolved techniques like rheology and synchrotron radiation X-ray scattering, substantial progress on the understanding of FIC has been achieved in past 20 years. In this Perspective, we first discuss some recent modifications and improvements on early coarse-grained approaches like the coil–stretch transition model for shish formation and the entropic reduction model for the enhancement of nucleation rate. Then breaking out the two-phase model of classical nucleation theory, flow-induced coil–helix transition, density fluctuation or phase separation, and isotropic–nematic transition are considered as intermediate orders in FIC. Establishing flow morphology and phase diagrams is essential for revealing the nonequilibrium nature of FIC, which will serve as structural roadmap for the processing of high performance polymer products.

Correlation of crystal alignment with interphase content in oriented high density polyethylene cast films

The microstructure and crystalline morphology of high density polyethylene (HDPE) cast films prepared in a wide range of draw ratios (1.6 to 148.8) were investigated. The flow-induced orientation of crystalline and amorphous phases was characterized using Fourier transform infrared spectroscopy (FTIR). The results showed that the draw ratio has a crucial role on the orientation state of the cast films. Scanning electron microscopy (SEM) images also confirmed this influence. The crystallinity of the films was examined using both differential scanning calorimetry (DSC) and Raman spectroscopy. Moreover, considering a three-phase structure (i.e. crystal, amorphous and interphase) for semi-crystalline polyethylene, Raman spectroscopy was also employed to estimate the amount of the so-called interphase in the HDPE cast films. As a result, the interphase content was found to decrease by increasing the applied draw ratio. The origin of this dependency was suggested to be due to a coil–stretch transition during elongation flow and the subsequent disentanglement. On the other hand, remarkable differences were observed in the CH2 bending vibration features of the Raman spectra of the cast films which were correlated with the applied draw ratios and with the calculated crystalline orientation functions.

Stretching DNA Molecules in Strongly Confining Nanofluidic Slits

We experimentally investigate the stretching and relaxation of individual double-stranded DNA molecules in nanofluidic slits with depths that span the regime between moderate and strong confinement. DNA molecules are stretched by the application of a quadrupole-like homogeneous elongational electric field. In a moderately confining slit we verify the previously observed existence of two distinct relaxation times resulting from the transition from a bulk-like entropic spring force to one that is confinement dependent. In a strongly confining slit with a depth equal to one persistence length we observe the return to a coil–stretch transition that is governed by a single strain rate related to the confined spring constant. By measuring the equilibrium extension as a function of the applied strain rate as well as the relaxation dynamics from a highly stretched initial state, we are able to infer a hydrodynamic friction coefficient in the moderately and strongly confining slits that is in good agreement for a long DNA molecule. Our results are helpful for informing theoretical models of the force–extension relation for semiflexible polymers in quasi-two-dimensional space.

Kinetic Process of Shish Formation: From Stretched Network to Stabilized Nuclei

On the basis of the duality of the shish-kebab superstructure, coil–stretch transition (CST) is well recognized as the molecular mechanism for shish-kebab formation in polymer melts, which, however, is challenged by recent results in flow-induced crystallization (FIC). In this work, we perform a real time investigation on FIC of polyethylene bimodal blends by combing a unique homemade extensional rheometer and synchrotron radiation small-angle X-ray scattering. The results show that the critical strain for shish formation decreases with increasing long chain concentration, which contradicts the role of CST but agrees well with stretched network model (SNM). Quantitative analyses indicate that the formation of shish is determined by the degree of network deformation rather than solely by strain or long chain concentration at a specific temperature. In addition, three types of shish with different stability are observed sequentially by increasing strain. On the basis of our results, strong support is given ...

Extreme-value statistics of work done in stretching a polymer in a gradient flow.

We analyze the statistics of work generated by a gradient flow to stretch a nonlinear polymer. We obtain the large deviation function (LDF) of the work in the full range of appropriate parameters by combining analytical and numerical tools. The LDF shows two distinct asymptotes: "near tails" are linear in work and dominated by coiled polymer configurations, while "far tails" are quadratic in work and correspond to preferentially fully stretched polymers. We find the extreme value statistics of work for several singular elastic potentials, as well as the mean and the dispersion of work near the coil-stretch transition. The dispersion shows a maximum at the transition.

Scaling Theory of Stretched Polymers in Nanoslits

We provide a scaling framework describing the different regimes attained by a slit-confined polymer, undergoing an external pulling force fel,slit. Linear and nonlinear force–extension relations are discussed in the limit of small and large elongations, resorting to the notion of self-avoiding pancakes. The crossover to a channellike behavior allows to explain the scaling of fel,slit as a function of the confinement h observed in recent tug-of-war experiments. The theoretical analysis provides also a qualitative explanation of DNA relaxation and coil–stretch transition experiments performed in nanoslits.

