Effect of Shear History on the Rheological Behavior of Lyotropic Liquid

Chapter 26

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Effect of Shear History on the Rheological Behavior of Lyotropic Liquid Crystals 1

P. Moldenaers, H. Yanase , and J. Mewis Department of Chemical Engineering, Katholieke Universiteit Leuven, de Croylaan 46, B-3030 Leuven, Belgium

Two liquid crystalline polybenzylglutamate solutions, adjusted to the same Newtonian viscosity, have been investigated rheologically. The steady state shear properties and the transient behaviour are measured. For the same kind of polymer, the dynamic moduli upon cessation of flow can either increase or decrease with time. This change in dynamic moduli shows a similar dependency on shear rate as the final portion of the stress relaxation but no absolute correlation exists between them. By comparing the transient stress during a stepwise increase in shear rate with that during flow reversal the flow—induced anisotropy of the material is studied. During the last ten years the interest in polymeric liquid crystals (PLCs) has been growing rapidly. Nevertheless our fundamental understanding of their flow behaviour is still rather limited. This is due to the fact that PLC rheology is much more complicated than that of ordinary isotropic polymeric fluids (1). Systematic and reliable data are lacking so far although this is the kind of information needed for the development and assessment of theoretical models for these unusual fluids. The purpose of this paper is to explore various aspects of the rheological behaviour of lyotropic liquid crystalline systems. Lyotropics are often used as model systems for thermotropics because their viscoelastic behaviour seems to be quite similar (I) and solutions are much more easier to handle and can be studied more accurately than melts. The emphasis is on transient data as these are essential for verifying viscoelastic models but are hardly available in the literature. Transient experiments can also provide insight in the development of flow-induced orientation and structure. The reported experiments include relaxation of the shear stress and evolution of 1

Current address: Kyoto University, Kyoto 606, Japan 0097-6156/90A)435-0370$06.00/0 © 1990 American Chemical Society Weiss and Ober; Liquid-Crystalline Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1990.

26. MOLDENAERSETAL.

Effect ofShear History on Rheological Behavior

the dynamic moduli upon cessation of flow as well as flow reversal and stepwise changes in shear rate. Experimental


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Two samples of poly()-benzylglutamate) in ra—cresol have been used. Polybenzylglutamates (PBGs) have proven to be useful as model systems to demonstrate characteristic aspects of PLC rheology (2-4). Thefirstsample under investigation consists of a solution of 12%, by weight, of PBLG (MW = 250000). The second one is a solution of PBDG (concentration 25%, MW = 310000). In both cases the concentration is high enough to ensure a fully liquid crystalline phase. At rest the materials are cholesteric, but during flow they develop into a nematic structure. For convenience they will be referred to as the PBLG and the PBDG sample although the relevant differences between the two samples are their concentration and molecular weight. No difference in the rheological behaviour, related to the L and the D form of the glutamates, is expected. The basic rheology of the PBLG sample under investigation has already been studied extensively (4-6). The rheological experiments were performed on a Rheometrics Mechanical Spectrometer RMS 705F. Cone and plate geometry was used in order to generate a homogeneous shear history throughout the sample, a prerequisite in order to analyse transient behaviour. All experiments have been performed at 293K. With liquid crystalline materials the flow can always be affected by the gap size or the measurement geometry. This has been shown not to be the transients the situation could be different because of propagation effects from the wall. Here two types of transients have been investigated for this purpose. Figure 1 indicates that the stress transients for stepwise changes in shear rate remain identical when the cone angle is doubled. Results independent of gap size have also been obtained for the evolution of the dynamic moduli after cessation of flow (7) (see below). The latter result is in contrast with available results for the relaxation of birefringence after cessation offlow.The time scale for the final part of this curve has been reported to depend on the gap size (3). For smaller gaps a slower optical relaxation was measured. Ar any rate, it can be concluded that, for the range of gap sizes used here, the rheological data are not affected. Hence an Ericksen number based on the gap size as the characteristic length scale will fail to scale the results (Burghardt, W. R.; Fuller, G. G., in press). Equilibrium Results Due to their intrinsic physical nature one expects liquid crystals to exhibit a yield stress in the zero shear limit. This yield stress, associated with region I in the three-region flow curve of Onogi and Asada (8), has been reported for various types of liquid crystalline materials. Figure 2 shows the steady shear flow results for the two samples. Because of the possibility of a yield stress, shear stresses were determined here by taking the average of a clockwise and a counterclockwise experiment. For the PBLG sample under investigation no indication of an upturn of the viscosity curve at the low shear rates could be detected. For the PBDG sample on the other hand, a small increase of the viscosity seems to occur in this region. However, an eventual yield stress will be very small for both samples and does not interfere with the experiments reported here.

Weiss and Ober; Liquid-Crystalline Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1990.

