We study the dynamics of bottlebrush polymer molecules in dilute solutions subjected to shear and uniaxial extensional flows using Brownian dynamics simulations with hydrodynamic interaction (HI). Bottlebrush polymers are modeled using a coarse-grained representation, consisting of a set of beads interacting pairwise via a purely repulsive potential and connected by finitely extensible nonlinear springs. We present the results for molecular stretching, stress, and solution viscosity during the startup of flow as well as under steady state as a function of side chain length while keeping the backbone length fixed. In extensional flow, the backbone fractional extension and the first normal stress difference decrease with an increase in side chain length at a fixed Weissenberg number (Wi). Using simulation results both in the presence of and in the absence of HI, we show that this is primarily a consequence of steric interaction resulting from the dense grafting of side chains. In shear flow, we observe a shear-thinning behavior in all cases, although it becomes less pronounced with increasing side chain length. Furthermore, nonmonotonicity in the backbone fractional extension is observed under shear, particularly at high Wi. We contextualize our simulation results for bottlebrush polymers with respect to existing studies in the literature for linear polymers and show that the unique dynamical features characterizing bottlebrush polymers arise on account of their additional molecular thickness due to the presence of densely grafted side chains.
REFERENCES
1.
G.
Polymeropoulos
, G.
Zapsas
, K.
Ntetsikas
, P.
Bilalis
, Y.
Gnanou
, and N.
Hadjichristidis
, “50th anniversary perspective: Polymers with complex architectures
,” Macromolecules
50
, 1253
–1290
(2017
).2.
S.
Peleshanko
and V. V.
Tsukruk
, “The architectures and surface behavior of highly branched molecules
,” Prog. Polym. Sci.
33
, 523
–580
(2008
).3.
L. R.
Hutchings
, S.
Agostini
, I. W.
Hamley
, and D.
Hermida-Merino
, “Chain architecture as an orthogonal parameter to influence block copolymer morphology. Synthesis and characterization of hyperbranched block copolymers: HyperBlocks
,” Macromolecules
48
, 8806
–8822
(2015
).4.
R. J. S.
Ivancic
, S. V.
Orski
, and D. J.
Audus
, “Structure–dilute solution property relationships of comblike macromolecules in a good solvent
,” Macromolecules
55
, 766
–775
(2022
).5.
W. H.
Stockmayer
and M.
Fixman
, “Dilute solutions of branched polymers
,” Ann. N. Y. Acad. Sci.
57
, 334
–352
(1953
).6.
B. H.
Zimm
and R. W.
Kilb
, “Dynamics of branched polymer molecules in dilute solution
,” J. Polym. Sci.
37
, 19
–42
(1959
).7.
P. A.
Small
, “Long-chain branching in polymers
,” Adv. Polym. Sci.
18
, 1
–64
(1975
).8.
J.
Roovers
and P. M.
Toporowski
, “Preparation and characterization of H-shaped polystyrene
,” Macromolecules
14
, 1174
–1178
(1981
).9.
S.
Perny
, J.
Allgaier
, D.
Cho
, W.
Lee
, and T.
Chang
, “Synthesis and structural analysis of an H-shaped polybutadiene
,” Macromolecules
34
, 5408
–5415
(2001
).10.
M. S.
Rahman
, H.
Lee
, X.
Chen
, T.
Chang
, R.
Larson
, and J.
Mays
, “Model branched polymers: Synthesis and characterization of asymmetric H-shaped polybutadienes
,” ACS Macro Lett.
1
, 537
–540
(2012
).11.
N. A.
Platé
and V. P.
Shibaev
, “Comb-like polymers. Structure and properties
,” J. Polym. Sci., Macromol. Rev.
8
, 117
–253
(1974
).12.
P.
Viville
, M.
Schappacher
, R.
Lazzaroni
, and A.
Deffieux
, “Highly-branched polymers: From comb to dendritic architectures
,” in Soft Matter Characterization
(Springer
, Netherlands
, 2008
), pp. 1339
–1377
.13.
H.
Xu
, H.
Wang
, S.
Li
, J.
Li
, X.
Wang
, and H.
Shi
, “Comb-like polymers
,” in Encyclopedia of Polymer Science and Technology
, 4th ed., edited by H. F.
Mark
(John Wiley & Sons Inc.
, 2017
), pp. 1
–45
.14.
K.
Khanna
, S.
Varshney
, and A.
Kakkar
, “Miktoarm star polymers: Advances in synthesis, self-assembly, and applications
,” Polym. Chem.
