Rigid Rodlike Macromolecules

The concentration of rigid rodlike molecules cannot be increased very much before spontaneous separation occurs into a concentrated ordered and a very dilute disordered phase, as required by thermodynamic relations, although the separation may occur at higher concentrations if there is some degree of flexibility, and may be delayed by steric hindrance so that a metastable disordered state may persist. The rotation of rigid rods at finite concentration is impeded by collisions and the rotatory relaxation time should increase rapidly with concentration. The theory has been treated by Doi and Doi and Edwards, who conclude that the relaxation time is approximately proportional to c L, where L is the molecular length. 

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Theory for Rigid Rodlike Macromolecules with Monodomains... 

Here, we present the molecular theory of Doi and coworkers (Doi 1981, 1983 Doi and Edwards 1978a, 1978b Kuzuu and Doi 1980, 1983, 1984) for predicting the rheological behavior of concentrated solutions of monodomains consisting of rigid rodlike macromolecules. 

In order to predict the nonlinear viscoelastic properties of concentrated solutions of rigid rodlike macromolecules, one must first solve Eq. (9.1) for the orientational distribution function /(u, t) and then Eq. (9.12) for stresses, for a given velocity field. Owing to the highly nonlinear nature of the system of equations, one must resort to numerical techniques to obtain solutions. Indeed, Kuzuu and Doi (1983, 1984) carried out numerical computations to predict nonlinear viscoelastic behavior. 

D. B. Cotts and G. C. Berry, Polymerization kinetics of rigid rodlike molecules - polycondensation of poly((benzo(l,2-D-5,4-D )bisoxazole-2,6-diyl)-l,4-phenylene). Macromolecules, 14 (1981) 930. 

U. S. Agarwal and D. V. Khakhar, Shear flow induced orientation development during homogeneous solution polymerization of rigid rodlike molecules. Macromolecules, 26 (1993) 3960-3965. 

Figure 2-10. A qualitative sketch of the dependence of the ratio of the shear stress to the shear rate in a simple shear flow. The upper curve represents the result that would be obtained if the fluid were Newtonian. The lower curve illustrates the shear-thinning behavior that is described in the text for the solution of rodlike macromolecules (or the suspension of rigid-rod particles) when the shear rate is large enough to produce partial alignment of the macromolecules (the particles) in the flow direction.

The intrinsic viscosity (rj) is a characteristic value of a single macromolecule in a given solvent and it is a measure of the hydrodynamic volume occupied by the polymer itself. It depends primarily on the molar mass (Mw), chain rigidity, and solvent quality. For anionic polyelectrolytes the presence of macroions and counterions in aqueous media causes coil expansion by intrachain electrostatic repulsion and extra dissipation of energy, thus explaining why the intrinsic viscosity of a polyelectrolyte can be higher than that of a neutral rodlike macromolecule of equal size. Thus, (rj) usually increases with an increase in the charge density of the macroion. 

Agarwal US, Mashelkar RA (1992) Diffusion of rigid rodlike molecules across interfaces implications in welding of liquid-crystalline polymers. Macromolecules 25 6703-6704 Brolly JB, Bower DI, Ward IM (1996) Diffusion and sorption of CO2 in poly(ethylene terephthal-ate) and poly(ethylene naphthalate). J Polym Sci Part B Polym Phys 34 769-780 Brooks GT (1992) Crystalline polyphthalamide composition having improved properties. US Patent 5,098,940, 24 Mar 1992... 

From a thermodynamic point of view, a blend of a flexible polymer and a rigid rodlike polymer exhibits less miscibility, because of the unfavorable low entropy of mixing of macromolecules even for athermal mixtures. Moreover, the phase separation is enhanced by the presence of liquid crystalline ordering. The affinity of two... 

The concept of a unique hydrodynamic volume for all rodlike polymers was derived from examination of the Mark-Houwink constants, K and a, of the equation [rj ] = KMa. Macromolecules with values of a greater than unity are commonly accepted to be stiff or rigid rods. However, it was also found that such molecules (even for values of a less than unity) obey a relation illustrated by close concordance with the curve in Fig. lb (13) flexible, branched or otherwise irregular polymers, on the other hand, show dispersion around the upper part of the curve. The straight line curve in Fig. lb implies that the constants K and a are not independent parameters for the regular macromolecules to which they apply. Poly (a- and polyQJ-phenylethyl isocyanide) fall on this line the former has a value of a > 1 while the latter has a value a < 1 (14) both polymers give linear concentration dependence of reduced specific viscosity for fractionated samples... 

The size and shape of a macromolecule can be determined by measuring the physical properties of isolated macromolecules in solution. Large rigid macromolecules that are derived from extended structures including the collagen triple helix result in rodlike rigid or semirigid structures. The size, shape, and physical parameters for macromolecules discussed in this book... 

Aromatic polyamides are generally made by low-temperature reactions of aromatic diamines and aromatic diacid chlorides in special solvents such as a 1 3 molar mixture of hexamethylphosphoramide A-methylpyrrolidone, as in reaction (4-50). Intensive stirring is required to attain high molecular weights because the polymer precipitates. These macromolecules are very rigid and rodlike. They form oriented liquid crystalline arrays in solution and require little postspinning orientation to produce extremely strong and stiff fibers. The polymer would not be made in the melt because it is infusible. It must be synthesized and handled in solution, and this requires the use of reactive precursors. 

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