Rheology of Concentrated Isotropic and ... - ACS Publications

Biomacromolecules 2002, 3, 742-753

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Rheology of Concentrated Isotropic and Anisotropic Xanthan Solutions: 3. Temperature Dependence Hu-Cheng Lee and David A. Brant* Department of Chemistry, University of California, Irvine, California 92697-2025 Received January 22, 2002; Revised Manuscript Received March 21, 2002

The oscillatory rheology of one rodlike and one semiflexible xanthan sample has been investigated as a function of temperature in the range of xanthan concentrations where the polymer forms a lyotropic liquid crystalline phase in aqueous NaCl solutions. Readily observed changes in the rheological observables at temperatures corresponding to phase boundaries permit construction of the biphasic chimney region of the temperature-composition phase diagram. The chimney region leans toward larger values of the polymer concentration with increasing temperature, presumably as a consequence of a reduction in the effective axial ratio of the helical polymer with increasing temperature. The results permit construction of plots of the rheological observables as a function of polymer concentration at temperatures T in the range 20 e T e 90 °C. Characteristic features of these curves observed at room temperature are preserved at higher temperatures, provided the xanthan double helix remains intact. The temperature dependence of the viscosity of isotropic xanthan solutions can be described with the Arrhenius law. For anisotropic solutions the viscosity increases with T at the higher end of the experimental temperature range, presumably because higher temperatures reduce the order parameter of the liquid crystalline phase with a concomitant increase in viscosity. At low NaCl concentration, and low polymer concentration, the xanthan helix order-disorder transition occurs at temperatures Tm below 90 °C. At temperatures above Tm the rheological observables reveal the onset of network formation involving xanthan chains released from the ordered helical structure. When these systems are cooled back below Tm, extensive network formation develops with large increases in viscosity and in the storage and loss moduli. Introduction In two earlier papers we have explored the roomtemperature rheology of aqueous xanthan in the range of polymer weight percent, W, from 1 to 20%.1,2 These studies focused on xanthan fraction X13F3 with weight average molecular weight Mw ) 154 000 g/mol and xanthan fraction X2F2 with Mw ) 480 000 g/mol. The chemical structure of xanthan is shown in Figure 1, where it will be noted that the polymer is ionic and carries up to two negative charges per repeating unit at neutral pH, if all pyruvate ketal groups on the side chains are intact. Both fractions were investigated in aqueous NaCl solution with NaCl molarities Cs ) 0.01, 0.10, and 1.0 mol/L. Fraction X13F3 with weight average contour length Lw ) 79 nm comprises just N ) 0.33 (weight average) Kuhn lengths and thus behaves effectively as a rigid rod at room temperature. Fraction X2F2 with Lw ) 247 nm and N ) 1.03 behaves as a semiflexible polymer at room temperature. As with other stiff polymers of high axial ratio, excluded volume effects dictate that aqueous xanthan form a lyotropic liquid crystalline phase above a critical concentration that depends on xanthan molecular weight distribution, salt concentration, pH, and temperature.3-7 Below a concentration Wi the system exists as a homogeneous isotropic phase. Above a concentration Wa the system forms a homogeneous anisotropic phase. In the narrow concentration * To whom correspondence should be addressed: telephone, +1 (949) 824-6019; fax, +1 (949) 824-8571; e-mail, [email protected].

range between Wi and Wa the system is biphasic, and the isotropic and cholesteric liquid crystalline phases coexist at concentrations Wi and Wa, respectively. A schematic version of the xanthan temperature-composition phase diagram is shown in Figure 2. The persistence length q of ordered xanthan is reported to be in the range from 100 to 150 nm.8-11 Although some have suggested that q may be as small as 65 nm,12 we have used the value q ) 120 at room temperature to calculate the number of Kuhn lengths in X13F3 and X2F2 reported above, because this value has been associated with the conditions of moderate to low ionic strength encountered in these studies.6,8 Only the fully charged form of xanthan present at neutral pH is considered in these studies. The earlier studies with X13F3 and X2F2 explored the rheology of the system moving horizontally at room temperature from the isotropic regime, across the biphasic “chimney” region of the phase diagram (Figure 2), and into the anisotropic domain.1,2 The steady shear (η) and dynamic (η*) viscosities increase strongly with W in the isotropic regime. Both η and η* decline precipitously in the biphasic region, as the much less viscous anisotropic phase increases in volume fraction with increasing W. For fully anisotropic solutions η and η* are effectively independent of W in the concentration range studied; the dependence on shear rate is also much diminished and, for X13F3, abolished completely. In strong contrast to flexible polyelectrolyes, η and η* are essentially independent of Cs in the isotropic domain,

10.1021/bm025510v CCC: $22.00 © 2002 American Chemical Society Published on Web 05/07/2002

Xanthan Liquid Crystal Rheology Temperature Dependence

Biomacromolecules, Vol. 3, No. 4, 2002 743

Figure 1. Repeating unit of xanthan showing cellulosic backbone with three sugar side chains on every second backbone glucose.

Figure 2. Schematic phase diagram for rodlike polymers with domains I (isotropic), A (anisotropic lyotropic liquid crystal), and B (biphasic). Horizontal dashed line intersects biphasic chimney region at Wi and Wa; vertical dashed line intersects chimney region at Ti and Ta.

