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Extensional Properties of Hydroxypropyl Ether Guar Gum Solutions Manuela R. Duxenneuner,†,‡ Peter Fischer,‡ Erich J. Windhab,‡ and Justin J. Cooper-White*,† Laboratory of Tissue Engineering and Microfluidics, Australian Institute for Bioengineering and Nanotechnology, The University of Queensland, Australia, and Laboratory of Food Process Engineering, Institute of Food Science and Nutrition, ETH Zurich, Switzerland Received December 7, 2007; Revised Manuscript Received August 15, 2008
The extensional properties of 2-hydroxypropyl ether guar gum solutions were investigated using a capillary breakup extensional rheometer (CaBER). Optimization of the geometric parameters of this device allowed for the measurement of the characteristic relaxation times and the apparent extensional viscosities of a series of dilute to semidilute guar gum solutions. The measured relaxation times were compared with predicted Zimm relaxation times, assuming that the hydrophobically modified guar was in a good solvent. Good agreement was found at low concentrations (0.01 wt % ≈ 0.17c*, where c* is the polymer overlap concentration), and this technique allowed for relaxation times on the order of 1 ms to be measured for solutions with shear viscosities of 2 mPa · s. Both the shear and (apparent) steady-state extensional viscosities of this set of industrially relevant fluids exhibited two regions of dependency on polymer concentration: linear up to concentrations of 0.2 wt % (c/c* ≈ 3) and power law thereafter, where interchain interactions became significant. The extracted relaxation times followed the same trend (i.e., having a near linear dependency on concentration up to 0.2 wt % and a power-law dependency on concentration up to 9c*). The results indicate that the transition from dilute to semidilute behavior occurs at a nominal concentration of ∼3c* instead of c*. The results presented suggest that interchain interactions for this modified guar are weak overall, and the solutions investigated are absent of entanglements over the whole range of frequencies and concentrations explored ((0.17-9)c*).
Introduction Guar gum is a long-chain polysaccharide biopolymer extracted from Cyamopsis tetragonolobus seeds and is widely used as a stabilizing, cogelling, and thickening agent in soups, puddings, sauces, mayonnaise, ice creams, and juices. This is mainly due to the fact that these hydrophilic macromolecules produce high viscosity solutions, suspensions, and gels at relatively low concentrations ( 70 mPa · s) because of the additional elastic stresses that arise from macromolecular extension. To control the dynamics of the thinning and breakup process and to make sure that we extract true material properties from the measurements, we had to determine the most appropriate sample aspect ratio and capillary length. The optimal sample aspect ratios, defined as Λ0 ) h0/2R0, are typically within the range of 0.5 e Λ e 1 to minimize or avoid the effect of initial reverse squeeze flow or sagging and bulging of the cylindrical
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Figure 7. Relaxation time, Θ, as a function of the normalized polymer concentration, c/c*. The relaxation time shows a power-law scaling behavior of 1.5 ( 0.5 for the semidilute concentration regime (3c* up to 9c*). In the dilute regime (c/c* ) 0.17), the measured relaxation time is similar to that of the calculated longest Zimm relaxation time, Θz (dashed line, eq 2).
Figure 6. (a) Dimensionless filament diameter, d(t)/d0, versus elapsed time, t, for different concentrations of HPGG solution. (b) Close-up of d(t)/d0 versus t for lower-concentration HPGG solutions (0.01 to 0.2 wt %). The data show a trend that is the same as that for the more concentrated guar solutions. The exponential thinning thread in the beginning of the experiments is fit to eq 1, whereas the linear behavior of the aged thread is fit to eq 3.
