In this work, we study morphological characteristics of the critically sized crystalline nuclei at initial stage of the shear-induced crystallization of a model single-component amorphous (glassy) system. These characteristics are estimated quantitatively through statistical treatment of the nonequilibrium molecular dynamics simulation results for the system under steady shear at various (fixed) values of the shear rate and at different temperatures. It is found that the sheared glassy system is crystallized through nucleation mechanism. From the analysis of time-dependent trajectories of the largest crystalline nuclei, the critical size nc and the nucleation time τc were defined. It is shown that the critically sized nuclei in the system are oriented within the shear-gradient xy-plane at moderate and high shear rates; and a tilt angle of the oriented nuclei depends on the shear rate. At extremely high shear rates and at shear deformation of the system more than 60%, the tilt angle of the nuclei tends to take the value respective to the shear direction. We found that this feature depends weakly on the temperature. Asphericity of the nucleus shape increases with increasing shear rate that is verified by increasing value of the asphericity parameter and by the contour of the pair distribution function calculated for the particles of the critically sized nuclei. The critical size increases with increasing shear rate according to the power-law, , whereas the shape of the critically sized nucleus changes from spherical to the elongated ellipsoidal. We found that the nc-dependencies of the nuclei deformation parameter evaluated for the system at different temperatures and shear rates are collapsed into unified master-curve.
References
1.
Janeschitz-Kriegl
, H.
, “Some remarks on flow induced crystallization in polymer melts
,” J. Rheol.
57
, 1057
–1064
(2013
).2.
Scelsi
, L.
, M. R.
Mackley
, H.
Klein
, P. D.
Olmsted
, R. S.
Graham
, O. G.
Harlen
, and T. C. B.
McLeish
, “Experimental observations and matching viscoelastic specific work predictions of flow-induced crystallization for molten polyethylene within two flow geometries
,” J. Rheol.
53
, 859
–876
(2009
).3.
Berthier
, L.
, and G.
Biroli
, “Theoretical perspective on the glass transition and amorphous materials
,” Rev. Mod. Phys.
83
, 587
–645
(2011
).4.
Ediger
, M. D.
, and P.
Harrowell
, “Perspective: Supercooled liquids and glasses
,” J. Chem. Phys.
137
, 080901
(2012
).5.
Greer
, L. A.
, “Metallic glasses
,” Science
267
, 1947
–1953
(1995
).6.
Lu
, Z. P.
, and C. T.
Liu
, “Glass formation criterion for various glass-forming systems
,” Phys. Rev. Lett.
91
, 115505
(2003
).7.
Mokshin
, A. V.
, and J.-L.
Barrat
, “Crystal nucleation and cluster-growth kinetics in a model glass under shear
,” Phys. Rev. E
82
, 021505
(2010
).8.
Löwen
, H.
, “Colloidal soft matter under external control
,” J. Phys.: Condens. Matter
13
, R415
–R432
(2001
).9.
Haw
, M. D.
, W. C. K.
Poon
, and P. N.
Pusey
, “Colloidal glasses under shear strain
,” Phys. Rev. E
58
, 4673
–4687
(1998
).10.
He
, G.-L.
, R.
Messina
, H.
Löwen
, A.
Kiriy
, V.
Bocharova
, and M.
Stamm
, “Shear-induced stretching of adsorbed polymer chains
,” Soft Matter
5
, 3014
–3017
(2009
).11.
Dasgupta
, R.
, H.
George
, E.
Hentschel
, and I.
Procaccia
, “Microscopic mechanism of shear bands in amorphous solids
,” Phys. Rev. Lett.
109
, 255502
(2012
).12.
Evans
, D. J.
, and G. P.
Morriss
, Statistical Mechanics of Non-Equilibrium Liquids
(Cambridge University
, New York
, 2008
).13.
Fang
, H.
, Y.
Zhang
, J.
Bai
, and Z.
Wang
, “Shear-induced nucleation and morphological evolution for bimodal long chain branched polylactide
,” Macromolecules
46
, 6555
–6565
(2013
).14.
Butler
, S.
, and P.
Harrowell
, “Kinetics of crystallization in a shearing colloidal suspension
,” Phys. Rev. E
52
, 6424
–6430
(1995
).15.
Mokshin
, A. V.
, B. N.
Galimzyanov
, and J.-L.
Barrat
, “Extension of classical nucleation theory for uniformly sheared systems
,” Phys. Rev. E
87
, 062307
(2013
).16.
Blaak
, R.
, S.
Auer
, D.
Frenkel
, and H.
Löwen
, “Crystal nucleation of colloidal suspensions under shear
,” Phys. Rev. Lett.
93
, 068303
(2004
).17.
Kerrache
, A.
, N.
Mousseau
, and L. J.
Lewis
, “Crystallization of amorphous silicon induced by mechanical shear deformations
,” Phys. Rev. B
84
, 014110
(2011
).18.
Shao
, Z.
, J. P.
Singer
, Y.
Liu
, Z.
Liu
, H.
