We investigate the short-time vibrational properties and structure of two-dimensional, bidisperse, colloidal glasses and supercooled liquids in the vicinity of the re-entrant glass transition, as a function of interparticle depletion attraction strength. The long-time spatiotemporal dynamics of the samples are measured to be non-monotonic, confirming that the suspensions evolve from repulsive glass to supercooled liquid to attractive glass with increasing depletion attraction. Here, we search for vibrational signatures of the re-entrant behavior in the short-time spatiotemporal dynamics, i.e., dynamics associated with particle motion inside its nearest-neighbor cage. Interestingly, we observe that the anharmonicity of these in-cage vibrations varies non-monotonically with increasing attraction strength, consistent with the non-monotonic long-time structural relaxation dynamics of the re-entrant glass. We also extract effective spring constants between neighboring particles; we find that spring stiffness involving small particles also varies non-monotonically with increasing attraction strength, while stiffness between large particles increases monotonically. Last, from study of depletion-dependent local structure and vibration participation fractions, we gain microscopic insight into the particle-size-dependent contributions to short-time vibrational modes in the glass and supercooled liquid states.
REFERENCES
1.
T.
Eckert
and E.
Bartsch
, “Re-entrant glass transition in a colloid-polymer mixture with depletion attractions
,” Phys. Rev. Lett.
89
, 125701
(2002
).2.
K. N.
Pham
, A. M.
Puertas
, J.
Bergenholtz
, S. U.
Egelhaaf
, A.
Moussaıd
, P. N.
Pusey
, A. B.
Schofield
, M. E.
Cates
, M.
Fuchs
, and W. C. K.
Poon
, “Multiple glassy states in a simple model system
,” Science
296
(5565
), 104
–106
(2002
).3.
W. C. K.
Poon
, “The physics of a model colloid polymer mixture
,” J. Phys.: Condens. Matter
14
(33
), R859
–R880
(2002
).4.
W. C. K.
Poon
, K. N.
Pham
, S. U.
Egelhaaf
, and P. N.
Pusey
, “Unsticking a colloidal glass, and sticking it again
,” J. Phys.: Condens. Matter
15
(1
), S269
–S275
(2002
).5.
C. K.
Mishra
, A.
Rangarajan
, and R.
Ganapathy
, “Two-step glass transition induced by attractive interactions in quasi-two-dimensional suspensions of ellipsoidal particles
,” Phys. Rev. Lett.
110
, 188301
(2013
).6.
C. K.
Mishra
, K.
Hima Nagamanasa
, R.
Ganapathy
, A. K.
Sood
, and S.
Gokhale
, “Dynamical facilitation governs glassy dynamics in suspensions of colloidal ellipsoids
,” Proc. Natl. Acad. Sci. U. S. A.
111
(43
), 15362
–15367
(2014
).7.
E.
Zaccarelli
and W. C. K.
Poon
, “Colloidal glasses and gels: The interplay of bonding and caging
,” Proc. Natl. Acad. Sci. U. S. A.
106
(36
), 15203
–15208
(2009
).8.
A.
Latka
, Y.
Han
, A. M.
Alsayed
, A. B.
Schofield
, A. G.
Yodh
, and P.
Habdas
, “Particle dynamics in colloidal suspensions above and below the glass-liquid re-entrance transition
,” Europhys. Lett.
86
(5
), 58001
(2009
).9.
S.
Mandal
, S.
Lang
, M.
Gross
, M.
Oettel
, D.
Raabe
, T.
Franosch
, and F.
Varnik
, “Multiple re-entrant glass transitions in confined hard-sphere glasses
,” Nat. Commun.
5
(1
), 4435
(2014
).10.
Z.
Brown
, M. J.
Iwanicki
, M. D.
Gratale
, X.
Ma
, A. G.
Yodh
, and P.
Habdas
, “Correlated rearrangements of disordered colloidal suspensions in the vicinity of the re-entrant glass transition
,” Europhys. Lett.
115
(6
), 68003
(2016
).11.
W.
Götze
, Complex Dynamics of Glass-Forming Liquids: A Mode-Coupling Theory
(Oxford University Press
, New York
, 2008
).12.
E.
Zaccarelli
, H.
Löwen
, P. P. F.
Wessels
, F.
Sciortino
, P.
Tartaglia
, and C. N.
Likos
, “Is there a re-entrant glass in binary mixtures?
,” Phys. Rev. Lett.
92
, 225703
(2004
).13.
W. R.
Chen
, S. H.
