Ageing, yielding, and rheology of nanocrystalline cellulose suspensionsBabak Derakhshandeh, George Petekidis, Sadaf Shafiei Sabet, Wadood Y. Hamad, and Savvas G. Hatzikiriakos Citation: J. Rheol. 57, 131 (2013); doi: 10.1122/1.4764080 View online: http://dx.doi.org/10.1122/1.4764080 View Table of Contents: http://www.journalofrheology.org/resource/1/JORHD2/v57/i1 Published by the The Society of Rheology Related ArticlesHigh frequency linear rheology of complex fluids measured from their surface thermal fluctuations J. Rheol. 57, 441 (2013) Mechanisms for different failure modes in startup uniaxial extension: Tensile (rupture-like) failure and necking J. Rheol. 57, 223 (2013) Overshoots in stress-strain curves: Colloid experiments and schematic mode coupling theory J. Rheol. 57, 149 (2013) Studying the origin of “strain hardening”: Basic difference between extension and shear J. Rheol. 57, 89 (2013) Normal stress measurements in sheared non-Brownian suspensions J. Rheol. 57, 71 (2013) Additional information on J. Rheol.Journal Homepage: http://www.journalofrheology.org/ Journal Information: http://www.journalofrheology.org/about Top downloads: http://www.journalofrheology.org/most_downloaded Information for Authors: http://www.journalofrheology.org/author_information

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Ageing, yielding, and rheology of nanocrystallinecellulose suspensions

Babak Derakhshandeh

Department of Chemical and Biological Engineering, The Universityof British Columbia, Vancouver, British Columbia V6T 1Z3, Canada

George Petekidisa)

FORTH, Institute of Electronic Structure & Laser, Heraklion, Crete, Greeceand Department of Materials Science and Technology, University of Crete,

Heraklion, Crete, Greece

Sadaf Shafiei Sabet

Department of Chemical and Biological Engineering, The Universityof British Columbia, Vancouver, British Columbia V6T 1Z3, Canada

Wadood Y. Hamad

FPInnovations, Vancouver, British Columbia V6S 2L9, Canada

Savvas G. Hatzikiriakosb)

Department of Chemical and Biological Engineering, The Universityof British Columbia, Vancouver, British Columbia V6T 1Z3, Canada

(Received 5 June 2012; final revision received 5 October 2012;published 7 November 2012)

Synopsis

This paper investigates yielding and flow of nanocrystalline cellulose (NCC) suspensions by

combining rheological measurements with light scattering echo (LS-echo). The NCC samples are

characterized using static and dynamic light scattering as well as polarized optical microscopy

coupled with a rotational rheometer. The storage modulus of the NCC suspensions is found to

increase with waiting time after shear rejuvenation. The microscopic particle rearrangements of the

NCC spindles are followed by LS-echo at both short and long waiting times under oscillatory shear

flow. We find that the onset of shear-induced irreversible microscopic particle rearrangements,

coincide with the strain at which storage and loss moduli cross over in the nonlinear viscoelastic

a)Electronic mail: georgp@iesl.forth.grb)Author to whom correspondence should be addressed; electronic mail: savvas.hatzi@ubc.ca

VC 2013 by The Society of Rheology, Inc.J. Rheol. 57(1), 131-148 January/February (2013) 0148-6055/2013/57(1)/131/18/$30.00 131

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regime identified by the macroscopic yield point of the sample. The yielding transition is found to

occur at a higher strain as the frequency of oscillation increases. VC 2013 The Society ofRheology. [http://dx.doi.org/10.1122/1.4764080]

I. INTRODUCTION

Pulp and paper industry is a major industry worldwide, producing communication

papers, packaging, boxes, tissue, hygiene products, and an assortment of disposable prod-

ucts. Fiber for this industry comes from pulping biomass, mostly trees in modern times.

As such, the industry is based on a sustainable, renewable, carbon-neutral resource

[Derakhshandeh et al. (2011)].

Wood fibers are composites made up of spirally wound fibrils of cellulose. These

fibrils consist of fully crystalline regions and amorphous less ordered regions. Effective

hydrolysis of cellulosic material using sulphuric acid results in the production of colloidal

suspensions of fully crystalline spindle-like particles referred to as nanocrystalline cellu-

lose (NCC) [Revol et al. (1992)]. Being inherently renewable, sustainable, and abundant,

cellulose nanocrystalline spindles conduct light and electricity and exhibit several other

intriguing properties summarized by Araki et al. (1998), Kloser and Gray (2010), and

Hamad and Hu (2010). These properties partly originate from the ability of the NCC

spindles to spatially self-assemble in different orientations depending on the concentra-

tion of cellulose in the suspension. In the dilute regime, NCC spindles are randomly ori-

ented within the suspension forming an isotropic phase. NCC spindles appear as

spheroids or ovaloids and the initial ordered domains are similar to tactoids [Roman and

Gray (2005); Habibi et al. (2010)]. Increasing the cellulose concentration, tactoids join

together and shape an anisotropic phase, which leads to a nematic liquid crystalline align-

ment [Revol et al. (1992)]. Further increase of the concentration to a critical value forms

a fully anisotropic phase with NCC spindles packed in a chiral nematic ordered phase. In

this case, the anisotropic phase consists of layers of NCC spindles arranged in a line

along a director, with the orientation of each director twisted about the perpendicular axis

from one layer to the next. As concentration increases further, NCC suspensions orient

under shear, exhibiting shear birefringence, and with time they split into an upper iso-

tropic phase and a lower anisotropic phase [Roman and Gray (2005); Habibi et al.(2010)].

