Director Tumbling Research Articles

Two negative minima of the first normal stress difference in a cellulose‐based cholesteric liquid crystal: Helix uncoiling

ABSTRACTThe shear rate dependence of material functions such as shear viscosity (η) and the first normal stress difference (N1) were given and interpreted earlier by Kiss and Porter. Their widely accepted work revealed the possibility of having a negative minimum of N1 for polymeric liquid crystals. In this work, we disclose for the first time the evidence of two negative N1 minima on a sheared cellulosic lyotropic system. The lower shear rate minimum is ascribed to the uncoiling of the cholesteric helix, as theoretically predicted earlier. Our findings contribute also to the understanding of the other minimum already reported in the literature and attributed to the nematic director tumbling mode. Moreover, the elastic change that the LC‐HPC sample undergoes during the helix unwinding of the cholesteric structure is also by means of oscillatory measurements. This study is a contribution for the understanding of the structure‐properties relationship linked with the complex rheological behavior of chiral nematic cellulose‐based systems and may help to improve their further processing. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017, 55, 821–830

New conception in continuum theory of constitutive equation for anisotropic crystalline polymer liquids

A new continuum theory of the constitutive equation of co-rotational derivative type is developed for anisotropic viscoelastic fluid—liquid crystalline (LC) polymers. A new concept of simple anisotropic fluid is introduced. On the basis of principles of anisotropic simple fluid, stress behaviour is described by velocity gradient tensor and spin tensor instead of the velocity gradient tensor in the classic Leslie—Ericksen continuum theory. Analyzing rheological nature of the fluid and using tensor analysis a general form of the constitutive equ- ation of co-rotational type is established for the fluid. A special term of high order in the equation is introduced by author to describe the sp- ecial change of the normal stress differences which is considered as a result of director tumbling by Larson et al. Analyzing the experimental results by Larson et al., a principle of Non- oscillatory normal stress is introduced which leads to simplification of the problem with relaxation times. The special behaviour of non- symmetry of the shear stress is predicted by using the present model for LC polymer liquids. Two shear stresses in shear flow of LC polymer liquids may lead to vortex and rotation flow, i.e. director tumbling in the flow. The first and second normal stress differences are calculated by the model special behaviour of which is in agree- ment with experiments. In the research, the com- putational symbolic manipulation such as computer software Maple is used. For the anisotropic viscoelastic fluid the constitutive equation theory is of important fundamental significance.

New conception in continuum theory of constitutive equation for anisotropic crystalline polymer liquids

A new continuum theory of the constitutive equation of co-rotational derivative type is developed for anisotropic viscoelastic fluid—liquid crystalline (LC) polymers. A new concept of simple anisotropic fluid is introduced. On the basis of principles of anisotropic simple fluid, stress behaviour is described by velocity gradient tensor and spin tensor instead of the velocity gradient tensor in the classic Leslie—Ericksen continuum theory. Analyzing rheological nature of the fluid and using tensor analysis a general form of the constitutive equ- ation of co-rotational type is established for the fluid. A special term of high order in the equation is introduced by author to describe the sp- ecial change of the normal stress differences which is considered as a result of director tumbling by Larson et al. Analyzing the experimental results by Larson et al., a principle of Non- oscillatory normal stress is introduced which leads to simplification of the problem with relaxation times. The special behaviour of non- symmetry of the shear stress is predicted by using the present model for LC polymer liquids. Two shear stresses in shear flow of LC polymer liquids may lead to vortex and rotation flow, i.e. director tumbling in the flow. The first and second normal stress differences are calculated by the model special behaviour of which is in agree- ment with experiments. In the research, the com- putational symbolic manipulation such as computer software Maple is used. For the anisotropic viscoelastic fluid the constitutive equation theory is of important fundamental significance.