but in the fully anisotropic domain both η and η* increase sharply as the ionic strength increases at a given polymer concentration W. In isotropic solutions the axial ratio and hydrodynamic volume of the stiff xanthan molecules are effectively insensitive to ionic strength, and the energy dissipated in shear does not depend on Cs at a given W. In the anisotropic phase, however, the longer range of the lateral electrostatic interactions between xanthan molecules forces the liquid crystal order parameter to become greater at lower ionic strengths, 13 and hence, the viscosity becomes smaller as Cs decreases at a given W. These and many other features of the room-temperature rheology of these systems are described in detail elsewhere, and the behaviors of the rodlike and semiflexible samples are contrasted.1,2 The preparation and characterization of fractions X13F3 and X2F2 are described in the initial paper of this series.1 In this paper, using the same two xanthan fractions, we describe the rheological consequences of passage through the biphasic “chimney” region of the phase diagram by changing the temperature. The situation is complicated under some conditions of W and Cs by intervention of the temperature-driven conversion of ordered helical xanthan to a disordered form. The nature of the ordered form of xanthan remains a topic of discussion,14 in part because no definitive

model based on diffraction analysis has emerged. Nevertheless, there is reasonably uniform agreement that xanthan samples that have undergone heating above the conformational transition temperature during isolation have a doublestranded helical character,15-19 particularly if they have also been degraded by sonication.11,12,20 It should be noted here that several workers have presented evidence for a different “native” ordered xanthan structure in samples that have never been subjected to elevated temperature or reduced ionic strength.11,21-24 The data presented here for pasteurized commercial xanthan samples that have been sonicated and fractionated are fully consistent with a stiff double helical structure that can be melted to a disordered form at a temperature Tm that depends on the concentration and molecular weight distribution of the polymer and the ionic details of the solution.25-29 In dilute xanthan solutions Tm rises from near room temperature in the absence of added salt to slightly above the boiling point of water when the salt concentration Cs reaches 0.10 M. In more concentrated xanthan solutions the ionic character of the polymer contributes to the ionic strength and increases Tm still further. It should be noted that thermal interconversion of the ordered and disordered forms occurs over a temperature range of 10 °C or more,27,30 and the limits of this range depend significantly on the observable property that is followed.31 Here we will identify Tm as the temperature at the onset of the thermally induced transition on the rising leg of the thermal cycle, because this is the most obvious indicator of the transition as detected in the present experiments. Difficulties in demonstrating a reduction of xanthan molecular weight during heating through the temperatureinduced conformational transition, and other evidence, have persuaded some workers that the ordered xanthan chains are folded on themselves in hairpin fashion to generate the double strand.11,22,28,29,32 Others have explained the difficulty in demonstrating a thermally induced reduction in molecular weight in terms of incomplete separation of the dimeric structure under the denaturing conditions used.31,33,34 It is clear, however, that regardless of the detailed character of the double stranded helix, thermal disruption of the xanthan ordered structure followed by cooling below the transition temperature Tm results in the formation of a highly entangled structure in which intermolecular interactions are very prevalent, provided the xanthan concentrations are near or

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Biomacromolecules, Vol. 3, No. 4, 2002

Lee and Brant Table 1. Phase Boundary Concentrations Wi and Wa for X13F3 and X2F2 at 23 °C X13F3

Wi Wa

Figure 3. Observed xanthan helix melting temperatures Tm for fraction X2F2 at Cs ) 0.01 M as a function of xanthan weight fraction W. Smooth curve calculated as described in text. All temperatures reported in °C.

above the overlap concentration.20,30,35-37 Our working assumption is that these intermolecular interactions share the characteristics of those stabilizing the ordered xanthan structure before thermal denaturation.20,30 Polymer concentrations W encountered here extend to 20% (w/w). The polyelectrolyte may therefore contribute significantly to the ionic strength of the solutions, particularly when Cs is small. Paoletti et al.27 have reported the experimental dependence of Tm on ionic strength I ) Cs for high molecular weight xanthan in 1-1 electrolytes at low polymer concentrations. The measured slope of the correlation is d(log I/d(1/ Tm)) ) -2090 K. Here we estimate the effective ionic strength Ie as Ie ) Cs + φzpCp, where zp is the number of polymeric charges per polymer chain and Cp is the molar concentration of polymer chains. The parameter φ modulates the contribution from polymeric charge due to counterion condensation (Manning ξ ) 2.42 for these xanthan samples) and nonidealilty effects present at the salt and polyelectrolyte concentrations encountered here. The measurable counterion activity coefficient or osmotic coefficient is often used for this purpose.38,39 We base zp and ξ on the measured pyruvate content of our xanthan sample1,40 assuming a double helical structure with characteristics deduced from fiber diffraction analysis.41 For the least concentrated xanthan solution (W ) 1.25 at Cs ) 0.01 M) the quantity zpCp ) 0.022 M, so the polymer makes a very significant contribution to the total ionic strength even at the low end of the polymer concentration range when Cs ) 0.01 M. By assuming a constant value φ ) 0.5 and taking Tm ) 45 °C at low xanthan concentration when Cs ) 0.01 M,27 we are able to describe the dependence of Tm on W at Cs ) 0.01 M observed for X2F2 in the present studies with reasonable accuracy using the correlation of Paoletti et al. This estimate of φ is to be compared with φ ) (2ξ)-1 ) 0.21 for the osmotic coefficient calculated from Manning’s limiting law42 and with φ ) 0.65 deduced for xanthan from counterion activity measurements in the absence of salt.39 The calculated correlation for Cs ) 0.01 M is shown in Figure 3; for all other salt concentrations

X2F2

0.01 M

0.10 M

1.0 M

0.01 M

0.10 M

1.0 M

4.52 5.93

6.66 8.34

9.68 11.76

2.15 3.11

4.61 6.30

6.68 8.47

studied here the Tm exceeds the highest temperatures reached in these experiments. The schematic phase diagram in Figure 2 recognizes the anticipated increase in xanthan double helical flexibility with increasing temperature. Thus, the chimney region of the diagram leans toward higher W as T increases to reflect the shift of Wi and Wa toward larger values with a decrease in axial ratio and/or rigidity with increasing T.43-47 Figure 2 does not contain features corresponding to disruption of the double helix at temperatures above Tm. These features would entail additional smeared “phase boundaries” between isotropic solutions of disordered xanthan and isotropic, biphasic, and anisotropic solutions of ordered xanthan. The values of Wi and Wa for xanthan fractions X2F2 and X13F3 were measured earlier for NaCl molarities Cs ) 0.01, 0.10, and 1.0 at 23 °C1 and are reported here in Table 1 for convenient reference. We demonstrate below that the phase diagram can be expanded into the domain of higher temperature using rheological measurements. The influence of ordered structure melting under conditions of low ionic strength will also become evident. It is conventional to characterize the temperature dependence of the viscosity η of a pure liquid or polymer solution with an activation energy Eη that governs a monotonic exponential temperature dependence described by eq 148 η ) η0 exp(-Eη/RT)