The rheology of rigid spindle-like suspensions and stiff rod-like polymers have been

the subject of numerous studies [Sherwood (1981); Wissbrun (1981); Mori et al. (1982);

Doi and Edwards (1986); Berry and Russel (1987); Davis and Russel (1987); Magda

et al. (1991); Petekidis et al. (1997); Petekidis et al. (1998a); Petekidis et al. (1998b);

Petekidis et al. (1998c); Petekidis et al. (2000); Dhont and Briels (2003); Pryamitsyn and

Ganesan (2008)]. Among the publications are also some noteworthy reviews of the field,

namely Ganani and Powell (1985) and Solomon and Spicer (2010).

The rheology of rod-like suspensions depends to a great extent on the size distribution,

the orientation, and the morphology of the rods under shear flow [Marchessault et al.(1961)]. The morphology of the rod-like chiral nematic systems during flow is often char-

acterized by the “three region flow curve,” a concept introduced by Onogi and Asada

(1980). This implies that the flow curve of the suspension is composed of three different

flow regimes corresponding to low, medium, and high shear rates. At low shear rates, the

domain structures of the suspension begin to deform. This translates into a shear-thinning

behavior where the viscosity decreases with shear rate following a power law dependence

of �0.5. The second region is a plateau over intermediate shear rates where a decrease in

the size of the domain structures occurs as a result of shear flow. A third shear-thinning

132 DERAKHSHANDEH et al.

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behavior is again observed at high shear rates where the chiral-nematic phases are being

disrupted and individual spindles are ordered with their axes aligned in the flow direction,

i.e., spindles exhibit nematic ordering. These flow regimes have been also observed for

NCC suspensions in studies of Orts et al. (1998) and Lima and Borsali (2004).

Besides the concentration, the orientation, and the aspect ratio of the spindles, the rhe-

ology of NCC suspensions also depends on the preparation process and flow history.

Araki et al. (1998) studied the rheology of NCC suspensions with respect to their prepa-

ration methods. It was found that H2SO4 and HCl-treated suspensions exhibited different

rheological behavior, while both entailed the same particle size and shape. Bercea and

Navard (2000) studied the rheology of rigid cellulose whisker suspensions at various con-

centrations. In semidilute systems (0–0.85 wt. %), two plateaus were observed in the flow

curves: One at low shear rates corresponding to the flow of isotropic and one at high

shear rates related to the flow of oriented suspensions. The viscosity at the high shear rate

plateau was found to be linearly proportional to the concentration and much lower than

that of the Newtonian low shear rate plateau. The latter is due to the orientation of rods in

the direction of flow makes, which causes a decrease of the drag force at high shear rates

and hence a viscosity drop [Orts et al. (1998)].

From the discussion above, it is evident that the processing of NCC suspensions alters

their microstructure through orientation and deformation of their constitutive elements.

The understanding of the behavior of such suspensions under different flow conditions

would significantly benefit from simultaneous measurements of their macroscopic me-

chanical properties (rheology) and their microscopic structure and dynamics. Dynamic

light scattering (DLS) techniques under oscillatory shear have been proven to be an

excellent means of acquiring this information [H�ebraud et al. (1997); H€ohler et al.(1997); Petekidis et al. (2002)]. This technique referred to as diffusing wave spectroscopy

(DWS) or light scattering echo (LS-echo) allows measurement of the autocorrelation

function of the scattering intensity under multiple scattering conditions from glassy sam-

ples subjected to oscillatory shear deformations. LS-echo has been utilized to investigate

the microscopic particle dynamics under shear in compressed emulsions [H�ebraud et al.(1997)], foams [H€ohler et al. (1997)], hard sphere glasses [Petekidis et al. (2002)], and

colloidal gels [Smith et al. (2007)].

In this study, LS-echo has been implemented simultaneously with conventional rhe-

ometry to study the time-dependent rheology of concentrated NCC suspensions with em-

phasis on the transition through yielding, an aspect that has received little attention for

the present system so far in literature. We first employ static and dynamic light scattering

techniques along with a polarized optical microscope to characterize the NCC suspen-

sions. A conventional rheometer is then used to study the macroscopic rheological behav-

ior of the concentrated samples, while the LS-echo technique is implemented to study the

corresponding behavior on the microscopic scale. The paper is organized in three sec-

tions. The first describes the LS-echo technique, its applications, and novel results. Then,

the materials, experimental methods, and measurement protocols established for this

study are presented. The results obtained by conventional rheometry and LS-echo techni-

ques and the key conclusions from this work are finally discussed and summarized.

II. LIGHT SCATTERING ECHO

Illumination of a random medium such as a colloidal suspension by laser light leads to

random diffraction in the far field referred to as the speckle pattern. The instantaneous

structure of the speckle depends on the instantaneous arrangement of the particles within

133RHEOLOGY OF NCC SUSPENSIONS

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the medium and their size and shape. Therefore, the speckle pattern changes due to parti-

cle motion in the suspension resulted from Brownian diffusion and/or shear flow. Accord-

ingly, the time correlation function of the intensity follows such particle dynamics. The

correlation function of the intensity of a single speckle can be obtained in either the sin-

gle scattering regime using DLS in the case of transparent samples [Berne and Pecora

(1976)] or in the limit of multiple scattering using DWS for opaque samples [Pine et al.(1988)].