Chen
, and F.
Mallamace
, “Small-angle neutron scattering study of the temperature-dependent attractive interaction in dense L64 copolymer micellar solutions and its relation to kinetic glass transition
,” Phys. Rev. E
66
, 021403
(2002
).14.
S.
Karmakar
, C.
Dasgupta
, and S.
Sastry
, “Short-time beta relaxation in glass-forming liquids is cooperative in nature
,” Phys. Rev. Lett.
116
, 085701
(2016
).15.
K. L.
Ngai
, “Relation between some secondary relaxations and the relaxations in glass-forming materials according to the coupling model
,” J. Chem. Phys.
109
(16
), 6982
–6994
(1998
).16.
C. K.
Mishra
, X.
Ma
, P.
Habdas
, K. B.
Aptowicz
, and A. G.
Yodh
, “Correlations between short- and long-time relaxation in colloidal supercooled liquids and glasses
,” Phys. Rev. E
100
, 020603
(2019
).17.
S.
Asakura
and F.
Oosawa
, “Interaction between particles suspended in solutions of macromolecules
,” J. Polym. Sci.
33
(126
), 183
–192
(1958
).18.
A.
Vrij
, “Polymers at interfaces and the interactions in colloidal dispersions
,” Pure Appl. Chem.
48
(4
), 471
–483
(1976
).19.
Y.
Mao
, M. E.
Cates
, and H. N. W.
Lekkerkerker
, “Depletion stabilization by semidilute rods
,” Phys. Rev. Lett.
75
, 4548
–4551
(1995
).20.
L.-J.
Chen
, S.-Y.
Lin
, C.-C.
Huang
, and E.-M.
Chen
, “Temperature dependence of critical micelle concentration of polyoxyethylenated non-ionic surfactants
,” Colloids Surf., A
135
(1–3
), 175
–181
(1998
).21.
R.
Verma
, J. C.
Crocker
, T. C.
Lubensky
, and A. G.
Yodh
, “Entropic colloidal interactions in concentrated DNA solutions
,” Phys. Rev. Lett.
81
, 4004
–4007
(1998
).22.
J. C.
Crocker
, J. A.
Matteo
, A. D.
Dinsmore
, and A. G.
Yodh
, “Entropic attraction and repulsion in binary colloids probed with a line optical tweezer
,” Phys. Rev. Lett.
82
, 4352
–4355
(1999
).23.
R.
Verma
, J. C.
Crocker
, T. C.
Lubensky
, and A. G.
Yodh
, “Attractions between hard colloidal spheres in semiflexible polymer solutions
,” Macromolecules
33
(1
), 177
–186
(2000
).24.
M.
Piech
and J. Y.
Walz
, “Depletion interactions produced by nonadsorbing charged and uncharged spheroids
,” J. Colloid Interface Sci.
232
(1
), 86
–101
(2000
).25.
K.
Lin
, J. C.
Crocker
, A. C.
Zeri
, and A. G.
Yodh
, “Colloidal interactions in suspensions of rods
,” Phys. Rev. Lett.
87
, 088301
(2001
).26.
M. D.
Gratale
, T.
Still
, C.
Matyas
, Z. S.
Davidson
, S.
Lobel
, P. J.
Collings
, and A. G.
Yodh
, “Tunable depletion potentials driven by shape variation of surfactant micelles
,” Phys. Rev. E
93
, 050601
(2016
).27.
A. D.
Dinsmore
, A. G.
Yodh
, and D. J.
Pine
, “Entropic control of particle motion using passive surface microstructures
,” Nature
383
(6597
), 239
–242
(1996
).28.
P. D.
Kaplan
, J. L.
Rouke
, A. G.
Yodh
, and D. J.
Pine
, “Entropically driven surface phase separation in binary colloidal mixtures
,” Phys. Rev. Lett.
72
, 582
–585
(1994
).29.
A. D.
Dinsmore
, A. G.
Yodh
, and D. J.
Pine
, “Phase diagrams of nearly-hard-sphere binary colloids
,” Phys. Rev. E
52
, 4045
–4057
(1995
).30.
A. D.
Dinsmore
, P. B.
Warren
, W. C. K.
Poon
, and A. G.
Yodh
, “Fluid-solid transitions on walls in binary hard-sphere mixtures
,” Europhys. Lett.
40
(3
), 337
–342
(1997
).31.
A. D.
Dinsmore
, D. T.
Wong
, P.
Nelson
, and A. G.