1
, 1171
(2010
).15.
N.
Hadjichristidis
, M.
Pitsikalis
, H.
Iatrou
, P.
Driva
, G.
Sakellariou
, and M.
Chatzichristidi
, “Polymers with star-related structures
,” in Polymer Science: A Comprehensive Reference
(Elsevier
, 2012
), pp. 29
–111
.16.
J. M.
Ren
, T. G.
McKenzie
, Q.
Fu
, E. H. H.
Wong
, J.
Xu
, Z.
An
, S.
Shanmugam
, T. P.
Davis
, C.
Boyer
, and G. G.
Qiao
, “Star polymers
,” Chem. Rev.
116
, 6743
–6836
(2016
).17.
A.-D.
Schlüter
, “Ladder polymers: The new generation
,” Adv. Mater.
3
, 282
–291
(1991
).18.
Y. C.
Teo
, H. W. H.
Lai
, and Y.
Xia
, “Synthesis of ladder polymers: Developments, challenges, and opportunities
,” Chem. - Eur. J.
23
, 14101
–14112
(2017
).19.
T.-Y.
Luh
, M.
Xie
, L.
Ding
, and C.
h Chen
, “Ladderphanes and related ladder polymers
,” in Ladder Polymers: Synthesis, Properties, Applications, and Perspectives
, edited by Y.
Xia
, M.
Yamaguchi
and T.-Y.
Luh
(Wiley-VCH GmbH
, 2023
), pp. 247
–284
.20.
F.
Zeng
and S. C.
Zimmerman
, “Dendrimers in supramolecular chemistry: From molecular recognition to self-assembly
,” Chem. Rev.
97
, 1681
–1712
(1997
).21.
A. W.
Bosman
, H. M.
Janssen
, and E. W.
Meijer
, “About dendrimers: Structure, physical properties, and applications
,” Chem. Rev.
99
, 1665
–1688
(1999
).22.
D. A.
Tomalia
and J. M. J.
Fréchet
, “A brief historical perspective
,” in Dendrimers and Other Dendritic Polymers
, edited by J. M. J.
Fréchet
and D. A.
Tomalia
(John Wiley & Sons Ltd.
, Chichester, UK
, 2001
), pp. xxvii
–xxxix
.23.
J.
Rzayev
, “Molecular bottlebrushes: New opportunities in nanomaterials fabrication
,” ACS Macro Lett.
1
, 1146
–1149
(2012
).24.
G.
Xie
, M.
Martinez
, M.
Olszewski
, S.
Sheiko
, and K.
Matyjaszewski
, “Molecular bottlebrushes as novel materials
,” Biomacromolecules
20
, 27
–54
(2019
).25.
H.
Liang
, B. J.
Morgan
, G.
Xie
, M. R.
Martinez
, E. B.
Zhulina
, K.
Matyjaszewski
, S. S.
Sheiko
, and A. V.
Dobrynin
, “Universality of the entanglement plateau modulus of comb and bottlebrush polymer melts
,” Macromolecules
51
, 10028
–10039
(2018
).26.
T.
Pelras
, C. S.
Mahon
, and M.
Müllner
, “Synthesis and applications of compartmentalised molecular polymer brushes
,” Angew. Chem., Int. Ed.
57
, 6982
–6994
(2018
).27.
T.
Pan
, S.
Dutta
, Y.
Kamble
, B. B.
Patel
, M. A.
Wade
, S. A.
Rogers
, Y.
Diao
, D.
Guironnet
, and C. E.
Sing
, “Materials design of highly branched bottlebrush polymers at the intersection of modeling, synthesis, processing, and characterization
,” Chem. Mater.
34
, 1990
–2024
(2022
).28.
S.
Lecommandoux
, F.
Chécot
, R.
Borsali
, M.
Schappacher
, A.
Deffieux
, A.
Brûlet
, and J. P.
Cotton
, “Effect of dense grafting on the backbone conformation of bottlebrush polymers: Determination of the persistence length in solution
,” Macromolecules
35
, 8878
–8881
(2002
).29.
L.
Feuz
, F. A. M.
Leermakers
, M.
Textor
, and O.
Borisov
, “Bending rigidity and induced persistence length of molecular bottle brushes: A self-consistent-field theory
,” Macromolecules
38
, 8891
–8901
(2005
).30.
A.
Yethiraj
, “A Monte Carlo simulation study of branched polymers
,” J. Chem. Phys.
