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Large amplitude oscillatory shear of xanthan gum solutions. Effect of sodium chloride (NaCl) concentration
Journal of Food Engineering 126 (2014) 165–172
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Large amplitude oscillatory shear of xanthan gum solutions. Effect of sodium chloride (NaCl) concentration J.A. Carmona, P. Ramírez ⇑, N. Calero, J. Muñoz Departamento de Ingeniería Química, Universidad de Sevilla, Facultad de Química, 41012 Sevilla, Spain
a r t i c l e
i n f o
Article history: Received 18 September 2013 Received in revised form 11 November 2013 Accepted 16 November 2013 Available online 23 November 2013 Keywords: Rheological properties Xanthan gum Nonlinear viscoelasticity LAOS
a b s t r a c t Large amplitude oscillatory shear (LAOS) results are shown to be useful to describe the mechanical behaviour of materials at large deformations, well beyond the linear viscoelastic region, which are closer to real processing conditions. We illustrate the applications of LAOS with xanthan gum aqueous dispersions at different NaCl concentrations, on account of the great technological interest in this bacterial polysaccharide. LAOS is shown to be much more sensitive than small amplitude oscillatory shear (SAOS) to the influence of NaCl concentration. This is illustrated by a complete rheological characterisation of the system by means of both full-cycle (average elastic modulus and dynamic viscosity) and local methods (strain-hardening and shear-thickening ratios). The different rheological behaviours observed were related to the microstructures of the xanthan gum molecules as a function of the NaCl content. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Xanthan gum is a high molecular-weight extracellular polysaccharide produced by Xanthomonas campestris. The backbone of the polysaccharide chain consists of two b-D-glucose units linked through the 1st and 4th positions and the side chain consists of two mannose and one glucuronic acid. The side chain is linked to every other glucose of the backbone at the 3rd position. About half of the terminal mannose units have a pyruvic acid group linked to their 4th and 6th positions. The other mannose unit has an acetyl group at the 6th position (Sworn, 2009). Xanthan gum is soluble in cold-water, and due to its rheological properties and thermal stability, it is commonly used as an effective stabilizer and thickener with many areas of application (Marcotte et al., 2001). Xanthan gum aqueous solutions exhibit high consistency at low gum concentrations, high viscosity at low shear rates and a marked shear-thinning nature. The rheological properties of xanthan gum solutions are closely related to its conformational state (ordered and disordered conformations) and stiffness (Renaud et al., 2005), which in turn are strongly dependent on the temperature and ionic strength of the medium (Dário et al., 2011). On the one hand xanthan gum in solutions with low ionic strength or at high temperature adopts more flexible, disordered structures. On the other hand, at high ionic strength solutions the xanthan backbone takes on ⇑ Corresponding author. Tel.: +34 954557179. E-mail address: [email protected] (P. Ramírez). 0260-8774/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jfoodeng.2013.11.009
an order, helical conformation (Renaud et al., 2005; Rochefort and Middleman, 1987). Traditionally, the rheological properties of xanthan gum aqueous solutions have been determined by flow curves and small amplitude oscillatory shear (SAOS). In recent years, large amplitude oscillatory shear tests (LAOS) have received increasing attention, given that they can provide valuable information for a better understanding of complex rheological behaviours and give a deeper insight into microstructural changes (Ewoldt et al., 2010). Furthermore, another reason for the growing interest in LAOS tests is their usefulness in describing the elastic and viscous properties of complex fluids at large deformations (outside the linear viscoelastic domain), which are closer to real processing and application conditions. For instance, it has been proved recently that LAOS measurements are related to the sensory and textural properties of food, which is a topic of great interest (Melito et al., 2013). The objective of this work was to study the influence of NaCl concentration on the rheological properties of aqueous solutions of a commercial ‘‘advanced performance’’ xanthan gum. This is obtained by the manufacturer by optimising the fermentation process such that it yields higher viscosities than standard xanthan gum solutions and enhanced behaviour if submitted to high pressure homogenisation. This rheological study involves flow curves, small amplitude oscillatory shear (SAOS) and large amplitude oscillatory shear (LAOS). The non-linear oscillatory response was analysed using the framework proposed by Ewoldt et al. (2008) in order to obtain meaningful physical parameters.
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2. Materials and methods 2.1. Theory In dynamic oscillatory shear tests, the strain is varied periodically, usually with a sinusoidal perturbation at a fixed frequency. Oscillatory shear tests can be divided into two regimes. One regime implies the linear viscoelastic response (small amplitude oscillatory shear, SAOS) and the other regime involves a nonlinear material response (large amplitude oscillatory shear, LAOS). As the strain amplitude is increased at a fixed frequency a progressive transition from linear to nonlinear viscoelastic rheological behaviour can occur. When the response is linear (at small strain amplitudes) the material is characterised by two components, one in phase with the strain (elastic or storage modulus G0 (x)) and the other 90° out of phase (viscous or loss modulus, G00 (x)). The conditions required for the linear viscoelastic regime include: (1) stress amplitude should be linearly proportional to the imposed strain amplitude and (2) a torque response that involves only the first harmonic. The first condition implies that both moduli are independent of strain amplitude. The absence of larger harmonics in the stress response as required by the second condition ensures that the response remains sinusoidal. In this case, both storage and loss moduli are a function of the material microstructure and the oscillatory frequency (x). When the strain increases, the contribution of higher-order harmonics becomes significant and the stress response is not a single-harmonic sinusoid due to contribution of the other harmonics. Fig. 1 shows the evolution of normalised stress with the strain amplitude. As may be clearly observed, the sinusoidal stress is distorted when the strain increases as a consequence of the contribution of higher harmonics. A physical interpretation of the nonlinearities observed in a LAOS test is difficult since this nonlinear rheological behaviour cannot be uniquely described in terms of the linear viscoelastic moduli, G0 and G00 . Different methods have been proposed to analyse LAOS; Lissajous curves (Philippoff, 1966; Tee and Dealy, 1975), Fourier
transform rheology (Wilhelm et al., 1998; Wilhelm, 2002), stress decomposition (Cho et al., 2005; Ewoldt et al., 2008; Yu et al., 2009), decomposition on characteristic waveforms (Klein et al., 2007), and analysis of parameters related to Fourier transform rheology (Debbaut and Burhin, 2002; Hyun and Wilhelm, 2009). A popular and useful tool to analyse LAOS data is the FourierTransform method, which uses the relative intensities of higher harmonics as a measure of nonlinearity (Kallus et al., 2001; Wilhelm et al., 1998; Wilhelm, 2002). For a sinusoidal strain input c = c0 sin (xt), the stress response can be represented completely by Fourier series in two scale (elastic and viscous) forms (Dealy and Wissbrun, 1990):
rðt; x; c0 Þ ¼ c0
X 0 Gn ðx; c0 Þ sinðnxtÞ þ G00n ðx; c0 Þ cosðnxtÞ
ð1Þ
n¼odd
rðt; x; c0 Þ ¼ c_ 0
X
g0n ðx; c0 Þ sinðnxtÞ þ g00n ðx; c0 Þ cosðnxtÞ
ð2Þ
n¼odd
where c0 is the strain amplitude, G0n and G00n are the elastic and viscous moduli for the n harmonic, c_ 0 is the maximum strain rate (1/s), and g0n and g00n are the apparent viscosity in phase and out of phase with strain input for the n harmonic, respectively. Only the odd harmonics are included in this representation because the stress response is assumed to be odd symmetry with respect to the directionality of strain or strain rate, i.e., the material response is unchanged if the coordinate system is reversed (Bird et al., 1987). Even harmonic terms can be observed in transient responses, secondary flows (Atalik and Keunings, 2004), or wall slip (Graham, 1995). In the linear viscoelastic region, Eq. (1) reduces to the first harmonic n = 1, and the stress is a function of G01 and G001 . When the strain increases, and the system undergoes a transition from the linear to nonlinear regime, higher harmonics gain ground with respect to the first. In spite of the fact that this framework is robust and allows us to detect nonlinearities and to calculate the higher harmonics, it does not result in a clear physical interpretation of the higher harmonics.
Fig. 1. Strain sweep of 0.4% (m/m) xanthan gum unsalted aqueous solution at a fixed frequency of 4 rad/s at 20 °C. In the viscoelastic linear region, the viscoleastic moduli are independent of strain, nevertheless in the non-linear region both moduli are a function of strain.