Li
, M.
Gopinadhan
, C. S.
O'Hern
, J.
Schroers
, and C. O.
Osuji
, “Shear-accelerated crystallization in a supercooled atomic liquid
,” Phys. Rev. E
91
, 020301
(2015
).19.
Mura
, F.
, and A.
Zaccone
, “Effects of shear flow on phase nucleation and crystallization
,” Phys. Rev. E
93
, 042803
(2016
).20.
Nosenko
, V.
, A. V.
Ivlev
, and G. E.
Morfill
, “Microstructure of a liquid two-dimensional dusty plasma under shear
,” Phys. Rev. Lett.
108
, 135005
(2012
).21.
Koumakis
, N.
, M.
Laurati
, S. U.
Egelhaaf
, J. F.
Brady
, and G.
Petekidis
, “Yielding of hard-sphere glasses during start-up shear
,” Phys. Rev. Lett.
108
, 098303
(2012
).22.
Kumaraswamy
, G.
, J. A.
Kornfield
, F.
Yeh
, and B. S.
Hsiao
, “Shear-enhanced crystallization in isotactic polypropylene. 3. Evidence for a kinetic pathway to nucleation
,” Macromolecules
35
, 1762
–1769
(2002
).23.
Keller
, A.
, and M. J.
Machin
, “Oriented crystallization in polymers
,” J. Macromol. Sci., Phys. B
1
, 41
–91
(1967
).24.
Roozemond
, P.
, and G.
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
).25.
Roozemond
, P.
, M.
van Drongelen
, Z.
Ma
, A.
Spoelstra
, D.
Hermida-Merino
, and G.
Peters
, “Self-regulation in flow-induced structure formation of isotactic polypropylene
,” Macromol. Rapid Commun.
36
, 385
–390
(2015
).26.
Graham
, R. S.
, and P. D.
Olmsted
, “Coarse-grained simulations of flow-induced nucleation in semicrystalline polymers
,” Phys. Rev. Lett.
103
, 115702
(2009
).27.
Graham
, R.
, and P.
Olmsted
, “Kinetic Monte Carlo simulations of flow induced nucleation in polymer melts
,” Faraday Discuss.
144
, 71
–92
(2010
).28.
McIlroya
, C.
, and P. D.
Olmsted
, “Deformation of an amorphous polymer during the fused-filament-fabrication method for additive manufacturing
,” J. Rheol.
61
, 379
–397
(2017
).29.
Viasnoff
, V.
, and F.
Lequeux
, “Rejuvenation and overaging in a colloidal glass under shear
,” Phys. Rev. Lett.
89
, 065701
(2002
).30.
Rottler
, J.
, and M. O.
Robbins
, “Shear yielding of amorphous glassy solids: Effect of temperature and strain rate
,” Phys. Rev. E
68
, 011507
(2003
).31.
Wallace
, M. L.
, and B.
Joós
, “Shear-induced overaging in a polymer glass
,” Phys. Rev. Lett.
96
, 025501
(2006
).32.
Koumakis
, N.
, M.
Laurati
, A. R.
Jacob
, K. J.
Mutch
, A.
Abdellali
, A. B.
Schofield
, S. U.
Egelhaaf
, J. F.
Brady
, and G.
Petekidis
, “Start-up shear of concentrated colloidal hard spheres: Stresses, dynamics, and structure
,” J. Rheol.
60
, 603
–623
(2016
).33.
Koumakis
, N.
, A. B.
Schofieldc
, and G.
Petekidis
, “Effects of shear induced crystallization on the rheology and ageing of hard sphere glasses
,” Soft Matter
4
, 2008
–2018
(2008
).34.
Mokshin
, A. V.
, and J.-L.
Barrat
, “Shear induced structural ordering of a model metallic glass
,” J. Chem. Phys.
130
, 034502
(2009
).35.
Shrivastav
, G. P.
, P.
Chaudhuri
, and J.
Horbach
, “Heterogeneous dynamics during yielding of glasses: Effect of aging
,” J. Rheol.
60
, 835
–847
(2016
).36.
Mokshin
, A. V.
, and B. N.
Galimzyanov
, “Scaling law for crystal nucleation time in glasses
,” J. Chem. Phys.
142
, 104502
(2015
).37.
Kashchiev
, D.
, Nucleation: Basic Theory with Applications
(Butterworth-Heinemann
, Oxford
, 2000
).38.
Kelton
, K. F.
, A. L.
Greer
, “The classical theory
,” Pergamon Mater. Ser.
15
, 19
–54
(2010
).39.
Kalikmanov
, V. I.
, Nucleation Theory; Lecture Notes in Physics
(Springer
, New York
, 2012
), Vol. 860
.40.
Wang
, X. W.
, J.
Ouyang
, and Z.
Liu
, “A phase field technique for modeling and predicting flow induced crystallization morphology of semi-crystalline polymers
,” Polymers
8
, 230
(2016
).41.
Dzugutov
, M.