Yodh
, “Hard spheres in vesicles: Curvature-induced forces and particle-induced curvature
,” Phys. Rev. Lett.
80
, 409
–412
(1998
).32.
K.-h.
Lin
, J. C.
Crocker
, V.
Prasad
, A.
Schofield
, D. A.
Weitz
, T. C.
Lubensky
, and A. G.
Yodh
, “Entropically driven colloidal crystallization on patterned surfaces
,” Phys. Rev. Lett.
85
, 1770
–1773
(2000
).33.
K. A.
Dawson
, “The glass paradigm for colloidal glasses, gels, and other arrested states driven by attractive interactions
,” Curr. Opin. Colloid Interface Sci.
7
(3–4
), 218
–227
(2002
).34.
K. N.
Pham
, S. U.
Egelhaaf
, P. N.
Pusey
, and W. C. K.
Poon
, “Glasses in hard spheres with short-range attraction
,” Phys. Rev. E
69
, 011503
(2004
).35.
H. N. W.
Lekkerkerker
and R.
Tuinier
, Colloids and the Depletion Interaction
(Springer Netherlands
, New York
, 2011
).36.
S.
Buzzaccaro
, R.
Rusconi
, and R.
Piazza
, “‘Sticky’ hard spheres: Equation of state, phase diagram, and metastable gels
,” Phys. Rev. Lett.
99
, 098301
(2007
).37.
M.
Laurati
, G.
Petekidis
, N.
Koumakis
, F.
Cardinaux
, A. B.
Schofield
, J. M.
Brader
, M.
Fuchs
, and S. U.
Egelhaaf
, “Structure, dynamics, and rheology of colloid-polymer mixtures: From liquids to gels
,” J. Chem. Phys.
130
(13
), 134907
(2009
).38.
M.
Laurati
, S. U.
Egelhaaf
, and G.
Petekidis
, “Nonlinear rheology of colloidal gels with intermediate volume fraction
,” J. Rheol.
55
(3
), 673
–706
(2011
).39.
J. C.
Conrad
and J. A.
Lewis
, “Structure of colloidal gels during microchannel flow
,” Langmuir
24
(15
), 7628
–7634
(2008
).40.
R.
Pandey
and J. C.
Conrad
, “Effects of attraction strength on microchannel flow of colloid–polymer depletion mixtures
,” Soft Matter
8
, 10695
–10703
(2012
).41.
M. A.
Lohr
, T.
Still
, R.
Ganti
, M. D.
Gratale
, Z. S.
Davidson
, K. B.
Aptowicz
, C. P.
Goodrich
, D. M.
Sussman
, and A. G.
Yodh
, “Vibrational and structural signatures of the crossover between dense glassy and sparse gel-like attractive colloidal packings
,” Phys. Rev. E
90
, 062305
(2014
).42.
M. D.
Gratale
, X.
Ma
, Z. S.
Davidson
, T.
Still
, P.
Habdas
, and A. G.
Yodh
, “Vibrational properties of quasi-two-dimensional colloidal glasses with varying interparticle attraction
,” Phys. Rev. E
94
, 042606
(2016
).43.
X.
Ma
, J.
Liu
, Y.
Zhang
, P.
Habdas
, and A. G.
Yodh
, “Excess entropy and long-time diffusion in colloidal fluids with short-range interparticle attraction
,” J. Chem. Phys.
150
(14
), 144907
(2019
).44.
J. R.
Savage
, D. W.
Blair
, A. J.
Levine
, R. A.
Guyer
, and A. D.
Dinsmore
, “Imaging the sublimation dynamics of colloidal crystallites
,” Science
314
(5800
), 795
–798
(2006
).45.
D.
Heckendorf
, K. J.
Mutch
, S. U.
Egelhaaf
, and M.
Laurati
, “Size-dependent localization in polydisperse colloidal glasses
,” Phys. Rev. Lett.
119
, 048003
(2017
).46.
X.
Ma
, Z. S.
Davidson
, T.
Still
, R. J. S.
Ivancic
, S. S.
Schoenholz
, A. J.
Liu
, and A. G.
Yodh
, “Heterogeneous activation, local structure, and softness in supercooled colloidal liquids
,” Phys. Rev. Lett.
122
, 028001
(2019
).47.
L. E.
Silbert
, A. J.
Liu
, and S. R.
Nagel
, “Vibrations and diverging length scales near the unjamming transition
,” Phys. Rev. Lett.
95
, 098301
(2005
).48.
A.