(1)

The parameters η0 and Eη are frequently temperature independent over fairly wide temperature ranges. We will employ this relationship, when applicable, in what follows to characterize the temperature dependence of η*. In temperature-driven transitions of lyotropic liquid crystals from the anisotropic to the isotropic state, the viscosity passes through extrema that cannot be characterized with eq 1. Experimental Section Sample preparation and rheological measurement procedures are given in the first paper of this series.1 All rheology experiments were done in the oscillatory mode at a frequency ω ) 5 s-1 in the linear viscoelastic regime. Cyclic temperature sweeps were carried out with a step size of 3 °C in the heating leg and 4 °C in the cooling leg. The sample was allowed to remain for 1 min at the set temperature before a measurement was made. To retard the evaporation of water from the samples at higher temperature, a thin layer of Newtonian oil was used to cover the outer rim of the solution between the parallel plates. The Newtonian oil is immiscible with water and proved not to interfere with the measured results. All the rheological parameters are reported in cgs


Figure 4. Temperature dependence of η*(ω) for X2F2 at Cs ) 0.01 M for several solutions that were fully isotropic at room temperature. All viscosities reported in poise.

units: poise for viscosity and dyn/cm2 for moduli. Temperatures are reported in °C. Units are not given in the plots or tables. As the temperature of the system was increased at constant xanthan concentration W, it was possible to identify a temperature Ti at the boundary between the biphasic chimney region and the fully isotropic region at temperatures above Ti. Likewise, the temperature Ta defines the boundary between the biphasic region and the homogeneous anisotropic region present at still lower temperatures. These phase boundary temperatures corresponding to a particular xanthan concentration are illustrated at the intersections of the vertical line drawn at W ) 0.15 with the respective phase boundary curves in Figure 2. Phase boundary temperatures Ti and Ta were determined only during the heating leg of the thermal cycle, because of irreversibility due to thermal disruption of ordered xanthan and/or other sources of hysteresis. The melting temperature, Tm, was also identified only on the ascending leg of the thermal cycle. The temperature Tf designates the highest temperature to which a given solution was taken in a thermal cycle. Results and Discussion Oscillatory Shear Rheology of X2F2 in 0.01 M Aqueous NaCl. Xanthan in the dilute regime undergoes the orderdisorder transition at a temperature of 45-50 °C at Cs ) 0.01 M.26,27,39 The temperature range covered here, 20-90 °C, thus embraces Tm under these salt conditions, even after taking into account the contribution of the polymer to the ionic strength (see below). Figure 4 shows the change of oscillatory shear viscosity η*(ω) with temperature T in thermal cycles in the concentration range where W < Wi for quiescent solutions at room temperature. Thus, all three solutions in Figure 4 were fully isotropic at the beginning of the thermal cycle, and no crossing of the phase boundaries in Figure 2 is anticipated. During the heating leg η*(ω) decreases with increasing T. At any given temperature, η*-


(ω) increases with W in both heating and cooling legs, which is normal for solutions in the isotropic regime.1,2 An increase in negative slope (deflection) occurs on every ascending temperature curve in Figure 4 around T ) 60 °C, where the disruption of ordered xanthan begins. Notice that the change in slope moves perceptibly to higher T as the polymer concentration and effective ionic strength are increased. The activation energy Eη averages 25.9 kJ/mol for the three isotropic X2F2 solutions when eq 1 is applied to the heating curves before the deflection. This activation energy in the concentrated isotropic regime is about 9 kJ/mol larger than that determined earlier for xanthan in aqueous 0.2 and 2% NaCl in the semidilute regime (0.08%).49 This is perhaps because in the concentrated isotropic regime the present xanthan molecules entangle significantly, as evidenced by the G′/G′′ crossover reported earlier at room temperature for X2F2.2 The cooling curve is distinctly different from the heating curve showing more than a 10-fold increase in viscosity at room temperature. This is clearly because in heating the solutions to Tf ) 90 °C, the double helix is at least partially disrupted and an extensive intermolecular network is formed on cooling back below Tm.20,30 The deflection points on the heating curves in Figure 4 indicate the onset of ordered helix disruption at the melting temperature Tm. Of course, kinetic effects associated with the present experiment may make Tm measured in this way somewhat different from that measured by other means closer to equilibrium. The viscosity decreases more rapidly with temperature after the deflection point than before, because double helical xanthan has a higher relative viscosity than the more flexible disordered form, which may include some fully or partially dissociated double strands. See Capron et al. for a review of the relevant literature.29 A melting temperature higher than the 45-50 °C reported for dilute xanthan solutions at Cs ) 0.01 M is consistent with the contribution of xanthan to the ionic strength and, perhaps, to failure of the system to achieve equilibrium at each stage of the heating process or to differences arising from the measured observable.31 Examination of Figure 4 shows that the deviations in the heating curves for W ) 1.25, 1.50, and 2.00 occur at about 59, 62, and 63 °C, respectively, consistent with the correlation in Figure 3. Figure 5 shows η*(ω) vs T for thermal cycles with samples that are biphasic and fully anisotropic at room temperature. To show the trends more clearly, the curve for the fully isotropic solution with W ) 2.00 from Figure 4 is repeated. Around room temperature η*(ω) decreases with increasing W as W passes through the biphasic regime, as reported in a previous paper.2 Note from Table 1 that the solutions with W ) 2.50 and 3.00 are biphasic at room temperature while that with W ) 3.53 is fully anisotropic. The curve for W ) 2.50 rises with increasing temperature as anisotropic phase is converted to isotropic phase moving up in T through the biphasic chimney. The curve reaches a maximum around T ) 41 °C, above which the system is fully isotropic. We identify this maximum with the temperature Ti marking the upper phase boundary for a solution with W ) 2.50. As for the curves in Figure 4, there is a deflection point on the W ) 2.50 curve at about Tm ) 68 °C beyond which the viscosity

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Lee and Brant

Figure 5. Temperature dependence of η*(ω) for X2F2 at Cs ) 0.01 M for several solutions that were biphasic or fully anisotropic at room temperature. Curve for fully isotropic sample at W ) 2.00% repeated from Figure 4.

