Of rodlike polymers

Charlet, A., Solution Processing of Rodlike Polymers into Ribbons, M.S. Thesis, Carnegie-Mellon University, Pennsylvania, 1981. 

The behavior of rodlike polymers in poor solvents has received comparatively little attention. However, the phase boundaries of the rodlike polypeptide poly-Y benzyl-a, L-glutamate in dimethylformamide (PBLG/DMF) have been determined over a temperature range spanning both poor and good solvent limits.(5,6) As expected from the Flory... 

Flory, in 1956, predicted that solutions of rodlike polymers could also exhibit LC behavior. The initial synthetic polymers found to exhibit LC behavior were concentrated solutions of poly(gamma-benzyl glutamate) and poly(gamma-methyl glutamate). These polymers exist in a helical form that can be oriented in one direction into ordered groupings, giving materials with anisotropic properties. 

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. 

A ternary system consisting of two polymer species of the same kind having different molecular weights and a solvent is the simplest case of polydisperse polymer solutions. Therefore, it is a prototype for investigating polydispersity effects on polymer solution properties. In 1978, Abe and Flory [74] studied theoretically the phase behavior in ternary solutions of rodlike polymers using the Flory lattice theory [3], Subsequently, ternary phase diagrams have been measured for several stiff-chain polymer solution systems, and work [6,17] has been done to improve the Abe-Flory theory. 

To explain the Green function method for the formulation of Dx, D and D, of the fuzzy cylinder [19], we first consider the transverse diffusion process of a test fuzzy cylinder in the solution. As in the case of rodlike polymers [107], we imagine two hypothetical planes which are perpendicular to the axis of the cylinder and touch the bases of the cylinder (see Fig. 15a). The two planes move and rotate as the cylinder moves longitudinally and rotationally. Thus, we can consider the motion of the cylinder to be restricted to transverse diffusion inside the laminar region between the two planes. When some other fuzzy cylinders enter this laminar region, they may hinder the transverse diffusion of the test cylinder. When the test fuzzy cylinder and the portions of such other cylinders are projected onto one of the hypothetical planes, the transverse diffusion process of the test cylinder appears as a two-dimensional translational diffusion of a circle (the projection of the test cylinder) hindered by ribbon-like obstacles (cf. Fig. 15a). 

In contrast to the case of rodlike polymers, no adequate expression of Vscf (a) is available for semiflexible polymers. Thus, at present, we cannot directly calculate F for semiflexible polymer solutions by Eq. (62). However, as will be shown in Sect. 8.2, we need no direct calculation of F to obtain (E) in a steady-state flow. So, in the following sections, we will be concerned only with the case of steady-state flow. 

In recent years, several computer simulations have been performed for the dynamics of rodlike polymers in concentrated solutions [119-123], using various models and methods. Although the models used are not necessarily realistic, the simulation gives us information about the quantities of theoretical importance but not experimentally measurable (e.g., DB and D ). Furthermore, the comparison between simulation and experimental results may reveal the factors mainly responsible for the dynamics under study. 

Bitsanis et al. [122,123] simulated Brownian motion of rodlike polymers over the concentration range 5 < LV < 150, where L and c are the length and number concentration of the rod, respectively, with the intermolecular potential u given by... 

As discussed in section 7.1.6.4, semidilute solutions of rodlike polymers can be expected to follow the stress-optical rule as long as the concentration is sufficiently below the onset of the isotropic to nematic transition. Certainly, once such a system becomes nematic and anisotropic, the stress-optical rule cannot be expected to apply. This problem was studied in detail using an instrument capable of combined stress and birefringence measurements by Mead and Larson [109] on solutions of poly(y benzyl L-glutamate) in m-cresol. A pretransitional increase in the stress-optical coefficient was observed as the concentration approached the transition to a nematic state, in agreement of calculations based on the Doi model of polymer liquid crystals [63]. In addition to a dependence on concentration, the stress-optical coefficient was also seen to be dependent on shear rate, and on time for transient shear flows. 

