- Email: [email protected]
Viscoelastic properties of aqueous guar gum derivative solutions under large amplitude oscillatory shear (LAOS)
Accepted Manuscript Title: Viscoelastic properties of aqueous guar gum derivative solutions under large amplitude oscillatory shear (LAOS) Author: Daniel Szopinski Gerrit A. Luinstra PII: DOI: Reference:
S0144-8617(16)30893-1 http://dx.doi.org/doi:10.1016/j.carbpol.2016.07.095 CARP 11394
To appear in: Received date: Revised date: Accepted date:
6-5-2016 12-7-2016 22-7-2016
Please cite this article as: Szopinski, Daniel., & Luinstra, Gerrit A., Viscoelastic properties of aqueous guar gum derivative solutions under large amplitude oscillatory shear (LAOS).Carbohydrate Polymers http://dx.doi.org/10.1016/j.carbpol.2016.07.095 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Viscoelastic properties of aqueous guar gum derivative solutions under large amplitude oscillatory shear (LAOS) Daniel Szopinski, Gerrit A. Luinstra* Institute for Technical and Macromolecular Chemistry, University of Hamburg, Bundesstraße 45, 20146 Hamburg, Germany
eMail: [email protected]
Highlights
Nonlinear viscoelastic properties of industrial relevant guar gum derivatives by large amplitude oscillatory shear flow (LAOS) Nonlinear stress waveforms were analyzed by FT-rheology and orthogonal stress decomposition along the MITlaos framework Rheological fingerprint in the Pipkin space is generated to visualize the influence and breakup of superstructures/aggregates as function of deformation and time scale Characteristic relaxation time of superstructures in aqueous guar gum derivative solutions is proposed
Abstract The industrial relevant nonlinear viscoelastic properties of aqueous carboxymethyl hydroxypropyl guar gum (CMHPG) and non-ionic hydroxypropyl guar gum (HPG) solutions between semi-dilute and concentrated solution state were investigated by large amplitude oscillatory shear flow (LAOS). Aqueous CMHPG and HPG solutions enter the nonlinear flow regime at deformations 0 > 100%. The nonlinear stress waveforms were analyzed by FTrheology and orthogonal stress decomposition along the MITlaos framework. A rheological fingerprint is generated (Pipkin space) showing that the guar gum derivative solutions undergo a shear-thinning at high strains, which is preceded by a thickening above a minimum
strain
rate
at
intermediate
strains.
The
influence
and
breakup
of
superstructures/aggregates gives a “rheological fingerprint”, a function of the applied deformation and time scale (Pipkin space). A characteristic process time was found that scales exponentially with the overlap parameter with an exponent of 4/2, and is proposed to represent the relaxation process of the superstructure in solution. Keywords Guar gum derivatives, large amplitude oscillatory shear (LAOS), hyperentanglement, stress decomposition, FT rheology 1
1 Introduction Guar gum is a water-soluble galactomannan from the endosperm of the guar bean (cyamopsis tetragonoloba). This class of heterogeneous polysaccharides have a linear backbone of -1,4 linked D-mannopyranosyl units and randomly arranged -1,6 linked Dgalactopyranosyl units as sidechains (Dea & Morrison, 1975; Hoffman & Svensson, 1978). The high molecular weight (1000-2000 kg·mol-1) of guar gum (and its derivatives) in combination with the formation of superstructures/aggregates in aqueous solutions leads to the excellent water-thickening properties, and makes it useful in food, agricultural and textile applications (Cheng & Prud’homme, 2000; Tayal, Pai, & Khan, 1999; Tizzotti et al., 2010). The formation of superstructures - so called “hyperentanglements” - is thought to result from segment-segment interactions of the mannose backbone at positions where the galactose side chains are absent (Goycoola, Morris, & Gidley, 1995; Morris, Cutler, Ross-Murphy, Rees, & Price, 1981; Wientjes et al., 2002). The mannose-to-galactose ratio in guar gum ranges from 1.6 and 1.8, varying with the biological source (Cheng, Brown, & Prud’homme, 2002). The substitution is relevant to the cold water solubility: galactomannans with mannose-to-galactose ratio of 3 and 4 respectively in tara gum and locust bean gum (Picout, Ross-Murphy, Jumel, & Harding, 2002) have a lower cold water solubility as native guar gum. Native guar gum may be chemically modified to enhance the thermal stability and hydration properties. Carboxymethylation (CM) and hydroxypropylation (HP) thus lead to the industrial relevant ionic and non-ionic guar gum derivatives (Figure 1) that are, amongst other, used as additives for fracturing fluids in oil recovery operations (Banerjee et al., 2009; Kesevan & Prud’homme, 1992; Lapasin, De Lorenzi, Pricl, & Torriano, 1995; Lei & Clark, 2007; Mukherjee, Sarkar, & Moulik, 2010; Zhang & Zhou, 2006). Knowledge on the dynamics of such systems in water is thus of more than academic interest, certainly with regard to typical processing operations like pumping und stirring. (Ewoldt, Winter, Maxey, McKinley, 2010; Khandavalli, Rothstein, 2015).
We recently established structure-property relationships in steady state shear flow, small oscillatory shear flow (SAOS) (Szopinski, Kulicke, & Luinstra, 2015) and extensional flow (CaBER) (Szopinski, Handge, Kulicke, Abetz, & Luinstra, 2016). A further insight in the behavior of guar gum solutions can be reached by the measurement of the flow behavior in large amplitude oscillatory shear flow (LAOS). These data are more relevant to polymer processing operations, where deformations are usually large. The viscoelastic response of 2
the complex system will depart from the linear behavior with increasing strain amplitude 0 . The elastic storage modulus and the viscous loss modulus then become functions of the strain amplitude 0 : the stress response to the applied sinusoidal strain in LAOS shows a non-sinusoidal waveform (Figure 2). The aim of the current work is to describe the nonlinear flow behavior of these rheological complex solutions and to build an understanding of the characteristics of the (temporary) structures that are present in solution.
2 Materials and methods 2.1 Materials Carboxymethyl hydroxypropyl guar gum (CMHPG, DSGal = 0.54, DSCM = 0.06, MSHP = 0.25, Mw = 1360 kg·mol-1) and hydroxypropyl guar gum (HPG, DSGal = 0.62, MSHP = 0.38, Mw = 1470 kg·mol-1) with typical degrees of substitution in industrial applications were used. These kinds of derivatives are easily prepared from native guar gum (Pasha & Ngn, 2008; Venkataiah & Mahadevan, 1982). The dry weight and insoluble residues were determined and considered in the sample preparation. The guar gum derivative solutions were vortexed and subsequent shaken at 25 °C for 12 h on an orbital shaker. Sodium nitrate (ReagentPlus,
99.0%) and sodium azide (ReagentPlus, 99.5%) were purchased from Sigma-Aldrich Chemicals and used as received. Demineralized water containing 0.1 M NaNO3 + 200 ppm NaN3 was used as the solvent to minimize the “polyelectrolyte effect” and to inhibit bacterial degradation. A comprehensive molecular weight and degree of substitution analysis of the used guar gum derivatives can be found in previous studies (Szopinski et al. 2015; Szopinski et al. 2016).
2.2 Rheometry Large amplitude oscillatory shear measurements were performed on a DHR-2 combined motor-transducer rheometer (TA Instruments, New Castle, USA) with a cone-plate geometry (diameter = 60 mm, angle = 2°, measuring gap = 50 µm). Large amplitude oscillatory shear (LAOS) experiments were performed at various frequencies in the range of 0.1 to 10 rad·s-1. The active deformation control (continuous oscillation mode) of the DHR-2 was used. Current advantages in the deformation control feedback loop of stress-controlled rheometers and correct motor mode settings allow a reasonable agreement with the nonlinear response of strain-controlled rheometers (Bae et al. 2013; Merger & Wilhelm, 2014). The motor mode was set to medium, showing similar results as in stiff mode.
3
The raw data was processed using the MITlaos software developed by Ewoldt (2007b). For the determination of the Chebyshev coefficients and the Fourier coefficients, at least four strain cycles were used with two previously applied conditioning cycles. The highest significant harmonic of the raw data was determined by discrete Fourier Transform analysis and used to reconstruct a noise-reduced stress signal, which was used in the consecutive analysis.