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Ewoldt et al. (2008) proposed a new framework to provide a unified physical interpretation of LAOS results. This was based on a geometric representation and the definition of new parameters that allowed the interpretation of the nonlinearities, which may not be fully explained using the fundamental viscoelastic functions G0 and G00 . The framework proposed by Ewoldt is based on orthogonal decomposition of the general stress into elastic and viscous stress responses proposed by (Cho et al., 2005) r(t) = r0 (t) + r00 (t). Cho used symmetric arguments to decompose the stress into the elastic stress r0 (odd symmetry with respect x ðx ¼ cc ¼ sin xtÞ 0 _ and even symmetry with respect y ðy ¼ c_c0 ¼ cos xtÞÞ and the vis00 cous stress r (even symmetry with respect x and odd symmetry with respect y). Using these definitions, Eqs. (1) and (2) can be rewritten as:
X
r0 ¼ c0
G0n ðx; c0 Þ sin nxt
ð3Þ
n odd
X
r00 ¼ c0
G00n ðx; c0 Þ cos nxt
X c c ¼ c0 r en ðx; c0 ÞTn c0 c 0 n odd
ð5Þ
X c_ c_ r00 _ ¼ c_ 0 v n ðx; c_ 0 ÞTn _ c0 c0
ð6Þ
n odd
where Tn
c c0
and Tn
c_ c_ 0
are nth order Chebyshev polynomials of
the first kind, and en ðx; c0 Þ and v n ðx; c_ 0 Þ are the elastic and viscous Chebyshev coefficients. The relation between the Chebyshev coefficients in the strain or strain rate domain and the Fourier coefficients in the time domain are thus given by:
en ¼ G0n ð1Þðn1Þ=2
vn ¼
G00n
x
G0M ¼
G0L ¼
The elastic and viscous stresses are plotted versus the strain (c) and strain rate ðc_ Þ input functions, and Chebyshev polynomials of the first kind are fitted to the plots (Ewoldt et al., 2008): 0
viscous and elastic behaviour from the first- and third-order Chebyshev coefficients. The elastic modulus was broken down into a minimum strain modulus, G0M (the tangent modulus measured at c = 0), and large strain modulus, G0L (the secant modulus measured at maximum strain), that took higher harmonic contributions into account. These two moduli may be seen in a Lissajous plot of shear stress versus applied strain. The plot r(t) vs. c(t) are named as elastic Lissajous–Bowditch curves (Fig. 2a and b). These plots allow for a quantitative interpretation of Fourier or Chebyshev coefficients. Analogously, in the viscous scale, Ewoldt defined g01 ¼ G001 =x (the average dissipated energy per cycle) and g0L and g0M as local parameters, which indicate the instantaneous viscosity at the smallest and largest strain-rates, respectively (Ewoldt et al., 2008).
ð4Þ
n odd
¼ g0n
n : odd
n : odd
ð7Þ ð8Þ
The third-order Chebyshev coefficients (e3 and t3) may then be used to determine material nonlinear viscoelastic behaviour. Thus, material viscoelastic behaviour is classified in six categories: strain-softening (e3 < 0), strain-stiffening (e3 > 0), linear elastic e3 = 0, shear thinning (v3 < 0), shear thickening (v3 > 0) and linear viscous v3 = 0 (Ewoldt et al., 2008). An important point to consider was the definition of viscoelastic moduli in the nonlinear regime. Thus, G0 and G00 can be clearly and uniquely defined for the linear viscoelastic regime in which the stress response is a single-harmonic sinusoid. In the nonlinear regime, the definition of viscoelastic moduli is not unique (Ganeriwala and Rotz, 1987). The methods used to calculate viscoelastic moduli can be grouped into two categories: full cycle methods and local methods. A full cycle method requires at least one entire cycle of oscillatory data (or half-cycle which is then mirrored), which allows G01 and G001 to be calculated from the first-order Fourier or Chebyshev coefficients. G01 , G001 are a measure of the average elasticity and dissipated energy respectively in the material response at each imposed pair of LAOS coordinates (co, x). However, the aforementioned parameters cannot differentiate the elastic and viscous local response of a material at small and large instantaneous strains. In contrast, the local methods allow the viscoelastic moduli at an instantaneous strain to be calculated (intracycle non-linearities). Thus, Ewoldt et al. (2008) developed a new interpretation of viscoelastic moduli in the nonlinear region. This consisted of deriving
167
X 0 da j ¼ nG ¼ e1 3e3 þ dc c¼0 n odd n
X 0 a j ¼ G ð1Þðn1Þ=2 ¼ e1 þ e3 . . . c c¼c0 n odd n
ð9Þ
ð10Þ
da 1 X 00 g0M ¼ _ jc_ ¼: 0 ¼ nG ð1Þðn1Þ=2 ¼ t1 3t3 þ . . . dc x n odd n
ð11Þ
a 1 X 00 g0L ¼ _ jc_ ¼: c_ 0 ¼ G ¼ t1 þ t3 þ . . . c x n odd n
ð12Þ
These two moduli may be seen in a Lissajous plot of shear stress versus applied strain rate (Fig. 2c and d). The plot r(t) vs. c_ ðtÞ are named as viscous Lissajous–Bowditch curves. The calculation of the following ratios ðG0L =G0M and g0L =g0M Þ is a second method in order to define the strain and strain rate dependence behaviour. Thus, G0L =G0M < 1 indicates strain softening and G0L =G0M > 1 strain stiffening or strain hardening. In addition, g0L =g0M < 1 indicates shear-thinning and g0L =g0M > 0 shear thickening. In the linear viscoelastic region (at small strain), G0L ¼ G0M ¼ G01 and g0L ¼ g0M ¼ g01 , and the Lissajous plot shows a perfect elliptical shape, which is distorted when the strain increases and viscoelastic nonlinearities appear (Ewoldt et al., 2008). Also, Ewoldt defined two new ratios to avoid the singularity as G0M ! 0 (13 and 14). Thus, the strain-hardening and shear-thickening ratios were calculated from the elastic moduli and instantaneous viscosities, respectively:
S¼
T¼
ðG0L G0M Þ G0L ðg0L g0M Þ
g0L
ð13Þ
ð14Þ
S > 0 and T > 0 indicate intracycle strain stiffening and intracycle shear thickening, respectively, whereas S < 0 and T < 0 correspond to intracycle strain softening and intracycle shear thinning, respectively. 2.2. Materials KELTROLÒ Advanced Performance ‘‘Food Grade’’ xanthan gum, generously donated by CP Kelco, was used to prepare 0.4% (m/m) gum solutions. Different sodium chloride concentraitons ranging from 0 to 0.5%(m/m) were added to the gum solutions. NaCl were purchased from Panreac (99.5%(m/m) purity). The solutions studied were prepared with ultrapure Milli-Q water. All ingredients were used as received.
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Fig. 2. Lissajous–Bowditch curves obtained from experimental oscillatory tests of aqueous xanthan gum solution at 1 rad/s (0.4%(m/m) without NaCl). (a and b) Elastic Lissajous–Bowditch curves (c0 = 10%, within the linear viscoelastic region (LVR)) and (c0 = 300%, non-linear region). (c and d) Viscous Lissajous–Bowditch curves (c0 = 10%) and (c0 = 300%). G0M and g0M values are obtained from the tangent at zero instantaneous strain and strain rate, respectively (solid lines), whereas G0L and g0L are the secant modulus at maximum strain and strain rate, respectively (dashed lines). G0M ¼ G0L and g0M ¼ g0L within LVR. Temperature 20 °C.