Quench sensitivity to defects and shear banding in nematic polymer film flows

A flow-orientation algorithm [S. Heidenreich, S. Hess, M.G. Forest, X. Yang, R. Zhou, Robustness of pulsating jet-like layers in sheared nano-rod dispersions, J. Non-Newtonian Fluid Mech., in press, doi:10.1016/j.physletb.2003.10.071; X. Yang, Z. Cui, M.G. Forest, J. Shen, Q. Wang, Dimensional robustness and instability of sheared, semi-dilute, nano-rod dispersions, SIAM Multiscale Model. Simul. 7 (2008) 622–654] for nematic (liquid crystalline) polymer films is coupled with the homogenized effective conductivity tensor of the rod-matrix composite [H. Zhou, X. Zheng, M.G. Forest, Q. Wang, R. Lipton, Extension-enhanced conductivity of liquid crystalline polymer nano-composites, Macromol. Symp. 28 (2005) 81–85; X. Zheng, M.G. Forest, R. Lipton, R. Zhou, Q. Wang, Exact scaling laws for electrical conductivity properties of nematic polymer nano-composite monodomains, Adv. Funct. Mater. 15 (4) (2005) 627–638; X. Zheng, M.G. Forest, R. Zhou, Q. Wang, R. Lipton, Anisotropy and dynamic ranges in effective properties of sheared nematic polymer nano-composites, Adv. Funct. Mater. 15 (2005) 2029–2035; X. Zheng, M.G. Forest, R. Lipton, R. Zhou, Nematic polymer mechanics: flow-induced anisotropy, Continuum Mech. Thermodyn. 18 (2007) 377–394; X. Zheng, M.G. Forest, R. Vaia, M. Arlen, A strategy for dimensional percolation in sheared nano-rod dispersions, Adv. Mater. 19 (22) (2007) 4038–4043] to simulate a simultaneous thermal quench and arrest of the film flow. The final orientational morphology yields nematic polymer film features that determine film performance: anisotropy and heterogeneity in the thermal conductivity tensor, and residual shear and normal stresses. With this numerical toolkit, we amplify an inherent source of nematic polymer film non-uniformity for identical processing conditions. It is well-known that steady parallel plate driving conditions yield unsteady nematic polymer behavior such as director tumbling and wagging, defects, and shear bands. We show that the timing of initial cooling and arrest of plate motion produces different solid films, even with identical isothermal and quench protocols! Simulations show flow reversal and gradient elasticity bands are created when the quench and plate arrest are applied in phase with isothermal shear bands and defect layers, reminiscent of effects reported for small molar mass liquid crystals [R.S. Akopyan, R.B. Alaverdian, E.A. Santrosian, Y.S. Chilingarian, Thermomechanical effects in the nematic liquid crystals, J. Appl. Phys. 90 (2001) 3371–3376; R.S. Hakobyan, G.L. Yesayan, B.Y. Zeldovich, Thermomechanical oscillations in hybrid nematic liquid crystals, Phys. Rev. E 73 (2006) 061707].

Orientation dynamics in commercial thermotropic liquid crystalline polymers in transient shear flows

In situ X-ray scattering measurements of molecular orientation under shear are reported for two commercial thermotropic liquid crystalline polymers (TLCPs), Vectra A950® and Vectra B950®. Transient shear flow protocols (reversals, step changes, and flow cessation) are used to investigate the underlying director dynamics. Synchrotron X-ray scattering in conjunction with a high-speed area detector provides sufficient time resolution to limit the total time spent in the melt during testing, whereas a redesigned X-ray capable shear cell provides a more robust platform for working with TLCP melts at high temperatures. The transient orientation response upon flow inception or flow reversal does not provide definitive signatures of either tumbling or shear alignment. However, the observation of clear transient responses to step increases or step decreases in shear rate contrasts with expectations and experience with shear-aligning nematics and suggests that these polymers are of the tumbling class. Finally, these two polymers show opposite trends in orientation following flow cessation, which appears to correlate with the evolution of dynamic modulus during relaxation. Specifically, Vectra B shows an increase in orientation upon flow cessation, an observation that can only be rationalized by the assumption of tumbling dynamics in shear. Together with prior observations of commercial LCP melts in channel flows, these results suggest that this class of materials, as a rule, exhibits director tumbling.