3 Results and discussion The nonlinear viscoelastic properties of ionic carboxymethyl hydroxypropyl guar gum (CMHPG) and hydroxypropyl guar gum (HPG) were determined at concentrations between the semi-dilute solution state (c* < c < c**) and the concentrated solution state (c** < c), representing the relevant region of industrial applications. Solutions of CMHPG were evaluated at concentrations between 0.50 and 1.25 wt% (overlap parameter c = 8.0320.24) and of HPG between 0.75 and 1.50 wt% (overlap parameter c = 8.90-17.75). CMHPG has a significantly higher overlap parameter than HPG of the same molar mass, resulting from the more rigid chain of CMHPG originating from the electrostatic repulsion between the carboxymethyl groups (Szopinski et al., 2015; Szopinski et al., 2016). The nonlinear response of CMHPG and HPG turned out to be very similar, and for that reason the reporting in the next sections is limited to CMHPG. It has been observed before, that the viscoelastic properties of CMHPG and HPG solutions can be related by the respective overlap parameter c (Szopinski et al., 2016). The analysis for HPG can be found in the supplementary information. Ionic (CMHPG) and non-ionic (HPG) guar gum derivative solutions were evaluated by FTrheology and the extended SD method to give a comprehensive impression of the nonlinear behavior and the onset of it. The evaluation of the distorted waves of the nonlinear response may be performed along two emerging methods, based on different coordinate frameworks (see Hyun et al. (2011) for a comprehensive review). The first - referred to as the Fourier Transform (FT) rheology (Wilhelm, 2002) - comprises a time-domain representation: The nonlinear stress response as a function of time t is transformed into a Fourier series, showing the contribution of higher harmonics in frequency space. The orthogonal stress decomposition (SD) builds on a deformation-domain representation. The total stress response is interpreted in terms of an elastic ' t and an orthogonal viscous contribution
' ' t (Cho et al., 2005). The SD method has the option of defining nonlinear viscoelastic moduli using Chebyshev polynomials of the first kind (Ewoldt et al. 2008). 4
3.1 Fourier transform rheology The nonlinear stress response t; , 0 of viscoelastic fluids may be described by a Fourier series with the elastic and viscous Fourier coefficients G'n and G' ' n according to Equation 1 (Wilhelm, 2002). Therefore, the time dependent stress response is transformed into a frequency dependent spectrum. The nonlinear stress response comprises contributions of the intensity I1 of the excitation angular frequency and the intensities of higher order harmonics (Figure 3).
t 0
G ' (,
n odd
n
0
)sin n t G ''n (, 0 )cos n t
(1)
The normalized FT rheology spectrum of an aqueous CMHPG solution (1.25 wt%, 0.1 M NaNO3 + 200 ppm NaN3) indicates the dominant nonlinear flow behavior with 13 significant harmonics under deformation of 0 1000% (Figure 3a). These harmonics were used to reconstruct noise-reduced stress signals that were used in the consecutive orthogonal stress decomposition (SD) method (vide infra). The relative intensity of the third harmonic I3/1 (with respect to the excitation) has been used to quantify nonlinearity in the stress response (Figure 3b). The usual quadratic dependence of the normalized third harmonic with strain amplitude I3 / 1 0 is indicated at medium strain amplitudes (100< 0 <400%). This “linear” 2
nonlinear regime of deformation is often referred to as medium amplitude oscillatory shear (MAOS) and allows a more elaborated distinction of nonlinear behavior besides the classical SAOS-LAOS classification (Hyun et al. 2006). The aqueous guar gum solutions of this study (see suppl.), however, show a significant noise in the MAOS regime and detection is near the torque resolution limit of the rheometer. A more reliable analysis and more extensive insights were obtained using the stress decomposition method.
3.1 Nonlinear viscoelastic parameter by orthogonal stress decomposition The total stress response t; , 0 of viscoelastic fluids may alternatively be separated into an elastic stress contribution as a function of strain ' t and a viscous stress contribution as a function of strain rate ' ' t following the orthogonal stress decomposition (SD) method (Cho et al., 2005). The elastic and viscous Chebyshev coefficients en and v n can be extracted from the elastic stress ' t and the viscous
5
stress ' ' t by fitting the data with Chebyshev polynomials of the first kind Tn along equation 2 (Ewoldt et al., 2008):
t;, 0 ' t '' t 0
e , T x , T y n
0
n
n, odd
0
n
0
n
(2)
n, odd
Ewoldt et al. (2008) introduced nonlinear viscoelastic moduli G 'M and G 'L that are derived from the obtained Chebyshev coefficients en and n . The minimum-strain modulus G 'M (at
0 ) and the large-strain modulus G 'L (at 0 ) can be determined from the elastic Chebyshev coefficients en according to Equation 3 and 4.
G 'M
G 'L
d d d d
e1 3e3 5e5 7e7 ...
(3)
e1 e3 e5 e7 ...
(4)
0
0
These moduli describe the local elastic response at minimum ( 0 ) and maximum ( 0 ) instantaneous strain and converge to the linear elastic modulus G'1 of the SAOS regime at intermediate strains and rates. Similarly, the minimum-strain rate dynamic viscosity 'M and the large-strain rate dynamic viscosity 'L can be determined from the viscous Chebyshev coefficients n . The graphical visualization of the total stress response as a function of strain (elastic Lissajous-Bowditch curve, Figure 4a) and as a function of strain-rate (viscous Lissajous-Bowditch curve, Figure 4b) allows a geometric interpretation of the nonlinear viscoelastic parameter (Ewoldt, 2008). The minimum-strain modulus resp. the minimumstrain viscosity is equivalent to the slope of the tangent at minimum strain ( 0 ) and the large-strain modulus and viscosity are equivalent to the slope of the secant at maximum strain ( 0 ). It is easily appreciated, that the CMHPG solutions show a significant deviation from linearity at deformations larger than 100% (Figure 4).
The elastic and viscous Lissajous-Bowditch curves of an aqueous CMHPG solution (1.25 wt%, 0.1 M NaNO3 + 200 ppm NaN3) may be arranged in the { , 0 }-Pipkin space to give a basic insight into the onset of nonlinear flow behavior on deforming the polysaccharide solution (Figure 5). This visualization gives an impression of the influence of the time scale on the nonlinear flow behavior, especially in the separated elastic resp. the viscous stress contributions. These are represented by the dotted lines in the closed loops of the Lissajous6
Bowditch representations (Figure 5a resp. 5b). The linear viscoelasticity is recognizable in the straight lines of the elastic and viscous contributions at strain amplitudes smaller than 0 < 100% (Figure 6b(left)). The slope of the viscous stress (dotted lines in the viscous Lissajous-Bowditch curves of Figure 5b,6b) is smaller at higher frequencies in that range, showing the typical shear-thinning of the system at higher frequencies. Similarly, the slope of the elastic stress increases with the frequency indicative of a higher elastic modulus (Figure 6a).
The linearity of the contributions is progressively lost with increasing strain amplitude 0 . The deviation from linearity of the elastic and viscous contributions can be used for marking the onset of the nonlinear behavior of CMHPG solutions: the slopes of the dotted lines become strain dependent too. The nonlinear behavior is predominantly viscous in origin. The total stress loop is close to the viscous stress part, especially at low frequencies and large strain amplitudes (and therefore large strain rates). Aqueous solutions of xanthan gum show a similar nonlinear behavior (Ewoldt et al., 2010). An increasing strain-stiffening occurs at increasing strain when 0 is larger than 100%. The elastic G 'L at maximum strain is increasingly larger than G 'M of zero strain (cf. Figure 5a, see Figure 7a for non-normalized Lissajous-Bowditch curves).