2.3. Methods 2.3.1. Solution preparation First, the gum was slowly added to Milli-Q water under mechanical stirring (Ikavisc MR-D1), which was continued for 3 h at 25 °C. Afterwards, the solution was heated at 70 °C for 45 min under continuous stirring. Then, NaCl was added to the heated gum solution. This was sonicated for at least 1 h to remove the air bubbles within the solution. The solutions were stored for 24 h at 4 °C. The 0.4% (m/m) Xanthan gum solution studied contained a NaCl concentration ranging from 0 to 0.5%(m/m). 2.3.2. Rheological measurements Rheological oscillatory experiments were conducted with an ARES-LS controlled-strain rheometer (TA Instruments), equipped with a cone & plate geometry (angle: 0.0402 rad; diameter: 50 mm). Steady shear flow tests were carried out by a controlled-stress AR2000 rheometer (TA Instruments) using an aluminium plate & plate geometry of low inertia with smooth surface (60 mm diameter). All rheological tests were performed at 20 °C, using a solvent trap to inhibit evaporation and were repeated three times. 2.3.2.1. Small amplitude oscillatory shear (SAOS). Strain sweep tests were performed in the strain range from 1% to 1000% at a fixed frequency of 0.25, 1, 4 and 16 rad/s. Frequency sweep tests (from 20 to 0.05 rad/s) were performed selecting a strain (5%) well within the linear range.
criteria: steady-state approximation: to allow 0.1% change of shear rate’’. The experimental data fitted the Carreau model (Eq. (15)) fairly well (R2 > 0.99).
g¼ 1þ
g0
2 1n 2
ð15Þ
c_ c_ c
where c_ c is the critical shear rate for the onset of the shear-thinning response, n is the flow index, g0 is the zero-shear viscosity. 2.3.2.3. Large amplitude oscillatory shear (LAOS). The LAOS analysis requires both raw strain and stress signal which were acquired by means of native control software (TA Orchestrator), using the arbitrary wave-shape test as described by (Ewoldt et al., 2008). The arbitrary wave-shape test allows the raw data to be captured. The sampling rate of the arbitrary wave-shape test was about 100 points/s, which allowed us to work in the frequency range studied. The arbitrary wave-shape tests were performed at a fixed frequency of 4 rad/s and the amplitude of strain applied were 10, 30, 100, 300 and 1000%. 2.3.2.4. Data processing. The raw data obtained from the arbitrary wave-shape test were processed with MITlaos software (Ewoldt et al., 2007). This software was used to calculate the Fourier coefficients, Chebyshev coefficients, decomposition of stress and the viscoelastic moduli such as, G0L ; G0M ; g0L and g0M . 3. Results and discussion 3.1. Small amplitude oscillatory shear (SAOS)
2.3.2.2. Steady shear flow curves. Flow curve tests were carried out from 0.3 to 20 Pa, following a step-wise protocol: 10 points per decade (log distribution) 5 min (maximum time)/point. Cut-off
Oscillatory stress sweep tests at four different frequencies (0.25, 1, 4 and 16 rad/s), and four NaCl concentrations ranging from 0% to
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0.5%(m/m) were carried out in order to estimate the maximum amplitude value of the sinusoidal shear strain function which guarantees linear viscoelastic behaviour. The same critical strain value (29% ± 3%) that defines the linear viscoelastic region (LVR) was obtained in all cases. Fig. 3 shows by way of example the oscillatory strain sweep at 4 rad/s. G0 and G00 were not affected, regardless of the applied strain throughout the linear viscoelastic range. G0 showed a steep decrease when increasing strain above the critical strain value. However, G00 underwent just a slight drop. No influence of NaCl concentration was detected within the linear viscoelastic region. Nevertheless, within the non-linear viscoelastic region a certain difference was observed for the system in the absence of salt. Fig. 4 shows G0 and G00 as a function of frequency within LVR (strain = 5%). The results were not affected by salt concentration as shown by G0 , and only a slight deviation of G00 at high frequencies for the xanthan gum solution without NaCl was observed. The slight increase in the viscous response at higher frequencies could indicate some microstructural changes for the system without salt. It was observed that the frequency dependence of the elastic modulus can be quantitatively described by a power law. A value of 0.23 was obtained for the slope of all the G0 vs. x curves. The solutions studied exhibited weak-gel viscoelastic behaviour as demonstrated by this slope value and by the fact that G0 values lay above those of G00 . These results were consistent with those previously reported for xanthan gum solutions (Pal, 1995; Song et al., 2006; Talukdar et al., 1996).
169
Fig. 4. Storage (G0 ) and loss (G00 ) moduli as a function of frequency for xanthan gum solutions (0.4% (m/m)) with different contents of NaCl: 0% (m/m), 0.025% (m/m), 0.1% (m/m) and 0.5% (m/m) at 20 °C and at 4 rad/s. Standard deviation of the mean (three replicates) for G0 and G00 < 5%.
3.2. Flow behaviour Fig. 5 provides a comparison between complex viscosity, derived from SAOS measurements and steady shear viscosity. The Cox-Merz rule was not followed throughout the salt range studied (for the sake of clarity only one complex viscosity is shown). The departure from Cox-Merz rule confirms the occurrence of a structured system, supporting that the weak-gel structure was clearly set. Flow curves exhibited shear-thinning behaviour and a trend to reach a Newtonian region at low shear rate. The experimental data fitted the Carreau model (Eq. (15)) fairly well (R2 > 0.99). No significant differences were found for all the systems studied, therefore the same fitting parameters were used, which are given in the inset of Fig. 3.
Fig. 5. Frequency dependence of complex viscosity derived from SAOS measurements for 0.4% (m/m) xanthan gum solution containing 0.5% (m/m) NaCl (filled symbols). Shear-rate dependence of steady shear viscosity for all the systems studied (open symbols). T = 20 °C. The line shows data fitting to the Carreau model whose parameters are given in the inset. Standard deviation of the mean (three replicates) for g < 10% and for g⁄ < 5%.
3.3. Large amplitude oscillatory shear (LAOS)
Fig. 3. Storage (G0 ) and loss (G00 ) moduli as a function of strain for xanthan gum solutions (0.4%(m/m)) with different contents of NaCl: 0%(m/m), 0.025%(m/m), 0.1%(m/m) and 0.5%(m/m) at 20 °C and at 4 rad/s. Standard deviation of the mean (three replicates) for G0 and G00 < 5%.
In order to gain a deeper insight into the rheological and structural behaviour of the system large amplitude oscillatory shear measurements were carried out. First, we determined the average elasticity and dissipated energy in the material response by means of full cycle method. Fig. 6a shows the first harmonic (average) elastic modulus for the 0.4% (m/m) xanthan solutions with NaCl ranging from 0% to 0.5% (m/m) at 4 rad s1. The elastic modulus decreases beyond the critical strain (29%) indicating a strain softening behaviour for all the studied systems. The elastic response is not clearly affected by salt concentration in the linear viscoelastic region as was previously indicated by SAOS results. Above the critical strain limiting the LVR an increasingly clear difference between the elastic modulus of the xanthan gum solution with and without NaCl was found. G01 of xanthan gum solutions containing NaCl show higher values than those of the unsalted solution. This could be due to the shielding of the electrostatic repulsion between the
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Fig. 6. Oscillatory shear tests of xanthan gum at 4 rad/s analysed by means of LAOS parameters 0.4% (m/m) aqueous with 0% (m/m), 0.025% (m/m), 0.1% (m/m) and 0.5% (m/ m) NaCl. (a) First harmonic (average) elastic modulus G01 . (b) First harmonic (average) dynamic viscosity g01 . Standard deviation of the mean (three replicates) for G01 and g01 < 5%.
Fig. 7. Oscillatory shear tests of xanthan gum solutions at 4 rad/s analysed by means of LAOS parameters 0.4% (m/m) xanthan gum with 0% (m/m), 0.025% (m/m), 0.1% (m/m) and 0.5% (m/m) NaCl. (a) e3/e1. (b) v3/v1. (c) Strain-stiffening ratio, S. (d) Shear-thickening ratio, T. T = 20 °C. Standard deviation of the mean (three replicates) for e3/e1, v3/v1, T and S. It is shown that data point size exceeds the error margins.
