General rigid bead-rod theory [O. Hassager, “Kinetic theory and rheology of bead-rod models for macromolecular solutions. II. Linear unsteady flow properties,” J. Chem. Phys. 60(10), 4001–4008 (1974)] explains polymer viscoelasticity from macromolecular orientation. By means of general rigid bead-rod theory, we relate the complex viscosity of polymeric liquids to the architecture of axisymmetric macromolecules. In this work, we explore the zero-shear and complex viscosities of 24 different axisymmetric polymer configurations. When nondimensionalized with the zero-shear viscosity, the complex viscosity depends on the dimensionless frequency and the sole dimensionless architectural parameter, the macromolecular lopsidedness. In this work, in this way, we compare and contrast the elastic and viscous components of the complex viscosities of macromolecular chains that are straight, branched, ringed, or star-branched. We explore the effects of branch position along a straight chain, branched-chain backbone length, branched-chain branch-functionality, branch spacing along a straight chain (including pom-poms), the number of branches along a straight chain, ringed polymer perimeter, branch-functionality in planar stars, and branch dimensionality.
REFERENCES
1.
O.
Hassager
, “Kinetic theory and rheology of bead-rod models for macromolecular solutions. II. Linear unsteady flow properties
,” J. Chem. Phys.
60
(10
), 4001
–4008
(1974
).2.
R. B.
Bird
, C. F.
Curtiss
, R. C.
Armstrong
, and O.
Hassager
, Dynamics of Polymeric Liquids
, 2nd ed. (John Wiley & Sons, Inc.
, New York
, 1987
), Vol. 2.3.
R. B.
Bird
, O.
Hassager
, R. C.
Armstrong
, and C. F.
Curtiss
, Dynamics of Polymeric Liquids
, 1st ed. (John Wiley and Sons, Inc.
, New York
, 1977
), Vol. 2.4.
R. B.
Bird
, H. R.
Warner
, Jr., and D. C.
Evans
, “Kinetic theory and rheology of dumbbell suspensions with Brownian motion
,” Adv. Polym. Sci.
8
, 1
(1971
).5.
R. B.
Bird
, A. J.
Giacomin
, A. M.
Schmalzer
, and C.
Aumnate
, “Dilute rigid dumbbell suspensions in large-amplitude oscillatory shear flow: Shear stress response
,” J. Chem. Phys.
140
, 074904
(2014
).6.
A. M.
Schmalzer
, R. B.
Bird
, and A. J.
Giacomin
, “Normal stress differences in large-amplitude oscillatory shear flow for dilute rigid dumbbell suspensions
,” J. Non-Newtonian Fluid Mech.
222
, 56
–71
(2015
).7.
R. B.
Bird
and W. J.
Drugan
, “An exploration and further study of an enhanced Oldroyd model
,” Phys. Fluids
, 29
(5
), 053103
(2017
).8.
W. E.
Stewart
and J. P.
Sørensen
, “Hydrodynamic interaction effects in rigid dumbbell suspensions. II. Computations for steady shear flow
,” Trans. Soc. Rheol.
16
(1
), 1
–13
(1972
).9.
O.
Hassager
, “Kinetic theory and rheology of bead-rod models for macromolecular solutions. I. Equilibrium and steady flow properties
,” J. Chem. Phys.
60
(5
), 2111
–2124
(1974
).10.
S. I.
Abdel-Khalik
, O.
Hassager
, and R. B.
Bird
, “The Goddard expansion and the kinetic theory for solutions of rodlike macromolecules
,” J. Chem. Phys.
61
(10
), 4312
–4316
(1974
).11.
R. B.
Bird
, O.
Hassager
, and S. I.
Abdel-Khalik
, “Co-rotational rheological models and the Goddard expansion
,” AIChE J.
20
(6
), 1041
–1066
(1974
).12.
R. B.
Bird
, “A modification of the Oldroyd model for rigid dumbbell suspensions with Brownian motion
,” Z. Angew. Math. Phys.
23
(1
), 157
–159
(1972
).13.
A. J.
Giacomin
and C.
Saengow
, “Molecular continua for polymeric liquids in large-amplitude oscillatory shear flow
,” Mod. Phys. Lett. B
32
(12/13
), 1840036
(2018
).14.
R. B.
Bird
and A. J.
Giacomin
, “Polymer fluid dynamics: Continuum and molecular approaches
,” Annu. Rev. Chem. Biomol. Eng.
7
, 479
–507
(2016
).15.