The technique of DWS or LS-echo [H�ebraud et al. (1997); H€ohler et al. (1997); Pete-

kidis et al. (2002)] analyzes the change in the speckle pattern from multiply scattering

samples subjected to oscillatory shear in order to determine the shear-induced particle

rearrangements. The normalized time correlation function is measured experimentally

from the time dependent scattered intensity, I(t):

gð2ÞðtÞ � hIðt0ÞIðt0 þ tÞihIðt0Þi2

; (1)

where t is the delay time and h i denotes average over t0. If the particles exhibit a purely

elastic deformation, i.e., if they return to their original position after one period of oscilla-

tion, the speckle pattern changes but returns to the original configuration. Therefore, the

normalized intensity correlation function, gð2ÞðtÞ � 1, regains its maximum value exhibit-

ing an “echo” of amplitude 1 at delay time t equal to T, the period of oscillation. Like-

wise, if such reversible and elastic response is extended to longer times, the correlation

function exhibits multiple echoes corresponding to an integral number of oscillatory

cycles. On the other hand, amplitudes of gð2ÞðtÞ � 1 smaller than 1 indicate shear-induced

irreversible particle rearrangements with the level of irreversibility being proportional to

the reduction of the amplitude. Therefore, the LS-echo technique provides detailed infor-

mation on the microscopic dynamics of soft matter under shear, particularly with respect

to the transition from elastic to plastic macroscopic response, related to microscopic re-

versible to irreversible transition, i.e., yielding.

At rest in the DWS limit of strong multiple scattering, it can be shown that the field

correlation function (or intermediate scattering function) measured at transmission geom-

etry can be approximated by

gð1ÞðtÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffigð2ÞðtÞ � 1

q� exp � 1

6nk2hDr2ðtÞi

� �; (2)

where n is the average number of scattering events, k ¼ 2pk where k is the wavelength in

the medium, and hDr2ðtÞi is the particle mean-square displacement after time t due to

Brownian motion. Under an oscillatory shear deformation, particles rearrange due to

Brownian and shear-induced diffusion. Therefore, the correlation function measured at

delay times of t¼mT (or the echo amplitudes) can be written as [Petekidis et al. (2002)]

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffigð2ÞðtÞ � 1

q� exp � 1

6nk2½hDr2ðtÞiB þ hDr2ðtÞiS�

� �; (3)

where hDr2ðtÞiB and hDr2ðtÞiS are the mean-square displacements due to Brownian and

shear forces and m¼ 1, 2, 3,… while T is the period of oscillation. The relevant length

scale probed under multiple scattering conditions in the transmission geometry is given

by lDWS ¼ffiffi6pffiffi

np

k, which results in lDWS � 180 nm for the system studied here. In summary,

with the technique of LS-echo the particle dynamics under oscillatory shear can be

134 DERAKHSHANDEH et al.

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determined by following the echo peaks with the trivial effect of affine motion due to

shear elimination. In this way, shear-induced diffusion can be studied and irreversible

particle rearrangements can be determined at the length scale of lDWS. Particularly, mi-

croscopic dynamic information can be obtained during the yielding of solid-like samples,

such as glasses and gels imposed by large amplitude oscillatory deformations.

III. EXPERIMENTAL

In this section, we briefly describe the material’s characterization methodology by

DLS and optical microscopy as well as the technical details of the rheometry and LS-

echo experiments.

A. Sample preparation

NCC suspensions were prepared by mixing spray-dried NCC powder (FPInnovation,

Canada) in de-ionized water to a concentration of 10 wt. %. To ensure proper dispersion

of NCC spindles in the suspension, each sample was sonicated with an ultrasonic device

for 20 min followed by rest for 30 min prior to any further characterization. The ultra-

sonic treatment was carried out in an ice bath to avoid desulfation of the sulfate groups

on the NCC surface due to sample overheating.

B. Characterization

1. Static and dynamic light scattering

An ALV-goniometer equipped with a Nd:YAG laser with a single-mode intensity of

�50 mW at k¼ 532 nm (Adlas DPY 325) was used along with an ALV-5000 full digital

correlator (320 channels) over a time range of 10�7 s< t< 10 s for the DLS measure-

ments. Dilute NCC suspensions of 2.3� 10�4 g/ml were tested in a thermostated refrac-

tive index matching toluene bath at T¼ 20 �C. Glan–Thomson polarizers were used in

the incident and scattered beams to ensure vertical (V) or horizontal (H) polarization. We

performed both polarized (VV) and depolarized (VH) DLS measurements. The intensity

correlation function gð2Þðq; tÞ is measured at different scattering wave vectors,

q ¼ 4pn sinðh=2Þ=k, where h is the scattering angle, k is the wavelength of the incident

light, and n is the index of refraction of the scattering medium. The field correlation func-

tion, determined by the Siegert relation, gð1ÞðtÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffigð2ÞðtÞ � 1

p, provides information on

the particle dynamics [Berne and Pecora (1976)].

Figure 1 depicts the autocorrelation functions in VV and VH geometries at 20 �C to-

gether with the distribution of the relaxation times. The latter is determined from inverse

Laplace transformation (ILT), using the program CONTIN. This method assumes that

gð1ÞðtÞ can be represented by a superposition of exponentials as [Petekidis et al. (1997)

and references therein]

gð1ÞðtÞ ¼ð

Lðln sÞexpð�t=sÞdðln sÞ: (4)

In this form, a continuous spectrum of relaxation times, L(ln s), can be determined along

with the characteristic relaxation times, s, corresponding to the maximum values of L(ln s).