Figure 6. Dependence of η*(ω) on W for X2F2 at Cs ) 0.01 M measured at several fixed temperatures on the heating and cooling legs of the thermal cycle.

decreases more rapidly with T. From Figure 5, Ti for W ) 3.00 and 3.53 is determined to be 47 and 56 °C, respectively, and Tm is determined to be 76 and 79 °C in excellent agreement with Figure 3. Note the substantial dependences of Ti and Tm on W illustrated here. In the case of Tm this is primarily an ionic strength effect, but Ti increases rapidly because the boundaries of the chimney region of the phase diagram (Figure 2) rise steeply with increasing W. The heating curve for W ) 3.53 shows a minimum around T ) 28 °C, which we provisionally identify with Ta. Below Ta only the anisotropic phase exists for which η*(ω) declines normally with increasing T. Thus, the biphasic domain at W ) 3.53 spans a temperature range Ti - Ta ) 28 °C. In the temperature range between Ti and Tm, all of the solutions in Figure 5 are in the isotropic regime, and the viscosity increases with an increase in W as expected. The behavior along the cooling curves is similar to that of the initially isotropic solutions in Figure 4 reflecting network formation among xanthan strands released from the double helix by heating above Tm. Only the cooling curve for W ) 3.53 is somewhat anomalous in that it shows a maximum in η*(ω) around T ) 34 °C. Because the difference Tf - Tm ) 11 °C is smallest for this sample, the ordered structure is not as thoroughly disrupted by heating, and there are fewer nonhelical xanthan strands available for network formation as the system is cooled back to room temperature. Data of the sort shown in Figures 4 and 5 can be usefully replotted in Figure 6 as η*(ω) vs W at several fixed temperatures taken from the heating and cooling legs of the thermal cycle. We have shown previously that the maxima in plots of oscillatory shear parameters such as η*(ω) against W can be identified with Wi.1,2 Thus, on the 20 °C heating curve in Figure 6 the peak in η*(ω) appears at W ) Wi ) 2.00 at the boundary between the fully isotropic and biphasic regimes at room temperature in agreement with the previous report (Table 1).2 When the temperature is raised to 38 °C, the peak on the heating curve in Figure 6 moves up to W ) Wi ) 3.00, as would be expected from the schematic phase

diagram in Figure 2. At 56 °C the solutions remain isotropic up to concentrations of at least W ) 3.53, so no peak appears to mark the position where W ) Wi. Moreover, 56 °C < Tm for all the solutions in question (Figure 3), so the double helix remains intact everywhere along this curve. As expected for isotropic solutions, η*(ω) increases monotonically with W at 56 °C. Note that for isotropic solutions η*(ω) decreases with increasing temperature at a given W, but for biphasic solutions with W > Wi the temperature dependence is reversed. The 80 °C heating curve lies above Tm for all W e 3.53 (Figure 3), so all of the solutions along this curve are isotropic and in the disordered state. The viscosities measured along this curve are generally smaller, owing to the higher temperature and, especially, to the disordered conformation of the chains, and rise monotonically with W. At the highest concentrations shown the viscosity of the isotropic solutions of disordered xanthan at 80 °C is greater than that of the biphasic and anisotropic solutions present at the same concentration at lower temperatures. When the heated solutions are cooled from Tf ) 90 °C back to 20 °C, the viscosity increases considerably due to the association of the melted xanthan strands. That the viscosity at W ) 3.53 is smaller than that of W ) 3.00 suggests, as mentioned earlier, that thermal conversion of the double helices was incomplete at Tf so that fewer cross-links develop on cooling at W ) 3.53. Other effects may also be at work here, as discussed below. The influence of Tf and of the “soak time” for which the solutions are kept at the desired temperature before a measurement is made are illustrated in Figure 7. The three heating curves for W ) 3.53 overlap each other regardless of soak time except at the highest temperatures encountered, where longer soak times produce slightly larger measured values of η*(ω). This shows not only that the system responds on heating with a relaxation time on the order of 1 min but also that the experiments are very reproducible, because fresh samples were reloaded for each thermal cycle. Equation 1 was used to fit the data points before Ta and the



Figure 7. Effects of soak time and Tf on η*(ω) for X2F2 at Cs ) 0.01 M for W ) 3.53.

Figure 8. Temperature dependence of G′(ω) and G′′(w) for X2F2 at Cs ) 0.01 M for several solutions that were fully isotropic at room temperature. All moduli reported in dyn/cm2.

