Flow-enhanced nucleation of the crystal phase under shear and uniaxial extension for a monodisperse melt of n-pentacontahectane (C150H302 or C150) chains was studied by nonequilibrium molecular dynamics simulation. The resulting acceleration in the crystal nucleation rate was correlated with macroscopically measurable properties of the flow field and with microscopic conformational statistics. Based on the fidelity of the observed correlations, several empirical models reported in the literature were evaluated for their abilities to account for the observed enhancement of the nucleation rate due to flow, and new models are proposed for data that do not comport with existing models. In agreement with prior reports, the nucleation rate was found to correlate well with first-normal stress difference, the second invariant of the deviatoric conformation tensor, and the stretch ratio, albeit with some differences from the existing models. New models based on conformational invariants for Kuhn segments are proposed and shown to describe the simulation data more accurately than those based on conformational behavior of entire chains. Within the applicability of the stress-optical rule, related models are proposed based on invariants of the extra stress tensor.
References
1.
2.
3.
Schneider
, W.
, A.
Köppl
, and J.
Berger
, “Non-isothermal crystallization of polymers
,” Int. Polym. Process.
2
, 151
–154
(1988
). 4.
Liedauer
, S.
, G.
Eder
, and H.
Janeschitz-Kriegl
, “On the limitations of shear induced crystallization in polypropylene melts
,” Int. Polym. Process.
10
, 243
–250
(1995
). 5.
Peters
, G. W. M.
, L.
Balzano
, and R. J. A.
Steenbakkers
, in Handbook of Polymer Crystallization
, edited by E.
Piorkowska
and G. C.
Rutledge
(Wiley
, Hoboken
, 2013
), pp. 399
–431
.6.
Graham
, R. S.
, “Modelling flow-induced crystallisation in polymers
,” Chem. Commun.
50
, 3531
–3545
(2014
). 7.
Liedauer
, S.
, G.
Eder
, H.
Janeschitz-Kriegl
, P.
Jerschow
, W.
Geymayer
, and E.
Ingolic
, “On the kinetics of shear induced crystallization in polypropylene
,” Int. Polym. Process.
8
, 236
–244
(1993
). 8.
Guo
, X.
, A. I.
Isayev
, and L.
Guo
, “Crystallinity and microstructure in injection moldings of isotactic polypropylenes. Part 1: A new approach to modeling and model parameters
,” Polym. Eng. Sci.
39
, 2096
–2114
(1999
). 9.
Ziabicki
, A.
, “The mechanisms of ‘neck-like’ deformation in high-speed melt spinning. 2. Effects of polymer crystallization
,” J. Nonnewton. Fluid Mech.
30
, 157
–168
(1988
). 10.
Koscher
, E.
, and R.
Fulchiron
, “Influence of shear on polypropylene crystallization: Morphology development and kinetics
,” Polymer
43
, 6931
–6942
(2002
). 11.
Doufas
, A. K.
, A. J.
McHugh
, and C.
Miller
, “Simulation of melt spinning including flow-induced crystallization: Part I. Model development and predictions
,” J. Nonnewton. Fluid Mech.
92
, 27
–66
(2000
). 12.
Zuidema
, H.
, G. W. M.
Peters
, and H. E. H.
Meijer
, “Development and validation of a recoverable strain-based model for flow-induced crystallization of polymers
,” Macromol. Theory Simul.
10
, 447
–460
(2001
). 13.
Steenbakkers
, R. J. A.
, G. W. M.
Peters
, H. E. H.
Meijer
, A.
Co
, G. L.
Leal
, R. H.
Colby
, and A. J.
Giacomin
, AIP Conf. Proc.
, 1027
, 493
–495
(2008
). 14.
Graham
, R. S.
, and P. D.
Olmsted
, “Coarse-grained simulations of flow-induced nucleation in semicrystalline polymers
,” Phys. Rev. Lett.
103
, 115702
(2009
). 15.
Coppola
, S.
, N.
Grizzuti
, and P. L.