Fluctuations in the coil-stretch transition of flexible polymers in good solvents: A peak due to nonlinear force relation

Long flexible polymers undergo a coil to stretch transition (CST) in an elongational flow. Near the CST, a peak can be observed in the fluctuations of the size of a molecule (|R|). Solvent effects on the fluctuations are studied using Brownian dynamics simulations of a nonlinear spring force relation that can represent real molecules. Ignoring the influence of hydrodynamic interactions, a linear region in the spring force relation is known to cause the peak in |R| fluctuations. In contrast, we find that a peak in the fluctuations can be obtained even for the nonlinear spring force relation. We analyze the influence of hydrodynamic interactions on the fluctuations using a dumbbell model with a conformation-dependent drag coefficient.

Rheology and mechanical degradation of high-molecular-weight partially hydrolyzed polyacrylamide during flow through capillaries

Abstract High-molecular-weight partially hydrolyzed polyacrylamides are widely used in enhanced oil recovery. Mechanical degradation of these polymers as a result of flow through pumps, chokes, valves and at the sand face has been recently reported to have a negative impact on the application. This study presents capillary flow measurements of high-molecular-weight hydrolyzed polyacrylamide (degree of hydrolysis=27.8%) in 2 wt% potassium chloride aqueous solvent. Flow was conducted at different flow rates through three different lengths of 125-μm stainless steel capillaries to investigate the apparent rheology and mechanical degradation. The apparent rheology was indicated by mobility reduction while the mechanical degradation was measured by the loss in viscosity of the solution effluent. The entry point contribution in the overall mobility reduction and degradation was evaluated by extrapolation. In the investigated range of shear rates, the polymer solution generally shows an initial apparent thickening behaviour up to 15,000 s−1, above which the behaviour becomes thinning. After the evaluation of the entry point contribution to the overall mobility reduction, the initial thickening behaviour is found to be due to the coil–stretch transition at the entry point. The flow in the bulk of the capillaries is found purely thinning in the whole shear rate range investigated. The total degradation is found to be almost constant, below 20%, up to the shear rate of 15,000 s−1. The degradation starts to increase above 15,000 s−1 due to the effect of shear in the bulk of the capillaries. The entry point degradation seem to contribute negligibly (below 5%) to the overall degradation up to 100,000 s−1, above which it sharply increases its effect on polymer degradation reaching 42% at 850,000 s−1. We believe that the results of this study will improve the execution of the polymer enhanced oil recovery by minimizing polymer mechanical degradation. High shear devices such as pumps, chokes, valves can have a detrimental effect on the mechanical stability of the polymer and hence should be utilized with caution. Also, more mechanically stable polymers can be utilized. Moreover, in the light of the current study, it is expected that the elongational flow of polymer at the sand face and the flow of polymer through perforations and/or fractures can also degrade the polymer, which need to be evaluated.

Impact of Solvent Quality on the Hysteresis in the Coil–Stretch Transition of Flexible Polymers in Good Solvents

Direct observations of long flexible polymers in elongational flow show a coil to stretch transition (CST) and hysteresis in this transition. In this article, solvent effects on the hysteresis of CST were examined using Brownian dynamics simulations of a dumbbell model with conformation dependent drag. A spring force relation that is able to capture the effects of solvent quality was used. Two methods of increasing the solvent quality were analyzed: (1) by increasing the number of Kuhn steps (NK) and keeping the excluded volume parameter (v/l3) constant, and (2) by increasing v/l3 and keeping NK constant. In the first case, the width of the hysteresis (ratio of upturn to downturn strain rates) increased with increase in NK. In the second case, the width of hysteresis decreased with increase in v/l3. This implies that molecules such as ss-DNA, which have v/l3 ≈ 1 in good solvents, will have less hysteresis than a molecule with the same NK in a Θ solvent.

Kinetic Monte Carlo Simulations of Flow-Assisted Polymerization.

We performed kinetic Monte Carlo simulations on a model of a polymerization process in the presence of a periodic oscillatory flow to explore the role of mixing in polymerization reactors. Application of an oscillatory flow field helps overcome the diffusive limitations that develop during a polymerization process due to an increase in the molecular weights of polymer chains, thereby giving rise to high rates of polymerization. A systematic increase in the flow strength results in a "dynamic" coil-stretch transition, leading to an elongation of polymer chains. Reactive ends of stretched (polymer) chains react more frequently than the reactive ends of coiled chains, which are screened by other monomers of the same chain. There exists a critical flow strength for the efficiency of polymerization processes. The kinetic Monte Carlo simulation scheme developed here exhibit great promise for the study of dynamic properties of polymer systems.

