Steady shear, small amplitude oscillatory shear
and capillary break-up extensional rheology
measurements of rod-like polymers
Azuraien Japper@Jaafar, Robert J. Poole
Department of Engineering, University of Liverpool, Brownlow Street, Liverpool, L69 3GH United
Kingdom
Steady and oscillatory shear measurements
Introduction
The rheology of two different semi-rigid “rod-like” polysaccharides in
aqueous solutions, Xanthan gum (XG, Ketrol TF from Kelco) and
Scleroglucan (SG, Tinocare GL from Ciba) were measured over a wide
range of concentration (0.01% - 0.75% w/w). Xanthan gum is a
polyelectrolyte produced using the bacterium Xanthomonas campestris.
Scleroglucan is a non-ionic polysaccharide produced by the fungi of genus
Sclerotium. The molecular weights of the polymers are reported by the
suppliers to be in excess of 106 g/mol.
105
XANTHAN GUM
104
10
1
10
0
10
-1
10
-2
10-3 -4
10
10
-3
10
-2
10
-1
0
10
10
Shear rate (1/s)
1
0s
0.12 s
0.14 s
0.08 s
-1
10
-2
10
-3
10
0.02 s
0.04 s
0.06 s
0
0.02
0.04
0.06
0.08
Time (s)
0.10 s
0.12 s
0.1
0.12
CaBER data
CaBER data
Exponential fit
Linear fit
Oliviera et. al. fit
0.14
10
-4
10
0
0.02
0.04
0.06
0.08
Time (s)
0.1
0.12
-3
10
-2
-1
10
10
Frequency, f (1/s)
0
DMID (t)
1
0.4
0.3
0.2
0.1
CaBER data
CaBER data
Exponential fit
Linear fit
0.8
0.7
Diameter (mm)
0.5
0.6
0.5
0.4
0.3
0.2
0.1
0
0.02
0.04
0.06
0.08
Time (s)
0.1
0.12
0.14

10
8



0.02
10
-2
10
10
0
c* = 0.019%
-1
c* = 0.067%
10
-3
10
-2
10
-1
0
10
10
Shear rate (1/s)
1
10
2
10
3
10
4
10
-2
10
-3
10
-2
-1
10
Concentration, c (w/w %)
10
0.04
0.06
0.08
Time (s)
0.1
0.12
0.14
0
1
100
10-1
10
10
G'-0.1% SG
G''-0.1% SG
G'-0.15% SG
G''-0.15% SG
G'-0.2% SG
G''-0.2% SG
G'-0.25% SG
G''-0.25% SG
G'-0.375% SG
G''-0.375% SG
G'-0.5% SG
G''-0.5% SG
Limit data
-2
-3
103
10
2
XG
2.91
c
SG
c1.33
10
1
10
-4
10
-3
-2
-1
10
10
Frequency, f (1/s)
10
0
10
10
1
1
0.1
0.2
0.3
0.4
0.5 0.6 0.7 0.80.9
Concentration, c (w/w %)









200

XG
Average XG
Ec1.35
SG
Average SG
1.39
Ec
0.4
0.6
Concentration, c (w/w %)








100



0.8
1
XG
Average XG
-0.7
rc
SG
Average SG
-1.0
rc

k 
DMID (t )   D1  1  exp  3t   V2 t  t 2 
t  t1 

 DMID (t ) 
,
 Do 
  2 ln 
  
4 dDMID (t )
,
Do
dt
 E    dD (t )
MID
dt
(Jones and Walters, Rheol Acta, 1987)
 
 E 3
Tr 
  



0.2
DMID (t)  D0 (GD 0 /σ )1/3 exp (-t / 3EX )
Alternatively you may calculate a Hencky strain at the midpoint, the strain rate
and estimate an apparent ‘extensional viscosity’:

50
(Oliviera et. al., JNNFM, 2006)
Trouton ratio is calculated from:

150
Experiment al elastic liquid
Ideal elastic liquid
σ
D MID (t)  0.1418 t c  t 
ηS

0.2
In this simple technique a cylindrical liquid bridge of the ‘test’ liquid is formed
between two circular plates 4 mm in diameter. An axial step strain is then applied
(i.e. the end plates are rapidly pulled apart to a fixed separation) which results in
the formation of an elongated liquid thread. The thread diameter reduces due to
surface tension and information about the extensional properties of the liquid can
be deduced from the evolution of the filament midpoint diameter which is
monitored using a laser micrometer.
A simple one-dimensional analysis, neglecting axial curvature and assuming that
the filament is axially uniform, shows that the filament can be characterised
simply by its midpoint diameter:
(McKinley and Tripathi, JoR, 2000) (Entov and Hinch, JNNFM, 1997)