Maffettone
, “Microrheological modeling of flow-induced crystallization
,” Macromolecules
34
, 5030
–5036 (2001
). 16.
Baert
, J.
, and P.
Van Puyvelde
, “Density fluctuations during the early stages of polymer crystallization: An overview
,” Macromol. Mater. Eng.
293
, 255
–273
(2008
). 17.
Shneidman
, V. A.
, “Communication: On nucleation statistics in small systems
,” J. Chem. Phys.
141
, 051101
(2014
). 18.
Wedekind
, J.
, R.
Strey
, and D.
Reguera
, “New method to analyze simulations of activated processes
,” J. Chem. Phys.
126
, 134103
(2007
). 19.
Nicholson
, D. A.
, and G. C.
Rutledge
, “Analysis of nucleation using mean first-passage time data from molecular dynamics simulation
,” J. Chem. Phys.
144
, 134105
(2016
). 20.
Rutledge
, G. C.
, in Handbook of Polymer Crystallization
, edited by E.
Piorkowska
and G. C.
Rutledge
(Wiley
, Hoboken
, 2013
), pp. 197
–214
.21.
Anwar
, M.
, J. T.
Berryman
, and T.
Schilling
, “Crystal nucleation mechanism in melts of short polymer chains under quiescent conditions and under shear flow
,” J. Chem. Phys.
141
, 124910
(2014
). 22.
Nicholson
, D. A.
, and G. C.
Rutledge
, “Molecular simulation of flow-enhanced nucleation in n-eicosane melts under steady shear and uniaxial extension
,” J. Chem. Phys.
145
, 244903
(2016
). 23.
Cassagnau
, P.
, J. P.
Montfort
, G.
Marin
, and P.
Monge
, “Rheology of polydisperse polymers: Relationship between intermolecular interactions and molecular weight distribution
,” Rheol. Acta
32
, 156
–167
(1993
). 24.
Fetters
, L. J.
, D. J.
Lohse
, D.
Richter
, T. A.
Witten
, and A.
Zirkel
, “Connection between polymer molecular weight, density, chain dimensions, and melt viscoelastic properties
,” Macromolecules
27
, 4639
–4647
(1994
). 25.
Stephanou
, P. S.
, C.
Baig
, G.
Tsolou
, V. G.
Mavrantzas
, and M.
Kröger
, “Quantifying chain reptation in entangled polymer melts: Topological and dynamical mapping of atomistic simulation results onto the tube model
,” J. Chem. Phys.
132
, 124904
(2010
). 26.
Everaers
, R.
, S. K.
Sukumaran
, G. S.
Grest
, C.
Svaneborg
, A.
Sivasubramanian
, and K.
Kremer
, “Rheology and microscopic topology of entangled polymeric liquids
,” Science
303
, 823
–826
(2004
). 27.
Paul
, W.
, D. Y.
Yoon
, and G. D.
Smith
, “An optimized united atom model for simulations of polymethylene melts
,” J. Chem. Phys.
103
, 1702
–1709
(1995
). 28.
Waheed
, N.
, M. S.
Lavine
, and G. C.
Rutledge
, “Molecular simulation of crystal growth in n-eicosane
,” J. Chem. Phys.
116
, 2301
–2309
(2002
). 29.
Waheed
, N.
, M. J.
Ko
, and G. C.
Rutledge
, “Molecular simulation of crystal growth in long alkanes
,” Polymer
46
, 8689
–8702
(2005
). 30.
Evans
, D. J.
, and G. P.
Morriss
, Statistical Mechanics of Nonequilibrium Liquids
(Academic
, London
, 1990
).31.
Evans
, D. J.
, “The frequency dependent shear viscosity of methane
,” Mol. Phys.
37
, 1745
–1754
(1979
). 32.
Hunt
, T. A.
, and B. D.
Todd
, “On the Arnold cat map and periodic boundary conditions for planar elongational flow
,” Mol. Phys.
101
, 3445
–3454
(2003
). 33.
Lees
, A. W.
, and S. F.
Edwards
, “The computer study of transport processes under extreme conditions
,” J. Phys. C Solid State Phys.