sample.56,68 The calculated aspect ratios for the HPGG solutions are on the order of 0.5, and the measurements showed steady and regular filament thinning from the time both plates were separated. It is also essential to keep the starting gap of the plates as small as possible to support the static liquid bridge because surface tension holds the initial fluid between the two plates, and the maximum stable sample size also depends on the fluid volume.69 In capillary breakup tests, the axial separation is typically performed such that the initial gap height h0 is smaller than the capillary length lcap ) (σ/Fg)1/2. The liquid filament is then stable, and interfacial tension forces dominate the gravitational forces (sagging). If h0/lcap > 1, then asymmetric effects such as gravitational drainage dominate the filament thinning.70 In this work, h0 e 1.5 mm, lcap ) 2.7 mm, and thus h0/lcap e 0.6. Polymer Relaxation Time. From the observation of the timedependent decrease in the filament diameter (Figure 6a,b), the CaBER determined relaxation times were extracted and are listed in Table 1. Figure 6b shows a close-up of Figure 6a for lower concentrations. The theoretical mechanism of the filament thinning and the verification of the following equations have been well documented elsewhere.51,52,58 To extract the relaxation time, Θ, for these guar solutions, we have utilized eq 1 in the region of exponential thinning
d(t) ) d0 exp(-t/3Θ)
(1)
where d0 is the initial value of the filament diameter after the plates have finished opening (maximal gap height, h). The
starting point of measuring the filament thinning, d(t), is indicated by t ) 0 in Figure 6 (d(t ) 0) ) d0). The smallest relaxation time, determined at c ) 0.01 wt %, was ∼1 ms, which is at the measurable limit of CaBER. Figure 7 illustrates the extracted relaxation time, Θ, as a function of the normalized guar gum concentration, c/c*. It shows that above the critical overlap concentration the characteristic polymer relaxation time strongly depends on the concentration, which has also been shown in the recent work of Bazilevskii et al.,70 Stelter et al.,53 and Tirtaatmadja et al.48 We observe a power-law concentration dependence (on the order 1.5 ( 0.5) on the relaxation time for HPGG of concentrations greater than ∼3c*. In the dilute concentration regime (0.01 wt % solution), this scaling behavior is not valid (as discussed next). However, the power-law behavior is clearly a manifestation of increasing interactions between HPGG molecules in solution with increasing concentration, although the relative weak dependency suggests that the interactions between chains are overall quite weak and may be purely hydrodynamic in nature. HPGG has been shown to display semiflexible behavior in solution and to lack significant hydrogen bonding interactions between chains at a d.s. above 0.6,13,15 which is then likely to correlate with the lack of strong interactions between chains and hence the observed near linear dependency of the relaxation time. This result also suggests that the shear thinning that is observed in shear viscosity measurements for this set of solutions is akin to that seen for rigid-rod solutions, which is more a result of HPGG alignment than of entanglement effects. The extracted polymer relaxation times for HPGG solutions were then compared with the Zimm (longest) relaxation time, Θz, for this biopolymer in a good solvent. It is defined by the Rouse-Zimm theory and can be approximately evaluated as
Θz =
1 [η]Mwηsolvent ζ(3ν) NAkBT
(2)
where NA is Avogadro’s number, kB is the Boltzmann constant, and ν is the excluded volume exponent characterizing the coil expansion in the given solvent. The prefactor (1/ζ(3ν)), in which ζ(x) is the Riemann zeta function, depends on the solvent quality and the hydrodynamic interaction in the polymer chain. In this work, it has been taken as a constant of value 0.463, taking ν ) 0.55 for a good solvent.48 The experimentally determined relaxation times are in reasonable agreement (considering the stated limitations of the CaBER) with the calculated Zimm relaxation time at the lowest concentration (c/c* ) 0.17).
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Figure 8. Apparent extensional viscosity, ηex, versus Hencky strain, εh, for different concentrations of HPGG in solution. As an example, the dotted line (associated with the 0.5 wt % solution) highlights the plateau from which the value of the steady-state apparent extensional viscosity was derived.
