Knowledge of the evolution in the mechanical properties of a curing polymer matrix is of great importance in composite parts or structure fabrication. Conventional rheometry, based on small amplitude oscillatory shear, is limited by long interrogation times. In rapidly evolving materials, time sweeps can provide a meaningful measurement albeit at a single frequency. To overcome this constraint, we utilize a combined frequency- and amplitude-modulated chirped strain waveform in conjunction with a homemade sliding plate piezo-operated rheometer (PZR) and a dual-head commercial rotational rheometer (Anton Paar MCR 702) to probe the linear viscoelasticity of these time-evolving materials. The direct controllability of the PZR, resulting from the absence of any kind of firmware and the microsecond actuator-sensor response renders this device ideal for exploring the advantages of this technique. The high frequency capability allows us to extend the upper limits of the accessible linear viscoelastic spectrum and, most importantly, to shorten the length of the interrogating strain signal (OWCh-PZR) to subsecond scales, while retaining a high time-bandwidth product. This short duration ensures that the mutation number (NMu) is kept sufficiently low, even in fast-curing resins. The method is validated via calibration tests in both instruments, and the corresponding limitations are discussed. As a proof of concept, the technique is applied to a curing vinylester resin. The linear viscoelastic (LVE) spectrum is assessed every 20 s to monitor the rapid evolution in the time and frequency dependence of the complex modulus. Comparison of the chirp implementation, based on parameters such as duration of the experiment, sampling frequency, and frequency range, in a commercial rotational rheometer with the PZR provides further information on the applicability of this technique and its limitations. Finally, FTIR spectroscopy is utilized to gain insights into the evolution of the chemical network, and the gap dependence of the evolving material properties in these heterogeneous systems is also investigated.

1.
Mours
,
M.
, and
H.
Winter
, “
Time-resolved rheometry
,”
Rheol. Acta
33
,
385
397
(
1994
).
2.
Markovitz
,
H.
, “
Boltzmann and the beginnings of linear viscoelasticity
,”
Trans. Soc. Rheol.
21
,
381
398
(
1977
).
3.
Fielding
,
S. M.
,
P.
Sollich
, and
M. E.
Cates
, “
Aging and rheology in soft materials
,”
J. Rheol.
44
,
323
369
(
2000
).
4.
Negi
,
A. S.
, and
C. O.
Osuji
, “
Time-resolved viscoelastic properties during structural arrest and aging of a colloidal glass
,”
Phys. Rev. E
82
,
031404
(
2010
).
5.
Kawasaki
,
T.
, and
H.
Tanaka
, “
Structural evolution in the aging process of supercooled colloidal liquids
,”
Phys. Rev. E
89
,
062315
(
2014
).
6.
Curtis
,
D.
,
A.
Holder
,
N.
Badiei
,
J.
Claypole
,
M.
Walters
,
B.
Thomas
,
M.
Barrow
,
D.
Deganello
,
M.
Brown
, and
P.
Williams
, “
Validation of optimal Fourier rheometry for rapidly gelling materials and its application in the study of collagen gelation
,”
J. Non-Newtonian Fluid Mech.
222
,
253
259
(
2015
).
7.
Larson
,
R. G.
, and
Y.
Wei
, “
A review of thixotropy and its rheological modeling
,”
J. Rheol.
63
,
477
501
(
2019
).
8.
Macosko
,
C. W.
, “
Rheological changes during crosslinking
,”
British Polym. J.
17
,
239
245
(
1985
).
9.
Snijkers
,
F.
,
R.
Pasquino
, and
A.
Maffezzoli
, “
Curing and viscoelasticity of vitrimers
,”
Soft Matter
13
,
258
268
(
2017
).
10.
Reiter
,
G.
, and
G. R.
Strobl
,
Progress in Understanding of Polymer Crystallization
(
Springer
, Heidelberg, Germany,
2007
), Vol. 714.
11.
Bates
,
F. S.
, and
G. H.
Fredrickson
, “
Block copolymer thermodynamics: Theory and experiment
,”
Annu. Rev. Phys. Chem.
41
,
525
557
(
1990
).
12.
Lehéricey
,
P.
,
P.
Snabre
,
A.
Delots
,
N.
Holten-Andersen
, and
T.
Divoux
, “
Time-resolved rheometry of drying liquids and suspensions
,”
J. Rheol.
65
,
427
436
(
2021
).
13.
Parisi
,
D.
,
J.
Seo
,
B.
Nazari
,
R. P.
Schaake
,
A. M.
Rhoades
, and
R. H.
Colby
, “
Shear-induced isotropic–nematic transition in poly (ether ether ketone) melts
,”
ACS Macro Lett.