The inset in Fig. 1 shows the decay rate, C¼ 1/s, deduced from the VV and VH geometries

corresponding to the translational and rotational diffusion, respectively [Berne and Pecora

(1976)]. It should be noted that VV decay rate exhibits a q2 dependence according to

135RHEOLOGY OF NCC SUSPENSIONS

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CVV¼ q2D while the VH decay rate shows a finite intercept according to CVH¼ q2Dþ 6Dr

with D and Dr the translational and rotational diffusion coefficients, respectively, which are

functions of the length, L, and diameter, d, of the spindle.

The dimensions of the NCC spindles were determined using both static and dynamic

light scattering. The total light scattering intensity in the VV polarization geometry is

shown in the Holtzer representation (lower inset of Fig. 1). The solid lines denote the

form factor of thick rigid rods [Berne and Pecora (1976); Benoit and Doty (1953)] with

length L¼ 270 nm and d¼ 20 nm and size polydispersity of PD¼ 2. The translational dif-

fusion determined from CVV was found to be D¼ 7.824� 10�8 cm2/s while the rotational

diffusion coefficient deduced from CVH was 439 s�1. Using the diameter d¼ 20 nm cal-

culated from the static light scattering, theoretical predictions for the translational and

rotational diffusion of rigid rods [Petekidis et al. (1998b); Petekidis et al. (1998c)] yield

values of L¼ 340 nm and L¼ 360 nm, respectively. Given the different moments of the

distribution involved in the averaging of polydisperse rods in static and dynamic light

scattering as well as in the averaging of the rotational and translational diffusivity, the

agreement between different methods is very good.

2. Polarized optical microscopy

In order to study the microstructure of NCC suspensions, photomicrographs were

taken using a polarized light microscope (Mitutoyo microscope set-up equipped with

Lumenera LU 165 color CCD camera and polarizer). The NCC suspension samples were

placed in glass parallel-plate geometry (43 mm diameter) of a rotational rheometer

(MCR-501 Anton Paar Physica) and the microstructure was observed with the micro-

scope at rest and under shear.

Typical micrographs of a 10 wt. % NCC suspension are shown in Fig. 2. The sample at

rest exhibits strong birefringence under polarized light as shown in Fig. 2(a). The irides-

cent colors observed in Fig. 2(a) indicate the presence of chiral nematic liquid crystalline

domains with different pitch sizes. By applying shear, these domains deform and align

themselves in the direction of shear as shown in Figs. 2(b) and 2(c). Increasing the shear

rate, the domains break and individual NCC particles align in the direction of the shear

flow. In this case, the polarized optical micrographs become dark as shown in Fig. 2(d).

FIG. 1. Autocorrelation functions of the scattered intensity in the VV and VH geometries together with the ILT for

a dilute NCC of 2:3� 10�4 g/ml at 20 �C. Top inset: VV and VH decay rates as a function of q2. Bottom inset:

Absolute light scattering intensity in the VV geometry in the Holtzer representation. The solid lines denote the form

factor of nearly rigid rods of length L¼ 270 nm and diameter of d¼ 20 nm with size polydispersity of PD¼ 2.

136 DERAKHSHANDEH et al.

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C. Experimental procedure

Rheological measurements were performed in the dynamic oscillatory and steady-

shear modes together with the LS-echo measurements. An Anton Paar Physica MCR-501

stress controlled rheometer coupled with a homemade LS-echo set-up was used to per-

form the experiments. NCC samples of 10 wt. % were placed in the rheometer between

two transparent parallel-plates of 25 mm in diameter, while the temperature was kept at

20 �C. Solvent evaporation was eliminated either using silicone oil to seal the periphery

of the sample or by saturating the measurement environment with water using a solvent

trap. The samples were illuminated from the above by a He-Ne laser with a wavelength

of k¼ 632 nm and the scattered light was detected from below by a single-mode fiber

connected to an avalanche photo-diode operating in the photon counting mode. A crossed

polarizer was placed before the fiber to cut out any residual single scattering. The signal

was then processed using a linear digital correlator with the delay channels clustered

around delay times s¼mT allowing the measurement of the narrow echoes following the

procedure used in Petekidis et al. (2002). Rheological measurements were composed of

rejuvenation at high strain amplitudes, dynamic frequency sweeps (DFS), dynamic strain

sweeps (DSS), and dynamic time sweeps (DTS) in conjunction with simultaneous LS-

echo measurements and steady-shear rate experiments.

IV. RESULTS AND DISCUSSION

A. Rheology

NCC suspensions were presheared at an initial high strain of c0¼ 200% at a frequency

of 10 Hz (62.8 rad/s) for 1000 s then left to rest for 300 s prior to any further experimental

measurements. Although care was taken to eliminate solvent evaporation, DFS were per-

formed prior and after each set of experiments to ensure consistency in the material’s

FIG. 2. Polarized optical micrographs of a 10 wt. % NCC suspension (a) at rest, and shear rates of (b) 0.1 s�1,

(c) 1 s�1, and (d) 10 s�1. The arrows denote the direction of flow and cross polarizers.

