Rheological measurements typically require at least 20–50 mg of sample. We set up a miniaturized sliding-plates shear rheometer (mgRheo) that requires only 2 mg sample or even less. We designed a flexure-based force-sensing device that could measure force ranging from the micronewton to millinewton scale, e.g., 40 μN–400 mN for one particular spring constant. The setup was strain-controlled by a piezostage and could perform standard rheological tests such as small amplitude oscillatory shear, step strain, and stress relaxation. The accuracy and consistencies were evaluated on polydimethylsiloxane viscoelastic standard, entangled poly(hexyl methacrylate), and polystyrene. The obtained phase angles quantitatively agreed with those from commercial rheometers. The exact values of the modulus are prone to the overfilling of the sample. The storage G′ and loss G″ moduli from the mgRheo were systematically higher than those from commercial rheometers (i.e., within 5% with careful trimming or 30% with excessive overfilling). Between 102 and 106 Pa, G′ and G″ were in good agreement with commercial rheometers. Such a setup allowed for general rheometric characterizations, especially obtaining linear viscoelasticity on soft matters that are synthetically difficult to obtain in a large quantity.

1.
R. F.
Garritano
,
Compensated rheometer
, US Patent No. 4,501,155 (
1985
).
2.
R. F.
Garritano
,
Apparatus and method for measuring viscoelastic properties of materials
, US Patent No. 4,601,195 (
1986
).
3.
G.
Raffer
,
Rotary viscometer with an air bearing
, US Patent No. 616,775,2B1 (
2001
).
4.
R. F.
Garritano
,
J. P.
Berting
, and
P. G.
Mode
,
Wide range dynamic rheometer
, US Patent No. 00693,191,5B2 (
2005
).
5.
Zhou
,
J.
,
J.
Yang
,
M. W.
Ishaq
, and
L.
Li
, “
Study of linear and cyclic graft polystyrenes with identical backbone contour in dilute solutions: Preparation, characterization, and conformational properties
,”
Macromolecules
55
,
1398
1411
(
2022
).
6.
Pan
,
X.
,
M.
Ding
, and
L.
Li
, “
Experimental validation on average conformation of a comblike polystyrene library in dilute solutions: Universal scaling laws and abnormal SEC elution behavior
,”
Macromolecules
54
,
11019
11031
(
2021
).
7.
Mo
,
J.
,
J.
Wang
,
Z.
Wang
,
Y.
Lu
, and
L.
An
, “
Size and dynamics of a tracer ring polymer embedded in a linear polymer chain melt matrix
,”
Macromolecules
55
,
1505
1514
(
2022
).
8.
Parisi
,
D.
,
M.
Kaliva
,
S.
Costanzo
,
Q.
Huang
,
P. J.
Lutz
,
J.
Ahn
,
T.
Chang
,
M.
Rubinstein
, and
D.
Vlassopoulos
, “
Nonlinear rheometry of entangled polymeric rings and ring-linear blends
,”
J. Rheol.
65
,
695
711
(
2021
).
9.
Huang
,
Q.
,
J.
Ahn
,
D.
Parisi
,
T.
Chang
,
O.
Hassager
,
S.
Panyukov
,
M.
Rubinstein
, and
D.
Vlassopoulos
, “
Unexpected stretching of entangled ring macromolecules
,”
Phys. Rev. Lett.
122
,
208001
(
2019
).
10.
Wang
,
Z.
,
Q.
Zhai
,
W.
Chen
,
X.
Wang
,
Y.
Lu
, and
L.
An
, “
Mechanism of nonmonotonic increase in polymer size: Comparison between linear and ring chains at high shear rates
,”
Macromolecules
52
,
8144
8154
(
2019
).
11.
Chen
,
T.
,
H. Y.
Zhao
,
R.
Shi
,
W. F.
Lin
,
X. M.
Jia
,
H. J.
Qian
,
Z. Y.
Lu
,
X. X.
Zhang
,
Y. K.
Li
, and
Z. Y.
Sun
, “
An unexpected N-dependence in the viscosity reduction in all-polymer nanocomposite
,”
Nat. Commun.
10
,
5552
(
2019
).
12.
Lo Verso
,
F.
,
J. A.
Pomposo
,
J.