9
,
950
956
(
2020
).
14.
Flory
,
P. J.
,
Principles of Polymer Chemistry
(
Cornell University
, Ithaca, NY,
1953
).
15.
Biron
,
M.
,
Thermosets and Composites: Material Selection, Applications, Manufacturing and Cost Analysis
(
Elsevier
, Amsterdam,
2013
).
16.
Adachi
,
T.
,
M.
Osaki
,
W.
Araki
, and
S.-C.
Kwon
, “
Fracture toughness of nano-and micro-spherical silica-particle-filled epoxy composites
,”
Acta Mater.
56
,
2101
2109
(
2008
).
17.
Du Plessis
,
H.
,
Fibreglass Boats: Construction, Gel Coat, Stressing, Blistering, Repair, Maintenance
(
A&C Black
, London,
2010
).
18.
O'Brien
,
D. J.
,
P. T.
Mather
, and
S. R.
White
, “
Viscoelastic properties of an epoxy resin during cure
,”
J. Compos. Mater.
35
,
883
904
(
2001
).
19.
Crasto
,
A.
, and
R.
Kim
, “
On the determination of residual stresses in fiber-reinforced thermoset composites
,”
J. Reinf. Plast. Compos.
12
,
545
558
(
1993
).
20.
Lin
,
S.
,
C.
Cao
,
Q.
Wang
,
M.
Gonzalez
,
J. E.
Dolbow
, and
X.
Zhao
, “
Design of stiff, tough and stretchy hydrogel composites via nanoscale hybrid crosslinking and macroscale fiber reinforcement
,”
Soft Matter
10
,
7519
7527
(
2014
).
21.
Holly
,
E. E.
,
S. K.
Venkataraman
,
F.
Chambon
, and
H. H.
Winter
, “
Fourier transform mechanical spectroscopy of viscoelastic materials with transient structure
,”
J. Non-Newtonian Fluid Mech.
27
,
17
26
(
1988
).
22.
Wijers
,
R.
,
A Chirp, a Roar and a Whisper
(
Nature Publishing Group
, New York,
2018
).
23.
Klauder
,
J. R.
,
A.
Price
,
S.
Darlington
, and
W. J.
Albersheim
, “
The theory and design of chirp radars
,”
Bell Syst. Tech. J.
39
,
745
808
(
1960
).
24.
Wilhelm
,
M.
, “
Fourier-transform rheology
,”
Macromol. Mater. Eng.
287
,
83
105
(
2002
).
25.
Ghiringhelli
,
E.
,
D.
Roux
,
D.
Bleses
,
H.
Galliard
, and
F.
Caton
, “
Optimal Fourier rheometry
,”
Rheol. Acta
51
,
413
420
(
2012
).
26.
Geri
,
M.
,
B.
Keshavarz
,
T.
Divoux
,
C.
Clasen
,
D. J.
Curtis
, and
G. H.
McKinley
, “
Time-resolved mechanical spectroscopy of soft materials via optimally windowed chirps
,”
Phys. Rev. X
8
,
041042
(
2018
).
27.
Rathinaraj
,
J. D. J.
,
J.
Hendricks
,
G. H.
McKinley
, and
C.
Clasen
, “
Orthochirp: A fast spectro-mechanical probe for monitoring transient microstructural evolution of complex fluids during shear
,”
J. Non-Newtonian Fluid Mech.
301
,
104744
(
2022
).
28.
Läuger
,
J.
,
K.
Wollny
, and
S.
Huck
, “
Direct strain oscillation: A new oscillatory method enabling measurements at very small shear stresses and strains
,”
Rheol. Acta
41
,
356
361
(
2002
).
29.
Athanasiou
,
T.
,
G. K.
Auernhammer
,
D.
Vlassopoulos
, and
G.
Petekidis
, “
A high-frequency piezoelectric rheometer with validation of the loss angle measuring loop: Application to polymer melts and colloidal glasses
,”
Rheol. Acta
58
,
619
637
(
2019
).
30.
Keshavarz
,
B.
,
D. G.
Rodrigues
,
J.-B.
Champenois
,
M. G.
Frith
,
J.
Ilavsky
,
M.
Geri
,
T.
Divoux
,
G. H.
McKinley
, and
A.
Poulesquen
, “
Time–connectivity superposition and the gel/glass duality of weak colloidal gels
,”
Proc. Natl. Acad. Sci. U.S.A.
118
,
e2022339118
(
2021
).
31.
Bouzid
,
M.