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LIQUID-CRYSTALLINE POLYMERS


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Figure 1. Effect of gap size on step-up transients for the PBLG sample; (cone angle: A : 0.02 rad; A : 0.04 rad) (75 = 0.05 (l/s);7 =0.5 (1/s) f

o

\

O Q

\

D Q_ O O

-1

-2

LOG SHEAR RATE ( S ~ ) 1

Figure 2. Steady shear flow results at 293 K; (Viscosity:0= PBLG sample;«= PBDG sample), (Positive N := PBLG;D= PBDG; negative :•= PBLG;«=PBDG) x



26. MOLDENAERS ET AL.


The two polybenzylglutamates differ in molecular weight. Their concentrations have been adjusted to give the same Newtonian viscosity. In the Newtonian shear rate region their normal stresses turn out to be identical as well. A comparison of the two samples might shed some light on the role of the viscosity as such in controlling the time scales of some transient phenomena. For the PBLG sample the concentration is about 1.5 times the critical concentration c*. For the PBDG the concentration reaches about 4c*. This means that the PBLG sample is in a concentration region where viscosity decreases with concentration whereas it might be increasing again for the PBDG (9). The first normal stress difference has also been reported to be a decreasing and subsequentely increasing function of concentration for PLCs in the low shear limit (2). The equality of viscosity andfirstnormal stress difference does of course not imply that the order parameter is the same for the two samples. The first normal stress difference exhibits a linear dependency on the shear rate in the region of constant viscosity for the two solutions in Figure 2. This proportionality is predicted by the Doi theory (10) and the Leslie-Ericksen theory (11) although the basic assumption in these theories, i.e. a monodomain structure, is not satisfied. Another prominent feature in Figure 2 is the occurrence of a negative first normal stress difference in an intermediate shear rate region for both samples. Negative normal stresses have been reported repeatedly for various liquid crystalline systems, including thermotropic ones (2. 12. 13j. The critical shear rate and the critical shear stress at the transition from a positive to a negative first normal stress difference (Figure 2) are considerably larger for the PBDG sample than for the PBLG one. This is in agreement with the data of Kiss and Porter (2. 14) who reported an increasing critical shear rate and critical shear stress with increasing concentration and molecular weight. The molecular theory, as originally presented by Doi (10), does not include the possibility of negative normal stresses in a shear flow. However, recently Marrucci and Maffettone (15) demonstrated with a two-dimensional analysis the existence of a shear rate region with negative normal stresses by using the total orientational distribution function in their calculations. Stress Relaxation upon Cessation of Flow For isotropic polymer fluids, stress relaxation upon cessation of flow reflects the relaxation time scales during the previous flow. As the relaxation spectrum is determined by the microstructure such measurements can be used to probe the effect of shear on the structure. This turns out to be a rather insensitive technique in polymer fluids because of changes which already occur during the relaxation (16). The liquid crystalline PBLG sample is characterized by a stress relaxation which depends on shear rate, even in the Newtonian region (Moldenaers, P.; Mewis, J. J. Non-Newtonian Fluid Mech., in press). This proves the existence of a shear rate dependent structure in the linear shear rate region. It was also found that the stress relaxation curve could be divided in two different sections. The temperature dependence of the initial part scales with the viscosity and does not depend on shear rate in the Newtonian region. The second part does not depend on temperature but scales with the inverse of the previous shear rate. The effect of the shear rate on the stress relaxation for the PBLG sample is shown in Figure 3 for the Newtonian as well as the non—Newtonian


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- 2 - 1

o LOG SHEAR RATE (s

1 -1

2

)

Figure 3. Comparison of the characteristic time scales for the stress relaxation and the evolution of the dynamic moduli (t(c)) upon cessation offlowfor the PBLG sample; (% stress relaxation:•: 50%;•: 60%; A : 70%;A: 80%;#: 90%)