137RHEOLOGY OF NCC SUSPENSIONS

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properties. DFS were performed over a range of frequencies, x, 0.1–100 rad/s at c0¼ 1%

and the variation of storage (G0) and loss (G00) moduli with frequency was followed.

Figure 3(a) shows a typical frequency sweep measurement made on a 10 wt. % NCC sus-

pension prior and after the experimental testing. This indicates that no evaporation

occurred in the sample as the same values of G0 and G00 were obtained for the sample

over the course of testing. Figure 3(a) also shows that the 10 wt. % suspension exhibits a

solid-like viscoelastic response with G0>G00 with both decreasing and approaching each

other at lower frequencies.

Next, DSS were performed and the limits of the linear viscoelastic response and the

G0 and G00 cross-over strains were measured. The frequency of oscillation was fixed at

1 Hz (6.28 rad/s) and 10 Hz (62.8 rad/s), while strain amplitude was increased progres-

sively from 0.1% to 100%. Figure 3(b) illustrates the variation of storage and loss moduli

with strain for a 10 wt. % NCC suspension at two frequencies of 1 Hz (6.28 rad/s) and

10 Hz (62.8 rad/s). The limits of the linear viscoelastic region were found to be c0� 2%

at x¼ 1 Hz (6.28 rad/s) and c0� 4% at x¼ 10 Hz (62.8 rad/s) while the cross-over of the

storage and loss moduli was determined as cc� 17% and 29% for x¼ 1 Hz (6.28 rad/s)

and 10 Hz (62.8 rad/s), respectively. The cross-over strain is one measure of the yield

strain of the sample, i.e., the strain amplitude marking the transition from a solid-like to a

FIG. 3. (a) Frequency sweeps on a 10 wt. % NCC suspension. Black symbols are the results obtained prior to

the experimental testing and white symbols are the results after performing all the experiments. Frequency

dependence of G0 and G0 0 falls on the same curve indicating the absence of artifacts, such as evaporation.

(b) Dynamic strain sweep at x¼ 1 Hz (6.28 rad/s) and 10 Hz (62.8 rad/s).

138 DERAKHSHANDEH et al.

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liquid-like response [Derakhshandeh et al. (2010)]. The increase of the cross-over yield

strain with frequency observed in Fig. 3(b) is similar to that reported for colloidal glasses

of spherical particles. This behavior is attributed to the increasing effect of Brownian

motions at lower frequencies, which facilitates local particle rearrangements and pro-

motes flow of the suspension [Petekidis et al. (2002)].

Once the limits of the linear viscoelastic response were identified by the DSS experi-

ments, DTS were performed for 1000 s at various stain amplitudes ranging from c0¼ 1%

to 200% corresponding to the different regions of viscoelastic response at two frequen-

cies of 1 Hz (6.28 rad/s) and 10 Hz (62.8 rad/s).

Figure 4(a) shows the variation of the storage modulus with time at a frequency of 10

Hz (62.8 rad/s) for 10 wt. % NCC samples. The storage modulus first exhibits a plateau

up to a critical time after which it increases monotonically with time exhibiting ageing.

Such ageing of the NCC suspensions is found to be more significant at lower strains. It

should be noted that similar behavior was observed at the lower frequency of 1 Hz

(6.28 rad/s).

FIG. 4. (a) Time sweeps for a 10 wt. % NCC at various strains and x¼ 10 Hz (62.8 rad/s) measured for 1000 s.

NCC samples exhibit aging as G0 begins to increase after a critical time (b) Viscosity with time at constant shear

rates. Viscosity increases more rapidly with time at lower applied shear rates. At higher rates, the viscosity

remains constant over the time period examined here.

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NCC samples were then studied under steady-shear flow. The variation of the viscos-

ity with time was followed at constant shear rates as shown in Fig. 4(b). The viscosity

was found to increase with time at lower shear rates, similar to that observed under the

oscillatory shear deformations. However, increasing the applied shear rate, the viscosity

was found to exhibit a constant value over the time scale of the experiment, i.e., no sign

of ageing was noticed. At large shear rates where the applied shear stresses are larger

than the yield stress, the material flows with a constant viscosity and ageing are elimi-

nated. However, at lower shear rates corresponding to shear stresses close to the yield

stress the system is only partially rejuvenated. In this case, ageing under shear leads to a

progressively increasing apparent viscosity as shown in Fig. 4(b). Likewise, it is expected

that during a constant low shear stress experiment, the shear rate would decrease con-

stantly with time. Such ageing under shear (thixotropy) has been observed in other sys-

tems, such as bentonite suspensions, gels, pastes [Barnes (1997) and references therein],

multiarm star glasses [Christopoulou et al. (2009)], and fiber suspensions [Derakhshan-

deh et al. (2012)].

B. Light scattering echo

The microscopic particle rearrangements during ageing of the NCC samples were

studied under oscillatory shear using the LS-echo technique. The echoes in the correla-

tion function, gð2ÞðtÞ � 1, during the short-term (0–300 s) and the long-term rheological

responses (600–900 s) were measured. These measurements were conducted by increas-

ing the strain amplitude to progressively shear melt the samples. Additionally, in order to

investigate the thixotropic response of the NCC suspensions, similar measurements were

performed by decreasing the strain amplitude from c0¼ 200% to c0¼ 1% while the corre-

lation functions were measured during the short-term regime (0–300 s).