G. Murrucci and N. Grizzuti, The effect of polydispersity on rotational diffusivity and shear viscosity of rodlike polymer in concentrated solutions, J. Polym. Sci., Polym. Lett. Ed., 21, 83 (1983). 

M. Doi, Rheological properties of rodlike polymers in isotropic and liquid crystalline phases, Ferroelectrics, 30, 247 (1980). 

M. Marrucci and P. L. Maffettone, Description of the liquid-crystalline phase of rodlike polymers at high shear rates, Macromolecules, 22,4076 (1989). 

We shall not attempt to review and compare critically various theories of liquid crystallinity in this chapter. Inasmuch as theory based on a lattice model has proved most successful in the treatment of liquid crystallinity in polymeric systems, we shall present an abbreviated account of that theory confined to its essential aspects. The versatility of this theory has permitted its extension to polydisperse systems, to mixtures of rodlike polymers with random coils and to some of the many kinds of semirigid chains. These ramifications of the theory will be discussed in this chapter... 

The contents of the review are as follows. The dynamics of rodlike polymers are reviewed in Section 2 followed by a review of previous experimental results of the polymerization kinetics of rodlike molecules in Section 3. Theoretical analyses of the problem following Smoluchowski s approach are discussed next (Section 4), and this is followed by a review of computational studies based on multiparticle Brownian dynamics in Section 5. The pairwise Brownian dynamics method is discussed in some detail in Section 6, and the conclusions of the review are given in Section 7. 

Starting with the seminal works of Riseman and Kirkwood [10] for dilute solutions and Doi and Edwards [11] for non-dilute solutions, several studies of the dynamics of rodlike polymers are reported in the literature. A comprehensive review of the dynamics of rodlike polymers is given by Tracy and Pecora [12] and a more detailed treatment may be found in the book by Doi and Edwards [13]. Here we review only the basics of the subject. 

The expressions for the diffusivities of rodlike polymers in dilute solutions can be written in the following general forms [12]... 

G. Szamel and K. S. Schweizer, Reptation as a dynamic mean field theory -self and tracer diffusion in a simple model of rodlike polymers, J. Chem. Phys., 100 (1994) 3127-3141. 

Bitsanis, H. T. Davis and M. Tirrell, Brownian dynamics of non-dilute solutions of rodlike polymers.2. High concentrations. Macromolecules, 23 (1990) 1157-1165. 

The hydrodynamic volume parameter [tj]M has been proven to be applicable also to the cases of rodlike polymers [3] and to separations in aqueous solvents [4] where, however, secondary nonexclusion mechanisms often superimpose and affect the sample elution behavior. In the latter situation, careful choice of eluent composition must be made in order to avoid anypossible polymer-packing interaction. 

In neither case were pendant phenyl groups of sufficient influence to significantly improve the solubility or offer processing solvent alternatives of practical value. The synthesis of articulated molecular structures was based on theoretical considerations of the phase equilibria of rodlike polymers.(11) Articulated PBO, PBT, and PDIAB polymers which contained diphenoxybenzene swivels" were synthesized(12) as were PBT and PBO structures with thermooxidatively stable biphenyl and bipyridyl "swivels".(13) Although differences from PBO, PBT and PDIAB in film-forming properties and solution behavior were observed,(14) the solubilities were not sufficiently altered to afford processing alternatives. 

Chu, S. G., Venkatraman, S., Berry, G. C., and Einaga, Y., Rheological properties of rodlike polymers in solution 1. Linear and nonlinear steady-state behavior. Macromolecules, 14, 939-946(1981). 

Doi, M., Molecular dynamics and rheological properties of concentrated solutions of rodlike polymers in isotropic and hquid crystalhne phases, J. Polym. Sci. Polym. Phys. Ed., 19, 229-243 (1981). 

In the case of rodlike polymers it is easy to calculate the size of the tube, but it is not so easy for flexible polymers where the picture of Fig. 

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