From capillary to elastic instability of jets of polymeric liquids: Role of the entanglement network of macromolecules

Semakov, A. V.; Skvortsov, I. Yu.; Куличихин, В. Г.; Malkin, A. Ya.

doi:10.1134/s0021364015100136

Cited by 17 publications

(40 citation statements)

References 7 publications

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“…The nematic transition is not considered here: it is assumed that concentration

ϕ ≲ d / l

or less.It may also be useful to comment that the SCC effect for the lateral demixing in extensional flows is always weak compared to the orientation‐induced thermodynamic (osmotic) driving force for

Wi > {Wi}_{c}

(i.e., in the regime of stretched chains): To see this, the osmotic pressure

Π ≃ T v^{*} c^{2} / 2

must be compared to the lateral viscous polymer stress

σ_{x x} \sim η_{x x} \overset{ɛ}{true}

, where the relevant viscosity

η_{x x} \propto R_{x}^{2}

and

R_{x} \propto 1 / \sqrt{f_{t}}

is the lateral chain size for

Wi = \overset{ɛ}{true} τ_{R} ≫ 1

(

f_{t} \propto \overset{ɛ}{true}

is the chain tension). Hence, the typical

σ_{x x}

is roughly independent of Wi for

Wi ≫ 1

, so the lateral SCC driving force is not expected to increase with Wi. The results of this study can be qualitatively applied to several polymer systems like solutions of PAN in DMSO, and PAAA or PEO water solutions . However, in most of the previous experimental studies on extension of very dilute solutions, the jet dynamics are strongly affected by the capillary effects related to the Plateau–Rayleigh instability whose interference with possible demixing and solvent release processes requires a special consideration.…”

Section: Discussionmentioning

confidence: 97%

“…However, in most of the previous experimental studies on extension of very dilute solutions, the jet dynamics are strongly affected by the capillary effects related to the Plateau–Rayleigh instability whose interference with possible demixing and solvent release processes requires a special consideration. That is why we rather draw attention to semidilute PAN in DMSO solutions, where the Plateau–Rayleigh instability is apparently suppressed. One such system is a PAN solution in DMSO with concentration (

ϕ \sim 1 %

) falling in the semidilute,

ϕ > ϕ^{*}

, and unentangled,

ϕ < ϕ_{e}

, regime.…”

Section: Discussionmentioning

confidence: 99%

“…For example, the SCC theory does not predict any phase separation in the presence of elongational flow in this regime . In contrast, recent rheological data show that such phase separation (extension‐induced solvent release) is possible for a number of polymer solutions . It is noteworthy that the SCC approach, when applied to unentangled systems at moderate Weissenberg numbers (Wi ∼ 1), predicts only a weak driving force for concentration wave amplification which (being comparable, albeit opposite, to the ideal‐gas osmotic pressure effect) is normally much weaker than the effect of excluded‐volume interactions of polymer segments.…”

Section: Introductionmentioning

confidence: 90%

“…) does not depend either on concentration or on polymer molecular weight:

n_{f} \sim (l / d) / | k_{T} |

depends mainly on T and the chain stiffness parameter l / d . For the PAN solutions, we expect

n_{f} ≳ 30

| k_{T} | ≲ 0.1

and

l / d \sim 5

(cf. the Appendix).…”

Section: Polymer/solvent Demixingmentioning

confidence: 99%

“…[The ideal‐gas contribution

Π_{id} = c T / N

is negligible as the chains are very long

(L / d) ϕ | k_{T} | ≫ 1

.] As a very rough estimate,

ϕ_{0} \propto 1 / \sqrt{N}

, while

ϕ_{c}

is independent of N , so

ϕ_{c} ≫ ϕ_{0}

for long chains (e.g.,

ϕ_{0} \sim 1 %

while

ϕ_{c} \sim | k_{T} | \sim 0.1

for

s ≲ 0.8

). Hence, there is a strong thermodynamic force for fibril compaction.…”

Section: Polymer/solvent Demixingmentioning

confidence: 99%

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

Semenov

Субботин

2017

J Polym Sci B Polym Phys

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Phase 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

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“…The nematic transition is not considered here: it is assumed that concentration

ϕ ≲ d / l

or less.It may also be useful to comment that the SCC effect for the lateral demixing in extensional flows is always weak compared to the orientation‐induced thermodynamic (osmotic) driving force for

