Studies on the Texture of Nematic Solutions of Rodlike Polymers

Studies on the Texture of Nematic Solutions of Rodlike Polymers.

3. Rheo-optical and Rheological Behavior in Shear

Zhanjie Tan and Guy C. Berry(a)

Department of Chemistry

Carnegie Mellon University

Pittsburgh, PA 15213

(a)Addressee for correspondence;
e-mail:

APPENDIX

This Appendix comprises two parts:

(1)A review of the literature on the rheological behavior of nematic solutions relevant to the study on the rheo-optical properties of nematic solutions of poly(1,4-phenylene terephthalamide), PPTA, to which it is linked.

(2)Supplementary data mentioned in the text for the creep and recovery for concentrations or gap separation in the parallel-plate rheometer.

1. SUPPLEMENTARY LITERATURE REVIEW

The steady-state flow properties of nematic solutions have received considerable theoretical attention under conditions for which a recently small deformation may be assumed, with the use of the Leslie-Ericksen (LE) constitutive equation [1, 2]. Following the finding that some, if not all, polymeric liquid crystalline solutions do not align in a slow shear flow [3-5], theoretical efforts have been motivated to understand the complex, nonlinear behavior observed with such materials in a shear deformation; it appears that some solvent-free thermotropic liquid crystalline materials may align under shear under some circumstances [6-8].

One theoretical tack has been to adapt the LE constitutive equation to describe the complex behavior of the director field in a shearing deformation, often using computational methods to extend analytical solutions. These treatments, most applicable to an initially defect-free state at equilibrium, predict a beautiful sequence of periodic distortions under special conditions of the shear rate and the thermodynamics of the nematic state of interest, with certain characteristic distortions given picturesque, suggestive names: tumbling and wig-wag (full or partial rotation of the director in the shear plane, respectively), kayaking (rotation of the director out of the shear plane, but not orthogonal to it), and log-rolling (with the director orthogonal to the shear plane) [9-26]. In other treatments, periodically placed roll-cells with a long-axis along the flow are predicted [23, 27, 28]

The relevance of these models to the behavior observed with nematic solutions of PPTA will be considered below. The director field distortion leading to the phase grating discussed in the text is consistent with the predictions of some models which give a "log rolling" flow, with the axes of the rodlike chains orthogonal to the flow, as a weak attractor in the flow dynamics of nematic fluids, albeit not a stable state [11, 12, 22, 29]. A log rolling regime has been reported in some cases in limited regimes of flow of polymeric nematics [30-32]. With increasing strain at larger shear rates, a field of line defects appeared, stretched along the flow direction [33], and with the optical appearance of loop defects observed during the coarsening of a nematic solution of poly(1,4–phenylene–2,6–benzobisthiazole), PBZT, at rest [34]. A similar field of defects has been reported in the shear deformation of a thermotropic nematic melt [31, 32]. and reported in some cases in limited regimes of flow of polymeric nematics [30-32]

Alternatively, so-called mesoscopic theories have been developed, partially motivated by the early postulate that the quiescent liquid crystalline solution comprises "domains" based on a typical optical appearance [35, 36], with the director field approximately uniform, and near its equilibrium value within each domain for the quiescent fluid, but with the director orientation randomly distributed among the domains. In these models, the LE constitutive equation is applied to deformation within the postulated domains, and the macroscopic behavior is obtained by an average over all domains with their various director field orientations with respect to the direction of deformation, including some provision for systematic change in the domain size during deformation [13, 37-43]. In some studies, it is assumed that the coarsening of the texture is evidence of a transition through some of these distortions to a final state of alignment in a steady-state fast flow, sometimes evaluated on the basis of appearance and birefringence in fast flow [5, 19, 44-50]. One of the important outcomes of some of these treatments is that owing to the absence of an internal time constant in the fluid dynamics, certain rheological properties are predicted to scale with strain during deformation in the slow flow (or region II) regime, or with the pseudo-strain, calculated as the product of the elapsed time and the previously imposed steady-state shear rate, during relaxation following steady flow. Although this has not been seen in the observed studies on PBZT [51, 52], studies on other mesogenic (nematic or twisted-nematic) polymer solutions have reported strain scaling [5, 37, 44, 53-65]. The relevant behavior observed here with PPTA solutions is discussed below.

Some theories have studied the role of disclination defects on rheological behavior [18, 29, 66-70], and some experimental studies have reported optically visible line defects in flow [32, 71-75]. A band structure transverse to the flow direction has frequently been reported during the initial stages of stress relaxation or recoil in the absence of an external stress [73, 76-85], and sometimes during fast steady-state shear flow [80, 83, 86-88]. More frequently, a striation pattern parallel to the flow has been reported over a range of moderate and fast flow [48, 61, 82, 89-92]. In many cases, a scattering streak along the radial direction is observed in fast flow, sometimes with a four-leaf lobe pattern either superposed on or preceding the development of the streak along the radial direction; such a pattern has been interpreted as arising from disclination defects in the texture in some cases [57, 61, 73, 74, 79, 82, 89, 91, 93-96]. Comparison will be made with these and other rheo-optical studies on liquid crystalline polymers to reveal similarities and differences with the behavior reported here [13, 30-32, 71, 72, 97-102].

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2. SUPPLEMENTARY FIGURES

Figure 5aThe recoil and transmission for a solution with weight fraction 0.0974 for platen separation of 500 µm. Shear stress of 20, 50, 120, and 200 Pa for the circles, squares, diamonds and triangles, respectively, corresponding to shear rates in steady-state flow of 0.024, 0.083, 0.27 and 0.65 sec-1 at the maximum radius, respectively.
Left: The steady-state compliance R() and transmission as functions of time  since cessation of steady-state flow;
Right: The total recoil R and transmission as functions of the pseudo strain given by the product of the shear rate in steady-state flow and the time  since cessation of that flow.