Polymer stiffness chain

The various mechanical properties of polyamides may be traced in many instances to the possibility of intermolecular hydrogen bonding between the polymer molecules and to the relatively stiff chains these substances possess. The latter, in turn, may be understood by considering still another equilibrium, this one among resonance structures along the chain backbone ... 

Within these temperature ranges the polymers are, like the polycarbonates, tough. Because of the stiff chain and the resultant high Tg, processing temperatures need to be above 300°C. 

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. 

Both low molecular weight materials [145] and polymers [146,147] can show liquid crystallinity. In the case of polymers, it frequently occurs in very stiff chains such as the Kevlars and other aromatic polyamides. It can also occur with flexible chains, however, and it is these flexible chains in the elastomeric state that are the focus of the present discussion. One reason such liquid-crystalline elastomers are of particular interest is the fact that (i) they can be extensively deformed (as described for elastomers throughout this chapter), (ii) the deformation produces alignment of the chains, and (iii) alignment of the chains is central to the formation of liquid-crystalline phases. Because of fascinating properties related to their novel structures, liquid-crystalline elastomers have been the subject of numerous studies, as described in several detailed reviews [148-150]. The purpose here will be to mention some typical elastomers exhibiting liquid crystallinity, to describe some of their properties, and to provide interpretations of some of these properties in molecular terms. 

Several factors related to chemical structure are known to affect the glass transition tempera lure. The most important factor is chain stiffness or flexibility of the polymer. Main-chain aliphatic groups, ether linkages, and dimethylsiloxane groups build flexibility into a polymer and lower Tg Aliphatic side chains also lower Tg, (he effect of the length of aliphatic groups is illustrated by the methacrylate series (4,38) ... 

Figure 5.6 shows that the PDMS data perfectly match the prediction of the simple Rouse model up to the highest Q-values, whereas the PIB data show severe deviations from the Rouse model (Fig. 5.3) and the stiff chain model (Fig. 5.4). From the fact that two polymers with very similar structural parameters but strongly different torsional barriers display completely different relaxation behaviour the conclusion is compelling that there must be an addi-...

Linear polymers, polystyrene and cellulose triacetate exhibit differences in hydrodynamic behavior in solution. Cellulose and its derivatives are known to have highly extended and stiff chain molecules below a Dp of about 300, but as the Dp Increases above 300 the chain tends to assume the character of a random coll (27,28). The assumption that hydrodynamic volume control fractionation in GPC may not be true for polystyrene and cellulose triacetate, though it has been found satisfactory for non-polar polymers in good solvents (29). 

The chain stiffness inflnences the height of the glass-rnbber transition temperatnre (and of the melting point), bnt not the stiffness of the polymer below Tg (in the glassy state). Extremely stiff chains show the effect of the formation of LCP s (liqnid-crystalline polymers), by which very high stiffness is reached, bnt only in the direction of the orientation. 

The free volume, i.e., the volume not occupied by the polymer molecules, is similar for polymers at the Tg and increases as the temperature is increased. More-mobile short chains have lower entropy values and hence lower Tm values, while less-mobile stiff chains have higher entropy values and higher Tm values. 

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. 

Figures 7 and 8 display such plots for various lyotropic liquid-crystalline polymer systems, which range in q from 5.3 to 200 nm. As expected, most data points come close to the theoretical curve. This finding suggests that liquid crystallinity of stiff-chain or semiflexible polymer solutions has its main origin in the hard-core repulsion of the polymers.

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 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... 

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