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O R I G I N A L P A P E R
Estimation of cellulose nanofibre aspect ratio
from measurements of fibre suspension gel point
Swambabu Varanasi Rongliang He
Warren Batchelor
Received: 6 February 2013 / Accepted: 9 June 2013 / Published online: 26 June 2013
Springer Science+Business Media Dordrecht 2013
Abstract Cellulose nanofibre aspect ratio controls
the properties of sheets made from nanofibres and
processing conditions, but aspect ratio is very difficult
to measure. In this paper, aspect ratio was estimated
from the gel point of a cellulose nanofibre suspension,
the solids concentration at which the transition from a
dilute to a semi-dilute suspension occurs. Four batches
of cellulose nanofibres were tested. Two were pro-
duced from softwood fibres using ball milling. Com-
mercially produced microfibrillated cellulose material
was also used, both in as supplied form and afterremoval of the larger fibres by filtering. The average
diameter measured from SEM images of fibres ranged
from 33 to 73 nm. One sample was too heavily treated
and an average dimension could not be measured. The
gel-point was measured both from the height of a layer
of cellulose nanofibres sedimented from a dilute
suspension or from the lowest solids concentration at
which a yield stress could be measured using a vane
rheometer. The two methods were closely in agree-
ment for all samples. Aspect ratio was then calculated
using either the effective medium (EMT) or crowding
number (CN) theories. Aspect ratio calculated with an
assumed fibre density of 1,500 kg/m3, using the CN
theory ranged from 155 to 60. Use of the EMT theory
reduced the calculated aspect ratio by between 11 and
23 %. Reducing the assumed density in suspension
from 1,500 to 1,166 kg/m3 reduced the calculated
aspect ratio by 1214 %. The heavily treated sample
had by far the lowest aspect ratio.
Keywords Cellulose nanofibres Gel point Aspect ratio Yield stress Sedimentation
Introduction
Cellulose is the most common organic polymer in the
world, representing 1.59 1012 tons of total annualbiomass growth, mostly in plants(Malcolm Brown et al.
1996). Since it is formed from CO2 gas in the
atmosphere via photosynthesis in plants, it is a sustain-
able and renewable source of material. Plant fibres
consist of cellulose nanofibrilsof 24 nm in diameteras a
structural unit which is made up of cellulose crystallites
of*4 nm in diameter (Malcolm Brown et al. 1996;
Jakob et al.1995). Green properties such as biocom-
patibility and biodegradability are also expected from
S. Varanasi W. Batchelor (&)Department of Chemical Engineering, Australian Pulp
and Paper Institute, Monash University,
Melbourne, Australia
e-mail: [email protected]
S. Varanasi
e-mail: [email protected]
R. He
Institute for Frontier Materials, Deakin University,
Geelong, VIC 3217, Australia
e-mail: [email protected]
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these naturally-occurring raw materials, which are
significantly advantageous for biomedical and environ-
mental applications over synthetic organic and inor-
ganic nanomaterials (Czaja et al. 2006). Over the last
two decades, the synthesis of cellulose nanofibres and
their applications in various fields have gained increas-
ing attention due to their high strength and stiffness,combined with low weight, biodegradability and
renewability (Siroand Plackett2010). Cellulose nano-
fibres can be used as reinforcing fibres in bio compos-
ites, strength additives (Ahola et al. 2008), and to
produce hydrogels, anti-microbial films (Czaja et al.
2006), and high-technology devices (Nogi et al.2009).
Although there are many methods available for
production of cellulose nanofibres (Eichhorn et al.
2010), one significant area still being developed is the
characterization of nanofibre dimensions (Zhang et al.
2012). Whilst a combination of microscopic techniqueswith image analysis can provide information on cellu-
lose nanofibre widths (Dufresne et al. 2000; Taniguchi
and Okamura1998; Janarthanan and Sain 2006), it is
more difficult to determine nanofibre lengths due to
entanglements and difficulties in identifying both ends
of individual nanofibres (Henriksson et al.2008; Ishii
et al. 2011). Recently, Zhang et al. used a sedimentation
method (Zhang et al. 2012) for measuring the aspect
ratio of nanofibres based on the method proposed by
Martinez et al. (Martinez et al. 2001) for wood pulp
fibres. Using this method, the aspect ratio is estimatedbased on the gel point concentration, the threshold
consistency at which a continuous network of fibres in
suspension forms. Below the gel point concentration,
the suspension does not contribute to the mechanical
strength (Derakhshandeh et al. 2011). The measured
aspect ratio has been shown to correlate with the
concentration range over which cellulose nanofibre
sheets could be formed using filtration (Zhang et al.