125
, 204901
(2006
).31.
J.
Paturej
, S. S.
Sheiko
, S.
Panyukov
, and M.
Rubinstein
, “Molecular structure of bottlebrush polymers in melts
,” Sci. Adv.
2
, e1601478
(2016
).32.
H.
Liang
, Z.
Cao
, Z.
Wang
, S. S.
Sheiko
, and A. V.
Dobrynin
, “Combs and bottlebrushes in a melt
,” Macromolecules
50
, 3430
–3437
(2017
).33.
S.
Dutta
, T.
Pan
, and C. E.
Sing
, “Bridging simulation length scales of bottlebrush polymers using a wormlike cylinder model
,” Macromolecules
52
, 4858
–4874
(2019
).34.
S.
Namba
, Y.
Tsukahara
, K.
Kaeriyama
, K.
Okamoto
, and M.
Takahashi
, “Bulk properties of multibranched polystyrenes from polystyrene macromonomers: Rheological behavior I
,” Polymer
41
, 5165
–5171
(2000
).35.
M.
Hu
, Y.
Xia
, G. B.
McKenna
, J. A.
Kornfield
, and R. H.
Grubbs
, “Linear rheological response of a series of densely branched brush polymers
,” Macromolecules
44
, 6935
–6943
(2011
).36.
B. R.
Sveinbjörnsson
, R. A.
Weitekamp
, G. M.
Miyake
, Y.
Xia
, H. A.
Atwater
, and R. H.
Grubbs
, “Rapid self-assembly of brush block copolymers to photonic crystals
,” Proc. Natl. Acad. Sci. U. S. A.
109
, 14332
–14336
(2012
).37.
S. J.
Dalsin
, M. A.
Hillmyer
, and F. S.
Bates
, “Linear rheology of polyolefin-based bottlebrush polymers
,” Macromolecules
48
, 4680
–4691
(2015
).38.
B. M.
Yavitt
, Y.
Gai
, D.-P.
Song
, H. H.
Winter
, and J. J.
Watkins
, “High molecular mobility and viscoelasticity of microphase-separated bottlebrush diblock copolymer melts
,” Macromolecules
50
, 396
–405
(2016
).39.
Y.
Tsukahara
, “Liquid crystal formation of multibranched polystyrene induced by molecular anisotropy associated with its high branch density
,” Polymer
36
, 3413
–3416
(1995
).40.
I. M.
Storm
, M.
Kornreich
, A.
Hernandez-Garcia
, I. K.
Voets
, R.
Beck
, M. A.
Cohen Stuart
, F. A. M.
Leermakers
, and R.
de Vries
, “Liquid crystals of self-assembled DNA bottlebrushes
,” J. Phys. Chem. B
119
, 4084
–4092
(2015
).41.
N.
Borodinov
, A.
Belianinov
, D.
Chang
, J.-M.
Carrillo
, M. J.
Burch
, Y.
Xu
, K.
Hong
, A. V.
Ievlev
, B. G.
Sumpter
, and O. S.
Ovchinnikova
, “Molecular reorganization in bulk bottlebrush polymers: Direct observation via nanoscale imaging
,” Nanoscale
10
, 18001
–18009
(2018
).42.
M.
Abbasi
, L.
Faust
, and M.
Wilhelm
, “Comb and bottlebrush polymers with superior rheological and mechanical properties
,” Adv. Mater.
31
, 1806484
(2019
).43.
C. R.
López-Barrón
, P.
Brant
, A. P. R.
Eberle
, and D. J.
Crowther
, “Linear rheology and structure of molecular bottlebrushes with short side chains
,” J. Rheol.
59
, 865
–883
(2015
).44.
C. R.
López-Barrón
, A. H.
Tsou
, J. R.
Hagadorn
, and J. A.
Throckmorton
, “Highly entangled α-olefin molecular bottlebrushes: Melt structure, linear rheology, and interchain friction mechanism
,” Macromolecules
51
, 6958
–6966
(2018
).45.
M.
Jacobs
, H.
Liang
, E.
Dashtimoghadam
, B. J.
Morgan
, S. S.
Sheiko
, and A. V.
Dobrynin
, “Nonlinear elasticity and swelling of comb and bottlebrush networks
,” Macromolecules
52
, 5095
–5101
(2019
).46.
L.-H.
Cai
, “Molecular understanding for large deformations of soft bottlebrush polymer networks
,” Soft Matter
16
, 6259
–6264
(2020
).47.