The importance of nonlinearity of guar solutions is demonstrated in the strain-stiffening ratio S (= G 'L G 'M ) / G 'L ) of about 120% at the highest strain (Figure 8a). The ratio S is the
relative increase in the elastic modulus between zero and highest strain (Ewoldt 2010) under the dynamics of LAOS as steady state. The strain-stiffening ratio S increases with higher strain amplitudes and is more and less concentration independent to strain amplitudes 0 < ~ 600%. The maximum of ratio S at highest strain is somewhat higher for more diluted solutions of CMHPG. Latter may be understood as a higher elastic resistance of the more extended individual chains or chain segments in the existing physical network of the slow relaxing system (i.e. with respect to the strain rate) consisting of entanglements and superstructures (vide infra). Higher concentrations of CMHPG lead to a smaller deformation of the individual chain (segments), and hence to a smaller nonlinearity. The nonlinear elastic moduli and dynamic viscosities converge to the linear elastic modulus G'1 and linear dynamic viscosity '1 at low strain amplitudes ( 0 < 100%) corresponding to the SAOS regime (Figure 8). 7
A strain induced shear-thinning is observed that increases with strain at lower frequencies. The viscosity at zero deformation 'M is continuously larger than the slope of the secant at maximum strain 'L at a frequency of 0.1 rad/s (Figure 5). The behavior at higher frequencies is more complex as at intermediate strain, a thickening of the solution may precede the strain induced thinning (Figure 8,9). This behavior is more pronounced at higher concentrations and at higher frequencies. The shear-thickening ratio T (= ( 'L 'M ) / 'L ) is a useful measure to encompass latter (Figure 8,9). The ratio T of CMHPG solutions at the lowest concentration studied of c = 0.50 wt% decreases at strain amplitudes over 500%, indicative of the above discussed shear-thinning behavior at higher strain. More concentrated solutions show a similar decrease at higher strains, however, only after a maximum in T at intermediate strains. Latter effect is significant and has a high reproducibility (cf. error bars in Figure 8b). The region of strain induced thickening becomes larger at higher concentrations, and the maximum of T is higher at higher concentrations. The maximum of T at e.g.
1 rad s1 is in the region of a strain of 300%. It has a value of 10% at the highest concentration. This shear-thickening behavior is very relevant for processing guar solutions, e.g. when fluctuations in pumping rate or concentrations occur. We
interpret
the
shear-thickening
as
originating
from
a
temporary
network
of
superstructures/hyperentanglements (vide infra). More of the segments between the network points become extended with higher strain and increasingly resist deformation, leading to the increase in S (Figure 8b, 9b), but only at sufficient high frequencies. The dynamics of the network relax the imposed stress of lower frequencies, explaining the absence of thickening in this region. The network has a higher density of network points at higher concentration and thus has a larger longest relaxation time. Consequently, the higher concentrated solutions appear to thicken at lower frequencies. The terminal shear-thinning results from a dissolution of the network at higher strain amplitudes; the network cannot reform at the rate of agitation. The temporary network is thus rheological relevant from a certain minimum strain and frequency, a typical nonlinear feature (Figure 9). A similar shear thickening behavior may be recognizable in xanthan gum solutions (Ewoldt et al. 2010). This kind of behavior is expected for polymer solutions able to form superstructures with relaxation times in the time scale of the LAOS experiment. The interpretation in this manner allows to correlate the onset frequency of shear-thickening to the relaxation time of the network. The dynamics of the superstructures are insufficient to relax the stress of deformation at that point. The frequency L at the onset of shearthickening (T > 0) was coarsely estimated from Figure 9, to obtain the longest relaxation time 8
of the network comprising the superstructures L
( L = 1/ L ; see supplementary
information, Table S1). The relaxation time of the transient network shows an exponential dependence on the overlap parameter (encompassing CMHPG and HPG), here with an exponent of about 4/2 (1.95 0.22) (Figure 10). The successful superposition of the relaxation times of CMHPG und HPG shows that these guar gum derivatives behave similarly in solution and thus have similar segment-segment interactions. The higher polymer coil expansion and rigidity of the anionic CMHPG chain originating from electrostatic repulsion of carboxymethyl entities is taken into account by referencing to the overlap parameter c instead of c Mw . The relaxation processes in guar gum derivative solutions of the chain segments, the temporary network of superstructures and the entanglements can then be put into a comprehensive picture as function of the overlap parameter (Figure 10). Measurements in elongational flow allowed to find the fastest processes of the system, which were related to relaxations of chain segments (Szopinski et al., 2016). These show a dependence of the overlap parameter with an exponent of 3/2. The longest relaxation times are now assigned to the network of superstructures having and dependence on the overlap parameter with a power of 4/2. Measurements in shear flow lead to intermediate relaxation times, and putatively have contribution from network and chain segment movements. The relaxation times in shear show a dependence on the overlap parameter with exponent of 7/2, reminiscent of both processes that indeed are usually thought to take place in shear processes of guar gum solutions (Szopinski et al., 2015).
Concluding remarks The nonlinear viscoelastic properties of semi-dilute and concentrated aqueous CMHPG and HPG solutions (0.1 M NaNO3 + 200 ppm NaN3) were studied by FT-rheology and orthogonal stress decomposition. The evaluation of elastic and viscous Lissajous-Bowditch curves reveals pronounced strain-stiffening, shear-thinning and – thickening behavior as function of strain and strain rate. This behavior is quantified by the determination of the strain-stiffening ratio S and shear-thickening ratio T and evaluated as functions of the applied strain amplitude 0 and angular frequency (Pipkin space). T passes through a maximum that is codependent on concentration, strain and frequency. The interpretation offered explains the behavior in terms of the dynamics of a temporary network. The associated relaxation time scales with the overlap parameter with an exponent of 4/2. The network has relaxation times much higher than those of chain segment movements, which scales with overlap parameter with an exponent of 3/2. The match of the sum of exponents to 7/2, the dependence of the 9
longest relaxation times in shear may be coincidentally; at the same time, it may show that the interpretation of the relaxation processes in terms of fast chain segment movements and slower network dynamics is a viable description of guar gum solutions. Knowledge of the dynamics of such systems in water at larger deformations is crucial with regard to typical processing operations like pumping und stirring, especially considering the intriguing shear thickening above a minimum strain rate at intermediate strains.
Acknowledgement The authors wish to thank Dimitri Merger (Karlsruhe Institute of Technology) for stimulating discussions concerning LAOS measurements on stress-controlled rheometers. Previous investigations in this field were supported by the DGMK in Project 633/03.
References Banerjee, P., Mukherjee, I., Bhattacharya, S., Datta, S., Moulik, S. P., & Sarkar, D. (2009). Sorption of water vapor, hydration, and viscosity of carboxymethylhydroxypropyl guar, diutan and xanthan gums and their molecular association with and without salts (NaCl, CaCl2, HCOOK, CH3COONa, (NH4)2SO4 and MgSO4) in aqueous solution. Langmuir, 25, 1164711656.
Cheng, Y., & Prud’homme, R. K. (2000). Enzymatic degradation of guar and substituted guar galactomannans. Biomacromolecules, 1, 782-788.
Cheng, Y., Brown, K. M., & Prud’homme, R. K. (2002). Characterization and intermolecular interactions of hydroxypropyl guar solutions. Biomacromolecules, 3, 456-461.
Dea, I. C. M., & Morrison, A. (1975). Chemistry interactions of seed galactomannans. Advances in Carbohydrate Chemistry and Biochemistry, 31, 241-312.
Ewoldt, R. H., Clasen, C., Hosoi, A. E., McKinley, G. H. (2007) Rheological fingerprinting of gastropod pedal mucus and synthetic complex fluids for biomimicking adhesive locomotion. Soft Matter, 3, 634-643.
10
Ewoldt, R. H., Hosoi, A. E., & McKinley, G. H. (2008). New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear. Journal of Rheology, 52, 14271458.
Ewoldt R. H., Winter, P., Maxey, J., & McKinley, G. H. (2010). Large amplitude oscillatory shear of pseudoplastic and elastoviscoplastic materials. Rheologica Acta, 49, 191-212.
Ferry, J. D. (1980) Viscoelastic properties of polymers, 3rd edition, Wiley, New York.
Goycoolea, F. M., Morris, E. R., & Gidley, M. J. (1995). Viscosity of galactomannans at alkine and neutral pH: Evidence of ‘hyperentanglement’ in solution. Carbohydrate Polymers, 27, 6971.
Hoffman, J., & Svensson, S. (1978). Studies of the distribution of the D-galactosyl side chains in guaran. Carbohydrate Research, 65, 65-71.
Hyun, K., Heun Kim, S., Hyun Ahn, K. (2002). Large amplitude oscillatory shear as a way to classify the complex fluids. Journal of Non-Newtonian Fluid Mechanics, 107, 51-65.
Hyun, K., Baik, E. S., Hyun Ahn, K., Lee, S. J., Sugimoto, M.; Koyama, K. (2006). Degree of branching of polypropylene measured from Fourier-transform rheology. Rheologica Acta, 46, 123-129.