1. Short-term behavior: Strain amplitude increase (c0¼ 1%–200%)

In order to study ageing and yielding transition of the NCC samples, the intensity cor-

relation function, gð2ÞðtÞ � 1, was measured by means of LS-echo technique under oscil-

latory shear flow deformations. The 1st, 3rd, 5th, 8th, 10th, and 15th echoes were

measured at various strains in the linear and nonlinear viscoelastic regimes at two fre-

quencies of x¼ 1 (6.28 rad/s) and 10 Hz (62.8 rad/s). We first present LS-echo data that

were measured during the short-term (0–300 s) rheological response of the samples.

Figures 5(a) and 5(b) show the evolution of the first echo for the short-term response

of the samples at frequencies of x¼ 1 (6.28 rad/s) and 10 Hz (62.8 rad/s). The first echo,

which appears at t ¼ 1=x [1 and 0.1 s for x¼ 1 Hz (6.28 rad/s) and x¼ 10 Hz (62.8 rad/

s), respectively], can be used to evaluate the reversibility of the particles motions within

the sample over a length-scale of lDWS � 180 nm and the time scale of one period of os-

cillation. At strain amplitudes smaller than 15% [at x¼ 1 Hz (6.28 rad/s) in Fig. 5(a)] and

25% [at x¼ 10 Hz (62.8 rad/s) in Fig. 5(b)], the amplitude of the first echo is equal to �1

indicating elastic deformation of the sample and reversible particle rearrangements, i.e.,

particles return to their initial positions within the length-scale of lDWS � 180 nm, after

one period of oscillation. The reversibility of particle motion observed here over delay

times equal to one period extends inside the nonlinear viscoelastic regime as identified

by the DSS experiments [Fig. 3(b)] where the limits of linear response were around 2%

and 4% for x¼ 1 (6.28 rad/s) and 10 Hz (62.8 rad/s), respectively.

Further increase of the strain amplitude to c0¼ 18% at x¼ 1 Hz (6.28 rad/s) and to

c0¼ 27% at x¼ 10 Hz (62.8 rad/s) reduces the amplitude of the first echo to about 0.82

and 0.84, respectively, indicating the onset of irreversible particle rearrangements within

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the time scale of one period. These critical strain amplitudes correspond to those at which

G0 and G00 cross over in the DSS measurements of Fig. 3(b). In other words, irreversible

particle rearrangements during a time scale of a period at the length scale of �180 nm

(approximately half of the spindle length) signify microscopic breaking of the cage or

tube that confines the asymmetric NCC spindles. Such microscopic rearrangements of

the spindles manifest themselves in the macroscopic shear melting (yielding) of the NCC

suspension which occurs not at the limits of the viscoelastic regime but rather near the G0

and G00 cross-over strain.

The initial decay rate, Cini¼ 1/sini, related to the oscillatory affine motion imposed on

the NCC spindles is shown in the inset of Fig. 5(b). The initial decay was found to

increase with the strain amplitude at constant frequency. The rationale for such behavior

is that increasing the strain amplitude at a constant frequency makes the average shear

FIG. 5. Correlation functions for a 10 wt. % NCC sample under oscillatory shear measured from 0 to 300 s at

(a) x¼ 1 Hz (6.28 rad/s) and (b) x¼ 10 Hz (62.8 rad/s). The evolution of the first echo is shown for various

strains. The echo amplitude drops significantly from 1 at c0¼ 15% and c0¼ 27% at x¼ 1 Hz (6.28 rad/s) and

x¼ 10 Hz (62.8 rad/s), respectively, exhibiting shear-induced irreversible rearrangement (yielding). This occurs

at a strain corresponding to the cross-over of G0 and G0 0 as shown in Fig. 3(b). The inset in (b) shows the initial

decay rate with strain at x¼ 10 Hz (62.8 rad/s). The linear dependence indicates the absence of wall slip.

141RHEOLOGY OF NCC SUSPENSIONS

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rate to increase according to _c ¼ xc0 and the initial decay time to decrease [Petekidis

et al. (2002)]. The linear increase of Cini with _c also provides clear evidence that the bulk

of the sample is sheared with _c ¼ xc0 as strain amplitude is increased and no slip is pres-

ent at the surface.

Generally, particles rearrange in the suspension due to the thermally induced Brown-

ian motions and/or shear-induced deformations. At low concentrations, the particles

move independently with the least interaction from their neighbouring particles. How-

ever, as the concentration of the particles within the suspension increases, direct particle

interactions as well as hydrodynamic forces influence the motion of individual particles.

In this case, particles are trapped within their nearest neighbouring cages where short-

time diffusion is feasible while the large-scale rearrangements are limited or completely

frozen. This picture, which broadly describes the frustration kinetics of the spherical col-

loids in transition to the glassy state [Pusey and van Megen (1987)], is the current basis

of most studies aiming in depth understanding of the glass transition in hard sphere col-

loids. When such colloidal samples are subjected to shear, additional particle rearrange-

ments are induced leading to breaking of the cage and thus shear melting of the sample.