H.
Liang
, S. S.
Sheiko
, and A. V.
Dobrynin
, “Supersoft and hyperelastic polymer networks with brushlike strands
,” Macromolecules
51
, 638
–645
(2018
).48.
C. R.
López-Barrón
and M. E.
Shivokhin
, “Extensional strain hardening in highly entangled molecular bottlebrushes
,” Phys. Rev. Lett.
122
, 037801
(2019
).49.
J. L.
Self
, C. S.
Sample
, A. E.
Levi
, K.
Li
, R.
Xie
, J. R.
de Alaniz
, and C. M.
Bates
, “Dynamic bottlebrush polymer networks: Self-healing in super-soft materials
,” J. Am. Chem. Soc.
142
, 7567
–7573
(2020
).50.
I.
Mitra
, X.
Li
, S. L.
Pesek
, B.
Makarenko
, B. S.
Lokitz
, D.
Uhrig
, J. F.
Ankner
, R.
Verduzco
, and G. E.
Stein
, “Thin film phase behavior of bottlebrush/linear polymer blends
,” Macromolecules
47
, 5269
–5276
(2014
).51.
Y.
Aviv
, E.
Altay
, L.
Fink
, U.
Raviv
, J.
Rzayev
, and R.
Shenhar
, “Quasi-two-dimensional assembly of bottlebrush block copolymers with nanoparticles in ultrathin films: Combined effect of graft asymmetry and nanoparticle size
,” Macromolecules
52
, 196
–207
(2018
).52.
A. H.
Mah
, T.
Laws
, W.
Li
, H.
Mei
, C. C.
Brown
, A.
Ievlev
, R.
Kumar
, R.
Verduzco
, and G. E.
Stein
, “Entropic and enthalpic effects in thin film blends of homopolymers and bottlebrush polymers
,” Macromolecules
52
, 1526
–1535
(2019
).53.
H.
Mei
, T. S.
Laws
, J. P.
Mahalik
, J.
Li
, A. H.
Mah
, T.
Terlier
, P.
Bonnesen
, D.
Uhrig
, R.
Kumar
, G. E.
Stein
, and R.
Verduzco
, “Entropy and enthalpy mediated segregation of bottlebrush copolymers to interfaces
,” Macromolecules
52
, 8910
–8922
(2019
).54.
H.
Xu
, F. C.
Sun
, D. G.
Shirvanyants
, M.
Rubinstein
, D.
Shabratov
, K. L.
Beers
, K.
Matyjaszewski
, and S. S.
Sheiko
, “Molecular pressure sensors
,” Adv. Mater.
19
, 2930
–2934
(2007
).55.
M.
Vatankhah-Varnoosfaderani
, W. F. M.
Daniel
, A. P.
Zhushma
, Q.
Li
, B. J.
Morgan
, K.
Matyjaszewski
, D. P.
Armstrong
, R. J.
Spontak
, A. V.
Dobrynin
, and S. S.
Sheiko
, “Bottlebrush elastomers: A new platform for freestanding electroactuation
,” Adv. Mater.
29
, 1604209
(2016
).56.
L.
Wei
, T. D.
Caliskan
, S.
Tu
, C. K.
Choudhury
, O.
Kuksenok
, and I.
Luzinov
, “Highly oil-repellent thermoplastic boundaries via surface delivery of CF3 groups by molecular bottlebrush additives
,” ACS Appl. Mater. Interfaces
12
, 38626
–38637
(2020
).57.
M.
Alaboalirat
, L.
Qi
, K. J.
Arrington
, S.
Qian
, J. K.
Keum
, H.
Mei
, K. C.
Littrell
, B. G.
Sumpter
, J.-M. Y.
Carrillo
, R.
Verduzco
, and J. B.
Matson
, “Amphiphilic bottlebrush block copolymers: Analysis of aqueous self-assembly by small-angle neutron scattering and surface tension measurements
,” Macromolecules
52
, 465
–476
(2019
).58.
J.
Nam
, Y.
Kim
, J. G.
Kim
, and M.
Seo
, “Self-assembly of monolayer vesicles via backbone-shiftable synthesis of Janus core–shell bottlebrush polymer
,” Macromolecules
52
, 9484
(2019
).59.
F.
Shao
, Y.
Wang
, C. M.
Tonge
, E. R.
Sauvé
, and Z. M.
Hudson
, “Self-assembly of luminescent triblock bottlebrush copolymers in solution
,” Polym. Chem.
