Coil-stretch Transition Research Articles

The effects of coil–stretch transition behavior of polyfluorene inks on single droplet formation during inkjet printing

For drop-on-demand (DOD) inkjet printing, stable and single ink droplet formation without satellite dots is the key to improve the print quality. The formation of stable and single droplet is influenced by filament break up and the polymer chain’s coil–stretch transition behavior. In this paper, the droplet formation behaviors of polyfluorene (PFO) ink at various driving voltages (V), polymer chain’s coil–stretch transition mechanism and its effects on single ink droplet formation are investigated. It indicates that when 58 <V ≤ 63 V, a single and stable droplet is formed with a pulse time of 38.5 μs. At this stage, the Weissenberg number (Wi) < 0.5, the PFO molecular chain is coiled to guarantee stable and single droplets. When V > 63 V, Wi > 0.5, the PFO molecular chain is stretched because of the high hydrodynamic forces, resulting unwanted satellite droplets. When 55 <V ≤ 58 V, the droplet shrinks into the nozzle, which indicates that the kinetic energy supplied by the deformation of the piezoelectric transducer isn't enough to force the droplet to be jetted from the nozzle.

Computer modelling of initial platelet adhesion during microvascular thrombosis

AbstractHemostasis is one of the most important protective mechanisms that functions to maintain vascular integrity and prevent bleeding. In arterial and microvascular circulation, where the near-wall shear stress is relatively high, the hemostatic response begins with aggregation of platelets on the injured endothelium or collagen. Regulation of hemostasis and thrombosis is immensely complex, as it depends on the blood cell adhesion and fluid dynamics. A possible regulatory mechanism relies on the coil-stretch transitions in a plasma protein — von Willebrand factor — that serves as a ligand to platelet adhesive membrane receptors. In this work, the initial stages of thrombus growth are studied using a 3D computer model that explicitly accounts for the shear-dependent vWf conformation.

Electric field induced coil-stretch transition of DNA molecule

The dynamics of single DNA molecules in a homogeneous planar elongational electric field is investigated in the framework of the Hookean Dumbbell model. For a Gaussian, rapidly changing advecting flow the Fokker-Planck equation for time-dependent probability density function of DNA elongation is obtained. The analytical solution for probability density function of time independent problem is derived. The coil-stretch transition is studied when the elongation of the DNA molecule is very small than the maximum length. The characteristic relaxation time is calculated as a function of the Weissenberg number. It is observed that the coil-stretch transition and characteristic relaxation time of DNA molecule strongly depend on the angle of the principal axis of molecule with respect to axis of elongation.

Bioinspired Shear-Flow-Driven Layer-by-Layer in Situ Self-Assembly.

Layer-by-layer (LbL) assembly is widely applied as a coating technique for the nanoscale control of architecture and related properties. However, its translational applications are limited by the time-consuming and laborious nature of the process. Inspired by the blood-clotting process, herein, we develop a shear-flow-driven LbL (SF-LbL) self-assembly approach that accelerates the adsorption rate of macromolecules by mechanically configuring the polymer chain via a coil-stretch transition, which effectively simplifies and speeds the diffusion-controlled assembly process. The structural characteristics and surface homogeneity of the SF-LbL films are improved, and diverse three-dimensional structures can be achieved. Functional SF-LbL-assembled surfaces for corneal modification are successfully fabricated, and the surface of wounded rat corneas and skin can be directly decorated in situ with SF-LbL nanofilms due to the advantages of this approach. Furthermore, in situ SF-LbL self-assembly has promise as a simple approach for the wound dressing for interventional therapeutics in the clinic, as illustrated by the successful in situ fabrication of drug-free layers consisting of chitosan and heparin on the dorsal skin of diabetic mice to rescue defective wound healing. This bioinspired self-assembly approach is expected to provide a robust and versatile platform with which to explore the surface engineering of nanofilms in science, engineering, and medicine.

Configurational Microphase Separation in Elongational Flow of an Entangled Polymer Liquid.

Manufacturing of plastics is typically performed via flow processing of a molten polymeric fluid. Until recently, conventional knowledge has maintained that the deformation of the constituent molecules under flow is homogeneous and obeys Gaussian statistics. In this study via virtual experimentation, an entangled polyethylene melt subjected to planar elongational flow displays an unanticipated microphase separation into a heterogeneous liquid composed of regions of either highly stretched or tightly coiled macromolecules, thus providing a natural realization of a biphasic coil-stretch transition.