5
, 1921
–1929
(1972
). 34.
Dobson
, M.
, “Periodic boundary conditions for long-time nonequilibrium molecular dynamics simulations of incompressible flows
,” J. Chem. Phys.
141
, 184103
(2014
). 35.
Hunt
, T. A.
, “Periodic boundary conditions for the simulation of uniaxial extensional flow of arbitrary duration
,” Mol. Simul.
42
, 347
–352
(2015
). 36.
Plimpton
, S.
, “Fast parallel algorithms for short-range molecular dynamics
,” J. Comput. Phys.
117
, 1
–19
(1995
). 37.
Tuckerman
, M.
, B. J.
Berne
, and G. J.
Martyna
, “Reversible multiple time scale molecular dynamics
,” J. Chem. Phys.
97
, 1990
–2001
(1992
). 38.
Yi
, P.
, C. R.
Locker
, and G. C.
Rutledge
, “Molecular dynamics simulation of homogeneous crystal nucleation in polyethylene
,” Macromolecules
46
, 4723
–4733
(2013
). 39.
Ungar
, G.
, J.
Stejny
, A.
Keller
, I.
Bidd
, and M. C.
Whiting
, “The crystallization of ultralong normal paraffins: The onset of chain folding
,” Science
229
, 386
–389
(1985
). 40.
Yi
, P.
, and G. C.
Rutledge
, “Molecular simulation of bundle-like crystal nucleation from n-eicosane melts
,” J. Chem. Phys.
135
, 024903
(2011
). 41.
Isayev
, A. I.
, T. W.
Chan
, K.
Shimojo
, and M.
Gmerek
, “Injection molding of semicrystalline polymers. I. Material characterization
,” J. Appl. Polym. Sci.
55
, 807
–819
(1995
). 42.
Isayev
, A. I.
, T. W.
Chan
, M.
Gmerek
, and K.
Shimojo
, “Injection molding of semicrystalline polymers. II. Modeling and experiments
,” J. Appl. Polym. Sci.
55
, 821
–838
(1995
). 43.
Irving
, J. H.
, and J. G.
Kirkwood
, “The statistical mechanical theory of transport processes. IV. The equations of hydrodynamics
,” J. Chem. Phys.
18
, 817
–829
(1950
). 44.
Doufas
, A. K.
, A. J.
McHugh
, C.
Miller
, and A.
Immaneni
, “Simulation of melt spinning including flow-induced crystallization: Part II. Quantitative comparisons with industrial spinline data
,” J. Nonnewton. Fluid Mech.
92
, 81
–103
(2000
). 45.
Doufas
, A. K.
, and A. J.
McHugh
, “Simulation of melt spinning including flow-induced crystallization. Part III. Quantitative comparisons with PET spinline data
,” J. Rheol.
45
, 403
–420
(2001
). 46.
Doufas
, A. K.
, and A. J.
McHugh
, “Simulation of film blowing including flow-induced crystallization
,” J. Rheol.
45
, 1085
–1104
(2001
). 47.
Doufas
, A. K.
, “A microstructural flow-induced crystallization model for film blowing: validation with experimental data
,” Rheol. Acta
53
, 269
–293
(2014
). 48.
Peters
, G. W. M.
, F. H. M.
Swartjes
, and H. E. H.
Meijer
, “A recoverable strain-based model for flow-induced crystallization
,” Macromol. Symp.
185
, 277
–292
(2002
). 49.
Swartjes
, F. H. M.
, G. W. M.
Peters
, S.
Rastogi
, and H. E. H.
Meijer
, “Stress induced crystallization in elongational flow
,” Int. Polym. Process.
18
, 53
–66
(2003
). 50.
van Meerveld
, J.
, M.
Hütter
, and G. W. M.
Peters
, “Continuum model for the simulation of fiber spinning, with quiescent and flow-induced crystallization
,” J. Nonnewton. Fluid Mech.
150
, 177
–195
(2008
). 51.
Steenbakkers
, R. J. A.
, and G. W. M.