charged side chains of xanthan gum which could lead to more compact structures which offer higher resistance to strain. Fig. 6b shows the first harmonic (average) dynamic viscosity for the 0.4% (m/m) xanthan solutions with NaCl ranging from 0% to 0.5% (m/m) at 4 rad s1. In contrast to G01 , a slight increase in the dynamic viscosity of the solutions was observed at the onset of the non-linear viscoelastic region before dropping regardless of NaCl concentration. This trend could be related to the common occurrence of a peak in G00 at the onset of the non-linear response which has been detected in many structured systems by means of SAOS tests. This was attributed by Lequeux et al. (1997) to a structural rearrangement preceding the collapse (Hyun et al., 2002; Lequeux et al., 1997). This effect is more marked for the system without NaCl. This fact could be a consequence of the occurrence of a more extended and disordered structure due to the electrostatic repulsion between the charged side chains of xanthan gum which initially offer a higher resistance to viscous flow. Nevertheless, the dynamic viscosity of the system without salt showed lower values at higher strains. This may be related to the drop in the elasticity indicating fewer points of interaction between xanthan molecules in
agreement with their progressive orientation in the flow direction (Rochefort and Middleman, 1987; Hyun et al., 2002). Further information on the influence of the salt concentration on the microstructure of xanthan gum can be obtained by analysing the viscoelastic moduli at instantaneous strains by means of both the Chebyshev coefficients and the above mentioned local method based on the S and T ratios. Fig. 7a and b show the parameters used to evaluate the intracycle elastic and viscous non-linearities; the third order elastic Chebyshev coefficient ratio, e3/e1; and the third order viscous Chebyshev coefficient ratio, t3/t1. e3/e1 and t3/t1 values within the LVR are close to zero. At strains above the critical one, two behaviours were observed for both elastic and viscous responses. At strains closer to the LVR the elastic ratio (Fig. 7a) was slightly negative, which corresponds to a strain-softening behaviour. However, at larger strains the sign of the parameters change from negative to positive indicating a transition from strain-softening to strain-stiffening behaviour. Furthermore, a clear difference at large strains was observed between the xanthan gum solutions without salt and with salt regardless of the amount of salt in the range studied 0.025–0.5%(m/m). This should be related to the presence
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more noticeable when no salt is added to the solution, which can be associated with a higher resistance to the flow accounting for the higher number of entanglements of the extended polymer in the absence of salt. At the highest strain-rate the intracycle behaviour became shear-thinning and all the systems showed the same values. The instantaneous elastic and viscous non-linearities can be also evaluated by means of the S and T ratios, as shown in Fig. 7c and d, respectively. Parameters S and T are obtained from Lissajous–Bowditch curves as explained above. The response is qualitatively analogous to those obtained from Chebyshev ratios. Shear-thickening ratio T and strain-stiffening ratio S show similar trends to t3/t1 and e3/e1 ratios, indicating that the methods support each other. 4. Conclusions
Fig. A1. Elastic Lissajous–Bowditch curves generated from experimental oscillatory tests of xanthan gum solution (0.4% (m/m) aqueous with 0% NaCl) at 20 °C. Solid lines are the total stress r(t)/rmax vs c(t)/c0. Dotted lines are the elastic stress r0 (t)/ rmax vs c(t)/c0. The maximum stress rmax is indicated above each curve.
Fig. A2. Viscous Lissajous–Bowditch curves generated from experimental oscillatory tests of xanthan gum solution (0.4% (m/m) aqueous with 0% NaCl) at 20 °C. Solid lines are the total stress r(t)/rmax vs c_ ðtÞ=c_ 0 . Dotted lines are the elastic stress r00 (t)/rmax vs c_ ðtÞ=c_ 0 . The maximum stress rmax is indicated above each curve.
of more extended polymer chains of the xanthan gum solution in the absence of salt which may offer more resistance to the elastic deformation, in accordance with the behaviour shown by G01 . Fig. 7b shows that the viscous ratios at 100% and 300% strain were positive, whereas at the highest strain (1000%) the sign became negative. The positive value of these parameters indicated a shear-thickening behaviour. This feature should be related to the well-known weak strain overshoot response obtained for xanthan gum solutions in start-up at the inception of shear experiments (Song et al., 2006; Hyun et al., 2002). The existence of this peak is due to a structural rearrangement, as explained above and confirms that the overshoot observed in stress growth experiments is a manifestation of nonlinear viscoelasticity rather than thixotropy. The shear-thickening behaviour at the onset of nonlinear behaviour is
The influence of NaCl addition on the rheological properties of a 0.4%(m/m) commercial ‘‘advanced performance’’ xanthan gum solution has been determined by means of oscillatory shear and steady shear flow curves. The information obtained from oscillatory frequency and strain sweep tests within the linear viscoelastic region demonstrated that regardless of the NaCl concentration used all the xanthan gum solutions studied behaved as a weak gel, and showed similar rheological properties. However, oscillatory strain sweep tests outside the linear viscoelastic region revealed slight differences for the xanthan solution in the absence of NaCl. All the systems studied exhibited shear thinning behaviour and a trend to reach a Newtonian region at low shear rates, which fitted fairly well the Carreau model. Flow curves were not influenced by sodium chloride addition. The departure from the Cox-Merz rule confirmed the occurrence of a structured system. Large amplitude oscillatory shear results were analysed by means of both full-cycle and local methods. A strain softening and shear-thinning behaviour was observed from the first harmonic (average) elastic modulus and dynamic viscosity respectively. The analysis of both parameters revealed significant differences associated with the dissimilar microstructures of the systems with and without NaCl. When NaCl is added the electrostatic repulsion between the side chains of the xanthan gum is shielded, leading to a more compact structure. A complete rheological characterisation of the systems was achieved by analysing the parameters deduced from local methods. Thus, a local strain stiffening behaviour was detected at large strains, which was more marked for the more extended conformation in the absence of NaCl. Furthermore, a local shear-thickening behaviour is observed at the onset of the non-linear viscoelastic region, which is also more evident for the system in the absence of NaCl. This response shifted to local shear thinning at higher strain rates congruently with flow curve results. LAOS is definitively proved to be a powerful tool that provides further rheological and therefore microstructural information about complex fluid systems. Acknowledgments The financial support received (Project CTQ2011-27371) from the Spanish Ministerio de Economía y Competitividad (MINECO) and from the European Commission (FEDER Programme) is kindly acknowledged Appendix A See Figs. A1 and A2.
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References Atalık, K., Keunings, R., 2004. On the occurrence of even harmonics in the shear stress response of viscoelastic fluids in large amplitude oscillatory shear. J. Nonnewton. Fluid Mech. 122, 107–116. Bird, R.B., Armstrong, R.C., Hassager, O., 1987. Dynamics of Polymeric Liquids: Volume 1 Fluid Mechanics. John Wiley & Sons Inc, New Yorkm, pp. 425–466 (second ed.). Cho, K.S., Hyun, K., Ahn, K.H., Lee, S.J., 2005. A geometrical interpretation of large amplitude oscillatory shear response. J. Rheol. 49 (3), 747–758. Dário, A.F., Hortêncio, L.M.A., Sierakowski, M.R., Neto, J.C.Q., Petri, D.F.S., 2011. The effect of calcium salts on the viscosity and adsorption behavior of xanthan. Carbohydr. Polym. 84 (1), 669–676. Dealy, J.M., Wissbrun, K.F., 1990. Melt Rheology and Its Role in Plastics Processing: Theory and Applications. Van Nostrand Reinhold, New York, pp. 217–222 (second ed.). Debbaut, B., Burhin, H., 2002. Large amplitude oscillatory shear and Fourier transform rheology for a high-density polyethylene: experiments and numerical simulation. J. Rheol. 46 (5), 1155–1176. Ewoldt, RH., Winter, P., McKinley, GH., 2007. MITlaos Version 2.1 Beta for MATLAB.MATLAB-Based Data Analysis Software for Characterizing Nonlinear Viscoelastic Responses to Oscillatory Shear Strain. Self-published, Cambridge, MA. Ewoldt, R.H., Hosoi, A.E., McKinley, G.H., 2008. New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear. J. Rheol. 52 (6), 1427–1458. Ewoldt, R.H., Winter, P., Maxey, J., McKinley, G.H., 2010. Large amplitude oscillatory shear of pseudoplastic and elastoviscoplastic materials. Rheol. Acta 49 (2), 191– 212. Graham, M.D., 1995. Wall slip and the nonlinear dynamics of large-amplitude oscillatory shear flows. J. Rheol. 39 (4), 697–712. Ganeriwala, S.N., Rotz, C.A., 1987. Fourier-transform mechanical analysis for determining the nonlinear viscoelastic properties of polymers. Polym. Eng. Sci. 27 (2), 165–178. Hyun, K., Kim, S.H., Ahn, K.H., Lee, S.J., 2002. Large amplitude oscillatory shear as a way to classify the complex fluids. J. Nonnewton. Fluid Mech. 107 (1–3), 51–65. Hyun, K., Wilhelm, M., 2009. Establishing a new mechanical nonlinear coefficient Q from FT-Rheology: first investigation on entangled linear and comb polymer model systems. Macromolecules 42 (1), 411–422.
