Rodlike polymer

The physical properties of the rodlike polymers differ from those of flexible polymers in many respects. 

Secondly, due to the large molecular anisotropy, rodlike polymers are much more easily oriented by an external field and show large birefringence. This enables us to use electric or magnetic birefringence as a practical tool to study the rotational motion of these polymers.  

Thirdly, the distinction between rodlike polymers and flexible polymers becomes more pronounced as concentration increases. Due to their larger size, the interaction of the rodlike polymers becomes important at a much lower concentration than with flexible polymers, and, as we shall show later, the effect of the entanglement is much mote remarkable. 

Fourthly, but not least, when the concentration becomes sufficiently high, rodlike polymers spontaneously orient towards some direction, and form a liquid crystalline phase. It is this capability of forming a highly ordered phase that produces strong fibres. 

In this and the following two chapters, we shall discuss the physical properties of such polymers. Although real polymers have finite rigidity and can bend to some extent, we shall mainly consider the extreme 

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It is worth recalling that any of the molecular force laws given by Eqs. (13-16) are derived within the framework of the freely-jointed model which considers the polymer chain as completely limp except for the spring force which resists stretching thus f(r) is purely entropic in nature and comes from the flexibility of the joints which permits the existence of a large number of conformations. With rodlike polymers, the statistical number of conformations is reduced to one and f(r) actually vanishes when the chain is in a fully extended state. 

Wade and Williams have reported the synthesis of a carborane-based analog of polyi/t-phenylene).122 The rodlike polymer (91) (Fig. 55) was prepared by the catalytic... 

Figure 55 The rodlike polymer (91) that is the carhorane-based analog of poly(/ -phenylene ). (Adapted from ref. 123.)...

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

The complex diffusion of the rodlike polymers during phase separation is also discussed. 

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. 

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. 

Table 4. Equations of state for isotropic rodlike polymer solutions derived from various theories...

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. 

In the second half of this article, we discuss dynamic properties of stiff-chain liquid-crystalline polymers in solution. If the position and orientation of a stiff or semiflexible chain in a solution is specified by its center of mass and end-to-end vector, respectively, the translational and rotational motions of the whole chain can be described in terms of the time-dependent single-particle distribution function f(r, a t), where r and a are the position vector of the center of mass and the unit vector parallel to the end-to-end vector of the chain, respectively, and t is time, (a should be distinguished from the unit tangent vector to the chain contour appearing in the previous sections, except for rodlike polymers.) Since this distribution function cannot describe internal motions of the chain, our discussion below is restricted to such global chain dynamics as translational and rotational diffusion and zero-shear viscosity. 

In addition to the above effects, the intermolecular interaction may affect polymer dynamics through the thermodynamic force. This force makes chains align parallel with each other, and retards the chain rotational diffusion. This slowing down in the isotropic solution is referred to as the pretransition effect. The thermodynamic force also governs the unique rheological behavior of liquid-crystalline solutions as will be explained in Sect. 9. For rodlike polymer solutions, Doi [100] treated the thermodynamic force effects by adding a self-consistent mean field or a molecular field Vscf (a) to the external field potential h in Eq. (40b). Using the second virial approximation (cf. Sect. 2), he formulated Vscf(a), as follows [4] ... 

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). 

For an infinitely thin rodlike polymer for which d/L = de/Le = 0, we have fi = F 0 = Fx0 = D 0/D = 1, and Eq. (46) reduces to Teraoka and Hay-aka wa s original expression [107] of Dx for rodlike polymers. At high concentrations, the results from the Green function method approach the one from the cage model [107], Teraoka [110] calculated stochastic geometry and probability of the entanglement for infinitely thin rods by use of the cage model, and evaluated px to be... 

In the infinitely thin rod limit, Eq. (50) reduces to Teraoka and Hayakawa s original expression of Dr for rodlike polymers [108]. The latter approaches the equation of Dr derived on the cage model [108, 111] at high concentrations. Teraoka et al. [Ill] estimated pr from calculations of stochastic geometry and probability of the entanglement for infinitely thin rods with the cage model, and obtained... 

Doi [4,100,114,117] formulated a(E) for rodlike polymer solutions by noticing that (E> is related to the change 8(AF) in the dynamic Helmholtz free energy of the system due to a virtual deformation k St in a short time 8t by... 

Here the dynamic free energy AF is calculated from the static free energy by replacing the equilibrium orientational distribution function by the time-dependent distribution function. The calculation of 8(AF) for a rodlike polymer solution goes through the following three steps. 

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... 

Fig. 16a, b. Computer simulation results for rodlike polymers in solution a the translational diffusion coefficients [122,123] b the rotational diffusion coefficient [119,122,123]... 

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