Persistent chain orientational correlation function

We examine this aspect of the spacer by computing the bond correlation function (BCF),

<(3cos 0j -l)/2>. This conforma-tionally averaged function of the angle between the first and jth bond of the chain is an indicator of the persistence of orientational correlations down the chain. For the all- trans conformation of an alkyl chain, for example, the BCF will be unity for j =... 

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 ... 

Fig. 2.6. Schematic representation of the orientational correlation function of a chain. The integral width determines the persistence length Ips...

The basic structure of the persistent chain has, indeed, already been introduced in Fig. 2.5 at the beginning of Sect. 2.3. It shows a chain with varying curvature being represented by a curve of length l t, which possesses at each point a well-defined tangent vector, e(/). In order to describe the chain structure, statistics was employed and the orientational correlation function iFor(A/) introduced by Eq. (2.5)... 

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