Wi > {Wi}_{c}

(i.e., in the regime of stretched chains): To see this, the osmotic pressure

Π ≃ T v^{*} c^{2} / 2

must be compared to the lateral viscous polymer stress

σ_{x x} \sim η_{x x} \overset{ɛ}{true}

, where the relevant viscosity

η_{x x} \propto R_{x}^{2}

and

R_{x} \propto 1 / \sqrt{f_{t}}

is the lateral chain size for

Wi = \overset{ɛ}{true} τ_{R} ≫ 1

(

f_{t} \propto \overset{ɛ}{true}

is the chain tension). Hence, the typical

σ_{x x}

is roughly independent of Wi for

Wi ≫ 1

Section: Discussionmentioning

confidence: 97%

ϕ \sim 1 %

) falling in the semidilute,

ϕ > ϕ^{*}

, and unentangled,

ϕ < ϕ_{e}

, regime.…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 90%

“…) does not depend either on concentration or on polymer molecular weight:

n_{f} \sim (l / d) / | k_{T} |

depends mainly on T and the chain stiffness parameter l / d . For the PAN solutions, we expect

n_{f} ≳ 30

| k_{T} | ≲ 0.1

and

l / d \sim 5

(cf. the Appendix).…”

Section: Polymer/solvent Demixingmentioning

confidence: 99%

“…[The ideal‐gas contribution

Π_{id} = c T / N

is negligible as the chains are very long

(L / d) ϕ | k_{T} | ≫ 1

.] As a very rough estimate,

ϕ_{0} \propto 1 / \sqrt{N}

, while

ϕ_{c}

is independent of N , so

ϕ_{c} ≫ ϕ_{0}

for long chains (e.g.,

ϕ_{0} \sim 1 %

while

ϕ_{c} \sim | k_{T} | \sim 0.1

for

s ≲ 0.8

). Hence, there is a strong thermodynamic force for fibril compaction.…”

Section: Polymer/solvent Demixingmentioning

confidence: 99%

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

Semenov

Субботин

2017

J Polym Sci B Polym Phys

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Phase separation in dilute polymer solutions at high‐rate extension

Субботин

Semenov

2016

J Polym Sci B Polym Phys

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In this article the demixing instability and phase segregation in unentangled polymer solutions of semiflexible chains at high‐rate uniaxial extension above the coil to stretched coil transition was studied. Orientation of the stretched chains was described in terms of an effective potential field. Based on the free energy analysis it was shown that the flow‐induced orientation of polymer segments could drastically reduce the energy of their steric repulsion. As a result attraction between the chains gain more importance, and this effect lead to the demixing process and eventual segregation of polymer from the solvent if the strain rate exceeds some critical value. A mean‐field theory was developed to study this flow‐induced phase separation effect. The phase diagrams of the system showing the spinodal and binodal transitions at different extension rates were calculated and discussed. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016, 54, 1066–1073

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A Scenario of a Fiber Formation Mechanism in Electrospinning: Jet Evolves Assemblies of Phase-Separated Strings That Eventually Split into As-spun Fibers Observed on the Grounded Collector

Wang

Hashimoto

2020

Macromolecules

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Electrospinning of polymer solutions involves selforganization of dissipative structures to order through fluctuations, providing one of the fundamental research topics in statistical physics of nonequilibrium systems. In this work, we found that the electrospun poly(vinyl alcohol) aqueous solutions evolve, in cascade, hierarchically self-organized dissipative structures along the electrospinning line as follows: first the flow-induced orientation and concentration fluctuations of polymer chains in the single-phase solution and subsequently a phase-separated structure composed of polymer-rich solution phases dispersed in polymer-poor matrix solution phase; the polymer-rich solution phases evolve assemblies of strings (designated as a "pre-string phase") that are composed of a bundle of chains oriented along the jet axis, which are swollen with solvent prior to crystallization. The pre-string phase eventually orders into "strings" with varying lateral size via intra-and inter-hydrogen bonds of highly stretched chains and subsequent solidification. The polymer-poor matrix solution phase itself subsequently evolves in cascade essentially the same dissipative structure as described above, viz., the assemblies of the newly born strings dispersed in the polymer-poor matrix solution phase, induced by a subsequent increase in polymer concentration in the matrix solution phase with increasing curvilinear distance z along the jet line via syneresis and vaporization of water molecules. We discovered that the assemblies of the strings grown in the jet are eventually split from the flowing jet line, through the processes of the jet whipping and jet colliding against the grounded collector, to result in the so-called as-spun fibers on the collector. The as-spun fibers are the stacks of the strings with varying lateral size ordered through solidification. We found that the cross sections of the fractured stacks of the strings were flattened into a ribbon shape due to deformation induced by the lateral pressure imposed on the stacks during their splitting and colliding process. We discovered also the fact that the splitting of the jet into the stacks of the strings and their piling on the already deposited as-spun fibers on the grounded collector is a universal phenomenon for various electrospun fibers, as will be described in the text.

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From capillary to elastic instability of jets of polymeric liquids: Role of the entanglement network of macromolecules

Cited by 17 publications

References 7 publications

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

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

Phase separation in dilute polymer solutions at high‐rate extension

A Scenario of a Fiber Formation Mechanism in Electrospinning: Jet Evolves Assemblies of Phase-Separated Strings That Eventually Split into As-spun Fibers Observed on the Grounded Collector

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