Rheol Acta (2003) 42: 590–604 DOI 10.1007/s00397-003-0316-9
Dana Grecov Alejandro D. Rey
Received: 18 December 2002 Accepted: 8 May 2003 Published online: 20 August 2003 Springer-Verlag 2003
D. Grecov Æ A.D. Rey (&) Department of Chemical Engineering, McGill University, 3610 University Street, Montreal, Quebec, H3A 2B2, Canada E-mail:
[email protected]
ORIGINAL CONTRIBUTION
Transient rheology of discotic mesophases
Abstract This paper presents an analysis of the role of orientation on the rheology of discotic mesophases subjected to slow shear start-up flows, using a projection of the Landau-de Gennes equations of nematodynamics. Analysis of the shear stress surface as a function of tilt and twist orientation with respect to the shear plane shows that the stress surface is dense in well-oriented and periodically located sets of maxima and minima. Thus overshoots and undershoot stress responses to shear-start up are predicted to be the rule rather than the exception. Inplane (within the shear plane) shear start-up stress responses can exhibit multiple, single, or no overshoots, depending on the number of maxima
Introduction Flow modelling of nematic liquid crystals is an active area of applied and fundamental research (Rey and Denn 2002). Nematic liquid crystals are orientationally ordered materials and arise with anisodiametric (rod-like or disk-like) molecules or particles. The state of orientation is characterized by the orientation distribution function (ODF), given in terms of surface spherical harmonics (de Gennes and Prost 1993). The second moment of the ODF is known as the tensor order parameter Q, and the eigenvector corresponding to the largest eigenvalue of Q is known as the director n. Flow modelling of nematic liquid crystals can be performed using the dynamics of the ODF (Doi and Edwards1986;
traversed on the way to steady state. Responses originating from orientations close to the vorticity axis lead to stress undershoots. Complex stress responses, such as a weak overshoot-strong undershoot sequence, are found for intermediate tilt-twist initial states. In-plane modes lead to amplitude and strain scaling. Out-of-plane modes do not display amplitude or strain scaling. These results provide will be useful to interpret and use transient shear rheological data of carbonaceous mesophases and highly filled suspensions of disc-like particles. Keywords Shear start-up Æ Discotic mesophases Æ Stress response Æ Stress overshoots Æ Stress scaling
Larson 1999; Marruci and Greco 1993), the dynamics of Q (Beris and Edwards 1994; Tsuji and Rey 1997; Rey and Denn 2002), and the dynamics of n (Leslie 1979), known as the Leslie-Ericksen model. A recent review (Rey and Denn 2002) describes all these models in sufficient detail. In this paper we use a previously presented tensor order parameter model (Tsuji and Rey 1997; Rey and Denn 2002) based on the Landau-de Gennes free energy that takes into account long-range elasticity, short-range elasticity and flow-induced effects. The Leslie-Ericksen (LE) model does not include short range elasticity, which is needed to capture defect nucleation. The nematic liquid crystal phase considered in this paper is the discotic nematic mesophase. Figure 1 shows
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Fig. 1 Definition of director n of a discotic nematic liquid crystal. The director n is the average director of the unit normals to the disk-like molecules
the molecular geometry, positional disorder, and uniaxial orientational order of discotic nematic liquid crystals (DNLCs). The partial orientational order of the molecular unit normal u is along the average orientation or director n (nÆn=1). The shear flow behaviour and rheology of DNLCs depends on the sign and magnitude of the reactive parameter k, which is the ratio of the flow aligning effect of the deformation rate and the tumbling (rotational) effect of the vorticity. For DNLCs it is known that k