This behavior is microscopically evidenced by the enhanced diffusion over large length

scales corresponding to out of cage motions [H�ebraud et al. (1997); H€ohler et al. (1997);

Petekidis et al. (2002)]. One major advantage of LS-echo is that the particle rearrange-

ments induced by the Brownian forces can be distinguished from those induced by the

shear forces by defining

Pðt ¼ mTÞ �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffigð2ÞðmTÞ � 1

q(5)

with t¼mT indicating that the correlation function is determined at delay times equal to

multiples of the oscillation period. Using Eqs. (3) and (5), the amplitude of the mth echoe

at a certain strain relative to its amplitude at low strains (linear regime) can then be deter-

mined by

PðmTÞLimc!0P

� exp � 1

6nk2hDr2ðmTÞis

� �: (6)

The decay of this quantity from 1 at low strain amplitudes reflects the shear-induced irre-

versible particle rearrangements that take place in the sample.

Figure 6 shows the amplitudes of the various echoes relative to those at small strains

[PðtÞ=Limc!0P] obtained for NCC samples at a frequency of x¼ 10 Hz (62.8 rad/s). The

solid line is the correlation function,ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffigð2ÞðtÞ � 1

p, of the NCC suspension at rest meas-

ured by multispeckle DLS in the transmission geometry. At a strain amplitude of

c0¼ 3%, the amplitudes of the echoes follow the correlation function at rest (solid line in

Fig. 6). This implies that at such small strain amplitudes, the shear-induced deformation

is in the linear regime and the mechanical nonlinearities are negligible. On the micro-

scopic scale, the NCC spindles exhibit a reversible motion after an integral number of

oscillations to their initial position within distance of about half of their length (corre-

sponding to lDWS). This indicates that at such small strain amplitudes NCC spindles rear-

range solely due to the thermally induced Brownian motions. However, as the strain

amplitude is increased beyond �10%–15%, P starts to decay below the correlation func-

tion at rest indicating that the spindles are rearranging irreversibly. Such microscopic

shear-induced particle motion corresponds to the macroscopic mechanical yielding of the

sample that takes place at similar strain amplitudes as shown in Fig. 3(b).

142 DERAKHSHANDEH et al.

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Figures 7(a) and 7(b) depict the variation in the amplitudes of the first and sixth echoes

as a function of the strain amplitude at two frequencies of 1 Hz (6.28 rad/s) and 10 Hz

(62.8 rad/s), respectively. There is no change in the height of the first echo up to the strain

amplitudes of 15% at x¼ 1 Hz (6.28 rad/s) and 27% at 10 Hz (62.8 rad/s). This again is a

direct microscopic probe showing a purely elastic deformation of the NCC spindles over

a distance of around half their length. However, increasing the strain amplitude beyond a

critical strain, the first echo drops as the suspensions begin to flow. This corresponds to

irreversible rearrangement of the spindles on the microscopic scale.

In order to quantify the rearrangement of the NCC spindles in the suspension, the

data of Fig. 6 were fitted to a stretched-exponential function, expðt=tcÞb, in order to

determine the relaxation time, tc, and power index b. The insets in Figs. 7(a) and 7(b)

show the variation of the relaxation time and power index with the applied strain at

frequencies of 1 Hz (6.28 rad/s) and 10 Hz (62.8 rad/s), respectively. The relaxation

time decreases with the applied strain amplitude showing that the spindles are rearrang-

ing faster as the strain amplitude and thus the average shear rate, _c ¼ xc0, is increased.

The relaxation time decreases with _c following a power law relationship, tc / _cn, with

n¼ 0.852 and 0.95 at x¼ 1 Hz (6.28 rad/s) and 10 Hz (62.8 rad/s), respectively. In other

words, the relaxation process becomes faster as the frequency of oscillation increases.

A sublinear decrease of the characteristic relaxation time representing the time required

for the spindles to move under oscillatory shear is reminisced of the shear-induced

long-time relaxation of hard sphere glasses subjected to steady shear [Besseling et al.(2007)].

The stretching exponent, b, was found to increase with shear rate. Additionally, at the

low frequency of 1 (Hz), b tends to 1 while at the frequency of 10 Hz (62.8 rad/s) and at

the higher strain amplitudes (or shear rates) it clearly exceeds 1 and reaches values close

to 2 at the highest strain amplitudes. Generally, single exponential (b¼ 1) or stretched-

exponential (b< 1) relaxations are representative of the diffusive processes while the

compressed exponentials (1<b< 2) indicate a combination of diffusion and ballistic

motion. The latter is likely caused by the strong collision induced rearrangements and

alignment of the spindles along the direction of shear as has been detected at steady-

shear rate (Fig. 2). This is likely the result of an effectively higher shear rate at a higher

frequency of 10 Hz (62.8 rad/s).

FIG. 6. Time dependence of echo heights, P(mT), at several strains and x¼ 10 Hz (62.8 rad/s). The solid line

represents the correlation function under application of no shear (Brownian motions). The deviation from “no

shear” correlation function is an indication of shear-induced irreversible rearrangements.

143RHEOLOGY OF NCC SUSPENSIONS

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Comparing the data from the two frequencies, it is noted that the critical strain for the

onset of irreversible rearrangements is smaller at x¼ 1 Hz (6.28 rad/s) (cc¼ 15%) than that

at x¼ 10 Hz (62.8 rad/s) (cc¼ 27%). This is in agreement with the yield strain data deter-

mined from the DSS shown in Fig. 4(b). In conjunction with the behavior of tc and b dis-

cussed above, these results suggest that the cage confining the NCC spindles at rest exhibits

stronger elasticity under oscillatory shear at higher frequencies. At lower frequencies,

Brownian motion induces short range rearrangements which assist the shear-induced cage

melting of the spindles. Increasing the frequency of oscillation, the role of the Brownian

motion is diminished and the samples yield at higher strain amplitudes. Similar observations

have been reported for hard sphere glasses [Petekidis et al. (2002); Petekidis et al. (2003)].

