Stiff Chain Polymers

The softening behaviour of a thermoplastic material depends to a large extent on the flexibility of the chain and the ability to crystallise. Significant cross-linking of a reasonably stiff-chained polymer will lead to material that is unlikely to soften below its decomposition temperature. Intermediate to the linear and cross-linked polymers are various ladder polymers in which the polymer molecule consists of a pair of more-or-less parallel chains bridged in a manner analogous to the rungs of a ladder. 

This article reviews the following solution properties of liquid-crystalline stiff-chain polymers (1) osmotic pressure and osmotic compressibility, (2) phase behavior involving liquid crystal phasefs), (3) orientational order parameter, (4) translational and rotational diffusion coefficients, (5) zero-shear viscosity, and (6) rheological behavior in the liquid crystal state. Among the related theories, the scaled particle theory is chosen to compare with experimental results for properties (1H3), the fuzzy cylinder model theory for properties (4) and (5), and Doi s theory for property (6). In most cases the agreement between experiment and theory is satisfactory, enabling one to predict solution properties from basic molecular parameters. Procedures for data analysis are described in detail. 

Before proceeding to a review of both scaled particle theory and fuzzy cylinder model theory, it would be useful to mention briefly the unperturbed wormlike (sphero)cylinder model which is the basis of these theories. Usually the intramolecular excluded volume effect can be ignored in stiff-chain polymers even in good solvents, because the distant segments of such polymers have little chance of collision. Therefore, in the subsequent reference to wormlike chains, we always mean that they are unperturbed . 

Table 1. Persistence length q and molar mass per unit contour length ML for liquid-crystalline stiff-chain polymers...

The numerical coefficients in these equations as well as the numerical constants Av>i in Eq. (32) are given in Table 5. In fact, Eq. (32) approximates the results of direct numerical analysis to within 3% for 0.0015< d< 0.15, N> 0.05, and L/d > 5, the conditions which are fulfilled by most stiff-chain polymer solution systems studied so far. Equation (32) is more accurate at small N than our previous theory [18], in which slightly different empirical equations for c, and cA were proposed. 

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 order to discuss the rheological properties of stiff-chain polymer solutions, we need an expression for stress. The stress a induced in a homogeneous isotropic or nematic solution by a macroscopic flow was formulated by Doi [114], who used the Kirkwood general theory [116] to show... 

Ferry and coworkers [118] extensively studied viscoelasticity of dilute solutions of stiff-chain polymers. Their results made clear that the stress or the storage and loss moduli for the solutions are sensitive to chain internal motions... 

The zero-shear viscosity r 0 has been measured for isotropic solutions of various liquid-crystalline polymers over wide ranges of polymer concentration and molecular weight [70,128,132-139]. This quantity is convenient for studying the stiff-chain dynamics in concentrated solution, because its measurement is relatively easy and it is less sensitive to the molecular weight distribution (see below). Here we deal with four stiff-chain polymers well characterized molecu-larly schizophyllan (a triple-helical polysaccharide), xanthan (double-helical ionic polysaccharide), PBLG, and poly (p-phenylene terephthalamide) (PPTA Kevlar). The wormlike chain parameters of these polymers are listed in Tables... 

In Sect. 6.3, we have neglected the intermolecular hydrodynamic interaction in formulating the diffusion coefficients of stiff-chain polymers. Here we use the same approximation by neglecting the concentration dependence of qoV), and apply Eq. (73) even at finite concentrations. Then, the total zero-shear viscosity t 0 is represented by [19]... 

We compare Eq. (74) with the experimental results for two more stiff-chain polymers, PBLG and poly(p-phenylene terephthalamide) (PPTA). Since avail-... 

Recently Sato et al. [144,145] have extended the viscosity equation, Eq. (74), to multicomponent solution containing stiff-chain polymer species with different lengths. They showed a favorable comparison of the extended theory with the viscosity data for the quasi-ternary xanthan solutions presented in Fig. 21. 

In this article, we have surveyed typical properties of isotropic and liquid crystal solutions of liquid-crystalline stiff-chain polymers. It had already been shown that dilute solution properties of these polymers can be successfully described by the wormlike chain (or wormlike cylinder) model. We have here concerned ourselves with the properties of their concentrated solutions, with the main interest in the applicability of two molecular theories to them. They are the scaled particle theory for static properties and the fuzzy cylinder model theory for dynamical properties, both formulated on the wormlike cylinder model. In most cases, the calculated results were shown to describe representative experimental data successfully in terms of the parameters equal or close to those derived from dilute solution data. 

RIS theory provides a relatively simle formalism for the evaluation of the persistence vector, a, for a chain that can be represented by a repeating sequence of independent virtual bonds such as polybenzobisoxazole (PBOI and polybenzobisthiazole IPBT). The present study combines RIS theory with long molecular dynamics simulations for small fragments in order to evaluate the limiting length of a for very stiff chains. The approach can be applied to other stiff chain polymers. 

Kurihara, M. Preprints of microsymposium on stiff chain polymers, Soc. Polym. Sci. Japan... 