Strategy to improve the characterization of chitosan by size exclusion chromatography coupled with multi angle laser light scattering

Here we present SEC-MALLS study for chitosan samples with weight average molar mass Mw between 33 and 427 kg/mol on columns packed with 8 μm porous particles. A low injection concentration on the order of 0.1–0.2 mg/mL must be used to avoid overloading of the SEC columns, due to the extended coil conformation of cationic chitosan in the dilute acid buffer as compared to neutral polymers. Additionally, SEC must be performed at an eluent flow rate no more than 0.5 mL/min for high molar mass chitosan samples. At flow rates of 1.0 and 1.5 mL/min, the elution of the largest chitosan species is delayed, which leads to a distortion of the molar mass distribution towards lower molar mass region. Such an abnormal behavior is due to a chromatographic mode transition from SEC to slalom chromatography, originated from the coil–stretch transition of chitosan chains in elongational flow through the packed columns.

Tumbling dynamics of inertial inextensible chains in extensional flow.

This paper investigates the effect of inertia on the dynamics of elongated chains to go beyond the overdamped case that is often used to study such systems. For that purpose, numerical simulations are performed considering the motion of freely jointed bead-rod chains in an extensional flow in the presence of thermal noise. The coil-stretch transition and the tumbling instability are characterized as a function of three parameters: the Péclet number, the Stokes number, and the chain length. Numerical results show that the coil-stretch transition remains when inertia is present and that it depends nonlinearly on the Stokes and Péclet numbers. Theoretical and numerical analyses also highlight the role of intermediate stable configurations in the dynamics of elongated chains: chains can indeed remain trapped for a certain time in these configurations, especially while undergoing a tumbling event.

Communication: A coil-stretch transition in planar elongational flow of an entangled polymeric melt.

Virtual experimentation of atomistic entangled polyethylene melts undergoing planar elongational flow revealed an amazingly detailed depiction of individual macromolecular dynamics and the resulting effect on bistable configurational states. A clear coil-stretch transition was evident, in much the same form as first envisioned by de Gennes for dilute solutions of high polymers, resulting in an associated hysteresis in the configurational flow profile over the range of strain rates predicted by theory. Simulations conducted at steady state revealed bimodal distribution functions, in which equilibrium configurational states were simultaneously populated by relatively coiled and stretched molecules which could transition from one conformational mode to the other over a relatively long time scale at critical values of strain rates. The implication of such behavior points to a double-well conformational free energy potential with an activation barrier between the two configurational minima.

Distinct transition in flow statistics and vortex dynamics between low- and high-extent turbulent drag reduction in polymer fluids

Flexible polymer additives are known to reduce the energy dissipation and friction drag in turbulent flows. As the fluid elasticity increases, the flow undergoes several stages of transitions. Much attention in the area has been focused on the onset of drag reduction (DR) and the eventual convergence to the maximum drag reduction (MDR) asymptote. Between the onset and MDR, recent experimental and numerical observations prompted the need to further distinguish the low- and high-extent drag reduction (LDR and HDR). Fundamental knowledge of this transition will be important for understanding turbulent dynamics in the presence of polymers, as well as for inspiring new flow control strategies for efficient friction reduction. We use direct numerical simulation (DNS) to explore all these transitions in the parameter space and, in particular, demonstrate that the LDR–HDR transition is not merely a quantitative effect of the level of drag reduction, but a qualitative transition into a different stage of turbulence. A number of sharp changes in flow statistics are found to accompany the transition and at HDR, turbulence becomes localized with vortices forming clusters. These observations suggest that polymer-induced drag reduction follows two distinct stages. The first starts at the onset of drag reduction, where the coil-stretch transition of polymers causes an overall suppression of turbulent fluctuations. The second starts at the LDR–HDR transition, where flow statistics become fundamentally changed in the log-law layer and turbulence localization is observed. A mechanism is then proposed for the latter based on the changing vortex regeneration dynamics between LDR and HDR.