Peters
, “A stretch-based model for flow-enhanced nucleation of polymer melts
,” J. Rheol.
55
, 401
–433
(2011
). 52.
Leonov
, A. I.
, “Analysis of simple constitutive equations for viscoelastic liquids
,” J. Nonnewton. Fluid Mech.
42
, 323
–350
(1992
). 53.
Custódio
, F. J. M. F.
, R. J. A.
Steenbakkers
, P. D.
Anderson
, G. W. M.
Peters
, and H. E. H.
Meijer
, “Model development and validation of crystallization behavior in injection molding prototype flows
,” Macromol. Theory Simul.
18
, 469
–494
(2009
). 54.
van Erp
, T. B.
, P. C.
Roozemond
, and G. W. M.
Peters
, “Flow-enhanced crystallization kinetics of iPP during cooling at elevated pressure: Characterization, validation, and development
,” Macromol. Theory Simul.
22
, 309
–318
(2013
). 55.
Roozemond
, P. C.
, and G. W. M.
Peters
, “Flow-enhanced nucleation of poly(1-butene): Model application to short-term and continuous shear and extensional flow
,” J. Rheol.
57
, 1633
–1653
(2013
). 56.
McHugh
, A. J.
, “Flow-induced crystallization from solution: The relative effects of extension and shearing flow fields
,” J. Appl. Polym. Sci.
19
, 125
–140
(1975
). 57.
McHugh
, A. J.
, “Mechanisms of flow induced crystallization
,” Polym. Eng. Sci.
22
, 15
–26
(1982
). 58.
Ziabicki
, A.
, “Crystallization of polymers in variable external conditions. II. Effects of cooling in the absence of stress and orientation
,” Colloid Polym. Sci.
274
, 705
–716
(1996
). 59.
Acierno
, S.
, S.
Coppola
, N.
Grizzuti
, and P. L.
Maffettone
, “Coupling between kinetics and rheological parameters in the flow-induced crystallization of thermoplastic polymers
,” Macromol. Symp.
185
, 233
–241
(2002
). 60.
Acierno
, S.
, S.
Coppola
, and N.
Grizzuti
, “Effects of molecular weight distribution on the flow-enhanced crystallization of poly(1-butene)
,” J. Rheol.
52
, 551
–566
(2008
). 61.
Zheng
, R.
, and P. K.
Kennedy
, “A model for post-flow induced crystallization: General equations and predictions
,” J. Rheol.
48
, 823
–842
(2004
). 62.
Kim
, K. H.
, A. I.
Isayev
, and K.
Kwon
, “Flow-induced crystallization in the injection molding of polymers: A thermodynamic approach
,” J. Appl. Polym. Sci.
95
, 502
–523
(2005
). 63.
Jolley
, K.
, and R. S.
Graham
, “Flow-induced nucleation in polymer melts: A study of the GO model for pure and bimodal blends, under shear and extensional flow
,” Rheol. Acta
52
, 271
–286
(2013
). 64.
Bernardin
, F. E.
, and G. C.
Rutledge
, “Semi-grand canonical Monte Carlo (SGMC) simulations to interpret experimental data on processed polymer melts and glasses
,” Macromolecules
40
, 4691
–4702
(2007
). 65.
van Meerveld
, J.
, G. W. M.
Peters
, and M.
Hütter
, “Towards a rheological classification of flow induced crystallization experiments of polymer melts
,” Rheol. Acta
44
, 119
–134
(2004
). 66.
Mead
, D. W.
, and L. G.
Leal
, “The reptation model with segmental stretch. I. Basic equations and general properties
,” Rheol. Acta
34
, 339
–359
(1995
). 67.
68.
Lodge
, A. S.
, “A network theory of flow birefringence and stress in concentrated polymer solutions
,” Trans. Faraday Soc.
52
, 120
–130
(1956
). 69.
See supplementary material at https://doi.org/10.1122/1.5091945 for the details of the force field used in this study.
© 2019 The Society of Rheology.
2019
The Society of Rheology
You do not currently have access to this content.