Hyun, K., Wilhelm, M. (2009). Establishing a new mechanical nonlinear coefficient Q from FT-rheology: First investigation of entangled linear and comb polymer model systems. Macromolecules, 42, 411-422.
Hyun, K., Wihelm, M., Klein, C. O., Cho, K. S., Nam, J. G., Ahn, K. H., Ewoldt, R. H., McKinley, G. H. (2011). A review of nonlinear oscillatory shear tests: Analysis and application of large amplitude oscillatory shear (LAOS). Progress in Polymer Science, 36, 1697-1753.
Kesevan, S., & Prud’homme, R. K. (1992). Rheology of guar and HPG crosslinked by borate. Macromolecules, 25, 2026-2032.
11
Khandavalli, S., Rothstein, J. P. (2015). Large amplitude oscillatory shear rheology of three differemt shear-thickening particle dispersions. Rheologica Acta, 54, 601-618.
Lapasin, R., Pricl, S., Tracanelli, P. (1992). Different behaviors of concentrated polysaccharide systems in large-amplitude oscillating fields. Rheologica Acta, 31, 374-380.
Lei, C., & Clark, P. E. (2007). Crosslinking of guar and guar derivatives, SPE Journal, 12, 316-321.
Merger, D., Wilhelm, M. (2014). Intrinsic nonlinearity from LAOStrain – experiments on various strain- and stress-controlled rheometers: a quantitative comparison. Rheologica Acta, 53, 621-634.
Morris, E. R., Cutler, A. N., Ross-Murphy, S. B., Rees, D. A., & Price, J. (1981). Concentration and shear rate dependence of viscosity in random coil polysaccharide solutions. Carbohydrate Polymers, 1, 5-21.
Mukherjee, I., Sarkar, D., & Moulik, S. P. (2010). Interaction of gums (guar, carboxymethylhydroxypropyl guar, diutan, and xanthan) with surfactants (DTAB, CTAB and TX-100) in aqueous medium. Langmuir, 26, 17906-17912.
Picout, D. R., Ross-Murphy, S. B., Jumel, K., Harding, S. E. (2002). Pressure cell assisted solution characterization of polysaccharides. 2. Locust bean gum and tara gum. Biomacromolecules, 3, 761-767.
Tayal, A., Pai, V. B., & Khan, S. A. (1999). Rheology and molecular weight changes during enzymatic degradation of a water-soluble polymer. Macromolecules, 32, 5567-5574.
Szopinski, D., Handge, U. A., Kulicke, W.-M., Abetz, V., & Luinstra, G. A. (2016). Extensional flow behavior of aqueous guar gum derivative solutions by capillary breakup elongational rheometry (CaBER). Carbohydrate Polymers, 136, 834-840.
12
Szopinski, D., Kulicke, W.-M., & Luinstra, G. A. (2015). Structure-property relationships of carboxymethyl hydroxypropyl guar gum in water and a hyperentanglement parameter. Carbohydrate Polymers, 119, 159-166.
Tizzotti, M., Labeau, M.-P., Hamaide, T., Drockenmuller, E., Charlot, A., & Fleury, E. (2010). Synthesis of thermosensitive guar-based hydrogels with tunable physico-chemical properties by click chemistry. Journal of Polymer Science, A: Polymer Chemistry, 48, 2733-2742.
Vananroye, A., Leen, P., Van Puyvelde, V., & Clasen, C. (2011). TTS in LAOS: validation of time-temperature superposition under large amplitude oscillatory shear. Rheologica Acta, 50, 795-807.
Wientjes, R. H. W., Duits, M. H. G., Jongschaap, R. J. J., & Mellema, J. (2000). Linear rheology of guar gum solutions. Macromolecules, 33, 9594-9605.
Wilhelm, M., Reinheimer, K., Kübel, J. (2012). Optimizing the sensitivity of FT-Rheology to quantify and differentiate for the first time the nonlinear mechanical response of dispersed beer foams of light and dark beer. Zeitschrift für Physikalische Chemie, 226, 547-567.
Zhang, L.-M., & Zhou, J.-F. (2006). Synergistic viscosity characteristics of aqueous mixed solutions of hydroxypropyl- and carboxymethyl-substituted guar gums. Colloids and Surfaces, A: Physicochemical and Engineering Aspects, 279, 34-39.
13
Figure 1. Chemical structure of native guar gum and chemically modified derivatives.
Figure 2. The storage modulus G’ and the loss modulus G’’ as functions of the strain 1 amplitude 0 for an aqueous CMHPG solution (1.25 wt%) at 10 rad s and the corresponding stress response in SAOS and LAOS.
14
Figure 3. (a) FT rheology spectrum (Relative intensity In/1 as a function of the normalized harmonic / 1 ) for a aqueous CMHPG solution (1.25 wt%) at a excitation angular frequency 1 of 1 1 rad s and 0 1000% (b) Relative intensity of the third harmonic I3/1 as a function
of the strain 0 for CMHPG at different concentrations (0.1 M NaNO3 + 200 ppm NaN3, T = 25 °C).
Figure 4. Geometric interpretation of the nonlinear (a) elastic moduli G 'L and G 'M and the (b) dynamic viscosities 'L and 'M for a aqueous CMHPG solution (1.25 wt%) at = 1 rad ·s-1 and 0 = 10 (1000%; T = 25 °C). The dashed lines represent the corresponding linear (first harmonic) material functions (0.1 M NaNO3 + 200 ppm NaN3, T = 25 °C).
15
Figure 5. (a) Elastic Lissajous-Bowditch curves arranged in the { , 0 }-Pipkin space (normalized total stress (t ) / max (solid lines) and normalized elastic stress '(t ) / max (eq 2; dotted lines) as functions of the normalized strain (t ) / 0 ) and (b) viscous LissajousBowditch curves (normalized total stress (t ) / max (solid lines) and normalized viscous stress '(t ) / max (eq 2; dotted lines) as functions of the normalized strain rate (t ) / 0 ) for a aqueous CMHPG solution (1.25 wt%, 0.1 M NaNO3 + 200 ppm NaN3, T = 25 °C).
16
Figure 6. (a) Elastic Lissajous-Bowditch curves (the total stress (t ) and the elastic stress ' (t ) as functions of the strain (t ) ) for various applied angular frequencies at linear ( 0 = 63%) and nonlinear ( 0 = 1000%) conditions (b) viscous Lissajous-Bowditch curves (the total stress (t ) and the viscous stress ' ' (t ) as functions of the strain (t ) ) for the applied angular frequencies at linear ( 0 = 63%) and nonlinear ( 0 = 1000%) conditions for a aqueous CMHPG solution (1.25 wt%, 0.1 M NaNO3 + 200 ppm NaN3, T = 25 °C).
17
Figure 7. (a) Elastic Lissajous-Bowditch curves (the total stress (t ) and the elastic stress
' (t ) as function of the strain (t ) ) for various strain amplitudes 0 at a constant angular frequency of = 1 rad·s-1 (b) viscous Lissajous-Bowditch curves (the total stress (t ) and the viscous stress ' ' (t ) as functions of the strain (t ) ) for strain amplitudes 0 at a constant angular frequency of = 1 rad·s-1 for a aqueous CMHPG solution (1.25 wt%, 0.1 M NaNO3 + 200 ppm NaN3, T = 25 °C).
18
Figure 8. (a) The minimum-strain elastic modulus G 'M , the large-strain elastic modulus G 'L , the linear (first harmonic) elastic modulus G '1 and the strain-stiffening ratio S (=
(G 'L G 'M ) / G 'L ) as functions of the strain amplitude 0 . (b) The minimum-strain viscosity 'M , the large-strain viscosity 'L , the linear (first harmonic) viscosity '1 and shearthickening ratio T (= ( 'L 'M ) / 'L ) as functions of the strain amplitude 0 for CMHPG at different concentrations at an angular frequency of 1 rad s1 (0.1 M NaNO3 + 200 ppm NaN3, T = 25 °C).
19
Figure 9. The strain-stiffening ratio S (a) and the shear-thickening ratio T (b) as functions of the angular frequency and the strain amplitude 0 (Pipkin space) for CMHPG solutions at various concentrations (0.1 M NaNO3 + 200 ppm NaN3, T = 25 °C).