J. L.
Lumley
, “Applicability of the Oldroyd constitutive equation to flow of dilute polymer solutions
,” Phys. Fluids
14
(11
), 2282
–2284
(1971
).16.
J. L.
Lumley
, “Erratum: Applicability of the Oldroyd constitutive equation to flow of dilute polymer solutions
,” Phys. Fluids
15
(11
), 2081
(1972
).17.
R. B.
Bird
, R. C.
Armstrong
, and O.
Hassager
, Dynamics of Polymeric Liquids
, 2nd ed. (Wiley
, New York
, 1987
), Vol. 1.18.
R. B.
Bird
and R. C.
Armstrong
, “Time-dependent flows of dilute solutions of rodlike macromolecules
,” J. Chem. Phys.
56
(7
), 3680
–3682
(1972
).19.
R. B.
Bird
, R. C.
Armstrong
, and O.
Hassager
, Dynamics of Polymeric Liquids
, 1st ed. (Wiley
, New York
, 1977
), Vol. 1.20.
H.
Giesekus
, “Strömungen mit konstantem Geschwindigkeitsgradienten und die Bewegung von darin suspendierten Teilchen
,” Rheol. Acta
2
(2
), 101
–112
(1962
).21.
J. H.
Piette
, L. M.
Jbara
, C.
Saengow
, and A. J.
Giacomin
, “Exact coefficients for rigid dumbbell suspensions for steady shear flow material function expansions
,” Phys. Fluids
31
(2
), 021212
(2019
).22.
A.
Gemant
, “Komplexe Viskosität
,” Naturwissenschaften
23
(25
), 406
–407
(1935
).23.
A.
Gemant
, “The conception of a complex viscosity and its application to dielectrics
,” Trans. Faraday Soc.
31
, 1582
–1590
(1935
).24.
R. B.
Bird
and A. J.
Giacomin
, “Who conceived the complex viscosity?
,” Rheol. Acta
51
(6
), 481
–486
(2012
).25.
A. J.
Giacomin
and R. B.
Bird
, “Erratum: Official nomenclature of The Society of Rheology: −η″
,” J. Rheol.
55
(4
), 921
–923
(2011
).26.
J. D.
Ferry
, Viscoelastic Properties of Polymers
, 3rd ed. (John Wiley & Sons
, New York
, 1980
).27.
R.
Pasquino
, T. C.
Vasilakopoulos
, Y. C.
Jeong
, H.
Lee
, S.
Rogers
, G.
Sakellariou
, G.
Allgaier
, A.
Takano
, A. R.
Brás
, T.
Chang
, and S.
Gooßen
, “Viscosity of ring polymer melts
,” ACS Macro Lett.
2
(10
), 874
–878
(2013
).28.
C.
Saengow
and A. J.
Giacomin
, “Normal stress differences from Oldroyd 8-constant framework: Exact analytical solution for large-amplitude oscillatory shear flow
,” Phys. Fluids
29
(12
), 121601
(2017
).29.
C.
Saengow
and A. J.
Giacomin
, “Exact solutions for oscillatory shear sweep behaviors of complex fluids from the Oldroyd 8-constant framework
,” Phys. Fluids
, 30
(3
), 030703
(2018
).30.
P.
Poungthong
, A. J.
Giacomin
, C.
Saengow
, and C.
Kolitawong
, “Series expansion for shear stress in large-amplitude oscillatory shear flow from Oldroyd 8-constant framework
,” Can. J. Chem. Eng.
97
, 1655
–1675
(2019
).31.
P.
Poungthong
, C.
Saengow
, A. J.
Giacomin
, and C.
Kolitawong
, “Power series for shear stress of polymeric liquid in large-amplitude oscillatory shear flow
,” Korea-Aust. Rheol. J.
30
(3
), 169
–178
(2018
).32.
J. M.
Dealy
and R. G.
Larson
, Structure and Rheology of Molten Polymers: From Structure to Flow Behavior and Back Again
(Hanser
, Munich
, 2005
).33.
A. M.
Schmalzer
and A. J.
Giacomin
, “Orientation in large-amplitude oscillatory shear, cover article
, Macromol. Theory Simul.
24
(3
), 171
(2015
).34.
L. M.
Jbara
and A. J.
Giacomin
, “Orientation distribution function pattern for rigid dumbbell suspensions in any simple shear flow
,” Macromol. Theory Simul.
28
(1
), 1800046
(2018
).35.
M. A.
Kanso
, L. M.
