The viscosity of dilute and semidilute unentangled deoxyribonucleic acid (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 behavior of DNA solutions. Interpretation of the shear rate dependence of viscosity in terms of suitably defined nondimensional 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 behavior at large shear rates.
References
1.
Bird
, R. B.
, R. C.
Armstrong
, and O.
Hassager
, Dynamics of Polymeric Liquids—Volume 1: Fluid Mechanics
, 2nd ed. (John Wiley
, New York
, 1987
).2.
Noda
, I.
, Y.
Yamada
, and M.
Nagasawa
, “Rate of shear dependence of the intrinsic viscosity of monodisperse polymer
,” J. Phys. Chem.
72
(8
), 2890
–2898
(1968
).3.
Liu
, T. W.
, “Flexible polymer chain dynamics and rheological properties in steady flows
,” J. Chem. Phys.
90
(10
), 5826
–5842
(1989
).4.
Doyle
, P. S.
, E. S. G.
Shaqfeh
, and A. P.
Gast
, “Dynamic simulation of freely draining flexible polymers in steady linear flows
,” J. Fluid Mech.
334
, 251
–291
(1997
).5.
Kotaka
, T.
, H.
Suzuki
, and H.
Inagaki
, “Shear-rate dependence of the intrinsic viscosity of flexible linear macromolecules
,” J. Chem. Phys.
45
(8
), 2770
–2773
(1966
).6.
Suzuki
, H.
, T.
Kotaka
, and H.
Inagaki
, “Shear-rate dependence of the intrinsic viscosity of flexible linear macromolecules. II. Solvent effect
,” J. Chem. Phys.
51
(4
), 1279
–1285
(1969
).7.
Mochimaru
, Y.
, “Possibility of a master plot for material functions of high-polymer solutions
,” J. Non-Newtonian Fluid Mech.
13
(3
), 365
–384
(1983
).8.
Hua
, C. C.
, and M. S.
Wu
, “Viscometric properties of dilute polystyrene/dioctyl phthalate solutions
,” J. Polym. Sci. Part B Polym. Phys.
44
(5
), 787
–794
(2006
).9.
Hur
, J. S.
, E. S. G.
Shaqfeh
, H. P.
Babcock
, D. E.
Smith
, and S.
Chu
, “Dynamics of dilute and semidilute DNA solutions in the start-up of shear flow
,” J. Rheol.
45
(2
), 421
–450
(2001
).10.
Teixeira
, R. E.
, H. P.
Babcock
, E. S. G.
Shaqfeh
, and S.
Chu
, “Shear thinning and tumbling dynamics of single polymers in the flow-gradient plane
,” Macromolecules
38
(2
), 581
–592
(2005
).11.
Schroeder
, C. M.
, R. E.
Teixeira
, E. S. G.
Shaqfeh
, and S.
Chu
, “Dynamics of DNA in the flow-gradient plane of steady shear flow: Observations and simulations
,” Macromolecules
38
(5
), 1967
–1978
(2005
).12.
Heo
, Y.
, and R. G.
Larson
, “Universal scaling of linear and nonlinear rheological properties of semidilute and concentrated polymer solutions
,” Macromolecules
41
(22
), 8903
–8915
(2008
).13.
Stewart
, W. E.
, and J. P.
Sorensen
, “Hydrodynamic interaction effects in rigid dumbbell suspensions. II. Computations for steady shear flow
,” Trans. Soc. Rheol.
16
, 1
–13
(1972
).14.
Fan
, X. J.
, “Viscosity, first normal-stress coefficient, and molecular stretching in dilute polymer solutions
,” J. Non-Newtonian Fluid Mech.
17
(2
), 125
–144
(1985
).15.
Bird
, R. B.
, O.
Hassager
, R. C.
Armstrong
, and C. F.
Curtiss
, Dynamics of Polymeric Liquids
(John Wiley and Sons
, New York
, 1987
), Vol. 2.16.
Zylka
, W.
, “Gaussian approximation and Brownian dynamics simulations for Rouse chains with hydrodynamic interaction undergoing simple shear flow
,” J. Chem. Phys.
94
(6
), 4628
–4636
(1991
).17.
Petera
, D.
, and M.
Muthukumar
, “Brownian dynamics simulation of bead-rod chains under shear with hydrodynamic interaction
,” J. Chem. Phys.
111
(16
), 7614
–7623
(1999
).18.
Aust
, C.
, M.
Kröger
, and S.
Hess
, “Structure and dynamics of dilute polymer solutions under shear flow via nonequilibrium molecular dynamics
,” Macromolecules
32
(17
), 5660
–5672
(1999
).19.
Prakash
, J. R.
, “Rouse chains with excluded volume interactions in steady simple shear flow
,” J. Rheol.
