Attractive colloidal glasses are unique as their dynamical arrest is a combination of entropic crowding effects and energetic bonds formation. When such systems are subjected to flow, their dynamics are activated in a way which differs from hard-sphere glasses that melt through a “convective cage release mechanism.” Here, we investigate the microscopic dynamics by measuring the relaxation spectrum during flow using orthogonal superposition rheometry. A small amplitude oscillatory strain is imposed perpendicularly to a steady shear flow, and superposition moduli are measured. Brownian dynamic simulations are utilized complementary to extract the moduli from mean-squared displacements using the generalized Stokes–Einstein relation. At low Péclet number, a crossover frequency between elastic and viscous moduli is detected, representing the relaxation time associated with shear-induced particles escape from their frustration (localization) under flow. For the repulsive glass, this is related to shear-induced cage renewal of particles. For attractive glasses, however, when particles escape their localized length (bonds), they move with no further hindrance with the escape time, which is independent of attraction strength and interestingly faster than that in the repulsive glass. This is attributed to particle localization at shorter length scales due to bonding. At high Péclet, a second low frequency crossover is observed and a low frequency elastic dominated response emerges. This elastic response may originate from slow relaxation of hydroclusters or be a consequence of more intricate nature of superposition moduli. At high frequencies, both orthogonal moduli increase relative to quiescent state due to shear-induced cage deformation, which slows down in-cage dynamics.

1.
Larson
,
R. G.
,
The Structure and Rheology of Complex Fluids
(
Oxford University
,
New York
,
1999
), Vol. 150.
2.
Pusey
,
P. N.
, and
W.
Van Megen
, “
Phase behaviour of concentrated suspensions of nearly hard colloidal spheres
,”
Nature
320
(
6060
),
340
342
(
1986
).
3.
Poon
,
W.
, “
Colloids as big atoms
,”
Science
304
,
830
831
(
2004
).
4.
Pusey
,
P. N.
, and
W.
van Megen
, “
Observation of a glass transition in suspensions of spherical colloidal particles
,”
Phys. Rev. Lett.
59
(
18
),
2083
2086
(
1987
).
5.
Brambilla
,
G.
,
D.
El Masri
,
M.
Pierno
,
L.
Berthier
,
L.
Cipelletti
,
G.
Petekidis
, and
A. B.
Schofield
, “
Probing the equilibrium dynamics of colloidal hard spheres above the mode-coupling glass transition
,”
Phys. Rev. Lett.
102
(
8
),
085703
(
2009
).
6.
Pusey
,
P.
,
E.
Zaccarelli
,
C.
Valeriani
,
E.
Sanz
,
W. C.
Poon
, and
M. E.
Cates
, “
Hard spheres: Crystallization and glass formation
,”
Phil. Trans. R. Soc. Lond. A
367
(
1909
),
4993
5011
(
2009
).
7.
Weeks
,
E. R.
,
J. C.
Crocker
,
A. C.
Levitt
,
A.
Schofield
, and
D. A.
Weitz
, “
Three-dimensional direct imaging of structural relaxation near the colloidal glass transition
,”
Science
287
(
5453
),
627
631
(
2000
).
8.
Lu
,
P. J.
,
E.
Zaccarelli
,
F.
Ciulla
,
A. B.
Schofield
,
F.
Sciortino
, and
D. A.
Weitz
, “
Gelation of particles with short-range attraction
,”
Nature
453
(
7194
),
499
503
(
2008
).
9.
Laurati
,
M.
,
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
).
10.
Tsurusawa
,
H.
,
J.
Russo
,
M.
Leocmach
, and
H.
Tanaka
, “
Formation of porous crystals via viscoelastic phase separation
,”
Nat. Mater.
16
(
10
),
1022
1028
(
2017
).
11.
Koumakis
,
N.
,
J. F.
Brady
, and
G.
Petekidis
, “
Complex oscillatory yielding of model hard-sphere glasses
,”
Phys. Rev. Lett.
110
,
178301
(
2013
).
12.
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
).
13.
Koumakis
,
N.
,
M.
Laurati
,
A.
Jacob
,
K.
Mutch
,
A.
Abdellali
,
A.
Schofield
,
S.
Egelhaaf
,
J.
Brady
, and
G.