Computational analytical approach to shear-extensional flow in fiber spinning of liquid crystalline polymer melt

A continuum theory of constitutive equation of co-rotational derivative type was developed for anisotropic viscoelastic fluid—liquid crystalline(LC) polymer. The theory was specialized to a constitutive equation of co-rotational type LCP-H model and LCP-Qs model. Using the constitutive equation of LCP-Qs model, the shear-extensional flow was studied for the extrusion process near the die exit of the fiber spinning of liquid crystalline polymer melt. Bifurcation of extensional viscosity was observed in the case without orientation and the two cases when the directors were parallel to flow and vertical to flow for the LC polymer melts. The extensional viscosity increases when the director rotates from the flow direction to that vertical to flow. Based on the LCP-Qs model a computational analytical theory was developed for extrusion process of LC polymer melt, contraction of the extrudate was predicted by the theory. The computational symbolic manipulation such as computer software Maple was used for the problem solution. An important conclusion can be drawn that the director tumbling has remarkable influence on extensional viscosity but no principal one on LC polymer melt extrusion.

Flow Behavior of Colloidal Rodlike Viruses in the Nematic Phase

The behavior of a colloidal suspension of rodlike fd viruses in the nematic phase, subjected to steady state and transient shear flows, is studied. The monodisperse nature of these rods combined with relatively small textural contribution to the overall stress make this a suitable model system to investigate the effects of flow on the nonequilibrium phase diagram. Transient rheological experiments are used to determine the critical shear rates at which director tumbling, wagging, and flow-aligning occurs. The present model system enables us to study the effect of rod concentration on these transitions. The results are in quantitatively agreement with the Doi-Edwards-Hess model. Moreover, we observe that there is a strong connection between the dynamic transitions and structure formation, which is not incorporated in theory.

Molecular orientation of a commercial thermotropic liquid crystalline polymer in simple shear and complex flow

In-situ X-ray scattering methods have been used to measure the average degree of molecular orientation in the commercial thermotropic copolyesteramide, Vectra B. Experiments were conducted in both homogeneous shear flow and in extrusion-fed channel flows that provided mixed shear/extensional deformations. In the channel flows, extension has a dramatic effect on the average orientation state in the vicinity of stagnation points or expansions/contractions in cross-sectional area. Of particular note, a temporary increase and subsequent decay in orientation observed in a 4:1 slit-contraction flow provides additional indirect evidence supporting the hypothesis that Vectra B exhibits director tumbling. This is consistent with results from other fully aromatic copolyesters but contrasts with findings in “model” thermotropes incorporating flexible spacers. Thus, it seems that the stiffer backbone of commercial main chain LCPs is the main feature which, apparently, leads to tumbling. Measurements of average molecular orientation in transient shear flows show some connections with the corresponding mechanical response, but fail to show the distinctive characteristics that have previously been associated with either tumbling or aligning in LCPs using similar procedures. These experiments might be adversely affected by the comparatively slow rate of data acquisition, which leads to lengthy experiments in which the sample is more prone to degradation.

Rheology of schizophyllan solutions in isotropic and anisotropic phase regions

In this paper, we discuss the rheological properties of aqueous solutions of a rigid triple-helical polysaccharide, schizophyllan (SPG), in isotropic, biphasic, and fully anisotropic phases. Both steady shear and dynamic rheological behaviors reveal remarkable changes when SPG solutions pass through the three phases. The steady shear flow exhibits shear thickening at low shear rates for anisotropic SPG liquid crystalline samples, which is attributed to the shear-induced cholesteric to nematic transformation. The first normal stress difference and transient rheological experiments demonstrate that director tumbling is absent or negligible in SPG liquid crystals in the range of examined shear rates. Additionally, the stress relaxation of SPG liquid crystals after flow cessation shows an inverse relation between the relaxation time and preshear rate, as expected by Larson and Mead’s theory [Larson and Mead (1989)]. Small amplitude oscillation measurements following flow cessation show decreasing complex modulus with time for SPG liquid crystals, which is probably related to an increase of molecular orientation after flow cessation. The evolutions of complex modulus after flow cessation are discussed in terms of chain persistence length.