46
(6
), 1353
–1380
(2002
).20.
Winkler
, R. G.
, “Conformational and rheological properties of semiflexible polymers in shear flow
,” J. Chem. Phys.
133
(16
), 164905
(2010
).21.
Grosberg
, A. Y.
, and A. R.
Khokhlov
, Statistical Physics of Macromolecules
(AIP
, New York
, 1994
).ISBN 9781563960710.22.
Schäfer
, L.
, Excluded Volume Effects in Polymer Solutions
(Springer-Verlag
, Berlin
, 1999
).23.
24.
Colby
, R. H.
, “Structure and linear viscoelasticity of flexible polymer solutions: Comparison of polyelectrolyte and neutral polymer solutions
,” Rheol. Acta
49
(5
), 425
–442
(2010
).25.
Jain
, A.
, B.
Dünweg
, and J. R.
Prakash
, “Dynamic crossover scaling in polymer solutions
,” Phys. Rev. Lett.
109
, 088302
(2012
).26.
Pan
, S.
, D. A.
Nguyen
, P.
Sunthar
, T.
Sridhar
, and J. R.
Prakash
, “Universal solvent quality crossover of the zero shear rate viscosity of semidilute DNA solutions
,” J. Rheol.
58
(2
), 339
–368
(2014
).27.
Shaqfeh
, E. S. G.
, “The dynamics of single-molecule DNA in flow
,” J. Non-Newtonian Fluid Mech.
130
(1
), 1
–28
(2005
).28.
Schroeder
, C. M.
, “Single polymer dynamics for molecular rheology
,” J. Rheol.
62
(1
), 371
–403
(2018
).29.
Zimm
, B. H.
, “Dynamics of polymer molecules in dilute solution: Viscoelasticity, flow birefringence and dielectric loss
,” J. Chem. Phys.
24
(2
), 269
–281
(1956
).30.
Prakash
, J. R.
, “The kinetic theory of dilute solutions of flexible polymers: Hydrodynamic interaction
,” in Advances in Flow and Rheology of Non-Newtonian Fluids
, Rheology Series, edited by D. A.
Siginer
, D.
De Kee
, and R. P.
Chhabra
(Elsevier Science
, Amsterdam
, 1999
), pp. 467
–517
.31.
Öttinger
, H. C.
, “Gaussian approximation for Rouse chains with hydrodynamic interaction
,” J. Chem. Phys.
90
, 463
–473
(1989
).32.
Prakash
, J. R.
, and H. C.
Öttinger
, “Universal viscometric functions for dilute polymer solutions
,” J. Non-Newtonian Fluid Mech.
71
, 245
–272
(1997
).33.
Prabhakar
, R.
, and J. R.
Prakash
, “Gaussian approximation for finitely extensible bead-spring chains with hydrodynamic interaction
,” J. Rheol.
50
, 561
–593
(2006
).34.
Wedgewood
, L. E.
, and H. C.
Öttinger
, “A model of dilute polymer solutions with hydrodynamic interaction and finite extensibility. II. Shear flows
,” J. Non-Newtonian Fluid Mech.
27
, 245
–264
(1988
).35.
Öttinger
, H. C.
, “Renormalization of various quantities for dilute polymer solutions undergoing shear flow
,” Phys. Rev. A
41
, 4413
–4420
(1990
).36.
Kumar
, K. S.
, and J. R.
Prakash
, “Universal consequences of the presence of excluded volume interactions in dilute polymer solutions undergoing shear flow
,” J. Chem. Phys.
121
(8
), 3886
–3897
(2004
).37.
Ryder
, J. F.
, and J. M.
Yeomans
, “Shear thinning in dilute polymer solutions
,” J. Chem. Phys.
125
(19
), 194906
(2006
).38.
Jendrejack
, R. M.
, J. J.
De Pablo
, and M. D.
Graham
, “Stochastic simulations of DNA in flow: Dynamics and the effects of hydrodynamic interactions
,” J. Chem. Phys.
116
(17
), 7752
–7759
(2002
).39.
Heo
, Y.
, and R. G.
Larson
, “The scaling of zero-shear viscosities of semidilute polymer solutions with concentration
,” J. Rheol.
49
(5
), 1117
–1128
(2005
).40.
Hsiao
, K.
, C.
Sasmal
, J. R.
Prakash
, and C. M.
Schroeder
, “Direct observation of DNA dynamics in semidilute solutions in extensional flow
,” J. Rheol.
61
(1
), 151
–167
(2017
).41.
Prabhakar
, R.
, C.
Sasmal
, D. A.
Nguyen
, T.
Sridhar
, and J. R.
Prakash
, “Effect of stretching-induced changes in hydrodynamic screening on coil-stretch hysteresis of unentangled polymer solutions
,” Phys. Rev. Fluids
2
(1
), 011301
(2017
).42.
