Semiflexible polymers, persistence length

We discuss now the scaling behavior of a single semiflexible PE in the bulk, including chain stiffness and electrostatic repulsion between monomers. For charged polymers, the effective persistence length is increased owing to electrostatic repulsion between monomers. This effect modifies considerably not only the PE behavior in solution but also their adsorption characteristics. 

In the part devoted to neutral polymers, we mentioned that semiflexible and stiff chains do not obey the behavior predicted by the Kuhn model. Restricted flexibility of the chain can be caused by the presence of stiff units with multiple bonds or bulky pendant groups, but it can be a result of external conditions or stimuli. In the preceding part, it was explained in detail that repulsive interactions together with entropic forces increase the stiffness of PE chains. Hence, a sudden pH change can be used as a stimulus affecting the stiffness of annealed PE chains. The properties of semiflexible polymers are usually treated at the level of the wormlike chain (WLC) model developed by Kratky and Porod [31]. The persistence length, /p, is an important parameter strongly related to the WLC model and has been used as the most common characteristic of chain flexibility—in both theoretical and experimental studies. It is used to describe orientational correlations between successive bond vectors in a polymer chain in terms of the normalized orientation correlation function, C(s) = (r,.r,+j). For the WRC model, this function decays exponentially ... 

The persistence length provides a measure of the flexibility of a polymer and is particularly useful in the case of semiflexible filaments. In the case of filaments that do not coil in solution, a measure of the end-to-end distance or the radius of gyration is not particularly useful in characterizing the molecule. The persistence length can be defined using the following formula ... 

As mentioned in the preceding sections, if the solute polymer has a persistence length p that is an appreciable firaction erfits contour length L, then it may form an ordered mesophase in moderately concentrated solutions, with symmetry between those of a liquid and a crystal. In the ordered mesophases of interest here, the material remains a fluid, but the solute exhibits orientational order while retaining translational disorder. The nematic mesophase will be assunwd, for whidi the solute chains tend to be parallel to each other - more complex symmetries are known [134, 135]. Nematic phases may be expected with moderately concentrated solutions of rodlike chains for p/L 1 for the isolated chain at infinite dilution, but may also form with moderately concentrated solutions of semiflexible chains for which p/L is smaller for the chain at infinite dilution [119]. In the latter ca the chain tmds to adopt a rodlike conformation in the nematic phase, with increase in its persistence loigth on formation of the ordered phase [119, 136]. 

The following three mechanisms of polymer chain flexibility are the best known in polymer physics freely jointed persistence, and rotational isomeric mechanisms [27]. The freely jointed mechanism corresponds to the simplest freely jointed model of a semiflexible polymer chain in which the chain is in the form of a sequence of hinged, long, rigid rods of length I and diameter d, with I d (Fig. 1.2a). In the persistence mechanism, the flexibility is due to gradual accumulation of the effect of small vibrations of valence angles, bonds, etc. A... 

---