average Eη in the fully anisotropic regime is 9.5 kJ/mol, which is much smaller than in isotropic regime (25.9 kJ/ mol). Viscosities on the cooling curve for Tf ) 89 °C with soak time 1 min are nearly 10 times larger than those on the two cooling curves for Tf ) 83 °C. For all of these experiments Tf exceeded Tm ) 79 °C measured for W ) 3.53 at Cs ) 0.01 M. Clearly the extent of thermally induced disorder on heating and the corresponding extent of crosslinking upon cooling depend on the relationship of Tf to Tm and, as shown by the differences in the two cooling curves for Tf ) 83 °C, on the soak time. We did not attempt an extensive analysis of the relaxation times characteristic of the cooling curves, but it appears they are somewhat longer than those on the heating leg. This is not surprising given the kinetic complications that must accompany network formation. The effects of much longer incubation times on xanthan solutions following a thermal cycle have recently been investigated by Yoshida et al.50 The solutions heated to Tf ) 83 °C show definite evidence of recurrence of the anisotropic phase on cooling (Figure 7). As noted earlier, the regions of positive slope in the η*(ω) vs T curves are clearly associated with passage through the biphasic domain of the phase diagram. The more than 10-fold increase in η* at 20 °C after cooling suggests, however, that the differences in the heating and cooling curves are not due simply to hysteresis in the textures of the biphasic and anisotropic systems following a quench below Ti. Instead we interpret the cooling curves for Tf ) 83 °C to mean that on cooling to 20 °C the system is anisotropic or, more likely, biphasic with significant extents of cross-linking present, at least in the isotropic phase. The maximum in the cooling curves occurs near 41 °C. This is to be compared with the maximum at Ti ) 56 °C on the heating curves. This difference again may signify in part some hysteresis in the phase transition on cooling, which may occur even in the absence of any helix disruption at Tf, but we are inclined to believe that is more importantly a reflection of a smaller mean Kuhn length for the sample following partial disruption of the double helix at Tf. This conclusion is documented

further in what follows. Surprisingly, there is even a hint in the cooling curve for Tf ) 89 °C that some anisotropic phase is recovered on cooling to 20 °C. The crossover frequencies ωc for X2F2 at Cs ) 0.01 M at room temperature are between 60 and 100 s-1,2 close to the upper frequency limit for our instrument in oscillatory shear mode. At ω ) 5 s-1, G′(ω) is smaller than G′′(ω) as shown in Figure 8 for solutions isotropic at room temperature. With the increase of temperature both G′(ω) and G′′(ω) decrease. For W ) 1.25, the signal of G′(ω) is too weak to be very useful in the heating cycle. The modulus G′′(ω) dominates under these conditions and shows the same deflection points on the heating curve as seen for η*(ω) in Figure 4. When the solution is cooled from Tf, both G′(ω) and G′′(ω) increase dramatically with G′(ω) growing more rapidly. The loss tangent G′′(ω)/G′(ω) is much smaller than that before the beginning of the thermal cycle. For W ) 2.00, G′(ω) even crosses over G′′(ω) when T drops back to 30 °C; i.e., the solution becomes more elastic than viscous and shows gellike characteristics after the thermal treatment. The networking of xanthan strands freed from the ordered structure contributes to the increase of both G′(ω) and G′′(ω). For the initially biphasic solution at W ) 2.50, the transition to pure isotropic phase is demonstrated in Figure 9 in the heating curves for both G′(ω) and G′′(ω). During the cooling process, G′(ω) crosses G′′(ω) when T is lower than 44 °C. The solution with W ) 3.53, which is fully anisotropic at room temperature, has a temperature range between 30 and 63 °C in which G′(ω) > G′′(ω) on the cooling curve. Below 30 °C, however, biphasic behavior reappears and the loss tangent moves above unity. Before leaving Figures 8 and 9 it is useful to note that G′′(ω) and, especially, G′(ω) begin to increase on the heating legs at temperatures above the corresponding Tm and before Tf is reached. Likewise, for W ) 1.5 and 2.0 in Figure 4 η*(ω) begins to increase on the heating curves for T > Tm. Clearly network formation begins in the temperature range just above Tm due simply to the abundance of interaction sites possessing unsatisfied valences for association on

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Figure 9. Temperature dependence of G′(ω) and G′′(w) for X2F2 at Cs ) 0.01 M for several solutions that were biphasic or fully anisotropic at room temperature.

Figure 10. Temperature dependence of η*(ω) for X13F3 at Cs ) 0.01 M for several solutions that were fully isotropic at room temperature.

xanthan strands released from the ordered phase above Tm. Despite the relative weakness of the individual association valences at this temperature, this behavior is entirely to be expected on the basis of models for xanthan double helix formation described earlier.31,51 The same phenomenon is exhibited in the heating curves in Figure 7 with Tf ) 83 °C. Here the heating curve with the longer soak time shows larger values of η*(ω) as T approaches Tf reflecting the network formation at T > Tm ) 79 °C even before the cooling begins. Oscillatory Shear Rheology of X13F3 in 0.01 M Aqueous NaCl. Figure 10 shows the change of η*(ω) with T during thermal cycles for the rodlike xanthan fraction X13F3 in solutions at Cs ) 0.01 M that are fully isotropic at room temperature. On heating η*(ω) decreases as expected with increasing T, but there is no obvious deflection point such as was observed for the melting of X2F2 (Figure 4). Indeed, it is not entirely clear whether the isotropic solution of xanthan rods will be more or less viscous than an isotropic