Anomalies in the coil-stretch transition of flexible polymers

The flow-induced coil-stretch transition of high molecular weight polymers has generally been held to be of first order. But evidence of significant slowing down in the rate at which the polymers relax to equilibrium in the vicinity of the transition suggests that the thermodynamic character of the transition may be less clear-cut. The above slowing down effect is actually characteristic of a second-order transition, and it points to the existence of a broad spectrum of conformational states in the transition region, analogous to the existence of fluctuations of all length scales at a critical point. In this paper, using a path integral approach based on a free-draining finitely extensible chain model, we calculate various polymer properties as a function of elongational flow as a way of exploring different statistical mechanical details of the coil-stretch transition. These properties include the molecular weight dependence of the flow-extension curve of the polymer, the distribution of its steady-state end-to-end distances, and the characteristic relaxation time τR of these distances. Among other findings, our calculations indicate that the coil-stretch transition is discontinuous in the N → ∞ limit, that the effective free energy of the chain is unimodal at all values of the flow, becoming broad and flat in the immediate vicinity of the transition, and that the ratio of τR to the Rouse relaxation time increases abruptly at the transition before eventually reaching a plateau value at large flow strengths. These aspects of the coil-stretch transition place it among a larger class of unconventional nominally first-order single chain transitions that include the adsorption transition of surface-tethered polymers and the escape transition of compressed polymers.

The influence of short chain branch on formation of shish‐kebab crystals in bimodal polyethylene under shear at high temperatures

ABSTRACTFormation of shish‐kebab crystals due to the coil–stretch transition under shear in the molten state using a bimodal polyethylene system with high molecular weight (HMW) fraction having different branch content was investigated. In specific, in situ small‐angle X‐ray scattering (SAXS) and wide‐angle X‐ray diffraction (WAXD) techniques were used to study the structure evolution of shish‐kebab crystals at high temperatures under simple shear. The SAXS results revealed that with the increase of branch content, shish‐kebab crystals became more stable at high temperatures (e.g., 139 °C). However, the shish length of the bimodal PE containing 0.11% branch was shorter than that with no branch. The WAXD results showed that the degree of crystallization for bimodal PE with HMW fraction having 0.11% branch increased with time but reached a plateau value of 1%, while that with no branch increased continuously till 11%. Furthermore, the crystal orientation of bimodal PE with HMW fraction having 0.11% branch was above 0.9 and maintained at a constant value, while that with no branch decreased from 0.9 to 0.1 upon relaxation. This study indicates that even though the crystallizability of the HMW fraction with branch content decreased, they could effectively stabilize the shear‐induced crystalline structure with shorter shish‐kebab crystals. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018, 56, 786–794

Knots modify the coil-stretch transition in linear DNA polymers.

We perform single-molecule DNA experiments to investigate the relaxation dynamics of knotted polymers and examine the steady-state behavior of knotted polymers in elongational fields. The occurrence of a knot reduces the relaxation time of a molecule and leads to a shift in the molecule's coil-stretch transition to larger strain rates. We measure chain extension and extension fluctuations as a function of strain rate for unknotted and knotted molecules. The curves for knotted molecules can be collapsed onto the unknotted curves by defining an effective Weissenberg number based on the measured knotted relaxation time in the low extension regime, or a relaxation time based on Rouse/Zimm scaling theories in the high extension regime. Because a knot reduces a molecule's relaxation time, we observe that knot untying near the coil-stretch transition can result in dramatic changes in the molecule's conformation. For example, a knotted molecule at a given strain rate can experience a stretch-coil transition, followed by a coil-stretch transition, after the knot partially or fully unties.

Extensional Strain Hardening Induced by π-π Interactions in Barely Entangled Polymer Chains: The Curious Case of Poly(4-vinylbiphenyl).

Aromatic π-π interactions between phenyl groups of adjacent chains in poly(4-vinylbiphenyl) (PVBP) have profound effects on the dynamics of this polymer. We report two unexpected nonlinear viscoelastic responses of PVBP when subjected to uniaxial flow. One is the unprecedented observation of extensional strain hardening (SH) in a barely entangled polymer melt. An even more intriguing finding is that SH of lightly (or even barely) entangled melts occurs at strain rates one order of magnitude below the coil-stretch transition predicted by Rouse theory (ϵ[over ˙]_{H}=0.5/τ_{R}).We postulate that this behavior is due to a molecular rearrangement mechanism (supported by x-ray diffraction measurements) that involves flow-induced π-π stacking of the phenyl groups, which results in an enhancement of the friction coefficient between polymer chains.