, “Glass formation in a simple monatomic liquid with icosahedral inherent local order
,” Phys. Rev. A
46
, R2984
–R2987
(1992
).42.
Roth
, J.
, “Shock waves in materials with Dzugutov-potential interactions
,” Phys. Rev. B
72
, 014125
(2005
).43.
Mokshin
, A. V.
, and J.-L.
Barrat
, “Shear-induced crystallization of an amorphous system
,” Phys. Rev. E
77
, 021505
(2008
).44.
Lees
, Q. W.
, and S. F.
Edwards
, “The computer study of transport processes under extreme conditions
,” J. Phys. C: Solid State Phys.
5
, 1921
–1929
(1972
).45.
Steinhardt
, P. J.
, D. R.
Nelson
, and M.
Ronchetti
, “Bond-orientational order in liquids and glasses
,” Phys. Rev. B
28
, 784
–805
(1983
).46.
Reinhardt
, A.
, and J. P. K.
Doye
, “Free energy landscapes for homogeneous nucleation of ice for a monatomic water model
,” J. Chem. Phys.
136
, 054501
(2012
).47.
Mickel
, W.
, S. C.
Kapfer
, G. E.
Schröder-Turk
, and K.
Mecke
, “Shortcomings of the bond orientational order parameters for the analysis of disordered particulate matter
,” J. Chem. Phys.
138
, 044501
(2013
).48.
ten Wolde
, P. R.
, M. J.
Ruiz-Montero
, and D.
Frenkel
, “Numerical calculation of the rate of crystal nucleation in a Lennard-Jones system at moderate undercooling
,” J. Chem. Phys.
104
, 9932
–9947
(1996
).49.
Mokshin
, A. V.
, and B. N.
Galimzyanov
, “Steady-state homogeneous nucleation and growth of water droplets: Extended numerical treatment
,” J. Phys. Chem. B
116
, 11959
–11967
(2012
).50.
Mokshin
, A. V.
, and B. N.
Galimzyanov
, “Ordering in model metallic glass upon external homogeneous shear
,” Bull. Russ. Acad. Sci. Phys.
77
, 281
–283
(2013
).51.
Roth
, J.
, and A. R.
Denton
, “Solid-phase structures of the Dzugutov pair potential
,” Phys. Rev. E
61
, 6845
–6857
(2000
).52.
Reguera
, D.
, and J. M.
Rubi
, “Homogeneous nucleation in inhomogeneous media. II. Nucleation in a shear flow
,” J. Chem. Phys.
119
, 9888
–9893
(2003
).53.
Lifshitz
, E. M.
, and L. P.
Pitaevskii
, Physical Kinetics
(Butterworth
, Washington
, 2006
).54.
Mokshin
, A. V.
, and B. N.
Galimzyanov
, “Kinetics of the crystalline nuclei growth in glassy systems
,” Phys. Chem. Chem. Phys.
19
, 11340
–11353
(2017
).55.
Weingartner
, N. B.
, C.
Pueblo
, F. S.
Nogueira
, K. F.
Kelton
, and Z.
Nussinov
, “A phase space approach to supercooled liquids and a universal collapse of their viscosity
,” Front. Mater.
3
, 1
–12
(2016
).56.
Holmqvist
, P.
, M. P.
Lettinga
, J.
Buitenhuis
, and J. K. G.
Dhont
, “Crystallization kinetics of colloidal spheres under stationary shear flow
,” Langmuir
21
, 10976
–10982
(2005
).57.
Tribout
, C.
, B.
Monasse
, and J. M.
Haudin
, “Experimental study of shear-induced crystallization of an impact polypropylene copolymer
,” Colloid Polym. Sci.
274
, 197
–208
(1996
).58.
Coccorullo
, I.
, R.
Pantani
, and G.
Titomanlio
, “Spherulitic nucleation and growth rates in an iPP under continuous shear flow
,” Macromolecules
41
, 9214
–9223
(2008
).59.
Zaccone
, A.
, H.
Wu
, D.
Gentili
, and M.
Morbidelli
, “Theory of activated-rate processes under shear with application to shear-induced aggregation of colloids
,” Phys. Rev. E
80
, 051404
(2009
).60.
Shen
, Y.
, S. B.
Jester
, T.
Qi
, and E. J.
Reed
, “Nanosecond homogeneous nucleation and crystal growth in shock-compressed SiO2
,” Nat. Mater.
15
, 60
–65
(2016
).61.
Cugliandolo
, L. F.
, J.
Kurchan
, and L.
Peliti
, “Energy flow, partial equilibration, and effective temperatures in systems with slow dynamics
,” Phys. Rev. E
55
, 3898
–3914
(1997
).62.
Somani
, R. H.
, L.
Yang
, B. S.
Hsiao
, T.
Sun
, N. V.
Pogodina
, and A.
Lustiger
, “Shear-induced molecular orientation and crystallization in isotactic polypropylene: Effects of the deformation rate and strain
,” Macromolecules
38
, 1244
–1255
(2005
).© 2017 The Society of Rheology.
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