Persistence length definition

By definition, this is equal to the substrate, or persistence, length Lp (see Sect. 3.4.2) which by this criterion can easily take values so large that nonlinear growth should be observed for small crystals in regime I. 

This formula is actually an exact definition of a very important quantity, I, which is known as the persistence length of a polymer chain. 

Equation 2.15 may be considered to be another definition of the persistence length (note that its original definition is eq 2.2). It states that the persistence length is a measure of chain stiffness associated with bending. Some authors prefer the notation (2A) to q, but we use the latter throughout this book. 

As discussed in Chapter 2, xanthan has a structure that is not quite a rigid rod since it has some degree of flexibility. This type of structure was described by Porod and Kratky as the worm-like chain model (Richards, 1980, p. 88). Although this may be visualised intuitively to be rather like a semi-flexible string of plastic pop-in beads, it requires the definition of the persistence length, /p, in order to develop the idea in a more quantitative way. This quantity is defined for an infinite polymer chain as follows ... 

The definition of a segment stiffness depends on its nature. If a long stiff segment can be described as a worm-like chain, characterized by a particular smooth and uniform curvature, then the chain persistence length is a good initial descriptor. For a hypothetical worm-like chain of contour length L and statistical mechanical average square of the unperturbed end-to-end distance o, it was shown by Porod and Kratky [49,50], that in the limit of L -> oo,... 

By using this result and taking the definition of the persistence length to be the projection of the end-to-end distance vector on the first step (Cantor and Schimmel 1980, Yamakawa 1997),... 

The persistence length a measures the correlation in the orientation of successive monomers as we move along a polymer chain. One useful definition which is easily apphed to the polyethylene model used here is ... 

Since we did not find adverse effects on zinc balance by the higher fiber diet containing spinach until the fourth week of study 3, balance studies should be carried out for longer periods of time to determine if negative zinc balances persist. Perhaps in the earlier studies on effects of spinach on calcium balance of human subjects, more definitive effects would have been noted if the spinach had been fed along with a higher fiber diet. Length of study period is also a likely factor, as some of the studies were carried out for less than 2 weeks. 

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