Lee and Brant

solution of the disordered polymer at a given temperature under these conditions of concentration and molecular weight. If anything, these curves may show a small decrease in slope beginning near T ) 60 °C. This temperature is close to the expected Tm for the least concentrated of these solutions (W ) 2.52) at Cs ) 0.01 M (if Figure 3 can be assumed applicable to X13F3 as well as to X2F2) and Tm is expected to be considerably larger than this for the most concentrated (W ) 4.54). The average Eη in the isotropic regime is found to be 20.5 kJ/mol when eq 1 is applied to the heating curves in Figure 10. This is 5 kJ/mol smaller than that of sample X2F2, perhaps because X2F2 is semiflexible and entangles while X13F3 is rigid and does not show evidence of entanglement in the accessible frequency range.1,2 At any given temperature, η*(ω) increases with W on the heating leg in Figure 10, which is normal for solutions in the isotropic regime. When the solutions are cooled, η*(ω) for W ) 2.52 increases by 30 times, while the solutions with larger W witness a progressively smaller relative increase in η*(ω). The clear message is that with increasing W the difference between Tf and Tm decreases and, progressively, fewer xanthan segments are released from the double helix at Tf to become available for network formation on cooling. The hysteresis seen in the curve for W ) 4.54 is reminiscent of thermal cycles (see below) in which it is clear that little or no thermal melting of the xanthan ordered structure has occurred. After the thermal treatment, η*(ω) at room temperature decreases with increasing concentration, in contrast to the corresponding case for X2F2 in Figure 4. For isotropic X2F2 at Cs ) 0.01 M, the double helix is largely melted because at these xanthan concentrations Tm < Tf. Thus, weak gel formation is well developed, and the viscosity after heat treatment increases with W. For isotropic X13F3 at Cs ) 0.01 M, the double helix melting is inhibited by the increase of Tm at the higher xanthan concentrations, and gel formation is suppressed, so the viscosity after heat treatment decreases with W. When W > Wi for X13F3 solutions at room temperature, the phase transition from biphasic or anisotropic to isotropic occurs with an increase of η*(ω) with T until Ti is reached, as shown in Figure 11. Notice from Table 1 that solutions with W ) 4.89 and 5.71 are biphasic and that with W ) 7.47 is anisotropic at 23 °C. After the solutions are converted into fully isotropic phase, η*(ω) decreases with T, although the amplitude of the decrease is quite small. Hysteresis in the thermal cycle diminishes as W increases. When W ) 5.71 and 7.47, Tm can be estimated (Figure 3) to equal and exceed Tf, respectively. The observed hysteresis in the curve for W ) 5.71 may be attributable in part to the fact that the detailed structure of the system in the biphasic domain is different depending on whether the system is quenched into that domain from a higher or lower temperature. For W ) 7.47, which is presumably fully anisotropic at 20 °C following cooling, the texture of the newly formed anisotropic phase may be different from that of the same solution before heating.2 Because the sample is polydisperse, it must be understood that some of the shorter chains in the sample will have been partially or fully melted at Tf with the



Table 2. Phase Boundary Temperatures Ti and Ta for X13F3 at Various W

Cs ) 0.01 M

Figure 11. Temperature dependence of η*(ω) for X13F3 at Cs ) 0.01 M for several solutions that were biphasic or fully anisotropic at room temperature.

Figure 12. Dependence of η*(ω) on W for X13F3 at Cs ) 0.01 M measured at several fixed temperatures on the heating and cooling legs of the thermal cycle.

consequence that the W ) 5.71 and 7.47 solutions cooled to 20 °C may also contain some gel-like fraction. The curve for W ) 4.89 is very similar to that for W ) 4.54 in Figure 10. The estimated values of Tm from Figure 3 are 85 and 83 °C, respectively, and both solutions show clear evidence of gel formation on cooling, although not as much as for the less concentrated solutions shown in Figures 4, 5, and 10. Note (Table 1) that at room temperature W ) 4.54 = Wi, while W ) 4.89 > Wi, and this may account for the small differences in these two curves. Plotting the viscosity of X13F3 at several fixed temperatures against xanthan concentration results in Figure 12. For viscosities taken from the heating leg at 20 °C, the peak appears at W ) 4.54, the same as Wi determined by phase volume analysis (Table 1).1 With increasing temperature, the peak is shifted to higher W, with Wi ) 5.49 at T ) 50 °C and Wi ) 7.47 for T ) 86 °C. When the heated solutions are cooled to room temperature, the curve of η*(ω) vs W looks distinctly different from that for X2F2 at Cs ) 0.01

W

Ti

4.72 4.89 5.09 5.30 5.49 5.71 5.92 6.50 7.47 8.52

26 32 38 44 47 55 61 71 90 >90

Cs ) 0.10 M Ta

41 56 70

W

Ti

7.25 7.77 8.05 8.27 8.51 9.57 10.63 11.52

50 59 62 68 72 86 >90

Cs ) 1.0 M Ta

30 53 71 >90

W

Ti

9.49 10.05 10.26 10.74 11.25 12.08 12.51 13.27 13.87 14.97 16.21

38 43 50 56 63 68 80 >90

Ta

30 40 50 60 71 >90

M shown in Figure 6. In Figure 6, the 20 °C viscosity curve from the cooling leg increases with concentration until W reaches 3.53, where there is a small drop. For X13F3, the curve for the cooling leg at T ) 20 °C tends to decrease monotonically. At low X13F3 concentration, the ionic strength contribution from xanthan molecules is modest, so Tm < Tf, the double helix is melted, and this facilitates the formation of networking and correspondingly higher viscosity on cooling. Because Tm increases with increasing W, the melting of double helix is inhibited, and less networking can be formed on cooling. For W > ≈6 melting of the double helix is no longer possible because Tm > Tf, and the curves before and after heat treatment show only minimal hysteresis. As one can see from Figure 12, solutions with W g 6.00 are brought to the isotropic regime at 90 °C, but the double helix does not melt. Thus, inhibition of double helix melting results from the increase in Tm with increasing Ie and not from the presence of anisotropic phase as was proposed by Capron et al.36 In the case of X2F2 at Cs ) 0.01 M, similar inhibition of double-helix melting should also be observed if the concentration were extended to W > ≈6. Oscillatory Shear Rheology of X2F2 and X13F3 in Higher NaCl Concentrations. When Cs ) 0.1 and 1.0 M, Tm > Tf for all xanthan concentrations studied here, so only the temperature-induced phase transition is observed and the viscosity changes accordingly with T. Plots of η*(ω) vs T for solutions fully isotropic at room temperature were generally featureless and could be characterized using eq 1. For solutions that were biphasic or fully anisotropic at room temperature, the maxima in plots of η*(ω) vs T corresponding to Ti were very easily observed, provided that the maxima occurred at T < Tf. For solutions that were fully anisotropic at room temperature, it was not always as easy to identify Ta as might be suggested, for example, by the minimum in the overlapping heating curves in Figure 7. The method used to extract Ta is detailed in what follows. The resulting values of Ti and Ta at Cs ) 0.01, 0.10, and 1.0 M are presented for X13F3 and X2F2 in Tables 2 and 3, respectively. For solutions isotropic at room temperature, fitting the decrease in η*(ω) with T using eq 1 yields the mean activation energies Eη in Table 4, averaged over all the corresponding concentrations W on the rising leg of the thermal cycle. Solutions rendered isotropic by heating were not included in this tabulation. Typical low molecular weight