Development and relaxation of orientation in sheared concentrated lyotropic solutions of hydroxypropylcellulose in m-cresol

Shear-induced orientation and the relaxation of orientation after the cessation of shear in 45 and 50 wt% solutions of cholesteric hydroxypropylcellulose (HPC) in m-cresol have been studied in situ by infrared spectroscopy and polarised microscopy. The shearing experiments were conducted at 30–80 °C at shear rates of 1–300 s −1, which covered the director tumbling, wagging and a small part of the steady-state shear rate regimes. The steady-state order parameter was proportional to the shear rate and the proportionality constant increased with increasing HPC concentration and decreasing temperature. The concentrated solutions studied showed steady-state alignment even in the tumbling regime. Three different shear-rate regions with different behaviours of the solutions after the cessation of shear were found in these concentrated HPC solutions. At low shear rates (1–5 s −1, referring to the 50% HPC solution) the polymer remained isotropic during shear but became gradually more oriented a few minutes after the cessation of shear, an observation that was substantiated by polarized microscopy. The order parameter reached a final plateau value and stayed constant at this level for long periods of time (∼24 h). At intermediate shear rates (from 5 to 50 s −1 for the 50% HPC solution), a detectable order parameter was recorded at steady shear and, after the cessation of shear, the structure returned to an almost isotropic state within a few minutes, after which the orientation gradually started to increase to approach a plateau value after about 150 min. At even higher shear rates (∼100 s −1 for to the 50% HPC solution), the initial steady shear order parameter relaxed to an almost isotropic state and remained constant at this level for time periods extending up to 24 h.

Transient 1–2 plane small-angle x-ray scattering measurements of micellar orientation in aligning and tumbling nematic surfactant solutions

A new x-ray shear cell capable of probing complex fluid structure in the flow-gradient (“1–2”) plane is used to study orientational dynamics of nematic surfactants in transient shear flows. Two surfactant systems are studied, one of which (SDS/decanol) apparently exhibits shear aligning dynamics and the other of which (CPyCl/hexanol) exhibits director tumbling. Data on the SDS/decanol system exhibit what appear to be common characteristics of aligning nematics: constant orientation state in steady shear; a single undershoot of long duration in average orientation upon flow reversal; and no significant orientation change upon step increase or decrease in shear rate or upon flow cessation. These data are discussed in light of similar measurements on shear aligning thermotropic liquid-crystalline polymers, and polydomain model predictions of transient orientation for aligning nematics. Shear reversal data on CPyCl/hexanol show an oscillatory response typical of tumbling materials, but in better qualitative agreement with the Larson–Doi polydomain model than similar recent measurements on lyotropic polymer solutions.

Transient molecular orientation and rheology in flow aligning thermotropic liquid crystalline polymers

Quantitative measurements of molecular orientation and rheology are reported for various transient shear flows of a nematic semiflexible copolyether. Unlike the case of lyotropic liquid crystalline polymers (LCPs), whose structure and rheology in shear are dominated by director tumbling, this material exhibits flow aligning behavior. The observed behavior is quite similar to that seen in a copolyester that we have recently studied [Ugaz and Burghardt (1998)], suggesting that flow aligning dynamics may predominate in main-chain thermotropes that incorporate significant chain flexibility. Since the flow aligning regime has received little attention in previous attempts to model the rheology of textured, polydomain LCPs, we attempt to determine whether available models are capable of predicting the orientation and stress response of this class of LCP. We first examine the predictions of the polydomain Ericksen model, an adaptation of Ericksen’s transversely isotropic fluid model which accounts for the polydo...

Shear Aligning Properties of a Main-Chain Thermotropic Liquid Crystalline Polymer

We report the first direct, quantitative measurements of the shear aligning properties of a main-chain thermotropic liquid crystalline polymer (LCP). We find that a model thermotrope with alternating mesogen and spacer structure is of the shear aligning type throughout its nematic range. The director rotates uniformly in the shear flow toward the Leslie alignment angle as probed by in situ flow conoscopy. The Leslie alignment angle becomes progressively closer to the flow direction as temperature decreases, corresponding to a decrease of the tumbling parameter λ with increasing order parameter S. Our measurements of λ(S) enable direct comparison with predictions from molecular models, which predict that shear alignment prevails in the limit of flexible nematic chains. This is in direct contrast to rodlike lyotropic LCPs for which director tumbling is the rule.