Colmenero
, and
A. J.
Moreno
, “
Tunable slow dynamics in a new class of soft colloids
,”
Soft Matter
12
,
9039
9046
(
2016
).
13.
Tuteja
,
A.
,
M. E.
Mackay
,
C. J.
Hawker
,
B.
Van Horn
, and
D. L.
Ho
, “
Molecular architecture and rheological characterization of novel intramolecularly crosslinked polystyrene nanoparticles
,”
J. Polym. Sci., Part B: Polym. Phys.
44
,
1930
1947
(
2006
).
14.
Zhu
,
Y.
,
J.
Luo
,
Q.
Zou
,
X.
Ouyang
,
Y.
Ruan
,
Y.
Liu
, and
G.
Liu
, “
Glassy feature in melts of 3-dimensional architectured polymer blends
,”
Polymer
238
,
124336
(
2022
).
15.
Zhang
,
W. B.
, and
S. Z. D.
Cheng
, “
Giant is different: Size effects and the nature of macromolecules
,”
Giant
1
,
100011
(
2020
).
16.
Liu
,
G.
,
X.
Feng
,
K.
Lang
,
R.
Zhang
,
D.
Guo
,
S.
Yang
, and
S. Z. D.
Cheng
, “
Dynamics of shape-persistent giant molecules: Zimm-like melt, elastic plateau, and cooperative glass-like
,”
Macromolecules
50
,
6637
6646
(
2017
).
17.
Erni
,
P.
,
M.
Varagnat
,
C.
Clasen
,
J.
Crest
, and
G. H.
McKinley
, “
Microrheometry of sub-nanolitre biopolymer samples: Non-Newtonian flow phenomena of carnivorous plant mucilage
,”
Soft Matter
7
,
10889
10898
(
2011
).
18.
Christopher
,
G. F.
,
J. M.
Yoo
,
N.
Dagalakis
,
S. D.
Hudson
, and
K. B.
Migler
, “
Development of a MEMS based dynamic rheometer
,”
Lab Chip
10
,
2749
2757
(
2010
).
19.
Braithwaite
,
G. J. C.
, and
G. H.
McKinley
, “
Microrheometry for studying the rheology and dynamics of polymers near interfaces
,”
Appl. Rheol.
9
,
27
33
(
1999
).
20.
Dealy
,
J. M.
, and
A. J.
Giacomin
, in
Rheological Measurement
, edited by
A. A.
Collyer
and
D. W.
Clegg
(
Springer
,
The Netherlands
,
1998
), pp.
237
259
.
21.
Mackay
,
M. E.
, in
Rheological Measurement
, edited by
A. A.
Collyer
and
D. W.
Clegg
(
Springer
,
The Netherlands
,
1998
), pp.
635
665
.
22.
Furst
,
E. M.
, and
T. M.
Squires
,
Microrheology
(
Oxford University
, Oxford,
2017
).
23.
Waigh
,
T. A.
, “
Microrheology of complex fluids
,”
Rep. Prog. Phys.
68
,
685
742
(
2005
).
24.
Chen
,
D. T.
,
E. R.
Weeks
,
J. C.
Crocker
,
M. F.
Islam
,
R.
Verma
,
J.
Gruber
,
A. J.
Levine
,
T. C.
Lubensky
, and
A. G.
Yodh
, “
Rheological microscopy: Local mechanical properties from microrheology
,”
Phys. Rev. Lett.
90
,
108301
(
2003
).
25.
Mason
,
T. G.
, “
Estimating the viscoelastic moduli of complex fluids using the generalized Stokes–Einstein equation
,”
Rheol. Acta
39
,
371
378
(
2000
).
26.
Mason
,
T. G.
,
K.
Ganesan
,
J. H.
van Zanten
,
D.
Wirtz
, and
S. C.
Kuo
, “
Particle tracking microrheology of complex fluids
,”
Phys. Rev. Lett.
79
,
3282
3285
(
1997
).
27.
Mason
,
T. G.
, and
D. A.
Weitz
, “
Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids
,”
Phys. Rev. Lett.
74
,
1250
1253
(
1995
).
28.
Tassieri
,
M.
, “
Linear microrheology with optical tweezers of living cells ‘is not an option'!
,”
Soft Matter
11
,
5792
5798
(
2015
).