,
B.
Keshavarz
,
M.
Geri
,
T.
Divoux
,
E.
Del Gado
, and
G. H.
McKinley
, “
Computing the linear viscoelastic properties of soft gels using an optimally windowed chirp protocol
,”
J. Rheol.
62
,
1037
1050
(
2018
).
32.
Bantawa
,
M.
,
B.
Keshavarz
,
M.
Geri
,
M.
Bouzid
,
T.
Divoux
,
G. H.
McKinley
, and
E.
Del Gado
, “
The hidden hierarchical nature of soft particulate gels
,”
Nat. Phys.
19
(
8
),
1178
1184
(
2023
).
33.
Lanczos
,
C.
, and
J.
Boyd
,
Discourse on Fourier Series
(
SIAM
, Philadelphia, PA,
2016
).
34.
Bachman
,
G.
,
L.
Narici
, and
E.
Beckenstein
,
Fourier and Wavelet Analysis
(
Springer
, New York,
2000
), Vol. 586.
35.
Oppenheim
,
A. V.
,
J. R.
Buck
, and
R. W.
Schafer
,
Discrete-time Signal Processing
(
Prentice Hall
,
Upper Saddle River, NJ
,
2001
), Vol. 2.
36.
Harris
,
F. J.
, “
On the use of windows for harmonic analysis with the discrete Fourier transform
,”
Proc. IEEE
66
,
51
83
(
1978
).
37.
Prabhu
,
K. M.
,
Window Functions and Their Applications in Signal Processing
(
Taylor & Francis
, Boca Raton, FL,
2014
).
38.
Kowatsch
,
M.
and
Stocker
,
H.
, “
Effect of Fresnel ripples on sidelobe suppression in low time-bandwidth production linear FM pulse compression
,”
IEE Proc. F
129, 41 (1982).
39.
Levanon
,
N.
, and
E.
Mozeson
,
Radar Signals
(
John Wiley & Sons
, Hoboken, NJ,
2004
).
40.
Nuttall
,
A.
, “
Some windows with very good sidelobe behavior
,”
IEEE Trans. Acoust. Speech Sign. Process.
29
,
84
91
(
1981
).
41.
Tukey
,
J. W.
, “An introduction to the calculation of numerical spectrum analysis,” in
Spectral Analysis of Time Series
, edited by B. Harris (
Wiley
,
New York
,
1967
), pp.
25
46
.
42.
Macosko
,
C. W.
,
Rheology: Principles, Measurements, and Applications
(
Wiley-VCH
, New York,
1994
).
43.
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
).
44.
Nyquist
,
H.
, “
Certain topics in telegraph transmission theory
,”
Trans. Am. Inst. Electr. Eng.
47
,
617
644
(
1928
).
45.
Horowitz
,
P.
,
W.
Hill
, and
I.
Robinson
,
The Art of Electronics
(
Cambridge University
,
Cambridge
,
1989
), Vol. 2.
46.
Starecki
,
T.
, “
Analog front-end circuitry in piezoelectric and microphone detection of photoacoustic signals
,”
Int. J. Thermophys.
35
,
2124
2139
(
2014
).
47.
Rathinaraj
,
J. D. J.
, and
G. H.
McKinley
, “
Gaborheometry: Applications of the discrete Gabor transform for time resolved oscillatory rheometry
,”
J. Rheol.
67
,
479
497
(
2023
).
48.
Rubinstein
,
M.
, and
R. H.
Colby
,
Polymer Physics
(
Oxford University
,
New York
,
2003
), Vol. 23.
49.
Abdurohman
,
K.
,
T.
Satrio
, and
N.
Muzayadah
, “
A comparison process between hand lay-up, vacuum infusion and vacuum bagging method toward e-glass
,”
J. Phys.: Conf. Ser.
1130
, 012018 (
2018
).
50.
Martin
,
J.
,
J.
Laza
,
M.
Morras
,
M.
Rodrıguez
, and
L.
Leon
, “
Study of the curing process of a vinyl ester resin by means of TSR and DMTA
,”
Polymer
41
,
4203
4211
(
2000
).
51.
Chambon
,
F.
, and
H. H.
Winter
, “
Linear viscoelasticity at the gel point of a crosslinking PDMS with imbalanced stoichiometry
,”
J. Rheol.
31
,
683
697
(
1987
).
52.
Lange
,
J.
,
N.
Altmann
,
C.
Kelly
, and
P.
Halley
, “
Understanding vitrification during cure of epoxy resins using dynamic scanning calorimetry and rheological techniques
,”
Polymer
41
,
5949
5955
(
2000
).