Kallus, S., Willenbacher, N., Kirsch, S., Distler, D., Neidhofer, T., Wilhelm, M., Spiess, HW., 2001. Characterization of polymer dispersions by Fourier transform rheology. Rheol. Acta 40 (6), 552–559. Klein, O.C., Spiess, H.W., Calin, A., Balan, C., Wilhelm, M., 2007. Separation of the nonlinear oscillatory responseinto a superposition of linear, strain hardening, strain softening, and wall slip response. Macromolecules 40 (12), 4250–4259. Lequeux, F., Hebraud, P., Munch, J.P., Pine, D. (1997). Mechanical regimes in concentrated emulsions. In: Proceedings of The second World Congress on Emulsions, Bordeaux, France, pp. 179–180. Marcotte, M., Taherian-Hoshahili, A.R., Ramaswamy, H.S., 2001. Rheological properties of selected hydrocolloids as a function of concentration and temperature. Food Res. Int. 34 (8), 695–703. Melito, H.S., Daubert, C.R., Foegeding, E.A., 2013. Relationships between nonlinear viscoelastic behavior and rheological, sensory and oral processing behavior of commercial cheese. J. Texture Stud. http://dx.doi.org/10.1111/jtxs.12021. Pal, R., 1995. Oscillatory, creep and steady flow behavior of Xanthan-thickened oilin-water emulsions. AIChE J. 41 (4), 783–794. Philippoff, W., 1966. Vibrational measurements with large amplitudes. Trans. Soc. Rheol. 10 (1), 317–334. Renaud, M., Belgacem, M.N., Rinaudo, M., 2005. Rheological behaviour of polysaccharide aqueous solutions. Polymer 46 (26), 12348–12358. Rochefort, W.E., Middleman, S., 1987. Rheology of xanthan gum: salt, temperature, and strain effects in oscillatory and steady shear experiments. J. Rheol. 31, 337. Song, K.-W., Kuk, H.-Y., Chan, G.-S., 2006. Rheology of concentrated xanthan gum solutions: oscillatory shear flow behavior. Korea–Aust. Rheol. J. 18 (2), 67– 81. Sworn, G., 2009. Xanthan gum. In: Phillips, GO., Williams, PA. (Eds.), Handbook of hydrocolloids. Woodhead Publishing, Cambriged, UK, pp. 186–188 (second ed.). Talukdar, M.M., Vinckier, I., Moldenaers, P., Kinget, R., 1996. J. Pharm. Sci. 85 (5), 537–540. Tee, T.T., Dealy, J.M., 1975. Nonlinear viscoelasticity of polymer melts. Trans. Soc. Rheol. 19 (4), 595–615. Wilhelm, M., Maring, D., Spiess, H.W., 1998. Fourier-transform rheology. Rheol. Acta 37 (4), 399–405. Wilhelm, M., 2002. Fourier-transform rheology. Macromol. Mater. Eng. 287 (2), 83– 105. Yu, W., Wang, P., Zhou, C., 2009. General stress decomposition in nonlinear oscillatory shear flow. J. Rheol. 53 (1), 215–238.
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Journal of Food Engineering journal homepage: www.elsevier.com/locate/jfoodeng
Large amplitude oscillatory shear of xanthan gum solutions. Effect of sodium chloride (NaCl) concentration J.A. Carmona, P. Ramírez ⇑, N. Calero, J. Muñoz Departamento de Ingeniería Química, Universidad de Sevilla, Facultad de Química, 41012 Sevilla, Spain
a r t i c l e
i n f o
Article history: Received 18 September 2013 Received in revised form 11 November 2013 Accepted 16 November 2013 Available online 23 November 2013 Keywords: Rheological properties Xanthan gum Nonlinear viscoelasticity LAOS
a b s t r a c t Large amplitude oscillatory shear (LAOS) results are shown to be useful to describe the mechanical behaviour of materials at large deformations, well beyond the linear viscoelastic region, which are closer to real processing conditions. We illustrate the applications of LAOS with xanthan gum aqueous dispersions at different NaCl concentrations, on account of the great technological interest in this bacterial polysaccharide. LAOS is shown to be much more sensitive than small amplitude oscillatory shear (SAOS) to the influence of NaCl concentration. This is illustrated by a complete rheological characterisation of the system by means of both full-cycle (average elastic modulus and dynamic viscosity) and local methods (strain-hardening and shear-thickening ratios). The different rheological behaviours observed were related to the microstructures of the xanthan gum molecules as a function of the NaCl content. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Xanthan gum is a high molecular-weight extracellular polysaccharide produced by Xanthomonas campestris. The backbone of the polysaccharide chain consists of two b-D-glucose units linked through the 1st and 4th positions and the side chain consists of two mannose and one glucuronic acid. The side chain is linked to every other glucose of the backbone at the 3rd position. About half of the terminal mannose units have a pyruvic acid group linked to their 4th and 6th positions. The other mannose unit has an acetyl group at the 6th position (Sworn, 2009). Xanthan gum is soluble in cold-water, and due to its rheological properties and thermal stability, it is commonly used as an effective stabilizer and thickener with many areas of application (Marcotte et al., 2001). Xanthan gum aqueous solutions exhibit high consistency at low gum concentrations, high viscosity at low shear rates and a marked shear-thinning nature. The rheological properties of xanthan gum solutions are closely related to its conformational state (ordered and disordered conformations) and stiffness (Renaud et al., 2005), which in turn are strongly dependent on the temperature and ionic strength of the medium (Dário et al., 2011). On the one hand xanthan gum in solutions with low ionic strength or at high temperature adopts more flexible, disordered structures. On the other hand, at high ionic strength solutions the xanthan backbone takes on ⇑ Corresponding author. Tel.: +34 954557179. E-mail address: [email protected] (P. Ramírez). 0260-8774/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jfoodeng.2013.11.009
an order, helical conformation (Renaud et al., 2005; Rochefort and Middleman, 1987). Traditionally, the rheological properties of xanthan gum aqueous solutions have been determined by flow curves and small amplitude oscillatory shear (SAOS). In recent years, large amplitude oscillatory shear tests (LAOS) have received increasing attention, given that they can provide valuable information for a better understanding of complex rheological behaviours and give a deeper insight into microstructural changes (Ewoldt et al., 2010). Furthermore, another reason for the growing interest in LAOS tests is their usefulness in describing the elastic and viscous properties of complex fluids at large deformations (outside the linear viscoelastic domain), which are closer to real processing and application conditions. For instance, it has been proved recently that LAOS measurements are related to the sensory and textural properties of food, which is a topic of great interest (Melito et al., 2013). The objective of this work was to study the influence of NaCl concentration on the rheological properties of aqueous solutions of a commercial ‘‘advanced performance’’ xanthan gum. This is obtained by the manufacturer by optimising the fermentation process such that it yields higher viscosities than standard xanthan gum solutions and enhanced behaviour if submitted to high pressure homogenisation. This rheological study involves flow curves, small amplitude oscillatory shear (SAOS) and large amplitude oscillatory shear (LAOS). The non-linear oscillatory response was analysed using the framework proposed by Ewoldt et al. (2008) in order to obtain meaningful physical parameters.