Twist Viscosity of a Side-Chain Liquid-Crystalline Polysiloxane Dissolved in a Tumbling Nematic Solvent

The dynamics of the twist distortion was characterized by electric-field-dependent dynamic light scattering (EFDLS) for a dilute solution of a side-chain liquid crystalline polysiloxane (SCLCP) dissolved in the tumbling nematic solvent, 4‘-octyl-4-cyanobiphenyl (8CB). The results show a decrease in twist relaxation rate on dissolution of the SCLCP due to a large increase in twist viscosity δγ1 with negligible change in twist elastic constant K22. By comparing the twist viscosity values, γ1 = α3 − α2, with previous measurements of the strain periodicity of oscillations in the shear stress transients due to director tumbling, γp = (π/δp)(1 + δp2), where δp = (−α3/α2)1/2, we further investigate the corresponding changes in Leslie viscosities, δα2 and δα3. The results indicate that δα2 and δα3 have opposite signs. These observations, together with literature data on the electrorheological behavior of these solutions, can be self-consistently described by a hydrodynamic model of the viscous dissipation by Brochard, modified through inclusion of an additional dissipation process which derives from an elastic torque between director rotation and LCP orientation.

Pressure-driven channel flows of a model liquid-crystalline polymer

Shear flows disrupt molecular orientation in liquid-crystalline polymers (LCPs) through director tumbling, and this causes difficulty in controlling the polymer structure and properties in injection molding and extrusion. In this paper we simulate LCP channel flows using the Doi theory. A Bingham closure is used to preserve director tumbling and wagging. The objective is to examine how contractions and expansions in a channel affect LCP orientation and to explore the possibility of using the channel geometry as a means of manipulating LCP order. A finite-element method is used to solve the coupled equations for fluid flow and polymer configuration. Results show that a contraction aligns the director with the streamline and improves molecular order, while an expansion drives the director away from the flow direction and reduces molecular order. If the expansion is strong enough, an instability develops downstream as disturbances in the flow and polymer configuration reinforce each other through the polymer stress. This instability generates a wave that spans roughly the central half of the channel and propagates downstream at the centerline velocity. For abrupt contractions or expansions, disclinations of ±1/2 strength arise in the corner vortex. The numerical results agree qualitatively with experiments when comparisons can be made. In particular, the wavy pattern following a sudden expansion is remarkably similar to previous experimental observations. The simulations suggest that using contractions and expansions may be a feasible strategy for controlling LCP order and morphology in processing.

Transient rheological behavior of lyotropic solutions of ethyl cellulose in m -cresol

Transient rheological features of anisotropic 30 and 40 wt.% ethyl-cellulose/m-cresol solutions were investigated, taking as a reference other lyotropes like poly(γ-benzylglutamate) in m-cresol, poly(p-phenylene-terephthalamide) in sulfuric acid and hydroxypropylcellulose in water. Strain scaling oscillations before reaching steady state, with a half-period of 20 strain units for 30 wt.% and 22.5 strain units for 40 wt.% in both stress growth and transient viscosity in creep, revealed that director tumbling takes place for ethylcellulose solutions. Large strain recoveries (2–3 strain units) obtained in recoil experiments confirmed the hypothesis of a tumbling regime. In contrast to the majority of reported lyotropes, we did not observe a master curve of strain recovery versus the product of preshear rate by time. This result appears to be associated with the existence of another mechanism of relaxation, in addition to unwinding of the defect texture created by tumbling. Dynamic viscoelastic results after cessation of flow suggest that a slower mechanism of relaxation, associated with texture or polydomain coarsening, takes place.

Tumbling dynamics in a nematic surfactant solution in transient shear flows

We report rheological and structural studies of a nematic surfactant solution (CPCl/hex) in transient shear flows. Upon step changes in steady shear flow conditions, the shear stress exhibits damped oscillations that scale with shear strain, attributed to director tumbling under shear. In situ small-angle x-ray scattering spectroscopy is used to measure changes in average micellar orientation during similar transient shear protocols; the measured orientation parameter also exhibits damped oscillations reflecting the underlying tumbling dynamics. Stress and structure data are compared with predictions of the Larson–Doi tumbling polydomain model. The model predictions are qualitatively similar to the experimental observations. In particular, orientation is observed to initially decrease upon shear flow reversal in CPCl/hex, in agreement with the Larson–Doi predictions but in contrast to previous results for model lyotropic solutions of poly(benzyl glutamate). Shear stress and average orientation are closely...