2012; Varanasi and Batchelor 2013). One criticism that
can be made of this method is that in order to observe a
visible sedimented layer the fibres must form structuresthat can scatter light in the visible range, thus requiring
complexes several hundred nanometres in size. An
alternative method to probing fibres in suspension that
avoids this problem is to study the suspension rheology.
The types of rheological measurements that can be
applied to fibre suspensions will depend on the solids
content of the suspension, i.e. whether the suspension
can be classified as dilute, semi-dilute or concentrated.
One previous report (Ishii et al. 2011) of cellulose
nanofibre length estimation used visco-elastic mea-
surements of dilute suspensions and estimated the fibre
length using the theory of linear visco-elasticity of
semi-flexible rod-like polymers in dilute suspension,
estimating the fibre length as 2.2 lm for 4 nm
diameter fibres, giving a very high aspect ratio of 550.
Other measurements in the concentrated and semi-dilute ranges include suspension yield stress measure-
ments (Mosse et al. 2012b) to investigate the interac-
tion of cationic polymers with cellulose fibres and
shear viscosity measurements for characterizing the
dispersion of carbon nanofibre suspensions colloidal
systems (Xu et al.2005) or TEMPO oxidised cellulose
nanofibre suspensions (Lasseuguette et al. 2008).
These are a particularly sensitive probe of fibre
suspensions because in the semi-dilute and concen-
trated regimes the rheological properties are often
dominated by the interaction and entanglement of thefibres, which in turn depend upon of the structural
properties such as diameter, length and aspect ratio.
In this paper we present a new method for
estimating the gel-point of cellulose nanofibre sus-
pensions by measuring suspension yield stress as a
function of concentration. We compare the results to
that obtained by sedimentation and estimate aspect
ratio by both methods.
Theory
There are three concentration regimes for particles
dispersed within a medium. Particles in suspension can
be in dilute, semi-dilute or concentrated states. Of
interest here is the boundary between these states. If the
volume concentration is denoted by U then the connec-
tivity threshold,Uc, is the boundary between the dilute
and semi-dilute regions, the lowest volume fraction
where the particles first form a continuous network and
the rigidity threshold,Ur, is the boundary between the
semi-dilute and concentrated regions, which is thelowest volume fraction at which the particle suspension
will exhibit mechanical stability under load (Celzard
etal. 2008). The connectivity threshold is also called the
gel point (Martinez et al.2001) .
In the work here, we shall consider the application
of the semi-empirical Crowding Number (CN) and of
the more rigorously derived Effective Medium theory
(EMT) to characterise the transition between states of
fibres in suspension.
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EMT was originally developed to solve problems
such as the conductivity of a material consisting of
particles dispersed in a medium. Of most relevance is
the extension of the theory to consider spheroids as the
dispersed particles (Celzard et al. 2000) and the
successful application to predicting the conductivity
of spheroid graphene dispersed in a matrix of air. Forprolate or oblate ellipsoids, Ucis given (Celzard et al.
2000) by
Uc 9Lc 1 Lc 2 Lc 15 9Lc 1
whereLcis the depolarization factor of the particles. If
the particle is modelled as a prolate ellipsoid with
equal minor axes, a and b then (Celzard et al.2000)Lcis given by
Lc 1 e2
2e3 ln
1 e1 e
2e
2
where e is the eccentricity which ise ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 a=c2q
where c is the major axis of the ellipsoid and when
expressed in terms of the fibre aspect ratio, A(= c/a),
yields e ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 A2p
. The rigidity threshold is then
related to the connectivity threshold byUr= 4Uc.
The Crowding Number (CN) theory has been
developed by Kerekes and Schell, based on earlier
work by Mason. The crowding number, N, is given byKerekes and Schell (1992) as
N 2=3 U l=d 2 2=3 UA2 3where l and d are the fibre length and diameter,
respectively, of the fibres in suspension. Based on the
number of contacts developed in a suspension, the
rigidity threshold has been identified as occurring at
N = 60 (Celzard et al. 2009) from which
Ur 90=A2 4
The connectivity threshold was experimentally deter-mined to be 16 4 (Martinez et al. 2001) from
analysis of PET measurements made on dilute fibre
sedimentation experiments, from which
Uc 24=A2 5The relationship between aspect ratio, A, and Urand
Ucis shown in Fig.1.