20
Figure 10. The longest relaxation time of superstructures L , the longest shear relaxation time S (determined by entanglements and superstructures) and the longest elongational relaxation time E (chain segment movement) of CMHPG and HPG as functions of the overlap parameter c (solvent: 0.1 M NaNO3 + 200 ppm NaN3 (T = 25°C)).
21
S0144-8617(16)30893-1 http://dx.doi.org/doi:10.1016/j.carbpol.2016.07.095 CARP 11394
To appear in: Received date: Revised date: Accepted date:
6-5-2016 12-7-2016 22-7-2016
Please cite this article as: Szopinski, Daniel., & Luinstra, Gerrit A., Viscoelastic properties of aqueous guar gum derivative solutions under large amplitude oscillatory shear (LAOS).Carbohydrate Polymers http://dx.doi.org/10.1016/j.carbpol.2016.07.095 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Viscoelastic properties of aqueous guar gum derivative solutions under large amplitude oscillatory shear (LAOS) Daniel Szopinski, Gerrit A. Luinstra* Institute for Technical and Macromolecular Chemistry, University of Hamburg, Bundesstraße 45, 20146 Hamburg, Germany
eMail: [email protected]
Highlights
Nonlinear viscoelastic properties of industrial relevant guar gum derivatives by large amplitude oscillatory shear flow (LAOS) Nonlinear stress waveforms were analyzed by FT-rheology and orthogonal stress decomposition along the MITlaos framework Rheological fingerprint in the Pipkin space is generated to visualize the influence and breakup of superstructures/aggregates as function of deformation and time scale Characteristic relaxation time of superstructures in aqueous guar gum derivative solutions is proposed
Abstract The industrial relevant nonlinear viscoelastic properties of aqueous carboxymethyl hydroxypropyl guar gum (CMHPG) and non-ionic hydroxypropyl guar gum (HPG) solutions between semi-dilute and concentrated solution state were investigated by large amplitude oscillatory shear flow (LAOS). Aqueous CMHPG and HPG solutions enter the nonlinear flow regime at deformations 0 > 100%. The nonlinear stress waveforms were analyzed by FTrheology and orthogonal stress decomposition along the MITlaos framework. A rheological fingerprint is generated (Pipkin space) showing that the guar gum derivative solutions undergo a shear-thinning at high strains, which is preceded by a thickening above a minimum
strain
rate
at
intermediate
strains.
The
influence
and
breakup
of
superstructures/aggregates gives a “rheological fingerprint”, a function of the applied deformation and time scale (Pipkin space). A characteristic process time was found that scales exponentially with the overlap parameter with an exponent of 4/2, and is proposed to represent the relaxation process of the superstructure in solution. Keywords Guar gum derivatives, large amplitude oscillatory shear (LAOS), hyperentanglement, stress decomposition, FT rheology 1
1 Introduction Guar gum is a water-soluble galactomannan from the endosperm of the guar bean (cyamopsis tetragonoloba). This class of heterogeneous polysaccharides have a linear backbone of -1,4 linked D-mannopyranosyl units and randomly arranged -1,6 linked Dgalactopyranosyl units as sidechains (Dea & Morrison, 1975; Hoffman & Svensson, 1978). The high molecular weight (1000-2000 kg·mol-1) of guar gum (and its derivatives) in combination with the formation of superstructures/aggregates in aqueous solutions leads to the excellent water-thickening properties, and makes it useful in food, agricultural and textile applications (Cheng & Prud’homme, 2000; Tayal, Pai, & Khan, 1999; Tizzotti et al., 2010). The formation of superstructures - so called “hyperentanglements” - is thought to result from segment-segment interactions of the mannose backbone at positions where the galactose side chains are absent (Goycoola, Morris, & Gidley, 1995; Morris, Cutler, Ross-Murphy, Rees, & Price, 1981; Wientjes et al., 2002). The mannose-to-galactose ratio in guar gum ranges from 1.6 and 1.8, varying with the biological source (Cheng, Brown, & Prud’homme, 2002). The substitution is relevant to the cold water solubility: galactomannans with mannose-to-galactose ratio of 3 and 4 respectively in tara gum and locust bean gum (Picout, Ross-Murphy, Jumel, & Harding, 2002) have a lower cold water solubility as native guar gum. Native guar gum may be chemically modified to enhance the thermal stability and hydration properties. Carboxymethylation (CM) and hydroxypropylation (HP) thus lead to the industrial relevant ionic and non-ionic guar gum derivatives (Figure 1) that are, amongst other, used as additives for fracturing fluids in oil recovery operations (Banerjee et al., 2009; Kesevan & Prud’homme, 1992; Lapasin, De Lorenzi, Pricl, & Torriano, 1995; Lei & Clark, 2007; Mukherjee, Sarkar, & Moulik, 2010; Zhang & Zhou, 2006). Knowledge on the dynamics of such systems in water is thus of more than academic interest, certainly with regard to typical processing operations like pumping und stirring. (Ewoldt, Winter, Maxey, McKinley, 2010; Khandavalli, Rothstein, 2015).
We recently established structure-property relationships in steady state shear flow, small oscillatory shear flow (SAOS) (Szopinski, Kulicke, & Luinstra, 2015) and extensional flow (CaBER) (Szopinski, Handge, Kulicke, Abetz, & Luinstra, 2016). A further insight in the behavior of guar gum solutions can be reached by the measurement of the flow behavior in large amplitude oscillatory shear flow (LAOS). These data are more relevant to polymer processing operations, where deformations are usually large. The viscoelastic response of 2
the complex system will depart from the linear behavior with increasing strain amplitude 0 . The elastic storage modulus and the viscous loss modulus then become functions of the strain amplitude 0 : the stress response to the applied sinusoidal strain in LAOS shows a non-sinusoidal waveform (Figure 2). The aim of the current work is to describe the nonlinear flow behavior of these rheological complex solutions and to build an understanding of the characteristics of the (temporary) structures that are present in solution.
2 Materials and methods 2.1 Materials Carboxymethyl hydroxypropyl guar gum (CMHPG, DSGal = 0.54, DSCM = 0.06, MSHP = 0.25, Mw = 1360 kg·mol-1) and hydroxypropyl guar gum (HPG, DSGal = 0.62, MSHP = 0.38, Mw = 1470 kg·mol-1) with typical degrees of substitution in industrial applications were used. These kinds of derivatives are easily prepared from native guar gum (Pasha & Ngn, 2008; Venkataiah & Mahadevan, 1982). The dry weight and insoluble residues were determined and considered in the sample preparation. The guar gum derivative solutions were vortexed and subsequent shaken at 25 °C for 12 h on an orbital shaker. Sodium nitrate (ReagentPlus,
99.0%) and sodium azide (ReagentPlus, 99.5%) were purchased from Sigma-Aldrich Chemicals and used as received. Demineralized water containing 0.1 M NaNO3 + 200 ppm NaN3 was used as the solvent to minimize the “polyelectrolyte effect” and to inhibit bacterial degradation. A comprehensive molecular weight and degree of substitution analysis of the used guar gum derivatives can be found in previous studies (Szopinski et al. 2015; Szopinski et al. 2016).
2.2 Rheometry Large amplitude oscillatory shear measurements were performed on a DHR-2 combined motor-transducer rheometer (TA Instruments, New Castle, USA) with a cone-plate geometry (diameter = 60 mm, angle = 2°, measuring gap = 50 µm). Large amplitude oscillatory shear (LAOS) experiments were performed at various frequencies in the range of 0.1 to 10 rad·s-1. The active deformation control (continuous oscillation mode) of the DHR-2 was used. Current advantages in the deformation control feedback loop of stress-controlled rheometers and correct motor mode settings allow a reasonable agreement with the nonlinear response of strain-controlled rheometers (Bae et al. 2013; Merger & Wilhelm, 2014). The motor mode was set to medium, showing similar results as in stiff mode.
3
The raw data was processed using the MITlaos software developed by Ewoldt (2007b). For the determination of the Chebyshev coefficients and the Fourier coefficients, at least four strain cycles were used with two previously applied conditioning cycles. The highest significant harmonic of the raw data was determined by discrete Fourier Transform analysis and used to reconstruct a noise-reduced stress signal, which was used in the consecutive analysis.