29.
Bayles
,
A. V.
,
T. M.
Squires
, and
M. E.
Helgeson
, “
Dark-field differential dynamic microscopy
,”
Soft Matter
12
,
2440
2452
(
2016
).
30.
Kőkuti
,
Z.
,
K. v.
Gruijthuijsen
,
M.
Jenei
,
G.
Tóth-Molnár
,
A.
Czirják
,
J.
Kokavecz
,
P.
Ailer
,
L.
Palkovics
,
A. C.
Völker
, and
G.
Szabó
, “
High-frequency rheology of a high viscosity silicone Oil using diffusing wave spectroscopy
,”
Appl. Rheol.
24
,
32
38
(
2014
).
31.
Cerbino
,
R.
, and
V.
Trappe
, “
Differential dynamic microscopy: Probing wave vector dependent dynamics with a microscope
,”
Phys. Rev. Lett.
100
,
188102
(
2008
).
32.
Pine
,
D. J.
,
D. A.
Weitz
,
P. M.
Chaikin
, and
E.
Herbolzheimer
, “
Diffusing wave spectroscopy
,”
Phys. Rev. Lett.
60
,
1134
1137
(
1988
).
33.
Robertson-Anderson
,
R. M.
, “
Optical tweezers microrheology: From the basics to advanced techniques and applications
,”
ACS Macro Lett.
7
,
968
975
(
2018
).
34.
Lin
,
J.
, and
M. T.
Valentine
, “
High-force NdFeB-based magnetic tweezers device optimized for microrheology experiments
,”
Rev. Sci. Instrum.
83
,
053905
(
2012
).
35.
Killgore
,
J. P.
,
D. G.
Yablon
,
A. H.
Tsou
,
A.
Gannepalli
,
P. A.
Yuya
,
J. A.
Turner
,
R.
Proksch
, and
D. C.
Hurley
, “
Viscoelastic property mapping with contact resonance force microscopy
,”
Langmuir
27
,
13983
13987
(
2011
).
36.
Yuya
,
P. A.
,
D. C.
Hurley
, and
J. A.
Turner
, “
Relationship between Q-factor and sample damping for contact resonance atomic force microscope measurement of viscoelastic properties
,”
J. Appl. Phys.
109
,
113528
(
2011
).
37.
Hurley
,
D. C.
,
S. E.
Campbell
,
J. P.
Killgore
,
L. M.
Cox
, and
Y.
Ding
, “
Measurement of viscoelastic loss tangent with contact resonance modes of atomic force microscopy
,”
Macromolecules
46
,
9396
9402
(
2013
).
38.
Martinez-Torres
,
C.
,
A.
Arneodo
,
L.
Streppa
,
P.
Argoul
, and
F.
Argoul
, “
Passive microrheology of soft materials with atomic force microscopy: A wavelet-based spectral analysis
,”
Appl. Phys. Lett.
108
,
034102
(
2016
).
39.
Dokukin
,
M. E.
, and
I.
Sokolov
, “
Quantitative mapping of the elastic modulus of soft materials with HarmoniX and PeakForce QNM AFM modes
,”
Langmuir
28
,
16060
16071
(
2012
).
40.
Pethrick
,
R. A.
, in
Rheological Measurement
, edited by
A. A.
Collyer
and
D. W.
Clegg
(
Springer
,
The Netherlands
,
1998
), pp.
99
137
.
41.
Iannuzzi
,
D.
,
K.
Heeck
,
M.
Slaman
,
S.
de Man
,
J. H.
Rector
,
H.
Schreuders
,
J. W.
Berenschot
,
V. J.
Gadgil
,
R. G. P.
Sanders
,
M. C.
Elwenspoek
, and
S.
Deladi
, “
Fibre-top cantilevers: Design, fabrication and applications
,”
Meas. Sci. Technol.
18
,
3247
3252
(
2007
).
42.
Beekmans
,
S. V.
, and
D.
Iannuzzi
, “
A metrological approach for the calibration of force transducers with interferometric readout
,”
Surf. Topogr.: Metrol. Prop.
3
,
025004
(
2015
).
43.
Y. Oh, M. R. Wilson, R.C. Major, S. A. S. Asif, and O.L. Warren, US8738315B2 (27 May 2014); available at https://patents.google.com/patent/US8738315B2/en.