The aspect ratio can be calculated from either the
connectivity or rigidity thresholds by the following
equations as given in Table 1, where the equations for
the EMT theory were determined by fitting the data in
Fig.1.
Finally, we are most readily able to measure the
solid fraction and not the volume fraction. If we wish
to relate the volume fraction to the solids fraction, C
(kg fibre/kg of suspension), then we may write
C qfU= qfU ql 1 U
where qf and ql are
the density of the fibres and liquid, respectively, which
if U 1 can be simplified as C qf=ql
U or
U ql=qf
C. The solids fraction forthe connectivity
and rigidity thresholds are then denoted Cc and Cr,
respectively. The appropriate fibre density to useremains an open question. The density of the cellulose
nanofibres in the dry state is approximately 1,500 kg/m3,
however it is not clear that this is applicable to a
suspension of cellulose nanofibres in water, where a
reduction of density due to an uptake of water into the
structure is likely. Recent measurements of moisture
diffusion of softwood, hardwood and cellulose nano-
fibre samples have suggested that two phases of water
exist, a slow diffusing phase tightly bound with the
cellulose fibrils and a faster diffusing phase more
loosely bound (Perkins and Batchelor 2012). Inparticular the measurements suggested that the tightly
bound phase had a maximum capacity of approxi-
mately 0.5 g water/g fibre (Perkins and Batchelor
2012). The addition of this water to the fibres would
reduce the density of the cellulose nanofibres in
suspension to (2/3)9 1,500 ? (1/3) 9 1,000 kg/m3
= 1,333 kg/m3. There exists a further complication
that the samples tested here are not fully separated. If
this is the case then they will form connected
0
20
40
60
80
100
120
140
160
180
0 0.01 0.02 0.03 0.04 0.05 0.06
AspectRaio
Phi
PhiC (EMT)
PhiC(CN)
PhiR(EMT)
PhiR(CN)
Fig. 1 Aspect ratio predicted from the connectivity (PhiC (Uc))
and Rigidity (PhiR (Ur)) thresholds using the EMT and CN
theories
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assemblies with reduced density due to the water
between the connected fibres. Given the uncertainties
in the density we will calculate aspect ratios estimated
from threshold solids concentration using three differ-
ent densities using the equations given in Table2
below.
Experimental
Material
Cellulose nanofibres were prepared using two different
methods. In the first method, nanofibres were prepared
as reported previously (Varanasi et al. 2012; Varanasi
and Batchelor 2013). Micro fibrillated cellulose (MFC)
supplied from DAICEL Chemical Industries Limited
(grade Celish KY-100G) was used as the starting
material for preparing cellulose nanofibres as well as
being tested. The material contains a mixture of
nanofibres and larger fibres and particles. The large
fibres and particles were filtered from the MFC sample
using a solids concentration of 0.5 kg/m3 and two
fabric filters with 100 lm openings to retain the larger
fibres on the fabric. The filtrate was centrifuged at
5,000 rpm for 20 min. After centrifuging, the super-
natant was discarded and only the nanofibres at the
bottom of tubes were collected. The yields of the
filtration process before and after centrifugation were
21.6 and 20 %, respectively. More details are given in
Zhang et al. (2012). The starting material was also used
for measurements. In this paper, the original sample
and the sample prepared by filtration have been
labelled as MFC and NF, respectively.
In the second method, cellulose nanofibres were
prepared using ball milling with a SPEX 8000 shaker
mill. Firstly, cellulose pulp sheet (NIST reference
material 8495) was cut into 5 9 5 cm pieces and
soaked in deionised water overnight in the refrigerator
to prepare 1 wt% solid suspension. The wet cellulose
pieces were then shredded using a conventionalkitchen blender and then stirred at 70 C overnight.
Then 20 g of 1 wt% cellulose pulp suspension, 45 g of
cerium-doped Zirconium balls (0.5 mm in diameter)
and 20 mL of deionised water were then placed in a
70 ml polypropylene container and milled using Spex
8000 ball mill for 60 and 90 min, for the NIST60 and
NIST90 grades, respectively. The final suspension was
filtered using a polyester mesh (opening size 125
micron) to remove the zirconium balls and any larger
remaining fibres. The filtrate was then stored in the
refrigerator and used as required. Results from earlierexperiments to manufacture cellulose nanofibres from
this starting material have been reported in Zhang et al.