11
, 1062
–1071
(2020
).60.
M. A.
Wade
, D.
Walsh
, J. C.-W.
Lee
, E.
Kelley
, K.
Weigandt
, D.
Guironnet
, and S. A.
Rogers
, “Color, structure, and rheology of a diblock bottlebrush copolymer solution
,” Soft Matter
16
, 4919
–4931
(2020
).61.
B. B.
Patel
, D. J.
Walsh
, D. H.
Kim
, J.
Kwok
, B.
Lee
, D.
Guironnet
, and Y.
Diao
, “Tunable structural color of bottlebrush block copolymers through direct-write 3D printing from solution
,” Sci. Adv.
6
, eaaz7202
(2020
).62.
M.
Abbasi
, L.
Faust
, K.
Riazi
, and M.
Wilhelm
, “Linear and extensional rheology of model branched polystyrenes: From loosely grafted combs to bottlebrushes
,” Macromolecules
50
, 5964
–5977
(2017
).63.
B. M.
Yavitt
, H.
Fei
, G.
Kopanati
, R.
Li
, M.
Fukuto
, H. H.
Winter
, and J. J.
Watkins
, “Long-range lamellar alignment in diblock bottlebrush copolymers via controlled oscillatory shear
,” Macromolecules
53
, 2834
–2840
(2020
).64.
H. Y.
Song
, L.
Faust
, J.
Son
, M.
Kim
, S. J.
Park
, S. k.
Ahn
, M.
Wilhelm
, and K.
Hyun
, “Small and medium amplitude oscillatory shear rheology of model branched polystyrene (PS) melts
,” Polymers
12
, 365
(2020
).65.
S. J.
Dalsin
, T. G.
Rions-Maehren
, M. D.
Beam
, F. S.
Bates
, M. A.
Hillmyer
, and M. W.
Matsen
, “Bottlebrush block polymers: Quantitative theory and experiments
,” ACS Nano
9
, 12233
–12245
(2015
).66.
S.
Alexandris
, K.
Peponaki
, P.
Petropoulou
, G.
Sakellariou
, and D.
Vlassopoulos
, “Linear viscoelastic response of unentangled polystyrene bottlebrushes
,” Macromolecules
53
, 3923
–3932
(2020
).67.
K. J.
Bichler
, B.
Jakobi
, and G. J.
Schneider
, “Dynamical comparison of different polymer architectures—Bottlebrush vs linear polymer
,” Macromolecules
54
, 1829
–1837
(2021
).68.
U.
Gürel
and A.
Giuntoli
, “Shear thinning from bond orientation in model unentangled bottlebrush polymer melts
,” Macromolecules
56
, 5708
–5717
(2023
).69.
D. J.
Walsh
and D.
Guironnet
, “Macromolecules with programmable shape, size, and chemistry
,” Proc. Natl. Acad. Sci. U. S. A.
116
, 1538
–1542
(2019
).70.
D. J.
Walsh
, S.
Dutta
, C. E.
Sing
, and D.
Guironnet
, “Engineering of molecular geometry in bottlebrush polymers
,” Macromolecules
52
, 4847
–4857
(2019
).71.
J. D.
Weeks
, D.
Chandler
, and H. C.
Andersen
, “Role of repulsive forces in determining the equilibrium structure of simple liquids
,” J. Chem. Phys.
54
, 5237
–5247
(1971
).72.
K.
Kremer
and G. S.
Grest
, “Dynamics of entangled linear polymer melts: A molecular-dynamics simulation
,” J. Chem. Phys.
92
, 5057
–5086
(1990
).73.
D. L.
Ermak
and J. A.
McCammon
, “Brownian dynamics with hydrodynamic interactions
,” J. Chem. Phys.
69
, 1352
–1360
(1978
).74.
H. C.
Öttinger
, Stochastic Processes in Polymeric Fluids
(Springer Berlin Heidelberg
, 1996
).75.
J.
Rotne
and S.
Prager
, “Variational treatment of hydrodynamic interaction in polymers
,” J. Chem. Phys.
50
, 4831
–4837
(1969
).76.
H.
Yamakawa
, “Transport properties of polymer chains in dilute solution: Hydrodynamic interaction
,” J. Chem. Phys.
53
, 436
–443
(1970
).77.
R. M.
Jendrejack
, M. D.
Graham
, and J. J.
de Pablo
, “Hydrodynamic interactions in long chain polymers: Application of the Chebyshev polynomial approximation in stochastic simulations
,” J. Chem. Phys.