However, at all concentrations above c/c* ) 0.17, the two times did not compare well, with deviations steadily increasing to be greater than an order of magnitude. (See Table 1.) For the HPGG, the relaxation time behavior as a function of concentration has not been reported, although this deviation from the calculated Zimm time at concentrations above c* is to be expected considering that the Rouse-Zimm model is a bead-spring model for coiled polymer solutions with no chain-chain interactions. (That is, it is valid only for c e c*.)71,72 Apparent Extensional Viscosity. Once the polymer molecules are fully extended within the thinning filament, the filament diameter then decreases linearly with time (Figure 6a,b)
d(t) ) d0 -
σt ηex
(3)
where σ is the surface tension and d0 is the initial filament diameter at time zero (after the initial plate separation event). For the self-thinning of the filament to be correctly described, a correction factor must be added to the time evolution term.56,62,73-76 For systems in which elastic stresses are dominant, the correction factor is unity,62,74 that is, eq 3 remains unchanged, whereas for inertial and inertia-less Newtonian viscous cylindrical filaments, the correction terms are 0.53 and 0.71, respectively.75 The apparent extensional steady-state viscosity, ηex, is determined by the ratio of the surface tension, σ, to the rate at which the filament diameter decreases with time48
ηex )
-σ δd(t)/δt
(4)
Subsequently, the apparent extensional viscosity values can be presented versus the Hencky strain, εh (Figure 8). In this Figure, the Hencky strain that is experienced by the fluid element at the axial midplane at time t is defined by
εh ) 2 ln
( ) d0 d(t)
(5)
The largest source of error in the calculation of ηex and εh is the accuracy with which the filament diameter can be measured. The minimum measurable diameter of the filament is dependent both on the camera resolution and on the quality of the image analysis software. The steady-state apparent extensional viscosities were determined from the data plateau for each concentration, as exemplified in Figure 8. Figure 9
Figure 9. Steady-state apparent extensional viscosity, ηex, as a function of the normalized polymer concentration c/c*. ηex follows a linear relationship within the dilute region (dashed line) and a powerlaw relationship (on the order of 2.3 ( 0.5) within the semidilute region (dotted line).
highlights the fact that the steady-state apparent extensional viscosities of these solutions continually increase with concentration, as expected. However, there are definitive trends: a linear dependence up to ∼3c*, followed by a power-law dependence (of 2.3 ( 0.5) up to our highest-studied concentration of ∼9c*. The error bars shown in Figure 9 represent contributions of errors in measuring the filament diameter with time and the surface tension. The data presented in Figures 4 and 9 indicate that the concentration dependencies of shear viscosity and apparent steady-state extensional viscosity on HPGG concentration are similar, showing obvious effects of interchain interactions above 3c* but not at c*. This discrepancy suggests that as a result of the known semiflexible nature of these biopolymers, the reduced levels of hydrogen bonding in modified guars,14-18 and the resultant inhibition of entanglements that such chain configurations and conformations cause, the use of the relationship c* ) 0.77/[η], which is explicitly valid for only a random-coil polymer, will lead to errors in calculating entanglement transitions in such systems. A better indication of a true c* with respect to the onset of significant polymer chain interactions is gained from steady-shear or extensional measurements. Morris et al.29 and subsequent others have suggested that from steadyshear measurements on pure guar (unmodified) solutions, the transition to concentrated solution behavior happens at a c* of 4/[η], which is very similar in magnitude to the noted transition from dilute to semidilute behavior from the data presented here. The fact that this transition concentration is observed to be nearly identical in both extensional and shear data and that linear and power-law dependencies are noted in both data sets as a function of concentration gives credence to our argument of a transition from dilute to semidilute behavior at a nominal concentration of ∼3c* for these modified guars. The dependencies that were noted prior to and above this shifted critical concentration, c*, are best exemplified by Figure 10, which shows a plot of Trouton ratio (Tr ) ηex/η0) versus concentration. We immediately note that there is a distinct transition concentration just above 3c*, with the Trouton ratio showing two regions of different linear dependencies on c/c*. The high values of Trouton ratio (Tr ) 440 for 0.01 wt %) recorded in the first region indicate that most of the extensional response is due to the alignment and extension of individual chains (Zimm-like behavior), with small but increasing effects of chain-chain interactions that are most likely purely hydrodynamic in nature (above c*). After ∼3c*, the dependency of the Trouton ratio on concentration decreases by an order of
Hydroxypropyl Ether Guar Gum Solutions
Figure 10. Trouton ratio (Tr ) ηex/η0), as a function of the normalized polymer concentration c/c*, decreases with concentration, displaying two linear relationships with a discrete slope change at the changeover from dilute to semidilute regions.