(2012).
Diameter distribution
SEM Images of MFC and Nanofibre samples were
taken using a JEOL SEM (JSM-7001F FEGSEM) and
NIST60 and NIST90 were taken using Supra 55 V
SEM. Samples were highly diluted and a drop of
suspension was cast on a metal plate, air dried and thenplatinum coated. Coated samples were imaged using
SEM. The magnification ranged from 3,000 to 80,000.
Diameter distribution of MFC, NF and NIST60
samples were measured from SEM images. NIST90
samples only contained a few fibres and square
particles so the diameter distribution was not mea-
sured for this sample.
From each image, the width of each nanofibre
observable in the image was measured using ImageJ.
The fibre diameters measured in each image were then
sorted into bins of 10 nm size and normalized tocounts/m2, by dividing by the total area of the image.
Table 1 Equations to calculate aspect ratio using the EMT
and CN theories
Uc (EMT) Ur(EMT) Uc (CN) Ur(CN)
A 2:52U0:58c A 5:64U0:58r A 4:90U0:5c A 9:49U0:5r
Table 2 Equations used
for calculating aspect ratio
from solids fraction, C
Assumed density,
qf(kg/m3
)
EMT, Cc EMT, Cr CN, Cc CN, Cr
1,500 A 3:19C0:58c A 7:13C0:58r A 6:0C0:5c A 11:61C0:5r1,333 A 2:98C0:58c A 6:66C0:58r A 5:66C0:5c A 10:95C0:5r1,166 A 2:76C0:58c A 6:17C0:58r A 5:29C0:5c A 10:24C0:5r
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Fractions were calculated by dividing the individual
bin counts/m2 with total counts/m2. In the event that a
bin had fibres measured at different magnifications,
the highest value of counts/m2 was used. Further
details of the method are given in Zhang et al. (2012).
Yield stress measurement
Yield stress was measured on fibre suspensions using
the Haake Rotovisco RV20 system with four vanes of
38 mm (diameter) by 76 mm (length). This method
was described in more detail in Mosse et al. (2012a, b).
The suspension with known concentration was placed
in a beaker and the vane fully immersed. The maximum
torque, quoted from the user manual, measurable by
the instrument was 0.049 Nm at 100 % full scale.
Rheometer can be operated at three different scales, 1,
10 and 100 % torque. Measurements were carried out
using the 1 % scale. Maximum measurable torque
value at 1 % scale is 4.9 9 10-4 Nm. The instrument
output is in volts. The smallest subdivision is 1/1,000 of
the maximum measureable torque and thus the lowest
possible torque value that can be measured is
4.9 9 10-7 Nm. All the values discussed in the results
are within the 1 % scale range. Beaker dimensions are
72 mm diameter and 92 cm length, and the beaker
diameter is much larger than the vane diameter,
minimising the chance of slip at the wall. Prior to each
measurement series at a given solids concentration, the
pulp suspension was stirred thoroughly using the vane
rotating at 500 rpm (the highest speed setting),
removing any air bubbles in the pulp and ensuring that
the pulp was evenly distributed throughout the beaker.
Each sample was mixed for a minimum of 2 min until
the suspension was completely clear. Five runs were
made for each sample at a given solids concentration.
Before each run, the sample was mixed for 10 s at
500 rpm, before being allowed to stand for 30 s.
Following this, a measurement was taken by initiating
shear flow at a rotation rate of 0.65 rpm, and recording
the torque measured as a function of time.
Yield stress is the maximum stress sustained by the
suspension at the onset of continuous motion. The
peak torque in each start-up of shear flow experiment
was converted to yield stress using following equation
(Dzuy and Boger1985):
Tm pD3
2
H
D 1
3
sy 6
where Tm is the maximum torque measured, D is the
diameter of the vane,His the height of the vane, and syis the yield stress.