44.
Ribotta
,
R.
, and
G.
Durand
, “
Mechanical instabilities of smectic-A liquid crystals under dilative or compressive stresses
,”
J. Phys.
38
,
179
204
(
1977
).
45.
Yamamoto
,
J.
,
H.
Nakamura
, and
K.
Okano
, “
Apparatus for measurement of complex shear modulus of liquid crystals at Low frequencies
,”
Jpn. J. Appl. Phys.
26
,
29
–31 (
1987
).
46.
Kirschenmann
,
L.
, and
W.
Pechhold
, “
Piezoelectric rotary vibrator (PRV) – a new oscillating rheometer for linear viscoelasticity
,”
Rheol. Acta
41
,
362
368
(
2002
).
47.
Willenbacher
,
N.
, and
C.
Oelschlaeger
, “
Dynamics and structure of complex fluids from high frequency mechanical and optical rheometry
,”
Curr. Opin. Colloid Interface Sci.
12
,
43
49
(
2007
).
48.
Schroyen
,
B.
,
D.
Vlassopoulos
,
P.
Van Puyvelde
, and
J.
Vermant
, “
Bulk rheometry at high frequencies: A review of experimental approaches
,”
Rheol. Acta
59
,
1
22
(
2020
).
49.
Roth
,
M.
,
M.
D’Acunzi
,
D.
Vollmer
, and
G. K.
Auernhammer
, “
Viscoelastic rheology of colloid-liquid crystal composites
,”
J. Chem. Phys.
132
,
124702
(
2010
).
50.
Schroyen
,
B.
,
J. W.
Swan
,
P.
Van Puyvelde
, and
J.
Vermant
, “
Quantifying the dispersion quality of partially aggregated colloidal dispersions by high frequency rheology
,”
Soft Matter
13
,
7897
7906
(
2017
).
51.
Clasen
,
C.
,
B. P.
Gearing
, and
G. H.
McKinley
, “
The flexure-based microgap rheometer (FMR)
,”
J. Rheol.
50
,
883
905
(
2006
).
52.
Clasen
,
C.
, and
G. H.
McKinley
, “
Gap-dependent microrheometry of complex liquids
,”
J. Non-Newtonian Fluid Mech.
124
,
1
10
(
2004
).
53.
Kojic
,
N.
,
J.
Bico
,
C.
Clasen
, and
G. H.
McKinley
, “
Ex vivo rheology of spider silk
,”
J. Exp. Biol.
209
,
4355
4362
(
2006
).
54.
Baik
,
S. J.
,
P.
Moldenaers
, and
C.
Clasen
, “
A sliding plate microgap rheometer for the simultaneous measurement of shear stress and first Normal stress difference
,”
Rev. Sci. Instrum.
82
,
035121
(
2011
).
55.
George
,
B.
,
Z.
Tan
, and
S.
Nihtianov
, “
Advances in capacitive, eddy current, and magnetic displacement sensors and corresponding interfaces
,”
IEEE Trans. Ind. Electron.
64
,
9595
9607
(
2017
).
56.
Wierschem
,
A.
, and
H.
Dakhil
, “
Measuring Low viscosities and high shear rates with a rotational rheometer in a thin-gap parallel-disk configuration
,”
Appl. Rheol.
24
,
26
31
(
2014
).
57.
Cheng
,
X.
,
J. H.
McCoy
,
J. N.
Israelachvili
, and
I.
Cohen
, “
Imaging the microscopic structure of shear thinning and thickening colloidal suspensions
,”
Science
333
,
1276
1279
(
2011
).
58.
Lin
,
N. Y. C.
,
J. H.
McCoy
,
X.
Cheng
,
B.
Leahy
,
J. N.
Israelachvili
, and
I.
Cohen
, “
A multi-axis confocal rheoscope for studying shear flow of structured fluids
,”
Rev. Sci. Instrum.
85
,
033905
(
2014
).
59.
Lin
,
N. Y. C.
,
X.
Cheng
, and
I.
Cohen
, “
Biaxial shear of confined colloidal hard spheres: The structure and rheology of the vorticity-aligned string phase
,”
Soft Matter
10
,
1969
1976
(
2014
).
60.
