Liquid crystalline polymers theory

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

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. 

The SD is a phase separation process usually occurring in systems consisting of more than two components such as in solutions or blends. However, in the present case the system employed is composed of one component of pure PET. In this case, what triggers such an SD type phase separation Doi et al. [24, 25] proposed a dynamic theory for the isotropic-nematic phase transition for liquid crystalline polymers in which they showed that the orientation process... 

The distinct properties of liquid-crystalline polymer solutions arise mainly from extended conformations of the polymers. Thus it is reasonable to start theoretical considerations of liquid-crystalline polymers from those of straight rods. Long ago, Onsager [2] and Flory [3] worked out statistical thermodynamic theories for rodlike polymer solutions, which aimed at explaining the isotropic-liquid crystal phase behavior of liquid-crystalline polymer solutions. Dynamical properties of these systems have often been discussed by using the tube model theory for rodlike polymer solutions due originally to Doi and Edwards [4], This theory, the counterpart of Doi and Edward s tube model theory for flexible polymers, can intuitively explain the dynamic difference between rodlike and flexible polymers in concentrated systems [4]. 

However, as accurate experimental data were accumulated, it has become apparent that these earlier theories of rodlike polymers fail to describe quantitatively the behavior of real liquid-crystalline polymers, which are not completely rigid but more or less flexible. 

The growing interest in liquid-crystalline polymers has stimulated many theoretical and experimental studies of their solutions, and the results have already been summarized by many authors. For instance, the statistical thermodynamic theories were reviewed by Flory [5], Odijk [6], Semenov and Khokhlov [7], Ciferri et al. [8], and Vroege and Lekkerkerker [9], while the dynamical theories were discussed by Doi and Edwards [4] and Moscicki [10]. 

In the present article, we focus on the scaled particle theory as the theoretical basis for interpreting the static solution properties of liquid-crystalline polymers. It is a statistical mechanical theory originally proposed to formulate the equation of state of hard sphere fluids [11], and has been applied to obtain approximate analytical expressions for the thermodynamic quantities of solutions of hard (sphero)cylinders [12-16] or wormlike hard spherocylinders [17, 18]. Its superiority to the Onsager theory lies in that it takes higher virial terms into account, and it is distinctive from the Flory theory in that it uses no artificial lattice model. We survey this theory for wormlike hard spherocylinders in Sect. 2, and compare its predictions with typical data of various static solution properties of liquid-crystalline polymers in Sects. 3-5. As is well known, the wormlike chain (or wormlike cylinder) is a simple yet adequate model for describing dilute solution properties of stiff or semiflexible polymers. 

Fig. 7. Comparison of experimental phase boundary concentrations between the isotropic and biphasic regions for various liquid-crystalline polymer solutions with the scaled particle theory for wormlike hard spherocylinders. ( ) schizophyllan water [65] (A) poly y-benzyl L-glutamate) (PBLG)-dimethylformamide (DMF) [66-69] (A) PBLG-m-cresoI [70] ( ) PBLG-dioxane [71] (O) PBLG-methylene chloride [71] (o) po y(n-hexyl isocyanate) (PHICH°Iuene at 10,25,30,40 °C [64] (O) PHIC-dichloromethane (DCM) at 20 °C [64] (5) a po y(yne)-platinum polymer (PYPt)-tuchIoroethane (TCE) [33] ( ) (hydroxypropyl)-cellulose (HPC)-water [34] ( ) HPC-dimethylacetamide (DMAc) [34] (N) (acetoxypropyl) cellulose (APC)-dibutylphthalate (DBP) [35] ( ) cellulose triacetate (CTA)-trifluoroacetic acid [72]...

Fig. 8. Comparison of experimental phase boundary concentrations between the biphasic and liquid crystal regions for various liquid crystalline polymer solutions with the scaled particle theory for hard wormlike spherocylinders. The symbols are the same as those in Fig. 7...

Fig. 12a-c. Polymer concentration dependence of the orientational order parameters S for three liquid-crystalline polymer systems a PBLG-DMF [92,93] b PHIC-toluene [94] c PYPt-TCE [33], Marks experimental data solid curves, theoretical values calculated from the scaled particle theory. The left end of each curve gives the phase boundary concentration cA... 

This paper presents summaries of unique new static and dynamic theories for backbone liquid crystalline polymers (LCPs), side-chain LCPs, and combined LCPs [including the first super-strong (SS) LCPs] in multiple smectic-A (SA) LC phases, the nematic (N) phase, and the isotropic (I) liquid phase. These theories are used to predict and explain new results ... 

Larson, R.G. Doi, M. Mesoscopic domain theory for textured liquid-crystalline polymers. J. Rheol. 1991, 35 (4), 539-563. 

Feng, J. Chaubal, C.V. Leal, L.G. Closure approximations for the Doi theory which to use in simulating complex flows of liquid-crystalline polymers J. Rheol. 1998, 42, 1095-1119. 

Wang, Q. A hydrodynamic theory for solutions of nonhomogeneous nematic liquid crystalline polymers of different configurations. J. Chem. Phys. 2002, 116 (20), 9120-9136. 

Roewer G, Herzog U, Trommer K, Muller E, Friihauf S (2002) Silicon Carbide - A Survey of Synthetic Approaches, Properties and Applications 101 59-136 Rosa A, Ricciardi G, Gritsenko O, Baerends EJ (2004) Excitation Energies of Metal Complexes with Time-dependent Density Functional Theory 112 49-116 Rosokha SV, Kochi JK (2007) X-ray Structures and Electronic Spectra of the it-Halogen Complexes between Halogen Donors and Acceptors with it-Receptors. 126 137-160 Rowan SJ, Mather PT (2008) Supramolecular Interactions in the Formation of Thermotropic Liquid Crystalline Polymers. 128 119-149... 

Some polymers manifest liquid crystalline ordering, which does not have the full long-range three-dimensional periodicity of crystallinity but is far more ordered than amorphicity. Since many excellent books and articles have been published on such polymers and the author does not have much that is new to add to this background information, very little will be said about polymer liquid crystallinity in this book. Van Krevelen [3] has reviewed liquid crystallinity in polymers in a readable manner and discussed its effects on properties for which quantitative structure-property relationships are available. Adams et al [41] have published a valuable compendium of articles covering the theory, synthesis, physical chemistry, processing and properties of liquid crystalline polymers. Woodward [42] has discussed and illustrated liquid crystallinity in polymers with many beautiful micrographs. 

ONSAGER THEORY FOR RIGID —ROD LIQUID CRYSTALLINE POLYMERS... 

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