Sedimentation
Estimates of nanofibre suspension gel point were madeby sedimentation experiments. This method was
described in more detail in Zhang et al. (2012). The
method was adapted for nanofibre suspensions from
calibration curves published for wood pulps by Marti-
nez et al. (Martinez et al. 2001). 250 ml of nanofibre
suspensions with solids concentration (=solids frac-
tion 9 suspension density) ranging from 0.5 to 5 kg/m3
were decanted into measuring cylinders. The suspen-
sion was agitated to suspend the fibres completely in the
cylinder, andthen the fibres were allowed to settle. Once
the fibres settled down completely, the height ofsediment in the cylinder was measured. A minimum
of 48 h was allowed for the sedimentation process.
Results and discussion
Fibre cross-section measurements
Figures2and3show the SEM images and distribution
of fibre diameter of the MFC sample, while the
corresponding data for the NF sample derived fromthe MFC sample are given in Figs. 4 and5. Figures2
and 3 show that the MFC sample contains nanofibres as
well as a few large fibres. The mean fibre diameter was
73 nm. These largefibres were mostly removed through
filtration, which reduced the mean diameter to 53 nm.
Figures6and7show that NIST60 sample contains
uniform nanofibres with average diameter of 33 nm.
The milling time of 60 min has produced a very
uniform sample with low fibre diameter. Figure8
shows an image of the NIST90 sample. This was milled
for 90 min. The increased milling time has clearlybroken down the nanofibres as observed in Fig. 8, as
the sample consists mostly of irregularly shaped
particles of low aspect ratio with only a few fibres.
Sedimentation data to calculate suspension gel
point
The sedimentation data obtained for all four samples is
shown in Fig. 9. For each sample, the sedimentation
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behaviour was measured of fibre suspensions with
different dilute concentrations. A graph of initial solid
concentration (C0) versus the ratio of sediment height
(hs) to initial suspension height (H0) was then plotted
Fig. 2 SEM image of MFC sample
Fig. 3 Diameter distribution of MFC sample
Fig. 4 SEM image of Nanofibres sample
Fig. 5 Distribution of fibre diameters for the nanofibre sample
Fig. 6 SEM Image of NIST60 sample
Fig. 7 Distribution of fibre diameters for the NIST60 sample
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and fitted with a quadratic equation. The linear term of
the fit then gives the gel concentration, gc. The resultsof the fits, fitting statistics and confidence intervals are
given in Table3.
Finally, it is interesting to consider whether the
rigidity threshold can be applied to this data. As
discussed previously, the rigidity threshold occurs at a
volume concentration that is 3.75 times (Crowding
number) or 4 times (EMF theory) (Celzard et al.2009)
the connectivity threshold. The fits to the data show
that these concentrations are only achieved at solids
concentrations well above what would be required to
produce Hs/H0 = 1, i.e. the lowest concentration
where the suspension does not sediment, suggesting
that the rigidity threshold is not applicable to sedi-
mentation data.
Yield stress measurements
Yield stress is one of the most important rheological
properties of semi-dilute or concentrated fibre suspen-
sions. Unless it is exceeded, flow does not take place.
Yield stress is the maximum stress reached when strain
is increased to initiate flow, after which stress
decreases. The maximum stress is called the ultimate
shear strength and used as a measure of apparent yield
stress (Liddel and Boger1996). A yield stress occurs
because the fibres form a continuous network, wherebyfibres are restrained from moving because of contacts
with other fibres (Derakhshandeh et al. 2011). The
corollary is that a dilute fibre suspension will display no
yield stress. In the work here yield stress is measured as
a function of solids concentration in order to determine
the transition from a dilute fibre suspension to a semi-
dilute fibre suspension, i.e. the solids concentration at
which a continuous network first forms.
There are many methods available to measure yield
stress. We used a vane rheometer, whereby the torque
was measured as a function of time. If the fibresuspension has a yield stress at that concentration, then
the torque value reaches maximum and then decreases
(Derakhshandeh et al. 2011). If the fibre suspension
does not have a yield stress at that concentration,
torque profile of fibre suspension will be like the
torque profile of water. This maximum torque value is
called the peak torque in the rest of discussion.