3 Results and discussion The nonlinear viscoelastic properties of ionic carboxymethyl hydroxypropyl guar gum (CMHPG) and hydroxypropyl guar gum (HPG) were determined at concentrations between the semi-dilute solution state (c* < c < c**) and the concentrated solution state (c** < c), representing the relevant region of industrial applications. Solutions of CMHPG were evaluated at concentrations between 0.50 and 1.25 wt% (overlap parameter c = 8.0320.24) and of HPG between 0.75 and 1.50 wt% (overlap parameter c = 8.90-17.75). CMHPG has a significantly higher overlap parameter than HPG of the same molar mass, resulting from the more rigid chain of CMHPG originating from the electrostatic repulsion between the carboxymethyl groups (Szopinski et al., 2015; Szopinski et al., 2016). The nonlinear response of CMHPG and HPG turned out to be very similar, and for that reason the reporting in the next sections is limited to CMHPG. It has been observed before, that the viscoelastic properties of CMHPG and HPG solutions can be related by the respective overlap parameter c (Szopinski et al., 2016). The analysis for HPG can be found in the supplementary information. Ionic (CMHPG) and non-ionic (HPG) guar gum derivative solutions were evaluated by FTrheology and the extended SD method to give a comprehensive impression of the nonlinear behavior and the onset of it. The evaluation of the distorted waves of the nonlinear response may be performed along two emerging methods, based on different coordinate frameworks (see Hyun et al. (2011) for a comprehensive review). The first - referred to as the Fourier Transform (FT) rheology (Wilhelm, 2002) - comprises a time-domain representation: The nonlinear stress response as a function of time t is transformed into a Fourier series, showing the contribution of higher harmonics in frequency space. The orthogonal stress decomposition (SD) builds on a deformation-domain representation. The total stress response is interpreted in terms of an elastic ' t and an orthogonal viscous contribution
' ' t (Cho et al., 2005). The SD method has the option of defining nonlinear viscoelastic moduli using Chebyshev polynomials of the first kind (Ewoldt et al. 2008). 4
3.1 Fourier transform rheology The nonlinear stress response t; , 0 of viscoelastic fluids may be described by a Fourier series with the elastic and viscous Fourier coefficients G'n and G' ' n according to Equation 1 (Wilhelm, 2002). Therefore, the time dependent stress response is transformed into a frequency dependent spectrum. The nonlinear stress response comprises contributions of the intensity I1 of the excitation angular frequency and the intensities of higher order harmonics (Figure 3).
t 0
G ' (,
n odd
n
0
)sin n t G ''n (, 0 )cos n t
(1)
The normalized FT rheology spectrum of an aqueous CMHPG solution (1.25 wt%, 0.1 M NaNO3 + 200 ppm NaN3) indicates the dominant nonlinear flow behavior with 13 significant harmonics under deformation of 0 1000% (Figure 3a). These harmonics were used to reconstruct noise-reduced stress signals that were used in the consecutive orthogonal stress decomposition (SD) method (vide infra). The relative intensity of the third harmonic I3/1 (with respect to the excitation) has been used to quantify nonlinearity in the stress response (Figure 3b). The usual quadratic dependence of the normalized third harmonic with strain amplitude I3 / 1 0 is indicated at medium strain amplitudes (100< 0 <400%). This “linear” 2
nonlinear regime of deformation is often referred to as medium amplitude oscillatory shear (MAOS) and allows a more elaborated distinction of nonlinear behavior besides the classical SAOS-LAOS classification (Hyun et al. 2006). The aqueous guar gum solutions of this study (see suppl.), however, show a significant noise in the MAOS regime and detection is near the torque resolution limit of the rheometer. A more reliable analysis and more extensive insights were obtained using the stress decomposition method.
3.1 Nonlinear viscoelastic parameter by orthogonal stress decomposition The total stress response t; , 0 of viscoelastic fluids may alternatively be separated into an elastic stress contribution as a function of strain ' t and a viscous stress contribution as a function of strain rate ' ' t following the orthogonal stress decomposition (SD) method (Cho et al., 2005). The elastic and viscous Chebyshev coefficients en and v n can be extracted from the elastic stress ' t and the viscous
5
stress ' ' t by fitting the data with Chebyshev polynomials of the first kind Tn along equation 2 (Ewoldt et al., 2008):
t;, 0 ' t '' t 0
e , T x , T y n
0
n
n, odd
0
n
0
n
(2)
n, odd
Ewoldt et al. (2008) introduced nonlinear viscoelastic moduli G 'M and G 'L that are derived from the obtained Chebyshev coefficients en and n . The minimum-strain modulus G 'M (at
0 ) and the large-strain modulus G 'L (at 0 ) can be determined from the elastic Chebyshev coefficients en according to Equation 3 and 4.
G 'M
G 'L
d d d d
e1 3e3 5e5 7e7 ...
(3)
e1 e3 e5 e7 ...
(4)
0
0
These moduli describe the local elastic response at minimum ( 0 ) and maximum ( 0 ) instantaneous strain and converge to the linear elastic modulus G'1 of the SAOS regime at intermediate strains and rates. Similarly, the minimum-strain rate dynamic viscosity 'M and the large-strain rate dynamic viscosity 'L can be determined from the viscous Chebyshev coefficients n . The graphical visualization of the total stress response as a function of strain (elastic Lissajous-Bowditch curve, Figure 4a) and as a function of strain-rate (viscous Lissajous-Bowditch curve, Figure 4b) allows a geometric interpretation of the nonlinear viscoelastic parameter (Ewoldt, 2008). The minimum-strain modulus resp. the minimumstrain viscosity is equivalent to the slope of the tangent at minimum strain ( 0 ) and the large-strain modulus and viscosity are equivalent to the slope of the secant at maximum strain ( 0 ). It is easily appreciated, that the CMHPG solutions show a significant deviation from linearity at deformations larger than 100% (Figure 4).
The elastic and viscous Lissajous-Bowditch curves of an aqueous CMHPG solution (1.25 wt%, 0.1 M NaNO3 + 200 ppm NaN3) may be arranged in the { , 0 }-Pipkin space to give a basic insight into the onset of nonlinear flow behavior on deforming the polysaccharide solution (Figure 5). This visualization gives an impression of the influence of the time scale on the nonlinear flow behavior, especially in the separated elastic resp. the viscous stress contributions. These are represented by the dotted lines in the closed loops of the Lissajous6
Bowditch representations (Figure 5a resp. 5b). The linear viscoelasticity is recognizable in the straight lines of the elastic and viscous contributions at strain amplitudes smaller than 0 < 100% (Figure 6b(left)). The slope of the viscous stress (dotted lines in the viscous Lissajous-Bowditch curves of Figure 5b,6b) is smaller at higher frequencies in that range, showing the typical shear-thinning of the system at higher frequencies. Similarly, the slope of the elastic stress increases with the frequency indicative of a higher elastic modulus (Figure 6a).
The linearity of the contributions is progressively lost with increasing strain amplitude 0 . The deviation from linearity of the elastic and viscous contributions can be used for marking the onset of the nonlinear behavior of CMHPG solutions: the slopes of the dotted lines become strain dependent too. The nonlinear behavior is predominantly viscous in origin. The total stress loop is close to the viscous stress part, especially at low frequencies and large strain amplitudes (and therefore large strain rates). Aqueous solutions of xanthan gum show a similar nonlinear behavior (Ewoldt et al., 2010). An increasing strain-stiffening occurs at increasing strain when 0 is larger than 100%. The elastic G 'L at maximum strain is increasingly larger than G 'M of zero strain (cf. Figure 5a, see Figure 7a for non-normalized Lissajous-Bowditch curves).