113
, 2894
–2900
(2000
).78.
R. M.
Jendrejack
, 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
, 7752
–7759
(2002
).79.
T.
Ando
, E.
Chow
, Y.
Saad
, and J.
Skolnick
, “Krylov subspace methods for computing hydrodynamic interactions in Brownian dynamics simulations
,” J. Chem. Phys.
137
, 064106
(2012
).80.
A.
Saadat
and B.
Khomami
, “Computationally efficient algorithms for incorporation of hydrodynamic and excluded volume interactions in Brownian dynamics simulations: A comparative study of the Krylov subspace and Chebyshev based techniques
,” J. Chem. Phys.
140
, 184903
(2014
).81.
D.
Knoll
and D.
Keyes
, “Jacobian-free Newton–Krylov methods: A survey of approaches and applications
,” J. Comput. Phys.
193
, 357
–397
(2004
).82.
See https://users.wpi.edu/~walker/NITSOL for
H. F.
Walker
, “NITSOL, a Fortran code for Newton-iterative solution of large-scale nonlinear systems
,” (2007
).83.
S.
Dutta
, M. A.
Wade
, D. J.
Walsh
, D.
Guironnet
, S. A.
Rogers
, and C. E.
Sing
, “Dilute solution structure of bottlebrush polymers
,” Soft Matter
15
, 2928
–2941
(2019
).84.
H.
Flyvbjerg
and H. G.
Petersen
, “Error estimates on averages of correlated data
,” J. Chem. Phys.
91
, 461
–466
(1989
).85.
R. B.
Bird
, C. F.
Curtiss
, R. C.
Armstrong
, and O.
Hassager
, Dynamics of Polymeric Fluids
(John Wiley & Sons Inc.
, New York
, 1987
), Vol. II
.86.
M. D.
Graham
, Microhydrodynamics, Brownian Motion, and Complex Fluids
(Cambridge University Press
, New York
, 2018
).87.
B.
Dünweg
, D.
Reith
, M.
Steinhauser
, and K.
Kremer
, “Corrections to scaling in the hydrodynamic properties of dilute polymer solutions
,” J. Chem. Phys.
117
, 914
–924
(2002
).88.
Z. Y.
Chen
and J.
Noolandi
, “Renormalization-group scaling theory for flexible and wormlike polymer chains
,” J. Chem. Phys.
96
, 1540
–1548
(1992
).89.
C.-C.
Hsieh
, L.
Li
, and R. G.
Larson
, “Modeling hydrodynamic interaction in Brownian dynamics: Simulations of extensional flows of dilute solutions of DNA and polystyrene
,” J. Non-Newtonian Fluid Mech.
113
, 147
–191
(2003
).90.
R. M.
Jendrejack
, D. C.
Schwartz
, J. J.
de Pablo
, and M. D.
Graham
, “Shear-induced migration in flowing polymer solutions: Simulation of long-chain DNA in microchannels
,” J. Chem. Phys.
120
, 2513
–2529
(2004
).91.
C.
Stoltz
, J. J.
de Pablo
, and M. D.
Graham
, “Concentration dependence of shear and extensional rheology of polymer solutions: Brownian dynamics simulations
,” J. Rheol.
50
, 137
–167
(2006
).92.
C. D.
Young
, Y.
Zhou
, C. M.
Schroeder
, and C. E.
Sing
, “Dynamics and rheology of ring-linear blend semidilute solutions in extensional flow. Part I: Modeling and molecular simulations
,” J. Rheol.
65
, 757
–777
(2021
).93.
D. J.
Mai
, A. B.
Marciel
, C. E.
Sing
, and C. M.
Schroeder
, “Topology-controlled relaxation dynamics of single branched polymers
,” ACS Macro Lett.
4
, 446
–452
(2015
).94.
D. J.
Mai
, A.
Saadat
, B.
Khomami
, and C. M.
Schroeder
, “Stretching dynamics of single comb polymers in extensional flow
,” Macromolecules
51
, 1507
–1517
(2018
).95.
S. F.
Patel
, C. D.
Young
, C. E.
Sing
, and C. M.
Schroeder
, “Nonmonotonic dependence of comb polymer relaxation on branch density in semidilute solutions of linear polymers
,” Phys. Rev. Fluids
5
, 121301
(2020
).96.
P. G.
de Gennes
, “Coil-stretch transition of dilute flexible polymers under ultrahigh velocity gradients
,” J. Chem. Phys.