Inkjet printing of viscoelastic polymer inks

Inkjet printing is a new fabricating method that can realize the precise film deposition. For polymer inks, the coil-stretch transition of polymer chains always impacts the ink droplet formation and a beads-on-a string structure filament is formed, thus generating unwanted satellite droplets. This review provides a short introduction of the dynamic process of the droplet formation. Then fluid rheological requirements for a printable polymer ink are summarized. Finally the strain hardening phenomenon of polymer chains in the filament formation and its impact on polymer ink-jetting are discussed. The research of viscoelastic polymer inks shows that rheological parameters and viscoelasticity are two key factors that determine the printability of polymer inks.

The effects of slit-like confinement on flow-induced polymer deformation.

This paper is broadly concerned with the dynamics of a polymer confined to a rectangular slit of width D and deformed by a planar elongational flow of strength γ̇. It is interested, more specifically, in the nature of the coil-stretch transition that such polymers undergo when the flow strength γ̇ is varied, and in the degree to which this transition is affected by the presence of restrictive boundaries. These issues are explored within the framework of a finitely extensible Rouse model that includes pre-averaged surface-mediated hydrodynamic interactions. Calculations of the chain's steady-state fractional extension x using this model suggest that different modes of relaxation (which are characterized by an integer p) exert different levels of control on the coil-stretch transition. In particular, the location of the transition (as identified from the graph of x versus the Weissenberg number Wi, a dimensionless parameter defined by the product of γ̇ and the time constant τp of a relaxation mode p) is found to vary with the choice of τp. In particular, when τ1 is used in the definition of Wi, the x vs. Wi data for different D lie on a single curve, but when τ3 is used instead (with τ3 > τ1) the corresponding data lie on distinct curves. These findings are in close qualitative agreement with a number of experimental results on confinement effects on DNA stretching in electric fields. Similar D-dependent trends are seen in our calculated force vs. Wi data, but force vs. x data are essentially D-independent and lie on a single curve.

Phase separation kinetics in unentangled polymer solutions under high‐rate extension

ABSTRACTPhase separation processes following high‐rate extension in unentangled polymer solutions are studied theoretically. The flow‐induced demixing is associated with the coil–stretch transition predicted in high‐molecular‐weight polymer solutions at high‐enough Weissenberg numbers. The developed mean‐field theory is valid in the dilute/semidilute solution regime, where the stretched coils overlap strongly. We elucidate and discuss the main kinetic stages of the polymer/solvent separation process including (i) growth of concentration fluctuations and formation of oriented protofibrils by anisotropic spinodal decomposition; (ii) development of well‐defined highly oriented and stiff fibrils forming an anisotropic network (cross‐linked fiber); (iii) microphase separation and lateral collapse of the network yielding dense oriented fiber. These novel predictions are in qualitative agreement with the experimental data. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017, 55, 623–637

An orientational order transition in a sheared suspension of anisotropic particles

Under Stokesian conditions, a neutrally buoyant non-Brownian spheroid in simple shear flow rotates indefinitely in any of a one-parameter family of closed (Jeffery) orbits characterized by an orbit constant $C$. The limiting values, $C=0$ and $C=\infty$, correspond to spinning and tumbling modes respectively. Hydrodynamics alone does not determine the distribution of spheroid orientations across Jeffery orbits in the absence of interactions, and the rheology of a dilute suspension of spheroids remains indeterminate. A combination of inertia and stochastic orientation fluctuations eliminates the indeterminacy. The steady-state Jeffery-orbit distribution arising from a balance of inertia and thermal fluctuations is shown to be of the Boltzmann equilibrium form, with a potential that depends on $C$, the particle aspect ratio ($\unicode[STIX]{x1D705}$), and a dimensionless shear rate ($Re\,Pe_{r}$, $Re$ and $Pe_{r}$ being the Reynolds and rotary Péclet numbers), and therefore lends itself to a novel thermodynamic interpretation in $C{-}\unicode[STIX]{x1D705}{-}Re\,Pe_{r}$ space. In particular, the transition of the potential from a single to a double-well structure, below a critical $\unicode[STIX]{x1D705}$, has similarities to a thermodynamic phase transition, and the small-$C$ and large-$C$ minima are therefore identified with spinning and tumbling phases. The hysteretic dynamics within the two-phase tumbling–spinning envelope renders the rheology sensitively dependent on the precise shear rate history, the signature in simple shear flow being a multivalued viscosity at a given shear rate. The tumbling–spinning transition identified here is analogous to the coil–stretch transition in the polymer physics literature. It should persist under more general circumstances, and has implications for the suspension stress response in inhomogeneous shearing flows.