Jbara
, A. J.
Giacomin
, C.
Saengow
, and P. H.
Gilbert
, “Order in oscillatory shear flow
,” Phys. Fluids
31
, 031902
(2019
).36.
L. M.
Jbara
and A. J.
Giacomin
, “Macromolecular tumbling and wobbling in large-amplitude oscillatory shear flow
,” Phys. Fluids
31
(2
), 021214
(2019
).37.
P. H.
Gilbert
and A. J.
Giacomin
, “Polymer orientation contributions in large-amplitude oscillatory shear flow
,” J. Non-Newtonian Fluid Mech.
244
, 85
–103
(2017
).38.
P. H.
Gilbert
and A. J.
Giacomin
, “Complex polymer orientation
,” Polymer
104
, 227
–239
(2016
).39.
A. J.
Giacomin
, P. H.
Gilbert
, and A. M.
Schmalzer
, “Fourier decomposition of polymer orientation in large-amplitude oscillatory shear flow
,” Struct. Dyn.
2
(2
), 024101
(2015
).40.
L. M.
Jbara
, “Macromolecular orientation of rigid dumbbells in shear flow
,” M.S. thesis, Polymers Research Group, Chemical Engineering Department, Queen’s University
, Kingston, Canada
, 2018
.41.
A. M.
Schmalzer
, “Large-amplitude oscillatory shear flow of rigid dumbbell suspensions
,” Ph.D. thesis, Mechanical Engineering Department, University of Wisconsin
, Madison, WI
, 2014
.42.
P. H.
Gilbert
and A. J.
Giacomin
, “Molecular origins of higher harmonics in large-amplitude oscillatory shear flow: Shear stress response
,” Phys. Fluids
28
(10
), 103101
(2016
).43.
J. M.
Dealy
and K. F.
Wissbrun
, Melt Rheology and its Role in Plastics Processing: Theory and Applications
(Van Nostrand Reinhold
, New York
, 1990
).44.
J. G.
Oakley
, J. A.
Yosick
, and A. J.
Giacomin
, “Molecular origins of nonlinear viscoelasticity
,” Mikrochim. Acta
130
, 1
–28
(1998
).45.
C.
Saengow
, A. J.
Giacomin
, and C.
Kolitawong
, “Exact analytical solution for large-amplitude oscillatory shear flow from Oldroyd 8-constant framework: Shear stress
,” Phys. Fluids
29
(4
), 043101
(2017
).46.
J. R.
Jones
, “Flow of elastico-viscous liquids in pipes with cores (Part I)
,” J. Mec.
3
(1
), 79
–99
(1964
).47.
J. R.
Jones
and R. S.
Jones
, “Flow of elastico-viscous liquids in pipes with cores (Part III)
,” J. Mec.
5
(3
), 375
–395
(1966
).48.
R. S.
Jones
, “Flow of an elastico-viscous liquid in a corrugated pipe
,” J. Mec.
6
(3
), 443
–448
(1967
).49.
J. R.
Jones
, “Flow of elastico-viscous liquids in pipes with cores (Part II)
,” J. Mec.
4
(1
), 121
–132
(1965
).50.
C. J.
Camilleri
and J. R.
Jones
, “The effect of a pressure gradient on the secondary flow of non-Newtonian liquids between non-intersecting cylinders
,” Z. Angew. Math. Phys.
17
(1
), 78
–90
(1966
).51.
C.
Saengow
, A. J.
Giacomin
, and C.
Kolitawong
, “Extruding plastic pipe from eccentric dies
,” J. Non-Newtonian Fluid Mech.
223
, 176
–199
(2015
).52.
C.
Saengow
, A. J.
Giacomin
, and C.
Kolitawong
, “Knuckle formation from melt elasticity in plastic pipe extrusion
,” J. Non-Newtonian Fluid Mech.
242
, 11
–22
(2017
).53.
C.
Saengow
and A. J.
Giacomin
, “Fluid elasticity in plastic pipe extrusion: Loads on die barrel
,” Int. Polym. Process.
32
(5
), 648
–658
(2017
).54.
M. A.
Kanso
, A. J.
Giacomin
, C.
Saengow
, and J. H.
Piette
, “Macromolecular architecture and complex viscosity
,” PRG Report No. 056, QU-CHEE-PRGTR–2019-56, Polymers Research Group, Chemical Engineering Department, Queen’s University
, Kingston, Canada
, 2019
, pp. 0
–72
.© 2019 Author(s).
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