60
, 5030
–5042
(1974
).97.
E. J.
Hinch
, “Mechanical models of dilute polymer solutions for strong flows with large polymer deformations
,” in Proceedings of Colloques Internationaux du CNRS
(Polymères et Lubrification, Editions du CNRS
, Paris
, 1974
), Vol. 233
, p. 241
.98.
C. M.
Schroeder
, H. P.
Babcock
, E. S. G.
Shaqfeh
, and S.
Chu
, “Observation of polymer conformation hysteresis in extensional flow
,” Science
301
, 1515
–1519
(2003
).99.
S.
Dutta
and C. E.
Sing
, “Two stretching regimes in the elasticity of bottlebrush polymers
,” Macromolecules
53
, 6946
–6955
(2020
).100.
P. S.
Doyle
and E. S.
Shaqfeh
, “Dynamic simulation of freely-draining, flexible bead-rod chains: Start-up of extensional and shear flow
,” J. Non-Newtonian Fluid Mech.
76
, 43
–78
(1998
).101.
C.
Sendner
and R. R.
Netz
, “Single flexible and semiflexible polymers at high shear: Non-monotonic and non-universal stretching response
,” Eur. Phys. J. E
30
, 75
–81
(2009
).102.
I. S.
Dalal
, N.
Hoda
, and R. G.
Larson
, “Multiple regimes of deformation in shearing flow of isolated polymers
,” J. Rheol.
56
, 305
–332
(2012
).103.
I. S.
Dalal
, C.-C.
Hsieh
, A.
Albaugh
, and R. G.
Larson
, “Effects of excluded volume and hydrodynamic interactions on the behavior of isolated bead-rod polymer chains in shearing flow
,” AIChE J.
60
, 1400
–1412
(2014
).104.
L.
Miao
, C. D.
Young
, and C. E.
Sing
, “An iterative method for hydrodynamic interactions in Brownian dynamics simulations of polymer dynamics
,” J. Chem. Phys.
147
, 024904
(2017
).105.
M. M.
Moghani
and B.
Khomami
, “Computationally efficient algorithms for Brownian dynamics simulation of long flexible macromolecules modeled as bead-rod chains
,” Phys. Rev. Fluids
2
, 023303
(2017
).106.
C. E.
Sing
and A.
Alexander-Katz
, “Giant nonmonotonic stretching response of a self-associating polymer in shear flow
,” Phys. Rev. Lett.
107
, 198302
(2011
).107.
A. V.
Lyulin
, D. B.
Adolf
, and G. R.
Davies
, “Brownian dynamics simulations of linear polymers under shear flow
,” J. Chem. Phys.
111
, 758
–771
(1999
).108.
P. S.
Doyle
, 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
).109.
C.
Schroeder
, R.
Teixeira
, E.
Shaqfeh
, and S.
Chu
, “Characteristic periodic motion of polymers in shear flow
,” Phys. Rev. Lett.
95
, 018301
(2005
).110.
S.
Gerashchenko
and V.
Steinberg
, “Statistics of tumbling of a single polymer molecule in shear flow
,” Phys. Rev. Lett.
96
, 038304
(2006
).111.
J. S.
Hur
, E. S. G.
Shaqfeh
, and R. G.
Larson
, “Brownian dynamics simulations of single DNA molecules in shear flow
,” J. Rheol.
44
, 713
–742
(2000
).112.
A.
Puliafito
and K.
Turitsyn
, “Numerical study of polymer tumbling in linear shear flows
,” Phys. D
211
, 9
–22
(2005
).113.
C. M.
Schroeder
, 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
, 1967
–1978
(2005
).114.
C.-C.
Huang
, G.
Sutmann
, G.
Gompper
, and R. G.
Winkler
, “Tumbling of polymers in semidilute solution under shear flow
,” EPL
93
, 54004
(2011
).115.
S. H.
Jeong
, S.
Cho
, and C.
Baig
, “Chain rotational dynamics in dilute polymer solutions and melts under shear flow
,” Polymer
281
, 126101
(2023
).116.
I.
Saha Dalal
, A.
Albaugh
, N.
Hoda
, and R. G.
Larson
, “Tumbling and deformation of isolated polymer chains in shearing flow
,” Macromolecules
45
, 9493
–9499
(2012
).117.
G.-L.
He
, R.
Messina
, and H.
Löwen
, “Statistics of polymer adsorption under shear flow
,” J. Chem. Phys.
