Nematodynamic theory

As mentioned, a lot of theoretical and experimental studies have been performed to understand physics and rheological properties of lyotropic LCPs. The molecular Doi approach with many improvements and experimental tests is well presented in the literature (e.g., see Ref. [5]). But the thermotropic LCPs were poorly understood till recently, in spite of many attempts to develop either nematodynamic or molecular description of their flow properties. The beauty of continuum approach is that it can be applied to molecular nematics ofboth different types, as well as to the nonyielding suspensions with shaped particles. Yet, general nematodynamic theories are multi-parametric. For example, the general LEP continuum LC theory contains five constitutive parameters [2]. Similarly, de Gennes potential proposed for the monodomain description of general weakly elastic behavior of LCE has also five parameters [37]. Because viscoelasticity is a combination of elastic and viscous effects, it is expected that even in easy theoretical schemes, the continuum approach to viscoelastic polymer nematodynamics should involve at least 10 constitutive parameters. 

This effect has mostly been observed for lyotropic LCPs, sometimes also for thermotropic ones. The existence of region I in Figure 11.1 is explained by the formation of texture, a domain structure observed in many, mostly lyotropic LCPs. The texture occurs during relaxation when the stress levels are very low, that is, when approaching the rest state. Such a three-region flow curve was first observed in Ref. [50] and explained theoretically for lyotropic LCPs in Refs [51, 52] (see also Refs [4, 5, 53]). These theoretical descriptions are typically complementary to the more fundamental monodomain nematodynamic theories of both the molecular and the continuous types. 

Our simulations of the above viscoelastic nematodynamics theory require the reliable and representative rheological data for LCPs, obtained for steady and transient shear flows and relaxation. We chose literature rheological data for two commercial LCPs, Titan and Zenith 6000 [49], as well as for two model polymers, a main-chain LCP, PSHQ9, and a side-chain LCP, PI-14-5CN [53]. 

It seems that the majority of thermotropic LCPs exhibit flow-aligning behavior. Thus, to describe the experimental observations for these polymers, the general viscoelastic nematodynamic theory [16,17] is used in our simulations with aligning assumption. 

Liquid Crystalline Polymers Theories, Experiments, and Nematodynamic Simulations of Shearing Flows... 

As mentioned, there exists neither molecular nor continuum theory for describing complicated properties of thermotropic LCPs, although many experimental data for this type of LCPs have been accumulated. One of the objectives of the new continuum theory of weakly nonlinear viscoelastic nematodynamics [22, 23] is to interpret and simulate experimental data, and create models of processing for LPCs. 

The simulations in this and following sections are based on the continuum theory of weak viscoelastic nematodynamics [22, 23]. The closed set of constitutive equations... 

In spite of many efforts, attempts to model complicated properties of liquid crystalline polymers (LCPs) are far from being complete. The constitutive equations of continuum type for thermotropic LCPs were proposed only last year. Multipara-metric character of these equations is the challenging problem for LCP simulations. The chapter by Chen and Leonov ( Liquid Crystalline Polymers Theories, Experiments, and Nematodynamic Simulations of Shearing Flows ) reviews the major findings in this field, describes new continuum theory valid for thermotropic LCPs, and illustrates simulations of their shearing flows. 

Nematodynamics as a Unified Hydrodynamic Theory Theory That Provides Physical Basis of Liquid Crystal Display Technology... 

Oseen [1] and Frank [2] far before the development of LCD technology. The dynamic continuum theory of nematics, which is frequently called the nematodynamics, was developed by Ericksen [3] and Leslie [4] (hereafter referred to as E-L theory) based on the classical mechanics just in time for the upsurge of LCD technology. In conjunction with the electrodynamics of continuous media, the static and dynamic continuum mechanics of Oseen-Erank and E-L theory provided theoretical tools to analyze quantitatively key phenomena, e.g., Freedericksz transition of various configurations and associated optical switching characteristics. For the details of E-L theory [5-7] and its development [9,10], please refer to the articles cited. 

Motivated by these criticisms, a unified hydrodynamics theory (hereafter referred to as UHT) of condensed matter [11-13] has been developed based on the theoretical framework of fundamental physical concept which is succinctly called the grand synthesis by Lubensky [14]. From its nature, the UHT is applicable to a wide range of hydrodynamics including various phases of liquid crystals, spin systems, even crystals, and so on. In the following, we briefly review the UHT of nematodynamics. 

Much research in the last few decades focused on the simulation of LCPs for various processes. Suitable rheological constitutive equations are required for this simulation. Leslie-Ericksen (LE) theory describes the flow behaviour and molecular orientation of many LCPs. LE model is limited to low shear rates and weak molecular distortions. But at high shear rate, the rate of molecular distortions is too fast. Doi and Edwards developed their model to describe the complex dynamics of macromolecules at high shear rate (Doi and Edwards 1978). Doi theory is applicable for lyotropic LCPs of small and moderate concentrations. Due to the complex nature of Doi theory, it is also challenging for simulation. Leonov s continuum theory of weak viscoelastic nematodynamics, developed on the basis of thermodynamics and constitutive relations, consider the nematic viscoelasticity, deformation of molecules as well as evolution of director. 

Leonov AI (1990) On the rheology of filled polymers. J Rheol 34 1039-1045 Leonov AI (2008a) Algebraic theory of linear viscoelastic nematodynamics. Math Phys Anal Geom 11 87-116... 

Leonov AI, Bassov NI, Kazankov YV (1977) The basic processing of thermosets and rubbers by injection molding (Russian). Chem Moscow 68-70 Leonov AI, Chen H (2010) Modeling and simulation in polymers. Wiley-VCH, Weinheim Leonov AI, Volkov VS (2002) A theory of viscoelastic nematodynamics. Rheol Acta Leonov AI, Volkov VS (2005) Weak viscoelastic nematodynamics Maxwell type. Condensed Matter... 

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