Ghosh
, V. K.
Chikkadi
, P.
Schall
, J.
Kurchan
, and D.
Bonn
, “Density of states of colloidal glasses
,” Phys. Rev. Lett.
104
, 248305
(2010
).49.
K.
Chen
, W. G.
Ellenbroek
, Z.
Zhang
, D. T.
Chen
, P. J.
Yunker
, S.
Henkes
, C.
Brito
, O.
Dauchot
, W.
van Saarloos
, A. J.
Liu
, and A. G.
Yodh
, “Low-frequency vibrations of soft colloidal glasses
,” Phys. Rev. Lett.
105
, 025501
(2010
).50.
D.
Kaya
, N. L.
Green
, C. E.
Maloney
, and M. F.
Islam
, “Normal modes and density of states of disordered colloidal solids
,” Science
329
(5992
), 656
–658
(2010
).51.
S.
Henkes
, C.
Brito
, and O.
Dauchot
, “Extracting vibrational modes from fluctuations: A pedagogical discussion
,” Soft Matter
8
, 6092
–6109
(2012
).52.
K.
Chen
, T.
Still
, S.
Schoenholz
, K. B.
Aptowicz
, M.
Schindler
, A. C.
Maggs
, A. J.
Liu
, and A. G.
Yodh
, “Phonons in two-dimensional soft colloidal crystals
,” Phys. Rev. E
88
, 022315
(2013
).53.
T.
Still
, C. P.
Goodrich
, K.
Chen
, P. J.
Yunker
, S.
Schoenholz
, A. J.
Liu
, and A. G.
Yodh
, “Phonon dispersion and elastic moduli of two-dimensional disordered colloidal packings of soft particles with frictional interactions
,” Phys. Rev. E
89
, 012301
(2014
).54.
P. J.
Yunker
, Z.
Zhang
, M.
Gratale
, K.
Chen
, and A. G.
Yodh
, “Relationship between neighbor number and vibrational spectra in disordered colloidal clusters with attractive interactions
,” J. Chem. Phys.
138
(12
), 12A525
(2013
).55.
P.
Keim
, G.
Maret
, U.
Herz
, and H. H.
von Grünberg
, “Harmonic lattice behavior of two-dimensional colloidal crystals
,” Phys. Rev. Lett.
92
, 215504
(2004
).56.
M. D.
Gratale
, P. J.
Yunker
, K.
Chen
, T.
Still
, K. B.
Aptowicz
, and A. G.
Yodh
, “Phonons in two-dimensional colloidal crystals with bond-strength disorder
,” Phys. Rev. E
87
, 052301
(2013
).57.
W.-S.
Wei
, M. A.
Gharbi
, M. A.
Lohr
, T.
Still
, M. D.
Gratale
, T. C.
Lubensky
, K. J.
Stebe
, and A. G.
Yodh
, “Dynamics of ordered colloidal particle monolayers at nematic liquid crystal interfaces
,” Soft Matter
12
, 4715
–4724
(2016
).58.
Y.
Zong
, K.
Chen
, T. G.
Mason
, and K.
Zhao
, “Vibrational modes and dynamic heterogeneity in a near-equilibrium 2D glass of colloidal kites
,” Phys. Rev. Lett.
121
, 228003
(2018
).59.
K.
Chen
, M. L.
Manning
, P. J.
Yunker
, W. G.
Ellenbroek
, Z.
Zhang
, A. J.
Liu
, and A. G.
Yodh
, “Measurement of correlations between low-frequency vibrational modes and particle rearrangements in quasi-two-dimensional colloidal glasses
,” Phys. Rev. Lett.
107
, 108301
(2011
).60.
A.
Ghosh
, V.
Chikkadi
, P.
Schall
, and D.
Bonn
, “Connecting structural relaxation with the low frequency modes in a hard-sphere colloidal glass
,” Phys. Rev. Lett.
107
, 188303
(2011
).61.
T. E.
Angelini
, E.
Hannezo
, X.
Trepat
, M.
Marquez
, J. J.
Fredberg
, and D. A.
Weitz
, “Glass-like dynamics of collective cell migration
,” Proc. Natl. Acad. Sci. U. S. A.
108
(12
), 4714
–4719
(2011
).62.
P.
Das
, H. G. E.
Hentschel
, E.
Lerner
, and I.
Procaccia
, “Robustness of density of low-frequency states in amorphous solids
,” Phys. Rev. B
102
, 014202
(2020
).63.
H.
Shen
, P.