53.
Harran
,
D.
, and
A.
Laudouard
, “
Rheological study of the isothermal reticulation of an epoxy resin
,”
J. Appl. Polym. Sci.
32
,
6043
6062
(
1986
).
54.
Aoki
,
M.
,
A.
Shundo
,
R.
Kuwahara
,
S.
Yamamoto
, and
K.
Tanaka
, “
Mesoscopic heterogeneity in the curing process of an epoxy–amine system
,”
Macromolecules
52
,
2075
2082
(
2019
).
55.
Lieleg
,
O.
, and
A. R.
Bausch
, “
Cross-linker unbinding and self-similarity in bundled cytoskeletal networks
,”
Phys. Rev. Lett.
99
,
158105
(
2007
).
56.
Lange
,
J.
,
R.
Ekelöf
, and
G. A.
George
, “
Charge-recombination luminescence as a monitor of network formation during cure of epoxy resins
,”
Polymer
40
,
149
155
(
1999
).
57.
Acha
,
B. A.
, and
L. A.
Carlsson
, “
Evaluation of cure state of vinylester resins
,”
J. Appl. Polym. Sci.
127
,
4777
4784
(
2013
).
58.
Saiev
,
S.
,
D.
Beljonne
,
R.
Lazzaroni
, and
P.
Roose
, “
Decoding elasticity build-up and network topology in free-radical cross-linking polymerization: A combined experimental and atomistic approach
,”
Macromolecules
56, 7396 (
2023
).
59.
Chung
,
K.
, and
E.
Greener
, “
Degree of conversion of seven visible light-cured posterior composites
,”
J. Oral Rehab.
15
,
555
560
(
1988
).
60.
Evonik Industries AG,
Silica Business Line: AEROSIL®–Fumed Silica Technical Overview
, 8th ed. (Evonik Industries, Essen, Germany, 2015).
61.
Raghavan
,
S. R.
, and
S. A.
Khan
, “
Shear-induced microstructural changes in flocculated suspensions of fumed silica
,”
J. Rheol.
39
,
1311
1325
(
1995
).
62.
Dullaert
,
K.
, and
J.
Mewis
, “
A model system for thixotropy studies
,”
Rheol. Acta
45
,
23
32
(
2005
).
63.
Barthel
,
H.
, “
Surface interactions of dimethylsiloxy group-modified fumed silica
,”
Coll. Surf. A
101
,
217
226
(
1995
).
64.
Nikzamir
,
M.
,
M.
Mortezaei
, and
M.
Jahani
, “
Effect of surface area of nanosilica particles on the cure kinetics parameters of an epoxy resin system
,”
J. Appl. Polym. Sci.
136
,
47958
(
2019
).
65.
Schrag
,
J. L.
, “
Deviation of velocity gradient profiles from the “gap loading” and “surface loading” limits in dynamic simple shear experiments
,”
Trans. Soc. Rheol.
21
,
399
413
(
1977
).
66.
Clasen
,
C.
, and
G. H.
McKinley
, “
Gap-dependent microrheometry of complex liquids
,”
J. Non-Newtonian Fluid Mech.
124
,
1
10
(
2004
).
67.
Liu
,
Y.
,
D.
Lorusso
,
D. W.
Holdsworth
,
T. L.
Poepping
, and
J. R.
de Bruyn
, “
Effect of confinement on the rheology of a yield-stress fluid
,”
J. Non-Newtonian Fluid Mech.
261
,
25
32
(
2018
).
68.
Yan
,
Y.
,
Z.
Zhang
,
D.
Cheneler
,
J.
Stokes
, and
M.
Adams
, “
The influence of flow confinement on the rheological properties of complex fluids
,”
Rheol. Acta
49
,
255
266
(
2010
).
69.
Yoshimura
,
A. S.
, and
R. K.
Prud'homme
, “
Wall slip effects on dynamic oscillatory measurements
,”
J. Rheol.
32
,
575
584
(
1988
).
70.
Sternstein
,
S.
, “Transient and dynamic characterization of viscoelastic solids,”
Adv. Chem. Ser.
203
,
123
(
1983
).
71.
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
(
2011
).
72.
Schweizer
,
T.
,
J.
van Meerveld
, and
H. C.
Öttinger
, “
Nonlinear shear rheology of polystyrene melt with narrow molecular weight distribution—Experiment and theory
,”
J. Rheol.
48
,
1345
1363
(
2004
).
73.
See supplementary material online for further supportive information on LVE and FTIR measurements.

Supplementary Material

You do not currently have access to this content.