magnitude (Tr ) 16 for 0.5 wt %), which indicates significant interchain interactions. Extension thinning has been seen for semidilute synthetic flexible polymer solutions, such as polystryrene; however, this is often described to be the result of constraint-release mechanisms that overcame entanglements prior to Rouse-like chain dynamics being observed.73 In the case of HPGG, the suspected absence of significant entanglements over the concentrations explored in this work suggest that the observed decreases in the Trouton ratios in both regimes of concentration are the result of increased interchain interactions, which are more often observed in rigid-rod systems, and not of entanglements per se. Revisiting the oscillatory shear experiments shown in Figure 3b confirms our hypothesis that entanglements are absent in these systems. The observed slope of 1.7 for the storage modulus indicates that there are indeed multiple relaxation events occurring in this system, which most likely correspond to increased interchain interactions such as hydrogen bonds or even hydrophobic-hydrophobic junctions but not to entanglements. These data succinctly confirm our previous conclusion, which was made from the CaBER relaxation time data, that the HPGG systems are not entangled and any shear thinning or reductions in the Trouton ratio (based on zero shear viscosity values) are the result of chain orientation under increasing hydrodynamic interactions with increases in concentration, as would be expected for rigid-rod systems. The suspected absence of entanglements in this hydrophobically modified guar system, even up to concentrations of ∼9c*, suggests that more insight into the explicit nature of the interactions that occur in this system is required. This will be the focus of our future work on this and other modified galactomannan biopolymers, such as locust bean gum.
Conclusions In this work, the shear viscosity, apparent steady-state extensional viscosity, and the solution relaxation times of HPGG solutions of concentrations ranging from 0.01 to 0.5 wt % were investigated using a CaBER. The shear viscosity and apparent steady-state extensional viscosity both increased with increasing concentration, following well-defined linear and power-law relationships pre- and post-transition from dilute to semidilute concentration regimes. A power-law dependency of 3.8 ( 0.5 for shear viscosity with concentration suggests a semiflexible polymer system, whereas the power-law dependency of the extensional viscosity of 2.3 ( 0.5 suggests that the interchain interactions present in this system, although expected to be quite weak, do contribute to the enhancement of the effect of
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individual chain contributions to the filament thinning dynamics. The Trouton ratio varied significantly with concentration, starting as high as 440 for 0.01 wt % and decreasing to 16 for 0.5 wt %, and followed two distinct linear behaviors. The onset of significant interactions among polymers in solution (or the critical overlap concentration (c*)) determined from steady-shear and extensional measurements did not agree with that calculated using c* ) 0.77/[η] ) 0.058 wt %, with the transition being at a value of ∼0.2 wt % (∼3c*). The experimentally determined relaxation time at the lowest concentration (0.01 wt %) agreed with the predicted Zimm relaxation time, with significant deviations noted above c*, as expected. However, unexpectedly, the measured relaxation times of all solutions exhibited only a weak (near linear) dependency on concentration (up to values of ∼9c*). These noted dependencies of shear and extensional properties of these solutions are suggested to be due to the intrinsic semiflexible nature of these modified guars along with their reduced levels of hydrogen bonding in solution (as a result of the hydrophobic substitution), which produces solutions that are absent of chain entanglements even though the investigated solutions span dilute to semidilute concentration regimes. Acknowledgment. We thank Michael Pollard for numerous discussions on the molecular structure of guar gums. We further acknowledge the ARC Discovery Grants Scheme (Australia), the UQ ICM (International Collaborative Mode) grant schemes, the ETH Fund TH-38/03-3, and the EU-STREP Fund NMP033339 “Controlled Release” for financial support of the joined project at ETH Zurich (Switzerland) and the University of Queensland (Brisbane, Australia). M.R.D. thanks the “Hochstrasser Stiftung” (Zurich, Switzerland) for supporting the additional living and travel costs.
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