Torque values as function of time at different
concentrations are shown in Figs.10, 11, 12 and 13
for MFC, NF, NIST90 and NIST60 suspensions,
respectively. In Fig.10, three replicates of torque
Fig. 8 SEM Image of NIST90 sample
Fig. 9 Sedimentation data
Table 3 Gel point solids
concentrations from
sedimentation method and
the standard errors of the fit
given in brackets
Sample Fitting equation Gel point solids
concentration (kg/m3
)
Solids mass
fraction
MFC y = 2.03x2? 1.78x, R
2= 0.98 1.78 (0.54) 0.00178
NF y = 1.98x2? 2.30x, R
2= 0.99 2.30 (0.27) 0.00230
NIST90 y = 5.65x2? 9.35x, R
2= 0.99 9.35 (0.50) 0.00935
NIST60 y = 1.59x, R2= 0.99 1.59 (0.02) 0.00159
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values as function of times for solids concentration of
2.5 kg/m3 are shown. These show that results were
consistent and reproducible. The deviation between
runs for a given sample was at most 10 %. There were
several interesting points from Figs. 10,11,12and13.
Figures10 and11contain measurements made at 0 %
solids concentration (distilled water only)and show thatthe vane rheometer has a small level of intrinsic drift.
All measurements showed a small initial increase
associated with commencement of rotation of the vanes
followed by a drift downwardsas the rotation continued.
The maximum peak torque observable when measuring
water alone was approximately 7.2 9 10-6 N m. The
effect of testing below and above the gel point can be
seen very clearly in Fig.11. The test at a solids
concentration of 2 kg/m3 was essentially indistinguish-
able from the water curve indicating that the fibre
suspension was dilute and the fibres did not form acontinuous network. Increasing the solids concentration
to 2.5 kg/m3 however produced an observable yield
stress with torque increasing to a yield stress of
2.5 9 10-5 N m after 10 s before flattening out. Some
other cases are less clear cut. For example the curve for
the MFC sample at 1.0 kg/m3 solids concentration
showed a similar shape to other solids concentrations
which displayed a yield stress but the maximum torque
reached was similar to that produced by water alone.
The first unambiguous evidence of a yield stress was
only observed when the solids concentration wasincreased to 1.5 kg/m3. An observable peak torque
was observed at minimum concentration of 2.5 kg/m3
for NF suspension, 10 kg/m3 for NIST90 suspension
and 1.5 kg/m3 for NIST60 suspension.
For the MFC and NF samples, Cc was determined
by fitting the data of yield stress versus concentration,
as described below. However, there was insufficient
sample for the NIST90 and 60 samples, so for these
two samples, Cc was determined as the lowest solids
fraction at which a yield stress could be measured.
For the MFC and NF samples, yield stress mea-
surements were carried for the samples at a range of
0
0.00005
0.0001
0.00015
0.0002
0.00025
0.0003
0.00035
0.0004
0.00045
0 10 20 30 40
Torque
(N.m
)
Time (sec)
2.5
2.5
2.5
1.5
1.0
0.5
0
Solids
Concentration
(kg/m3)
Fig. 10 Torque measured from instrument as function of time
for MFC sample and three individual measurement for solids
concentration 2.5 kg/m3
0
0.000005
0.00001
0.000015
0.00002
0.000025
0.00003
0 5 10 15 20 25
Torque(N.m
)
Time (sec)
2.5
2.0
0
Solids
Concentration
(Kg/m3)
Fig. 11 Torque measured from instrument as function of time
for NF sample
0.000000
0.000005
0.000010
0.000015
0.000020
0.000025
0.000030
0.000035
0.000040
0 5 10 15 20 25
Torque(N.m
)
Time (sec)
10
8.0
6.0
SolidsConcentration
(Kg/m3
)
Fig. 12 Torque measured from instrument as function of time
for NIST90 Sample
0.000000
0.000005
0.000010
0.000015
0.000020
0.000025
0 2 4 6 8
Torque(N.m
)
Time (sec)
2.5
1.5
Solids
Concentration(Kg/m3)
Fig. 13 Torque measured from instrument as function of time
for NIST60 sample
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different concentrations at which peak torque was
observed. Yield stress was calculated from peak
torques at different concentrations higher than the
minimum concentration as mentioned in the experi-
mental procedure for MFC and NF suspensions and
plotted against concentration in Figs.14 and 15.