0
-1
Newtonian liquid



6
4



SCLEROGLUCAN
0.6

250
0.9
XANTHAN GUM
0.7
t>0
12
0.14
1
0.8
20
18
16
14
2
-2
0.5% Scleroglucan at 20C (i,f=0.5, 2.2)
CaBER data
CaBER data
Exponential fit
Linear fit
Steady uniaxial extensional viscosity, E (Pas)
10-1
10
10
101
-4
0.14 s
0.5% Xanthan gum at 20C (i,f=0.5, 2.2)
0.9
Diameter (mm)
Diameter (mm)
-2
0
10-3
4
G'-0.025% XG
G''-0.025% XG
G'-0.05% XG
G''-0.05% XG
G'-0.1% XG
G''-0.1% XG
G'-0.15% XG
G''-0.15% XG
G'-0.2% XG
G''-0.2% XG
G'-0.25% XG
G''-0.25% XG
G'-0.375% XG
G''-0.375% XG
G'-0.5% XG
G''-0.5% XG
G'-0.75% XG
G''-0.75% XG
Limit data
D = 4 mm
Trouton ratio
10
CaBER data
CaBER data
Oliviera et. al. fit
Exponential fit
Linear fit
10
102
Plotting o versus concentration provides a convenient way of estimating c*, the so-called critical overlap
concentration, for both polymers. Below c*, which for XG is approximately 0.067% (670 ppm) and for SG,
0.019% (190 ppm), both solutions are dilute and o scales approximately as c1.44, above the critical overlap
concentration, interactions between the molecules occur and o increases much more rapidly with concentration.
SCLEROGLUCAN
10-1
XG
1.44
oc
oc5.18
SG
1.44
oc
3.20
oc
10-4
100
XANTHAN GUM
Diameter (mm)
100
10
10
1
Storage and loss modulus, G', G'' (Pa)
Storage and loss modulus, G', G'' (Pa)
10
t =- 20 ms
0.10 s
3
100
h0 = 2 mm
0.08 s
10
10
2
0.0075% SG
0.01% SG
0.015% SG
0.02% SG
0.025% SG
0.0375% SG
0.05% SG
0.075% SG
0.1% SG
0.15% SG
0.2% SG
0.25% SG
0.375% SG
0.5% SG
C-Y fit
10
 f = hf / h 0
hf  8.8 mm
0.06 s
2
3
101
Capillary break-up
measurements
0.04 s
10
10
Zero shear viscosity, o (Pas)
10
2
0.01% XG
0.025% XG
0.0375% XG
0.05% XG
0.07% XG
0.1% XG
0.15% XG
0.2% XG
0.25% XG
0.375% XG
0.5% XG
0.75% XG
C-Y fit
Relaxation time,  (s)
3
Shear viscosity,  (Pas)
Shear viscosity,  (Pas)
10
Steady and oscillatory shear measurements
•TA Instrument Rheolyst AR 1000N controlled stress rheometer
•Small amplitude oscillatory shear (SAOS) measurements only possible for
higher concentration solutions
•All SAOS measurements were conducted in linear viscoelastic region
Capillary break-up measurements
•ThermoHaake capillary break-up extensional rheometer (CaBER) with
laser micrometer (resolution~10m)
•High-speed digital imaging using Dantec Dynamics Nano Sense MKIII
high-speed camera at 2000 frames per second with Nikon 60mm f/2.8 lens
0.02 s
SCLEROGLUCAN
104
103
Methods
0s
104
0.4
0.6
Concentration, c (w/w %)
0.8
1
Newtonian-like linear thinning of the filament was observed sometime later after
the initial step strain
Steady uniaxial extensional viscosity increases with concentration
The magnitude of the Trouton ratio confirms the non-Newtonian behaviour of
both polymers as Tr >>3. However, the Trouton ratio exhibits a decrease in
magnitude with increasing concentration
Conclusions
•G is greater than G until the crossover frequency, which increases as the concentration decreases indicating that the behaviour corresponds to semi-rigid polymer chains and some
entanglements still exist, as suggested by Lee (2001).
•Due to the semi-rigid nature of the molecules, Newtonian-like linear filament thinning behaviour was observed in capillary break-up experiments.
•Steady uniaxial extensional viscosity increases almost linearly with concentration. These results suggest that as concentration increases, the polymer exhibits a more ordered molecular structure
resulting in increase molecular contact between molecules which subsequently leads to stronger molecular interactions and hence greater extensional behaviour.
•The magnitude of the Trouton ratio (>>3) confirms the non-Newtonian behaviour of these polymer even though Newtonian-like linear thinning was observed in the capillary break-up
experiments.