Polymer science is underdeveloped in terms of descriptions of the structure and properties of stiff-chain polymers. The conducting polymers fall mostly within this blind spot. They also present a number of novel possibilities such as the conversion from a flexible-chain precursor to a rigid-chain polymer, and the conversion between doped and undoped states in the soluble polythiophenes. Likewise, solid-state physics has yet really to tackle the transport of electrons in, and between, disordered, twisted chains. For each of the disciplines involved, the explosion of interest in conducting polymers has brouht a host of new question and new ideas. The process is far from over. 

V. N. Tzvetkov, Stiff-Chain Polymer Molecules, Nauka, Leningrad, 1986. 

In a rubbery polymer with flexible macromolecular chains (PDMS for example) the cavities forming the free-volume are clearly separated from each other. The detailed evaluation of the movement of a penetrant particle from cavity (1) to the neighboring (2), did not show any immediate back jumps (2) — (1). This is mainly do to the fact that the channel between (1) and (2) closes quiet quickly. In a polymer with stiff chains (glassy polyimide (PI) for example) the individual cavities are closer to each other and a rather large number of immediate back jumps ocurred during the time interval simulated (120). This indicates that once a channel between two adjacent cavities in a stiff chain polymer is formed it will stay open for some 100 ps. This makes the back jump (2) - (1) of the penetrant more probable than a jump to any other adjacent hole (3). This process seems to be one cause for the general tendency that the diffusion coefficient of small penetrants in stiff chain glassy polymers is smaller than in flexible chain rubbery polymers. 

The parameter AP accounts for a specific contribution of the plastic material to the diffusion process. Phenomenologically speaking AP has the role of a conductance of the polymer matrix towards the diffusion of the migrant (Chapter 6). Higher values of AP in such polymers as PE lead to increased DP-values while in stiff chain polymers such as polyesters and polystyrenes lower AP-values account for smaller diffusion coefficients for the same migrant. The parameters b and c account for the specific contributions of the migrant and the diffusion activation energy respectively. 

The qnD values of cellulose and its derivatives lie between 3 and 25 nm and are larger than those of typical vinyltype polymer ( 1 nm), but markedly smaller than those of typical stiff chain polymers, such as DNA (Table 14)67). Thus, the chains of cellulose and its derivatives can be considered as semi-flexible. It may be concluded that both the pearl-necklace chain and the wormlike chain models are adequately applicable to these polymers. 

Some examples of stiff-chain polymers able to form a liquid-crystalline phase in the solution are listed in Table l1. The ratio of the statistical segment length1 of a polymer chain, 1, to its width, d, (last column of Table 1) measures the degree of chain stiffness. For flexible macromolecules fid 1 stiff-chain macromolecules are those for which fid t> 1. 

Table 1. Examples of stiff-chain polymers able to form a lyotropic liquid-crystalline phase when dissolved in the solvent listed in third column... 

Aromatic polyamides and polyesters are examples of stiff chain polymers. Poly(p-phenylene terephthalamide) (Kevlar , 1-23) can be made by reaction (4-50) in a mixture of hexamethylphosphoramide and /V-methylpyrrolidone ... 

Elasticity at high shear rates is also bound to influence tack force in the nip of an offset press. Besides shear rate the elasticity is Influenced by the molecular weight and molecular structure of the dissolved polymers, and interactions between the pigment particles, the vehicle, and the dissolved polymer molecules. Of particular interest is the effect of the molecular mobility of stiff-chain polymers such as polyindene on elasticity and tack force at the shear rates encountered in an offset printing nip. 

Tack forces generated during ink film splitting are not well defined or easily measured with existing instrumentation. However, it is suggested that ink tack is related to ink elasticity, or more fundamentally, to molecular mobility of stiff chain polymer additives to lithographic inks. 

Yamakawa and co-workers were led to develop the HW model [Yoshizaki et al., 1980] by the observation that for some stiff-chain polymer-solvent systems, the KP model generates physically incorrect values of the characteristic parameters Ip and Ml, The following results were obtained [Yoshizaki et al., 1980, 1988], with L expressed in units of... 

Indeed, Teramoto and co-workers [Sato et al., 1991, 2003 Ohshima et al. 1995] have pointed out that the viscosity of stiff-chain polymers is affected dramatically by chain flexibility. To illustrate this, in Figure 1.15, Sato et al. [2003] compare... 

Bohdanecky, M., New method for estimating the parameters of the wormhke chain model from the intrinsic viscosity of stiff-chain polymers, Macromolecules, 16, 1483-1492 (1983). 

Sato, T., Takada, Y, and Teramoto, A., Dynamics of stiff-chain polymers in isotropic solution, flexibility effect. Macromolecules, 24, 6220-6226 (1991). 

Hofmann, D., Enhialgo-Castano, M., Lebret, A., Heuchel, M., and Yampolsldi, Y., Molecular modeling investigation of free volume distributions in stiff chain polymers with conventional and ultrahigh free volume comparison between molecular modeling and positron lifetime studies. Macromolecules, 36, 8528-8538 (2003). 

W. G. Miller, Stiff chain polymer lyotropic liquid crystals, Ann. Rev. Phys. Chem. 29,519 (1978). 

---