The effect of temperature and concentration on N1 and tumbling in a liquid crystal polymer

The shear rate γ̇min at the relative minimum in the N1 flow curve is studied as a function of temperature and concentration for liquid crystalline (hydroxypropyl)cellulose (HPC). For lyotropes, at least, γ̇min is the shear rate necessary to halt director “tumbling” and align the molecules. HPC is a convenient polymer for studying the relationship between lyotropic and thermotropic liquid crystalline polymers because it exhibits a pure thermotropic phase at elevated temperatures, and room temperature lyotropic phases at moderate concentrations in m-cresol. At the highest possible polymer concentration at which reliable rheology data can be obtained (around 70 wt % polymer), indirect evidence for director tumbling is observed, in that N1 retains a local minimum versus shear rate. For the highest concentrations this minimum N1 value is positive, rather than negative, as is the case at lower concentrations and as is predicted by the Doi theory. Empirical time–temperature and time–concentration shifting can be used to estimate γ̇min from measured values of the shear viscosity.

In Situ X-ray Scattering Study of a Model Thermotropic Copolyester under Shear: Evidence and Consequences of Flow-Aligning Behavior

While director tumbling is responsible for much of the unique rheological behavior of lyotropic liquid-crystalline polymers (LCPs), it is not clear whether tumbling routinely occurs in main-chain thermotropes. We present experiments on a model thermotropic LCP under shear, using in-situ X-ray scattering as a probe of molecular orientation. This model LCP, PSHQ6-12, was synthesized by Chang and Han [Macromolecules 1996, 29, 2383] and consists of rigid mesogens randomly copolymerized with flexible spacer chains of two different lengths. This architecture suppresses crystallization and lowers the nematic-isotropic transition temperature to an accessible level, allowing a well-defined thermal history to be established prior to flow. We present measurements of molecular orientation in steady shear flow, during relaxation, and during shear flow start-up. The evolution of molecular orientation observed during flow inception and the observation of shear-induced transparency in the material lead to the hypothesis that PSHQ6-12 is shear aligning rather than tumbling. Consequences of this hypothesis are explored by polydomain simulations based on Ericksen's transversely isotropic fluid model, which are capable of capturing many aspects of the experimentally observed rheology and shear-induced structure.

Molecular orientation and rheology in sheared lyotropic liquid crystalline polymers

This article summarizes recent experiments relating measurements of molecular orientation to bulk rheological behavior in liquid crystalline polymers (LCPs) under shear. The principal experimental techniques are flow birefringence and x-ray scattering. Since LCPs usually exhibit a “polydomain” texture, measurements of flow-induced orientation reflect both the local distribution of molecular orientation around the director and the heterogeneous distribution of director orientations in the sheared LCP. In model lyotropic solutions of poly(benzyl glutamate) (PBG) and hydroxypropylcellulose (HPC), there are clear structural signatures of a transition from director tumbling dynamics at low Deborah number to flow alignment at high Deborah number. Rheo-optical measurements of the full refractive index tensor in PBG allow the orientation predictions of microstructural theories for LCP rheology to be quantitatively tested. At low shear rates the two model materials differ: PBG solutions exhibit significant orientation, while HPC solutions show little orientation. This is correlated with the presence of so-called “Region I” shear thinning in HPC solutions. Conversely, in PBG solutions of high concentration, x-ray scattering measurements demonstrate that Region I arises from the presence of a hexagonal phase. The model systems are further differentiated in relaxation. Molecular orientation increases in PBG solutions, but decreases in HPC solutions upon flow cessation; these differences are manifested in the evolution of dynamic properties. Finally, structural investigations of a PBG solution and a nematic surfactant solution during step changes in shear conditions are used to interrogate tumbling dynamics at low shear rates and test microstructural tumbling models.