26. MOLDENAERSETAL.

Effect of Shear History on Rheological Behavior

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shear rate region. The relaxation behaviour of the more concentrated PBDG solution is displayed in Figure 4. Qualitatively the relaxation behaviour of the two mesomorphic materials is similar. In particular the tail of the relaxation curve changes inversely proportional to the previous shear rate, whereas the initial part tends to become independent of shear rate. However, the final relaxation takes much longer in the more concentrated PBDG sample than for the PBLG one, notwithstanding their identical Newtonian viscosities. The data could be explained by a molecular reorientation mechanism for the fast part and a change in supermolecular structure, domains or defects, for the slow part. A comparison of the present results with the rheo-optical relaxation data, reported by Asada et al. for similar materials (3) seems indicated. These authors found that the relaxation time of the birefringence increases inversely proportional to the previous shear rate and proportionally to the third power of the molecular weight. Concentration did hardly affect the rheo-optical time scale at identical stress levels. For the molecular weight of the two samples under investigation here, one would thus expect a time constant for the PBDG sample which is twice that of the PBLG sample. The tail of the stress relaxation curves in Figures 3 and 4 yields a ratio of about 3, quite comparable with that of the optical relaxation. Thus both phenomena could be governed by the same mechanisms. Oscillatory Testing upon Cessation of Flow The evolution of the structure of a material upon cessation of flow can be probed by several techniques. Measuring the variation of the linear dynamic moduli has proven to be useful in this respect. For the PBLG sample both G and G" decrease monotonically upon cessation of flow (4). Moreover, the time scale of this effect changes inversely proportional to the previous shear rate, even in the Newtonian region. Figure 5 compares the evolution of G" for the PBLG and the PBDG sample at a frequency of 10 rad/s. The previous shear rate amounted to 3 reciprocal seconds for both materials. The moduli continue to change over an extensive period of time, suggesting a slow evolution from theflow-inducedstructure to the zero-shear one. The inverse proportionality with shear rate was also found in elastic recovery following cessation offlow(J7). There are also some striking differences between the two samples. For the PBLG solution, having the lowest molecular weight and concentration, the moduli decrease monotonously. On the contrary, the PBDG sample, with the higher concentration and molecular weight, displays an initial increase of the moduli, followed by a subsequent decrease. This difference was found to persist over a wide range of shear rates but the maximun for the PBDG solution tends to become less prominent at low shear rates. It can not be excluded that the moduli of the PBLG sample might also display a maximum for the dynamic moduli but then after an immeasurably short time, although measurements at low shear rates, where the changes become sufficiently slow, show aflatplateau rather than a maximum. A second difference is more quantitative. The time over which the moduli evolve is considerably larger for the PBDG sample than it is for the PBLG sample. In Figure 3 the characteristic time (t(c)) for the change of the moduli in the PBLG sample as a function of shear rate is also included. This kinetic factor has been defined as the time after which the moduli have completed one third of their total decay. It is concluded from Figure 3 that t(c) is larger than the average relaxation time but displays the same shear 1




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Figure 4. Comparison of the characteristic time scales for the stress relaxation and the evolution of the dynamic moduli (t(m)) upon cessation of flow for the PBDG sample; (% stress relaxation: v : 40%; other symbols as in Figure 3).



26. MOLDENAERS ET AL.


rate dependency. The decay time could not be accurately determined for the PBDG sample as the scatter on the data was larger, the time for the moduli to reach their maximun value (t(m)) is included instead in Figure 4. It can be seen in Figure 5 that the characteristic time t(c) for the evolution of the moduli of the PBDG sample will be much larger than t(m). Hence, comparing the two samples shows that the difference between the time scales for the stress relaxation and the evolution of the dynamic moduli is much greater for the more concentrated solution. The effect of temperature and shear rate suggests that the final relaxation is associated with structural changes as detected by the dynamic moduli. However the present lack of correlation is counterindicative of an absolute correspondence between the two time scales. Isotropic polymeric systems as well as particulate systems might also show time-dependent moduli after cessation of flow. As long as the shear does not induce structure growth, the moduli always increase with time after flow. An increase of the moduli upon cessation of flow has also been reported for thermotropic PLCs (18) as well as for lyotropic solutions of hydroxypropyl cellulose in water (19) and in acetic acid (20). The possibility of changing in either direction seems to be characteristic for mesomorphic materials. A fundamental theory for describing complex moduli does not exist for such materials. The present results, combined with the information about optical relaxation mentioned above, could be explained on the basis of reorientation of domains or defects. The different domains orient differently, even randomly, at rest whereas flow causes an overall orientation. Depending on the molecular interaction the flow could then cause an increase or decrease in moduli as recently suggested by Larson (21). Flow Reversal and Stepwise Changes in Shear Rate A change in flow direction might be a useful test method for picking up the anisotropy expected during flow in liquid crystals. Figures 6 and 7 display the response of the shear stress to a sudden reversal in flow direction for the two samples. All shear rates are in the Newtonian region and the shear stress is scaled with the equilibrium value, in order to facilitate comparison. In all cases a complex, damped oscillatory pattern is registered. In addition, the transients for different final shear rates could be superimposed for each solution by scaling the curves with strain (Moldenaers, P; Mewis, J. J. Non—Newtonian Fluid Mech., in press). The frequency of the damped oscillation does however depend on the actual solution under consideration. According to figures 6 and 7 the period is approximately 50% higher for the system with the highest molecular weight and concentration, possibly reflecting a stronger coupling between the individual molecules. Published transients for various PLCs all seem to have rather similar frequencies (22^. 23). The separate effect of concentration and molecular weight still remain to be investigated. In a second experiment the shear rate is suddenly changed, without altering the direction of flow., i.e. a stepwise increase in shear rate. This also causes a stress transient with a damped oscillatory component, scaling with strain. It is possibly caused by director tumbling as a means to readjust to the new conditions (Burghardt, W.R.; Fuller, G. G., in press). A comparison of the step-up and flow reversal experiments (Figure 7).indicates that the oscillatory components have a phase shift of nearly 180°. This experiment is one of the very few rheological tests which provide a direct proof of the anisotropic behaviour of PLCs during flow. It also indicates, together with