Increasing suspension concentration increases yieldstress because the increase in the number of fibre
contacts and entanglements, increases the strength of
the fibre network formed. The dependency of the yield
stress values on fibre weight percentage (=solids
concentration 9 100/suspension density) has been
correlated using a power-law model sy aCbm, whereCmis the fibre weight percentage. The resulting fitted
constants are shown in the Table 4. These values are
consistent with literature values for wood pulp fibre
suspensions, which for a ranged from 1.8\ a\ 24.5
while values of b ranged from 1.69\ b\ 3.02
(Kerekes et al. 1985). Many key variables contributing
to these differences were not measured or reported
(Derakhshandeh et al. 2011). For example, Dalpke and
Kerekes (2005) reported that a and b values depend
upon aspect ratio (Dalpke and Kerekes 2005). The
fitting constants for MFC and NF suspensions are
within the range of previously reported results. Yield
stress value reported for MFC suspension at concen-
tration of 5 kg/m3 is 0.7 Pa which is close to the values
reported in Karppinen et al. (2011).
It can be inferred from Figs. 10,11,12and13that
minimum yield stress values for MFC sample is
between the solids concentrations of 11.5 kg/m3, for
NF suspension between 2.0 and 2.5 kg/m3
, forNIST90 suspension between 8.0 and 10 kg/m3, for
NIST60 suspension 1.251.5 kg/m3. Assuming lowest
possible yield stress can be measured as
1.84 9 10-5 N m torque or a yield stress of 0.11 Pa,
then the corresponding concentration values were
found from the power law fitting equation.
The gel points in Table 5calculated from the yield
stress measurements are in excellent agreement with
those obtained from the sedimentation data and given
in Table3. The NF sample has lower aspect ratio
compared to MFC although the NF sample has a loweraverage diameter than the MFC sample. There are
likely to be two factors contributing to this. Firstly, the
highest aspect ratio nanomaterial may have been
removed with the supernatant after centrifugation. In
addition, the higher aspect ratio nanofibres may have
been retained preferentially on the fibres retained on
the filter mat. The gel-points measured for the MFC,
NF and NIST60 samples are also in good agreement
with previous measurements from the literature. Gel
0 0.5 1 1.50
2
4
6
8
10
12
14
16
18
Fibre weight percentage
Yields
tress(Pa)
Experimental
Kerekes et.al.(1985)
Fig. 14 Effect of fibre weight percentage on yield stress for
MFC suspension
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
5
10
15
20
25
30
35
40
Fibre weight percentage
Yield
stress
(Pa)
Experimental
Kerekes et.al.(1985)
Fig. 15 Effect of fibre weight percentage on yield stress for NF
suspensions
Table 4 Power-law fitting constants for MFC and NF samples
Sample Power law fitting constants
a b
MFC 6.70 2.34
NF 6.34 2.57
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points estimated by sedimentation for three nanofibre
samples derived from the same precursor material as
the NIST90 and 60 samples, ranged from 1.76 to
5.37 kg/m3 (Zhang et al. 2012) while the gel-point
estimated from the change of slope of viscosity as a
function of solids concentration of a MFC sample
prepared by TEMPO oxidation of sulphite pine pulpwas approximately 2 kg/m3 (Lasseuguette et al. 2008).
The data of Ishii et al. (2011) showed a boundary
between dilute and semi-dilute suspensions of nano-
fibre prepared by TEMPO oxidation of bleached
hardwood kraft pulp was between 0.1 and 0.2 kg/m3.
They estimated the boundary based on the terminal
relaxation time of dilute suspensions. They have done
measurements at 0.1 kg/m3 and 0.2 kg/m3 but inter-
mediate concentrations were not tested.
Calculated aspect ratios
Table6 shows the aspect ratios calculated from all
four samples using the values ofCc calculated from the
sedimentation and yield stress measurements, using
the EMT and CN theories at several different densities
of the fibres in suspension, as given in Table 2.
The Table6 shows firstly that estimated aspect
ratio using either sedimentation or yield stress mea-
surements still has considerable sources of uncer-
tainty. We do not know the correct density of the fibresin suspension to use, and neither the model of a
straight cylindrical fibre used in the CN theory or of a
spheroid used in the EMT theory completely repre-
sents the reality of the fibres in suspension. The basic
Crowding Number theory is based on single averages
only. Kropholler and Sampson (2001) reported that
mean Crowding Number of fibre with a distribution of
lengths is higher than that for fibres of uniform lengths
equal to mean by a factor that is dependent only on the
coefficient of variation of fibre length. The crowding
number does not depend too strongly on coefficient of
variation of the length distribution. EMT is actually
based on inclusions with same aspect ratio and shape
while allowing an arbitrary distribution of lengths. No
method is available to calculate length distribution
from average aspect ratio measurement.However it is encouraging that the data set is quite
consistent between samples and with the different
theories and fibre densities used. From the data the
ranking order of aspect ratio is NIST60 having the
largest aspect ratio followed by the MFC, the NF and
the NIST90 samples, independent of the fibre density
or the theory used. There is also excellent qualitative
agreement between the SEM images of the different
samples and the calculated aspect ratios. The exces-
sive treatment applied to produce fibre fragmentation
in the NIST90 samples is observable both in the SEMimage shown in Fig. 8as well as producing sedimen-
tation curves and yield stress measurements that are
substantially different to the other three samples. The
aspect ratio estimated for the nanofibre prepared by
Ishii et al. (2011) based on the method reported here
assuming gel point concentration as 0.2 kg/m3 is 440,
when the fibre density is assumed to be 1,500 kg/m3.