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2. Materials and methods 2.1. Theory In dynamic oscillatory shear tests, the strain is varied periodically, usually with a sinusoidal perturbation at a fixed frequency. Oscillatory shear tests can be divided into two regimes. One regime implies the linear viscoelastic response (small amplitude oscillatory shear, SAOS) and the other regime involves a nonlinear material response (large amplitude oscillatory shear, LAOS). As the strain amplitude is increased at a fixed frequency a progressive transition from linear to nonlinear viscoelastic rheological behaviour can occur. When the response is linear (at small strain amplitudes) the material is characterised by two components, one in phase with the strain (elastic or storage modulus G0 (x)) and the other 90° out of phase (viscous or loss modulus, G00 (x)). The conditions required for the linear viscoelastic regime include: (1) stress amplitude should be linearly proportional to the imposed strain amplitude and (2) a torque response that involves only the first harmonic. The first condition implies that both moduli are independent of strain amplitude. The absence of larger harmonics in the stress response as required by the second condition ensures that the response remains sinusoidal. In this case, both storage and loss moduli are a function of the material microstructure and the oscillatory frequency (x). When the strain increases, the contribution of higher-order harmonics becomes significant and the stress response is not a single-harmonic sinusoid due to contribution of the other harmonics. Fig. 1 shows the evolution of normalised stress with the strain amplitude. As may be clearly observed, the sinusoidal stress is distorted when the strain increases as a consequence of the contribution of higher harmonics. A physical interpretation of the nonlinearities observed in a LAOS test is difficult since this nonlinear rheological behaviour cannot be uniquely described in terms of the linear viscoelastic moduli, G0 and G00 . Different methods have been proposed to analyse LAOS; Lissajous curves (Philippoff, 1966; Tee and Dealy, 1975), Fourier
transform rheology (Wilhelm et al., 1998; Wilhelm, 2002), stress decomposition (Cho et al., 2005; Ewoldt et al., 2008; Yu et al., 2009), decomposition on characteristic waveforms (Klein et al., 2007), and analysis of parameters related to Fourier transform rheology (Debbaut and Burhin, 2002; Hyun and Wilhelm, 2009). A popular and useful tool to analyse LAOS data is the FourierTransform method, which uses the relative intensities of higher harmonics as a measure of nonlinearity (Kallus et al., 2001; Wilhelm et al., 1998; Wilhelm, 2002). For a sinusoidal strain input c = c0 sin (xt), the stress response can be represented completely by Fourier series in two scale (elastic and viscous) forms (Dealy and Wissbrun, 1990):
rðt; x; c0 Þ ¼ c0
X 0 Gn ðx; c0 Þ sinðnxtÞ þ G00n ðx; c0 Þ cosðnxtÞ
ð1Þ
n¼odd
rðt; x; c0 Þ ¼ c_ 0
X
g0n ðx; c0 Þ sinðnxtÞ þ g00n ðx; c0 Þ cosðnxtÞ
ð2Þ
n¼odd
where c0 is the strain amplitude, G0n and G00n are the elastic and viscous moduli for the n harmonic, c_ 0 is the maximum strain rate (1/s), and g0n and g00n are the apparent viscosity in phase and out of phase with strain input for the n harmonic, respectively. Only the odd harmonics are included in this representation because the stress response is assumed to be odd symmetry with respect to the directionality of strain or strain rate, i.e., the material response is unchanged if the coordinate system is reversed (Bird et al., 1987). Even harmonic terms can be observed in transient responses, secondary flows (Atalik and Keunings, 2004), or wall slip (Graham, 1995). In the linear viscoelastic region, Eq. (1) reduces to the first harmonic n = 1, and the stress is a function of G01 and G001 . When the strain increases, and the system undergoes a transition from the linear to nonlinear regime, higher harmonics gain ground with respect to the first. In spite of the fact that this framework is robust and allows us to detect nonlinearities and to calculate the higher harmonics, it does not result in a clear physical interpretation of the higher harmonics.
Fig. 1. Strain sweep of 0.4% (m/m) xanthan gum unsalted aqueous solution at a fixed frequency of 4 rad/s at 20 °C. In the viscoelastic linear region, the viscoleastic moduli are independent of strain, nevertheless in the non-linear region both moduli are a function of strain.
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Ewoldt et al. (2008) proposed a new framework to provide a unified physical interpretation of LAOS results. This was based on a geometric representation and the definition of new parameters that allowed the interpretation of the nonlinearities, which may not be fully explained using the fundamental viscoelastic functions G0 and G00 . The framework proposed by Ewoldt is based on orthogonal decomposition of the general stress into elastic and viscous stress responses proposed by (Cho et al., 2005) r(t) = r0 (t) + r00 (t). Cho used symmetric arguments to decompose the stress into the elastic stress r0 (odd symmetry with respect x ðx ¼ cc ¼ sin xtÞ 0 _ and even symmetry with respect y ðy ¼ c_c0 ¼ cos xtÞÞ and the vis00 cous stress r (even symmetry with respect x and odd symmetry with respect y). Using these definitions, Eqs. (1) and (2) can be rewritten as:
X
r0 ¼ c0
G0n ðx; c0 Þ sin nxt
ð3Þ
n odd
X
r00 ¼ c0
G00n ðx; c0 Þ cos nxt
X c c ¼ c0 r en ðx; c0 ÞTn c0 c 0 n odd
ð5Þ
X c_ c_ r00 _ ¼ c_ 0 v n ðx; c_ 0 ÞTn _ c0 c0
ð6Þ
n odd
where Tn
c c0
and Tn
c_ c_ 0
are nth order Chebyshev polynomials of
the first kind, and en ðx; c0 Þ and v n ðx; c_ 0 Þ are the elastic and viscous Chebyshev coefficients. The relation between the Chebyshev coefficients in the strain or strain rate domain and the Fourier coefficients in the time domain are thus given by:
en ¼ G0n ð1Þðn1Þ=2
vn ¼
G00n
x
G0M ¼
G0L ¼
The elastic and viscous stresses are plotted versus the strain (c) and strain rate ðc_ Þ input functions, and Chebyshev polynomials of the first kind are fitted to the plots (Ewoldt et al., 2008): 0
viscous and elastic behaviour from the first- and third-order Chebyshev coefficients. The elastic modulus was broken down into a minimum strain modulus, G0M (the tangent modulus measured at c = 0), and large strain modulus, G0L (the secant modulus measured at maximum strain), that took higher harmonic contributions into account. These two moduli may be seen in a Lissajous plot of shear stress versus applied strain. The plot r(t) vs. c(t) are named as elastic Lissajous–Bowditch curves (Fig. 2a and b). These plots allow for a quantitative interpretation of Fourier or Chebyshev coefficients. Analogously, in the viscous scale, Ewoldt defined g01 ¼ G001 =x (the average dissipated energy per cycle) and g0L and g0M as local parameters, which indicate the instantaneous viscosity at the smallest and largest strain-rates, respectively (Ewoldt et al., 2008).
ð4Þ
n odd
¼ g0n
n : odd
n : odd
ð7Þ ð8Þ
The third-order Chebyshev coefficients (e3 and t3) may then be used to determine material nonlinear viscoelastic behaviour. Thus, material viscoelastic behaviour is classified in six categories: strain-softening (e3 < 0), strain-stiffening (e3 > 0), linear elastic e3 = 0, shear thinning (v3 < 0), shear thickening (v3 > 0) and linear viscous v3 = 0 (Ewoldt et al., 2008). An important point to consider was the definition of viscoelastic moduli in the nonlinear regime. Thus, G0 and G00 can be clearly and uniquely defined for the linear viscoelastic regime in which the stress response is a single-harmonic sinusoid. In the nonlinear regime, the definition of viscoelastic moduli is not unique (Ganeriwala and Rotz, 1987). The methods used to calculate viscoelastic moduli can be grouped into two categories: full cycle methods and local methods. A full cycle method requires at least one entire cycle of oscillatory data (or half-cycle which is then mirrored), which allows G01 and G001 to be calculated from the first-order Fourier or Chebyshev coefficients. G01 , G001 are a measure of the average elasticity and dissipated energy respectively in the material response at each imposed pair of LAOS coordinates (co, x). However, the aforementioned parameters cannot differentiate the elastic and viscous local response of a material at small and large instantaneous strains. In contrast, the local methods allow the viscoelastic moduli at an instantaneous strain to be calculated (intracycle non-linearities). Thus, Ewoldt et al. (2008) developed a new interpretation of viscoelastic moduli in the nonlinear region. This consisted of deriving
167
X 0 da j ¼ nG ¼ e1 3e3 þ dc c¼0 n odd n
X 0 a j ¼ G ð1Þðn1Þ=2 ¼ e1 þ e3 . . . c c¼c0 n odd n
ð9Þ
ð10Þ
da 1 X 00 g0M ¼ _ jc_ ¼: 0 ¼ nG ð1Þðn1Þ=2 ¼ t1 3t3 þ . . . dc x n odd n
ð11Þ
a 1 X 00 g0L ¼ _ jc_ ¼: c_ 0 ¼ G ¼ t1 þ t3 þ . . . c x n odd n
ð12Þ
These two moduli may be seen in a Lissajous plot of shear stress versus applied strain rate (Fig. 2c and d). The plot r(t) vs. c_ ðtÞ are named as viscous Lissajous–Bowditch curves. The calculation of the following ratios ðG0L =G0M and g0L =g0M Þ is a second method in order to define the strain and strain rate dependence behaviour. Thus, G0L =G0M < 1 indicates strain softening and G0L =G0M > 1 strain stiffening or strain hardening. In addition, g0L =g0M < 1 indicates shear-thinning and g0L =g0M > 0 shear thickening. In the linear viscoelastic region (at small strain), G0L ¼ G0M ¼ G01 and g0L ¼ g0M ¼ g01 , and the Lissajous plot shows a perfect elliptical shape, which is distorted when the strain increases and viscoelastic nonlinearities appear (Ewoldt et al., 2008). Also, Ewoldt defined two new ratios to avoid the singularity as G0M ! 0 (13 and 14). Thus, the strain-hardening and shear-thickening ratios were calculated from the elastic moduli and instantaneous viscosities, respectively:
S¼
T¼
ðG0L G0M Þ G0L ðg0L g0M Þ
g0L
ð13Þ
ð14Þ
S > 0 and T > 0 indicate intracycle strain stiffening and intracycle shear thickening, respectively, whereas S < 0 and T < 0 correspond to intracycle strain softening and intracycle shear thinning, respectively. 2.2. Materials KELTROLÒ Advanced Performance ‘‘Food Grade’’ xanthan gum, generously donated by CP Kelco, was used to prepare 0.4% (m/m) gum solutions. Different sodium chloride concentraitons ranging from 0 to 0.5%(m/m) were added to the gum solutions. NaCl were purchased from Panreac (99.5%(m/m) purity). The solutions studied were prepared with ultrapure Milli-Q water. All ingredients were used as received.