750


Lee and Brant

Table 3. Phase Boundary Temperatures Ti and Ta for X2F2 at Various W

Cs ) 0.01 M W

Ti

2.50 3.00 3.53

41 47 56

Ta

28

Cs ) 0.10 M W

Ti

5.10 5.29 5.39 5.50 5.64 6.06 6.54 7.33 8.01 8.83 10.06

28 32 33 36 45 54 61 74 83 >90

Cs ) 1.0 M Ta

W

Ti

Ta

41 52 61 71 >90

6.79 6.99 7.27 7.47 8.32 8.70 9.14 9.53 10.99 12.00 12.73

28 31 40 42 49 58 60 73 85 >90

26 37 40 50 60 69 82

Table 4. Mean Activation Energy, Eη (kJ/mol), for Viscous Flow of Isotropic X2F2 and X13F3 Solutions X2F2

X13F3

0.01 M

0.10 M

1.0 M

0.01 M

0.10 M

1.0 M

25.9

24.0

16.6

20.5

20.5

19.2

thermotropic nematics display Eη ≈ 22 and 11.5 kJ/mol for the isotropic and anisotropic phases, respectively.52,53 For X2F2 there is some indication in Table 4 that Eη declines as Cs increases. A rationale for this observation is not apparent. The mean concentration W of the solutions contributing to Eη increases as Cs increases while the Debye radius and range of electrostatic interactions decrease. Moreover, the viscosities of these solutions at a given W are nearly independent of Cs.1,2 The stiffness of X2F2 as measured by its persistence length is not a strong function of Cs.6,8 Hence, it is not clear why the activation energy for viscous flow, which should reflect the ease with which the polymer molecules move with respect to one another, should decline with increasing Cs. Indeed, both G′(ω) and G′′(ω) increase for X2F2 with Cs at room temperature at a given W in the isotropic regime to suggest that polymer entanglement increases.1,2 The viscosity of solutions in the biphasic regime increases with T and passes through a maximum, if T exceeds Ti. Clearly, η*(ω) is not expected to conform to the simple exponential temperature dependence of eq 1. Surprisingly, neither does η*(ω) obey eq 1 for solutions that are completely anisotropic. Figure 13 for X13F3 at Cs ) 1.0 M shows the typical temperature dependence of η*(ω) on the rising temperature curve for solutions that are anisotropic at room temperature; the cooling leg (not shown) displays only the mild hysteresis characteristic of solutions for which Tm > Tf (Figure 11). Similar plots of η*(ω) vs T have been reported for thermotropic main-chain liquid crystalline polyethers.54 The curve in Figure 13 for W ) 12.51 illustrates the ease with which Ti can be identified at the maximum of the heating curve. The minimum in η*(ω) is, however, difficult to locate precisely and cannot be confidently identified with Ta. Consider, for example, the curves for W ) 16.21 and 17.75, which overlap closely in the whole range of temperature up to Tf ) 86 °C. The negative slope at lower T is replaced by a small positive slope following a broad minimum. According to expectations from Figure 2, Ta for W ) 17.75 should be greater than that for W ) 16.21, but

Figure 13. Temperature dependence of η*(ω) for X13F3 at Cs ) 1.0 M for several solutions that were fully anisotropic at room temperature. Only the increasing temperature leg of the thermal cycle is shown.

in the T range covered, the two curves are scarcely distinguishable, so one must conclude that Ta > Tf for both of these concentrations. The increase in η*(ω) with T beyond the broad minimum is postulated to be a consequence of a thermally induced reduction in the order parameter of the anisotropic phase, which leads to an increase in η*(ω). We reason here in analogy with the reduction in order parameter and corresponding increase in viscosity arising from addition of salt to the anisotropic phase of xanthan.1,2 The curve for W ) 14.97 in Figure 13 departs perceptibly from those for W ) 16.21 and 17.75 at about T ) 71 °C, above which it displays the sharp increase anticipated with the appearance of isotropic phase. We somewhat arbitrarily identify this point of departure with Ta for W ) 14.97. This device is used to assign all the values of Ta reported in Tables 2 and 3. It is clear from this discussion that the temperatures Ta reported here for the boundary between the biphasic and anisotropic regions of the phase diagram are somewhat more uncertain than the reported values of Ti. The data in Tables 2 and 3 are used to construct temperature-composition phase diagrams for X2F2 and X13F3 in Figure 15 for the biphasic chimney region of the diagram. The typical dependence of η*(ω) on W for X2F2 at Cs ) 1.0 M at temperatures below Tm is illustrated in Figure 14 for several different temperatures; similar curves result for X2F2 at Cs ) 0.1 M and X13F3 at Cs ) 0.1 and 1.0 M. These curves, based on measurements along the rising leg of the temperature cycle, are identical in shape to those measured at room temperature and reported earlier,1,2 where it was shown that the peak occurs at W ) Wi. Similar data for poly(benzyl-L-glutamate) (PBLG) have been reported by Miller et al.44 There are some interesting features that deserve comment. First, as the temperature rises, Wi increases, because increasingly larger W is required to induce the formation of anisotropic phase as the polymer flexibility increases. The peak viscosities increase with T, which indicates that η*(ω) rises more rapidly with W than it decreases with T in the isotropic phase. This feature is not



Figure 14. Dependence of η*(ω) on W for X2F2 at Cs ) 1.0 M measured at several fixed temperatures on the heating leg of the thermal cycle.

