Semiflexible-chain polymers

This system of rigid blocks with flexible spacers may serve as a model of polymers with a limited flexibih ty. In his early work Flory considered the behavior of semiflexible chain polymers by introducing the flexibility parameter / which represents the fraction of bonds which are not in a colhnear position in the... 

Comparison of eqns [10] and [ 11 ] to eqns [2] and [3] points out that long wormlike chain acquires on the large scale the random coil conformation and its large-scale properties coincide with those of an equivalent freely jointed chain comprising Ni = L/2lp statistical segments each of length t = 2lp. Hence, both the freely jointed and the wormlike persistence chain models can be applied for desaiption of large-scale conformational properties of flexible and semiflexible chain polymers. 

Certain general relations used with the polarized static scattering from isotropic solutions are gathered in this section. Relations for the depolarized scattering from isotropic solutions are given in the section on Isotropic Solutions of Semiflexible Chain Polymers, and the static scattering from ordered solutions is considered in the section on Nematic Solutions of Semiflexible Chain Polymers. 

The focus of this chapter is on an intermediate class of models, a picture of which is shown in Fig. 1. The polymer molecule is a string of beads that interact via simple site-site interaction potentials. The simplest model is the freely jointed hard-sphere chain model where each molecule consists of a pearl necklace of tangent hard spheres of diameter a. There are no additional bending or torsional potentials. The next level of complexity is when a stiffness is introduced that is a function of the bond angle. In the semiflexible chain model, each molecule consists of a string of hard spheres with an additional bending potential, EB = kBTe( 1 + cos 0), where kB is Boltzmann s constant, T is... 

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. 

Investigations in the past years have proved that applying the concept of flexible spacer, polymers can be synthesized systematically, which exhibit the l.c. state. Owing to the flexible linkage of the mesogenic molecules to the polymer main chain, very similar relations can be expected with respect to 1-l.c., like chemical constitution and phase behavior, or dielectric properties and field effects for the l.c. side chain polymers. This will be in contrast to main chain polymers, where the entire macromolecule, or in case of semiflexible polymers parts of the macromolecules, form the l.c. structure. The introduction of a flexible spacer between backbone and mesogenic group can be performed in a broad variety of chemical reactions. Some arbitrarily... 

V2 = 1). The transition (partial or complete) into the liquid crystalline state occurs only after the system is heated above the glass-transition point. For real polymeric systems with semiflexible chains, the liquid crystalline state in the initial solution often is not realized, so the formation of nonequilibrium amorphous polymer upon the introduction of a nonsolvent is quite probable. 

The real liquid crystalline polymers exhibit finite flexibility. This kind of polymer was studied extensively by Khokhlov and his co-workers. Assume that the semiflexible chain has the total contour length L, and Kuhn length l and diameter D, and L l D. Analogous to the Onsager model, the free energy of the polymer in solution is composed of the conformational... 

FIGURE 5.7. Collapse transition of a flexible polymer chain (solid line) and a semiflexible chain (dashed line) of a limited length (see the text for an explanation). 

So far, polymer chains have been assumed to be perfectly flexible there is no energy difference in trans and gauche. Each subsequent statistical unit can be placed in any one of the nearest neighboring (n.n) cells at equal probability. For semiflexible chains, the energy for bending the chain should be considered. 

Let / be the probability for an arbitrarily chosen bond to be in the gauche position. In lattice theory, the hypothetical crystalline state in which polymers are all trans position and regularly arranged is chosen as the reference state (see Figure 2.15). For semiflexible chains, the disorientation is not complete. The chain entropy remains at... 

Amphiphilic behavior is related to conducting polymers and to mesomorphic polymers for several reasons. First, doping of PANi with surfactant molecules has been found to induce liquid crystallinity. Second, alkylation of semiflexible conducting polymers (PT and PANi) favors the formation of layered structures. Third, both rigid and flexible macromolecules with alkyl side chains may be considered as diphilic, in which case lyotropic behavior is to be expected. In the next section examples of mesomorphism and structural organization for macromolecules with flexible side groups will be given. 

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