Stoltz
, C.
, J. J.
De Pablo
, and M. D.
Graham
, “Concentration dependence of shear and extensional rheology of polymer solutions: Brownian dynamics simulations
,” J. Rheol.
50
(2
), 137
–167
(2006
).43.
Huang
, C.-C.
, R. G.
Winkler
, G.
Sutmann
, and G.
Gompper
, “Semidilute polymer solutions at equilibrium and under shear flow
,” Macromolecules
43
(23
), 10107
–10116
(2010
).44.
Jain
, A.
, P.
Sunthar
, B.
Dünweg
, and J. R.
Prakash
, “Optimization of a Brownian-dynamics algorithm for semidilute polymer solutions
,” Phys. Rev. E
85
, 066703
(2012
).45.
Saadat
, A.
, and B.
Khomami
, “Matrix-free Brownian dynamics simulation technique for semidilute polymeric solutions
,” Phys. Rev. E
92
(3
), 033307
(2015
).46.
Sasmal
, C.
, K.
Hsiao
, C. M.
Schroeder
, and J. R.
Prakash
, “Parameter-free prediction of DNA dynamics in planar extensional flow of semidilute solutions
,” J. Rheol.
61
(1
), 169
–186
(2017
).47.
de Gennes
, P.-G.
, Scaling Concepts in Polymer Physics
(Cornell University
, Ithaca
, 1979
).48.
Pan
, S.
, D.
Ahirwal
, D. A.
Nguyen
, P.
Sunthar
, T.
Sridhar
, and J. R.
Prakash
, “Viscosity radius in dilute polymer solutions: Universal behaviour from DNA rheology and Brownian dynamics simulations
,” Macromolecules
47
(21
), 7548
–7560
(2014
).49.
See Supplementary Material at https://doi.org/10.1122/1.5010203 for (i) description of DNA sample preparation and solvent viscosities for DNA solutions, (ii) shear rheometry procedures, (iii) zero shear rate viscosities for both dilute and semidilute DNA and polystyrene samples, (iv) temperature dependence of semidilute solution relaxation times, and (v) plots and tabulated values of raw shear viscosity as a function of shear rate for dilute and semidilute DNA and polystyrene samples at various temperatures and concentrations, including the corresponding solvent viscosities.
50.
Pincus
, P.
, “Excluded volume effects and stretched polymer chains
,” Macromolecules
9
(3
), 386
–388
(1976
).51.
Laib
, S.
, R. M.
Robertson
, and D. E.
Smith
, “Preparation and characterization of a set of linear DNA molecules for polymer physics and rheology studies
,” Macromolecules
39
(12
), 4115
–4119
(2006
).52.
Polymer Handbook
, edited by J.
Brandrup
, E. H.
Immergut
, and E. A.
Grulke
, 4th ed. (John Wiley and Sons
, New York
, 1999
).53.
Kumar
, K. S.
, and J. R.
Prakash
, “Equilibrium swelling and universal ratios in dilute polymer solutions: Exact Brownian dynamics simulations for a delta function excluded volume potential
,” Macromolecules
36
(20
), 7842
–7856
(2003
).54.
Doi
, M.
, and S. F.
Edwards
, The Theory of Polymer Dynamics
(Clarendon
, Oxford, New York
, 1986
).55.
Liu
, Y.
, Y.
Jun
, and V.
Steinberg
, “Concentration dependence of the longest relaxation times of dilute and semi-dilute polymer solutions
,” J. Rheol.
53
(5
), 1069
–1085
(2009
).56.
Colby
, R. H.
, D. C.
Boris
, W. E.
Krause
, and S.
Dou
, “Shear thinning of unentangled flexible polymer liquids
,” Rheol. Acta
46
(5
), 569
–575
(2007
).57.
Rushing
, T. S.
, and R. D.
Hester
, “Intrinsic viscosity dependence on polymer molecular weight and fluid temperature
,” J. Appl. Polym. Sci.
89
(10
), 2831
–2835
(2003
).58.
Pilař
, J.
, and J.
Labský
, “Solvent dependence of polystyrene local segmental dynamics in dilute solution by spin-label X-band ESR
,” Macromolecules
36
(3
), 913
–920
(2003
).59.
Marko
, J. F.
, and E. D.
Siggia
, “Stretching DNA
,” Macromolecules
28
(26
), 8759
–8770
(1995
).60.
Prabhakar
, R.
, S.
Gadkari
, T.
Gopesh
, and M. J.
Shaw
, “Influence of stretching induced self-concentration and self-dilution on coil-stretch hysteresis and capillary thinning of unentangled polymer solutions
,” J. Rheol.
60
(3
), 345
–366
(2016
).© 2018 The Society of Rheology.
2018
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