This compares well with the aspect ratio of 550
estimated by Ishii et al. (2011) from terminal relax-
ation times. They reported that nanofibres are dis-
persed without entanglement.It is also encouraging that the two independent
methods of measuring Cc are also in excellent
agreement, despite sedimentation relying on the
formation of structures large enough to scatter visible
light, while the yield stress measurement relies on the
establishment of a continuous network of fibres. The
results suggest that either method could be chosen
depending on equipment availability and the rapidity
with which the measurements are required.
There still remains the question as to the meaning of
the aspect ratio estimated here. As is observable in theSEM images of the fibres in Figs. 2, 4 and 6, the
nanofibres are often not fully separated and often form
network type structures. It is open question as to
whether fibre lengths calculated by dividing aspect
ratio by average fibre diameter are physically
reasonable.
However, as discussed in the theory, the statistics of
fibre contacts in suspension depend only on aspect
ratio. The aspect ratio controls both the connectivity
Table 5 Gel points for MFC,NF, NIST90 and NIST60 sam-
ples from yield stress measurements
Suspension Gel point concentration
of suspension (kg/m3
)
Solids mass
fraction (kg/kg)
MFC 1.76 1.76E-03
NF 2.4 2.4E-03
NIST90 10 10E-03
NIST60 1.5 1.5E-03
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(gel-point) and rigidity thresholds. We have demon-
strated previously a method to rapidly form cellulose
nanofibre sheets (Varanasi and Batchelor2013) using
commercial woven filters. We have shown that almost
100 % retention is possible if the sheets are formed at
solids concentrations above the gel-point. The contin-
uous network of nanofibres, whether individual orpresent as networks, prevents the nanofibres from
being pulled through the 125 lm filter openings under
the applied vacuum. Sheets were unable to be formed
through filtration when the initial solids content was
less than the gel-point (Varanasi and Batchelor2013).
It should be noted that, when using this method, we
were readily able to form sheets using filtration from
the MFC, NF and NIST60 samples, which all have
high aspect ratios, but that it proved impossible to
form a sheet using the NIST90 sample, which had a
very low aspect ratio.
Conclusion
Two simple methods were developed for measuring
suspension gel point for cellulose nanofibres based on
either yield stress measurements or sedimentation.
Aspect ratios were calculated using effective medium
theory (EMT) and Crowding number (CN) theory.
Both theories showed reasonable agreement with each
other. Four different types of cellulose nanofibres were
prepared and tested. Aspect ratios were calculated for
assumed density of fibre in suspension ranging from
1,166 to 1,500 kg/m3. Aspect ratios of MFC, NF,
NIST90 and NIST60 are 142, 125, 62 and 150 at
density of 1,500 kg/m3. Suspension gel point andAspect ratio calculated from either the sedimentation
or suspension yield stress methods are quite consistent
between samples and with the different theories and
fibre densities used.
Acknowledgments The authors would like to acknowledge
the facilities used with the Monash Center for Electron
Microscopy. The authors would like to thank Wade Mosse
and Mae-Gene Yew for assisting us with rheological
measurements and Liyuan Zhang and A.Prof. Takuya Tsuzuki
for helping us to develop the method for separating nanofibres
from MFC sample. We acknowledge the financial support of theAustralian Research Council, Australian Paper, Nopco
Australasia, Norske Skog, SCA Hygiene Australasia and Visy
through Linkage Project Grants LP0989823 and LP0990526.
Swambabu Varanasi thanks Monash University for a MGS and
FEIPRS Scholarship.
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