Ramaswamy
,
M.
,
N. Y. C.
Lin
,
B. D.
Leahy
,
C.
Ness
,
A. M.
Fiore
,
J. W.
Swan
, and
I.
Cohen
, “
How confinement-induced structures alter the contribution of hydrodynamic and short-ranged repulsion forces to the viscosity of colloidal suspensions
,”
Phys. Rev. X
7
,
041005
(
2017
).
61.
Granick
,
S.
, and
H.-W.
Hu
, “
Nanorheology of confined polymer melts. 1. Linear shear response at strongly adsorbing surfaces
,”
Langmuir
10
,
3857
3866
(
1994
).
62.
Kolitawong
,
C.
, and
A.
Giacomin
, “
Sliding plate rheometer and its applications
,”
J. KMUTNB
19
,
109
115
(
2009
).
63.
Giacomin
,
A. J.
,
T.
Samurkas
, and
J. M.
Dealy
, “
A novel sliding plate rheometer for molten plastics
,”
Polym. Eng. Sci.
29
,
499
504
(
1989
).
64.
Yu
,
S.
,
S. N.
Fry
,
D. P.
Potasek
,
D. J.
Bell
, and
B. J.
Nelson
, “
Characterizing fruit fly flight behavior using a microforce sensor with a new comb-drive configuration
,”
J. Microelectromech. Syst.
14
,
4
11
(
2005
).
65.
Beyeler
,
F.
,
S.
Muntwyler
, and
B. J.
Nelson
, “
A six-axis MEMS force—Torque sensor with micro-Newton and nano-Newtonmeter resolution
,”
J. Microelectromech. Syst.
18
,
433
441
(
2009
).
66.
Krenger
,
R.
,
J. T.
Burri
,
T.
Lehnert
,
B. J.
Nelson
, and
M. A. M.
Gijs
, “
Force microscopy of the Caenorhabditis elegans embryonic eggshell
,”
Microsyst. Nanoeng.
6
,
29
(
2020
).
67.
Pisani
,
M.
,
A.
Yacoot
,
P.
Balling
,
N.
Bancone
,
C.
Birlikseven
,
M.
Çelik
,
J.
Flügge
,
R.
Hamid
,
P.
Köchert
,
P.
Kren
,
U.
Kuetgens
,
A.
Lassila
,
G. B.
Picotto
,
E.
Şahin
,
J.
Seppä
,
M.
Tedaldi
, and
C.
Weichert
, “
Comparison of the performance of the next generation of optical interferometers
,”
Metrologia
49
,
455
467
(
2012
).
68.
Dong
,
Y.
,
P.
Hu
,
M.
Ran
,
Z.
Le
,
H.
Fu
,
H.
Yang
, and
R.
Yang
, “
Phase modulation depth setting technique of a phase-generated-carrier under AOIM in fiber-optic interferometer with laser frequency modulation
,”
Opt. Express
28
,
31700
31713
(
2020
).
69.
Dong
,
Y.
,
P.-C.
Hu
,
H.
Fu
,
H.
Yang
,
R.
Yang
, and
J.
Tan
, “
Long range dynamic displacement: Precision PGC with sub-nanometer resolution in an LWSM interferometer
,”
Photonics Res.
10
,
59
67
(
2022
).
70.
Dong
,
Y.
,
P.
Hu
,
M.
Ran
,
H.
Fu
,
H.
Yang
, and
R.
Yang
, “
Correction of nonlinear errors from PGC carrier phase delay and AOIM in fiber-optic interferometers for nanoscale displacement measurement
,”
Opt. Express
28
,
2611
2624
(
2020
).
71.
Gudlavalleti
,
S.
,
B. P.
Gearing
, and
L.
Anand
, “
Flexure-based micromechanical testing machines
,”
Exp. Mech.
45
,
412
419
(
2005
).
72.
Davies
,
G. A.
, and
J. R.
Stokes
, “
On the gap error in parallel plate rheometry that arises from the presence of air when zeroing the gap
,”
J. Rheol.
49
,
919
922
(
2005
).
73.
Cho
,
K. S.
,
Viscoelasticity of Polymers: Theory and Numerical Algorithms
(
Springer
,
The Netherlands
,
2016
).
74.