Chain Deformation on the Formation of Shish Nuclei under Extension Flow: An in Situ SANS and SAXS Study

By combining extensional rheological and in situ small-angle neutron and synchrotron X-ray scattering (SANS, SR-SAXS) techniques, the correlation between chain deformation and morphology of nucleus in a lightly cross-linked deuterated PE (D-PE)/hydrogenated PE (H-PE) blend has been studied at different draw ratios. The deformation of molecular chain obtained by SANS shows that shish forms at a rather small chain deformation of about 1.3, which does not support either coil–stretch transition or the simple stretch network model. Combining these data with the SAXS results, we speculate that the conformation ordering couples with density, instead of single chain conformation, is the key factor for shish formation. Meanwhile, due to the different alignment of the center of mass of the stretched network in samples with different draw ratios, a periodic concentration modulation of D-PE appears after crystallization of the samples stretched to the hardening zone, which, however, does not occur under the small dra...

Polymer extension under flow: Some statistical properties of the work distribution function.

In an extension of earlier studies from this group on the application of the Jarzynski equality to the determination of the elastic properties of a finitely extensible Rouse model of polymers under flow [A. Ghosal and B. J. Cherayil, J. Chem. Phys. 144, 214902 (2016)], we derive several new theoretical results in this paper on the nature of the distribution function P(w) that governs the long-time limit t>>1 of the fluctuations in the work w performed by the polymer during flow-induced stretching. In particular, we show that an expression for the average of the nth power of the work, ⟨wn(t)⟩, can be obtained in closed form in this limit, making it possible to exactly calculate three important statistical measures of P(w): the mean μ, the skewness γ1, and the kurtosis γ2 (apart from the variance σ2). We find, for instance, that to leading order in t, the mean grows linearly with t at a constant value of the dimensionless flow rate Wi and that the slope of the μ-t curve increases with increasing Wi. These observations are in complete qualitative agreement with data from Brownian dynamics simulations of flow-driven double-stranded DNA by Latinwo and Schroeder [Macromolecules 46, 8345 (2013)]. We also find that the skewness γ1 exhibits an interesting inversion of sign as a function of Wi, starting off at positive values at low Wi and changing to negative values at larger Wi. The inversion takes place in the vicinity of what we interpret as a coil-stretch transition. Again, the finding exactly reproduces behavior seen in other numerical and experimental work by the above group Latinwo et al. [J. Chem. Phys. 141, 174903 (2014)]. Additionally, at essentially the same value of Wi at which this sign inversion takes place, we observe that the kurtosis reaches a minimum, close to 1, providing further evidence of the existence of a coil-stretch transition at this location. Our calculations reproduce another numerical finding: a power law dependence on Wi of the rate of work production that is characterized by two distinct regimes, one lying below the putative coil-stretch transition, where the exponent assumes one value, and the other above, where it assumes a second.

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

Thanks to direct observation and manipulation of DNA in micro/nanofluidic devices, we are now able to elucidate the relationship between the polymer microstructure and its rheological properties, as well as to design new single-molecule platforms for biophysics and biomedicine. This allows exploration of many new mechanisms and phenomena, which were previously unachievable with conventional methods such as bulk rheometry tests. For instance, the field of polymer rheology is at a turning point to relate the complex molecular conformations to the nonlinear viscoelasticity of polymeric fluids (such as coil-stretch transition, shear thinning, and stress overshoot in startup shear). In addition, nanofluidic devices provided a starting point for manipulating single DNA molecules by applying basic principles of polymer physics, which is highly relevant to numerous processes in biosciences. In this article, we review recent progress regarding the flow and deformation of DNA in micro/nanofluidic systems from both fundamental and application perspectives. We particularly focus on advances in the understanding of polymer rheology and identify the emerging research trends and challenges, especially with respect to future applications of nanofluidics in the biomedical field.