Petekidis
, “
Start-up shear of concentrated colloidal hard spheres: Stresses, dynamics, and structure
,”
J. Rheol.
60
(
4
),
603
623
(
2016
).
14.
Ballesta
,
P.
,
R.
Besseling
,
L.
Isa
,
G.
Petekidis
, and
W. C. K.
Poon
, “
Slip and flow of hard-sphere colloidal glasses
,”
Phys. Rev. Lett.
101
,
258301
(
2008
).
15.
Ballesta
,
P.
,
N.
Koumakis
,
R.
Besseling
,
W. C. K.
Poon
, and
G.
Petekidis
, “
Slip of gels in colloid-polymer mixtures under shear
,”
Soft Matter
9
,
3237
3245
(
2013
).
16.
Besseling
,
R.
,
L.
Isa
,
P.
Ballesta
,
G.
Petekidis
,
M. E.
Cates
, and
W. C. K.
Poon
, “
Shear banding and flow-concentration coupling in colloidal glasses
,”
Phys. Rev. Lett.
105
,
268301
(
2010
).
17.
Ballauff
,
M.
,
J. M.
Brader
,
S. U.
Egelhaaf
,
M.
Fuchs
,
J.
Horbach
,
N.
Koumakis
,
M.
Krüger
,
M.
Laurati
,
K. J.
Mutch
,
G.
Petekidis
,
M.
Siebenbürger
,
T.
Voigtmann
, and
J.
Zausch
, “
Residual stresses in glasses
,”
Phys. Rev. Lett.
110
,
215701
(
2013
).
18.
Moghimi
,
E.
,
A. R.
Jacob
, and
G.
Petekidis
, “
Residual stresses in colloidal gels
,”
Soft Matter
13
(
43
),
7824
7833
(
2017
).
19.
Van Megen
,
W.
,
T.
Mortensen
,
S.
Williams
, and
J.
Müller
, “
Measurement of the self-intermediate scattering function of suspensions of hard spherical particles near the glass transition
,”
Phys. Rev. E
58
(
5
),
6073
6085
(
1998
).
20.
Van Megen
,
W.
, and
S.
Underwood
, “
Glass transition in colloidal hard spheres: Mode-coupling theory analysis
,”
Phys. Rev. Lett.
70
(
18
),
2766
2769
(
1993
).
21.
Kobelev
,
V.
, and
K. S.
Schweizer
, “
Strain softening, yielding, and shear thinning in glassy colloidal suspensions
,”
Phys. Rev. E
71
(
2
),
021401
(
2005
).
22.
Pham
,
K. N.
,
A. M.
Puertas
,
J.
Bergenholtz
,
S. U.
Egelhaaf
,
A.
Moussaıd
,
P. N.
Pusey
,
A. B.
Schofield
,
M. E.
Cates
,
M.
Fuchs
, and
W. C.
Poon
, “
Multiple glassy states in a simple model system
,”
Science
296
(
5565
),
104
106
(
2002
).
23.
Pham
,
K.
,
S.
Egelhaaf
,
P.
Pusey
, and
W. C.
Poon
, “
Glasses in hard spheres with short-range attraction
,”
Phys. Rev. E
69
(
1
),
011503
(
2004
).
24.
Eckert
,
T.
, and
E.
Bartsch
, “
Re-entrant glass transition in a colloid-polymer mixture with depletion attractions
,”
Phys. Rev. Lett.
89
(
12
),
125701
(
2002
).
25.
Willenbacher
,
N.
,
J. S.
Vesaratchanon
,
O.
Thorwarth
, and
E.
Bartsch
, “
An alternative route to highly concentrated, freely flowing colloidal dispersions
,”
Soft Matter
7
(
12
),
5777
5788
(
2011
).
26.
Jacob
,
A. R.
,
A. S.
Poulos
,
S.
Kim
,
J.
Vermant
, and
G.
Petekidis
, “
Convective cage release in model colloidal glasses
,”
Phys. Rev. Lett.
115
(
21
),
218301
(
2015
).
27.
Simmons
,
J.
, “
A servo-controlled rheometer for measurement of the dynamic modulus of viscoelastic liquids
,”
J. Sci. Instrum.
43
(
12
),
887
892
(
1966
).