Arfken
,
G. B.
,
H. J.
Weber
, and
F. E.
Harris
,
Mathematical Methods for Physicists: A Comprehensive Guide
(
Elsevier Science
, New York,
2011
).
75.
Johnston
,
M. T.
, and
R. H.
Ewoldt
, “
Precision rheometry: Surface tension effects on low-torque measurements in rotational rheometers
,”
J. Rheol.
57
,
1515
1532
(
2013
).
76.
Cardinaels
,
R.
,
N. K.
Reddy
, and
C.
Clasen
, “
Quantifying the errors due to overfilling for Newtonian fluids in rotational rheometry
,”
Rheol. Acta
58
,
525
538
(
2019
).
77.
Snijkers
,
F.
, and
D.
Vlassopoulos
, “
Cone-partitioned-plate geometry for the ARES rheometer with temperature control
,”
J. Rheol.
55
,
1167
1186
(
2011
).
78.
McKenna
,
G. B.
, “
Commentary on rheology of polymers in narrow gaps
,”
Eur. Phys. J. E
19
,
101
108
(
2006
).
79.
Henson
,
D. J.
, and
M. E.
Mackay
, “
Effect of gap on the viscosity of monodisperse polystyrene melts: Slip effects
,”
J. Rheol.
39
,
359
373
(
1995
).
80.
Li
,
Y.
,
M.
Hu
,
G. B.
McKenna
,
C. J.
Dimitriou
,
G. H.
McKinley
,
R. M.
Mick
,
D. C.
Venerus
, and
L. A.
Archer
, “
Flow field visualization of entangled polybutadiene solutions under nonlinear viscoelastic flow conditions
,”
J. Rheol.
57
,
1411
1428
(
2013
).
81.
Liu
,
G.
,
H.
Ma
,
H.
Lee
,
H.
Xu
,
S.
Cheng
,
H.
Sun
,
T.
Chang
,
R. P.
Quirk
, and
S. Q.
Wang
, “
Long-chain branched polymers to prolong homogeneous stretching and to resist melt breakup
,”
Polymer
54
,
6608
6616
(
2013
).
82.
Rasmussen
,
H. K.
,
J. H.
Christensen
, and
S.
Gøttsche
, “
Inflation of polymer melts into elliptic and circular cylinders
,”
J. Non-Newtonian Fluid Mech.
93
,
245
263
(
2000
).
83.
Tassieri
,
M.
,
M.
Laurati
,
D. J.
Curtis
,
D. W.
Auhl
,
S.
Coppola
,
A.
Scalfati
,
K.
Hawkins
,
P. R.
Williams
, and
J. M.
Cooper
, “
i-Rheo: Measuring the materials’ linear viscoelastic properties “in a step”!
,”
J. Rheol.
60
,
649
660
(
2016
).
84.
Liu
,
G.
, and
S. Q.
Wang
, “
A particle tracking velocimetric study of stress relaxation behavior of entangled polystyrene solutions after stepwise shear
,”
Macromolecules
45
,
6741
6747
(
2012
).
85.
Liu
,
C. Y.
,
M.
Yao
,
R. G.
Garritano
,
A. J.
Franck
, and
C.
Bailly
, “
Instrument compliance effects revisited: Linear viscoelastic measurements
,”
Rheol. Acta
50
,
537
546
(
2011
).
86.
Gottlieb
,
M.
, and
C. W.
Macosko
, “
The effect of instrument compliance on dynamic rheological measurements
,”
Rheol. Acta
21
,
90
94
(
1982
).
87.
Mackay
,
M. E.
, and
P. J.
Halley
, “
Technical note: Angular compliance error in force rebalance torque transducers
,”
J. Rheol.
35
,
1609
1614
(
1991
).
88.
Liu
,
S.
,
X.
Cao
,
J.-Q.
Zhang
,
Y.-C.
Han
,
X.-Y.
Zhao
, and
Q.
Chen
, “
Toward correct measurements of shear rheometry
,”
Acta Polym. Sin.
52
,
406
422
(
2021
).
89.
See supplementary material at https://www.scitation.org/doi/suppl/10.1122/8.0000494 for algorithm for processing SAOS raw data (Fig. S1), and practical temperature calibration curve (Fig. S2).

Supplementary Material

You do not currently have access to this content.