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o CL

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2

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LOG TIME (s)

Figure 5. Transient loss moduli after cessation of flow; (7=3 (1/s); w= 10 rad/s;A= PBLG; A = PBDG)

STRAIN

Figure 6. Transient scaled shear stress after flow reversal for the PBLG sample; (y.A= 1 ( l / s ) ; A = 0.5(1/8))



26. MOLDENAERSETAL.

0 l_ 0

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Effect of Shear History on Rheological Behavior

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• • • • • • , i 25 50 STRAIN

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, I 75

Figure 7. Comparison of the scaled shear stress after flow reversal and stepwise increase in shear rate for the PBDG sample; (flow reversal: 7: A = 1 (1/s); A = 0.4 (1/s); stepwise increase in shear rate: ^ = 0.1 (1/s); ^ = 1 (1/s) O)


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the strain scaling, that the oscillatory part of the shear stress is associated with an oriented structural feature, which forms a small angle with the flow direction. The director itself comes to mind first. Theoretically it could satisfy the experimental requirements, according to the standard theories. However experimental evidence seems to indicate an orientation of the director in the flow direction itself (24). Further experimentation is required to solve this problem. Acknowledgments


This work was supported by a grant from AKZO International Research, Arnhem, The Netherlands. Literature Cited 1. Wissbrun, K. F. J. Rheol. 1981, 25, 619-662. 2. Kiss, G.; Porter, R. S. J. Polym. Sci.: Polym. Phys. Ed. 1980, 18, 361-388. 3. Asada, T.; Onogi, S.; Yanase, Y. Polym. Eng. Sci. 1984, 24, 355-360. 4. Moldenaers, P.; Mewis, J. J. Rheol. 1986, 30, 567-584. 5. Mewis, J.; Moldenaers, P. Chem. Eng. Commun. 1987, 53, 33-47. 6. Mewis, J.; Moldenaers, P. Mol. Cryst. Liq. Cryst. 1987, 153, 291-300. 7. Moldenaers, P. Ph. D. Thesis, Katholieke Universiteit Leuven, Leuven, Belgium, 1987 8. Onogi, S.; Asada, T. in Rheology; Astarita, G.; Marrucci. G.; Nicolais, L., Eds; Plenum: New York, 1980; Vol. 1, p.127. 9. Asada, T,; Tanaka, T.; Onogi, S. J. Appl. Polym. Sci.: Appl. Polym. Symp. 1985, 41, 229-239. 1985, 41, 229-239. 10. Doi, M. J. Polym. Sci.,: Polym. Phys. Ed. 1981, 19, 229-243. 11. Leslie, F. M . in Advances in Liquid Crystals; Brown, G. H., Ed.; Academic Press: New York, 1979; Vol. 4, p. 1. 12. Navard, P. J. Polym. Sci.: Polym. Phys. Ed. 1986, 24, 435-442. 13. Gotsis, A. D.; Baird, D. G. J. Rheol. 1986, 25, 275. 14. Kiss, G.; Porter, R. S. J. Polym. Sci.: Polym. Symp. 1978, 65, 193-211. 15. Marrucci, G.; Maffettone, P. L. Macromolecules 1989, 22, 4076-4082. 16. De Cleyn, G.; Mewis, J. J. Non-Newtonian Fluid Mech. 1981, 9, 91-105. 17. Larson, R. G.; Mead, D. W. J. Rheol., 1989, 33, 1251-1281. 18. Wissbrun K. F.; Griffin, A. C. J. Polym. Sci.: Polym. Phys. Ed., 1982, 20, 1835-1845. 19. Ernst, B.; Navard, P.; Haudin, J. M . J. Polym. Sci.: Part B: Polym. Phys., 1988, 26, 211-219. 20. Moldenaers, P.; Mewis, J. in Proc. Xth Int. Cong. on Rheol., 1988, Sydney, Vol. 2, p. 134. 21. Larson, R. G.; Mead, D. W. J. Rheol., 1989, 33, 185-206. 22. Doppert, H. L.; Picken, S. J. Mol. Cryst. Liq. Cryst., 1987, 153, 109-116. 23. Viola, G. G.; Baird, D. G. J. Rheol., 1986, 30, 601-628. 24. Yanase, H. Ph. D. Thesis, Kyoto University, Kyoto, Japan, 1988. RECEIVED

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Effect of Shear History on the Rheological Behavior of Lyotropic Liquid

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