28.
Tanner
,
R.
, “
Comparative studies of some simple viscoelastic theories
,”
Trans. Soc. Rheol.
12
(
1
),
155
182
(
1968
).
29.
Mewis
,
J.
, and
G.
Schoukens
, “
Mechanical spectroscopy of colloidal dispersions
,”
Faraday Discuss. Chem. Soc.
65
,
58
64
(
1978
).
30.
Zeegers
,
J.
,
D.
van den Ende
,
C.
Blom
,
E. G.
Altena
,
G. J.
Beukema
, and
J.
Mellema
, “
A sensitive dynamic viscometer for measuring the complex shear modulus in a steady shear flow using the method of orthogonal superposition
,”
Rheol. Acta
34
(
6
),
606
621
(
1995
).
31.
Vermant
,
J.
,
P.
Moldenaers
,
J.
Mewis
,
M.
Ellis
, and
R.
Garritano
, “
Orthogonal superposition measurements using a rheometer equipped with a force rebalanced transducer
,”
Rev. Sci. Instrum.
68
(
11
),
4090
4096
(
1997
).
32.
Vermant
,
J.
,
L.
Walker
,
P.
Moldenaers
, and
J.
Mewis
, “
Orthogonal versus parallel superposition measurements1
,”
J. Nonnewton. Fluid Mech.
79
(
2–3
),
173
189
(
1998
).
33.
Kim
,
S.
,
J.
Mewis
,
C.
Clasen
, and
J.
Vermant
, “
Superposition rheometry of a wormlike micellar fluid
,”
Rheol. Acta
52
(
8–9
),
727
740
(
2013
).
34.
Colombo
,
G.
,
S.
Kim
,
T.
Schweizer
,
B.
Schroyen
,
C.
Clasen
,
J.
Mewis
, and
J.
Vermant
, “
Superposition rheology and anisotropy in rheological properties of sheared colloidal gels
,”
J. Rheol.
61
(
5
),
1035
1048
(
2017
).
35.
Sung
,
S. H.
,
S.
Kim
,
J.
Hendricks
,
C.
Clasen
, and
K. H.
Ahn
, “
Orthogonal superposition rheometry of colloidal gels: Time-shear rate superposition
,”
Soft Matter
14
,
8651
8659
(
2018
).
36.
Lin
,
N. Y.
,
C.
Ness
,
M. E.
Cates
,
J.
Sun
, and
I.
Cohen
, “
Tunable shear thickening in suspensions
,”
Proc. Natl. Acad. Sci. U.S.A.
113
(
39
),
10774
10778
(
2016
).
37.
Asakura
,
S.
, and
F.
Oosawa
, “
On interaction between two bodies immersed in a solution of macromolecules
,”
J. Chem. Phys.
22
,
1255
1256
(
1954
).
38.
Aarts
,
D.
,
R.
Tuinier
, and
H.
Lekkerkerker
, “
Phase behaviour of mixtures of colloidal spheres and excluded-volume polymer chains
,”
J. Phys. Condens. Matter
14
(
33
),
7551
7561
(
2002
).
39.
Fleer
,
G. J.
, and
R.
Tuinier
, “
Analytical phase diagram for colloid-polymer mixtures
,”
Phys. Rev. E
76
(
4
),
041802
(
2007
).
40.
Ballesta
,
P.
, and
G.
Petekidis
, “
Creep and aging of hard-sphere glasses under constant stress
,”
Phys. Rev. E
93
,
042613
(
2016
).
41.
Koumakis
,
N.
,
E.
Moghimi
,
R.
Besseling
,
W. C.
Poon
,
J. F.
Brady
, and
G.
Petekidis
, “
Tuning colloidal gels by shear
,”
Soft Matter
11
(
23
),
4640
4648
(
2015
).
42.
Moghimi
,
E.
,
A. R.
Jacob
,
N.
Koumakis
, and
G.
Petekidis
, “
Colloidal gels tuned by oscillatory shear
,”
Soft Matter
13
(
12
),
2371
2383
(
2017
).
43.
Heyes
,
D.
, and
J.
Melrose
, “
Brownian dynamics simulations of model hard-sphere suspensions
,”
J. Nonnewton. Fluid Mech.
46
(
1
),
1
28
(
1993
).