FIG. 7. The strain dependence of the first and sixth echo heights at (a) x¼ 1 Hz (6.28 rad/s) and (b) x¼ 10 Hz

(62.8 rad/s). Insets show the strain dependence of the relaxation time and power index obtained by the fits of a

stretched-exponential function. The solid lines are drawn as an eye-guide.

144 DERAKHSHANDEH et al.

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2. Short-term behavior: Strain decrease from 200% to 1%

To investigate the thixotropic effects triggered by the direction of change in the applied

strain, DTS experiments were performed by decreasing the strain amplitude from c0¼ 200%

to 1% and echoes were measured during the short-time rheological response of 0–300 s. The

NCC samples were found to yield at a strain amplitude of �25% at which point the ampli-

tude of the first echo drops significantly from 1. The yield strain measured here is fairly simi-

lar to that obtained by increasing the strain amplitude from 1% to 200%. This indicates that

the direction of the applied strain (increase or decrease) does not affect the yielding transition

in the NCC samples on both the macroscopic and the microscopic levels.

3. Long-term behavior: Strain increase from 1% to 200%

The long-term rheological response of the NCC samples to the application of constant

strains, i.e., the upward region of the DTS measurements, was studied by using the LS-

echo technique from 600 to 900 s.

Figure 8 shows the variation in the amplitude of different echoes obtained at various

strain amplitudes and at a frequency of x¼ 10 Hz (62.8 rad/s). These data were fitted to a

stretched-exponential function to extract the relaxation time of the NCC samples. The

relaxation time has been plotted as a function of the strain amplitude in the inset of

Fig. 9. The relaxation time decreases from 2.7 to 0.12 s and the power index increases

from 0.14 to 1.4 as the strain amplitude increases from 15% to 200%, respectively. Here

again, the relaxation time decreases with _c following a power law relationship, tc / _cn,

with n¼ 1.057. The relaxation times measured here are higher than those measured for

the short-term rheological response of the samples due to ageing.

Figure 9 shows the variation in the amplitude of the first echo with strain. Irreversible

particle rearrangement (yielding) begins at a strain of �33%, which is larger than that

required to irreversibly deform the samples during 0–300 s. This is consistent with the

rheological data obtained from DTS experiments showing ageing in the NCC samples,

which leads to a stronger solid that accommodates larger strain amplitudes before it

yields due to irreversible particle rearrangements.

The plateau (or slower decrease) of the first echo observed at strain amplitudes of

larger than �50% in Fig. 9 could be corroborated by a temporary change of the localiza-

tion of the spindles in a cage, which is more elastic at c0 50% allowing partially

FIG. 8. Time dependence of echo heights, P, at several strains for a 10 wt. % NCC suspension at x¼ 10 Hz

(62.8 rad/s) measured from 600 to 900 s.

145RHEOLOGY OF NCC SUSPENSIONS

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reversible motion of the spindles under oscillatory shear. Thus, while the original cage

structure (at rest) progressively, but rather abruptly breaks above the yield strain (�33%)

allowing significant delocalization of spindles up to 50%, at strains higher than the latter,

a more elastic, possibly anisotropic cage is formed, which slows down further enhance-

ment of irreversible rearrangements as strain amplitude is increased. The fact that this

behavior is more evident at long times (Fig. 9) while at short times (Fig. 7) it is barely

detected suggests that such cage restructuring (possibly involving some alignment of the

spindles) progresses slowly with time under large amplitude oscillatory shear.

V. CONCLUSIONS

NCC suspensions are characterized using DLS as well as polarized optical micros-

copy. NCC suspensions are found to be polydisperse systems composed of rigid spindle-

like particles exhibiting birefringence under shear flow deformations.

The reported rheological results show that concentrated NCC suspensions exhibit age-

ing under both oscillatory and shear flow deformations. The DTS under constant strain

amplitudes indicate that the storage modulus of NCC samples increases more rapidly

with time as the amplitude of the applied strain decreases. These observations are also

confirmed by the results obtained from the LS-echo. This technique is used to study the

dynamics of the NCC spindles under oscillatory shear flow deformations. It is found that

the particle motions are essentially reversible at strain amplitudes lower than the yield

strain, as anticipated for an elastic distortion. However, beyond the yield strain the ampli-

tude of the echo heights significantly drops, implying irreversible changes in the particle

positions, i.e., yielding. The yield strains measured by the LS-echo technique are found

to correspond to the strains at which storage and loss moduli cross over.

ACKNOWLEDGMENTS

The authors would like to acknowledge NSERC for the CRD Grant (CRD-379851-

2008) and EU funding through ToK “Cosines” (MTKD-CT-2005-029944). They also

FIG. 9. The strain dependence of the first and sixth echo heights for a 10 wt. % NCC sample under oscillatory

shear [x¼ 10 Hz (62.8 rad/s)] measured from 600 to 900 s. There is no strain dependence in the height of the

first echo below c0� 33% at which point sample yields irreversibly. Inset shows the relaxation time and power

index obtained by the fits of a stretched-exponential function.

146 DERAKHSHANDEH et al.

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thank Antje Larsen (FORTH) for valuable assistance with the light scattering

measurements.

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