The importance of nonlinearity of guar solutions is demonstrated in the strain-stiffening ratio S (= G 'L G 'M ) / G 'L ) of about 120% at the highest strain (Figure 8a). The ratio S is the
relative increase in the elastic modulus between zero and highest strain (Ewoldt 2010) under the dynamics of LAOS as steady state. The strain-stiffening ratio S increases with higher strain amplitudes and is more and less concentration independent to strain amplitudes 0 < ~ 600%. The maximum of ratio S at highest strain is somewhat higher for more diluted solutions of CMHPG. Latter may be understood as a higher elastic resistance of the more extended individual chains or chain segments in the existing physical network of the slow relaxing system (i.e. with respect to the strain rate) consisting of entanglements and superstructures (vide infra). Higher concentrations of CMHPG lead to a smaller deformation of the individual chain (segments), and hence to a smaller nonlinearity. The nonlinear elastic moduli and dynamic viscosities converge to the linear elastic modulus G'1 and linear dynamic viscosity '1 at low strain amplitudes ( 0 < 100%) corresponding to the SAOS regime (Figure 8). 7
A strain induced shear-thinning is observed that increases with strain at lower frequencies. The viscosity at zero deformation 'M is continuously larger than the slope of the secant at maximum strain 'L at a frequency of 0.1 rad/s (Figure 5). The behavior at higher frequencies is more complex as at intermediate strain, a thickening of the solution may precede the strain induced thinning (Figure 8,9). This behavior is more pronounced at higher concentrations and at higher frequencies. The shear-thickening ratio T (= ( 'L 'M ) / 'L ) is a useful measure to encompass latter (Figure 8,9). The ratio T of CMHPG solutions at the lowest concentration studied of c = 0.50 wt% decreases at strain amplitudes over 500%, indicative of the above discussed shear-thinning behavior at higher strain. More concentrated solutions show a similar decrease at higher strains, however, only after a maximum in T at intermediate strains. Latter effect is significant and has a high reproducibility (cf. error bars in Figure 8b). The region of strain induced thickening becomes larger at higher concentrations, and the maximum of T is higher at higher concentrations. The maximum of T at e.g.
1 rad s1 is in the region of a strain of 300%. It has a value of 10% at the highest concentration. This shear-thickening behavior is very relevant for processing guar solutions, e.g. when fluctuations in pumping rate or concentrations occur. We
interpret
the
shear-thickening
as
originating
from
a
temporary
network
of
superstructures/hyperentanglements (vide infra). More of the segments between the network points become extended with higher strain and increasingly resist deformation, leading to the increase in S (Figure 8b, 9b), but only at sufficient high frequencies. The dynamics of the network relax the imposed stress of lower frequencies, explaining the absence of thickening in this region. The network has a higher density of network points at higher concentration and thus has a larger longest relaxation time. Consequently, the higher concentrated solutions appear to thicken at lower frequencies. The terminal shear-thinning results from a dissolution of the network at higher strain amplitudes; the network cannot reform at the rate of agitation. The temporary network is thus rheological relevant from a certain minimum strain and frequency, a typical nonlinear feature (Figure 9). A similar shear thickening behavior may be recognizable in xanthan gum solutions (Ewoldt et al. 2010). This kind of behavior is expected for polymer solutions able to form superstructures with relaxation times in the time scale of the LAOS experiment. The interpretation in this manner allows to correlate the onset frequency of shear-thickening to the relaxation time of the network. The dynamics of the superstructures are insufficient to relax the stress of deformation at that point. The frequency L at the onset of shearthickening (T > 0) was coarsely estimated from Figure 9, to obtain the longest relaxation time 8
of the network comprising the superstructures L
( L = 1/ L ; see supplementary
information, Table S1). The relaxation time of the transient network shows an exponential dependence on the overlap parameter (encompassing CMHPG and HPG), here with an exponent of about 4/2 (1.95 0.22) (Figure 10). The successful superposition of the relaxation times of CMHPG und HPG shows that these guar gum derivatives behave similarly in solution and thus have similar segment-segment interactions. The higher polymer coil expansion and rigidity of the anionic CMHPG chain originating from electrostatic repulsion of carboxymethyl entities is taken into account by referencing to the overlap parameter c instead of c Mw . The relaxation processes in guar gum derivative solutions of the chain segments, the temporary network of superstructures and the entanglements can then be put into a comprehensive picture as function of the overlap parameter (Figure 10). Measurements in elongational flow allowed to find the fastest processes of the system, which were related to relaxations of chain segments (Szopinski et al., 2016). These show a dependence of the overlap parameter with an exponent of 3/2. The longest relaxation times are now assigned to the network of superstructures having and dependence on the overlap parameter with a power of 4/2. Measurements in shear flow lead to intermediate relaxation times, and putatively have contribution from network and chain segment movements. The relaxation times in shear show a dependence on the overlap parameter with exponent of 7/2, reminiscent of both processes that indeed are usually thought to take place in shear processes of guar gum solutions (Szopinski et al., 2015).
Concluding remarks The nonlinear viscoelastic properties of semi-dilute and concentrated aqueous CMHPG and HPG solutions (0.1 M NaNO3 + 200 ppm NaN3) were studied by FT-rheology and orthogonal stress decomposition. The evaluation of elastic and viscous Lissajous-Bowditch curves reveals pronounced strain-stiffening, shear-thinning and – thickening behavior as function of strain and strain rate. This behavior is quantified by the determination of the strain-stiffening ratio S and shear-thickening ratio T and evaluated as functions of the applied strain amplitude 0 and angular frequency (Pipkin space). T passes through a maximum that is codependent on concentration, strain and frequency. The interpretation offered explains the behavior in terms of the dynamics of a temporary network. The associated relaxation time scales with the overlap parameter with an exponent of 4/2. The network has relaxation times much higher than those of chain segment movements, which scales with overlap parameter with an exponent of 3/2. The match of the sum of exponents to 7/2, the dependence of the 9
longest relaxation times in shear may be coincidentally; at the same time, it may show that the interpretation of the relaxation processes in terms of fast chain segment movements and slower network dynamics is a viable description of guar gum solutions. Knowledge of the dynamics of such systems in water at larger deformations is crucial with regard to typical processing operations like pumping und stirring, especially considering the intriguing shear thickening above a minimum strain rate at intermediate strains.
Acknowledgement The authors wish to thank Dimitri Merger (Karlsruhe Institute of Technology) for stimulating discussions concerning LAOS measurements on stress-controlled rheometers. Previous investigations in this field were supported by the DGMK in Project 633/03.
References Banerjee, P., Mukherjee, I., Bhattacharya, S., Datta, S., Moulik, S. P., & Sarkar, D. (2009). Sorption of water vapor, hydration, and viscosity of carboxymethylhydroxypropyl guar, diutan and xanthan gums and their molecular association with and without salts (NaCl, CaCl2, HCOOK, CH3COONa, (NH4)2SO4 and MgSO4) in aqueous solution. Langmuir, 25, 1164711656.
Cheng, Y., & Prud’homme, R. K. (2000). Enzymatic degradation of guar and substituted guar galactomannans. Biomacromolecules, 1, 782-788.
Cheng, Y., Brown, K. M., & Prud’homme, R. K. (2002). Characterization and intermolecular interactions of hydroxypropyl guar solutions. Biomacromolecules, 3, 456-461.
Dea, I. C. M., & Morrison, A. (1975). Chemistry interactions of seed galactomannans. Advances in Carbohydrate Chemistry and Biochemistry, 31, 241-312.
Ewoldt, R. H., Clasen, C., Hosoi, A. E., McKinley, G. H. (2007) Rheological fingerprinting of gastropod pedal mucus and synthetic complex fluids for biomimicking adhesive locomotion. Soft Matter, 3, 634-643.
10
Ewoldt, R. H., Hosoi, A. E., & McKinley, G. H. (2008). New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear. Journal of Rheology, 52, 14271458.
Ewoldt R. H., Winter, P., Maxey, J., & McKinley, G. H. (2010). Large amplitude oscillatory shear of pseudoplastic and elastoviscoplastic materials. Rheologica Acta, 49, 191-212.
Ferry, J. D. (1980) Viscoelastic properties of polymers, 3rd edition, Wiley, New York.
Goycoolea, F. M., Morris, E. R., & Gidley, M. J. (1995). Viscosity of galactomannans at alkine and neutral pH: Evidence of ‘hyperentanglement’ in solution. Carbohydrate Polymers, 27, 6971.
Hoffman, J., & Svensson, S. (1978). Studies of the distribution of the D-galactosyl side chains in guaran. Carbohydrate Research, 65, 65-71.
Hyun, K., Heun Kim, S., Hyun Ahn, K. (2002). Large amplitude oscillatory shear as a way to classify the complex fluids. Journal of Non-Newtonian Fluid Mechanics, 107, 51-65.
Hyun, K., Baik, E. S., Hyun Ahn, K., Lee, S. J., Sugimoto, M.; Koyama, K. (2006). Degree of branching of polypropylene measured from Fourier-transform rheology. Rheologica Acta, 46, 123-129.
Hyun, K., Wilhelm, M. (2009). Establishing a new mechanical nonlinear coefficient Q from FT-rheology: First investigation of entangled linear and comb polymer model systems. Macromolecules, 42, 411-422.