Statistics of polymer extensions in turbulent channel flow

We present direct numerical simulations of turbulent channel flow with passive Lagrangian polymers. To understand the polymer behavior we investigate the behavior of infinitesimal line elements and calculate the probability distribution function (PDF) of finite-time Lyapunov exponents and from them the corresponding Cramer's function for the channel flow. We study the statistics of polymer elongation for both the Oldroyd-B model (for Weissenberg number Wi<1) and the FENE model. We use the location of the minima of the Cramer's function to define the Weissenberg number precisely such that we observe coil-stretch transition at Wi ≈1. We find agreement with earlier analytical predictions for PDF of polymer extensions made by Balkovsky, Fouxon, and Lebedev [Phys. Rev. Lett. 84, 4765 (2000)] for linear polymers (Oldroyd-B model) with Wi <1 and by Chertkov [Phys. Rev. Lett. 84, 4761 (2000)] for nonlinear FENE-P model of polymers. For Wi >1 (FENE model) the polymer are significantly more stretched near the wall than at the center of the channel where the flow is closer to homogenous isotropic turbulence. Furthermore near the wall the polymers show a strong tendency to orient along the streamwise direction of the flow, but near the center line the statistics of orientation of the polymers is consistent with analogous results obtained recently in homogeneous and isotropic flows.

Regulation of DNA conformations and dynamics in flows with hybrid field microfluidics

Visualizing single DNA dynamics in flow provides a wealth of physical insights in biophysics and complex flow study. However, large signal fluctuations, generated from diversified conformations, deformation history dependent dynamics and flow induced stochastic tumbling, often frustrate its wide adoption in single molecule and polymer flow study. We use a hybrid field microfluidic (HFM) approach, in which an electric field is imposed at desired locations and appropriate moments to balance the flow stress on charged molecules, to effectively regulate the initial conformations and the deformation dynamics of macromolecules in flow. With λ-DNA and a steady laminar shear flow as the model system, we herein studied the performance of HFM on regulating DNA trapping, relaxation, coil-stretch transition, and accumulation. DNA molecules were found to get captured in the focused planes when motions caused by flow, and the electric field were balanced. The trapped macromolecules relaxed in two different routes while eventually became more uniform in size and globule conformations. When removing the electric field, the sudden stretching dynamics of DNA molecules exhibited a more pronounced extension overshoot in their transient response under a true step function of flow stress while similar behaviors to what other pioneering work in steady shear flow. Such regulation strategies could be useful to control the conformations of other important macromolecules (e.g., proteins) and help better reveal their molecular dynamics.

Models of flexible polymers in good solvents: relaxation and coil–stretch transition

We analyze the impact of solvent quality on relaxation dynamics and the coil–stretch transition (CST) using Brownian dynamics simulations of a new bead–spring model. A new spring force relation, which can represent the polymer in theta to good solvent, is developed to obtain the force–extension (FE) behavior of molecules. Due to different regions of the FE curve, we find that the relaxation and CST behavior are altered. A simple force balance is used to explain different regions of the flow and relaxation behavior. Using a model that neglects conformation dependent drag, it is found that some molecules will have two different exponential decays in relaxation and the CST will be modified for others.

Electrophoretic stretching of tethered polymer chains by travelling-wave electric fields: tunable stretching, expedited coil–stretch transition, and a new paradigm of dynamic molecular probing

The use of low-frequency travelling wave fields in electrophoretic stretching of charged polymer chains is investigated theoretically. We find, using a simple elastic dumbbell model, that the stretching behavior with and without fluctuations can show a number of distinctive features that cannot be seen in usual steady or alternating current electric fields. In the deterministic study without fluctuations, we show that an end-tethered charged polymer chain can be pulled by asymmetric strokes generated by a travelling wave field and kept extended along the wave. It is found that while the averaged chain extension can be increased by raising the field strength, it can be decreased by increasing the wave speed. This is a new example that stretching a polymer chain can be realized in a time periodic field with zero mean. As the free energy landscape here acts like a vibrating harmonic oscillator having double or multiple wells, a stretched chain trapped in an energy groove created by a travelling wave field can hop back to the lower energy coil state due to fluctuations. In this stochastic study, we develop a theory and carry out Brownian dynamics simulations to show that as long as the wave speed does not exceed the damping threshold and fluctuations do not prevail to diminish stretching, increasing the wave speed can help the chain maintain its stretch by preventing it from hopping to the coil state. In addition, two distinct hopping kinetics, Arrhenius and Kramers modes, can exist to govern the respective coil–stretch transitions in the double-well and multiple-well scenarios, depending on the extent of stretching. These features are the results of cooperative effects of travelling wave fields and fluctuations, and further manifested by tongue-like coil–stretch phase diagrams. Applications of the present stretching to dynamic molecular probing are also illustrated by monitoring and regulating the molecular transport over a cyclically stretching polymer chain at the nanoscale or single-molecule level.