44.
Foss
,
D. R.
, and
J. F.
Brady
, “
Brownian dynamics simulation of hard-sphere colloidal dispersions
,”
J. Rheol.
44
(
3
),
629
651
(
2000
).
45.
Sierou
,
A.
, and
J. F.
Brady
, “
Accelerated Stokesian dynamics simulations
,”
J. Fluid Mech.
448
,
115
146
(
2001
).
46.
Cheng
,
X.
,
J. H.
McCoy
,
J. N.
Israelachvili
, and
I.
Cohen
, “
Imaging the microscopic structure of shear thinning and thickening colloidal suspensions
,”
Science
333
(
6047
),
1276
1279
(
2011
).
47.
Foss
,
D. R.
, and
J. F.
Brady
, “
Structure, diffusion and rheology of Brownian suspensions by Stokesian dynamics simulation
,”
J. Fluid Mech.
407
,
167
200
(
2000
).
48.
Wagner
,
N. J.
, and
J. F.
Brady
, “
Shear thickening in colloidal dispersions
,”
Phys. Today
62
(
10
),
27
32
(
2009
).
49.
Hsiao
,
L. C.
,
S.
Jamali
,
E.
Glynos
,
P. F.
Green
,
R. G.
Larson
, and
M. J.
Solomon
, “
Rheological state diagrams for rough colloids in shear flow
,”
Phys. Rev. Lett.
119
(
15
),
158001
(
2017
).
50.
Koumakis
,
N.
,
A.
Pamvouxoglou
,
A.
Poulos
, and
G.
Petekidis
, “
Direct comparison of the rheology of model hard and soft particle glasses
,”
Soft Matter
8
(
15
),
4271
4284
(
2012
).
51.
Lindemann
,
F. A.
, “
Ueber die berechnung molekularer eigenfrequenzen
,”
Phys. Z.
11
,
609
612
(
1910
).
52.
Priya
,
M.
, and
T.
Voigtmann
, “
Nonlinear rheology of dense colloidal systems with short-ranged attraction: A mode-coupling theory analysis
,”
J. Rheol.
58
(
5
),
1163
1187
(
2014
).
53.
Amann
,
C. P.
, and
M.
Fuchs
, “
Transient stress evolution in repulsion and attraction dominated glasses
,”
J. Rheol.
58
(
5
),
1191
1217
(
2014
).
54.
Sciortino
,
F.
, “
Disordered materials: One liquid, two glasses
,”
Nat. Mater.
1
(
3
),
145
156
(
2002
).
55.
Pham
,
K.
,
G.
Petekidis
,
D.
Vlassopoulos
,
S.
Egelhaaf
,
W.
Poon
, and
P.
Pusey
, “
Yielding behavior of repulsion-and attraction-dominated colloidal glasses
,”
J. Rheol.
52
(
2
),
649
676
(
2008
).
56.
Mason
,
T. G.
, “
Estimating the viscoelastic moduli of complex fluids using the generalized Stokes–Einstein equation
,”
Rheol. Acta
39
(
4
),
371
378
(
2000
).
57.
Sentjabrskaja
,
T.
,
E.
Babaliari
,
J.
Hendricks
,
M.
Laurati
,
G.
Petekidis
, and
S. U.
Egelhaaf
, “
Yielding of binary colloidal glasses
,”
Soft Matter
9
(
17
),
4524
4533
(
2013
).
58.
Jacob
,
A. R.
,
Yielding and particle rearrangements in hard sphere glasses
, Ph.D. thesis,
Department of Materials Science and Technology, University of Crete
,
2016
.
59.
Metri
,
V.
, and
W.
Briels
, “
Brownian dynamics investigation of the boltzmann superposition principle for orthogonal superposition rheology
,”
J. Chem. Phys.
150
(
1
),
014903
(
2019
).
60.
See the supplementary material at https://doi.org/10.1122/1.5080717 for information on the aging of colloidal glasses, determination of the limit of linear response regime both at quiescent state and under shear, DFS results without normalizing the frequency and shear rate, the horizontal and vertical shift factors used to build the time-shear rate superposition curves, the DFS for various attraction strengths from BD simulations, and finally, the long-time diffusivity for various attraction strengths.

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