Hyun, K., Wihelm, M., Klein, C. O., Cho, K. S., Nam, J. G., Ahn, K. H., Ewoldt, R. H., McKinley, G. H. (2011). A review of nonlinear oscillatory shear tests: Analysis and application of large amplitude oscillatory shear (LAOS). Progress in Polymer Science, 36, 1697-1753.
Kesevan, S., & Prud’homme, R. K. (1992). Rheology of guar and HPG crosslinked by borate. Macromolecules, 25, 2026-2032.
11
Khandavalli, S., Rothstein, J. P. (2015). Large amplitude oscillatory shear rheology of three differemt shear-thickening particle dispersions. Rheologica Acta, 54, 601-618.
Lapasin, R., Pricl, S., Tracanelli, P. (1992). Different behaviors of concentrated polysaccharide systems in large-amplitude oscillating fields. Rheologica Acta, 31, 374-380.
Lei, C., & Clark, P. E. (2007). Crosslinking of guar and guar derivatives, SPE Journal, 12, 316-321.
Merger, D., Wilhelm, M. (2014). Intrinsic nonlinearity from LAOStrain – experiments on various strain- and stress-controlled rheometers: a quantitative comparison. Rheologica Acta, 53, 621-634.
Morris, E. R., Cutler, A. N., Ross-Murphy, S. B., Rees, D. A., & Price, J. (1981). Concentration and shear rate dependence of viscosity in random coil polysaccharide solutions. Carbohydrate Polymers, 1, 5-21.
Mukherjee, I., Sarkar, D., & Moulik, S. P. (2010). Interaction of gums (guar, carboxymethylhydroxypropyl guar, diutan, and xanthan) with surfactants (DTAB, CTAB and TX-100) in aqueous medium. Langmuir, 26, 17906-17912.
Picout, D. R., Ross-Murphy, S. B., Jumel, K., Harding, S. E. (2002). Pressure cell assisted solution characterization of polysaccharides. 2. Locust bean gum and tara gum. Biomacromolecules, 3, 761-767.
Tayal, A., Pai, V. B., & Khan, S. A. (1999). Rheology and molecular weight changes during enzymatic degradation of a water-soluble polymer. Macromolecules, 32, 5567-5574.
Szopinski, D., Handge, U. A., Kulicke, W.-M., Abetz, V., & Luinstra, G. A. (2016). Extensional flow behavior of aqueous guar gum derivative solutions by capillary breakup elongational rheometry (CaBER). Carbohydrate Polymers, 136, 834-840.
12
Szopinski, D., Kulicke, W.-M., & Luinstra, G. A. (2015). Structure-property relationships of carboxymethyl hydroxypropyl guar gum in water and a hyperentanglement parameter. Carbohydrate Polymers, 119, 159-166.
Tizzotti, M., Labeau, M.-P., Hamaide, T., Drockenmuller, E., Charlot, A., & Fleury, E. (2010). Synthesis of thermosensitive guar-based hydrogels with tunable physico-chemical properties by click chemistry. Journal of Polymer Science, A: Polymer Chemistry, 48, 2733-2742.
Vananroye, A., Leen, P., Van Puyvelde, V., & Clasen, C. (2011). TTS in LAOS: validation of time-temperature superposition under large amplitude oscillatory shear. Rheologica Acta, 50, 795-807.
Wientjes, R. H. W., Duits, M. H. G., Jongschaap, R. J. J., & Mellema, J. (2000). Linear rheology of guar gum solutions. Macromolecules, 33, 9594-9605.
Wilhelm, M., Reinheimer, K., Kübel, J. (2012). Optimizing the sensitivity of FT-Rheology to quantify and differentiate for the first time the nonlinear mechanical response of dispersed beer foams of light and dark beer. Zeitschrift für Physikalische Chemie, 226, 547-567.
Zhang, L.-M., & Zhou, J.-F. (2006). Synergistic viscosity characteristics of aqueous mixed solutions of hydroxypropyl- and carboxymethyl-substituted guar gums. Colloids and Surfaces, A: Physicochemical and Engineering Aspects, 279, 34-39.
13
Figure 1. Chemical structure of native guar gum and chemically modified derivatives.
Figure 2. The storage modulus G’ and the loss modulus G’’ as functions of the strain 1 amplitude 0 for an aqueous CMHPG solution (1.25 wt%) at 10 rad s and the corresponding stress response in SAOS and LAOS.
14
Figure 3. (a) FT rheology spectrum (Relative intensity In/1 as a function of the normalized harmonic / 1 ) for a aqueous CMHPG solution (1.25 wt%) at a excitation angular frequency 1 of 1 1 rad s and 0 1000% (b) Relative intensity of the third harmonic I3/1 as a function
of the strain 0 for CMHPG at different concentrations (0.1 M NaNO3 + 200 ppm NaN3, T = 25 °C).
Figure 4. Geometric interpretation of the nonlinear (a) elastic moduli G 'L and G 'M and the (b) dynamic viscosities 'L and 'M for a aqueous CMHPG solution (1.25 wt%) at = 1 rad ·s-1 and 0 = 10 (1000%; T = 25 °C). The dashed lines represent the corresponding linear (first harmonic) material functions (0.1 M NaNO3 + 200 ppm NaN3, T = 25 °C).
15
Figure 5. (a) Elastic Lissajous-Bowditch curves arranged in the { , 0 }-Pipkin space (normalized total stress (t ) / max (solid lines) and normalized elastic stress '(t ) / max (eq 2; dotted lines) as functions of the normalized strain (t ) / 0 ) and (b) viscous LissajousBowditch curves (normalized total stress (t ) / max (solid lines) and normalized viscous stress '(t ) / max (eq 2; dotted lines) as functions of the normalized strain rate (t ) / 0 ) for a aqueous CMHPG solution (1.25 wt%, 0.1 M NaNO3 + 200 ppm NaN3, T = 25 °C).
16
Figure 6. (a) Elastic Lissajous-Bowditch curves (the total stress (t ) and the elastic stress ' (t ) as functions of the strain (t ) ) for various applied angular frequencies at linear ( 0 = 63%) and nonlinear ( 0 = 1000%) conditions (b) viscous Lissajous-Bowditch curves (the total stress (t ) and the viscous stress ' ' (t ) as functions of the strain (t ) ) for the applied angular frequencies at linear ( 0 = 63%) and nonlinear ( 0 = 1000%) conditions for a aqueous CMHPG solution (1.25 wt%, 0.1 M NaNO3 + 200 ppm NaN3, T = 25 °C).
17
Figure 7. (a) Elastic Lissajous-Bowditch curves (the total stress (t ) and the elastic stress
' (t ) as function of the strain (t ) ) for various strain amplitudes 0 at a constant angular frequency of = 1 rad·s-1 (b) viscous Lissajous-Bowditch curves (the total stress (t ) and the viscous stress ' ' (t ) as functions of the strain (t ) ) for strain amplitudes 0 at a constant angular frequency of = 1 rad·s-1 for a aqueous CMHPG solution (1.25 wt%, 0.1 M NaNO3 + 200 ppm NaN3, T = 25 °C).
18
Figure 8. (a) The minimum-strain elastic modulus G 'M , the large-strain elastic modulus G 'L , the linear (first harmonic) elastic modulus G '1 and the strain-stiffening ratio S (=
(G 'L G 'M ) / G 'L ) as functions of the strain amplitude 0 . (b) The minimum-strain viscosity 'M , the large-strain viscosity 'L , the linear (first harmonic) viscosity '1 and shearthickening ratio T (= ( 'L 'M ) / 'L ) as functions of the strain amplitude 0 for CMHPG at different concentrations at an angular frequency of 1 rad s1 (0.1 M NaNO3 + 200 ppm NaN3, T = 25 °C).
19
Figure 9. The strain-stiffening ratio S (a) and the shear-thickening ratio T (b) as functions of the angular frequency and the strain amplitude 0 (Pipkin space) for CMHPG solutions at various concentrations (0.1 M NaNO3 + 200 ppm NaN3, T = 25 °C).
20
Figure 10. The longest relaxation time of superstructures L , the longest shear relaxation time S (determined by entanglements and superstructures) and the longest elongational relaxation time E (chain segment movement) of CMHPG and HPG as functions of the overlap parameter c (solvent: 0.1 M NaNO3 + 200 ppm NaN3 (T = 25°C)).
21