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Fig. 2. Lissajous–Bowditch curves obtained from experimental oscillatory tests of aqueous xanthan gum solution at 1 rad/s (0.4%(m/m) without NaCl). (a and b) Elastic Lissajous–Bowditch curves (c0 = 10%, within the linear viscoelastic region (LVR)) and (c0 = 300%, non-linear region). (c and d) Viscous Lissajous–Bowditch curves (c0 = 10%) and (c0 = 300%). G0M and g0M values are obtained from the tangent at zero instantaneous strain and strain rate, respectively (solid lines), whereas G0L and g0L are the secant modulus at maximum strain and strain rate, respectively (dashed lines). G0M ¼ G0L and g0M ¼ g0L within LVR. Temperature 20 °C.
2.3. Methods 2.3.1. Solution preparation First, the gum was slowly added to Milli-Q water under mechanical stirring (Ikavisc MR-D1), which was continued for 3 h at 25 °C. Afterwards, the solution was heated at 70 °C for 45 min under continuous stirring. Then, NaCl was added to the heated gum solution. This was sonicated for at least 1 h to remove the air bubbles within the solution. The solutions were stored for 24 h at 4 °C. The 0.4% (m/m) Xanthan gum solution studied contained a NaCl concentration ranging from 0 to 0.5%(m/m). 2.3.2. Rheological measurements Rheological oscillatory experiments were conducted with an ARES-LS controlled-strain rheometer (TA Instruments), equipped with a cone & plate geometry (angle: 0.0402 rad; diameter: 50 mm). Steady shear flow tests were carried out by a controlled-stress AR2000 rheometer (TA Instruments) using an aluminium plate & plate geometry of low inertia with smooth surface (60 mm diameter). All rheological tests were performed at 20 °C, using a solvent trap to inhibit evaporation and were repeated three times. 2.3.2.1. Small amplitude oscillatory shear (SAOS). Strain sweep tests were performed in the strain range from 1% to 1000% at a fixed frequency of 0.25, 1, 4 and 16 rad/s. Frequency sweep tests (from 20 to 0.05 rad/s) were performed selecting a strain (5%) well within the linear range.
criteria: steady-state approximation: to allow 0.1% change of shear rate’’. The experimental data fitted the Carreau model (Eq. (15)) fairly well (R2 > 0.99).
g¼ 1þ
g0
2 1n 2
ð15Þ
c_ c_ c
where c_ c is the critical shear rate for the onset of the shear-thinning response, n is the flow index, g0 is the zero-shear viscosity. 2.3.2.3. Large amplitude oscillatory shear (LAOS). The LAOS analysis requires both raw strain and stress signal which were acquired by means of native control software (TA Orchestrator), using the arbitrary wave-shape test as described by (Ewoldt et al., 2008). The arbitrary wave-shape test allows the raw data to be captured. The sampling rate of the arbitrary wave-shape test was about 100 points/s, which allowed us to work in the frequency range studied. The arbitrary wave-shape tests were performed at a fixed frequency of 4 rad/s and the amplitude of strain applied were 10, 30, 100, 300 and 1000%. 2.3.2.4. Data processing. The raw data obtained from the arbitrary wave-shape test were processed with MITlaos software (Ewoldt et al., 2007). This software was used to calculate the Fourier coefficients, Chebyshev coefficients, decomposition of stress and the viscoelastic moduli such as, G0L ; G0M ; g0L and g0M . 3. Results and discussion 3.1. Small amplitude oscillatory shear (SAOS)
2.3.2.2. Steady shear flow curves. Flow curve tests were carried out from 0.3 to 20 Pa, following a step-wise protocol: 10 points per decade (log distribution) 5 min (maximum time)/point. Cut-off
Oscillatory stress sweep tests at four different frequencies (0.25, 1, 4 and 16 rad/s), and four NaCl concentrations ranging from 0% to
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0.5%(m/m) were carried out in order to estimate the maximum amplitude value of the sinusoidal shear strain function which guarantees linear viscoelastic behaviour. The same critical strain value (29% ± 3%) that defines the linear viscoelastic region (LVR) was obtained in all cases. Fig. 3 shows by way of example the oscillatory strain sweep at 4 rad/s. G0 and G00 were not affected, regardless of the applied strain throughout the linear viscoelastic range. G0 showed a steep decrease when increasing strain above the critical strain value. However, G00 underwent just a slight drop. No influence of NaCl concentration was detected within the linear viscoelastic region. Nevertheless, within the non-linear viscoelastic region a certain difference was observed for the system in the absence of salt. Fig. 4 shows G0 and G00 as a function of frequency within LVR (strain = 5%). The results were not affected by salt concentration as shown by G0 , and only a slight deviation of G00 at high frequencies for the xanthan gum solution without NaCl was observed. The slight increase in the viscous response at higher frequencies could indicate some microstructural changes for the system without salt. It was observed that the frequency dependence of the elastic modulus can be quantitatively described by a power law. A value of 0.23 was obtained for the slope of all the G0 vs. x curves. The solutions studied exhibited weak-gel viscoelastic behaviour as demonstrated by this slope value and by the fact that G0 values lay above those of G00 . These results were consistent with those previously reported for xanthan gum solutions (Pal, 1995; Song et al., 2006; Talukdar et al., 1996).
169
Fig. 4. Storage (G0 ) and loss (G00 ) moduli as a function of frequency for xanthan gum solutions (0.4% (m/m)) with different contents of NaCl: 0% (m/m), 0.025% (m/m), 0.1% (m/m) and 0.5% (m/m) at 20 °C and at 4 rad/s. Standard deviation of the mean (three replicates) for G0 and G00 < 5%.
3.2. Flow behaviour Fig. 5 provides a comparison between complex viscosity, derived from SAOS measurements and steady shear viscosity. The Cox-Merz rule was not followed throughout the salt range studied (for the sake of clarity only one complex viscosity is shown). The departure from Cox-Merz rule confirms the occurrence of a structured system, supporting that the weak-gel structure was clearly set. Flow curves exhibited shear-thinning behaviour and a trend to reach a Newtonian region at low shear rate. The experimental data fitted the Carreau model (Eq. (15)) fairly well (R2 > 0.99). No significant differences were found for all the systems studied, therefore the same fitting parameters were used, which are given in the inset of Fig. 3.
Fig. 5. Frequency dependence of complex viscosity derived from SAOS measurements for 0.4% (m/m) xanthan gum solution containing 0.5% (m/m) NaCl (filled symbols). Shear-rate dependence of steady shear viscosity for all the systems studied (open symbols). T = 20 °C. The line shows data fitting to the Carreau model whose parameters are given in the inset. Standard deviation of the mean (three replicates) for g < 10% and for g⁄ < 5%.
3.3. Large amplitude oscillatory shear (LAOS)
Fig. 3. Storage (G0 ) and loss (G00 ) moduli as a function of strain for xanthan gum solutions (0.4%(m/m)) with different contents of NaCl: 0%(m/m), 0.025%(m/m), 0.1%(m/m) and 0.5%(m/m) at 20 °C and at 4 rad/s. Standard deviation of the mean (three replicates) for G0 and G00 < 5%.