Dynamics of threads and polymers in turbulence: power-law distributions andsynchronization

We study the behavior of threads and polymers in a turbulent flow. These objects havefinite spatial extension, so the flow along them differs slightly. The corresponding dragforces produce a finite average stretching and the thread is stretched most of the time.Nevertheless, the probability of shrinking fluctuations is significant and is known to decayonly as a power law. We show that the exponent of the power law is a universal numberindependent of the statistics of the flow. For polymers the coil–stretch transition exists: theflow must have a sufficiently large Lyapunov exponent to overcome the elastic resistanceand stretch the polymer from the coiled state it takes otherwise. The probability ofshrinking from the stretched state above the transition again obeys a power law but with anon-universal exponent. We show that well above the transition the exponent becomesuniversal and derive the corresponding expression. Furthermore, we demonstratesynchronization: the end-to-end distances of threads or polymers above the transition aresynchronized by the flow and become identical. Thus, the transition from Newtonian tonon-Newtonian behavior in dilute polymer solutions can be seen as an orderingtransition.

Deformation of a flexible polymer in a random flow with long correlation time

The effects induced by long temporal correlations of the velocity gradients on the dynamics of a flexible polymer are investigated by means of theoretical and numerical analysis of the Hookean and finitely extensible nonlinear elastic (FENE) dumbbell models in a random renewing flow. For Hookean dumbbells, we show that long temporal correlations strongly suppress the Weissenberg-number dependence of the power-law tail characterising the probability density function (PDF) of the elongation. For the FENE model, the PDF becomes bimodal, and the coil–stretch transition occurs through the simultaneous drop and rise of the two peaks associated with the coiled and stretched configurations, respectively.

Coil-stretch transition in an ensemble of polymers in isotropic turbulence

We study the statistical properties of ensembles of polymers in isotropic turbulence numerically in the one-way coupling regime. A linear polymer chain passively convected by turbulence is modeled by a line of beads, each of which is connected by a finitely extensible nonlinear elastic force and subject to Brownian motion. We find that when the Weissenberg number Wi(η)<1, the polymer chain has a coiled configuration, while for Wi(η)>10, it remains stretched for a much longer time than the typical time scale of the fluctuating turbulent velocity gradient. Various statistical quantities characterizing the ensemble of polymers, such as the mean, variance, autocorrelation time, and probability density function of the end-to-end vector distance, indicate that the coil-stretch transition occurs at Wi(η)=3-4. We also find that this trend is insensitive to the number of beads N(b) ( N(b)=20 or N(b)=2), provided that the parameters in the model with a small number of beads are properly generated from the one with a large number of beads (i.e., using the formula of Jin and Collins). Finally, the Wi(η) effects on the alignment of the end-to-end vector versus the principal axis of the rate of strain tensor and on the polymer elongation are examined from the viewpoint of local flow topology.

Elastic stresses in random flow of a dilute polymer solution and the turbulent drag reduction problem

Abstract In this short review I argue that the progress in our understanding the mechanism of turbulent drag reduction is conditioned by obtaining experimental data on dynamics and statistics of polymer stretching and elastic stresses in inertial turbulence at high Reynolds numbers that is a technically challenging task. The suggested way out of the currently unresolved technical problem is to collect the same data in elastic turbulence, which is a smooth random flow similar to that found in inertial turbulence below the dissipation scale. Since the polymer stretching and elastic stresses in inertial turbulence are influenced only by small scales, it is appropriate to use information on the polymer stretching and elastic stresses obtained in elastic turbulence. The experimental data on the statistics of the polymer stretching, the coil–stretch transition, and elastic stresses together with spatial distribution and values of the rms of the velocity gradients were collected in elastic turbulence for the last several years. This information serves a basis for a new hypothesis of turbulent drag reduction. To cite this article: V. Steinberg, C. R. Physique 10 (2009).