present in the PBLG data.44 At the higher temperatures the system may not have been converted at high W completely to anisotropic phase, but the collection of curves in the high W region strongly suggests that η*(ω) is effectively independent of W and T in the anisotropic regime. We showed earlier that η*(ω) is also independent of ω for xanthan in the anisotropic regime at room temperature,1,2 and this is probably true at higher temperatures as well. Similar plots to those in Figure 14 constructed from the cooling curves show small thermal hysteresis effects but do not contain features corresponding to the extensive tenuous network formation seen in Figures 4-12 for the data gathered at Cs ) 0.01 M. Phase Diagrams. Figure 15 shows the chimney region of the lyotropic liquid crystal phase diagram for xanthan fractions X13F3 and X2F2 determined experimentally from the experiments reported here; the points at 23 °C determined by phase volume analysis (Table 1)1 are included for comparison with those determined rheologically. There appear to be no previous reports of a temperature-composition phase diagram for xanthan to serve as a basis for comparison with Figure 15. Linear fits to the measured points are extrapolated beyond the actual data points in some cases to facilitate comparisons. The phase boundaries lean toward higher polymer concentration with increasing T as anticipated in drawing the schematic Figure 2. This behavior is ascribed to an increase in polymer flexibility as the temperature is raised, as proposed by Miller et al. for poly(benzyl-Lglutamate).43,44,55 The tilt is also consistent with temperaturecomposition phase diagrams for the neutral triple helical polysaccharides schizophyllan and scleroglucan reported by Teramoto and co-workers.45-47 As the polymer becomes more flexible with increasing T, the effective axial ratio decreases and, according to the Flory lattice theory,4 the critical concentrations Wi and Wa should increase. There is some indication in Figure 15 that the width of the biphasic domain increases with increasing T, which is also consistent with a rationale for the tilt of the chimney in

Figure 15. (a) Phase boundaries measured rheometrically in the chimney region of the lyotropic liquid crystal phase diagram for aqueous xanthan X13F3 at Cs ) 0.01, 0.10, and 1.00 M. Filled symbols denote points Wi,Ti on the boundary between the isotropic and biphasic domains; open symbols denote points Wa,Ta on the boundary between the biphasic and anisotropic domains. (b) Phase boundaries measured rheometrically in the chimney region of the lyotropic liquid crystal phase diagram for aqueous xanthan X2F2 at Cs ) 0.01, 0.10, and 1.00 M. Filled symbols denote points Wi,Ti on the boundary between the isotropic and biphasic domains; open symbols denote points Wa,Ta on the boundary between the biphasic and anisotropic domains.

terms of reduction in effective axial ratio.4 Moreover, the biphasic region is broader for the lower molecular weight fraction X13F3, as expected from the Flory theory. Odijk’s more recent treatment of lyotropic behavior in semiflexible polymers confirms that Wi and Wa should increase with increasing flexibility.5 It suggests, however, that the width of the biphasic regime should narrow relative to that for rodlike polymers. Theories designed for lyotropic liquid crystal behavior of uncharged stiff polymers must be applied cautiously to stiff polyelectrolytes. We showed previously that even at Cs ) 1.0 M the xanthan phase boundaries occur at considerably smaller values of Wi and Wa than those observed for stiff uncharged polysaccharides of the same axial ratio; for xanthan the excluded volume driving phase

752


separation includes a significant contribution to the effective diameter of the helix from electrostatic interactions.2 Sato et al., following Odijk, have developed a quantitatively accurate theory of the lyotropic phase equilibrium of semiflexible xanthan of fixed persistence length.6 Liu and Norisuye suggest that the xanthan persistence length should vary inversely with Kelvin temperature, provided the polymer displays a uniform resistance to bending along its length.56 Using this idea one would expect the persistence length of xanthan to decrease by almost 20% over the temperature range of the present experiments. The contour length of X2F2 is longer relative to the cooperative correlation length of the xanthan helix than that for the case for X13F3. With increasing T, one might therefore expect X2F2 to depart from uniform bending behavior more than X13F3 due to the appearance of helical defects remote from the helix termini.57,58 Examination of the phase boundaries in Figure 15, however, shows scant evidence that the effective axial ratio of X2F2 is any more sensitive to T than is that of X13F3.

Lee and Brant

References and Notes (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19)

Conclusions

(20)

The lyotropic liquid crystal temperature-composition phase diagrams for aqueous xanthan fractions X2F2 and X13F3 at NaCl concentrations Cs ) 0.01, 0.10, and 1.00 M have been constructed using rheological probes of the behavior of solutions in the xanthan concentration range 1 e W e 20% (w/w). The chimney region of the phase diagram leans toward higher W with increasing T, presumably because the effective axial ratio of the xanthan helix declines with increasing T. For Cs ) 0.01 M the xanthan double helix undergoes a transformation to a disordered form for the smaller values of W, where Tm < Tf. Larger polymer concentrations, and larger values of Cs, raise the effective ionic strength of the system until Tm > Tf, and the temperature-driven helix order-disorder transition is no longer observed. In those systems for which the orderdisorder transition appears, η*(ω), G′(ω), and G′′(ω) increase dramatically on cooling the system from Tf back to room temperature. This occurs because an extensive network is formed among xanthan strands released from the ordered helical structure at temperatures above Tm. Thermal cycles for samples with Tm > Tf show only modest hysteresis in η*(ω), G′(ω), and G′′(ω) on cooling. It is shown that plots of the rheological variables against W at elevated temperatures are identical in shape to those observed at room temperature so long as the integrity of the xanthan double helix is preserved. The temperature dependence of η*(ω) for isotropic helical xanthan solutions can be adequately characterized by the simple Arrhenius law. In biphasic systems extrema appear in plots of η*(ω) vs T that obviate use of the Arrhenius expression. In anisotropic solutions η*(ω) vs T displays a broad minimum. The region of positive slope at higher T is attributed to a temperature-induced decrease in the order parameter of the liquid crystal and a consequent increase in η*(ω) with increasing T.

(21)

Acknowledgment. This work was supported by NIH Grant GM 33062.

(22) (23) (24) (25) (26)

(27) (28) (29) (30) (31) (32) (33) (34) (35) (36) (37) (38) (39) (40) (41)

(42) (43)

(44) (45) (46)

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