132
, 124903
(2010
).118.
H. P.
Babcock
, D. E.
Smith
, J. S.
Hur
, E. S. G.
Shaqfeh
, and S.
Chu
, “Relating the microscopic and macroscopic response of a polymeric fluid in a shearing flow
,” Phys. Rev. Lett.
85
, 2018
–2021
(2000
).119.
J. S.
Hur
, 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
, 421
–450
(2001
).120.
D.
Pearson
, E.
Herbolzheimer
, N.
Grizzuti
, and G.
Marrucci
, “Transient behavior of entangled polymers at high shear rates
,” J. Polym. Sci., Part B: Polym. Phys.
29
, 1589
–1597
(1991
).121.
J. J.
Magda
, C. S.
Lee
, S. J.
Muller
, and R. G.
Larson
, “Rheology, flow instabilities, and shear-induced diffusion in polystyrene solutions
,” Macromolecules
26
, 1696
–1706
(1993
).122.
K.
Osaki
, T.
Inoue
, and T.
Uematsu
, “Stress overshoot of polymer solutions at high rates of shear: Semidilute polystyrene solutions with and without chain entanglement
,” J. Polym. Sci., Part B: Polym. Phys.
38
, 3271
–3276
(2000
).123.
I. N.
Haugan
, M. J.
Maher
, A. B.
Chang
, T.-P.
Lin
, R. H.
Grubbs
, M. A.
Hillmyer
, and F. S.
Bates
, “Consequences of grafting density on the linear viscoelastic behavior of graft polymers
,” ACS Macro Lett.
7
, 525
–530
(2018
).124.
S. J.
Dalsin
, M. A.
Hillmyer
, and F. S.
Bates
, “Molecular weight dependence of zero-shear viscosity in atactic polypropylene bottlebrush polymers
,” ACS Macro Lett.
3
, 423
–427
(2014
).125.
K.
Terao
, T.
Hokajo
, Y.
Nakamura
, and T.
Norisuye
, “Solution properties of polymacromonomers consisting of polystyrene. 3. Viscosity behavior in cyclohexane and toluene
,” Macromolecules
32
, 3690
–3694
(1999
).126.
M.
Kikuchi
, T.
Mihara
, Y.
Jinbo
, Y.
Izumi
, K.
Nagai
, and S.
Kawaguchi
, “Characterization of rodlike poly(n-hexyl isocyanate) macromonomers and their polymacromonomers by light scattering, SAXS, intrinsic viscosity, and scanning force microscopy
,” Polym. J.
39
, 330
–341
(2007
).127.
Y.
Nakamura
and T.
Norisuye
, “Brush-like polymers
,” in Soft Matter Characterization
(Springer
, Netherlands, Dordrecht
, 2008
), pp. 235
–286
.128.
Z.
Li
, M.
Tang
, S.
Liang
, M.
Zhang
, G. M.
Biesold
, Y.
He
, S.-M.
Hao
, W.
Choi
, Y.
Liu
, J.
Peng
, and Z.
Lin
, “Bottlebrush polymers: From controlled synthesis, self-assembly, properties to applications
,” Prog. Polym. Sci.
116
, 101387
(2021
).129.
T.
Pan
, S.
Dutta
, and C. E.
Sing
, “Interaction potential for coarse-grained models of bottlebrush polymers
,” J. Chem. Phys.
156
, 014903
(2022
).130.
B. B.
Patel
, T.
Pan
, Y.
Chang
, D. J.
Walsh
, J. J.
Kwok
, K. S.
Park
, K.
Patel
, D.
Guironnet
, C. E.
Sing
, and Y.
Diao
, “Concentration-driven self-assembly of PS-b-PLA bottlebrush diblock copolymers in solution
,” ACS Polym. Au
2
, 232
–244
(2022
).131.
T.
Pan
, B. B.
Patel
, D. J.
Walsh
, S.
Dutta
, D.
Guironnet
, Y.
Diao
, and C. E.
Sing
, “Implicit side-chain model and experimental characterization of bottlebrush block copolymer solution assembly
,” Macromolecules
54
, 3620
–3633
(2021
).132.
R. S.
Dembo
, S. C.
Eisenstat
, and T.
Steihaug
, “Inexact Newton methods
,” SIAM J. Numer. Anal.
19
, 400
–408
(1982
).133.
Y.
Saad
and M. H.
Schultz
, “GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems
,” SIAM J. Sci. Stat. Comput.
7
, 856
–869
(1986
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
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