In order to gain a deeper insight into the rheological and structural behaviour of the system large amplitude oscillatory shear measurements were carried out. First, we determined the average elasticity and dissipated energy in the material response by means of full cycle method. Fig. 6a shows the first harmonic (average) elastic modulus for the 0.4% (m/m) xanthan solutions with NaCl ranging from 0% to 0.5% (m/m) at 4 rad s1. The elastic modulus decreases beyond the critical strain (29%) indicating a strain softening behaviour for all the studied systems. The elastic response is not clearly affected by salt concentration in the linear viscoelastic region as was previously indicated by SAOS results. Above the critical strain limiting the LVR an increasingly clear difference between the elastic modulus of the xanthan gum solution with and without NaCl was found. G01 of xanthan gum solutions containing NaCl show higher values than those of the unsalted solution. This could be due to the shielding of the electrostatic repulsion between the
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Fig. 6. Oscillatory shear tests of xanthan gum at 4 rad/s analysed by means of LAOS parameters 0.4% (m/m) aqueous with 0% (m/m), 0.025% (m/m), 0.1% (m/m) and 0.5% (m/ m) NaCl. (a) First harmonic (average) elastic modulus G01 . (b) First harmonic (average) dynamic viscosity g01 . Standard deviation of the mean (three replicates) for G01 and g01 < 5%.
Fig. 7. Oscillatory shear tests of xanthan gum solutions at 4 rad/s analysed by means of LAOS parameters 0.4% (m/m) xanthan gum with 0% (m/m), 0.025% (m/m), 0.1% (m/m) and 0.5% (m/m) NaCl. (a) e3/e1. (b) v3/v1. (c) Strain-stiffening ratio, S. (d) Shear-thickening ratio, T. T = 20 °C. Standard deviation of the mean (three replicates) for e3/e1, v3/v1, T and S. It is shown that data point size exceeds the error margins.
charged side chains of xanthan gum which could lead to more compact structures which offer higher resistance to strain. Fig. 6b shows the first harmonic (average) dynamic viscosity for the 0.4% (m/m) xanthan solutions with NaCl ranging from 0% to 0.5% (m/m) at 4 rad s1. In contrast to G01 , a slight increase in the dynamic viscosity of the solutions was observed at the onset of the non-linear viscoelastic region before dropping regardless of NaCl concentration. This trend could be related to the common occurrence of a peak in G00 at the onset of the non-linear response which has been detected in many structured systems by means of SAOS tests. This was attributed by Lequeux et al. (1997) to a structural rearrangement preceding the collapse (Hyun et al., 2002; Lequeux et al., 1997). This effect is more marked for the system without NaCl. This fact could be a consequence of the occurrence of a more extended and disordered structure due to the electrostatic repulsion between the charged side chains of xanthan gum which initially offer a higher resistance to viscous flow. Nevertheless, the dynamic viscosity of the system without salt showed lower values at higher strains. This may be related to the drop in the elasticity indicating fewer points of interaction between xanthan molecules in
agreement with their progressive orientation in the flow direction (Rochefort and Middleman, 1987; Hyun et al., 2002). Further information on the influence of the salt concentration on the microstructure of xanthan gum can be obtained by analysing the viscoelastic moduli at instantaneous strains by means of both the Chebyshev coefficients and the above mentioned local method based on the S and T ratios. Fig. 7a and b show the parameters used to evaluate the intracycle elastic and viscous non-linearities; the third order elastic Chebyshev coefficient ratio, e3/e1; and the third order viscous Chebyshev coefficient ratio, t3/t1. e3/e1 and t3/t1 values within the LVR are close to zero. At strains above the critical one, two behaviours were observed for both elastic and viscous responses. At strains closer to the LVR the elastic ratio (Fig. 7a) was slightly negative, which corresponds to a strain-softening behaviour. However, at larger strains the sign of the parameters change from negative to positive indicating a transition from strain-softening to strain-stiffening behaviour. Furthermore, a clear difference at large strains was observed between the xanthan gum solutions without salt and with salt regardless of the amount of salt in the range studied 0.025–0.5%(m/m). This should be related to the presence
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more noticeable when no salt is added to the solution, which can be associated with a higher resistance to the flow accounting for the higher number of entanglements of the extended polymer in the absence of salt. At the highest strain-rate the intracycle behaviour became shear-thinning and all the systems showed the same values. The instantaneous elastic and viscous non-linearities can be also evaluated by means of the S and T ratios, as shown in Fig. 7c and d, respectively. Parameters S and T are obtained from Lissajous–Bowditch curves as explained above. The response is qualitatively analogous to those obtained from Chebyshev ratios. Shear-thickening ratio T and strain-stiffening ratio S show similar trends to t3/t1 and e3/e1 ratios, indicating that the methods support each other. 4. Conclusions
Fig. A1. Elastic Lissajous–Bowditch curves generated from experimental oscillatory tests of xanthan gum solution (0.4% (m/m) aqueous with 0% NaCl) at 20 °C. Solid lines are the total stress r(t)/rmax vs c(t)/c0. Dotted lines are the elastic stress r0 (t)/ rmax vs c(t)/c0. The maximum stress rmax is indicated above each curve.
Fig. A2. Viscous Lissajous–Bowditch curves generated from experimental oscillatory tests of xanthan gum solution (0.4% (m/m) aqueous with 0% NaCl) at 20 °C. Solid lines are the total stress r(t)/rmax vs c_ ðtÞ=c_ 0 . Dotted lines are the elastic stress r00 (t)/rmax vs c_ ðtÞ=c_ 0 . The maximum stress rmax is indicated above each curve.
of more extended polymer chains of the xanthan gum solution in the absence of salt which may offer more resistance to the elastic deformation, in accordance with the behaviour shown by G01 . Fig. 7b shows that the viscous ratios at 100% and 300% strain were positive, whereas at the highest strain (1000%) the sign became negative. The positive value of these parameters indicated a shear-thickening behaviour. This feature should be related to the well-known weak strain overshoot response obtained for xanthan gum solutions in start-up at the inception of shear experiments (Song et al., 2006; Hyun et al., 2002). The existence of this peak is due to a structural rearrangement, as explained above and confirms that the overshoot observed in stress growth experiments is a manifestation of nonlinear viscoelasticity rather than thixotropy. The shear-thickening behaviour at the onset of nonlinear behaviour is
The influence of NaCl addition on the rheological properties of a 0.4%(m/m) commercial ‘‘advanced performance’’ xanthan gum solution has been determined by means of oscillatory shear and steady shear flow curves. The information obtained from oscillatory frequency and strain sweep tests within the linear viscoelastic region demonstrated that regardless of the NaCl concentration used all the xanthan gum solutions studied behaved as a weak gel, and showed similar rheological properties. However, oscillatory strain sweep tests outside the linear viscoelastic region revealed slight differences for the xanthan solution in the absence of NaCl. All the systems studied exhibited shear thinning behaviour and a trend to reach a Newtonian region at low shear rates, which fitted fairly well the Carreau model. Flow curves were not influenced by sodium chloride addition. The departure from the Cox-Merz rule confirmed the occurrence of a structured system. Large amplitude oscillatory shear results were analysed by means of both full-cycle and local methods. A strain softening and shear-thinning behaviour was observed from the first harmonic (average) elastic modulus and dynamic viscosity respectively. The analysis of both parameters revealed significant differences associated with the dissimilar microstructures of the systems with and without NaCl. When NaCl is added the electrostatic repulsion between the side chains of the xanthan gum is shielded, leading to a more compact structure. A complete rheological characterisation of the systems was achieved by analysing the parameters deduced from local methods. Thus, a local strain stiffening behaviour was detected at large strains, which was more marked for the more extended conformation in the absence of NaCl. Furthermore, a local shear-thickening behaviour is observed at the onset of the non-linear viscoelastic region, which is also more evident for the system in the absence of NaCl. This response shifted to local shear thinning at higher strain rates congruently with flow curve results. LAOS is definitively proved to be a powerful tool that provides further rheological and therefore microstructural information about complex fluid systems. Acknowledgments The financial support received (Project CTQ2011-27371) from the Spanish Ministerio de Economía y Competitividad (MINECO) and from the European Commission (FEDER Programme) is kindly acknowledged Appendix A See Figs. A1 and A2.
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