Tan
, and L.
Xu
, “Probing the role of mobility in the collective motion of nonequilibrium systems
,” Phys. Rev. Lett.
116
, 048302
(2016
).64.
A.
Baranyai
and D. J.
Evans
, “Direct entropy calculation from computer simulation of liquids
,” Phys. Rev. A
40
, 3817
–3822
(1989
).65.
H. M.
Ho
, B.
Lin
, and S. A.
Rice
, “Three-particle correlation functions of quasi-two-dimensional one-component and binary colloid suspensions
,” J. Chem. Phys.
125
(18
), 184715
(2006
).66.
A. S.-Y.
Sheu
and S. A.
Rice
, “Transient ordering in a quasi-two-dimensional binary liquid near freezing
,” J. Chem. Phys.
129
(12
), 124511
(2008
).67.
B.
Illing
, S.
Fritschi
, H.
Kaiser
, C. L.
Klix
, G.
Maret
, and P.
Keim
, “Mermin–Wagner fluctuations in 2D amorphous solids
,” Proc. Natl. Acad. Sci. U. S. A.
114
(8
), 1856
–1861
(2017
).68.
S.
Vivek
, C. P.
Kelleher
, P. M.
Chaikin
, and E. R.
Weeks
, “Long-wavelength fluctuations and the glass transition in two dimensions and three dimensions
,” Proc. Natl. Acad. Sci. U. S. A.
114
(8
), 1850
–1855
(2017
).69.
Y. N.
Ohshima
and I.
Nishio
, “Colloidal crystal: Bead–spring lattice immersed in viscous media
,” J. Chem. Phys.
114
(19
), 8649
–8658
(2001
).70.
C.
Brito
and M.
Wyart
, “Geometric interpretation of previtrification in hard sphere liquids
,” J. Chem. Phys.
131
(2
), 024504
(2009
).71.
E.
Burkel
, “Phonon spectroscopy by inelastic x-ray scattering
,” Rep. Prog. Phys.
63
(2
), 171
–232
(2000
).72.
S.
Hosokawa
, M.
Inui
, Y.
Kajihara
, K.
Matsuda
, T.
Ichitsubo
, W.-C.
Pilgrim
, H.
Sinn
, L. E.
González
, D. J.
González
, S.
Tsutsui
, and A. Q. R.
Baron
, “Transverse acoustic excitations in liquid Ga
,” Phys. Rev. Lett.
102
, 105502
(2009
).73.
V. M.
Giordano
and G.
Monaco
, “Fingerprints of order and disorder on the high-frequency dynamics of liquids
,” Proc. Natl. Acad. Sci. U. S. A.
107
(51
), 21985
–21989
(2010
).74.
K.
Trachenko
and V. V.
Brazhkin
, “Collective modes and thermodynamics of the liquid state
,” Rep. Prog. Phys.
79
(1
), 016502
(2015
).75.
M.
Schindler
and A. C.
Maggs
, “Truncated correlations in video microscopy of colloidal solids
,” Soft Matter
8
, 3864
–3874
(2012
).76.
M. L.
Manning
and A. J.
Liu
, “Vibrational modes identify soft spots in a sheared disordered packing
,” Phys. Rev. Lett.
107
, 108302
(2011
).77.
J.
Rottler
, S. S.
Schoenholz
, and A. J.
Liu
, “Predicting plasticity with soft vibrational modes: From dislocations to glasses
,” Phys. Rev. E
89
, 042304
(2014
).78.
M.
Mosayebi
, P.
Ilg
, A.
Widmer-Cooper
, and E.
Del Gado
, “Soft modes and nonaffine rearrangements in the inherent structures of supercooled liquids
,” Phys. Rev. Lett.
112
, 105503
(2014
).79.
H.
Tong
and N.
Xu
, “Order parameter for structural heterogeneity in disordered solids
,” Phys. Rev. E
90
, 010401
(2014
).80.
H.
Tong
, H.
Hu
, P.
Tan
, N.
Xu
, and H.
Tanaka
, “Revealing inherent structural characteristics of jammed particulate packings
,” Phys. Rev. Lett.
122
, 215502
(2019
).81.
X.
Yang
, H.
Tong
, W.-H.
Wang
, and K.
Chen
, “Emergence and percolation of rigid domains during the colloidal glass transition
,” Phys. Rev. E
99
, 062610
(2019
).© 2021 Author(s). Published under an exclusive license by AIP Publishing.
2021
Author(s)
You do not currently have access to this content.
